Which sentence can represent the inequality One-half x + three-fourths greater-than-or-equal-to 5 and one-fourth?
The sum of half of a number and three-fourths is at least five and one quarter.
Half the sum of a number and three-fourths is not more than five and one quarter.
The sum of half of a number and three-fourths is at most five and one quarter.
Half the sum of a number and three-fourths is not less than five and one quarter.

Answers

Answer 1

Answer:

  The sum of half of a number and three-fourths is at least five and one quarter

Step-by-step explanation:

It's all about making sense of an English sentence.

  "half the sum ..." is different from "the sum of half ..."

And ...

  "at least" and "not less than" mean the same (≥)

  "not more than" and "at most" mean the same (≤)

_____

Since all of the expressions are written out in words, it is a matter of matching the ideas expressed. That's a problem in reading comprehension, not math.

__

"One-half x + three-fourths [is] greater-than-or-equal-to 5 and one-fourth"

  means the same as ...

"The sum of half of a number and three-fourths is at least five and one quarter"

Answer 2

Final answer:

The correct sentence for the inequality one-half x + three-fourths ≥ 5 and one-fourth is 'The sum of half of a number and three-fourths is at least five and one quarter'.

Explanation:

The correct representation of the inequality one-half x + three-fourths ≥ 5 and one-fourth (0.5x + 0.75 ≥ 5.25) in a sentence is The sum of half of a number and three-fourths is at least five and one quarter. This means that when you take half of a certain number (which we call x), add three-fourths to it, the result should be no less than five and one quarter. The other options either incorrectly suggest that the inequality is an equation, or misrepresent the inequality by suggesting the sum is 'at most' or not more or less than the given value, which changes the meaning of the original inequality.


Related Questions

Suppose that six guests check their hats when they arrive at the Cigar Parlor and that these hats are returned randomly when they leave. Determine the probability that no guest will receive the proper hat.

Answers

Answer:

0.1667

Step-by-step explanation:

There are 6! ways to arrange the hats. The number of ways for which no guest will receive the proper hat is 5! (since there are 5 wrong hats for the first guest, 4 for the second guest, and so on). The probability that no guest will receive the proper hat is:

[tex]P=\frac{5!}{6!}=0.1667[/tex]

The probability is 0.1667.

6.3.6. Among the early attempts to revisit the death postponement theory introduced in Case Study 6.3.2 was an examination of the birth dates and death dates of three hundred forty-eight U.S. celebrities (144). It was found that sixteen of those individuals had died in the month preceding their birth month. Set up and test the appropriate H0 against a one-sided H1. Use the 0.05 level of significance.

Answers

Answer:

So the Null hypothesis is rejected in this case

Step-by-step explanation:

  The number of celebrities is  n = 348

   

So to solve this we would assume that p is the percentage of people that died on the month preceding their birth month  

     

  Generally if there is no death postponement then p will be mathematically evaluated as

            [tex]p = \frac{1}{12}[/tex]  

This implies the probability of date in one month out of the 12 months

Now from the question we can deduce that the hypothesis we are going to be testing is  

  [tex]Null Hypothesis \ \ H_0 : p = 0.083[/tex]

This is a hypothesis is stating that a celebrity  dies in the month preceding their birth

  [tex]Alternative \ Hypothesis H_1 : p < 0.083[/tex]

   This is a hypothesis is stating that a celebrity does not die in the month preceding their birth

       is c is the represent probability for each celebrity which either c = 0 or c = 1

Where c = 0 is that the probability  that the celebrity does not die on the month preceding his/ her birth month

     and  c =  1  is that the probability  that the  celebrity dies on the month preceding his/ her birth month

  Then it implies that

   for  

       n= 1 + 2 + 3 + .... + 348  celebrities

Then the sum of c for each celebrity would be  [tex]c_s = 16[/tex]

i.e The number of celebrities that died in the month preceding their birth month

We are told that the significance level is  [tex]\alpha = 0.05[/tex], the the z value of [tex]\alpha[/tex] is

              [tex]z_{\alpha } = 1.65[/tex]

This is obtained from the z-table

Since this test is carried out on the left side of the area under the normal curve then the critical value will be

                 [tex]z_{\alpha } = - 1.65[/tex]

So what this implies is that  [tex]H_o[/tex] will be rejected if

                [tex]z \le -1.65[/tex]

Here z is the test statistics

Now z is mathematically evaluated as follows

                  [tex]z = \frac{c - np}{\sqrt{np_o(1- p_o)} }[/tex]

                [tex]z = \frac{16 - (348 *0.083)}{\sqrt{348*0.083 (1- 0.083)} }[/tex]

                [tex]z =-2.50[/tex]

From our calculation we see that the value of z is less than [tex]-1.65[/tex] so the Null hypothesis will be rejected

   Hence this tell us that the  evidence provided is not enough to conclude  that 16 celebrities died a month to their birth month

Final answer:

The question involves statistical hypothesis testing where the null hypothesis (H0) suggests no significant increase in celebrity deaths before their birth month, and the alternative hypothesis (H1) suggests a significant increase. Using significance level 0.05 and the provided data, the p-value is compared to decide on H0.

Explanation:

The question provided relates to setting up and testing a null hypothesis (H0) against a one-sided alternative hypothesis (H1) in the context of statistical hypothesis testing. Specifically, it involves determining whether the occurrence of celebrity deaths in the month preceding their birth month is statistically significant using a significance level of 0.05. To address this, the null hypothesis would state that there is no significant increase in the frequency of deaths in the month before the celebrities' birth month compared to any other month. The alternative hypothesis would state that there is a significant increase in deaths in the month preceding the birth month of celebrities. We would use the data provided (16 out of 348 celebrities dying in the month before their birth month) to calculate the p-value and compare it with the alpha level of 0.05 to decide whether to reject the null hypothesis or not.

Solve the equation using the distributive property and properties of equality.
-5(a+3) =-55
What is the value of a?

A -14

B -8

C 8

D 14

Answers

The answer is c

Step-by-step explanation:

Answer:

answwr is c and i got it right

Step-by-step explanation:

can someone please help I don’t get it and I just want answers I have been trying to solve this for 1 hour now

Answers

Answer:

1. y + 10 - 3/2y = -y/2 + 10

2. 2r+ 7r-r - 9 = 8r - 9

3.  7 + 4p-5+p+2q = 2 + 5p + 2q

Step-by-step explanation:

basically you can add terms that have the same variable

integers can be added together, Xs can be added, Zs, Ys, As, Bs, Cs, you get the point

1. y + 10 - 3/2y = -y/2 + 10

2. 2r+ 7r-r - 9 = 8r - 9

3.  7 + 4p-5+p+2q = 2 + 5p + 2q (do not add different variables p and q ) together

try 4-6 on your own to get this skill down, if you need help with those just let me know

Angle measure represented by 36.7 rotations counterclockwise

Answers

Answer:

13,212° or 73.4π radians

Step-by-step explanation:

Each rotation is 360° or 2π radians. So, 36.7 rotations is ...

  36.7×360° = 13,212°

or

  36.7×2π = 73.4π radians

Vehicles entering an intersection from the east are equally likely to turn left, turn right, or proceed straight ahead. If 50 vehicles enter this intersection from the east, use technology and the normal approximation to the binomial distribution to find the exact and approximate probabilities of the following. (Round your answers to four decimal places.) (a)

Answers

Answer:

The probability that at least two-third of vehicles in the sample turn is 0.4207.

Step-by-step explanation:

Let X = number of vehicles that turn left or right.

The proportion of the vehicles that turn is, p = 2/3.

The nest n = 50 vehicles entering this intersection from the east, is observed.

Any vehicle taking a turn is independent of others.

The random variable X follows a Binomial distribution with parameters n = 50 and p = 2/3.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

np ≥ 10n(1 - p) ≥ 10

Check the conditions as follows:

[tex]np=50\times \frac{2}{3}=33.333>10\\\\n(1-p)=50\times \frac{1}{3}= = 16.667>10[/tex]

Thus, a Normal approximation to binomial can be applied.

So, [tex]X\sim N(np, np(1-p))[/tex]

Compute the probability that at least two-third of vehicles in the sample turn as follows:

[tex]P(X\geq \frac{2}{3}\times 50)=P(X\geq 33.333)=P(X\geq 34)[/tex]

                        [tex]=P(\frac{X-\mu}{\sigma}>\frac{34-33.333}{\sqrt{50\times \frac{2}{3}\times\frac {1}{3}}})[/tex]

                        [tex]=P(Z>0.20)\\=1-P(Z<0.20)\\=1-0.5793\\=0.4207[/tex]

Thus, the probability that at least two-third of vehicles in the sample turn is 0.4207.

The test statistic of zequals2.32 is obtained when testing the claim that pgreater than0.3. a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed. b. Find the​ P-value. c. Using a significance level of alphaequals0.10​, should we reject Upper H 0 or should we fail to reject Upper H 0​?

Answers

Answer:

a) We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.3[/tex]  

Alternative hypothesis:[tex]p > 0.3[/tex]  

Right tailed test

b) [tex]p_v =P(z>2.32)=0.0102[/tex]  

c) So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

Step-by-step explanation:

Part a: Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.3[/tex]  

Alternative hypothesis:[tex]p > 0.3[/tex]  

Right tailed test

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

For this case the statistic is given by [tex] z_{calc}= 2.32[/tex]

Part b: Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>2.32)=0.0102[/tex]  

Part c

So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

Final answer:

The hypothesis test is right-tailed. The P-value should be assessed using a standard normal distribution, and if it is less than the significance level of α0.10, the null hypothesis should be rejected. However, the exact P-value for z=2.32 needs to be determined before a decision can be made.

Explanation:

The test statistic of z=2.32 is obtained when testing the claim that p>0.3. This indicates the hypothesis test in question is right-tailed, as the alternative hypothesis (Ha) suggests that the proportion is greater than 0.3 (p>0.3).

To determine the P-value, we look at the area to the right of our z-test statistic in the standard normal distribution. Given that our z-value is 2.32, the P-value would typically be found using a z-table or statistical software. However, the provided reference states that for a z-test value of 3.32, which seems to be a typo since our z-value is 2.32, the P-value would be 0.0103. We need to correct this and find the P-value for z=2.32, which we would expect to be larger than the P-value for z=3.32 since 2.32 is closer to the mean of the standard normal distribution.

P-value interpretation is critical when deciding whether to reject the null hypothesis (H0). In this case, if we use a significance level of α=0.10, we compare the P-value to this significance level. If the P-value is less than α, we reject H0; if it's greater, we fail to reject H0. Without the exact P-value for z=2.32, we cannot make a definitive decision, but typically, a z-value of 2.32 would result in a P-value less than 0.10, which leads to rejection of H0.

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Find the rectangular coordinates of the point (sqrt3,pi/6)

Answers

Answer:

[tex](x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)[/tex]

Step-by-step explanation:

The rectangular coordinates of the point are:

[tex](x,y) = \left(\sqrt{3}\cdot \cos\frac{\pi}{6}, \sqrt{3}\cdot \sin\frac{\pi}{6}\right)[/tex]

[tex](x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)[/tex]

Answer:

B

Step-by-step explanation:

An actor invested some money at 5% simple interest, and $41,000 more than 4 times the amount at 9%. The total annual interest earned from the investment was $35,260. How much did he invest at 5% and 9%?

Answers

Answer:

The amount invested at 5%=$77,000The amount invested at 9%=$349,000

Step-by-step explanation:

Let the amount invested at 5% simple interest =$x

He invested $41,000 more than 4 times the amount at 9%.

This amount is: $(4x+41000)

Total Annual Interest Earned = $35,260

Therefore, Time=1 year

Simple Interest[tex]=\frac{Principal X Rate X Time}{100}[/tex]

Therefore, his total interest

=Interest from Investment 1 + Interest from Investment 2

[tex]35260=\left(\frac{x*5*1}{100} \right)+\left(\frac{4x+41000*9*1}{100} \right)\\35260=0.05x+(0.36x+3690)\\35260-3690=0.05x+0.36x\\31570=0.41x\\\text{Divide both sides by 0.41}\\x=\$77000[/tex]

Therefore:

The amount invested at 5%=$77,000

The amount invested at 9%=$(4*77,000+41000)=$349,000

In a test of hypothesis, the null hypothesis is that the population proportion is equal to .58 and the alternative hypothesis is that the population proportion is greater than .58. Suppose we make the test at the 2.5% significance level. A sample of 1200 elements selected from this population produces a sample proportion of .62. What is the value of the test statistic, z?

Answers

Answer:

z statistic = 2.82

Step-by-step explanation:

Sample size = 1200

Null hypothesis, [tex]H_{0}[/tex]: p = 0.58

Alternative hypothesis, [tex]H_{a}[/tex]: p > 0.58

From the null and alternative hypothesis, we can derive that Hypothesized proportion, [tex]p_{0}[/tex] = 0.58 = 58%

Significance level = 2.5% = 0.025

Sample proportion, [tex]p_{1}[/tex] = 0.62 = 62%

Test statistic, z:

[tex]z_{statistic} = \frac{p_{1} -p_{0} }{\sqrt{\frac{p_{0}( 1 -p_{0} )}{n} } }[/tex]

[tex]z_{statistic} = \frac{0.62-0.58}{\sqrt{\frac{0.58(1-0.58)}{1200} } }[/tex]

[tex]z statistic =\frac{0.04}{\sqrt{0.000203} }[/tex] [tex]= \frac{0.04}{0.0142}[/tex]

[tex]z statistic = 2.82[/tex]

The value of the test statistic 'z' for the given hypothesis test is approximately 5.65, calculated using the provided sample proportion, hypothesized population proportion, and sample size.

The question asks for the calculation of the test statistic 'z' for a hypothesis test where the null hypothesis states that the population proportion is equal to .58 and the alternative hypothesis says that the population proportion is greater than .58. This is tested at a 2.5% significance level with a sample size of 1200 and sample proportion of .62.

To calculate the test statistic z, use the formula:

z = (p' - p) / √(p(1 - p)/n)

where:

p' is the sample proportion (0.62)p is the hypothesized population proportion (0.58)n is the sample size (1200)

Now, plug in the values:

z = (0.62 - 0.58) / √(0.58(1 - 0.58)/1200)

z ≈ 5.65

This is the value of the test statistic z for conducting the hypothesis test.

The length and width of a rectangle are measured as 31 cm and 28 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.

Answers

Answer:

[tex]\Delta A = 5.9\,cm^{2}[/tex]

Step-by-step explanation:

The area of an rectangle is given by the following formula:

[tex]A = w\cdot h[/tex]

Where:

[tex]w[/tex] - Width, in centimeters.

[tex]h[/tex] - Height, in centimeters.

The differential of the expression is derived hereafter:

[tex]\Delta A = \frac{\partial A}{\partial w} \cdot \Delta w + \frac{\partial A}{\partial h}\cdot \Delta h[/tex]

[tex]\Delta A = h \cdot \Delta w + w \cdot \Delta h[/tex]

[tex]\Delta A = (31\,cm)\cdot (0.1\,cm) + (28\,cm)\cdot (0.1\,cm)[/tex]

[tex]\Delta A = 5.9\,cm^{2}[/tex]

Using differentials the maximum error in the calculated area of the rectangle wi’ould be 5.9 cm

The area formular of a rectangle is :

Area = Length(l) × width(w) w = 28 cml = 31 cm Error, Δe = 0.1cm

Maximum error can be defined thus :

Δmax = (L × Δe) + (W × Δe)

Δmax = (L × Δe) + (W × Δe)

Δmax = (31 × 0.1) + (28 × 0.1)

Δmax = 3.1 + 2.8

Δmax = 5.9 cm

Hence, the maximum error in the calculated area value is 5.9 cm.

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Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that​ revenue, Upper R (x )​, and​ cost, Upper C (x )​, are in thousands of​ dollars, and x is in thousands of units. Upper R (x )equals9 x minus 2 x squared​, Upper C (x )equalsx cubed minus 3 x squared plus 4 x plus 1

Answers

Answer:

-1.39

Step-by-step explanation:

Revenue and cost as a function of units sold are [tex]u(x) = 9x-2x^{2}[/tex]and[tex]c(x)=x^{3}-3x^{2}+4x+1[/tex]  respectively.

we are have to know for which value or input units are these functions at maximum which translates to for how many units is the revenue maximum and for how many same units is our cost minimum.

If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in five years?
A=P(1+r/n)^nt

Answers

Answer:

$5,805.92

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 3% into a decimal:

3% -> [tex]\frac{3}{100}[/tex] -> 0.03

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

[tex]A=5,000(1+\frac{0.03}{4})^{4(5)}[/tex]

[tex]A=5,805.92[/tex]

The value of the investment after 5 years will be $5,805.92

Investment value after 5 years, compounded quarterly at 3%, is approximately $5,805.83.

let's calculate step by step.

1. First, let's convert the annual interest rate to decimal form:

 [tex]\[ r = 3\% = \frac{3}{100} = 0.03 \][/tex]

2. Now, let's plug in the given values into the compound interest formula:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

  where:

[tex]- \( P = $5000 \)\\ - \( r = 0.03 \)\\ - \( n = 4 \)\\ - \( t = 5 \)[/tex]

3. Substituting these values into the formula, we get:

[tex]\[ A = 5000 \left(1 + \frac{0.03}{4}\right)^{4 \times 5} \][/tex]

4. Simplifying inside the parentheses:

[tex]\[ A = 5000 \left(1 + 0.0075\right)^{20} \][/tex]

5. Calculating [tex]\( (1 + 0.0075) \):[/tex]

 [tex]\[ 1 + 0.0075 = 1.0075 \][/tex]

6. Now, raise [tex]\( 1.0075 \)[/tex]  to the power of [tex]\( 20 \):[/tex]

[tex]\[ (1.0075)^{20} \][/tex]

  Using a calculator,[tex]\( (1.0075)^{20} \)[/tex] is approximately [tex]\( 1.161166 \).[/tex]

7. Finally, multiply this result by [tex]\( 5000 \):[/tex]

 [tex]\[ A = 5000 \times 1.161166 \]\\ \[ A \approx 5,805.83 \][/tex]

So, the value of the investment in five years, compounded quarterly at a 3% interest rate, would be approximately $5,805.83.

here is complete question:-

"If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in five years?"

Suppose that 650 lb of coffee are sold when the price is $4 per pound, and 400 lb are sold at $8 per pound. a. List the data points (use price as the independent variable). b. Find the slope of the line joining the points.

Answers

Answer:

a. (4, 650), (8, 400)

b. -62.5

Step-by-step explanation:

a......................

Data points are (4, 650) and (8, 400) since price is independent variable and weight of coffee is dependent

b......................

Slope = (y2-y1)/(x2-x1)

Slope = (400 - 650)/(8-4) = -250/4 = - 62.5

Final answer:

The data points representing the price and quantity of coffee sold are ($4, 650) and ($8, 400). The slope of the line connecting these points, which shows the relationship between price and quantity, is -62.5.

Explanation:

This question is about mathematical calculations used in economics, specifically related to pricing and demand. Let's turn these scenarios into data points, with price ($4 and $8) as the independent variable and quantity (650 lbs and 400 lbs) as the dependent variable. So, your data points are ($4, 650) and ($8, 400).

To find the slope of the line connecting these points, use the slope formula. The slope(m) is equal to the difference in the y-values divided by the difference in the x-values. So, m = (400-650) / (8-4) = -250/4 = -62.5.

Thus, the slope of the line connecting these two points, representing the relationship between the price and quantity of coffee sold, is -62.5.

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The Indian Ocean is 2/10 of the area of the worlds oceans. What fraction represents the area of the remaining oceans that make up the worlds oceans? Write in simplest form.

Answers

Answer: 8/10 or 4/5

Step-by-step explanation:

10/10 - 2/10 = 8/10

Answer:

Since 10 - 2 = 8

The fraction of the remaining oceans would be 8/10

And if you simplify both 8 and 10 by 2

Meaning you divide them by two

8 ÷ 2 = 4

10 ÷ 2 = 5

Our new fraction is 4/5

~DjMia~

An architect was asked to build a special staircase in a new building. The staircase will be built like a helix that rotates around the outside of a cylindrical waterfall. Because it is a helix, the beginning of the staircase begins at a point directly above the position where the staircase ends at the bottom base of the column. Describe how to find the length of the staircase if the cylinder it surrounds is 30 m in height and has a radius of 12 m

Answers

Answer:

[tex]\Delta s \approx 754.579\,m[/tex] (See explanation below).

Step-by-step explanation:

Each floor has a height of 3 meters. Then, the number of floors of the cylinder is:

[tex]n = \frac{30\,m}{3\,m}[/tex]

[tex]n = 10\,floors[/tex]

Let consider that spiral makes a revolution per floor. Then, the parametric equations of the spiral are:

[tex]x = r\cdot \cos \theta[/tex]

[tex]y = r\cdot \sin \theta[/tex]

[tex]z = \Delta h \cdot \frac{\theta}{2\pi}[/tex]

Length of the staircase can be modelled by using the formula for arc length:

[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{\left(\frac{dx}{d\theta} \right) ^{2}+\left(\frac{dy}{d\theta} \right)^{2}+\left(\frac{dz}{d\theta}\right)^{2}}} \, d\theta[/tex]

[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{\left(-r\cdot \sin \theta\right)^{2}+\left(r\cdot \cos \theta\right)^{2}+\left(\frac{\Delta h}{2\pi} \right)^{2}} } \, d\theta[/tex]

[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{r^{2}+\frac{(\Delta h)^{2}}{4\pi^{2}} }} \, d\theta[/tex]

[tex]\Delta s = \sqrt{(12\,m)^{2}+\frac{(3\,m)^{2}}{4\pi^{2}} } \cdot (20\pi-0)[/tex]

[tex]\Delta s \approx 754.579\,m[/tex]

The police department in NYC is trying to determine if it is worth the cost to install a speed sensor and traffic camera on a highway near the city. They will install the speed sensor and traffic camera if convinced that more than 20% of cars are speeding. The police department selects a random sample of 100 cars on the highway, measures their speed, and finds that 28 of the 100 cars are speeding. A significance test is performed using the hypotheses.
Hoo: p=0 .20
Ha:p > 0.20
Where p is the true proportion of all cars on the highway that are speeding. The resulting p-value is 0.023. What conclusion would you make at the alpha level of 0.05 level?
A conclusion can be made that since the alpha level is less than the p-level, then we fail to reject the null hypothesis due p-value being 0.023 being greater than alpha level 0.05.

Answers

Final answer:

At a 5 percent significance level and with a p-value of 0.023, we reject the null hypothesis, concluding that more than 20% of cars are speeding.

Explanation:

The question involves determining whether to reject the null hypothesis based on a p-value from a statistical test concerning the true proportion of cars that are speeding on a highway. Since the p-value of 0.023 is less than the alpha level of 0.05, we would reject the null hypothesis (H0: p = 0.20). At the 5 percent significance level, there is sufficient evidence to conclude that more than 20% of cars are speeding on the highway.

Since the p-value is less than the alpha level of 0.05, we reject the null hypothesis. Therefore, the police department should consider installing the speed sensor and traffic camera.

To determine if the police department should install a speed sensor and traffic camera based on a significance test, we need to examine the hypotheses:

H0: p = 0.20 (the true proportion of cars speeding is 20%)

H1: p > 0.20 (the true proportion of cars speeding is greater than 20%)

Given that in a random sample of 100 cars, 28 were speeding, the test resulted in a p-value of 0.023. At the alpha level of 0.05, since the p-value (0.023) is less than alpha (0.05), we reject the null hypothesis.

In conclusion, at the 5 percent significance level, there is sufficient evidence to conclude that the true proportion of cars speeding is greater than 20%, justifying the installation of the speed sensor and traffic camera.

( WILL MARK BRAINLIEST IF CORRECT)
Jalil plays hockey. When Jalil takes a shot on goal, the probability that he scores is . If Jalil takes 80 shots on goal in a season, how many times can he expect to score a goal?

Answers

Answer:

60

Step-by-step explanation:

1/2 of 80 is 40.1/4 is 20.40 plus 20 equals 60.

Answer:

80x

Step-by-step explanation:

The probability is needed for this, so I put it as x.

If it was .25, he could expect to score 20 times.

Lue is rolling a random number cube.The cube has six sides,and each one is labeled with a number 1 through 6. What is the probability that he will roll a sum of 12 in two rolls

Answers

Answer:

2%

Step-by-step explanation:

You do 12÷6×1=2

I used PEMDAS

Final answer:

The probability that Lue will roll a sum of 12 on two rolls of a standard six-sided die is 1/36 or about 2.78%, as only the combination (6,6) results in the sum of 12.

Explanation:

Probability of Rolling a Sum of 12

To calculate the probability that Lue will roll a sum of 12 on two rolls of a six-sided die, we need to consider all the possible combinations that can result in a sum of 12. These combinations are (6,6). Since each die is independent, we calculate the probability for one die and then square it for two dice, because there is only one way to get a six on a die, and there are six faces. Therefore, the probability of rolling a six is:

1/6

To find the probability of rolling two sixes, we multiply the probabilities of each independent event:

(1/6) × (1/6) = 1/36

So, the probability that Lue will roll a sum of 12 in two rolls is 1/36, or approximately 2.78%.

A Campus Republicans fundraiser offers raffle tickets for $14 each. The prize for the raffle is a $400 television set, which must be purchased with the proceeds from the ticket sales. Find a function that gives the profit/loss for the raffle as it varies with the number of tickets sold. How many tickets must be sold for the raffle sales to equal the cost of the prize

Answers

Answer:

##  Profit/Loss = [tex]14x-400[/tex]

##  29 tickets

Step-by-step explanation:

Profit/Loss is Revenue - Cost

For the fundraisers:

Revenue comes from tickets sold at $14 each

x tickets sold, means the revenue is:

14x

Now, cost is what they are going to give out, that is $400 TV Set, so the cost is:

400

Hence, Profit/Loss would be:

Profit/Loss = [tex]14x-400[/tex]

Raffle sales equaling the cost of prize is basically when we break-even, or when profit/loss is equal to 0. So we solve the equation:

Profit/Loss = 14x - 400

0 = 14x - 400

14x = 400

x = 28.57

We can't sell fractional tickets, so we have to sell 29 tickets in order to break even

A right triangular prism is constructed so that its height is
equal to the leg length of the base.
What expression represents the volume of the prism, in
cubic units?
o 1x2 + x
2x3
2x²+x

Answers

The solution is, Volume of prism = 1/2x³ + x², is the expression which represents the volume of the prism, in cubic units.

What is volume?

Volume can be stated as the space taken by an object. Volume is a measure of three-dimensional space. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

here, we have,

Given that:

The oblique prism below has an isosceles right triangle base and the length of the base is x

=> the area of the base: 1/2 × x × x = 1/2

The vertical height of the prism is (x + 2)

=> The volume of the oblique prism is:

V = the base area * the vertical height

<=> V = 1/2* x² * (x + 2)

<=> V =  1/2x³ + x²

Hence, The solution is, Volume of prism = 1/2x³ + x², is the expression which represents the volume of the prism, in cubic units.

To learn more about volume of the prism from the given link

brainly.com/question/15892907

#SPJ7

which is the value of this expression when m equals 3 and n equals -5


(6m with exponent of -1 x n with the exponent of 0) another exponent of -3

Answers

When you have a negative exponent, you move the base with the negative exponent to the other side of the fraction to make the exponent positive.

For example:

[tex]\frac{1}{2y^{-3}} =\frac{y^3}{2}[/tex]    ("y" is the base with the negative exponent)

[tex]x^{-5}[/tex] or [tex]\frac{x^{-5}}{1} =\frac{1}{x^5}[/tex]

When you multiply an exponent directly to a base with an exponent, you multiply the exponents together.

For example:

[tex](y^3)^2=y^{(3*2)}=y^6[/tex]

[tex](x^2)^4=x^{(2*4)}=x^8[/tex]

[tex](2n)^3[/tex] or [tex](2^1n^1)^3=2^{(1*3)}n^{(1*3)}=2^3n^3=8n^3[/tex]

When you have an exponent of 0, the result will always equal 1

For example:

[tex]x^0=1[/tex]

[tex]5^0=1[/tex]

[tex]y^0=1[/tex]

[tex](6m^{-1}*n^0)^{-3}[/tex]      I think you should first make the exponents positive

[tex]\frac{1}{(\frac{6}{m^1} *n^0)^3}[/tex]    

Since you know:

m = 3

n = -5    Substitute/plug it into the equation

[tex]\frac{1}{(\frac{6}{(3)^1}*(-5)^0)^3 }[/tex]

[tex]\frac{1}{(2*1)^3}[/tex]

[tex]\frac{1}{2^3}[/tex]

[tex]\frac{1}{8}[/tex]      

Can someone please answer these for me?!

Answers

Answer:

base : 9

three points : (1,0), (9,1), (81,2)

domain : x>0

range : all real number

asymptote : x=0

Answer:

x=0

Step-by-step explanation:

I need to write a 5-paragraph eassy, so please help me it is base on an article name "Schools in Maryland Allow Elementary Students to Carry Cellphones, by Amanda Lenhart, The Washington Post" here are some pic. I just need help writing two paragraph. I already have my Introduction, Body Paragraph #1 and my Body paragraph #2 just need my Body paragraph #3 and my Conclusion I will give brainlis and 30 pnt.

Prompt:

Write an argumentative essay answering the questions: Should students be allowed to carry cellphones on campus? You must support your claim with evidence from the text. You may also use relevant examples from your own experience, observations, and other readings.

Directions:

Before you begin, read the text below, which presents information about the advantages and disadvantages of carrying a cell phone at school. Use the Student Writing Checklist on the back of this page to plan and write a multi-paragraph essay that addresses the prompt. Use your own words, except when quoting directly from the text.

PLEASE DONT WAST THEM

An NBA fan named Mark claims that there are more fouls called on his team 1 point
any other team, but the commissioner says that the number of fouls called
against his team are no different than any other team. Mark finds that the
average number of fouls in any game in the NBA is 11.5. He takes a random
sample of 34 of games involving his team and finds that there are an
average of 12.2 fouls against his team, with a standard deviation of 1.6 fouls.
What is the correct conclusion? Use a = 0.05

a) The p value is 2.55 indicating insufficient evidence for his claim.

b)The p-value is 0.008, indicating sufficient evidence for his claim.

c)The p-value is 0.008, indicating insufficient evidence for his claim.

d)The p-value is 2.55, indicating sufficient evidence for his claim.

Answers

Answer:

[tex]t=\frac{12.2-11.5}{\frac{1.6}{\sqrt{34}}}=2.551[/tex]    

[tex] df = n-1=34-1=33[/tex]

[tex]p_v =P(t_{(33)}>2.551)=0.008[/tex]  

Since the p value is less than the significance level of 0.05 we have enough evidence to reject the null hypothesis in favor of the claim

And the best conclusion for this case would be:

b)The p-value is 0.008, indicating sufficient evidence for his claim.

Step-by-step explanation:

Information provided

[tex]\bar X=12.2[/tex] represent the sample mean fould against

[tex]s=1.6[/tex] represent the sample standard deviation

[tex]n=34[/tex] sample size  

represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is higher than 11.5 fouls per game:  

Null hypothesis:[tex]\mu \leq 11.5[/tex]  

Alternative hypothesis:[tex]\mu > 11.5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

The statistic is given by:

[tex]t=\frac{12.2-11.5}{\frac{1.6}{\sqrt{34}}}=2.551[/tex]    

P value

The degreed of freedom are given by:

[tex] df = n-1=34-1=33[/tex]

Since is a one side test the p value would be:  

[tex]p_v =P(t_{(33)}>2.551)=0.008[/tex]  

Since the p value is less than the significance level of 0.05 we have enough evidence to reject the null hypothesis in favor of the claim

And the best conclusion for this case would be:

b)The p-value is 0.008, indicating sufficient evidence for his claim.

To the nearest tenth of a second, how much time would it take the penny to hit the ground?

0.5 seconds
0.6 seconds
0.7 seconds
0.8 seconds

Answers

Answer:0.6 sec

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.6 is the answer just took the test

what is the vertex for the graph of y-3=-(x+2)^2

Answers

Answer:

  (-2, 3)

Step-by-step explanation:

In the form ...

  y -k = a(x -h)^2

the vertex is (h, k).

Your equation has k = 3, a = -1, h = -2, so the vertex is ...

  (h, k) = (-2, 3)

Suppose that Drake works for a research institute in Greenland and is given the job of treating wild polar bears there for hypothyroidism using medicated darts. The appropriate dosage depends on the bear's mass. Eager to head into the wilderness, he prints out the statistics he needs and sets off, planning to prepare the darts along the way.

Two days into his trek, however, Drake spills a cup of coffee on the printout. Unwilling to admit to his boss what happened, he decides to estimate the polar bear mass with the information he has remaining. He knows the population standard deviation to be ?=60 kg, and he has data from a simple random sample of n = 10 polar bears from Greenland. Their masses, in kg, are

275,250,325,310,240,360,350,400,380,400

The sample mean polar bear mass is x (there is the line on top of x) =329 kg.

-First, determine if the requirements for a z?confidence interval are met.

A) The requirements are not met because the population standard deviation is not known.

B) The requirements are not met because there is an outlier in the sample, indicating that polar bear masses do not come from a normal distribution or that the sample was not a simple random sample.

C)The requirements are met because the sample is a simple random sample from a normal distribution with a known population standard deviation.

D) The requirements are met because the sample is a simple random sample from a normal distribution and the standard deviation can be estimated from the sample.

-Next, calculate the lower and upper limits (bounds) for a 99% confidence interval for the mean polar bear mass in Greenland. Give your answer precise to one decimal place.

lower limit= _________kg

upper limit=_________kg

-Finally, summarize the results.

A) There is 99% confidence that the polar bear mass sample mean is between the lower and upper limits of the confidence interval.

B) There is a 99% chance that a randomly selected polar bear in Greenland will have a mass between the lower and upper limits of the confidence interval.

C) There is a 99% chance that the Greenland polar bear mass population mean is between the lower and upper limits of the confidence interval.

D) There is 99% confidence that the lower and upper limits of the confidence interval contains the Greenland polar bear mass population mean.

Answers

Step-by-step explanation:

Check the attached file for solution and

simulation screen shot

R-Code:

Sample mean

sd = 60 Population Standard deviation

n = 10 Sample size

conf.level = 0.99 Confidence level

[tex]\alpha = 1-conf.level[/tex]

[tex]z\star = \round(\qnorm(1-\alpha/2),2); z.\star[/tex]

[tex]E = \round(z* \times \sigma/\sqrt(n),2); E[/tex]

[tex]x= c(E,-E)[/tex]

A local soccer team has 6 more games that it will play. If it wins its game this weekend, then it will play its final 5 games in the upper bracket of its league, and if it loses, then it will play its final 5 games in the lower bracket. If it plays in the upper bracket, then it will independently win each of its games in this bracket with probability 0.3, and if it plays in the lower bracket, then it will independently win each of its games with probability 0.4. If the probability that it wins its game this weekend is 0.5, what is the probability that it wins at least 3 of its final 5 games?

Answers

Answer:

Probability that it wins at least 3 of its final 5 games = .02387

Step-by-step explanation:

Given -

The probability of win the weekend game = 0.5

The probability of loose  the weekend game = 0.5

If he wins the game this weekend then it will play its final 5 games in the upper bracket of its league

In this case,  probability of success is (p) = 0.3

probability of failure is (q) = 1 - p = 0.7

Let X be number of game won out of last five games

probability that it wins at least 3 of its final 5 games

( 1 )

[tex]P(X\geq3)[/tex] = [tex]P(X\geq3/first\; game\; won)[/tex] ( probability of first game won )

               =   [tex]0.5\times[/tex]P( X =3 ) + [tex]0.5\times[/tex]P( X =4) + [tex]0.5\times P(X = 5)[/tex]

                =  [tex]0.5\times\binom{5}{3}(0.3)^{3}(0.7)^{2} + 0.5\times\binom{5}{4}(0.3)^{4}(0.7)^{1}[/tex] + [tex]0.5\times\binom{5}{5}(0.3)^{5}(0.7)^{0}[/tex]

                 = [tex]0.5\times\frac{5!}{(3!)(2!)}\times(0.3)^{3}\times(0.7)^{2} + 0.5\times\frac{5!}{(4!)(1!)}\times(0.3)^{4}\times(0.7)^{1}[/tex] + [tex]0.5\times\frac{5!}{(5!)(0!)}\times(0.3)^{5}\times(0.7)^{0}[/tex]= = .065 + .014 + .001215  = .080

               

If he loose the game this weekend then it will play its final 5 games in the lower bracket of its league

In this case,  probability of success is (s) = 0.4

probability of failure is (t) = 1 - s = 0.6

( 2 )

[tex]P(X\geq3/first\; game\; lost)[/tex] ( probability of first game lost )

= [tex]0.5\times P(X = 3) + 0.5\times P(X = 4)[/tex] + [tex]0.5\times P(X=5)[/tex]

= [tex]\binom{5}{3}(0.4)^{3}(0.6)^{2} + 0.5\times\binom{5}{4}(0.4)^{4}(0.6)^{1}[/tex]+ [tex]0.5\times\binom{5}{5}(0.4)^{5}(0.6)^{0}[/tex]

= [tex]0.5\times\frac{5!}{(3!)(2!)}\times(0.4)^{3}\times(0.6)^{2} + 0.5\times\frac{5!}{(4!)(1!)}\times(0.4)^{4}\times(0.6)^{1}[/tex] + [tex]0.5\times\frac{5!}{(5!)(0!)}\times(0.4)^{5}\times(0.6)^{0}[/tex] = = .1152 + .0384 + .00512 = .1587

Required probability = ( 1 ) + ( 2 ) = .02387

What is the area of the kite? A kite has a height of 10 meters and a base of 8 meters.

Answers

Answer:

80 meters (8*10=80)

Answer:

80

Step-by-step explanation:

10 times 8= 80

to find the area is always lenght × height × weight

to find the perimeter is always lenght × lenght × heigth × heigth

example...

a house with the height of 5 and the lenght of 1 .find the perimeter

5+5+1+1= 12

PLEASE HELP ASAP geometry question 100 MAJOR POINTS!!!

Answers

Answer:

7

Step-by-step explanation:

The surface area is the lateral area plus the base area. The base area is 9*5=45. Since there are two bases, its 90. Subtract that from 286 to get the lateral surface area, which is 196. The lateral surface area is the base perimeter*height. The base perimeter is 9+9+5+5= 28. 196/28=height. The height is 7

Answer:

Height= 7in

Step-by-step explanation:

Use the surface area formula and pulg in.

2(wl)(hl)(hw)=286

divide by 2 to get it to the other side.

143=45+9h+5h

subtract 45 and divide by 14 (9+5)

the height is 7

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