3•(7+10)=G+30 use the distributive property to solve

Answer:

Null hypothesis:[tex]\mu = 52.6[/tex]  

Alternative hypothesis:[tex]\mu \neq 52.6[/tex]  

[tex]z=\frac{52.8-52.6}{\frac{1.6}{\sqrt{250}}}=1.976[/tex]    

[tex]p_v =2*P(z>1.976)=0.0482[/tex]  

Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.

Step-by-step explanation:

Information provided

[tex]\bar X=52.8[/tex] represent the sample mean  for the MPG of the cars

[tex]\sigma=1.6[/tex] represent the population standard deviation

[tex]n=250[/tex] sample size  of cars

[tex]\mu_o =52.6[/tex] represent the value that we want to test

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

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test

Hypothesis

We need to conduct a hypothesis in order to check if the true mean of MPG is different from 52.6 MPG, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 52.6[/tex]  

Alternative hypothesis:[tex]\mu \neq 52.6[/tex]  

Since we know the population deviation the statistic is given by:

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

Calculate the statistic

Replacing we have this:

[tex]z=\frac{52.8-52.6}{\frac{1.6}{\sqrt{250}}}=1.976[/tex]    

Decision

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

[tex]p_v =2*P(z>1.976)=0.0482[/tex]  

Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.

Answer:

Probability that a student will score more than 1700 points is 0.50.

Step-by-step explanation:

We are given that the mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points.

Let X = Scores results on a test

So, X ~ N([tex]\mu=1700,\sigma^{2} =75^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

               Z = [tex]\frac{ X -\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean score = 1700 points

            [tex]\sigma[/tex] = standard deviation = 75 points

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, the probability that a student will score more than 1700 points is given by = P(X > 1700 points)

  P(X > 1700) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{1700-1700}{75}[/tex] ) = P(Z > 0) = 1 - P(Z [tex]\leq[/tex] 0)

                                                        = 1 - 0.50 = 0.50

Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0 in the z table which has an area of 0.50.

Hence, the probability that a student will score more than 1700 points is 50%.

Answer:

a. True

Question 13 of the attached image;

Step-by-step explanation:

Confidence interval, in statistics can be defined as the probability that a population parameter will fall between two set values( upper and lower bound) for a certain proportion of times. Therefore, there's 99% chance that the true difference in RDI levels between men and women is contained within the 99% Confidence interval shown in the previous questions.

The statement is a matter of statistical inference and would be true if the interval was correctly computed using appropriate methods. While the 99% confidence level suggests we are highly confident the true value lies within the interval, it is not a direct measure of probability.

The statement 'There is a 99% chance that the true difference in RDI levels between men and women is contained in the interval already computed' is an assertion relating to statistical inference, specifically, confidence intervals. If this interval was correctly computed using appropriate statistical methods, then it would be true that we are 99% confident that the true difference in RDI levels between mean and women is within this interval. However, it's worth noting that a 99% confidence interval does not necessarily mean there is a 99% probability that the value lies within the interval, it rather suggests that if we were to repeat this study 100 times, we would expect the true mean difference to be within the computed confidence interval 99 times.

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Answer:

[tex]n=\frac{0.2(1-0.2)}{(\frac{0.05}{1.64})^2}=172.13[/tex]  

And rounded up we have that n=173

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]p[/tex] represent the real population proportion of interest

[tex]\hat p[/tex] represent the estimated proportion for the sample

n is the sample size required (variable of interest)

[tex]z[/tex] represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution  

[tex]p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})[/tex]  

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.10[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:  

[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]  

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)  

And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)

We can assume that the estimates proportion is [tex]\hat p=\frac{14}{70}=0.2[/tex]. And replacing into equation (b) the values from part a we got:  

[tex]n=\frac{0.2(1-0.2)}{(\frac{0.05}{1.64})^2}=172.13[/tex]  

And rounded up we have that n=173

The experimental probability that the band will play an encore at its next show is 7/12 or approximately 0.5833.

To find the experimental probability that the band will play an encore at its next show, we need to divide the number of times the band played an encore by the total number of shows. In this case, the band played an encore at 7 out of 12 shows. To calculate the experimental probability, divide 7 by 12. So, the experimental probability that the band will play an encore at its next show is 7/12 or approximately 0.5833.

Answer:

yes

Step-by-step explanation:

no

maybe

perhaps

done

Answer:

3

Step-by-step explanation:

The region representing the solution to a system of inequalities is where the shading of all individual inequalities overlap on a graph. In this case, the provided inequalities should be graphed individually, and the overlapping shaded area is the solution.

The region that represents the solution to a system of inequalities is the area in a graph where all the inequality solutions overlap. In the given inequalities:

First, graph each inequality individually on the coordinate plane using a method that makes sense (linear inequality graphing for this case). The region that is shaded by both inequalities, or resides in the overlap of the shading of the individual inequalities, represents the solution to the system of inequalities.

Do recall that when dealing with 'greater than' or 'less than' signs, we use dashed lines to represent the boundary where inequality is not equal to the boundary. If the sign was 'greater than or equal to' or 'less than or equal to', we would use solid lines.

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Answer:

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

Step-by-step explanation:

Final answer:

Equations can have differing numbers of solutions: linear equations typically have one, while quadratic equations usually have two, but may have one or none depending on their discriminant. Inequalities often have a range of solutions, representing values that satisfy the inequality condition.

Explanation:

The number of solutions an equation has can vary depending on the type of equation. Linear equations typically have one solution, representing where the line intersects the x-axis on a graph. Equations that involve an unknown squared, also known as quadratic equations, generally have two solutions; these solutions represent the x-intercepts or the points where the parabola crosses the x-axis. However, there are cases where a quadratic equation might have one or no real solutions depending on its discriminant (b2 - 4ac).

Inequalities are different from equations. They often have a range of solutions rather than exact values, because they represent values that are less than (<), less than or equal to (≤), greater than (>), or greater than or equal to (≥) a certain number, rather than being exactly equal to it. A simple linear inequality, for instance, has a set of all possible solutions that make the inequality true, which can be illustrated as a region on a number line or in coordinate space.

Answer: 28

Step-by-step explanation:

Answer:

28 pints

Step-by-step explanation:

There are 4 quarts in a gallon

There are 2 pints in a quart

We know 10 guarts = 10/4 = 2 .5 gallons = 2 gallons 2 guarts

Subtracting the 10 quarts in the kitchen

9 gallons - 2 gallons 2 quarts

Changing 1 gallon to 4 quarts

8 gallons 4 quarts - 2 gallons 2 quarts = 6 gallons 2 quarts

Then he used 3 gallons in the living room

6 gallons 2 quarts - 3 gallons = 3 gallons 2 quarts

Changing gallons to quarts

3*4 = 12 12 quarts + 2 quarts = 14 quarts

Now we need to change to pints

14 quarts * 2 pints = 28 pints

Answer:

  Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.

Step-by-step explanation:

The unit rate is the change in y for a 1-unit change in x. Since the graph of a proportion will go through the origin, it is appropriate to look at the y-value for x = 1 (one unit from the origin).

___

The ratio of units up to units to the right is also the unit rate when the fraction is reduced to lowest terms. It is a "unit" rate when the denominator of the fraction is 1 unit.

Answer:

A

Step-by-step explanation:

Answer:

Option choice D

Step-by-step explanation:

It wont be that big of an error.

Brainliest?

Answer:

[tex]P(\bar X <38)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 38 we got:

[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]

So then we want to find this probability:

[tex] P(z<-1.265)[/tex]

And we can use the normal standard distribution or excel and we got:

[tex] P(z<-1.265)=0.103[/tex]

Step-by-step explanation:

For this case we define the random variable X as the annual income for people at certain city. And we know the following properties:

[tex] E(X) = 42, Sd(X) =42[/tex]

They select a sample size of n = 90>30. So then we can assume that the central limit can be applied.

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

We want to calculate this probability:

[tex]P(\bar X <38)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 38 we got:

[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]

So then we want to find this probability:

[tex] P(z<-1.265)[/tex]

And we can use the normal standard distribution or excel and we got:

[tex] P(z<-1.265)=0.103[/tex]

Answer:

14.19

Step-by-step explanation:

The equation of the ellipse with height = 26 cm and width = 16 cm is - [tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex]  and the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point is 9.81cm

We have a wooden plaque in the shape of an ellipse with height 26 centimeters and width 16 centimeters.

We have to find equation for the ellipse and use it to find the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point.

The general form of the equation of ellipse is -

[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } =1[/tex]

Where -

a is the length of semi major axis.

b is the length of semi minor axis.

In the question given to us -

height of ellipse = length of major axis = 2a =26

width of ellipse = length of minor axis = 2b = 16

Therefore -

a = 13 cm  

and

b = 8 cm

Substituting the values in the equation of ellipse, we get -

[tex]\frac{x^{2} }{(13)^{2} } +\frac{y^{2} }{(8)^{2} } =1[/tex]

[tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex]

Now, at y = 6 cm above the center -

[tex]\frac{x^{2} }{169 } = 1 - \frac{36 }{64} }\\\\\frac{x^{2} }{169 } = 0.57\\x^{2} = 169\times0.57\\x = 9.81 cm[/tex]

Hence, the equation of the ellipse with height = 26 cm and width = 16 cm is - [tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex]  and the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point is 9.81cm

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Answer:

[tex]3.372-1.96\frac{0.66}{\sqrt{5}}=2.793[/tex]    

[tex]3.372+1.96\frac{0.66}{\sqrt{5}}=3.951[/tex]    

We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2  is between (2.793; 3.951)

Step-by-step explanation:

Data provided

2.69, 5.76, 2.67, 1.62, and 4.12

We can calculate the sample mean with this formula:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X=3.372[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma=0.66[/tex] represent the population standard deviation

n=5 represent the sample size  

Confidence interval :

The two sided confidence interval for the true mean is given by:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

We have the confidence level given of 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]

Replacing into the formula for the interval we have this:

[tex]3.372-1.96\frac{0.66}{\sqrt{5}}=2.793[/tex]    

[tex]3.372+1.96\frac{0.66}{\sqrt{5}}=3.951[/tex]    

We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2  is between (2.793; 3.951)

Final answer:

The 95% confidence interval for the mean adhesion of the bacterial strain Acinetobacter, based on the given measurements and standard deviation, is [2.795, 3.949] dyne-cm².

Explanation:

The question asks us to find a 95% confidence interval for the mean adhesion of the bacterial strain Acinetobacter based on five given measurements and a known standard deviation. To calculate the confidence interval, we can use the formula for the confidence interval of the mean when the standard deviation is known:

mean ± Z*(standard deviation/√n),

where Z is the Z-value corresponding to the desired level of confidence from the standard normal distribution, and n is the sample size.

First, we need to calculate the mean of the given measurements:

Since we are looking for a 95% confidence interval and the standard deviation (σ) is 0.66 dyne-cm² with a sample size (n) of 5, our formula becomes:

3.372 ± (Z * 0.66 / √5)

To find the appropriate Z-value, we look at the standard normal distribution table for a two-sided 95% confidence interval, which gives us a Z-value of approximately 1.96.

Plugging this Z-value into the formula, we can calculate the confidence interval:

3.372 ± (1.96 * 0.66 / √5) = 3.372 ± 0.577

Therefore, the 95% confidence interval for the mean adhesion is [2.795, 3.949] dyne-cm².

Answer: The correct answer is an UNFILLED CIRCLE

Step-by-step explanation: An organism can be homozygous dominant, if it carries two copies of the same dominant allele, or homozygous recessive, if it carries two copies of the same recessive allele.

A homozygous dominant is represented by an UNFILLED CIRCLE.

Answer:

r(x) = 56x + 99

Step-by-step explanation:

You need to add the two equations together:

r(x) = (24x+48) + (51+32x)

r(x) = 24x + 32x + 48 + 51

r(x) = 56x + 99

Answer:

Step-by-step explanation:

Took the test

Answer:

7 fishes

Step-by-step explanation:

Given the growth of the population of fish which is modeled by the exponential function:

[tex]P(t)=7 \cdot b^t[/tex]

Where:

t=time in weeks after release

b=growth rate of the fish

At t=0

[tex]P(0)=7 \cdot b^0\\P_0=7 \cdot 1 \\P_0=7[/tex]

The initial number, [tex]P_0[/tex] of fish which was released into the lake is 7.

Answer:

y=2x+4

y=-1/2x+4

linear quations

both have the same y intercept (=4).

y=2x+4  is positive straight line, slope = 2

y=-1/2x+4 is negative straight line, slope=-1/2

Step-by-step explanation:

Answer:

3 schools did

Step-by-step explanation:

Answer:

In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR

Step-by-step explanation:

Probability of a teacher being certified in Cardio-Pulmonary Resuscitation (CPR).

36 of 80

So

[tex]p = \frac{36}{80} = 0.45[/tex]

In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

45% of the days

0.45*180 = 81

In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR

To calculate the number of days a teacher certified in CPR will be on bus duty, use the ratio of certified teachers (9/20) multiplied by the total number of school days (180), resulting in an expectation of 81 days.

The student is asking to calculate the number of days one can expect a teacher certified in CPR to be on bus duty at a local intermediate school. Given that 36 out of 80 teachers are certified in CPR, the ratio of certified to non-certified teachers is 36/80, which can be simplified to 9/20. To find out how many days a teacher on bus duty will likely be certified in CPR, we apply this ratio to the total number of school days, which is 180.

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Answer:

You have every right to be angry, but that doesn't give you the right to be mean.

He drank life before spitting it out.

My Mum tries to be cool by saying that she likes all the same things that I do.

Step-by-step explanation:

Pauline can purchase 3 grey parrots and 7 blue lovebirds with her budget of $1040 to fulfill the requirement of buying a total of 10 birds.

To figure out how many of each bird Pauline can buy, we can setup and solve a system of equations:

Solving the system:

Therefore, Pauline should purchase 3 grey parrots and 7 blue lovebirds.

Answer:

"90% confidence" means there is a probabilty of 90% that the population mean (average compensation for the population of party clowns) lies within the confidence interval.

Step-by-step explanation:

The confidence interval is a range of values in which, according to the level of confidence that is calculated, is likely to include a parameter of the population. In this case, this parameter is the population mean compensation of party clowns.

The level of confidence is 90%, so there is 90% of confidence (or probability) that the population mean compensation for party clowns lie within $9394 and $9926.

None of the options below is correct.

Answer:

A) Pd = 13/28

B) Pd = 7/16

Step-by-step explanation:

Given;

Drama = 2

Comedy = 1

Science fiction = 5

Total = 8

a) The probability of selectingat least one drama movie Pd;

Pd = 1 - Pd'

Without replacement;

Probability of not selecting a drama movie Pd' is;

Pd' = 6/8 × 5/7 = 15/28

Pd = 1 - 15/28

Pd = 13/28

b) with replacement;

Probability of not selecting a drama movie Pd' is;

Pd' = 6/8 × 6/8 = 9/16

Pd = 1 - 9/16

Pd = 7/16

Answer:

The student GPA is 3.1875

Step-by-step explanation:

First we calculate the grade point by multiplying the grade with the weight;

= (3.9 * 5) + (2.1 * 3) + (2.9 * 4) + (3.4 * 4)

= 19.5 + 6.3 + 11.6 + 13.6

= 51

Total weight = 5+3+4+4=16

GPA = 51/16=3.1875

To calculate the student's GPA, we multiply each course grade by its credit hours, sum those totals to get the quality points, and then divide by the total number of credits. In this case, the student's GPA is 3.1875.

To calculate a student's Grade Point Average (GPA) for a term, each course grade is multiplied by the course's credit hours to get the total quality points for that course. Then, the sum of all quality points is divided by the total number of credit hours taken.

Step-by-Step GPA Calculation

For each course, multiply the grade by the number of credits:

(3.9 × 5) + (2.1 × 3) + (2.9 × 4) + (3.4 ×4).

Sum the results of these multiplications to get the total quality points.

Sum the total number of credits: 5 + 3 + 4 + 4.

Divide the total quality points by the total number of credits.

Let's do the math:

(3.9 × 5) = 19.5

(2.1 × 3) = 6.3

(2.9 × 4) = 11.6

(3.4 × 4) = 13.6

Total quality points = 19.5 + 6.3 + 11.6 + 13.6 = 51

Total credits = 5 + 3 + 4 + 4 = 16

The student's GPA for the term is the total quality points divided by the total credits:

GPA = 51 / 16 = 3.1875.

Answer:

The decay rate expressed as a percentage is of 24%.

Step-by-step explanation:

The equation for the value of the car has the following format:

[tex]y(t) = y0(1-r)^{t}[/tex]

In which y(t) is the value of the car after t years, y0 is the initial value and r is the decay rate, as a decimal.

In this problem:

y=48000(0.76)^t

So

Comparing to the general formula:

1 - r = 0.76

r = 1 - 0.76

r = 0.24

To convert from decimal to percentage, we multiply by 100

The decay rate expressed as a percentage is of 24%.

The final inequality that defines the shaded region on the graph is y ≥ -2 + 2x. Here option A is correct.

Given Linear Equation:

The general form of a linear equation is y = mx + c, where c is the y-intercept (the value of y when x = 0). Given that the point (0, -2) lies on the line, c = -2. The equation is then y = mx - 2.

Equation: y = mx - 2

Using Another Point on the Line:

The point (2, 2) is also on the line. Substitute x = 2 and y = 2 into the equation:

2m - 2 = 2

Solve for m:

2m = 4

m = 2

Now we know m = 2, so the equation becomes:

y = 2x - 2

Inequality for Shaded Region:

The inequality sign ≥ suggests that the shaded region is above the line. Therefore, the inequality for the shaded region is:

y ≥ 2x - 2

Rewriting the Inequality:

To match the given form y ≥ -2 + 2x, rearrange terms:

y ≥ -2 + 2x. Here option A is correct.

Complete question:

Which inequality describes the graph?

The answer is: No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.

Answer:

The answer is C.

Step-by-step explanation:

You times 40 by $8:50 to get what he earned for the 40 hours. This will get you $340. To get the overtime pay, it's 1.5 times $8.50. This will get you $12.75, so times it by 10 to get the overtime pay. You end up with $127.50. You add both pays together (340 + 127.5) to get $467.50.

Answer:

-11

Step-by-step explanation:

I got it wrong, sorry! T-T