How do i know if 4/6 < 3/10?

9514 1404 393

Answer:

  81m^4·n^4

Step-by-step explanation:

"Simplify" in this context means "remove parentheses." The applicable rule of exponents is ...

  (ab)^c = (a^c)(b^c)

__

  [tex](3mn)^4=3^4m^4n^4=\boxed{81m^4n^4}[/tex]

Answer: 0.63333333333

Step-by-step explanation: Use a calculator.

Answer: 19/30

Step-by-step explanation:

You want to find a common denominator that works for all fractions and add a subtract them and the simplify

You solve this question by finding the maximum possible number of different combinations, then adding one extra person.

3 possible shirts * 2 possible pants for each shirt = 6 combinations of pants and shirts.

6 + 1 = 7

Therefore, the minimum is:

7 People

Answer:

1/50 times 2/99 = 2/4950

divide numerator and denominator by 2 and the answer you should get is 1/2475 and in decimal form it equals 0.00040404040404040

Step-by-step explanation:

Answer:

Base= 5.09 cm x 5.09 cm; height = 1.69 cm

Step-by-step explanation:

-> materials has a square base of side length, dimension will be: x . x = x²

'y' represents height

->For dimensions of 4 silver plated sides= xy each

->dimensions of the nickel plated top= x²

Volume = yx²

44=yx² => y= 44/x²

Cost of the sides will be( 4 * xy * $3 )

Cost of the top and the bottom will be  (2 * x² * $1)

For the Total cost: 12xy + 2x²

substituting value of 'y' in above equation,

=> Total cost = 12x (44/x²) + 2x² = 528 / x + 2x²

To Minimum critical point => d [cost] / dx = 0

=> - 528/x² + 4x =0

132/x² - x =0

132 - x³ = 0

x³ = 132

Taking cube root on both sides

∛x³ = ∛(132)

x= 5.09

=> y = 44/5.09² =>1.69

Dimensions of the box :

Base= 5.09 cm x 5.09 cm; height = 1.69 cm

Answer:

The percentage of ounces Leah has left of her coffee is 68.18%.

Step-by-step explanation:

The decrease percentage is computed using the formula:

[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]

It is provided that Leah originally had 22 ounce coffee.

Then she drinks 7 ounces of coffee.

Decrease = 7 ounces

Original = 22 ounces

Compute the percentage of ounces Leah has left of her coffee as follows:

[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]

                 [tex]=\frac{22-7}{22}\times 100\\\\=\frac{15}{22}\times 100\\\\=68.1818182\%\\\\\approx 68.18\%[/tex]

Thus, the percentage of ounces Leah has left of her coffee is 68.18%.

Answer:

Length of arc=4π

Step-by-step explanation:

Length of arc=¤/360 x 2xπxr

Where:

¤=72

r=10

Length of arc=72/360 x 2xπx10

Length of arc=0.2 x 20π

Length of arc=4π

Find the attachment for complete solution

Answer:

B

Step-by-step explanation:

choose brainliest

Answer:

y=10

Step-by-step explanation:

(y-10)^2=0

Take the square root of each side

sqrt((y-10)^2)=sqrt(0)

y-10 =0

Add 10 to each side

y-10+10=0+10

y = 10

Answer:

asdasd

Step-by-step explanation:

miles ÷ miles/hour = hours

Just divide the miles by the mph

4.5/12.5 = 0.36 hours

(0.36 hours)(60 min/hour) = 21.6 minutes

(0.6 minutes)(60 seconds/minute) = 36 seconds

Time:  21 minutes 36 seconds

Answer:

0.36 hours

Step-by-step explanation:

Miles ÷ Miles/hour = hours

4.5 miles ÷ 12.5 mph = 0.36 hours

Answer:

{(5,3) , (6,1), (7,-1), (8,-3)}

Step-by-step explanation:

inverse of (x,y) is (y,x)

inverse of { (3,5), (1, 6), ( -1, 7), (-3, 8)} is

{(5,3) , (6,1), (7,-1), (8,-3)}

Answer:

O Confirm, because the p-value is much smaller.

Step-by-step explanation:

The p-value is the probability used to determine whether to accept or reject an null hypothesis. Higher p-value means that there is evidence in favour of the null hypothesis while smaller p-value means that there is stronger evidence in favour of the alternative hypothesis. For the case above, the p-value is smaller which means that the new study confirms the results of the first study which also have a small p-value.

Given:

It is given that the function represents the data in the table.

We need to determine the function.

Slope:

The slope can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let us substitute the coordinates (1,6.5) and (4,8) in the above formula, we get;

[tex]m=\frac{8-6.5}{4-1}[/tex]

[tex]m=\frac{1.5}{3}[/tex]

[tex]m=0.5[/tex]

Thus, the slope is 0.5

y - intercept:

The y - intercept is the value of y when x = 0.

Thus, from the table, when x = 0 the corresponding y value is 6.

Therefore, the y - intercept is [tex]b=6[/tex]

Equation of the function:

The equation of the function can be determined using the formula,

[tex]y=mx+b[/tex]

Substituting the values [tex]m=0.5[/tex] and [tex]b=6[/tex], we get;

[tex]y=0.5x+6[/tex]

Thus, the equation of the function is [tex]y=0.5x+6[/tex]

Hence, Option C is the correct answer.

Answer:

8x-32

Step-by-step explanation:

Because 8 multiples X and gives 8x and also multiples-4 and gives you -32

:.8x-32

Answer:

[tex]a.\ \mu_p=750\ \ , \sigma_p=0.005\\\\b.\ \mu_p=150\ \ , \sigma_p=0.0113\\\\c.\ \mu_p=75\ \ , \sigma_p=0.0160[/tex]

Step-by-step explanation:

a. Given p=0.15.

-The mean of a sampling proportion  of n=5000 is calculated as:

[tex]\mu_p=np\\\\=0.15\times 5000\\\\=750[/tex]

-The standard deviation is calculated using the formula:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.15(1-0.15)}{5000}}\\\\=0.0050[/tex]

Hence, the sample mean is μ=750 and standard deviation is σ=0.0050

b. Given that p=0.15 and n=1000

#The mean of a sampling proportion  of n=1000 is calculated as:

[tex]\mu_p=np\\\\=1000\times 0.15\\\\\\=150[/tex]

#-The standard deviation is calculated as follows:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{1000}}\\\\\\=0.0113[/tex]

Hence, the sample mean is μ=150 and standard deviation is σ=0.0113

c. For p=0.15 and n=500

#The mean is calculated as follows:

[tex]\mu_p=np\\\\\\=0.15\times 500\\\\=75[/tex]

#The standard deviation of the sample proportion is calculated as:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{500}}\\\\\\=0.0160[/tex]

Hence, the sample mean is μ=75 and standard deviation is σ=0.0160

9514 1404 393

Answer:

  w = 250m

Step-by-step explanation:

As the problem statement tells you, the independent variable, the number of minutes he reads, causes a change in the dependent variable, the number of words read. This is modeled by ...

  w = 250m

Answer: B. w = 250m

Step-by-step explanation: i answered the question and got it right :)

Answer:

y=-6x+7    (Negative Slope)

Step-by-step explanation:

This equation is in slope intercept form.

7= y-intercept

-6= slope

This means that when you plot this on a graph, your slope will be negative.

Answer:

$120

Step-by-step explanation:

Area of wall: 12*5=60 square feet

price = 60*2=$120

Answer:

(a)0.5

(b)0.625

Step-by-step explanation:

Out of 100 MBA students

Total Sample Space, n(S)=100

(a)Let event A be the event  that an MBA student has at least four years of work experience.

n(A)=15+35=50

Therefore:

[tex]P(A)=\dfrac{n(A)}{n(S)} =\dfrac{50}{100}=0.5[/tex]

The probability that this student has at least four years of work experience is 0.5.

(b)Conditional probability that given that a student has at least three years of work experience,this student has at least four years of work experience.

P(at least 4 years|the student has at least three years of experience)

[tex]=\dfrac{50/100}{80/100} =\dfrac{5}{8}=0.625[/tex]

The probability that a randomly selected first-year MBA student has at least four years of work experience is 0.5 or 50%.

The question involves the concept of probability in statistics, a part of Mathematics. Here, we are given that there are a total of 100 first-year MBA students. The number of students with at least four years of work experience combines the students with four years and five or more years of work experience. Thus, the students with at least four years of work experience are 15 (four years of work experience) + 35 (five or more years of work experience), which equals 50.

The probability is determined by dividing the number of favorable outcomes by the total number of outcomes. Hence, the probability that a randomly selected first-year MBA student has at least four years of work experience is calculated as 50 (students with at least four years' experience) divided by 100 (total students), which equals 0.5 or 50%.

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Answer:

The scroll is 1949 years old, thus the archeologists are right.

Step-by-step explanation:

The decay equation of ¹⁴C is:

[tex] A = A_{0}e^{-\lambda*t} [/tex]   (1)

Where:

A₀: is the initial activity

A: is the activity after a time t = 79%*A₀

λ: is the decay rate

The decay rate is:

[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]    (2)

Where [tex]t_{1/2}[/tex]: is the half-life of ¹⁴C = 5730 y

By entering equation (2) into equation (1) we can find the age of the scrolls.

[tex] A = A_{0}e^{-\lambda*t} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t} [/tex]

Since, A = 79%*A₀, we have:

[tex]\frac{79}{100}A_{0} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]

[tex]ln(\frac{79}{100}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]

Solving the above equation for t:

[tex]t = -\frac{ln(79/100)}{\frac{ln(2)}{t_{1/2}}}[/tex]

[tex]t = -\frac{ln(75/100)}{\frac{ln(2)}{5730 y}} = 1949 y[/tex]

Hence, the scroll is 1949 years old, thus the archeologists are right.

I hope it helps you!

Answer:

The hypothesis is correct.

Step-by-step explanation:

Using the half-life equation, the number of years (1,900) can be substituted for t and the half-life (5,730) can be substituted for h. Since the original amount is not known but the percent remaining is known, any value can be used for the original amount. Using 100 will be the easiest. Plugging these values into the equation gives 79.47 remaining. If 79.47 of the original 100 units are left, that is 79.47 percent. Since radiometric dating gives an estimate of age, the archeologists’ hypothesis is correct.

Answer:

2/6 or 1/3

Step-by-step explanation:

3 and 6 are multiples of 3

so that is 2 out of 6 numbers on a fair dice.

Answer:

in many random samples, 95% of the confidence intervals will contain a sample average between 24cm and 27cm.

Step-by-step explanation:

We then interpret this interval that  95% would contain a sample average forearm length between 24cm and 27cm.

The average is defined as the mean  equal to the ratio of the sum of the values ​​of a given number to the total number of values ​​in the set.

The formula for finding the average of given numbers or values ​​is very simple. We just need to add all the numbers and  divide the result by the given number of values. So the  formula for mean in mathematics is given as follows:

Mean = sum of values/ number of values ​​

Suppose we have given  n as number of values ​​like x1, x2, x3 ,..., xn. The average or  mean of the given data is equal to:

Mean = (x1 x2 x3 … xn)/n

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This is a composite function problem in high school mathematics. To solve the problem, first evaluate g(-4), then substitute that result into the function f(x). Using these steps, the composite function f(g(-4)) equals -114.

First, it is crucial to identify that this is a question involving composite functions, specifically applying the function f(g(x)). In this case, the function g(x) is not provided in the question, so I'll assume we have a typo. If g(x) has been given as 3x + 1, then g(-4) would equal -11. We substitute -11 into the function f(x)=10x-4, we get f(-11)=10*(-11)-4, which results in f(-11)=-114.

The composite function f(g(-4)) is thus -114.

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Answer:

6.575 trillion BTUs

Step-by-step explanation:

Let represent the annual energy consumption of the town as E

The rate of annual energy consumption *  energy consumption at time past

dE/dt * E

dE/dt =K

k = the proportionality constant

c= the integration constant

(dE/dt=) kdt

lnE = kt + c

E(t) = e^kt+c ⇒ e^c e^kt  e^c is a constant, and e^c = E₀

E(t) = E₀ e^kt

The initial consumption of energy is E(0)=4.4TBTU

set t = 0 then

4.4 = E₀ e⇒ E₀ (1)

E₀ = 4.4

E (t) = 4.4e^kt

The consumption after 5 years is t = 5, e(5) = 5.5TBTU

so,

E(5) = 5.5 = 4.4e^k(5)

e^5k = 5/4

We now take the log 5kln = ln(5/4)

5k(1) = ln(5/4)

k = 1/5 ln(5/4) = 0.04463

We find  the town's annual energy consumption, after 9 years

we set t=9  

E(9) = 4.4e^0.04463(9)

= 4.4(1.494301) = 6.5749TBTUs

Therefore the annual energy consumption of the town after 9 years is

= 6.575 trillion BTUs

Step-by-step explanation:

A question is asked with options for answers, but in reality, there is only one question stating that it is correct.

The z-score for the sample mean in this case is 0.5, which is calculated using the z-score formula, Z = (X - μ) / σ, where X is the sample mean, μ is the population mean, and σ is the standard deviation.

The subject here pertains to the calculation of a z-score, which is a statistical measurement describing a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.

Given the sample mean (56), population mean (50), and standard deviation (12), and the formula for the z-score, which is Z = (X - μ) / σ, we can compute for the z-score as follows:

Substituting these values into the equation, we have: Z = (56 - 50) / 12 = 0.5. Hence, the z-score of the sample mean is 0.5.

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Answer:

[tex] P(z<-1.55)=0.0606[/tex]

Step-by-step explanation:

For this case we want to find this probability:

[tex] P(z<-1.55)[/tex]

Because they want the area to the left of the value. We need to remember that the normal standard distribution have a mean of 0 and a deviation of 1.

We can use the following excel code: =NORM.DIST(-1.55,0,1,TRUE)

And we got:

[tex] P(z<-1.55)=0.0606[/tex]

The other possibility is use the normal standard table and we got a similar result.

Answer:

y = 3

Step-by-step explanation:

y = (3x² + 3x + 6) / (x² + 1)

The power of the numerator and denominator are equal, so as x approaches infinity, y approaches the ratio of the leading coefficients.

y = 3/1

The horizontal asymptote will be;

⇒ y = 3

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The algebraic expression is,

''The horizontal asymptote off of x equals quantity 3 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.''

Now,

We can formulate;

⇒ f (x) = ( 3x² + 3x + 6 ) / (x² + 1)

Hence, We get the horizontal asymptote as;

We know that;

A function f is said to have a horizontal asymptote y = a;

⇒ [tex]\lim_{x \to \infty} f (x) = a[/tex]

So, We get;

⇒ [tex]\lim_{x \to \infty} f (x) = \lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1}[/tex]

⇒ [tex]\lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1} = \lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)}[/tex]

⇒ [tex]\lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)} = 3[/tex]

⇒ y = 3

Thus, The horizontal asymptote will be;

⇒ y = 3

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Answer:

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 500, \pi = \frac{421}{500} = 0.842[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874[/tex]

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

The 95% confidence interval is (0.81,0.874) and this can be determined by using the confidence interval formula and using the given data.

Given :

The formula for the confidence interval is given by:

[tex]\rm CI = p\pm z\sqrt{\dfrac{p(1-p)}{n}}[/tex]  --- (1)

where the value of p is given by:

[tex]\rm p =\dfrac{421}{500}=0.842[/tex]

Now, the value of z for 95% confidence interval is given by:

[tex]\rm p-value = 1-\dfrac{0.05}{2}=0.975[/tex]

So, the z value regarding the p-value 0.975 is 1.96.

Now, substitute the value of z, p, and n in the expression (1).

[tex]\rm CI = 0.842\pm 1.96\sqrt{\dfrac{0.842(1-0.842)}{500}}[/tex]

The upper limit is 0.81 and the lower limit is 0.874 and this can be determined by simplifying the above expression.

So, the 95% confidence interval is (0.81,0.874).

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