Assume that 0 < x < pi/2 and 0 < y < pi/2. Find the exact value of cos(x-y) if cos(x)=3/5 and cos(y)=4/5
a. 25/24
b. -25/24
c. 24/25
d. -24/25

Answer:

40 in^2

Step-by-step explanation:

The area of the trapezoid is found by

A = 1/2 (b1+b2)h  where b1 and b2 are the lengths of the bases and h is the height

   = 1/2 (7+3)*8

   = 1/2 (10)*8

   = 40 in^2

Answer:

ok the answer is 40

Step-by-step explanation:

a+b/2*h

7+3/2*8

7+3=10

10/2=5

5*8=40

Answer:

B C E are the answers

Step-by-step explanation:

hope it helps

Only the equations -1(x/4) + 3/4 = 12 and (-x/4) + 3/4 = 12 are equivalent to the original equation. The other equations provided do not hold the same properties of distribution and are not equivalent to the original equation.

When comparing these equations to the original, we must take into consideration the properties of distribution, a crucial component of algebra. The original equation is -1/4(x) + 3/4 = 12. Let's go through the options one by one:

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Answer:

The answer is $5.

Step-by-step explanation:

$10 divided by 2 packs = $5

OR

$10 divided by 4 to get the per pack price which is $2.50 each

Then multiply $2.50 times 2 packs = $5

Hope this helps!!

Answer:

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

274 shelters will be needed.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 250, \sigma = 75[/tex]

If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights?

What is the percentile of 350?

This is the pvalue of Z when X = 350.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{250 - 150}{75}[/tex]

[tex]Z = 1.33[/tex]

[tex]Z = 1.33[/tex] has a pvalue of 0.9082.

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

If not, what number of shelter openings will be needed?

The 95th percentile, which is X when Z = 1.645. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 150}{75}[/tex]

[tex]X - 150 = 1.645*75[/tex]

[tex]X = 274[/tex]

274 shelters will be needed.

The current shelter capacity of 350 will not be sufficient for 95% of nights according to the normal distribution of the number of women in shelters each night. To have enough capacity for 95% of the nights, the city's shelter would need approximately 397 bed openings.

The subject of this question relates to a discipline in statistics called normal distribution. Essentially, we have the mean number of women in shelters each night (250) and the standard deviation (75). Since the council wants the capacity to be enough for 95% of nights, we need to find the number corresponding to the 95th percentile in this normal distribution.

In a normal distribution, 95% of the data falls within 1.96 standard deviations of the mean. So, we will calculate the upper limit of the capacity using the following formula: Upper Limit = Mean + (1.96 * Standard Deviation)

By substituting the given mean and standard deviation (250 and 75 respectively), we get: Upper Limit = 250 + (1.96 * 75) = 397.

So, a shelter capacity of 350 will not be sufficient to house most abused women on 95% of all nights. The city's shelters would need 397 openings to meet this requirement.

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Answer:

[tex]z = \frac{21.3-21}{\frac{1.2}{\sqrt{50}}}= 1.77[/tex]

Step-by-step explanation:

Data given and notation  

[tex]\bar X=21.3[/tex] represent the sample mean

[tex]\sigma=1.2[/tex] represent the population standard deviation

[tex]n=50[/tex] sample size represent the value that we want to test

[tex]\alpha[/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)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 21, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 21[/tex]  

Alternative hypothesis:[tex]\mu > 21[/tex]  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

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

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]z = \frac{21.3-21}{\frac{1.2}{\sqrt{50}}}= 1.77[/tex]

Answer:

58.1377674149945 inches. (Round to whatever you need)

Step-by-step explanation:

Here we turn to Pythagoras theorem.

Because there is a right angled triangle,

Let the two shorter sides (length and width) be a and b and the longer side (diagonal) be c

A² + B² = C²

38² + 44² = 3380inches² (this is not the area. It's how Pythagoras theorem works)

Then the square root of this is 58.1377674149945 inches. (Round to whatever you need)

So that is the length of the diagonal

Answer:

By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars

Step-by-step explanation:

We have no information about the distribution, so we use the Chebyshev's theorem to solve this question.

Chebyshev Theorem:

75% of the data within 2 standard deviations of the mean.

89% of the data within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 37

Standard deviation = 8

What is the probability of a randomly selected state having between 21 and 53 multi-million dollars

21 = 37 - 2*8

So 21 is 2 standard deviations below the mean.

53 = 37 + 2*8

So 52 is 2 standard deviations above the mean.

By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars

Given:

Given that the graph OACE.

The coordinates of the vertices OACE are O(0,0), A(2m, 2n), C(2p, 2r) and E(2t, 0)

We need to determine the midpoint of EC.

Midpoint of EC:

The midpoint of EC can be determined using the formula,

[tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Substituting the coordinates E(2t,0) and C(2p, 2r), we get;

[tex]Midpoint=(\frac{2t+2p}{2},\frac{0+2r}{2})[/tex]

Simplifying, we get;

[tex]Midpoint=(\frac{2(t+p)}{2},\frac{2r}{2})[/tex]

Dividing, we get;

[tex]Midpoint=(t+p,r)[/tex]

Thus, the midpoint of EC is (t + p, r)

Hence, Option A is the correct answer.

Answer:

-7/2

Step-by-step explanation:

[tex]slope = \frac{ - 4 - 10}{7 - 3} \\ \hspace{24 pt} = \frac{ - 14}{4} \\ \hspace{24 pt}= - \frac{7}{2} \\ \huge{ \red{ \boxed{\therefore \: slope = - \frac{7}{2} }}}[/tex]

Final answer:

To construct a confidence interval for the true mean daily fees collected at the parking garage, the normal distribution should be used. Using a 90% confidence level, the confidence interval is calculated as $116 to $136. Based on the confidence interval, it is possible that the consultant's prediction of $130 per day could be correct.

Explanation:

(a) To construct the confidence interval, we should use the normal distribution. This is because the sample size is large enough (14 days) and the Central Limit Theorem applies, which states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

(b) To construct a 90% confidence interval, we need to find the critical value corresponding to a 90% confidence level. The critical value for a 90% confidence level can be found using a z-table. From the z-table, we find that the critical value is approximately 1.645. The margin of error is calculated as the critical value multiplied by the standard deviation of the sample mean, which is the standard deviation divided by the square root of the sample size. In this case, the margin of error is (1.645 x 15) / √14. We can then construct the confidence interval by subtracting and adding the margin of error to the sample mean. The 90% confidence interval for the true mean daily fees collected at this parking garage is approximately $116 to $136.

(c) Based on the confidence interval, we can see that the range of $116 to $136 includes the predicted average of $130 per day by the consultant. Therefore, it is possible that the consultant could have been correct.

Answer:

Average

6.8

Step-by-step explanation:

[tex]\frac{5+3+5+30+4+5+4+3+4+5}{10}=6.8[/tex]

Given:

Given that the pie chart shows the relative frequency distribution resulting from a survey of 6000 US rural households with internet connections in a certain year.

We need to determine the total number of households with each type of internet in the survey.

Cable modem:

Since, the relative frequency distribution for cable modem is 0.142

The total number of households that use cable modem is given by

[tex]0.142 \times 6000=852[/tex]

Thus, 852 households use cable modem.

DSL:

Since, the relative frequency distribution for DSL is 0.092

The total number of households that use DSL is given by

[tex]0.092 \times 6000=552[/tex]

Thus, 552 households use DSL.

Dialup:

Since, the relative frequency distribution for dialup is 0.747

The total number of households that use dialup is given by

[tex]0.747 \times 6000=4482[/tex]

Thus, 4482 households use dialup.

Others:

Since, the relative frequency distribution for others is 0.019

The total number of households that use others is given by

[tex]0.019 \times 6000=114[/tex]

Thus, 114 households use others.

Answer:

The margin of error increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the​ parameter, the larger the margin error.

Step-by-step explanation:

Margin of Error is a statistical measure of random sampling error insurvey results.

Level of confidence reflects percentage range around sample mean, that can be expected to contain population actual parameter.

High level of confidence means larger range band of confidence interval, supposed to contain the population parameter. This further implies  high expected variation between sample statistic & actual parameter i.e Margin Error increases.

The margin of error increases as the level of confidence increases because the smaller the expected proportion of intervals that will contain the​ parameter, the larger the margin of error (C).

The correct answer is C. The margin of error increases as the level of confidence increases because the smaller the expected proportion of intervals that will contain the​ parameter, the larger the margin of error. When we calculate a confidence interval, we need to balance our desire for a higher level of confidence with the need for a smaller margin of error.

For example, let's say we want to estimate the proportion of students at a school who prefer chocolate ice cream. If we want to be extremely confident in our estimate, let's say 99% confident, there will be a larger margin of error since we need to consider a smaller proportion of intervals that will contain the true proportion.

On the other hand, if we were only interested in being 90% confident, there would be a smaller margin of error since we can include a larger proportion of intervals that will contain the true proportion.

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Answer:

[tex]z=\frac{0.55 -0.6}{\sqrt{\frac{0.6(1-0.6)}{80}}}=-0.913[/tex]  

[tex]p_v =P(z<-0.913)=0.181[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduate students show that only 44 students have ever done so is not significantly lower than 0.6

Step-by-step explanation:

Data given and notation

n=80 represent the random sample taken

X=44 represent the students that have bought merchandise on-line at their site

[tex]\hat p=\frac{44}{80}=0.55[/tex] estimated proportion of graduate students show that only 44 students have ever done so

[tex]p_o=0.6[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

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

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion of interest is lower than 0.6 or 60%, so then the system of hypothesis are.:  

Null hypothesis:[tex]p \geq 0.6[/tex]  

Alternative hypothesis:[tex]p < 0.6[/tex]  

When we conduct a proportion test we need to use the z statistic, 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  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.55 -0.6}{\sqrt{\frac{0.6(1-0.6)}{80}}}=-0.913[/tex]  

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 significance level assumed for this case is [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

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

[tex]p_v =P(z<-0.913)=0.181[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduate students show that only 44 students have ever done so is not significantly lower than 0.6

The subject of this question is Science in Middle School. The student is learning about scientific models by making a model of air flow in their classroom or room in their house.

The subject of this question is Science and the grade level is Middle School. In this question, the student is learning about scientific models by making a model of how air flows through their classroom or a room in their house. The student can use this activity to gain a better understanding of how air moves in closed spaces and the factors that affect its flow.

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Answer:

D.

Step-by-step explanation:

AAS triangle congruence theorem. These triangle have the same side, angle and other angle

The theorem that would determine if two right triangles are congruent or not are AAS Triangle Congruence Theorem.

If two right triangles have similar sizes and shapes, they are considered to be congruent triangles. In other terms, two right triangles are described to be congruent if the lengths of their respective sides and angles are the same.

The angle-angle-side (AAS) theorem posits that when two angles and any side of a triangle are equivalent to two angles and any side of some other triangle, then the triangles are considered to be congruent triangles.

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2/3 of 1 is simply 2/3 or 0.667

Answer:

It will take 34.79 years before the solar panel is only able to produce 300 watts of power

Step-by-step explanation:

The equation for the amount of electricity that a solar panel is capable has the following format:

[tex]Q(t) = Q(0)e^{-kt}[/tex]

In which Q(t) is the amount after t years, Q(0) is the initial amount and k is the exponential decay constant.

After ten years, a solar panel produces 89% of the electricity that it was able to produce when it was brand new.

This means that [tex]Q(10) = 0.89Q(0)[/tex]. So

[tex]Q(t) = Q(0)e^{-kt}[/tex]

[tex]0.89Q(0) = Q(0)e^{-10k}[/tex]

[tex]e^{-10k} = 0.89[/tex]

[tex]\ln{e^{-10k}} = \ln{0.89}[/tex]

[tex]-10k = \ln{0.89}[/tex]

[tex]10k = -\ln{0.89}[/tex]

[tex]k = \frac{-\ln{0.89}}{10}[/tex]

[tex]k = 0.01165[/tex]

So

[tex]Q(t) = Q(0)e^{-0.01165t}[/tex]

Initially capable of producing 450 watts of power

This means that [tex]Q(0) = 450[/tex]

How long will it take before the solar panel is only able to produce 300 watts of power?

This is t for which Q(t) = 300. So

[tex]Q(t) = 450e^{-0.01165t}[/tex]

[tex]450 = 300e^{-0.01165t}[/tex]

[tex]e^{-0.01165t} = \frac{300}{450}[/tex]

[tex]\ln{e^{-0.01165t}} = \ln{\frac{300}{450}}[/tex]

[tex]-0.01165t = \ln{\frac{300}{450}}[/tex]

[tex]0.01165t = -\ln{\frac{300}{450}}[/tex]

[tex]t = -\frac{\ln{\frac{300}{450}}}{0.01165}[/tex]

[tex]t = 34.79[/tex]

It will take 34.79 years before the solar panel is only able to produce 300 watts of power

The decay constant 'k' for the solar panel's power production can be calculated using the formula for exponential decay, and turns out to be approximately -0.0116. Using this decay constant, it would take approximately 19.5 years for the solar panel to only produce 300 watts of power.

The subject of your question involves an understanding of exponential decay in the context of the power production of a solar panel. The decay is represented by the mathematical formula N=N0exp-kt, where N0 is the initial quantity of the substance, N is the quantity of the substance after time t, k is the decay constant, and e is Euler's number, a mathematical constant approximately equal to 2.71828.

In the scenario you've presented in your question, we know that the solar panel is producing 89% of its original power after 10 years. This can be expressed in our formula as: 0.89 = exp-10k. Solving this equation for k, we'll find that k is approximately equal to -0.0116.

To determine the duration before the solar panel's power production drops to 300 watts, we'll use the same formula, setting N0 at 450 watts and N at 300 watts. Therefore, the equation will be: 300 = 450 * exp-0.0116t. Solving this equation, you'll find that it will take approximately 19.5 years for the solar panel to only produce 300 watts of power.

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Answer:

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

Step-by-step explanation:

The quotient is the number which is generated when we perform division operations on two numbers.

The quotient of 2/5 and 4/5.

The quotient of 2/5 and 4/5 is determined in the following steps given below.

[tex]\rm Quotient =\dfrac{\dfrac{2}{5}}{\dfrac{4}{5}}\\\\Quotient =\dfrac{2}{5}\times \dfrac{5}{4}\\\\ Quotient =\dfrac{2}{4}\\\\Quotient =\dfrac{1}{2}[/tex]

Hence, the quotient of 2/5 and 4/5 is 1/2.

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Given:

Given that the length of the side of the square is 12 cm.

The  given figure consists of two circles with radius of 3 cm each.

We need to determine the area of the shaded region.

Area of the square:

The area of the square can be determined using the formula,

[tex]A=s^2[/tex]

Substituting s = 12, we get;

[tex]A=12^2[/tex]

[tex]A=144 \ cm^2[/tex]

Thus, the area of the square is 144 square cm.

Area of the two circles:

The area of the circle can be determined using the formula,

[tex]A=\pi r^2[/tex]

Substituting r = 3, we get;

[tex]A=(3.14)(3)^2[/tex]

[tex]A=(3.14)(9)[/tex]

[tex]A=28.26 \ cm^2[/tex]

The area of 2 circles is given by

[tex]A=2(28.26)[/tex]

[tex]A=56.52 \ cm^2[/tex]

Thus, the area of the two circles is 56.52 square cm.

Area of the shaded region:

The area of the shaded region can be determined by subtracting the area of the two circles from the area of the square.

Thus, we have;

Area = Area of square - Area of two circles.

Substituting the values, we get;

[tex]Area = 144- 56.52[/tex]

[tex]Area=87.5 \ cm^2[/tex]

Thus, the area of the shaded region is 87.5 square cm.

Answer:

The answer is C (3.5)(0.25)

Step-by-step explanation:

Because to find the area of a rectangle you multiply the base times the height . The formula looks like this.

A=bh

Answer:

Answer Is (3.5)(0.25)

Step-by-step explanation:

Because You'll Need To Multiply The Length,3.5,And The Width,0.25, To Find The Area Of This Rectangle.

Answer:

[tex]y = 2x -9[/tex]

Step-by-step explanation:

To find the equation of a line using slope and a point, first use the slope to create the basic line using the slope and work from there.

For instance, the base equation here is

[tex]y = 2x[/tex]

This line passes through the point (0, 0).

You can then plug in a value for x. In this case, use the value of 3, as it corresponds with your question.

[tex]y = 2 * 3[/tex]

A point on the line of y = 2x would thus be (3, 6).

To make the y-value equal -3, you must then subtract from the original equation. There are 9 units between 6 and -3, so you must subtract nine units in the equation. You should get this at the end:

[tex]y = 2x -9[/tex]

Answer:

15.525 feet

Step-by-step explanation:

GIVEN: A watermelon is thrown down from the [tex]7th[/tex] floor of Urey Hall at UCSD. If the initial height of the watermelon is [tex]21.0\text{ meters}[/tex], and it is thrown straight downward with an initial downward velocity of [tex]3.00\text{ m/s}[/tex].

TO FIND: How far will the watermelon have fallen from its starting height after [tex]1.5[/tex] seconds.

SOLUTION:

initial height of watermelon [tex]=21\text{ meter}[/tex]

initial velocity of watermelon[tex]=3\text{ m/s}[/tex]

acceleration due to gravity [tex]=9.8\text{m/s}^2[/tex]

According to newton's law of motion

[tex]S=ut+\frac{1}{2}at^2[/tex]

when [tex]t=1.5[/tex] seconds

[tex]S=3\times1.5+\frac{1}{2}\times9.8\times1.5^2[/tex]

[tex]S=4.5+11.025[/tex]

[tex]S=15.525\text{ feet}[/tex]

Hence watermelon will have fallen 15.525 feet from its starting height after 1.5 seconds

Answer:

$102.96

Step-by-step explanation:

Lets take this one part at a time.

the dealership pays 12000 for the car, so they start at -12000 for how much money they have.

The dealership wants to make a 32% profit.  This means they want to make back the 12000 plus 32% of that.  what is 32% of 12000?  just multiply 12000 bty .32  In the end it works out that the price they sell it for is 15840

I do want to mention that there is a chance the 32% might also be accounting the bonus.  So in other words the dealership spent 12000 for the car then however much in paying the bonus, and they want to make a 32% profit on both of these combined.  I do not think that is what it is asking for, but I wanted to mention it.

Anyway, with a sales price of $15,840 it says the bonus is 6.5% of that.  to find that just do the multiplication .065 * 15840 = 1029.60.  So this is the bonus normally.

Now the question says the salesperson offers a 10 percent discount.  This changes the sales price (by 10%) and the bonus they earn.  let's calculate both.

First 10% discount of the sales price is .9*15840 = 14,256

Then 6.5% of that is .065*14256 = 926.64 So this is the new bonus.

The question wants the difference of the two bonuses, and difference is subtraction.  so 1029.60 - 926.64 = 102.96 So if the salesperson offers a 10% discount they lose $102.96

Answer:

6 at tens place is 10 times 6 at unit place.

Step-by-step explanation:

We are given that  a number

50,866

Underlined digits are 66.

We  have to find the relationship between underlined digits.

Unit place =6

Tens place=

Tens place value=[tex]6\times 10=60[/tex]

Unit pace value=6

6 at tens place is 10 times 6 at unit place.

This is required relation relation between underlined digits 66.

Answer:

x1= 2/3, x2 = -4

Step-by-step explanation:

3x² + 10x + c = 0

Formula for the roots of the quadratic equation is

[tex]x = \frac{-b +/-\sqrt{b^2-4ac} }{2a}[/tex]

Where  a = 3, b=10, c=c  for our equation 3x² + 10x + c = 0.

[tex]x=\frac{-10+/-\sqrt{10^{2}-4*3c} }{2*3} \\\\x=\frac{-10+/-\sqrt{100-12c} }{6} \\\\x_{1} =\frac{-10+\sqrt{100-12c} }{6} \\\\x_{2} =\frac{-10-\sqrt{100-12c} }{6} \\\\x_{1}-x{_2}=\frac{-10+\sqrt{100-12c} }{6} -(\frac{-10-\sqrt{100-12c} }{6} )\\\\x_{1}-x{_2}= \frac{2\sqrt{100-12c} }{6} =\frac{\sqrt{100-12c} }{3} \\\\x_{1}-x{_2}=\frac{\sqrt{100-12c} }{3} = 4\frac{2}{3} =\frac{14}{3} \\\\\sqrt{100-12c} =14\\(\sqrt{100-12c} )^{2}=14^{2}100-12c = 196\\12c=100-196\\c=-8[/tex]

[tex]x=\frac{-10+/-\sqrt{100-12(-8)} }{6} = \frac{-10+/-\sqrt{196} }{6} =\frac{-10+/-14}{6} \\\\x_{1} =\frac{4}{6} =\frac{2}{3} \\x_{2} =\frac{-24}{6} =-4[/tex]

Answer:

[tex]t=\frac{115.72-120}{\frac{57.49}{\sqrt{35}}}=-0.440[/tex]    

[tex]df=n-1=35-1=34[/tex]  

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

[tex]p_v =P(t_{(34)}<-0.440)=0.3314[/tex]  

Step-by-step explanation:

Data given and notation  

[tex]\bar X=115.72[/tex] represent the sample mean

[tex]s=57.49[/tex] represent the sample standard deviation

[tex]n=35[/tex] sample size  

[tex]\mu_o =120[/tex] represent the value that we want to test

[tex]\alpha[/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)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is less than the historical value, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 120[/tex]  

Alternative hypothesis:[tex]\mu < 120[/tex]  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{115.72-120}{\frac{57.49}{\sqrt{35}}}=-0.440[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=35-1=34[/tex]  

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

[tex]p_v =P(t_{(34)}<-0.440)=0.3314[/tex]  

Answer:

b = 28

Step-by-step explanation:

8*21 then 168/6 = 28

Answer:

b = 28

Step-by-step explanation:

[tex] \frac{6}{8} = \frac{21}{b} \\ \\ b = \frac{21 \times 8}{6} \\ \\ b = \frac{7\times 8}{2} \\ \\ b = 7 \times 4 \\ \\ \huge \red{ \boxed{ b = 28}}[/tex]

Answer:

Step-by-step explanation:

X = cost of PB  

Y = cost of J

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Dividing everything in the first equation by 2:

3X + 2Y =  966 <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Elimination method... let's multiply the first equation by 3 and the second equation by -2.

   9X +   6Y =   2898

-10X + -6Y  = -3134

-X = -236

X =  236 --> so the price of the PB is 236 pennies or $2.36

Plugging into the second equation as the numbers are a bit smaller,

5X + 3Y = 1567

5(236) + 3Y = 1567

1180 + 3Y = 1567

3Y = 387

Y = 129. So the price of the jelly is 129 pennies or $1.29.

Now we check:  4 x $1.29 + 6*2.36 = $19.32

                       3 x $1.29 + 5 x 2.36 = $15.37

The answers are verified and highlighted in bold.

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

By setting up a system of equations to represent the cost of the items bought by Erin and Adam, you can solve to find the cost of the 'j' (jelly) and 'p' (peanut butter). It's similar to solving a problem to find the cost of different fruits in a fruit basket.

We can solve this problem using algebra, particularly the system of linear equations. Let's denote 'j' as the cost of a jar of jelly and 'p' as the cost of a jar of peanut butter. We will use the information given in the question to set up two equations:

For Erin's purchases, it is 4j + 6p = $19.32. For Adam's purchases, it is 3j + 5p = $15.67.

Now, you can solve this system of equations using the substitution or elimination method, and find the cost of the jar of peanut butter and jelly.

Notice that this example is similar to finding the cost of fruit when we know the total price and the number bought, like in the fruit basket example provided earlier. This is an example of solving for unknowns using algebraic equations.

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