Throwback Thursday
How much would a $75
vacuum cost with a 8%
sales tax added to it?
(Explain how to get it please)

Answer:

a)

The null hypothesis is \(H_0: p = 0.91\).

The alternate hypothesis is \(H_1: p < 0.91\).

The decision rule is: accept the null hypothesis for \(z > -1.645\), reject the null hypothesis for \(z < -1.645\).

Since \(z = -1.79 < -1.645\), we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.

b)

The p-value for this test is 0.0367. Since this p-value is less than the significance level of \(\alpha = 0.05\), we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.

Step-by-step explanation:

Question a:

Perform the appropriate hypothesis test to determine whether this is significant evidence that the percentage of athletes who graduate is less than for the student population at large:

At the null hypothesis, we test if the proportion is the same as the student population, of 91%. Thus:

\(H_0: p = 0.91\)

At the alternate hypothesis, we test that the proportion for athletes is less than 91%, that is:

\(H_1: p < 0.91\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

Test if the proportion is less at the 0.05 level:

The critical value is z with a p-value of 0.05, that is, z = -1.645. Thus, the decision rule is: accept the null hypothesis for \(z > -1.645\), reject the null hypothesis for \(z < -1.645\).

0.91 is tested at the null hypothesis:

This means that \(\mu = 0.91, \sigma = \sqrt{0.91*0.09}\)

A sports reporter contacted 152 athletes randomly sampled from that same university and time period and found that 132 of them had graduated within 6 years.

This means that \(n = 152, X = \frac{132}{152} = 0.8684\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.8684 - 0.91}{\frac{\sqrt{0.91*0.09}}{\sqrt{152}}}\)

\(z = -1.79\)

Since \(z = -1.79 < -1.645\), we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.

(b) (3 points) Calculate the P-value for this test. Explain how this P-value can be use to test the hypotheses in part (a).

The p-value of the test is the probability of finding a sample proportion of 0.8684 or below. This is the p-value of z = -1.79.

Looking a the z-table, z = -1.79 has a p-value of 0.0367.

The p-value for this test is 0.0367. Since this p-value is less than the significance level of \(\alpha = 0.05\), we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.

The ratio between the amount of problems she finished and the problems she still had left is given by the division between those amount. Since this ratio is 9:4, if we call the amount of homework she still has left as x, we have the following relation

Solving for x, we have

She still has 20 problems left to solve. The total amount of problems is given by the sum between the problems she already finished and the problems left to solve, then, the total amount of problems is

65 problems.

Answer:

x = 11

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

given

\(log_{3}\) (2x + 5) = 3 , then

2x + 5 = 3³ = 27 ( subtract 5 from both sides )

2x = 22 ( divide both sides by 2 )

x = 11

After evaluating the limit we have came to find that the limit of       \(\lim_{x\rightarrow 1 }\frac{x-2}{x^2-10x + 25}\) as x approaches 1 is −0.0625

In mathematics, a limit is the value that a function, sequence, or index approaches as an input or as an index approaches a specific value. Limits are crucial to calculus and mathematical analysis and are necessary for the definitions of continuity, derivatives, and integrals.

The idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network, in addition to sharing a connection with the category theory concepts of limit and direct limit.

A limit of a function is typically expressed in formulas as

\({\displaystyle \lim _{x\to c}f(x)=L,}\)

To find the limit

⇒ \(\lim_{x\rightarrow 1 }\frac{x-2}{x^2-10x + 25}\)

Evalúe 2 as x

⇒ \(\frac{1-2}{1^2-10(1) + 25}\)

⇒ \(\frac{-1}{-9 + 25}\)

⇒ \(\frac{-1}{16}\)

⇒−0.0625

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Therefore, the x-coordinate is 1/2.

A coordinate is a value that represents a point's position in a given system of reference. In two-dimensional (2D) space, coordinates typically consist of two values, x and y, that represent the point's position along the horizontal and vertical axes, respectively.

Given by the question.

To find the x-coordinate of the point where the terminal side intersects the unit circle, we first need to determine the quadrant in which the terminal side lies based on the angle measure of 60 degrees.

Since 60 degrees is in the first quadrant (0 to 90 degrees), the x-coordinate will be positive.

Next, we can use the fact that the terminal side intersects the unit circle, which means its distance from the origin is 1.

Since the angle measure is 60 degrees, we can construct a right triangle with the terminal side as the hypotenuse, and one leg parallel to the x-axis.

The opposite side to the angle t will be sin (60), and the adjacent side to the angle t will be cos (60).

Using the trigonometric identity cos (60) = 1/2, we can see that the x-coordinate of the point where the terminal side intersects the unit circle is: cos (60) = 1/2.

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Answer: 50 and 59

I divided 2950 by 25 because I knew it would somehow factor into that since it ends in 50. Then, I got 25 and 118. From there, I just divided 118 by 2 since I knew that it would end in a 9 and I multiplied 25 by 2. Not sure if this is really helpful, but you also try using a GCF calculator and look up all the factors of that number next time!

Answer:

40.56 ft

Step-by-step explanation:

The perimeter of a circle is equivalent to \(2\pi r\), where r = radius. Therefore, the perimeter of a semicircle should be \(\frac{2\pi r}{2}\)

In this case, we're given the diameter of the semicircle as 8, so we divide the diameter by 2 and get the radius as 4. Now, let's solve the circumference of the semicircle.

Now, we're given the lengths of the rectangle as 8, 10, and 10. The perimeter of the rectangle (excluding the inner side) is 28.

28 + 12.56 = 40.56

Therefore, the perimeter is 40.56 ft.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

Option 4: Triangle DBC is congruent to triangle RQP

The probability of getting an even number or a 1 is 11/20

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given that there are 20 cards numbers 1,2... 20.

A card is randomly drawn.

We have to find the probability of drawing either 1 or even card.

P(drawing even card) = no of even cards/total cards = 10/20= 0.5

P(drawing one) = no of 1's/total cards = 1/20 = 0.05

P(drawing both one and even card) = 0 (since impossible)

Hence P(drawing even or one) =0.5+0.05-0

=0.55

= 11/20

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Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

Answer:

The number can be expressed in multiple forms

Fraction form \(x=\frac{2962}{67}\)  or decimal form  \(x=44.21\)

Step-by-step explanation:

Lets break the problem down

"times" is multiplication *

The difference between 2 numbers is subtraction  \((x-y)\)

A number plus a number is addition \(x+y\)

\(68(x-45)=x+-98\)

Lets solve for \(x\).

Lets start on the left side.

Distribute 68 to the terms inside the parenthesis.

\(68x-3060=x+-98\)

A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign.

\(68x-3060=x-98\)

Subtract \(x\) from both sides of the equation.

\(68x-3060-x=-98\)

Subtract \(x\) from \(68x\).

\(67x-3060=-98\)

Add 3060 to both sides of the equation.

\(67x=2962\)

Divide both sides of the equation by 67.

\(x=\frac{2962}{67}\) or as a decimal \(x=44.21\)

The graph has a minimum point and is a parabola. Therefore, change the minimal value in the formula y = 3x2 + 7x + m. The value at the minimum point must be smaller than zero because the graph has two x-intercepts. The minimum point of the graph, which is a parabola, lies at x=-b/2a = -7/6.

What is Graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

The graph has a minimum point and is a parabola.

Therefore, change the minimal value in the formula y = 3x^2 + 7x + m.

The value at the minimum point must be smaller than zero because the graph has two x-intercepts.

The graph is a parabola, with x=-b/2a = -7/6 as the minimum.

3(49/36) – 49/6 + m < 0

49/12 – 49/6 + m < 0

(49-98)/12 + m < 0

-49/12 + m < 0

m < 49/12

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Answer:

\(\displaystyle{f(x)=3^x-5}\)

Step-by-step explanation:

Being translated up-down means that the value exists outside of x. Therefore, we can cancel B and C choice since those are horizontal (left-right) translation.

Our only choice is A and D. However, D is being translated up since it's +5. Thus, the only correct answer that a function is being translated down is:

\(\displaystyle{f(x)=3^x-5}\)

or A choice.

By direct calculation, we will find that the given equation is equal to 2

So we want to solve the equation:

\(\frac{4 + 8}{2*(6 - 3)}\)

First, let's simplify that quotient by solving the operations in the numerator and denominator.

4 + 8  = 12

2*(6 - 3) = 2*3 = 6

So we can rewrite:

\(\frac{4 + 8}{2*(6 - 3)} = \frac{12}{6} = 2\)

The equation is equal to 2.

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Answer:

\(x = 40\)

\(y = 5\)

Step-by-step explanation:

\(4x = 2x+80\\2x = 80\\x = 40\)

Edit: Solve for Y

A straight line is 180 degrees so one side (the x side) is 160°, The Y side is 20, and  you can work backwards by -

\(8y - 20 = 20\\8y = 40\\y = 5\)

Answer:

12/36

Step-by-step explanation:

hope it helps

Answer:

the solution set is { - 7, - 3 }

Step-by-step explanation:

(x + 3)(x + 7) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

x + 7 = 0 ( subtract 7 from both sides )

x = - 7

solution set is { - 7, - 3 }

Answer:

290 dollars

Step-by-step explanation:

$44(to rent the car) x 5 = $220

$7( for insurance) x 5 = $35

35$ for gas

Add all those prices up:

220 + 35 + 35= 290

I hope this helps...

Answer:

Answer = 3/7

Step-by-step explanation:

(6/7) ×(1/2)

= 3/7

Answer:4x pieces of gum

Step-by-step explanation: since you don't know how much x is, the answer includes the variable.

Answer:21

Step-by-step explanation:

cu   u=-(5-12)=-7   c=-3    -7(-3)=21

Answer:

21

Step-by-step explanation:

The transformation function can be represented as vwxyz \($\rightarrow$\)qrstu = (v,w,x,y,z) \($\rightarrow$\) (q,r,s,t,u).

This algebraic representation of the transformation of pentagon vwxyz into pentagon qrstu is using the notation of a function. A function takes an input (in this case, the coordinates of pentagon vwxyz) and produces an output (in this case, the coordinates of pentagon qrstu). This transformation can be represented by the notation (v,w,x,y,z) \($\rightarrow$\) (q,r,s,t,u). This notation means that the coordinates (v,w,x,y,z) are being transformed into the coordinates (q,r,s,t,u). This notation is a concise way of expressing the transformation of pentagon vwxyz into pentagon qrstu. It is important to note that the transformation itself is not specified; the notation is simply used as a way of representing the transformation.

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Answer:

BT=CT the first one because BAT=CAT and bc cut the similar vector between these two triangle

The slope of the line is 10.

The slope represents the speed of the sprinter which is 10 meters per secs.

The slope of a line that is plotted on a graph can be determined by using any two points on the line then apply the formula below:

Slope (m) = change in y / change in x.

The graph given below is a proportional graph because it passes through the origin (0, 0), so, we only need one point on the line to find the value of m, which is the ratio of y to x.

Using one point on the line, (2, 20):

Slope (m) = 20/2 = 10

The slope, 10, means that the Olympic-level sprinter travels a distance of 20 m per secs, which is his speed.

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Answer:

a=-1

Step-by-step explanation:

1/2a=1/4a+2

by cross multiplying,

2a=4a+2

2a-4a=2

-2a=2

a=2/-2

a=-1

hope you understood  :)

QUESTION : > FIND THE ARE OF THE TRIANGLE WITH THE FOLLOWING COORDINATES.

A. (-5,9)

B . (1,-7)

C . (8,4)

ANSWER :> A.

(-5,9).

HOPE IT HELPS

THANK ME LATER.

a) The range is the set of all values of y that satisfies the function. On the graph, it is between the highest value of y on the graph and the lowest value of y on the graph. Looking at the graph,

minimum point = - ∞

maximum point = 4

Range = (- ∞, 4]

b) The domain is the set of all values of x that satisfies the function. On the graph, it is between the highest value of x on the lft graph and the lowest value of x on the graph. Looking at the graph,

minimum point = - ∞

maximum point = 6

Domain = (- ∞, 6]

c) f(- 2) = 4

d) f(x) = 0 at x = - 4 and x = 0

e) The intervals on which f(x) is decreasing is

From x = - 2 to x = 0

f) The minimum is the lowest point on the graph. Thus, there is a relative minimum at

x = 0

Answer:

Day 5 ................

The value of f(5) is e^5 + 5/3, which is exactly 150.0798257693, and the value of f(11) is e^11 + 11/3, which is approximately 59877.808.

The function is f(x)= e^x + 1/3x

To find the value of f(5), put the value of x = 5 in the function f(x)= e^x + 1/3x. Which is equal to f(5) = e^5 + 5/3.

Similarly, to find the value of f(11), put the value of x = 11 in the function f(x)= e^x + 1/3x.

Which is equal to f(11) = e^11 + 11/3

f(11) = 59874.141715198 + 3.6666666667

f(11) = 59877.808381865

f(11) ≈ 59877.808

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