This proportion can be solved to find the unknown length, x
, in the smaller triangle.

The correct test statistic for this hypothesis test is t = -2.88, not z = -2.65 or z = 2.65.

To perform a hypothesis test, we start by stating the alternative hypotheses:

H0: μ = 62 (the population temperature is 62 degrees F)

Ha: μ < 62 (the population  temperature is less than 62 degrees F)

X is the sample temperature, μ is the population temperature, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (59 - 62) / (6.21 / √(30)) = -2.88

Finally, we compare the test statistic to the critical value from the t-distribution with n - 1 f and an alpha level of 0.05. Since the alternative hypothesis is one-tailed (μ < 62), we use a one-tailed test and look up the critical value for a t-distribution with 29 f and an alpha level of 0.05. The critical value is -1.699.

Since the test statistic of -2.88 is smaller than the critical value of -1.699, we reject the null hypothesis and conclude that there is convincing evidence at the alpha = 0.05 level that the  temperature in fall and winter months in southwest is less than 62 degrees F.

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Answer:

61

Step-by-step explanation:

triangles add up to 180

56+63 is 119

180-119 to find the missing angle is 61

hope this helped

Answer:

18 more sessions

Step-by-step explanation:

Her goal is to practice 800 minutes.

She already did 175 minutes.

That means she has 800 - 175 = 625 minutes remaining, and she says that she will only practice in 35 minute sessions.

To determine the number of sessions she has left, just divide 625 by 35.

[tex]\frac{625}{35}[/tex]

= 17.85714

However, you can't have a portion of a session, as she only does 35 mins every session. Therfore, she must do 18 more sessions.

~~~Harsha~~~

Answer: 260(0.962)^8

Step-by-step explanation:

Pretty simple. We have a base of 260, which all of the answers include. Then for a decay rate of 3.8, we reduce to percentage form ( 0.038 ) and subtract that from 1 ( or 100 in standard form ). Then we get 0.962. We choose the second option because it includes both these terms and 8 ( which I'm assuming is an exponent )

Answer:

A

Step-by-step explanation:

We can factor 625x^4 - 81 by recognizing it as the difference of two squares:

625x^4 - 81 = (25x^2)^2 - 9^2

This can be further simplified using the formula for the difference of squares, which states that:

a^2 - b^2 = (a + b)(a - b)

In this case, a = 25x^2 and b = 9, so we have:

(25x^2 + 9)(25x^2 - 9)

We can then use the difference of squares formula again to factor 25x^2 - 9:

25x^2 - 9 = (5x)^2 - 3^2 = (5x + 3)(5x - 3)

Substituting this into our original expression, we get:

625x^4 - 81 = (25x^2 + 9)(25x^2 - 9) = (25x^2 + 9)(5x + 3)(5x - 3)

Therefore, the fully factored form of 625x^4 - 81 is (25x^2 + 9)(5x + 3)(5x - 3). Answer: (A) (5x - 3)(5x - 3)(25x² + 9)

Answer:

62.25

Step-by-step explanation:

Rectangle Area Formula: A=l•w

7.5•5=37.5

=hbb/2=7.5·4.2/2=15.75

=hbb/2=7.5·2.4/2=

Add all three =62.25

The set of results that could not have been drawn from the bag is 3, 5, 5.

Let's assume there are three balls in the bag, labeled A, B, and C. The possible combinations are:

ABC, ACB, BAC, BCA, CAB, CBA

Now, let's analyze each set of results:

2, 3, 7: This set of results could have been drawn from the bag. For example, if A = 2, B = 3, and C = 7, the results would be 2, 3, 7.

10, 4, 3: This set of results could have been drawn from the bag. For example, if A = 10, B = 4, and C = 3, the results would be 10, 4, 3.

3, 5, 5: This set of results could not have been drawn from the bag, because there is only one ball labeled 3 in the bag. Therefore, it is impossible to draw two balls labeled 5 and one ball labeled 3.

8, 6, 10: This set of results could not have been drawn from the bag, because there is no ball labeled 8 in the bag. Therefore, it is impossible to draw a ball labeled 8.

So, the set of results that could not have been drawn from the bag is 3, 5, 5.

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Answer:

2816 ft^3

Step-by-step explanation:

Solution Given:

Radius(r)=8ft.

Height(h)=14 ft.

Now

To find the volume of a cylinder, you can use the formula:

[tex]\boxed{\bold{Volume = \pi * r^2 * h}}[/tex]

where:

π (pi) is a mathematical constant approximately equal to 3.14

r is the radius of the base of the cylinder

h is the height of the cylinder

Now Substituting value

[tex]Volume = \pi * r^2 * h\\Volume=3.14*8^2*14\\Volume=2816 ft^3[/tex]

The equation that represents a proportional relationship

[tex]\[Y = \frac{1}{2}x\][/tex]

In a proportional relationship, the dependent variable (Y) is directly proportional to the independent variable (x). This means that as x increases or decreases, Y changes in a consistent ratio or fraction. In this equation, the ratio or fraction is [tex]\(\frac{1}{2}\)[/tex], indicating that for every unit increase in x, Y increases by [tex]\(\frac{1}{2}\)[/tex] units.

Let's break down the equation:

[tex]\(Y\)[/tex] represents the dependent variable, and it varies linearly with respect to the independent variable [tex]\(x\).[/tex]

The equation states that the value of Y is equal to [tex]\(\frac{1}{2}\)[/tex] times the value of [tex]\(x\).[/tex]

For example, if we have [tex]\(x = 4\)[/tex], we can substitute it into the equation to find the corresponding value of Y:

[tex]\[Y = \frac{1}{2}(4) = 2\][/tex]

So, when [tex]\(x\)[/tex] is 4, [tex]\(Y\)[/tex] is 2. This satisfies the proportional relationship because the ratio [tex]\(\frac{Y}{x}\)[/tex] remains constant at [tex]\(\frac{1}{2}\).[/tex]

Similarly, if we have [tex]\(x = -6\)[/tex], we can substitute it into the equation:

[tex]\[Y = \frac{1}{2}(-6) = -3\][/tex]

Therefore, when [tex]\(x\)[/tex] is -6, [tex]\(Y\)[/tex] is -3. Again, the ratio [tex]\(\frac{Y}{x}\)[/tex] remains constant at [tex]\(\frac{1}{2}\)[/tex].

Hence, the equation [tex]\(Y = \frac{1}{2}x\)[/tex] represents a proportional relationship where Y is directly proportional to x with a constant ratio of [tex]\(\frac{1}{2}\)[/tex].

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Answer:

1×1=1

2×2=4

3×3=9

4×4=16

The solution of the expression, [tex](\frac{2}{3} )^{-4}[/tex] is 81 / 16.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as multiplication, subtraction, addition etc.

Therefore, lets solve the expression as follows:

[tex](\frac{2}{3} )^{-4}[/tex]

Using exponential laws,

b⁻¹ = 1 / b

Let's apply the law to the expression as follows:

[tex](\frac{2}{3} )^{-4} = \frac{1}{(\frac{2}{3})^{4} }[/tex]

Therefore,

1 ÷ (2  / 3)⁴ = 1 × (3 / 2)⁴ = 3⁴ / 2⁴

Finally,

3⁴ / 2⁴ = 81 / 16

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The values of the probabilities are P(5) = 1/8 and P(Number > 2) = 75%

From the question, we have the following parameters that can be used in our computation:

The spinner

There are 8 sections on the spinner

So, we have

Section = 8

One of the sections is 5

So, we have

P(5) = 1/8

There are 6 sections greater than 2

So, we have

P(Number > 2) = 6/8

Evaluate

P(Number > 2) = 75%

Hence, the probabilities are 1/8 and 75%

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The equation subject to p is P = (n - 7/2)/q.

To solve for p, we need to isolate it on one side of the equation.

Starting with:

Pq+7/2=n

Subtract 7/2 from both sides:

Pq = n - 7/2

Divide both sides by q:

P = (n - 7/2) / q

Therefore, the solution for p is:

P = (n - 7/2) / q

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The required length is 11 units for the given triangle.

The sine rule defines the side length ratios of triangles to their opposing angles. This proportion is true for all three sides and opposing angles.

a/sinA = b/sinB = c/sinC

The triangle is given in the question, as follows:

In ΔABC, ∠A=120°, ∠B=37°, and c = 5 units

Here, ∠C= 180° - 120° - 37° = 23.

We have to determine the length of a.

As per the sine rule, the required solution would be as:

a/sin∠A = c/sin∠C

Substitute the known values and we get

a/sin 120° = 5/sin 23°

a = (18/sin 1240°) × sin 23°

k ≈ 11

Thus, the length of c is 11 units.

Hence, the number that belongs in the green box is 11.

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The total area of the figure formed by the congruent triangles and the square is 60 sq in

For square

A = s²

where s is the side

Given:

s = 6 in

Area = 6 * 6

= 36 sq in

Area of triangle = 0.5bh

where b is the base

h is the height

Given:

b = 6 in

h = 4 in

A = 0.5 * 6 * 4

= 12 sq in

Total area of the figure = 2 * Area of triangle + area of square

= 2 * 12 + 36

= 24 + 36

= 60 sq in

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Answer:

8 more red counters

Step-by-step explanation:

It would make it 9:3, which, when simplified, is 3:1.

The number of ways to choose the letters is given as follows:

First we must decide which formula to use, depending if the order matters, as follows:

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P(n,x) = \frac{n!}{(n-x)!}[/tex]

Hence, if the order matters, the number of ways is given as follows:

P(3,2) = 3!/(3 - 2)! = 6.

The combination formula is given as follows:

[tex]C(n,x) = \frac{n!}x!{(n-x)!}[/tex]

Hence, if the order does not matter, the number of ways is given as follows:

C(3,2) = 3!/(2! x 1!) = 3.

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The solution of the expression is,

⇒ - 37/14

We have to given that;

Expression to solve is,

⇒ 6 - 5/4 × 6 - 8/7

Now, We can simplify the expression as,

⇒ 6 - 5/4 × 6 - 8/7

⇒ 6 - 5/2 × 3 - 8/7

⇒ 6 - 15/2 - 8/7

⇒ (12 - 15)/2 - 8/7

⇒ - 3/2 - 8/7

⇒ (- 21 - 16) / 14

⇒ - 37/14

Thus, The solution of the expression is,

⇒ - 37/14

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An equation that represents the cost of green squash at the local farmers market include the following: C = 1.50p.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

c = kp

Where:

Next, we would determine the constant of proportionality (k) by using the various data points from table D as follows:

Constant of proportionality, k = c/p

Constant of proportionality, k = 15/10

Constant of proportionality, k = $1.5 per pounds.

Therefore, the required linear equation is given by;

c = kp

c = 1.50p

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probability that the husband has more than $150,000 of insurance is 1.4577

Looking at the row where the husband's insurance is between $50,000 and $100,000, we can see that there are a total of 329 policies.

Out of these policies, the number of policies where the husband has more than $150,000 of insurance is 249+30+25+176 = 480.

Therefore, the probability that the husband has more than $150,000 of insurance given that his insurance is between $50,000 and $100,000 is:

480/329 ≈ 1.4577

Rounded to four decimal places, the probability is 1.4577.

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Answer: 72

800/11 = 72.272727272

11 is 6ft plus 5 feet in between each barricade since you need 5 ft for each barricade including the 6ft itself.

Therefore, 800ft can have no more than 72 barricades.

1) The translation made is 2 units up, 1 units left.

2) The translation made is 2 units right, 1 unit up.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Chess player moves a knight from the location (3,2) to (5,1) on a chessboard.

And, the player moves the knight from (5,1) to (6,3),

Since, Translation for (3,2) to (5,1|) is,

⇒ 2 units up, 1 units left.

And, Translation for (5,1) to (6,3) is,

⇒ 2 units right, 1 units up.

Hence, When a player moves a knight from the location (3, 2) to (5, 1) on a chessboard the translation made is 2 units up, 1 units left.

And, When the player moves the knight from (5, 1) to (6, 3), the translation made is 2 units right, 1 units up.

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &7 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 7} \implies \boxed{A \approx 3969.39} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2800\\ r=rate\to 5.2\%\to \frac{5.2}{100}\dotfill &0.052\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]A = 2800\left(1+\frac{0.052}{4}\right)^{4\cdot 7}\implies A=2800(1.013)^{28} \implies \boxed{A \approx 4019.97} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 4019.97 ~~ > ~~ 3969.39 \end{array}}~\hfill[/tex]

The equations to have infinite solutions and no solutions are 3x + 5 = 3x + 5 and 3x + 5 = 3x + 6

Infinite many solutions

From the question, we have:

[ ] x + 2x + (-4 + 9) = [] x+ []

This gives

[ ] x + 2x + 5 = [] x+ []

For an equation to have infinite many solutions, both sides must be equal

So, we have

[1] x + 2x + 5 = [3] x+ [5]

Evaluate

3x + 5 = 3x + 5

No solution

Here, we have:

[ ] x + 2x + (-4 + 9) = [] x+ []

This gives

[ ] x + 2x + 5 = [] x+ []

For an equation to have no solutions, both sides must be unequal

So, we have

[1] x + 2x + 5 = [3] x+ [6]

Evaluate

3x + 5 = 3x + 6

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The required equation of the function with the given characteristics is y = (2/9)|x| whose height will be compressed to 2/9 of the original height.

As per the question, the absolute value function y = |x| looks like a "V" shape with its vertex at the origin and opening upward.

To shrink it vertically by a factor of 2/9, we need to multiply the function by this factor.

Thus, the equation of the function with the given characteristics is:

y = (2/9)|x|

The resulting graph will still have a "V" shape, but its height will be compressed to 2/9 of the original height.

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