The model for long-term average temperature f (x), in degrees Celsius, at the Willburn airport is represented by the equation f of x is equal to 5 times cosine of the quantity x over 12 end quantity plus 14 and 5 tenths period If x represents the month of the year, in which months will the temperature be 17°C?

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:C

Took the test

Step-by-step explanation:

The  equations of an asymptote of the hyperbola are y = 3x - 5 and y = -3x - 5.

The standard form of a hyperbola is:

(x-h)²/a² - (y-k)²/b² = 1

The general equation of the asymptotes for a hyperbola centered at (h,k) with semi-axes a and b is given by:

(y - k) = ± (b/a)(x - h)

To find the equations of the asymptotes of the hyperbola with equation:

(x-2)²/2² - (y-1)²/6² = 1

Plugging in the values, we get:

(y - 1) = ± (6/2)(x - 2)

Simplifying:

y - 1 = ± 3(x - 2)

y = ± 3x - 5

Therefore, the equations of the asymptotes for the given hyperbola are y = 3x - 5 and y = -3x - 5.

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To find the volume of the solid, you need to calculate the area of each cross-section and then multiply that by the thickness of the section (which is the distance along the y-axis).

(a) Squares: The cross-sections are squares with sides of length y. The area of a square is side^2, so the area of each square is y^2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the square cross-sections is y^2 * y

(b) Semicircles: The cross-sections are semicircles with radii of length y. The area of a semicircle is (pi * r^2) / 2 , so the area of each semicircle is (pi * y^2) / 2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semicircular cross-sections is (pi * y^2) / 2 * y

(c) Equilateral triangles: The cross-sections are equilateral triangles with side length of y. The area of an equilateral triangle is (s^2 * √3)/4. so the area of each equilateral triangle is (y^2 * √3) / 4. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the equilateral triangle cross-sections is (y^2 * √3) / 4 * y

(d) Semi-ellipses: The cross-sections are semi-ellipses whose heights are twice the lengths of their bases. The area of a semi-ellipse is πab/2, where a and b are the lengths of the semi-major and semi-minor axes respectively. Therefore the area of each semi-ellipse will be (πy^2)/2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semi-ellipse cross-sections is (πy^3)/2

It is important to note that this is a theoretical volume calculation, as the shape of the solid does not have a closed form representation by these functions, but rather, these are an approximation.

Also, for any of these volumes to be meaningful, we have to integrate over the range of the variable y, since it is bounded by the equations y=x, y=0 and x=1, the variable y is limited.

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The length of one side of the garage originally is 15.7 feet.

The length of one side of the garage now is 19.3 feet.

The percentage increase will be 18.65%.

It should be noted that the area = side × side

1. There's a 50% increment. This will be:

= New area = 248 × (100% + 50%)

= 248 × 1.5

= 372ft²

Therefore, the sides or length will be:

= ✓372

= 19.3 feet

2. Length of original garage will be:

= ✓248

= 15.7 feet

3. The percentage increase will be:

= (19.3 - 15.7)/19.3 × 100

= 18.65%

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Step-by-step explanation:

Your picture is not clear so sorry

Answer:

its super blurry

Step-by-step explanation:

The value of L in terms of W in the rectangle is L = 120 - W.

The area of the rectangular pen in terms of W is 120W - W².

The length and width of the rectangular pen when the area is 2000 feet are 100 ft and 20 ft.

The perimeter of the rectangular pen is 240 feet. The length is represented as L and the width is represented as W.

The perimeter of a rectangle is the sum of the whole side of the rectangle.

Therefore, let's find the L in terms of W.

perimeter of a rectangle = 2(L + W)

240 = 2L + 2W

120 = L + W

L = 120 - W

The area of the rectangular pen in terms of W is as follows:

area of the rectangular pen = LW

area of the rectangular pen = (120 - W)W

area of the rectangular pen = 120W - W²

If the area of the rectangular pen is 2000 ft², the length and the width is as follows:

2000 = 120W - W²

W² - 120W + 2000 = 0

W² - 100W  - 20W + 2000 = 0

W(W - 100) - 20(W - 100) = 0

(W - 100)(W - 20) = 0

W = 100 and W = 20

Therefore,

L = 100 ft

W = 20 ft

Therefore, the value of L = 120 - W. The area of the rectangular pen in terms of W is 120W - W².

If the area of the rectangular pen is 2000 ft², the length is 100 ft and the width is 20 ft.

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Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Using percentages we know that the coffee choc Ripple is the most popular flavor with 36% of people liking it.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.

To represent percentages, the symbol "%" is typically written after the number.

So, we know that:
Vanilla = 12%

Chocolate = 17%

Cookies and cream strawberry = 6%

Coffee and Choc Ripple = 36%

Since the flavor of coffee and choc Ripple is liked by 36% of the people. Hence, it is the most popular flavor.

Therefore, using percentages we know that the coffee choc Ripple is the most popular flavor with 36% of people liking it.

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Answer:

C

Step-by-step explanation:

Using the Venn Diagram principles, the number of customers at the supermarket who purchased both shirts and pants is 26.

A Venn Diagram shows a pictorial or graphical representation of the relationship (similarities and differences) between data sets.

In a Venn Diagram, overlapping circles or other shapes can be used to depict the logical relationships between two or more data sets or items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, using the formula of Venn Diagram, we can conclude that at this supermarket with 118 customers, 26 customers purchased both shirts and pants.

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Answer:

4t*4t*4t*4t*4t

Step-by-step explanation:

Answer:

42 blue beads

Step-by-step explanation:

Solution:

Let's suppose the numbers as 13x, 7x and 4x respectively..

Where,

Orange = 13x

Blue = 7x

White = 4x

According to the question,

13x - 4x = 54

or, 9x = 54

or, x = 54/9

or, x= 6

Now,

Blue beads = 7x

= 7 × 6

= 42..

Answer:

a. In the explanation.

b. The point estimate of the difference can be calculated as the difference between the sample mean and the population mean:

\(d=M-\mu=24.95-23.8=1.15\)

c. Test statistic t = 0.90

P-value = 0.1932

The null hypothesis failed to be rejected.

Step-by-step explanation:

We have a sample, wich mean and standard deviation are calculated as:

\(M=\dfrac{1}{14}\sum_{i=1}^{14}(27.8+23.84+25.25+21+17.52+19.61+...+26.94+27.24)\\\\\\ M=\dfrac{349.34}{14}=24.95\)

\(s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{14}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(27.8-(24.95))^2+(23.84-(24.95))^2+...+(27.24-(24.95))^2]}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(8.106)+(1.238)+...+(5.23)]}\\\\\\ s=\sqrt{\dfrac{304.036}{13}}=\sqrt{23.39}\\\\\\s=4.8\)

This is a hypothesis test for the population mean.

The claim is that the consumption of milk in the Midwest is significantly higher than the national average.

Then, the null and alternative hypothesis are:

\(H_0: \mu=23.8\\\\H_a:\mu> 23.8\)

The significance level is 0.01.

The sample has a size n=14.

The sample mean is M=24.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.8.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.8}{\sqrt{14}}=1.28\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{24.95-23.8}{1.28}=\dfrac{1.15}{1.28}=0.9\)

The degrees of freedom for this sample size are:

\(df=n-1=14-1=13\)

This test is a right-tailed test, with 13 degrees of freedom and t=0.9, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t>0.9)=0.1932\)

As the P-value (0.1932) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the consumption of milk in the Midwest is significantly higher than the national average.

Answer:

hope this helps :)

Step-by-step explanation:

Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

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Step-by-step explanation:

that's all

thank you

Answer:

I could be wrong, but I believe that the answer is D, none. This is because there is only proof of one congruent side and angle.

Step-by-step explanation:

None of the options can prove that the triangles are congruent so option (D) will be correct.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

In the given figure only one side and one angle are the same.

But for congruency three pairs should be the same which is not present in the figure hence none of the above is valid

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Answer:1.6

Step-by-step explanation:

Answer:

A - The exponent of 3 is 7/9.

Step-by-step explanation:

The expression 3^(7/9) can be read as "3 to the power of 7/9".
This means that the number 3 is being multiplied by itself 7/9 times.

For example
3^(2/3) can be written as cube root of 3, cube root of 3 is equal to 3^(1/3) .

When the exponent of an expression is a fraction, it can be written in radical form, with the denominator of the fraction as the index of the radical. However, it's not true in this case as the index is not 9 but 7.

So, the correct answer is A - The exponent of 3 is 7/9.

Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").

Answer:

Step-by-step explanation:

base area=41.57 in²

height=9 in

volume=41.57×9=374.13 in³

The surface area of the larger solid is approximately 172 mm sq. approx

Given

The volume of the smaller solid = 540 mm cube

The volume of the larger solid = 857.5 mm cube

The surface area of the smaller solid = 108 mm sq.

Required to find the surface area of the larger solid =?

Let the surface area of the larger solid be x.

(surface area of smaller solid) / (volume of smaller solid) = (surface area of larger solid) / (volume of larger solid)

Putting the values in the above formula we get the value of x.

108 mm^2 / 540 mm^3 = x / 857.5 mm^3

x = 171.5 mm sq

Thus, the surface area of the larger solid is approximately 172 mm sq

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Answer:

\(\\\)

Step-by-step explanation:

We know that the total number of kids is 150. We can find the number of kids with green, brown, and gray eyes using the given percentages:

\(\sf\dashrightarrow Green\: eyes = 6\: kids\)

\(\sf\dashrightarrow Brown\: eyes = 0.52 \times 150 = 78\: kids\)

\(\sf\dashrightarrow Gray\: eyes = 0.16 \times 150 = 24\: kids\)

\(\\\)

To find the number of kids with blue eyes, we can subtract the number of kids with green, brown, and gray eyes from the total number of kids:

\(\sf\dashrightarrow Blue\: eyes = 150 - 6 - 78 - 24\)

\(\sf\dashrightarrow Blue\: eyes = 42\: kids\)

\(\\\)

Finally, we can calculate the percentage of kids with blue eyes by dividing the number of kids with blue eyes by the total number of kids and multiplying by 100:

\(\sf\implies Percentage = \dfrac{42}{150} \times 100\)

\(\sf\implies Percentage = \dfrac{4,200}{150}\)

\(\sf\implies Percentage = \green{28\%}\)

\(\\\)

\(\\\)

Therefore, 28% of the kids have blue eyes.

Answer:

Step-by-step explanation:

hola como estas

a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

msec = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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