Use a half-angle identity to find an exact value of sin 67.5° .

Standard error (SE) is a measure of the variability of the sample mean estimate, and it is calculated using the sample size and the standard deviation of the population. Smaller SEs result in narrower confidence intervals (CI) while larger SEs result in wider CIs.

Social media (SM) can affect the width of a confidence interval by influencing the sample size and standard deviation. For instance, if the sample size is small, the CI will be wider than if the sample size is large, regardless of SM. However, SM can influence the sample size by providing access to a larger or smaller population.

In addition, SM can affect the standard deviation by introducing bias or error in the data collection process. For example, if a survey is conducted through SM and the responses are voluntary, the sample may not be representative of the population, leading to a larger standard deviation.

In summary, SM can impact the width of a CI by influencing the sample size and standard deviation, but other factors, such as the sampling method and level of precision desired, should also be taken into consideration.

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Answer:

[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))

Step-by-step explanation:

Given:

Which of the relations given by the following sets of ordered pairs is a function?

A. ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))

B. ((1,2), (2, 3), (3,4), (2, 1), (1, 0))

C. ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3))

D. ((1,3), (1, 1), (1, 1), (1,3), (1,5)}

Solve:

Knowing that; In order to know if a set of ordered pairs is a function or not we must see that if every x value have one or more than one y value that a function. If there is more than one same x value then it isn't a function.

Summary:

x value can't be duplicate but y can - in a working function

Hence, based on what we see in the answer choices;

[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6)) is a function. Due to none repeat x values.

[B]((1,2), (2, 3), (3,4), (2, 1), (1, 0)) isn't a function. Due to repeat x -values (1 and 2)

[C] ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3)) isn't a function. Due to repeat x-values (2)

[D]  ((1,3), (1, 1), (1, 1), (1,3), (1,5)} isn't a function. Due to repeat x-values (1)

RevyBreeze

Answer:

-----------------------

The average price Jaffar paid for the 5 books is $17.

To find the total cost of the 5 books, we multiply the average price by the number of books:

Now, we'll add up the prices of the first four books:

Finally, we'll subtract the sum of the first four books from the total cost to find the price of the fifth book:

So, Jaffar paid $18 for the fifth book.

Answer:

C

Step-by-step explanation:

6.724 is larger than 6.719

Answer:

to be honest I'm not sure how to do this question plz

By defining that h(t) = 0 means that the ball is in the ground, we conclude that the ball is thrown at t = 0, and hits the ground again at t = 2.

The height equation is:

h(t) = -14*t^2 + 28*t

When t = 0, we have: h(0)  = 0

So it is in the ground, meaning that it is thrown at the time t = 0.

We need to find the other root of the quadratic equation, so we need to solve:

-14*t^2 + 28*t = 0

We can rewrite this as:

t*(-14*t + 28) = 0

The parenthesis is zero when:

-14*t + 28 = 0

t = 28/14 = 2

So at t = 2, the ball hits the ground.

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Answer:

The equation is;

f(x) = -2·x² + 5·x - 1

Step-by-step explanation:

The general form of a quadratic equation  or function f(x) is, f(x) = y = a·x² + b·x + c

Given that the points representing the quadratic function are;

(-1, -8), (0, -1), (1, 2) which  are of the form (x, y)

When x = -1, f(x) = y = -8

Plugging in the above values into the general form of a quadratic function, we have;

-8 = a·(-1)² + b·(-1) + c = a - b + c

-8  = a - b + c.........................(1)

When x = 0, y = -1, we have;

-1 = a·(0)² + b·(0) + c = c

c = -1.......................................(2)

When x = 1, y = 2, which gives;

2 = a·(1)² + b·(1) + c = a + b + c

2 = a + b + c........................(3)

Adding equation (1) to equation (3), we have;

-8 + 2 = a - b + c + a + b + c

-8 + 2 = 2·a + 2·c

From equation (2) c = -1, we get;

-8 + 2 = -6 = 2·a + 2·c = 2·a + 2 × (-1)

-6 = 2·a - 2

-4 = 2·a

a = -2

From equation (3), we have

2 = a + b + c

Substituting the values of a, and c gives;

2 = -2 + b - 1

b = 2 + 2 + 1 = 5

b = 5

The equation is therefore;

f(x) = -2·x² + 5·x - 1.

Answer:

b

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer: 720 cm

Step-by-step explanation:

Riley has a solar panel with a width of 25 inches. To get the proper inclination for her climate, she needs a night triangluar support frame that has one leg twice as long as the other leg. To the nearest tenth.The dimensions of the triangular support frame should be approximately 11.2 inches by 22.4 inches.

To solve this problem, we can use the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the shorter leg of the triangular support frame "x" inches. Since the other leg is twice as long as the shorter leg, it will be "2x" inches. The solar panel's width (25 inches) will act as the hypotenuse in this case.

According to the Pythagorean theorem: 25^2 = x^2 + (2x)^2 625 = x^2 + 4x^2 Combining the x terms: 625 = 5x^2 Dividing by 5: 125 = x^2 Now, we'll take the square root of both sides: x ≈ 11.2 (to the nearest tenth)

So, the shorter leg (x) should be approximately 11.2 inches long, and the longer leg (2x) should be approximately 22.4 inches long.

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I need help too on this one

Answer:

you lowest tempeture in the mesosphere is -96

Step-by-step explanation:

Answer:

3rd table

because each component in y has a unique component in x

To calculate the total charge within the cylinder with dimensions r=1.5 and h=3, we use the potential function V = 5r + 4 cos Ø in cylindrical coordinates.

The total charge can be obtained by integrating the charge density over the volume of the cylinder.

The potential V within the cylinder is given by V = 5r + 4 cos Ø, where r represents the radial distance from the axis of the cylinder and Ø represents the angle in the cylindrical coordinate system. To calculate the total charge within the cylinder, we need to integrate the charge density over its volume.

The charge density ρ can be related to the potential by ρ = -∇²V, where ∇² is the Laplacian operator. In cylindrical coordinates, the Laplacian operator takes the form:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز + ∂²/∂z²

Since the potential function V does not depend on the z coordinate, the Laplacian reduces to:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز

Applying this operator to the potential function V, we find:

∇²V = (1/r) ∂/∂r (r ∂V/∂r) + (1/r²) ∂²V/∂ز

To find the charge density, we substitute this expression into ρ = -∇²V:

ρ = -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز

To calculate the total charge, we integrate the charge density ρ over the volume of the cylinder:

Q = ∫∫∫ ρ dV = ∫∫∫ -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز dV

The integration is performed over the cylindrical coordinates r, Ø, and z, with appropriate limits. Evaluating this integral will give us the total charge within the cylinder.

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The tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.

First, let's find the derivative of the given function y = 1 + 60x³ − 2x⁵ using the power rule for differentiation:

dy/dx = 0 + 3(60)x² - 5(2)x⁴

= 180x² - 10x⁴

To find the critical points, we set the derivative equal to zero and solve for x:

180x² - 10x⁴ = 0

Factoring out common terms, we get:

10x²(18 - x²) = 0

Setting each factor equal to zero, we have:

10x² = 0 or 18 - x² = 0

From the first equation, we find x = 0.

From the second equation, we have:

18 - x² = 0

x² = 18

Taking the square root, we get:

x = ±√18

= ±3√2

So the critical points are x = 0, x = 3√2, and x = -3√2.

Now we need to evaluate the slope at these critical points. We can do this by plugging each x-value into the derivative:

When x = 0:

dy/dx = 180(0)² - 10(0)⁴ = 0

When x = 3√2:

dy/dx = 180(3√2)² - 10(3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080

When x = -3√2:

dy/dx = 180(-3√2)² - 10(-3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080

The slope is 0 when x = 0 and 1080 when x = 3√2 or x = -3√2.

Therefore, the tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.

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The complete question is as follows:

At which points on the curve y = 1 + 60x³ − 2x5⁵ does the tangent line have the largest slope?

The mean of the total length is 36 inches, and the standard deviation is 0.17 inches. This means that on average, the total length of the sticks will be 36 inches, and there will be a variation of approximately 0.17 inches around this mean length.

The mean of the total length for both Alex and Brandon can be determined by multiplying the mean length of a single stick by the number of sticks required for each toy. In this case, each toy requires four 9-inch long sticks.

Mean of the total length for both Alex and Brandon: 4 sticks * 9 inches = 36 inches.

Since both Alex and Brandon have sticks with the same mean length and standard deviation, the standard deviation of the total length for both of them remains the same.

Standard deviation of the total length for both Alex and Brandon: 0.17 inches.

Therefore, The mean of the total length is 36 inches, and the standard deviation is 0.17 inches. This means that on average, the total length of the sticks will be 36 inches, and there will be a variation of approximately 0.17 inches around this mean length.

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Answer:

C.tan 44° = y over 110

Step-by-step explanation:

Took the test

The height of the lighthouse is 106.5m

Using the given diagram, we get

tan 44° = y / 110

0.965 = y / 110

y = 0.965 * 110 = 106.5m

The answer is 106.5m

The height of the object. The angle at which the observer views the topmost point of the object (angle of elevation) The angle at which the observer views the object when the observer is on top of a tower/building (angle of depression).

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The exact area of Hexagon B is 54√3 square inches.

The area of a regular hexagon can be calculated using the formula:

Area = (3√3/2) * s²

where s is the length of the side of the hexagon.

For Hexagon A, given that the side length is 8 inches and the area is 96√3 square inches, we can use the formula to find the exact area:

96√3 = (3√3/2) * 8²

To find the exact area of Hexagon B, we need to substitute the side length of 6 inches into the formula:

Area = (3√3/2) * 6²

Calculating this expression gives us the exact area of Hexagon B:

Area = (3√3/2) * 36

Area = 54√3 square inches

Hexagon B's precise area is 54√3 square inches as a result.

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The derivative of of f(x) = 10 is 0

The derivative of a function is the measure of the rate of change of the function. They are fundamental to the solution of problems in calculus and differential equations.

Here the function is not changing as 10 is a constant. So, if f(x) = c where c is a constant then f'(x) = 0 as the derivative of a constant is always zero.

Mathematically:

           d(f(x))/dx = \(\lim_{h \to 0}\) (f(x+h) - f(x))/h

There  is no x to substitute for x + h so no difference is noticed:

             \(\lim_{h \to 0}\) (f(x+h) - f(x))/h =   \(\lim_{h \to 0}\) (10 - 10)/h = 0

Hence, the derivative of f(x) = 10 is 0

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In  Arithmetic Progression , 56 inches of snowfall will cause the snowplow to be immobile.

What is Arithmetic Progression in math?

Let x inches of snowfall will cause the showplow to be immobile .

By a.p. formula ,

                aₙ = a + ( n - 1) d

                 aₙ= 0 ( show plow's speed is 0 ,miles/hour )

              a = 39

              n = x inches

             d = - 2.5 mile/hour

         0 = 39 + ( n - 1 ) ( -2.5)

            ( n - 1 ) ( -2.5) = -39

              n- 1 = -39/2.5 = 15.6

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At the end of 2 years, Jackson will have $3,048.19 on deposit in his savings account.

To solve this problem, we can use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)\)

where A is the amount on deposit at the end of the period, P is the principal (or initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $120 (since that's how much Jackson deposits at the end of each month), r = 0.03 (since the interest rate is 3%), n = 12 (since the interest is compounded monthly), and t = 2 (since we're looking at a 2-year period).

First, we need to find the total amount that Jackson deposits over the 2-year period:
Total deposits = $120/month x 12 months/year x 2 years = $2,880

Next, we can use the compound interest formula to find the amount on deposit at the end of 2 years:
\(A = $2,880(1 + 0.03/12)^{(12 \times 2)\) = $3,048.19

Therefore, Jackson will have $3,048.19 on deposit in his savings account at the end of 2 years, assuming he makes no withdrawals during that period.

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52 tiles are there in the 25th figure in this pattern.

A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.

A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.

Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another.

Sometimes a pattern is also referred to as a sequence.

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Answer:

\(-\frac{3}{2}\)

Step-by-step explanation:

You count up 3 units. Then you count to the left 2 units. It is negative because the line is slanted to the left.

Simplified form of the expression 8 ( 3 + 4 ) using the Distributive Property of Multiplication over Addition is 56

To apply the Distributive Property of Multiplication over Addition, you need to multiply the number outside the parentheses by each term inside the parentheses and then add the products together.

In this case, the number outside the parentheses is 8, and the terms inside the parentheses are 3 and 4. So, you can apply the distributive property as follows:

8 ( 3 + 4 ) = 8 × 3 + 8 × 4

Multiply the numbers

= 24 + 32

Add the numbers

= 56

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Answer:

5(7b+3c-2)

Step-by-step explanation:

Common factor of 5

35b/5= 7b
15c/5= 3c
-10/5= -2

Take the common factor and multiply it by the quotients
5(7b+3c-2)