A wagon is pulled with a force of 80 pounds by a handle that
makes an angle of 20° with the horizontal.
A
What is the horizontal component of the force correct to the
nearest tenth?
27.4
B
75.2
80
20°
C
76.2
D 76.4

Using a trigonometric relation, we can see that the value of x is 10.39

Here we have a right triangle. We can see that we know the measures of the hypotenuse, and the angle opposite to the side x.

Then to get the value of x, we can use the trigonometric relation:

sin(a) = (opposite cathetus)/hypotenuse.

Replacing the values that we know, we will get.

sin(60°) = x/12

solve that for x:

12*sin(60°) = x

10.39 = x

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The surface area of this composite solid is 265.36 units².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[3 × 5 + (3× 10) + (5 × 10)]

Surface area of rectangular prism = 2[15 + 30 + 50]

Surface area of rectangular prism = 190 units².

Surface area (SA) of a cylinder = 2πrh + 2πr²

Surface area (SA) of a cylinder = 2 × 3.14 × 2 × 4 + 2 × 3.14 × 2²

Surface area (SA) of a cylinder = 50.24 + 25.12

Surface area (SA) of a cylinder = 75.36 units².

Therefore, we have:

Surface area of composite solid = 190 units² + 75.36 units².

Surface area of composite solid = 265.36 units²

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Answer:

45/49

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

9/14 * 10/7 = 90/98

divide the numerator and the denominator by 2.

90 * 2 = 45

98 * 2 = 49

45/49

Answer: 49.4 thats the answer i devided it

Answer:

a set of numbers in order of least to greatest

Where the above is given, Area of Δ ACB ≈ 282.62

The area of a triangle is given as

Area = 1/2 Base x Height

In this case,

Base = AB

Height = CP

Thus, it is correct to state that Area of Δ ACB = 1/2AB * CP.

First we need to find the height and hypotenuse of the triangle.

that is CP and CB.

CB = a/Cos (63)

CB = 26.43227

CP = √(CB²-PB²)

CP = √(26.4322711750232² - 12²)

CP = 23.55133

Area of ΔPCB = (CP x PB)/2

(12 × 23.551326066062)/ 2

= 141.30796

Since ΔPCB = ΔPCA

and ΔACB = ΔPCB + ΔPCA

Thus,

Area of  ΔACB = 141.30796 + 141.30796 = 282.61592

≈ 282.62

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

The missing side of the right triangle is √57

To find the missing side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Let's assume the missing side is represented by the variable x.

According to the Pythagorean theorem:

(2√6[tex])^2 + x^2 = 9^2[/tex]

Simplifying, we have:

[tex]4 \times 6 + x^2 = 81\\24 + x^2 = 81\\x^2 = 81 - 24\\x^2 = 57[/tex]

Taking the square root of both sides, we get:

x = √57

Thus, the missing side of the right triangle is √57

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The volume of the trapezoidal prism is 420 cm³

Volume is the amount of space that is occupied by a three dimensional shape or object.

The volume of a trapezoidal prism is the product of the base area and its height.

For the trapezoidal prism:

Area of base = (1/2)(15 + 5) * 7 = 70 cm²

Volume of Prism = Area of base * height = 70 cm² * 6 cm = 420 cm³

The volume of the figure is 420 cm³

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The preparation of the income statement of Buildex Company's adjusted trial balance is as follows:

Buildex Company

Services revenue           $70,500

Interest revenue                 5,700

Total revenue                $76,200

Expenses:

Depreciation expense   $4,700

Wages expense            52,000

Insurance expense         4,400

Supplies expense           2,700

Utilities expense              1,700

Total expenses          $65,500

Net income                 $10,700

The income statement is a financial statement that shows the financial performance of a business over a period.

In the income statement, the total expenses are deducted from the total revenue to compute the profit or loss.

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Use the following selected accounts and amounts with normal balances from Buildex Company's adjusted trial balance to prepare its income statement for the year ending December 31. Hint: Not all accounts need to be used.

Cash                        $10,400           Depreciation expense $4,700

Building                   185,000           Wages expense          52,000

Accounts payable      9,400           Insurance expense        4,400

Services revenue    70,500           Supplies expense          2,700

Interest revenue        5,700           Utilities expense             1,700

The x-intercept in the graph represent the height where the football was when the ball was kicked.

The x-intercept is the point where the graph of the line crosses the x-axis.

Therefore, the x-intercept the value of x when y equals to zero.

Therefore, let's find what the x-intercept of the graph represent in terms of the football.

The graph shows the height of the ball in metres after t second.

The y axis represent the height while the x-axis represent the time.

Hence, he x-intercept represents the height where the football was when the ball was kicked.

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The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is

B) C=360 degrees s over A

The relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:

s = A / 360 * C

Make C the subject of the formula

s = AC / 360

360s = AC

rearranging

AC = 360s

C = 360 degrees s / A

C = (s / A) * 360°

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Answer:

[tex]\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}[/tex]

Step-by-step explanation:

In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.

This is because:

Therefore, this can be expressed as:

[tex]\dfrac{s}{C}=\dfrac{A}{360^{\circ}}[/tex]

Cross multiply:

[tex]360^{\circ} \cdot s=C \cdot A[/tex]

Now, divide both sides by A to isolate C:

[tex]\dfrac{360^{\circ} \cdot s}{A}=C[/tex]

Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:

[tex]\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}[/tex]

The solution to the system of equations is  x = 5.4 and y = -1.4

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

-x=y-4 y=4x+9

So, we have

-x = y - 4

y = 4x + 9

Rewrite the equation as

x = -y + 4

y = 4x + 9

So, we have

y = 4(-y + 4) + 9

Open the bracket and evaluate

5y = 9 - 16

So, we have

y = -1.4

Recall that

x = -y + 4

So, we have

x = 1.4 + 4

Evaluate

x = 5.4

Hence, the solution is  x = 5.4 and y = -1.4

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Step-by-step explanation:

prism

v=1/2 X 12cm X 8cm

V= 48

rectangular prism

v=80cm+48cm

v=128cm

The vertical asymptote of the function are x = ±1/2

Given that we need to determine what is value of the vertical asymptote of the function =

(2x + 1) / (4x²-1)

To find the vertical asymptote of the function f(x) = (2x + 1) / (4x² - 1), we need to determine the values of x for which the denominator becomes zero.

This is because division by zero is undefined, and the function may have vertical asymptotes at those points.

The denominator of the function is 4x² - 1.

To find the values of x that make the denominator zero, we can set it equal to zero and solve for x:

4x² - 1 = 0

Adding 1 to both sides:

4x² = 1

Dividing both sides by 4:

x² = 1/4

Taking the square root of both sides:

x = ±√(1/4)

Simplifying further, we get:

x = ±1/2

Therefore, the values of x that make the denominator zero are x = -1/2 and x = 1/2. These are the vertical asymptotes of the function.

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Translation =

What is value of the vertical asymptote of the function =

(2x + 1) / (4x²-1)

Fred will pay $43.05 in sales tax if he buys the new refrigerator.

To calculate the sales tax Fred will pay for the new refrigerator, we first need to find the amount of the sales tax.

The cost of the new refrigerator is $615.

To calculate the sales tax, we multiply the cost by the tax rate of 7%:

So, Sales tax = 7% of $615

Sales tax = (7/100) x $615

Sales tax = $43.05

Therefore, Fred will pay $43.05 in sales tax if he buys the new refrigerator.

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The number of combinations of the 5 white balls and 1 red ball are possible is 1.

We are given that;

White balls=5

Red ball=1

Now,

To find the number of combinations of 5 white balls and 1 red ball, we can use the combinations formula12:

[tex]nCr = n! / (r! (n-r)!)[/tex]

where n is the total number of objects, r is the number of objects to be selected, and ! is the factorial operator.

we can plug in these values into the formula:

[tex]6C6 = 6! / (6! (6-6)!) 6C6 = 6! / (6! 0!) 6C6 = 1 / (1 1) 6C6 = 1[/tex]

So, there is only one combination of 5 white balls and 1 red ball. This makes sense because the order of selection does not matter in a combination. No matter how we arrange the balls, we will always have the same group of 5 white balls and 1 red ball.

Therefore, by combinations and permutations the answer will be 1.

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The curved surface area of the cylinder is 24 cm².

We have,

To find the curved surface area of a cylinder, we need to know its height (h) and the circumference of its base (C).

Given:

Circumference (C) = 4 cm

Height (h) = 6 cm

The formula to calculate the curved surface area of a cylinder is A =  Ch, where A is the curved surface area, C is the circumference, and h is the height.

Substituting the given values:

A = 4 cm x 6 cm

A = 24 cm²

Therefore,

The curved surface area of the cylinder is 24 cm².

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The quadratic equation in standard form that corresponds to the graph shown above is f(x) = x² + 2x - 8

In Mathematics and Geometry, the standard form of a quadratic function can be modeled and represented by using the following mathematical expression;

y = ax² + bx + c

Where:

In this scenario and exercise, we would write a quadratic function that represent f(x) in standard form and with a leading coefficient of 1 by using the roots (-4, 0) and (2, 0) as follows;

f(x) = (x + 4)(x - 2)

f(x) = x² - 2x + 4x - 8

f(x) = x² + 2x - 8

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Answer:

Not a right triangle

Step-by-step explanation:

[tex]10^2+15^2\stackrel{?}{=}18^2\\100+225\stackrel{?}{=}324\\325\neq324[/tex]

As the sides of the triangle do not follow the Pythagorean Theorem, then the triangle is not a right triangle.

The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

The roots of the quadratic equation are the values of x that make the equation equal to zero.

Therefore, if a quadratic equation has the roots 3 + i and 3 - i, it can be written in the factored form as (x - (3 + i))(x - (3 - i)) = 0. Expanding this product yields x² - (3 + i + 3 - i)x + (3 + i)(3 - i) = 0.

Simplifying this expression further results in the quadratic equation x² - 6x + 10 = 0.

The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.

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The sum between n = 1 and n = 5 is 15.5, so the correct option is the second one.

Here we have the summatory:

[tex]\sum^{5}_{n = 1} 2^{n - 2}[/tex]

So we just need to add the 5 terms (between n = 1 and n = 5)

So we will get the sum:

S = [ 2¹⁻² + 2²⁻² + 2³⁻² + 2⁴⁻² + 2⁵⁻²]

S = [2⁻¹ + 2⁰ + 2¹ + 2² + 2³]

S = [0.5 + 1 + 2 + 4 +8]

S = 15.5

So the correct option is the second one.

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Answer:

0.168 ft aprox

Step-by-step explanation:

To solve this problem, we can use similar triangles and proportions. Let's denote the distance ahead of the car where the light beam hits the ground as "x" (in feet).

According to the given information, the light beam drops 2 inches for every 26 feet horizontally. We can set up the following proportion:

2 inches / 26 feet = x inches / x + 26 feet

To solve for x, we can cross-multiply and solve the resulting equation. Let's convert inches to feet to maintain consistent units:

2 inches = 2/12 feet = 1/6 feet

1/6 feet / 26 feet = x feet / x + 26 feet

1/6 * (x + 26) = 26 * x

x/6 + 26/6 = 26x

x + 26 = 156x

156x - x = 26

155x = 26

x = 26 / 155 ≈ 0.168 ft

Therefore, the headlights will hit the ground approximately 0.168 feet (or 2.016 inches) ahead of the car.

The value of the given expression is,

[tex]4^{- 5/2[/tex] =  1/32

[tex](1/16) ^ {- 3/2[/tex] = 64

We have to given that,

Expressions to solve are,

⇒ [tex]4^{- 5/2[/tex]

And, [tex](1/16) ^ {- 3/2[/tex]

We  know that,

Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself

Now, We can simplify the given expression,

By using law of exponents

We get,

⇒ [tex]4^{- 5/2}[/tex]

⇒ [tex]2^{2(- 5/2)}[/tex]

⇒ 2⁻⁵

⇒ 1/2⁵

⇒ 1/32

Thus,

The value of   [tex]4^{- 5/2[/tex] =  1/32

The given expression is,

⇒[tex](1/16) ^ {- 3/2[/tex]

By using law of exponents

We get,

⇒ [tex]16 ^{3/2}[/tex]

⇒ [tex](4^2)^{3/2}[/tex]

⇒ 4³

⇒ 64

The value of  [tex](1/16) ^ {- 3/2[/tex] = 64

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B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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2.63 is the value or quotient of 616/265 using long division.

We have to find the value of 616/265

In the given division the numerator is a dividend and the number in the denominator is a divisor.

616 is the dividend and 265 is the divisor.

When we perform long division the quotient will be 2.63 which is the require value.

       2.63  

____________

265 | 616

-530

______

860

-795

______

650

-530

______

120

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Beth and Kelly were on vacation for 6 days.

Let's assume that Beth and Kelly were on vacation for "x" days.

For Beth:

The cost per day for dog sitting at Rover Sleepover is $24.50.

Beth also paid a fee of $90.50 for food and cleaning.

So the total cost for Beth's dog sitting can be expressed as:

Total cost for Beth = (Cost per day × Number of days) + Cleaning fee

Total cost for Beth = ($24.50 × x) + $90.50

For Kelly:

The cost per day for dog sitting at Pet Palace is $32.

Kelly also paid a fee of $45.50 for cleaning.

So the total cost for Kelly's dog sitting can be expressed as:

Total cost for Kelly = (Cost per day × Number of days) + Cleaning fee

Total cost for Kelly = ($32 × x) + $45.50

Since both Beth and Kelly spent the same total amount of money, we can set up an equation:

($24.50 × x) + $90.50 = ($32 × x) + $45.50

Simplifying the equation, we get:

$24.50x + $90.50 = $32x + $45.50

Moving the variables to one side and constants to the other side:

$32x - $24.50x = $45.50 - $90.50

Combining like terms, we have:

$7.50x = $45

Dividing both sides of the equation by $7.50:

x = $45 / $7.50

x = 6

Therefore, Beth and Kelly were on vacation for 6 days.

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In the equation [tex]y = -2(0.5)^x[/tex], the initial amount (a) is -2, and the growth/decay factor (b) is 0.5.

In the given equation, [tex]y = -2(0.5)^x[/tex], we can identify the initial amount and the growth/decay factor.

The equation is in the form of exponential decay, as the base (0.5) is between 0 and 1, resulting in the function decreasing as x increases.

The initial amount, denoted as "a," is the coefficient in front of the exponential term. In this case, the initial amount is -2. This means that when x = 0, y = -2.

The growth/decay factor, denoted as "b," is the base of the exponential term. In this equation, the base is 0.5. The value of the base determines how quickly the function decreases or decays.

To summarize:

Initial amount (a) = -2

Growth/decay factor (b) = 0.5

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The reflections are described below.

We know that,

There are two types of reflection:

Reflection with respect to X-axis:

The x-coordinates of a point stay constant when it is mirrored across the X-axis. However, the Y-coordinates are changed into their inverse signs.

As a result, the X-axis reflection of the point (x, y) is (x, -y).

Reflection with respect to Y- axis:

The Y-coordinates of a point stay constant when it is mirrored across the Y-axis. However, the X-coordinates are changed into their inverse signs.

As a result, the Y-axis reflection of the point (x, y) is (-x, y).

Now the reflection is as following:

The point (x, y) when reflected across the x-axis becomes (x', y') = (x, -y)

The point (x, y) when reflected across the y-axis becomes (x', y') = (-x, y)

The point (x, y) when reflected across the line y = x becomes (x', y') = (y, x)

The point (x, y) when reflected across the line y = -x becomes (x', y') = (-y, x)

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The calculated volume of the sphere is 44602.24 ft³

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

Radius = 22 ft

The volume of a sphere can be expressed as;

V = 4/3πr³

Where

r = 22

substitute the known values in the above equation, so, we have the following representation

V = 4/3π * 22³

Evaluate

V = 44602.24

Therefore the volume of the sphere is 44602.24 ft³

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Question

Determine the volume of the following spheres with the given dimensions. to break the code find the mean of all your answers. round your answers to the hundreth place. use 3.14 for an approximation for pi.

Radius = 22 ft