A guy wire runs from the top of a cell tower to a metal stake in the ground. Jacob places a 9-foot tall pole to support the guy wire. After placing the pole, Jacob measures the distance from the stake to the pole to be 1 ft. He then measures the distance from the pole to the tower to be 11 ft. Find the length of the guy wire, to the nearest foot.

In a normal distribution, x = -5 and z = -3.14 means that x = -5 is 3.14 standard deviations to the left of the mean

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

Distribution = Normal

z = -3.14

z = -5

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, a z-score of -3.14 indicates that the value is 3.14 standard deviations below the mean.

Since x is given as -5, we know that this value is 3.14 standard deviations below the mean value, which can be determined by multiplying the standard deviation by the z-score.

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D) 110 = 16 + 10h

C) 16 = 110 – h

Step-by-step explanation:

Think about it. She NEEDS $110 but she only has $16. So now it's $110=$16 {or C}.

She can EARN the rest {H} by working her hours.

Answer:

x=166

Step-by-step explanation:

180-14= 166

x=166

The rational function that is graphed below include the following: A. f(x) = 1/(x - 1)(x - 5).

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

Therefore, when x = 1, the rational function become undefined;

f(x) = 1/(x - 1)(x - 5)

f(x) = 1/(1 - 1)(x - 5)

f(x) = 1/0 (undefined).

Also, when x = 5, the rational function is undefined;

f(x) = 1/(x - 1)(x - 5)

f(x) = 1/(x - 1)(5 - 5)

f(x) = 1/0 (undefined).

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The homogenous equation is

dv/du = -u + v = -(u - v)/u + v = -(x - y)/x + y = -x2 + 2xy + y2 + 2x + 6y = C

Given the differential equation:

dy/dr = x - y - 1/x + y + 3

To make this equation homogeneous, we can make the substitutions:

x = u + h

y = v + k

where h and k are constants. The derivative of y with respect to r becomes:

dy/dr = (du/dr)(v + k) + (du/du)(u + h) = (du/dr)v + (du/dr)k + (du/du)u + (du/du)h

Matching coefficients in the equation above to those in the original differential equation, we have:

(du/dr)k = -1/2 (1/u + v)

(du/du)h = 1/2 (x - y)

Solving for h and k, we have:

h = -x + y

k = -1/2 (1/u + v)

Substituting back into the original equation, we have:

dy/dr = x - y - 1/x + y + 3 = -(u + h) + (v + k) + (u + h) + (v + k) + 3 = 2v + 2k + 3

This is now a homogeneous equation and can be written as:

dv/du = -u + v = -(u - v)/u + v = -(x - y)/x + y = -x2 + 2xy + y2 + 2x + 6y = C

So the general solution to the differential equation is:

x^2 - 2xy - y^2 - 2x - 6y = C

where C is an arbitrary constant of integration.

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Answer:

36π cm^2

Step-by-step explanation:

area= πr^2

= 36π cm^2

Time taken to walk across 100 yard field is 60 minutes.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Speed of Slauson = 5 ft./min

That is, in 1 minute, Slauson can walk 5 feet.

We have to find the time taken to walk 100 yard.

1 yard = 3 feet

100 yard = 300 feet

Speed = Distance / Time

Time = Distance / Speed

Time = 300 / 5 = 60 minutes

Hence it will take 60 minutes to walk across a 100 yard field.

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The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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Answer:

[tex] \frac{5}{6} + \frac{5}{8} = \frac{4 \times 5 + 3 \times 5}{24} = \frac{20 + 15}{24} = \frac{35}{24} = 1 \frac{11}{24} [/tex]

Answer:

Original Number is 37

Step-by-step explanation:

Let

x = First digit

y = Second digit

x + y = 10

∴y = 10 - x

Original Number = 37

3 + 7 = 10

When reversed:

New Number is 36 more than the original Number:

37 + 36 = 73

∴New Number = 73

The top speed of Scooter B is calculated and is given by the equation A = 6 miles/hour

Speed is defined as the rate of change of position of an object in any direction. The rate of change of distance over a particular interval of time is known as Speed. The speed is a scalar quantity which has no direction but only magnitude. The SI unit of speed is meter per second or kilometer per hour

Speed = Distance / Time

Given data ,

Let the top speed of Scooter A be represented as = A miles per hour

Let the top speed of Scooter B be = ( A + 2 ) miles per hour

The time traveled = 3 hours

So , Distance = Speed x Time

The distance traveled = 24 miles

So , 24 = ( A + 2 ) 3

On simplifying the equation , we get

24 = 3A + 6

3A = 18

A = 6 miles per hour

Hence , the top speed is 6 miles per hour

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Answer:

1177 178.12

Step-by-step explanation:

Answer:

y is the dependent variable and it is the total amount of money that she has saved.  

X is the dependent variable and it is the number of months that she has saved.

Step-by-step explanation:

y = 15x + 50

This is what the equation would look like.  If you tell me how many months she has saved, I can tell you how much is in her account.

The value of the expression 3.0 / 1.5 is 2.0.

The int() function returns the numeric integer equivalent from a given expression. It converts the specified value into an integer number. Floating point numbers represent real numbers such as 3.14159 or -2.5. The value of the given expression using int() function is 2.0. This is because when you divide 3.0 by 1.5, the result is 2.0. Here are the steps to solving the expression:

1. Start with the numerator (3.0) and the denominator (1.5).

2. Divide the numerator by the denominator.

3. The result is the value of the expression.

So, the value of the expression 3.0 / 1.5 is 2.0.

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The absolute amount of the difference between the measured and real value, divided by the actual value, is multiplied by 100 to determine the percent inaccuracy.

1. Divorce the measured value from the true value.

2. Calculate the result's absolute value.

3. Subtract the true value.

4. Increase by 100.

A measure of how closely a measured value matches an actual value is called percent error. By taking the absolute difference between the measured and real values, dividing by the actual values, and multiplying by 100, it is determined. We may determine the percentage difference between our measured value and the real value using this calculation. For instance, the error would be 20% if the real value was 10 and the measured value was 8. It is determined in the following manner step by step: first, deduct the measured value from the real value, then calculate the absolute value of the outcome. Multiply by 100 after dividing the result by the actual value. Percent Error = |Measured Value - Actual Value| Actual Value x 100 is the formula for this problem.

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1. The scale factor is 2

2. angle C is 67.47 degrees

3. angle Z is 75.56 degrees

4. 6 units

The scale factor is calculated used reference points and comparing the points

Using WZ  = 3 units and AD = 6 units, let the scale factor be k

WZ * k = AD

3 * k = 6

k = 2

Angle C corresponds to angle XYZ = 67.47 degrees

Angle Z corresponds to angle CDA = 75.56 degrees

Side AD is gotten by counting the number of units in the x direction and this is 6 units

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Answer: 11.2 inch

Step-by-step explanation:

Answer: B: 113.04cm^2

Step-by-step explanation:

The value of the ratios 16: 4 and 8: 2 in the simplest form is 4:1. Then the ratios are equivalent to each other.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The ratios are given below.

16: 4 and 8: 2

Simplify the ratio, then we have

16: 4 = 4: 1

8: 2 = 4: 1

The value of the ratios 16: 4 and 8: 2 in the simplest form is 4:1. Then the ratios are equivalent to each other.

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Answer:

A. 1809.6 cm²

Step-by-step explanation:

The formula for the surface area of a sphere is:

Surface Area = 4πr^2

where r is the radius of the sphere.

Substituting the given value of radius, r = 12cm, we get:

Surface Area = 4π(12)^2

= 4π(144)

= 576π

≈ 1809.6 cm² (rounded to the nearest tenth)

Therefore, the answer is (a) 1809.6 cm²

The given function f is differentiable at all values of x except x=10.

One of the most crucial topics is continuity and differentiability, which aids students in understanding ideas like continuity at a point, continuity on an interval, derivative of functions, and many more. However, it is quite challenging to maintain the continuity and differentiability of functional parameters.

Function f  is differentiable at x=a if and only if f'(a) exists.

for this function

[tex]f(x)=\frac{1}{x-10}\\\\f'(x)=-(x-10)^{-2}\\\\f'(x)= -1/(x-10)[/tex]

The given function is differentiable at all values of x except x=10.

The complete question is-

How do you describe the X values at which f is differentiable?

f(x)= 1/(x-10)

a) at x=10 b) at x not equal to 10 c) all values of x d) all values of x except 10.

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The maximum height of the rocket is 256 feet and the time it takes the rocket to reach this height is 4 seconds.

The rocket will be in the air for 8 seconds.

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y = -16t² + 128t _____(1)

This can be assumed as an equation of a parabola.

i.e

y = ax² + bx

so,

a = -16 and b = 128

To find the maximum height of the rocket, we need to find the vertex of the parabola.

The vertex is given by the formula.

t = -b/2a

t = -128/(2 x -16)

t = 4

Substitute t = 4 in (1).

y = -16 x 4² + 128 x 4

y = 256 feet

So,

The maximum height of the rocket is 256 feet.

When the rocket is on the ground.

y = 0

-16t² + 128t = 0

t (-16t + 128) = 0

t = 0 or -16t + 128 = 0

t = 0 and -16t = 128

t = 0 and t = -8 (rejected)

Since the rocket is launched at t = 0,

The rocket will be in the air for 8 seconds.

i.e

8 - 0 = 8

Therefore,

The maximum height is 256 feet and it will be in 4 seconds.

The rocket will be in the air for 8 seconds.

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Answer:

$5111.76

Step-by-step explanation:

compounded daily means 365 times interest is compounded per year, so

A=4156x[tex](1+\frac{0.0345}{365}) ^{365x6}[/tex] ≈ 5111,76

Answer:

Step-by-step explanation:

To find the inverse of the function f(x) = 4x - 2, we need to switch the roles of x and y, and then solve for y:

x = 4y - 2

x + 2 = 4y

y = (x + 2) / 4

So the inverse of f(x) is g(x) = (x + 2) / 4.

To graph f(x) and g(x), we can plot their points on the same coordinate system. Here is the graph:

Graph of f(x) and g(x)

The blue line represents f(x) = 4x - 2, and the orange line represents g(x) = (x + 2) / 4, which is the inverse of f(x). Notice how the two lines are reflections of each other across the line y = x, which is a characteristic of inverse functions.

The inverse of the function is f-1(x) = (x + 2)/4

Inverse functions are pairs of functions that "undo" each other.

Specifically, if a function f maps x to y, its inverse function g maps y back to x such that g(f(x)) = x and f(g(y)) = y for all values of x and y in their respective domains

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

f(x) = 4x - 2

Rewrite as

y = 4x - 2

Swap x and y

So, we have

x = 4y - 2

This gives

4y = x + 2

Divide by 4

y = (x + 2)/4

This means that the inverse is f-1(x) = (x + 2)/4

See attachment for the graph of the functions

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The number of each kind of package that were shipped include the following:

Standard-Delivery: = 61

Express Delivery: = 61

The total number of packages that was delivered in a day = 138.

The total cost for the delivery for a day = $669.00

The charges for each standard-delivery package = $2.50

The charges for express-delivery package = $8.50

The total charges for both = $11

The charges for Standard-Delivery

= 2.50/11 × 669.00

= 1672.5/11

= $152.1

The number of Standard-Delivery that was shipped = 152.1/2.5 = 61

The charges for Express Delivery:

= $669.00-$152.1

= $516.9

The number of Express Delivery that was shipped;

=516.9/8.5 = 61.

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Answer:

13

Step-by-step explanation:

11+2^2 -2

= 11+4-2

= 15-2

= 13

The length of the missing side (hypothenuse) is equal to 5

"Information available from the question"

Opposite side of the triangle(y) = 3

Adjacent side of the triangle (z)= 4

Hypothenuse side of the triangle = x

Pythagorean Theorem

This formula is used to find the missing side of a right angle triangle if two sides are given.

[tex]x^{2} =y^2+z^2[/tex]

Let's substitute the values into the formula and solve for the hypothenuse

[tex]x^{2} =3^2+4^2[/tex]

[tex]x^{2}[/tex] = 9 + 16

[tex]x^{2}[/tex] = 25

[tex]x=\sqrt{25}[/tex]

x = 5

The length of the missing side (hypothenuse) is equal to 5.

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Answer:

20

Step-by-step explanation:

Due to the fact that there are an unlimited number of values that are either more than or less than the variable x.

Rationales are intelligent, independent, and capable of both stubbornness and skepticism. Rationales typically spend a lot of time and effort trying to comprehend the manner in which the universe of ideas works.

Every number that can be stated as a percentage or as a portion of a whole integer is considered rational. (For instance, -7, 2/3, and 3.75) Irrational numbers are those that can't be stated as a ratio of two integers or a fraction. They cannot be expressed in any finite way.

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