The force required to compress a spring varies directly as the change in the length of the spring. If a force of 15 pounds is required to compress a certain spring 5 ​inches, how much force is required to compress the spring 8 ​inches?

Remember that a function is a relation between two sets of numbers where the first set is called domain, and the second set is called range.

The main characteristic that defines a function is that a domain element can be associated with only one element of the range set. In other words, one input value cannot have two different output values.

Therefore, the right answer is the third choice

Because this represents a function and its inverse also represents a function, that is, it's inverse have the characteristic of a function. The following set represents the inverse

As you can observe, this inverse set also follows the function definition, because every single input is associated with only one output.

Answer: its 2

Step-by-step explanation:

hope it helps you

907.46 is the answer.

The value of x is 58.51 degree.

We have,

Perpendicular= 8

Base = 4.9

Using trigonometry

tan x = Perpendicular/ Base

tan x = 8/4.9

tan x= 1.63265306122449

x = 58.51253064

Thus, the value of x is 58.51 degree.

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Answer:

It would be, No solution.

Step-by-step explanation:

This is because you can't divide something from zero.

The population of the island after 10 years will be approximately 2385.

The formula for exponential growth is \(y = y_0e^{(kt)}.\)

The formula for exponential decay is \(y = y_0e^{(-kt)}\).

Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.

Given,  an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.

∴ The population be 10 years from now will be,

\(y_{10} = y_0e^{(0.03)\times10}\).

We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.

\(y_{10} = 1767e^{0.3}\).

\(y_{10} = 1767\times1.35\).

\(y_{10} = 2385\).

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Answer:

8/9

Step-by-step explanation:

find the Least Common denominator, then change the numerators as need. Divide, then simplify

Answer:

59 1/2

Step-by-step explanation:

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

The value is   \(p-value  =  0.22663\)

Step-by-step explanation:

From the question we are told that

    The proportion of bruised tomatoes p =  0.08

    The  null hypothesis is  \(H_o  :   p =  0.08\)

    The alternative hypothesis is  \(H_a  :  p >  0.08\)

    The sample size is  n  =  600

    The number of bruised tomatoes from the sample selected is  k  =  53

    The test statistics is  z =0.75

Generally the p-value is mathematically represented as

      \(p-value  =  P(Z > z)\)

=>    \(p-value  =  P(Z > 0.75)\)

From the z-table  

    \(P(Z > 0.75) =  0.22663\)

So  

    \(p-value  =  0.22663\)

Answer:

P-value ≈ 0.2266

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

a. compounded semiannually, n = 2

b. compounded quarterly, n = 4

c. compounded monthly, n = 12

d. compounded continuously

Answer:

8

Step-by-step explanation:

First, let’s say the number is x

Then follow the steps

12x+6

36x+18

36x+9

12x+3=99

So x=8

Answer:

Use Mathpapa to find your answer.

Step-by-step explanation:

It's a good, and powerful program.

Answer:

-3 is a solution.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

3 - 4r ≥ 15

Step 2: Solve for r

Step 3: Compare

This is true. -3 is less than or equal to -3.

Answer: 45.1

Step-by-step explanation:

The area of the figure is about 45 square cm.

A triangle is a polygon with 3 sides.

Given the quadrilateral ABCD.

The sum of the interior angles of a triangle is 180°, therefore,

44° + 38° + m∠C = 180°

m∠C = 180° - 44° - 38°

m∠C = 98°

Now, using the sine law in triangle BDC, it follows:

sin44°/ BC = sin98°/10

BC = (10·sin44°)/ sin98°

BC ≈ 7

The area of a triangle is half the product of its two sides and the sine of the included angle, therefore, the area of triangle BDC is:
A₁ = (1/2)× 10×7× sin38°

A₁ = 21.5

Now, in triangle ABD,

cos55° = AD/10

AD = 10 cos55°

Similarly,

sin55° = AB/10

AB = 10sin 55°

Hence, the area of the triangle ABD is:

A₂ = (1/2) × (10 cos55°) ×(10sin 55°)

A₂ = 23.5

Therefore, the total area of the figure is:

A = A₁ + A₂

A = 21.5 + 23.5

A = 45.0

Hence, the area of the figure is about 45 square cm.

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Answer:

\(x=11\)

Step-by-step explanation:

It is a linear pair

\(7x + 12 + 8x + 3 = 180\)

\(15x + 15 = 180-15\\15x = 165\)

\(x=11\)

Conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

       To graph the function g( x) = - f( x 4), we need to start with the graph of the function f( x) = | x| and  also apply the given  metamorphoses.  The function f( x) = | x| represents the absolute value function, which is a V- shaped graph symmetric with respect to the y- axis.  

First, we shift the graph of f( x) = | x| horizontally by 4 units to the left by replacing x with( x 4). This results in f( x 4).  Next, we multiply the entire function by-1, which reflects the graph vertically. This gives us- f( x 4).  Combining these  metamorphoses, we've the function g( x) = - f( x 4). To graph g( x), we can  compass a many points and  also draw the graph by connecting them.

Let's start with the original graph of f( x) = | x| and apply the  metamorphoses

For f( x)  x = -3,-2,-1, 0, 1, 2, 3  

f( x) =  3, 2, 1, 0, 1, 2, 3  For

g( x) = - f( x 4)  x = -7,-6,-5,-4,-3,-2,-1  

g( x) = -3,-2,-1, 0,-1,-2,-3

conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

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Answer: Assuming that event A has occurred

Step-by-step explanation:

The conditional probability of B given A can be found by​ assuming that event A has occurred, and then calculating the probability that event B will occur.

So, the correct answer is d.

The conditional probability of B given A, denoted as P(B|A), represents the probability of event B occurring given that event A has already occurred.

It is calculated by assuming that event A has occurred and then determining the probability of event B occurring under that assumption.

Mathematically, the conditional probability is calculated as:

P(B|A) = P(A and B) / P(A)

Where P(A and B) represents the probability of both events A and B occurring together, and P(A) represents the probability of event A occurring.

Therefore, option d. assumes that event A has occurred and then calculates the probability that event B will occur, which aligns with the definition of conditional probability.

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I had to edit my answer bc it was wrong ignore this block teehee sorry

Answer:

99, 93, 87, 81

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

b

Answer:

No, No, Yes, Yes, Yes

Step-by-step explanation:

the next part of it is  Z = 5 , and boundry point. and then > 5

IQR = Q3-Q1 = 53 - 36 = 17

Answer:

A sample of 2017 should be taken.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is of:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of 0.30.

This means that \(\pi = 0.3\)

Confidence level:

Not given, so I will use 95%.

This means that \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

a. [2.5 pts] How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of 0.02?

A sample of n should be taken.

n is found fo M = 0.02. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.02 = 1.96\sqrt{\frac{0.3*0.7}{n}}\)

\(0.02\sqrt{n} = 1.96\sqrt{0.3*0.7}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.02}\)

\((\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.02})^2\)

\(n = 2016.8\)

Rounding up:

A sample of 2017 should be taken.

Answer:

88

Step-by-step explanation:

The distance traveled by a rider on a Ferris wheel can be calculated by finding the circumference of the wheel and then multiplying it by the number of complete laps.

The formula for the circumference of a circle is:

C = πd

where C is the circumference, d is the diameter, and π is a constant approximately equal to 3.14.

In this case, the diameter of the Ferris wheel is 14 meters, so the radius (half the diameter) is 7 meters.

C = πd = π(14) = 43.9823 meters (rounded to 4 decimal places)

To find the distance traveled after 2 complete laps, we need to multiply the circumference by 2:

distance = 2C = 2(43.9823) = 87.9646 meters

Rounding to the nearest meter, the distance traveled by a rider after 2 complete laps is 88 meters.

Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, \(\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}\).

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

\(f(x)=2x+100\)

This can be checked by using the values given in the problem:

\(f(30)=2(30)+120=180\\f(50)=2(50)+120=220\)

The base rate of $120 and $2 per person satisfies the given equation and established values.

Answer:

14.3

Step-by-step explanation:

$71.50 for 5 tickets

71.50 ÷ 5 = 14.3 there's no need to round the result.