For the function y=F(x), when x = 4, its y-value is 18.

Choose all true statements.
A. The functions value is 4 at 18
B. The point (4,18) is on the graph of the function
C. The functions value is 18 at 4
D. F(4)=18
E. The point (18,4) is on the graph of the function
F. F(18)=4

We can use the distance formula to find the distances between the fire hydrants and determine whether they form a right triangle. The value of y is 4.

The distance between (0,0) and (2,5) is:

√((2-0)² + (5-0)²) = √29

The distance between (0,0) and (7,y) is:

√((7-0)² + (y-0)²) = √(49 + y²)

The distance between (2,5) and (7,y) is:

√((7-2)² + (y-5)²) = √(25 + (y-5)²)

If these distances form a right triangle, then the Pythagorean theorem must be satisfied:

(√29)² + (√(49 + y²))² = (√(25 + (y-5)²))²

Simplifying this expression, we get:

29 + 49 + y² = 25 + (y-5)²

Expanding the square on the right-hand side, we get:

29 + 49 + y² = 25 + y² - 10y + 25

Simplifying this expression, we get:

y = 4

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With 98% confidence, we estimate that the population standard deviation of the number of chocolate chips in all cookies lies within the range of 0.2 to 0.4

To construct a confidence interval estimate of the standard deviation of the number of chocolate chips in all cookies, we can use the chi-square distribution. Since the sample is large and the number of chocolate chips is assumed to be normally distributed, we can apply the chi-square distribution to estimate the population variance and standard deviation.

Given:

Sample size (n) = 50

\(Sample mean (x) = 22.43\)

Sample standard deviation (s) = 2.14

To find the confidence interval for the population variance, we can use the chi-square distribution with (n - 1) degrees of freedom. For a 98% confidence level, the critical values for the chi-square distribution are 25.9875 (lower tail) and 75.913 (upper tail). Using these critical values, the confidence interval for the population variance is approximately (s² / upper bound, \(s^2\) / lower bound) or \((2.14^2 / 75.913, 2.14^2 / 25.9875)\) which simplifies to (0.060, 0.152).

To find the confidence interval for the standard deviation, we take the square root of the values in the confidence interval for the variance. Therefore, the confidence interval for the standard deviation is approximately (√0.060, √0.152) or (0.245, 0.390) rounded to the tenths place.

Therefore, with 98% confidence, we estimate that the population standard deviation of the number of chocolate chips in all cookies lies within the range of 0.2 to 0.4.  

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Using division, we can find that the best statement that describes the given expression is:

Add 8 to half the difference of 6 and 2, then subtract 1.

One of the fundamental mathematical operations is division, which entails breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 pupils are required to be split into groups of five for a sporting event? The division operation can quickly and easily fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will be a total of 6 groups, each with 5 pupils. Use the beginning number, 30, which is obtained by multiplying 6 by 5, to check this response.

8 + fraction 1 over 2 x (6 − 2) − 1.

The above is expressed mathematically as:

8 + 1/2(6 - 2) - 1

Therefore, the statement that describes this expression from the options given correctly is :

Add 8 to half the difference of 6 and 2, then subtract 1.

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We can use division to determine that the following statement best captures the meaning of the given expression:

To make up the difference between 6 and 2, add 8 and then take away 1.

Division, which involves dividing a larger number into smaller groups with the same number of components, is one of the basic mathematical operations. For instance, if 30 students must be divided into groups of five for a sporting event, how many groups will be formed. Such problems can be rapidly and readily resolved by the division operation. In this instance, we need to multiply 30 by 5. The outcome is 30 x 5 = 6.

There will be 6 groups in total, each with 5 students. To verify this response, use the starting number, 30, which is produced by dividing

6 by 5.

1 x (6 x 2) + 8 plus fraction 1 over 2 = 8.

The following can be represented mathematically:

8 + 1/2(6 - 2) - 1

Therefore, from the available possibilities, the statement that accurately represents this expression is:

To make up the difference between 6 and 2, add 8 and then take away 1.

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Answer:

7.2 hours slept

Step-by-step explanation:

30%>.30

.30*24=7.2 hours

Hope this will help!

When a two-way table shows one relationship between two variables, but the relationship reverses when a third variable is introduced, it indicates the presence of a confounding variable.

A confounding variable is an additional factor that is related to both the independent and dependent variables, and it can distort or influence the observed relationship between the two variables of interest. In such cases, the initial relationship observed in the two-way table may be misleading or inaccurate because the third variable is influencing the relationship. It highlights the importance of considering and controlling for potential confounding variables in order to accurately understand and interpret the relationship between the two primary variables.

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Answer:

-4

Step-by-step explanation:

Answer:

15,000.

Step-by-step explanation:

1.5 · 10⁴ = 15,000

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

Equations are mathematical statements with the equals (=) sign on each side and two algebraic expressions in the center.

Coefficients, variables, operators, constants, terms, and the equal to sign are just a few of the components that make up an equation. The "=" symbol and terms on both sides are always needed when writing an equation.

calculation

Let s = brittany 's age now

Let t = steve's age now

s = 3t

s + 9 = 2 (t+9)

s + 9 = 2t + 27

s = 2t + 27 - 9

s = 2t + 18

Substitute 3t for s and find t

3t = 2t + 18

3t - 2t = 18

t = 18 yrs is steve's age

then

s = 3(18)

s = 54 yrs is brittany's age

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

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By answering the presented question, we may conclude that As a result, function the solution is y = x/3.

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

A direct variation function has the formula y = kx, where k is the proportionality constant. We may utilise the supplied coordinates (-9, -3) and (-12, -4) to obtain k as follows:

(using the point (-9, -3)) -3 = k(-9)

-4 = k(-12) (using the coordinates -12, -4)

When we solve for k in both equations, we get:

k = -3/9 = -1/3 \sk = -4/-12 = 1/3

We made a mistake in one of the equations since the values of k are not the same. The first equation is clearly erroneous since it suggests k = -1/3, which is not the same as k = 1/3 from the second equation. As a result, the proper equation for the direct variation function is:

y = (1/3)x

As a result, the solution is y = x/3.

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The Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 can be obtained by expanding the function around x = 0 using the Taylor series. Here they are:

Order n = 0:

P0(x) = f(0)

Order n = 1:

P1(x) = f(0) + f'(0)x

Order n = 2:

P2(x) = f(0) + f'(0)x + (f''(0)x^2)/2

Order n = 3:

P3(x) = f(0) + f'(0)x + (f''(0)x^2)/2 + (f'''(0)x^3)/6

Order n = 4:

P4(x) = f(0) + f'(0)x + (f''(0)x^2)/2 + (f'''(0)x^3)/6 + (f''''(0)x^4)/24

Note that f'(0) represents the derivative of the function evaluated at x = 0, f''(0) represents the second derivative evaluated at x = 0, and so on.

These polynomials can be used to approximate the function near x = 0. The higher the order of the polynomial, the closer the approximation to the actual function.

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Answer:

y = 2.5x

Step-by-step explanation:

The equation representing direct proportion is

y = kx ← k is the constant of proportion

Here k = 2.5 , thus

y = 2.5x ← equation of proportion

Answer:

A

Step-by-step explanation:

what the other guy said

Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

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Answer:

1: 20 ounce carton is a better buy, its 6 cents per ounce, while the 12 ounce is 8 cents per ounce.

2: The ant walked for 405 hours (i think)

Step-by-step explanation:

:l boredom

X method is the method to find the factors of the polynomial equation.The factor of the given polynomial is,

\(x^2+16x-3x-48=(x+16)(x-3)\)

Thus the option 3 is the correct option,

X method is the method to find the factors of the polynomial equation.

The standard form of the quadratic equitation is given as,

\(ax^2+bx+c\)

Given information-

The equation given in the problem is,

\(x^2+13x-48\)

Compare the above equation with the standard form. We get,

\(a=1\\b=13\\c=-48\)

To find out the factor of above equation using X method, follow the steps.

        \(ac=1\times(-48)\\ac=-48\)

       \(b=13\)

         \(x^2+16x-3x-48=x(x+16)-3(x+16)\)

         \(x^2+16x-3x-48=(x+16)(x-3)\)

Hence the factor of the given polynomial is,

\(x^2+16x-3x-48=(x+16)(x-3)\)

Thus the option 3 is the correct option,

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Answer:

d

Step-by-step explanation:

Answer:79°

Step-by-step explanation:

Given the 124° angle, the other angle formed by that line and the top side of the square must be 56°, as they are supplementary angles (they must add up to 180°). This means that the angle formed by that same line and the bottom side of the square is also 56° since it is a corresponding angle and the top and bottom sides of a square are parallel. The angle that a diagonal of a square forms with the sides of a square is always 45°.

So now we have a triangle (in red in my diagram) with angles of 45°, 56°, and x°. The sum of the angles of a triangle must always equal 180°, so we solve for x:

56 + 45 + x = 180

x = 180 - 56 - 45 = 79

So angle x must be 79°.

Answer:

9 is the prime of it

Answer:

Prime factorization: 23 is prime. The exponent of prime number 23 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 23 has exactly 2 factors.

3.749 9.9 24.62 9.798

Okay, so take this with a grain of salt

Answer:

Not a function

Step-by-step explanation:

Since 2 different points have the same x-coordinte, the relation is not a function.

Answer:

I is 1/2 Y is 1/2 in Z is a half

Answer:

4 is the coefficient of x

The given company has two major departments: Development and Marketing. A total of twelve employees are selected randomly from each of the department and their ages are recorded. It is also mentioned that both of the departments have an employee who is of age 56 years. It is equally unusual to have a 56-year-old employee in both the departments.

To solve this problem, we need to determine the spread of the ages in each department. The spread of the ages in each department can be determined by calculating the range. The range is the difference between the maximum age and the minimum age in each department. We will then compare the range in both departments. The department with the greater range will be considered to be more unusual to have a 56-year-old employee.

The following are the ages of the employees in the Development and Marketing departments respectively: Development Department: 43, 24, 38, 56, 29, 22, 45, 47, 40, 33, 28, 30Marketing Department: 41, 56, 35, 23, 26, 49, 42, 50, 38, 29, 55, 46The range of the Development department can be calculated as: Range = Maximum Age - Minimum Age= 56 - 22= 34The range of the Marketing department can be calculated as: Range = Maximum Age - Minimum Age= 56 - 23= 33As we can see, the range in both departments is close. The range of the Development department is 34 and the range of the Marketing department is 33.

Therefore, it is difficult to determine which department is more unusual to have a 56-year-old employee. Hence, the answer is that it is equally unusual to have a 56-year-old employee in both the departments.

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Find the least common multiple of the denominators of the fractions. Write equivalent fractions that have the least common multiple as the denominator.

Answer:

\(\frac{133}{66}\)

Step-by-step explanation:

we require 2 equations with the repeating digits placed after the decimal point.

let x = 2.01515... ( multiply both sides by 10 and 1000 )

10x = 20.1515.... (1)

1000x = 2015.1515... (2)

subtract (1) from (2) thus eliminating the repeating digits

990x = 1995 ( divide both sides by 990 )

x = \(\frac{1995}{990}\) = \(\frac{133}{66}\) ← in simplest form

Answer:

The next number is 24. :)

Answer:

the answer is C.two parallel lines.

Answer:

The inequality form is -4<x<-2

The Interval Notation is (-4, -2]

I hope this helps!

Answer:

5

Step-by-step explanation:

subtract 192 from 379 and you get 187 so that is for adults then subtract 187 from 192 to get the answer which is 5

Answer:

The boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.

Step-by-step explanation:

Let x be the time (in hours) that the boat traveled at 10 miles per hour, and let y be the time (in hours) that it traveled at 30 miles per hour.

We know that:

x + y = 6 (the total time the boat traveled)

We also know that the boat traveled a total distance of 140 miles, which can be expressed as:

10x + 30y = 140

We can use the first equation to solve for one of the variables in terms of the other:

y = 6 - x

Substituting this expression for y into the second equation, we get:

10x + 30(6 - x) = 140

Simplifying and solving for x, we get:

10x + 180 - 30x = 140

-20x = -40

x = 2

Therefore, the boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.

Answer:

30

Step-by-step explanation:

You multiply 3*5 and then times 2. Hope that helped.

Answer:A he is correct because the inner circle is a dilation of the outer circle

Step-by-step explanation: just did the test

The statement "He is correct because the inner circle is a dilation of the outer circle" is the best explanation.

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables.

The radius of the inner circle is 2 units, while the radius of the outer circle is 5 units.

Since dilations provide similar figures because multiplying by the scale factor yields proportionate sides while keeping the angle measure and form constant.

Troy is accurate if he claims the two circles are similar.

Hence, the statement (A) "He is correct because the inner circle is a dilation of the outer circle" is the best explanation.

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Answer:

x = 12

Step-by-step explanation:

ZY is a midsegment and is half the measure of SQ, that is

x + 2 = \(\frac{1}{2}\) (3x - 8) ← multiply through by 2 to clear the fraction

2x + 4 = 3x - 8 ( subtract 2x from both sides )

4 = x - 8 ( add 8 to both sides )

12 = x