The height that a ball bounces varies directly asthe height from which it was dropped. A tennis balldropped from 12 inches bounces bounces 8.4 inches. From whatheight was the tennis ball dropped if it bounces 56inches.

The letter used to represent Pearson's product-moment correlation coefficient is "r".

This coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no linear correlation.

To calculate Pearson's correlation coefficient, we first standardize the variables by subtracting their means and dividing by their standard deviations. Then, we calculate the product of the standardized values for each pair of corresponding data points. The sum of these products is divided by the product of the standard deviations of the two variables. The resulting value is the correlation coefficient "r".

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Answer:

Trees, moguls, slope, length, condition

Step-by-step explanation:

If a run doesn't have that many trees to dodge or avoid, it would be a very easy run. If the run has moguls, or little bumps in the snow, it might have a higher trail rating. If the trail is very steep, it might also have a higher trail rating, as you need more experience to ski on steeper slopes.

Step-by-step explanation:

Trees,moguls,slope,length,condition

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

If two lines form wide and narrow angles, it implies that they intersect at a point. If two lines form wide and narrow angles, then the lines must intersect.

When two lines intersect, they form four angles around the point of intersection. These angles can be classified based on their measurements. If two lines form a wide angle and a narrow angle, it means that they intersect and create angles of different sizes.

A wide angle is greater than 90 degrees, while a narrow angle is less than 90 degrees. This indicates that the lines are not parallel or perpendicular to each other, but instead, they intersect at an angle that is neither right (90 degrees) nor straight (180 degrees).

In conclusion, it is assumed that two lines cross at a place when they form wide and narrow angles.

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Answer:

27.7 (rounded)

Step-by-step explanation:

Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Review the following subtraction rules and properties:

Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year

To find: Difference in tuition fees paid by Ahab and his sister?

Solution:

To find the difference in their fees we have to perform simply normal subtraction

Subtract the fees of his sister from Ahab's fees which is as follows:

\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

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Answer:

The length of the base of this parallelogram is 34.2

Step-by-step explanation:

To calculate the length, we work backward and calculate the base by doing area/height

We have 690.84/20.2 = 34.2

I hope this explained your confusion

Answer:

Yes

Step-by-step explanation:

Answer:

Just push next... also the next question is -

Which of the following statements is true when comparing numbers using a number line?

The number closest to zero is always the least.

The number farthest from zero is always the greatest.

The number farthest right is always the least.

The number left is always the least.

YOUR ANSWER IS

D. The number left is always the least.

Your welcome peoples

Answer:

f(3) = -9

Step-by-step explanation:

Given that,

→ f(x) = -7x + 12

Then the value of f(3) will be,

→ f(3) = -7(3) + 12

→ f(3) = -21 + 12

→ [ f(3) = -9 ]

Hence, the value is -9.

Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:\(\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\]\) Multiplying the equation by the least common multiple of the denominators, we get:\(\[16 + 8 = 2x\]\) Simplifying, we get:\(\[2x = 24\]\)Dividing both sides by 2, we get:\(\[x = 12\]\)Therefore, it takes Cindy 12 hours to rake the yard alone.

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Answer:

50 people

Step-by-step explanation:

so to solve this we can use cross multiplying:

first we know that 20% = 10 people and 80% = x people (we put x because we don't know how many people)

then we set it up:

\(\frac{10}{20}\) = \(\frac{x}{80}\)

= 20x = 800

= x = 40

now it asks how many people were surveyed in total so we add the 10 + 40 = 50

50 people were surveyed

Answer:

The real distance would be 16

Step-by-step explanation:

If the scale is 1/2, that means each distance on the map is half of what the real distance is. So 8 x 2 =16.

Answer:

80 miles.

Step-by-step explanation:

Since 1/2 an inch is 5 miles, that would mean one inch is 10 miles.  Now that we know one inch is 10 miles, we can multiply 10 x 8 to get 80.  Therefore, the real distance between the two citied is 80 miles.

Hope it helped and have a great day :)

Answer:

the answer is (x+6)2-4

The correct equation of the translated function, g(x) is,

⇒ g(x) = (x + 4)² 6

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

here, we have,

Given that:

The function is,

,⇒ f (x) = x²

Here, f(x) has vertex point is (0,0)

and g(x) vertex point is (-4,6)

Hence, The general form of equation with vertex is

⇒ y = a (x - h)² + k

where (h, k) are the vertex.

So, the equation of g(x) form is

⇒ g(x) = (x + 4)² + 6

Therefore, Option D is correct.

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After using linear equation - Randy paid $7.25 for each sub sandwich.

What are linear equations with one variable?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 4x+4=8 only has one variable.

we are given that,

cost of one hamburger = $5.75

let us assume the cost of one sub sandwich to be $x

thus the cost of three sub sandwiches will be $3x.

we know his total came out to be $27.50

therefore,

we are given that

cost of one hamburger + 3 sub sandwiches = $27.50

= 5.75 + 3x = 27.50

= 3x = 27.50 - 5.75

= 3x = 21.75

= x = 21.75/3

= x = $7.25

thus we know that one sub sandwich costs randy $7.25.

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The 90% confidence interval for the standard deviation of the population is between `2.29` and `4.67`.

To calculate a 90% confidence interval for standard deviation with a sample size of 20, we can use the chi-squared distribution.  

Step 1: Find the chi-squared critical valuesFor a 90% confidence interval, we need to find the chi-squared critical values with 19 degrees of freedom. We can use a chi-squared table or a calculator to find the critical values.

Using a calculator, we can use the following formula: `X²α/2, n-1` and `X²1-α/2, n-1`. Plugging in the values, we get: `X²0.05, 19` = 30.144 and `X²0.95, 19` = 10.117

Step 2: Calculate the confidence interval Now we can calculate the confidence interval using the formula: `sqrt((n-1) × s²) / sqrt(X²α/2, n-1) ≤ σ ≤ sqrt((n-1) × s²) / sqrt(X²1-α/2, n-1)`

Plugging in the values, we get: `sqrt((20-1) × 3.55²) / sqrt(30.144)` ≤ σ ≤ `sqrt((20-1) × 3.55²) / sqrt(10.117)` Simplifying the equation, we get: `2.29` ≤ σ ≤ `4.67`

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Extraneous solution of the equation : x = 4

Given,

√x²+9=x+1

Here,

To solve for x ,

Square both sides,

x² + 9 = (x +1)²

Simplifying further,

x² + 9 = x² + 1 + 2x

Combine like terms ,

x² - x² + 9 - 1 = 2x

8 = 2x

x = 4

Thus the solution of x is 4.

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Answer:

\( \frac{14}{6} + \frac{1}{5} = \frac{70 + 6}{30} = \frac{38}{15} \)

Answer:38/15

Step-by-step explanation:

First we have to make the denominator of both the decimals,lets see:6 and 5 are the  denominator.They can both be turned into 30! The 14/6 ’s 6 is time 5 to get to 30 so 14/6 x =70/30 and the other is 1/5 =6/30.

So: 70/30 + 6/30=76/30!

Simplified: 38/15

Hope this helped!

Hope you have a great day!

Good luck !

lfu29

Answer:

pretty sure its acute

Step-by-step explanation:

Answer:  -2x + 5y = 8

Step-by-step explanation:

Since the lines must be parallel, the slopes must be the same, so keep the coefficients of x and y

Substitute the values of x and y from the given coordinate  (6,4) to find the new constant, b, the y-intercept.

-2x + 5y = b

-2(6) + 5(4) = b

-12 + 20 = b

8 = b

Rewrite the original equation substituting the new b for the original -15

-2x + 5y = 8

The solution of the given equation is -6 and 1.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Here, given equation:

  (x+2)(x+3) = 12

 x(x+3)+2(x+3) = 12

 x² + 3x + 2x + 6 = 12

 x² + 5x + 6 - 12 = 0

 x² + 5x - 6 = 0

 x² + 6x - x - 6 = 0

 x(x+6) -1(x+6) = 0

 (x+6)(x-1) = 0

Now, x + 6 = 0      or      x - 1 = 0

        x = -6           or      x = 1

Thus, the solution of the given equation is -6 and 1.

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The slope-intercept form equation of the line is y=(-2/3)x-(17/3) when the line is passing through the points (2,7) and (-1,-5).

Finding the ratio of vertical change to horizontal change between any two distinct points on a line yields the slope. Occasionally, the ratio is written as a quotient, which produces the same number for every two distinct points on the same line. A negative rise refers to a diminishing line. The line could be functional, set by a road surveyor, or depicted in a diagram that represents a road or a roof as a description or a plan.

The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope.

The slope-intercept form is y=mx+c

Given points are (2,7) and (-1,-5)

Slope m= (y₂-y₁)/(x₂-x₁)

m=(-5+7)/(-1-2)

m=-2/3

By substituting m value in the above equation we get,

y=(-2/3)x + c

Given that, the above equation is passing through the point (-1,-5)

-5=(-2/3)(-1)+c

c=-5-(2/3)

c=-17/3

y=(-2/3)x-(17/3)

Therefore, the equation of the slope-intercept form is y=(-2/3)x-(17/3)

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Answer: 17.5%

Step-by-step explanation:

Flipping tails: 50%

Rolling at least 14: 35%

Total: 50% x 35% = 17.5%

I donno if i'm right

Answer:

Step-by-step explanation:

Multiplying y by a value greater than 1 results in a vertical stretch. When the sign of it is negative there is a reflection over the x-axis. The appropriate choice is shown below.

__

The second attachment shows how the graph is flipped and stretched.

To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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Answer:

the company must buy 22 gallons to paint this entire area

Step-by-step explanation:

The circumference of the tank is given and is C = 2(pi)r, where r is the area.                                                                              

                                                                                                             118 ft

Here the circumference is C = 2(pi)(r) = 118 ft, which   leads to r = ------------ ≈

18.79 ft ≈ r                                                                                                     2(pi)

The area of the sides is A = (circumference)(height), or approximately

(118 ft)(50 ft) = 5900 ft², and the area of the top is A = πr², which here comes to (π)(18.79 ft)² ≈ 1109 ft².  Combining these two sub-areas, we get:

A(total) = 1109 ft² + 5900 ft² ≈ 7009 ft²

To determine how many gallons of paint will be needed to paint only the top and sides, we divide 7009 ft² by the coverage rate, which is

320 ft²

-----------

1 gallon

which results in:

7009 ft²

----------------------  ≈  21.9 gallons

320 ft² / gallon                          

Since the paint comes only in full gallon cans, the company must buy 22 gallons to paint this entire area.                                                        

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

1/3

Step-by-step explanation:

If you add all the n's, it would make 3n=1.  Divide both sides by 3 and get n=1/3

Answer:

0.333 or 1/3

Step-by-step explanation:

0.333*3=1