The water in the swimming pool was as blue as the sky.

True or false. The author uses this figurative language to help the reader understand the color of the water.

True
False

Frequency :

The frequency of a particular data is the number of times the particular data value occurs. We represent the value of frequency as f.

Relative frequency :

Relative frequency is the fraction or proportion times an answer occurs in the data set.

Relative frequency can be written in decimal, fraction and percent.

To find the relative frequency, divide the frequency by the total number of data values.

Cumulative frequency :

Cumulative frequency is the collection of all previous frequencies together.

Cumulative frequency is also called frequency of non-exceedance.

There are two types of Cumulative Frequency Curves (or Ogives) :

1. More than type Cumulative Frequency Curve.

2. Less than type Cumulative Frequency Curve.

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(a) SST = 1772,   SSR= 1420.79,  SSE=353.05

(b) Coefficient of determination is 0.8018.

(c) Sample correlation coefficient is 0.8954.

The average score can be obtained as

y = ∑y / n

  = 330 / 6

y = 55

The least-square regression line is given as:

y' = 23.221 + 0.318x

Using the above stated regression equation; the predicted values of overall score can be obtained for the given values of price.

y' = 23.321 + 0.318(170) = 77.281

(a) The formula for computing SST is given as:

SST = ∑ (yi - y)²

SST = 1772

Hence the value of SST is 1772.

The formula for computing SSR is given as:

SSR = ∑ (yi' - y)²

SSR = 1420.79

Hence the value of SSR is 1420.79.

The formula for computing SSE is given as:

SSE = ∑(yi - y')²

SSE = 353.05

(b) The coefficient of determination is given by the formula:

R² = [tex]\frac{SSR}{SST}[/tex]

   = [tex]\frac{1420.79}{1772}[/tex]

R²= 0.8954

Hence the value of the coefficient of determination is 0.8018.

(c) The correlation coefficient is computed as:

r = [tex]\sqrt{R^{2} }[/tex]

 = [tex]\sqrt{0.8018}[/tex]

r = 0.8954

Hence the value of the correlation coefficient is 0.8954.

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By analytic geometry, the resulting expression for the value t in the geometric system formed by two parallel lines is t = b + n.

In this question we find the case of two parallel lines, in which we are asked to derive an equation to replace the value t seen in the figure. By analytic geometry, two lines are parallel when they have the same slope. Slope is defined by the following formula:

m = Δy / Δx

Where:

The slope of each line is described below:

Line j

m = (t - a - n) / (x₂ - x₁)

Line k

m' = (b - a) / (x₂ - x₁)

Then, we eliminate m, m' and (x₂ - x₁) by assumption of parallelism:

t - a - n = b - a

t - n = b

t = b + n

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Answer:

  c = 5

Step-by-step explanation:

You want to solve 24c +60 = 36c.

This is sometimes referred to as a "2-step linear equation," because it can be solved in two steps.

The first step collects the variable terms on one side of the equal sign. This is done by subtracting the unwanted variable term from both sides of the equation.

  24c +60 -24c = 36c -24c . . . . . . subtract 24c

  60 = 12c . . . . . . . . . collect terms

The second step is to divide by the coefficient of the variable. This gives you the variable by itself:

  60/12 = (12c)/12

  5 = c . . . . . . . . . . . perform the division

The solution is c = 5.

__

Additional comment

As you can see, we like to write the answer as "variable = constant." We solved the equation to give "constant = variable." Of course, the properties of equality tell you these are interchangeable forms.

The point here is that some folks unnecessarily go to the trouble to manipulate the equation so the variable term ends up on the left. The solution is just as valid when the variable term ends up on the right side of the equal sign.

If you recognize that all of the numbers have a common divisor of 12, you can divide by that first:

  24c +60 = 36c

  2c +5 = 3c

Then subtract the variable term on the left to get the answer.

  2c +5 -2c = 3c -2c

  5 = c

The material that she has left after the cut of 1/2 yard of the material is 2/5 yards left

While I show you how to solve this problem, I would like to highlight some of the words and how they convert into a mathematical equation.

"She cut 1/3 yard off the material."

 This means you multiply whatever you are starting with by 1/3.

 So in this case Mineko begins with 3/5 yards.

 So,

3/5 • 1/3 = 1/5

She used 1/5 yard to make the pillow.

This will translate to Mineko having left

Therefore 3/5-1/5

She has 2/5 yards left.

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The interest earned almost is $337.50 when a $4,500 type of saving account have earns 2.5% simple interest for almost 3 years.

Simple Interest = Principal x Interest Rate x Time/ 100

The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest. Simple interest does not compound, so the creditor only has to pay interest on the principal sum and the borrower never has to pay interest on the interest that has already accrued.

The principal, or initial amount of a loan, is used to compute simple interest. Compound interest is often referred to as "interest on interest" since it is computed using the main amount and the interest that has accrued over the course of previous periods.

Here Principal= 4500

Rate= 2.5%

Time= 3 years

Using Simple Interest

SI = ( P x R xT)/100

SI = (4500 x 2.5 x 3) /100

SI = 33750/100

SI = $337.50

Hence, the interest earned is $337.50

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Correct Question:

Calculate the interest earned on a $4,500 saving account that earns 2.5% simple interest over 3 years.

There is sufficient evidence to conclude that μ, the true mean tension of the rackets, is less than 58 PSI.

The customer determined the tension of each racket after receiving them and came up with the following summaries: 0.9 PSI of standard deviation, 58 as the sample mean.

When we choose alpha as 5% = 0.05, it means that we reject the null hypothesis whenever the p value from the hypothesis test is less than this. If not, we will accept the null hypothesis.

You can use a p value as low as 0.05 and still reject the null hypothesis H0.

On calculating the p value we get it as less than 0.05.

Therefore, we will accept the null hypothesis.

Hence , the true mean tension of the racket is 28 psi .

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Answer:

For the boys' team, the tallest kid is 84 inches while the shortest is 75 inches making the range 9.

For the girls, the tallest is 75 inches tall while the shortest is 66, making the range 9.

Both the boys and the girls have a range of 9 but together, with the tallest boy and the shortest girl, the range is 18 inches.

Hope this helps! Have a nice day!

The perimeter of a triangle is: 12cm.

The area of triangle is: [tex]6 cm^2\\[/tex]

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

Therefore, this triangle is sometimes called the right triangle or 90-degree triangle.

The characteristics a right-angle triangle possesses.

Let x be the one side of the triangle.

Then the other side will be x + 1 cm.

Hypotenuse is 5 cm.

Using right angled triangle property and (a + b)²=a²+b²+2ab

[tex]x^2 + (x+1)^2 = 5^2\\\implies x^2 + x^2 + 2x + 1 = 25\\\implies 2x^2 + 2x = 24\\\implies 2x^2 + 2x -24 = 0\\\implies x^2 + x -12 = 0\\[/tex]

Solving this equation:

x = -4 or x = 3

since the length of triangle can't be negative therefor x = 3.

which means sides are 3, 4 and 5

Perimeter = sum of all three side

Therefore, Perimeter = 3 + 4 + 5 = 12cm.

Area = (height * base)/2

Therefore, Area = [tex]3*4/2 = 12/2 = 6 cm^2[/tex]

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The value for x in the given equation is -24.

Combine.  1/2 and x.

2x/6 + 24/3 = (x/6 + 14/2) -3

2x/6 + 48/6 = (x+42)/6 - 18/6

2x = 42 - 18 - 48

2x = -48

x = -24

A direct variation is a proportionality relationship in which two quantities follow a direct relationship.

An INEQUALITY is a statement which shows that two quantities are not equal or may not be equal. If two quantities are not equal, then one is greater than the other.

≥ (greater than or equal to) means at least that amount or more.

≤ (less than or equal to) means at most that amount or less.

To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Please click the image to view the graph

6x + 2y > 10

Replace the input variable in the formula with the value provided.

Calculate the result.

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Answer:

Let's call the number of diners at the Italian restaurant x, and the number of diners at the Mexican restaurant y. We can set up the following system of equations to represent the problem:

Italian restaurant: $20 + 2x = $30 + $1y

Mexican restaurant: $30 + $1y = $20 + 2x

Subtracting $20 from both sides of the first equation and $30 from both sides of the second equation, we get:

Italian restaurant: 2x = $10 + $1y

Mexican restaurant: $1y = $10 + 2x

Multiplying both sides of the first equation by 1/2, we get:

x = $5 + $0.5y

Substituting this expression for x in the second equation, we get:

$1y = $10 + 2($5 + $0.5y)

Expanding the expression on the right side, we get:

$1y = $10 + $10 + $1y

Subtracting $1y from both sides, we get:

0 = $10

This equation is true, so the system of equations is consistent.

Since the total donations from each restaurant would be the same, we can set the total donations equal to each other and solve for the number of diners at each restaurant. The total donation from the Italian restaurant is $20 + 2x, and the total donation from the Mexican restaurant is $30 + $1y. Setting these expressions equal to each other, we get:

$20 + 2x = $30 + $1y

Subtracting $20 from both sides and $1 from both sides, we get:

2x - 2 = $10 + $1y - $1

Combining like terms on both sides, we get:

2x - 2 = $10 + $1y - $1

2x - 2 = $9 + $1y

2x - $9 - $1y = 2 - $9

2x - $1y = -$7

Dividing both sides by 2, we get:

x - $0.5y = -$3.5

Substituting this expression for x in the first equation, we get:

$20 + 2(-$3.5) = $30 + $1y

Simplifying the expression on the left side, we get:

$20 - $7 = $30 + $1y

Subtracting $20 from both sides, we get:

-$7 = $10 + $1y

Subtracting $10 from both sides, we get:

-$17 = $1y

Dividing both sides by -1, we get:

$17 = -$1y

Multiplying both sides by -1, we get:

-$17 = $1y

Dividing both sides by $1, we get:

-$17/$1 = $1y/$1

Simplifying the expression on the left side, we get:

-17 = y

Thus, the number of diners at the Mexican restaurant is -17, and the number of diners at the Italian restaurant is x = $5 + $0.5y = $5 + $0.5(-17) = $5 - $8.5 = -$3.5.

Since the number

Answer:

The first way is rectangular. You also converted it wrong for the first one. the inches aren's squared. you're converting regular inches into regular feet, instead it should be square inches into square feet.

And Ping is sewing a square tablecloth, not a rectangular one. you have to add the 9 inches on both sides, not just one. You can convert it either way you want, but you have to add the 9 inches to both.

The equation of circle will be;

⇒ x² + y² = 25

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle with the center at the origin and which passes through the point (4,-3).

Now,

Since, The center of circle = (0, 0)

And, The point passes through the circle = (4, - 3)

We know that;

The equation of circle with center (0, 0) and radius 'r' is,

⇒ x² + y² = r²

Here, The circle with the center at the origin and which passes through the point (4,-3).

Hence, The radius is distance between the (0, 0) and (4, - 3).

So, We get;

⇒ r = √(4 - 0)² + (- 3 - 0)²

⇒ r = √ 16 + 9

⇒ r = √25

⇒ r = 5

Thus, The equation of circle with Centre (0, 0) and radius '5' is,

⇒ x² + y² = 5²

⇒ x² + y² = 25

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If the unknown value y varies inversely with the cube of x and when x = 4 ,then y = 1. then, if x = 1 the value of y equals to 1/64.

What do you mean by inversely proportional?

When two values are inversely proportionate, or when an increase in one causes a reduction in the other and vice versa, this relationship is referred to as inverse proportionality. Direct proportion is in opposition to it. Alternatively, if one variable is directly proportional to the reciprocal of the other, they are said to be inversely proportional.

As given in the question, the unknown value y varies inversely with the cube of x.

It means,

[tex]\frac{y}{x^3} = constant[/tex]

Putting the values as,

When x=4 , then y=1

constant = 1/64

Putting this value is constant in above equation,

1/64 = y/x³

1/64 = y/1

y = 1/64

Hence, the value of y = 1/64.

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"Fail to reject the null hypothesis" is the correct conclusion for the test.

We have given that,

a P-value of 1.018943 is calculated on a hypothesis test with significance level set at 0.01.

That means p-value is greater that significance level.

And we know that if p-value is greater than significance level then the effect is statistically not significant. There is no enough evidence to reject the null hypothesis.

A p-value greater than 0.01 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected.

High p-value indicates that your evidence is not strong enough to suggest an effect exist in the population. An effect might exist but it's possible that the effect size is too small, that sample size is too small or there is too much variability for the hypothesis test to detect it.

Therefore "Fail to reject the null hypothesis" is the correct conclusion for the given test.

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Answer:

I think it's 1428 : 2499

Step-by-step explanation:

1428 divided by 4 = 357

7 times 357 = 2499

Basically you have to balance both ratios to get the correct answer.

The time period the projectile at least 160 feet above the ground is 2 sec to 5sec.

What is time period?

The duration of time that a behavior lasts or a condition persists. Depending on the type of activity or situation under consideration, it may be measured in seconds or in millions of years.

Given function that represents height of the projectile above the ground is s feet is s = - 16t² + 112t.

To find the time period is the projectile at least 160 feet above the ground, make an inequality:

- 16t² + 112t  ≥ 160

Subtract 160 from both sides:

- 16t² + 112t - 160 ≥ 0

Divide both sides by 16:

- t² + 7t - 10 ≥ 0

- t² + 2t + 5t - 10 ≥ 0

-t(t -2) + 5(t - 2) ≥ 0

(t - 2)( -t+ 5) ≥ 0

Either, t - 2 ≥ 0 → t ≥ 2

or, -t + 5  ≥ 0 → t ≤ 5

2 ≤ t ≤ 5

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Answer:

Step-by-step explanation:

The correlation coefficient is a measure of the strength and direction of the relationship between two variables. It ranges from -1 to 1, with -1 indicating a strong negative relationship, 0 indicating no relationship, and 1 indicating a strong positive relationship.

To find the correlation coefficient in this case, you can use the formula:

correlation coefficient = (slope * standard deviation of Y) / standard deviation of X

Plugging in the values you provided, we have:

correlation coefficient = (1.25 * standard deviation of Y) / standard deviation of X

The value of the correlation coefficient depends on the standard deviations of Y and X, which you have not provided. Without these values, it is not possible to calculate the correlation coefficient.

complete analysis (carrying out steps A-H in section 4.4 from the Stewart textbook)

results as The graph of f(2) = et te is a straight line with a y-intercept of 1.

A) f(2) = et te

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers

Step B) Find any x-intercepts:

x-intercepts: None

Step C) Find any y-intercepts:

y-intercept: f(0) = e0te = 1

Step D) Find any vertical asymptotes:

Vertical asymptotes: None

Step E) Find any horizontal asymptotes:

Horizontal asymptote: None

Step F) Find any points of inflection:

Points of inflection: None

Step G) Find any symmetry:

Symmetry: None

Step H) Sketch the graph:

The graph of f(2) = et te is a straight line with a y-intercept of 1.

B) f(x) = tan-(+)

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers except -π/2, π/

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The equations are given whose graphs enclose a region. when the area of the region is 301.5

The given function is f(x) and g(x), we need to calculate the area.

A = ₐ∫ᵇ (f(x) + g(x)) dx

A = ₀∫³ (x² + 15(x + 5)) dx

A = ₀∫³ (x²dx  + ₀∫³15(x + 5)) dx

A =  (x³/3) + 15x²/2 + 75x

A = ₀[x³/3]³ + ₀[15x²/2 + 75x]³

A = [(3 - 0)³/3] + [15(3 - 0)²/2 + 75(3 - 0)]

A = 27/3 + 15(9/2) + 75(3)

A = 9 + 15(4.5) + 7

A = 76.5 + 225

A = 301.5

Therefore, the equations are given whose graphs enclose a region. when the area of the region is 301.5

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Answer:

Step-by-step explanation:

The vertex form of a quadratic function is given by the equation f(x) = a(x - h)² + k, where (h, k) is the coordinates of the vertex of the parabola, and a is a constant coefficient.

To find the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7, we can first use the formula for the x-coordinate of the vertex of a quadratic function, which is given by h = -b / 2a. In this case, the quadratic function is f(x) = x² + 8x + 7, so b = 8 and a = 1. Plugging these values into the formula, we get:

h = -8 / 2(1) = -4

Therefore, the value of h is -4.

Next, we can use the formula for the y-coordinate of the vertex of a quadratic function, which is given by k = f(h) = a(h - h)² + k. In this case, we know that the value of h is -4, and we can plug this value into the original quadratic function to get the value of k:

k = f(-4) = (-4)² + 8(-4) + 7 = 16 - 32 + 7 = -9

Therefore, the value of k is -9.

Finally, we can use the equation f(x) = a(x - h)² + k to find the value of a. Since we know that the coordinates of the vertex are (-4, -9) and the equation of the quadratic function is f(x) = x² + 8x + 7, we can plug these values into the equation to solve for a:

f(x) = a(x - h)² + k

x² + 8x + 7 = a(x - (-4))² + (-9)

We can then distribute the squared term and simplify the equation to get:

x² + 8x + 7 = a(x² - 8x + 16) + (-9)

x² + 8x + 7 = a(x²) - 8a(x) + 16a + (-9)

We can then collect like terms to get:

x² + 8x + 7 = a(x²) - 8ax + 16a - 9

Comparing the coefficients of the x², x, and constant terms on both sides of the equation, we can see that a = 1.

Therefore, the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7 are a = 1, h = -4, and k = -9.

To find the equivalent expression, we can simplify the fraction by using the rule for exponents that says that when we divide two powers with the same base, we can subtract the exponents. Using this rule, we get:

(8^(-10)) / (8^4 * 8^0) = 8^(-10) / 8^4 = 8^(-10+4) = 8^(-6)

So the equivalent expression is: 1/8^6 = 8^(-6)

The correct answer is: 1 divided by 8 raised to the fourteenth power = 8^(-6)

To find the equivalent expression for the fraction 8^(-10)/8^4*8^0, we can use the property of exponents that states that any number raised to the power of 0 is equal to 1. Therefore, 8^0 is equal to 1.

Using the quotient rule of exponents, which states that when dividing two powers of the same base, we can subtract the exponents, we can simplify the expression to:

8^(-10)/8^4*8^0 = 8^(-10)/8^4 * 1 = 8^(-6).

Therefore, the equivalent expression to 8^(-10)/8^4*8^0 is 8^(-6). The correct answer is therefore 1 divided by 8 raised to the fourteenth power, or option A.

Answer: 6

Step-by-step explanation: To solve we first start by adding like terms in our equation which is 30 + 54 = x(5+9) which becomes 84=x(14). Now we need to isolate the x variable by dividing both sides by 14.

x(14) ÷ 14 = x, 84 ÷ 14 = 6

This leaves us with the answer x = 6

Linear, polynomial, and quadratic functions can be both increasing or decreasing functions. Exponential function is monotonically increasing function. The derivative of a function may be used to determine whether the function is increasing or decreasing. Exponential functions eventually exceed all other increasing functions.

Function, in mathematics, refers to an expression or rule that describes a relationship between two or more variables. A function is said to be an increasing function when the y-value increases as the x-value increases and vice versa. In order to determine whether the function is increasing or decreasing, the derivative of a function may be used on any intervals in its domain.  If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. From the given function options, Exponential functions eventually exceed all other increasing functions as the one of variable is in the exponential leading an exponential increase and not a constant increase.

Note: The question is incomplete. The complete question probably is: From the following, Which functions are increasing? How to know if a function is increasing or decreasing?; Which section of the function is increasing?; Which type of increasing function eventually exceeds all other increasing functions? A) linear B) exponential C) polynomial D) quadratic.

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From the given sequences following are the arithmetic sequences :

1. 3, 7, 11, 15, 19

5. 1, 1/2, 0, -1/2

7. 1, 0, -1, -2, -3

10. 9.5, 7.5, 5.5, 3.5, ...

As given in the question,

Arithmetic sequences are :-

1) yes, because the difference between the terms is same.

7 - 3 = 11-7 = 15 -11 = 4

5)yes, because the difference between the terms is same.

1/2 -1 = 0 -1/2 = -1/2 -0 = -1/2

7)yes, because the difference between the terms is same.

0 - 1 = -1 -0 = -2 -(-1) = -1

10)yes, because the difference between the terms is same.

7.5 - 9.5 = 5.5 - 7.5 = 3.5 -5.5 = -2

Difference between consecutive terms of these sequences are not equal . so these are not arithmetic sequences :-

2,3,4,6,8, 9

Arithmetic sequence

In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 .. is arithmetic because the difference between consecutive terms is always two.

Therefore, the arithmetic sequences are :

1. 3, 7, 11, 15, 19

5. 1, 1/2, 0, -1/2

7. 1, 0, -1, -2, -3

10. 9.5, 7.5, 5.5, 3.5, ...

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The coordinates of point C are (-5.5, 3.2)

Coordinates:

A coordinate is a set of numbers that describes a point in a specific space. It is used to pinpoint a location, whether on a map, a graph, a plane, or in a three-dimensional space. In 2-D space, coordinates are usually written in the form (x, y), where x indicates the horizontal position and y is the vertical position of the point. In 3-D space, a third coordinate (z) is needed to specify the depth. Coordinates are also used to identify points on a graph. Finally, coordinates can be used to define a plane in three-dimensional space, where 3 coordinates are needed to define the plane’s position.

Given,

(x,y) = (x + 4.5, y -6.2)

So,

(x + 4.5, y -6.2) = (-1,-3)

Therefore;

x + 4.5 = -1

= -1 - 4.5

= -5.5

y - 6.2 =  -3

= - 3 + 6.2

= 3.2

hence, the coordinates of point C are (-5.5, 3.2)

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Answer:

  2093pi/90 cm

Step-by-step explanation:

You want the exact length of the arc subtended by a 182° central angle in a circle of radius 23 cm.

The length of an arc of a circle is given by ...

  s = rθ

where θ is the central angle in radians.

The radian measure of an angle of 182° is ...

  182°(π/180°) = 91π/90 . . . . radians

Then the arc length is ...

  s = (23 cm)(91π/90) = 2093π/90 cm

Answer:

Only I

Step-by-step explanation:

I. √36 > 5

√36 = 6

6 > 5

Its true

II. 7 < √10

√10 = 3.16 approximately

Hence, 7 > √10

But 7 < √10 is wrong

III. √(17 - 8) > √(17 + 8)

√(17 - 8) = √9 = 3

√(17 + 8) = √25 = 5

√(17 - 8) < √(17 + 8)

But, √(17 - 8) > √(17 + 8) is wrong

Answer:

1.) √36 > 5

Step-by-step explanation:

1.) √36 > 5

= 6 > 5( it is true because 6 is greater than 5)

2.) 7 < √10

= 7 < 3.16 ( it is false because 7 is greater than 3.16)

3.)√17–√8 > √17 + √8

= 4.12 – 2.82 > 4.12 + 2.82

= 1.3 > 6.94( it is false because 6.94 is greater than 1.3)

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