Two parallel lines are cut by a transversal, as shown. If m 21 = 114°, what is m 22?


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a. Correlation coefficient, r. =0.76751

b. Linear regression line y=6.5071+1.3929x

c. mean amount of sugar when temp. is 1.7

  then y=8.87503

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.

According to linear regression, sales are predicted to equal 168 + 23 advertising when using advertising as the predictor variable. This means that if spending on advertising is increased by one million euros, sales should grow by 23 million euros, and if no advertising was done, sales should be 168 million euros.

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Using the trigonometric function of sine, the value of x is 10.1 units

From the given right triangle

The length of the hypotenuse = 16 units

The given angle = 39 degrees

The opposite side of the angle = x units

Here we have to use the trigonometric functions

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

Use the equation of sin θ

Substitute the values in the equation

Sin 39 = x / 16

x = 16 × sin 39

x = 10.1 units

Therefore, the value of x is 10.1 units

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x=7/6

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To turn the specified limit, which is a Riemann sum, within the known interval, [2, 6], and variable, [tex]x_i[/tex], to a definite integral, the value, Δx is dx as n approaches infinity, to get;

[tex]\displaystyle \lim\limits_{n\to \infty}\sum\limits^n_{i=1}x_i\cdot \ln \left(1+x_i^2 \right) \Delta x, [2, \,6] = \int\limits^6_2 {x\cdot \ln \left(1+x_i^2 \right)} \, dx[/tex]

A Riemann sum is an approximation of an integral, which is the area of a region, by making use of the sum of simplified slices that make up the region.

A definite integral is a calculation used to find the area under a graph of a function by making use of very small or infinitesimal stripes of the region under the graph of the function.

The expression in the question is a Riemann sum

[tex]\lim\limits_{n \to \infty} \sum\limits_{i=1}^n x_i\cdot ln \left(1 + x_i^2 \right) \Delta x, [2, 6][/tex]

The Riemann sum can be converted into a definite integral, using the equation, [tex]\displaystyle{\lim\limits_{n \to \infty} \sum\limits_{i=1}^n f(x_i)\Delta x = \int\limits^b_a {f(x)} \, dx }[/tex]as follows;

The value of Δx is the value which values in the parenthesis are multiplying on the left, therefore; Δx is replaced with dx, as n → ∞

The limits of the Riemann sum in the question = [2, 6]

[tex]f(x_i) = x_i \cdot \ln\left(1 + x_i^2 \right)[/tex], therefore, [tex]f(x) = x \cdot \ln\left(1 + x^2 \right)[/tex]

Plugging in the the above values into the expression for the Riemann sum, we get the following definite integral;

[tex]\displaystyle{\lim\limits_{n \to \infty} \sum\limits_{i=1}^n x_i\cdot \ln \left(1 + x_i^2 \right) \Delta x, [2, 6] = \int\limits^6_2 {x\cdot \ln\left(1 + x^2\right)} \, dx[/tex]

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The price of the pipette for company A and company B will be $480 and $420, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A research facility supervisor was keen on purchasing another pipette. Organization A was selling 2 pipettes for £300 not as much as Organization B was selling 3 pipettes for. For a solitary pipette, Organization A was more costly by £60 than Organization B.

Let 'x' be the price of the pipette of company A and 'y' be the price of the pipette of company B. Then the equations are given as,

2x = 3y - 300         ...1

x = y + 60                 ...2

From equations 1 and 2, then we have

2(y + 60) = 3y - 300

2y + 120 = 3y - 300

y = 420

Then the value of x is given as,

x = 420 + 60

x = 480

The price of the pipette for company A and company B will be $480 and $420, respectively.

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Answer: 9

Step-by-step explanation:

The factors of the given expression 54a⁴ +16ab³ are (C) 2a(27a³+8b³).

Writing a number or other quantitative item as the result of numerous factors—typically smaller or easier objects of the same kind—is known as factorization or factoring in math.

For instance, the equation x2 - 4 and the integer 15 can both be multiplied by the number 3 5.

So, we got the expression:

54a⁴ +16ab³

Now, factorize as follows:

54a⁴ +16ab³

Both 54 and 16 are multiples of 2 and have variables as common:

2a(27a³ + 8b³)

Therefore, the factors of the given expression 54a⁴ +16ab³ are (C) 2a(27a³+8b³).

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114/9 > √150 that is, 114/9 is greater than √150

Given,

We have to compare √150 and 114/9 using  <, >, or =

Comparison between two numbers;

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than."

Here,

First we have to find the value of √150 and 114/9

That is,

The value of √150 = 12.25

The value of 114/9 = 12.66

Therefore,

We came to know that 114/9 is greater than √150 that is, 114/9 > √150

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Answer:

x = 4

Step-by-step explanation:

2x + 1 ≥ 0

2x ≥ -1

2/2 x ≥ -1/2

x ≥ -1/2

√(2x+1)² = (4-1)²

2x + 1 = 3²

2x = 9 - 1

2x = 8

2/2 x = 8/2

x = 4

Answer:

5.73

Step-by-step explanation:

I solved it by just multiplying and adding. I didn't use pemdas so it might be wrong and if it is I'm sorry..

Clark will have $5820.80 in his account when he turns 22.

With an example, what is compound interest?

The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.

Clark reportedly placed $5000 at a constant 3.8% interest rate when he was 18 years old.

Using the compound interest calculation, we can calculate how much Clark will make when he turns 22.

[tex]A=P . e^{rT}[/tex]

A= Amount after T years.

P= Principal amount.

e= Mathematical constant e.

r= Interest rate (in decimal form).

T=  Time in years.

Let's decimalize the interest rate we've been given.

3.8 percent = 3.8/100 = 0.038

When we enter our provided values into the formula above, we will obtain,

[tex]A=5000 * e^{0.038(22-18)} \\A=5000*e^{0.038(4)}\\A=5000*e^{0.152}\\A=5000*1.1641\\A=5820.80[/tex]

Clark will therefore have $5820.80 in his account when he turns 22.

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Answer: 20/100 or 1/5 (reduced)

Step-by-step explanation: To find the fraction, it is helpful to write a proportion. So. if we know every # will be out of 100, we can infer that it will be our whole (can also be represented by being written as 1 ) So now, if we move the decimal 2 places, we now have our fraction 20 out of 100. You can reduce this by dividing the 20 by 20 and the 100 by 20, to get 1/5. I hoped this helped.

The value of the MN is 4 according to the assumption on the number line.

According to the statement

We have to find that the value of the MN with the help of the value of the x.

So, For this purpose, we know that the

A number line is a horizontal line that has equally spread number increments.

Now,

Assuming that L, M, and N are points on a number line with L < M < N,

According to the assumption, the equation become

2x + x+1 = 7

3x +1 =7

3x =6

x = 2.        

Now, the value of the MN become:

MN = 2x

MN = 2*2

MN = 4.

So, The value of the MN is 4 according to the assumption on the number line.

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Answer:

y = 3/4x - 1

Step-by-step explanation:

4x + 3y = 7

3y = -4x + 7

y = -4/3x + 7/3

The slope of the given line is -4/3 so the slope of a line perpendicular to it is 3/4 (negative reciprocal).

y = 3/4x + b

Substitute x = 4 and y = 2:

2 = 3/4(4) + b

2 = 3 + b

b = -1

Thus the final equation is y = 3/4x - 1

Answer:

Below

Step-by-step explanation:

x - y = 8     find slope of this line , parallel slope is the same

 re-arrange the given line equation to y = mx + b form (m= slope)

y = (1) x-8    has slope = 1

Answer:10

Step-by-step explanation:3/5x10=6

Answer:

Step-by-step explanation:

13

Answer: 13

Step-by-step explanation:

I hope it helps

Answer:

  yes

Step-by-step explanation:

You want to know if a function can have the characteristic that the limit at a point does not exist, but the function is defined at that point.

A function has no limit at a point if the limit from the left is different from the limit approaching from the right.

Consider the sign function ...

  [tex]\text{sign}(x)=\begin{cases}-1,&x < 0\\0,&x=0\\1,&x > 0\end{cases}[/tex]

The left limit as x → 0 is -1; the right limit as x → 0 is +1, so the limit as x → 0 "does not exist." However, the function is defined at x=0.

The function is defined everywhere, but the limit as x→0 does not exist.

The measurements of the figures that should be equal in order for the ratio of volumes between the volumes of the cone, sphere, and cylinder of 1:2:3 to be true is; The radius and the height

A ratio is a comparison between the magnitudes or measurements of items, expressing the number of times one item in the ratio is contained within another item in the ratio.

The formula for the volume of a cone, [tex]V_p[/tex] is, [tex]V_p[/tex] = (1/3)·π·r₁²·h₁

The formula for the volume of a sphere, [tex]V_s[/tex], is [tex]V_s[/tex] = (4/3)·π·r₂³

The formula for the volume of a cylinder, [tex]V_c[/tex], is [tex]V_c[/tex] = π·r₃²·h₃

The ratio of the volumes in the question is 1:2:3

Therefore; The volume of the sphere is twice the volume of the cone, and the volume of the cylinder is three times the volume of the cone, which indicates;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁...(1)

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁...(2)

Equation (1) indicates that we have;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁

Where, h₁ = 2·r₂, we get;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·(2·r₂) = (4/3)·π·r₁²·r₂

Therefore; r₁ = r₂, and the diameter of the sphere is equal to the height of the cone

The radius of the cone is equal to the radius of the sphere

Equation (2) indicates;

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁ = π·r₁²·h₁

Therefore;

r₃²·h₃ = r₁²·h₁

r₃ = r₁

h₃ = h₁

The radius of the cone = The radius of the cylinder

The height of the cone = The height of the cylinder

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The solution for this system of linear equations are x=-18 y=-71

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: 3x+2y=1

                  −x+5y=−23

[tex]\left[\begin{array}{ccc}3&2\\-1&5&\\\end{array}\right][/tex]  . [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]  = [tex]\left[\begin{array}{ccc}1\\-23\\\end{array}\right][/tex]

                      [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]   =   [tex]\left[\begin{array}{ccc}5&1\\-2&3&\\\end{array}\right][/tex] . [tex]\left[\begin{array}{ccc}1\\-23\\\end{array}\right][/tex]

                       [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-18\\-71\\\end{array}\right][/tex]

Hence, The solution for this system of linear equations are x=-18 y=-71

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Answer: y = -5/6x - 23/6

(Read the explanation first to make sure it's correct)

Step-by-step explanation:

A parallel line means that it has the same slope as the equation:

5x + 6y = 11

Let's first convert this standard form equation into slope-intercept form:

y = -5/6x + 11/6

So that means that our new line also has a slope of:

-5/6

So far, for our new equation we have:

y = -5/6x + b

Next, let's plug in the values of our point to the equation:

-3 = 5/6 + b

So b = -23/6

So the equation in slope-intercept form is:

y = -5/6x - 23/6

The following equation are perpendicular to each other .

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, perpendicular lines have slopes that are the opposite of the reciprocal of each other.

Hence,

The equation perpendicular to y = 1 / 3 x + 4 is  y = -3x - 4.

The equation perpendicular to y = 2 / 5 x - 7 is  y = - 5 / 2 x + 7.

The equation perpendicular to y = - 5 / 2 x + 8 is  y = 2 / 5 x - 6.

The equation perpendicular to y = -2x + 6 is  y = 1 / 2 x + 3.

The equation perpendicular to y = 7 / 5 x - 9 is  y = - 5 / 7 x - 11.

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Answer:

The slope of a line parallel to the line with slope m=3/4 is also m=3/4. Parallel lines have the same slope.

Answer:

C. 7°F

Step-by-step explanation:

The equation that calculates the number of scoops of ice cream that can be purchased is 0.20x = 5, and the number of scoops that can be purchased is 25.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The definition of an equation is algebra is a mathematical assertion that shows the equality of two mathematical equations.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, we know that 1 scoop of ice cream is $0.20.

Anna wants to purchase scoops for $5.00.

Let, the number of scoops is x.

Now, form the equation as follows:

0.20x = 5

x = 5/0.20

x = 25

Therefore, the equation that calculates the number of scoops of ice cream that can be purchased is 0.20x = 5, and the number of scoops that can be purchased is 25.

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Answer:

height = 4cm

Step-by-step explanation:

volume of right-circular cylinder = πr²h

h = r

so

πr²r or πr³

πr³ = 64π

r³ = 64

r = 4

h = 4

The solution is, 12000 pound was the ball's actual weight.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While on vacation in Missouri, Sue's family stopped to see the world's largest ball of nylon twine.

Before they got there, Sue predicted the ball would weigh 6,000 pounds.

Her prediction was 50% less than the actual weight of the ball.

let, the ball's actual weight = x

now, 50% of x = x/2

ATQ, x/2 = 6,000 pounds.

so, x = 12000

Hence, The solution is, 12000 pound was the ball's actual weight.

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Answer: It takes more five to reach that answer

Step-by-step explanation:

For a given t-value is 1.67 in an upper-tailed test , the interval below that contains the p-value is 0.05487.. So, the correct option is option (d) .

Values are given as,

test- statistic , t-value = 1.67

degree of freedom = 21

Using upper tailed test,

Using EXCEL function to find the p-value:

Function : =T.DIST.RT (t-value , deg -freedom)

Settings : =T.DIST.RT (1.67 , 21) = 0.05487

We used only positive value to find the upper tailed p-value .

lower tailed p-value ,

Settings : =T.DIST.RT ( - 1.67 , 21) = 0.94516

So, 0.05 < p-value < 0.95.. The interval value of p-value for upper tailed test is 0.005..

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The distance from the lighthouse is 64 ft and the distance from Maya to the lighthouse is 56 ft

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

Height of lighthouse = 48 ft

Height of Maya = 6 ft

Using the above parameters and the attached figure, we have the following equivalent ratio

48 : x = 6 : 8

Multiply the second ratio by 8

So, we have

48 : x = 48 : 64

This means that

x = 64

From the figure, we have

y + 8 = x

Recall that

x = 64

So, we have

y + 8 = 64

Evaluate

y = 56

Hence, the distance is 56 ft

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