Determine the measure of the interior angle at vertex E.

The required value of 'a' in the equation of proportionality is 32.

What is direct proportion?

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

It is symbolised by the proportional sign ∝.

For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x & y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant.

Given, a = 8b

When b = 4 then

So, a = 8*4 = 32

Hence, the required value of 'a' in the equation of proportionality is 32.

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josh is 3 years older than 4 times kim's age. the sum of their ages is less than 43. inequality for the situation, then the oldest age kim could be.

4k + 3 < 43

k < 10

We are given that Josh is 3 years older than 4 times Kim's age. We can express this as 4k + 3, where k represents Kim's age. We are told that the sum of their ages is less than 43, so we can write this as an inequality: 4k + 3 < 43. To find the oldest age Kim could be, we can solve this inequality for k. To do this, we subtract 3 from both sides, giving us 4k < 40. Finally, we divide both sides by 4, giving us k < 10. Therefore, the oldest age Kim could be is 10.

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Answer:

I believe the answer is 5

Step-by-step explanation:

Answer: -6

Step-by-step explanation:

(0,y)

at y intercept, x is 0. therefore sub x with 0 and solve

y= 3(0)-12/0+2

= -12/2

=-6

Answer:

$3.78

Step-by-step explanation:

To find the new price of the speaker after the sale, you can use the following formula:

New price = (1 + discount percentage) * (original price - discount amount)

In this case, the discount percentage is 40%, or 0.4, and the discount amount is 40% of the original price, or 0.4 * $4.50 = $1.80. Plugging these values into the formula, we get:

New price = (1 + 0.4) * ($4.50 - $1.80)

= 1.4 * $2.70

= $3.78

So the new price of the speaker after the sale and the subsequent price increase is $3.78.

Cylinder's volume = πr^2h = π(5 cm)^2(10 cm) = 785.398 cm^3 and Hemispherical top's volume = 2/3πr^3 = 2/3π(5 cm)^3 = 523.598 cm^3

a) To calculate the volume of the cylinder, we need to use the equation for the volume of a cylinder, which is πr^2h, where π is pi, r is the radius, and h is the height. In this case, the radius is 5 cm and the height is 10 cm, so the equation becomes π(5 cm)^2(10 cm) = 785.398 cm^3.

b) To calculate the volume of the hemispherical top, we need to use the equation for the volume of a hemisphere, which is 2/3πr^3, where π is pi and r is the radius. In this case, the radius is 5 cm, so the equation becomes 2/3π(5 cm)^3 = 523.598 cm^3.

Cylinder's volume = πr^2h = π(5 cm)^2(10 cm) = 785.398 cm^3

Hemispherical top's volume = 2/3πr^3 = 2/3π(5 cm)^3 = 523.598 cm^3

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(a) The total score of Jesse's card is 1

(b) The value of each of the two cards can either be 0 or cards with different signs

In the question,

(a) Jesse's card are 3 , -5 , 9 and -6

We have to find the total

You should know that,

Adding a positive integer is like addition but adding a negative integer is like subtraction

So, Total score = 3 + (-5) + 9 + (-6)

=> 3 - 5 + 9 - 6

=> 1

Jesse's total score is 1

(b) Jesse has picked two cards which are not affecting her total score

So, either he got two zeroes or two cards with opposite signs with same magnitudes

Like 1 and -1 etc.

The two doesn't affect his score because their effect got cancelled out

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The coordinates after the reflection of the points will be(7, -3).

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse.

Given that, (-7,3) is reflected across the x-axis, and then the y-axis.

When reflected across x-axis, it will be (-7, -3)

And again when reflected across y-axis it will be (7, -3)

Hence, The coordinates after the reflection of the points will be(7, -3)

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R is equivalence relation and cl (-7) = cl(5)

cl (-6) = cl (0)

cl (-2) = cl(1) = cl(4) = cl( 7)

A reflexive, symmetric, transitive binary connection is an equivalence relation. One such illustration of an equivalence relation is the relation of equipollence between line segments in geometry.

demonstrate the equivalence of R. We must demonstrate

1). reflexive

x +2x = 3x and 3/ 3x  = 3/x +2x

(x,x) ∈ R

R is reflexive

2). symmetric

let (x,y )  ∈ R

x + 2y = 3a for some a ∈ R

consider y +2x = y + 2(3a - 2y)

6a - 3y = 3(2a - y) = 3k

3/y +2x

so (y,x)  ∈ R

R is symmetric

3). transitive

(x,y) and (y,x) ∈ R

3/x+2y and 3/y+2x

x+2y =3a and y +2x = 2b for some a,b

consider x+2z = 3a - 2y + 2 (3b-y/2)

3a +3b -3y

3(a+b-y)

3/x+2z

(x,z) ∈ R

R is tansitive

so R is equivalence relation

b).S = (-7, -6, -2,0,1,4,5,7)

cl (x) = { y∈ z , x∈ y }

cl (x) = {y∈ z , x +2y = 3a}

cl (x) =  {y∈ z , y = 3a - x /2}

cl (-7) = {y∈ z , y = 3a +7  /2}

cl (-7) = cl(5)

cl (-6) = cl (0)

cl (-2) = cl(1) = cl(4) = cl( 7)

R is equivalence relation

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If you graph a linear characteristic you may get a immediately line. There also are nonlinear functions. If you graph the coordinates of a nonlinear characteristic you may now no longer get a immediately line.

One of the very best ways (however now no longer the handiest way) to differentiate among a linear and a nonlinear characteristic is to have a take a observe the graph of the characteristic.

A linear equation is an equation with  variables whose graph is a line. The graph of the linear equation is a hard and fast of factors withinside the coordinate aircraft that every one are answers to the equation. If all variables constitute actual numbers you can graph the equation via way of means of plotting sufficient factors to understand a sample after which join the factors to encompass all factors.

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The expression that is the same as sin⁻¹ x is (b) arcsin x

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

sin^-1 x

When this expression is rewritten, we have the following representation

sin⁻¹ x

The above expression is pronounced as arc-sin of x

And it can be represented as

arcsin x

This means that the equivalent expression of the given expression is (b) arcsin x

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The equation in slope-intercept form would be; y = 5x + 33

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given that line passes through points (-8, – 7) and (-6, – 3).

Now we will write in slope-intercept form,

y = m x + b .

Now to find m, we use the formula;

m = y₂ - y₁ / x₂ - x₁

Then,

m = { -3 - (-7)} / { 6 - (-8)}

m = 4 / 14

m = 2/7

Thus, y = 5x +33

Therefore,  its equation in slope-intercept form would be; y = 5x + 33

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Answer:

[tex]\boxed{0}[/tex]

_________________________________________________________

For degrees, coterminal angle formula is: θ ± 360 * n For radians, coterminal angle formula is: θ ± 2π * n In the above formulas, n refers to a multiple of full rotations, which equals to 360 degrees or 2π.

⇒ θ ± 360

⇒  θ ± 2π

⇒ 0 360 degrees or 2π.

Therefore, your answer is 0

_____________________

Hope this helps!

Please mark me brainless!

Answer:

x≈33.36

Step-by-step explanation:

The marks on the lines mean they are the same lenth, that means the other two angles are both 29 degrees. Because triangle angles add up to 360, we can add the two 29 degree angles and subtract them from 360 to get the angle of the equation. From here we can solve to find x.

[tex]29+29=58[/tex]

[tex]360-58=302[/tex]

[tex]11x-65=302\\[/tex]

[tex]11x=367[/tex] (add 65 on both sides)
[tex]x[/tex]≅[tex]33.36[/tex] (divide 11 on both sides)

Answer:

  -1

Step-by-step explanation:

You want to evaluate (8x -5) for x = 1/2.

Put the value where x is in the expression, then do the arithmetic.

  8x -5 = 8(1/2) -5

  = 4 -5

  = -1

The value of the expression is -1.

Answer:

$1.25

Step-by-step explanation:

150 / 120

Answer:

$1.25

Step-by-step explanation:

You can find the average cost per coconut by dividing the total price by the number of coconuts. 150 divided by 120 is $1.25. Therefore, each coconut costs $1.25.

The formula for the volume of a circular cone:

If the height(h) of the circular cone is given then,

V = 1/3 * π * r² * h

If the slant height(l) of the circular cone is given then,

V = 1/3 * π * r² * √(l² - r²)

the volume of a cone if the height is 10 cm and the diameter is 6 cm is 94.25 cubic centimeters

We know that a right circular cone has a circular base with the apex above the center of the base.

For a right circular cone, with radius r and height h

The formula for the volume of a right circular cone is,

V = 1/3 * π * r² * h

We need to find the the volume of a right circular cone with a circumference.

We know that circumference C = 2πr

From circumference we find the radius of circular base.

Then using the formula for the volume of a right circular cone, we find the volume.

The volume of a circular cone:

If the height(h) of the circular cone is given then,

V = 1/3 * π * r² * h

If the slant height(l) of the circular cone is given then,

V = 1/3 * π * r² * √(l² - r²)

Now we need to find the the volume of a cone if the height is 10 cm and the diameter is 6 cm

From diameter, the radius of the circular base of the cone would be,

r = 6/2

r = 3 cm

also, h = 10 cm

So, V = 1/3 * π * 3² * 10

V = 94.25 cu.cm.

Therefore, the volume of a cone if the height is 10 cm and the diameter is 6 cm is 94.25 cubic centimeters

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None of the solutions are appropriate since the result of the equation z + (z+6) will be equal to 2z + 6.

A mathematical expression is the result of combining a number of mathematical symbols with an arithmetic operator, a variable, and a constraint.

In a different sense, expression is highly helpful in identifying the root or end value of a constraint.

for instance, 3x + 5y

The expression restriction is denoted by the symbols = or, >.

Given the phrase,

z + (z+6)

opening the bracket

z + z + 6

⇒ 2z + 6

Hence

"2z + 6 will be the value of the equation z + (z+6)."

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The simplest definition of point-slope form is a line equation expressed using a single line point and the line's slope.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.

An equation for a line stated using a single point on the line and the line's slope is a straightforward definition of point-slope form.

The slope is defined as the rise over run, or the proportion of the change in the y values over the change in the x values, and the point form is denoted by the letters (x,y).

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$2256000 is the top rate paid the previous year.

percentage, a relative value indicating hundredth parts of any quantity.

Given that top rate paid one year for a 30 - second TV ad during the Super Bowl was 6% greater than the previous year's top rate.

If the new top rate paid was $2.4 million then we need to find the top rate paid the previous year.

Convert 6% to the decimal by dividing with 100 is 0.06

0.06×2400000

144000

Now subtract 144000 from 2.4 million.

2400000-144000

2256000

Hence, the top rate paid the previous year is $2256000.

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The expression that represents her overall change in depth is given as follows:

-10 + 10.

The changes in depth are represented using integer numbers, as follows:

Liz dives 10 feet below the surface of the water, hence the integer number is of:

-10.

Then she returns to the surface, that is, moving 10 feet in the direction of the surface, hence the integer number is given as follows:

10.

Then the addition operation that represents her overall change in depth

-10 + 10.

Which has a result of zero, as she finished at the same place that she started.

The problem is given by the image shown at the end of the answer.

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Abby will choose $2,400 every quarter for 4 years.

Abby will have $30455.65  if she invests at 6% compounded quarterly

What is interest rates?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

The formula of compounded quarterly is

A = P ( 1 + r/n)^(4t)

P = Principal =  $24,000

n = 4

r = rate of interest = 6% = 0.06

t = time = 4 years

Putting the value of P, r, t in the formula of compounded quarterly:

A = 24000 ( 1 + 0.06/4)^(4×4)

A = 30455.65.

Future Value of an Ordinary Annuity

[tex]S = R[\frac{(1+i)^n-1}{i} ][/tex]

Where

S is the future value;

R is the periodic payment;

i is the interest rate per period;

n is the number of periods.

The value of R is $2,400, i = 0.06/4 = 0.015

n = (4 × 4) = 16

[tex]S = 2400[\frac{(1+0.015)^{16}-1}{0.015} ][/tex]

S = 43037.69

Abby choose: $2,400 every quarter for 4 years.

Abby will have $30455.65  if she invests at 6% compounded quarterly.

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Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To determine the probability of each of the five smallest y values, we can use the probability of each possible outcome and the number of ways that outcome can occur.

P(y = 1) = probability that the first component is defect-free = 0.8

P(y = 2) = probability that the first component is defective and the second component is defect-free = (1 - 0.8) * 0.8 = 0.16

P(y = 3) = probability that the first two components are defective and the third component is defect-free = (1 - 0.8) * (1 - 0.8) * 0.8 = 0.032

P(y = 4) = probability that the first three components are defective and the fourth component is defect-free = (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * 0.8 = 0.0064

P(y = 5) = probability that the first four components are defective and the fifth component is defect-free = (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * 0.8 = 0.00128

We can see that the probability of each y value is simply the probability of the previous y value multiplied by (1 - 0.8) = 0.2. This means that the probability distribution of y is given by the formula P(y) = 0.2^(y - 1) * 0.8.

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Answer:

Below

Step-by-step explanation:

The probability of Z    given Y  would be

      7  out of (15+7) = 7/22

The average value of the trigonometric equation f(x) = - 2 · sin x + 5 · cos x over the interval [π, 2π] is equal to 2 / π.

In this question we find the definition of a trigonometric equation consisting in the sum of two trigonometric functions on a given interval [a, b], of which we must determine its average value by means of the following integral equation:

[tex]m = \frac{1}{b - a} \cdot \int\limits^b_a {f(x)} \, dx[/tex]

Where:

First, write the entire trigonometric equation and the bounds of the interval:

f(x) = - 2 · sin x + 5 · cos x, a = π, b = 2π

Second, obtain the result of the integral equation:

[tex]m = -\frac{2}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\sin x} \, dx + \frac{5}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\cos x} \, dx[/tex]

[tex]m = \frac{2}{\pi}\cdot \cos x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex] + [tex]\frac{5}{\pi}\cdot \sin x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex]  

m = (2 / π) · (cos 2π - cos π) + (5 / π) · (sin 2π - sin π)

m = (2 / π) · (1 - (- 1)) + (5 / π) · (0 - 0)

m = 2 / π

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The value of x will make on similar to SRQ by the SSS similarity theorem is 25.

From the figure :

NM = 10

SR = 20

NO = 8

QR = x

SAS Similarity Theorem:

states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

NO/NM = SR/QR

substitute the values

8/10 = 20/x

cross multiplication

8x = 200

dividing both sides by 8

x = 25

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Full question :

What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?What value of will make the triangles similar by the similarity theorem?; How do you find similar triangles in SSS?; How do you find the value of X that makes triangles similar?

Answer:

x=−10,y=−5

Step-by-step explanation:

The Remainder in the Synthetic division is three, for given problem

1 |__1___2__-3__3 is 3.

So, the correct option is option(c).

The Synthetic Division:

It is defined as the method of dividing the polynomial by the binomial is known as the synthetic division. It stands for polynomial division. Here, the division principle is performing in the coefficient of the polynomial.

We have given that the synthetic division is

1 |__1___2__-3__3

We find out the remainder in the synthetic division :

Multiply the carry-down value (i.e 1) by the test zero on the left, and carry the result(i.1×1 = 1) up into the next column inside:

1 | 1 2 -3 3

|______________

1

Add down the column( 2+1 = 3) :

1 | 1 2 -3 3

|____1_________

1 3

Multiply the previous carry-down value (i.e 3) by the test zero, and carry the new result up into the last column:

1 | 1 2 -3 3

|____1____3____

1 3 0

1 | 1 2 -3 3

|____1____3___0_

1 3 0 3

three, last carry-down value is the remainder.

Therefore, the remainder is 3. The option c is correct.

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Complete question:

What is the remainder in the synthetic division problem below?

a. 6

b. 4

c. 3

d. 5

Points (0,200) and (200,0) fall outside of the feasible region hence they cannot be the optimal solution.

For the given condition,

Points are (48,84), (0,120), (0,0), (90,0)

The objective function is,

maximize 4X + 10Y

Take point (48, 84), here X = 48 and Y = 84

Substitute values in the objective function equation as shown below;

Z = 4 * 48 + 10 * 84

  = 1032

For point (0,120)

Z = 4 * 0 + 10 * 120

  = 1200

For point (0,0)

Z = 4 * 0 + 10 * 0 =0

For point (90,0)

Z = 4 * 90 + 10 * 0

  = 360

The value of the objective function is maximum at point (0,120). Its value is 1,200.

The viable region does not include points (0,200) and (200,0), hence they cannot be the best option.

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