Read the description of a proportional relationship. Ever since Brian was a small child, his favorite food has always been carrots. He likes them so much he wants to plant a garden in his backyard just to grow carrots. There is a proportional relationship between the size of Brian's garden (in square feet), x, and the number of carrots he can grow at a time, y. The equation that models this relationship is y=4x. What size garden does Brian need to grow 20 carrots at a time?

15x² - 10 = 0 is a quadratic equation which has complex solutions.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. There should be two solutions to quadratic equations. If you think about the discriminant formula, two roots can be real, equal, or imaginary.

Given,

Quadratic equation:

15x² - 10 = 0

15x² = 10

x² = 10/15

Roots:

x = ±√10/15

15x² - 10 = 0 is a quadratic equation which has complex solutions.

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The solution of the system of equations is x = 1 and y = -1.

What is a two-variable linear equation?

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equivalent to zero, it then is said to be a linear equation in 2 factors. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

SOLUTION TO WORK OUT

the equations are resolved

8x + 3y = 5 & 3x − 2y = 5

EVALUATION

The equations in the given system are

8x + 3y = 5 - - - - - - - (1) (1)

3x − 2y = 5 - - - - - - - (2) (2)

Equation 1's two sides multiplied by two gives us

16x + 6y = 10 - - - - - - (3) (3)

Equation 2's two sides are multiplied by three to get

9x - 6y = 15 - - - - - - (4) (4)

Equation 3 and Equation 4 together give us

25x = 25

⇒ x = 1

Equation 1 is completed when x = 1.

8 + 3y = 5

⇒ 3y = 5 - 8

⇒ 3y = - 3

⇒ y = - 1

FINAL RESPONSE

Consequently, the needed answer is x = 1 and y = - 1.

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The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

Given that,

In just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

We have to find how many weeks are there in a pound.

A rate is a ratio that is utilized to compare the quantities of several commodities. A unit rate is a rate with one as the denominator. Whenever a rate's denominator, such as the price per unit of a certain number of items, is not 1.

So, we can write has

This is the fraction of the number of pounds and number of weeks.

=30pounds / 12 weeks

=2.5 pounds

Therefore, The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

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Considering the expression of a line, the equation of the line that passes through the points (-9,-7) and (-11,-6) is the equation of the line is y= -1/2x -23/2.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of a line can be calculated as:

m= (y₂ - y₁)÷ (x₂ -x₁)

Substituting the value of the slope m and the value of one of the points in y=mx +b, the value of the "b" can be obtained.

Being (x₁, y₁)= (-9, -7) and (x₂, y₂)= (-11, -6), the slope m can be calculated as:

m= (-6 - (-7))÷ (-11 -(-9))

m= (-6 +7)÷ (-11 +9)

m= (1)÷ (-2)

m= -1/2

Considering point 1 and the slope m, you obtain:

-7= (-1/2)×(-9) + b

-7= 9/2 +b

-7 -9/2= b

-23/2= b

Finally, the equation of the line is y= -1/2x -23/2.

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Answer:

See the picture below

Step-by-step explanation:

The probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.

The cumulative distribution function of X is:[tex]F(x)= 1- 10/x[/tex]  ( for x > 10)

X = the entire lifespan of a definite type of electronic device in hours, then the probability function of X,

here we use the cumulative distribution function, which is used to specify random variables,

F(X)= 1 - 10/X is cumulative distribution function,

then the probability that at least 3 devices will work for 15 hours

P(X[tex]\geq[/tex]15)= 1- P(X<15)

            = F(15)

            = 1- 10/15

            =5/15

            =0.333

Hence, the probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.

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Based on the concept of unitary method, the amount of time he spent on the bicycle is 5.6 hours.

Unitary method:

Unitary method is used for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

Jim began a 182​-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 5 hours.

Here we need to find the amount of time he spent on the bicycle if Jim walks at a rate of 4 miles per hour and rides at 40 miles per​ hour.

Let us consider x be the hours on the bike for distance 40x miles.

We know that, he spent 5 - x hours walking for distance 4(5 - x) miles or it can be written as

=> 20 - 4x

And we also know that those two, 40x and 20 - 4x, add to 182 miles

=> 40x + 20 - 4x + 182

=> 36x + 202

=> 36x = 202

=> x = 5.6

And the units calculation is m/h*h=m

If the value of x = 5.6 hours on the bike for 139.5 miles, then 5 - x =0.6 hours walking for 4 miles.

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To determine the degree measure of one angle of a 30-sided regular polygon.

The degree measure of one angle of a 30 sided regular polygon is 168°​.

What is a regular polygon?

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.

The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.

We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is

(Side - 2) × 180°

(30 - 2) × 180°

= 5040°

Measure of each angle of 30-gon

= 5040°/30

= 168°​

Thus, the degree measure of One angle of a 30 sided regular polygon is 168°​

Hence the answer is, The degree measure of one angle of a 30 sided regular polygon is 168°​.

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Given trigonometric expression in algebraic form would be,

cos(arcsin(x - h/r)) =  ± [√(r² - (x - h)²)]/r

In this question, we need write the expression in algebraic form.

Given trigonometric expression is cos(arcsin(x - h/r))

Let y = arcsin(x - h/r)

so, sin(y) = (x - h)/r

By trigonometric identity,

sin^2(y) + cos^2(y) = 1

we have cos(y) = ±√(1 - sin²y)

cos(arcsin(x - h/r)) = ±√[1 - ((x - h)/r)^2]

                             = ± [√(r² - (x - h)²)]/r

Therefore, given trigonometric expression in algebraic form would be,

cos(arcsin(x - h/r)) =  ± [√(r² - (x - h)²)]/r

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If the perimeter of the parallelogram is 102 feet, then the value of m is 12.75

The perimeter of the parallelogram = 102 feet

The perimeter of the parallelogram = 2(l + w)

Where l is the length and w is the width of the parallelogram

The length of the parallelogram = 3m

The width of the parallelogram = m

Substitute the values in the equation of the perimeter

102 = 2(3m + m)

102 = 2(4m)

102 = 8m

m = 102 / 8

Divide the terms

m = 12.75

Hence, if the perimeter of the parallelogram is 102 feet, then the value of m is 12.75

The complete question is:

The perimeter of the parallelogram is 102 feet. Find m. Write your answer as a decimal or mixed number.

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Answer:

1: Supplementary angle; x = 95

2: Complementary angle; x = 31 [(2x-3)+x]

3: vertical angle; x = 90

4: supplementary angle; x = 92 [x+(x-4)]

Step-by-step explanation:
1: 180-85 = 95 (x)

2: (2x-3)+x = 90 evaluates into x = 31

3: all sides are equal so if one side is 90 then the rest are

4: x+(x-4) = 180 evaluates into x = 92

Let me know if you need any more help.

The side of the cube is 6 cm.

What is the Volume of a prism?

The area that a prism takes up is referred to as its volume. A prism is a solid, three-dimensional structure with two identical faces and additional faces that resemble parallelograms. It is a polyhedron whose nomenclature is influenced by the various basic forms. Every prism has a particular base, whether it be a triangular prism (triangular base), square prism (square base), rectangular prism (rectangular base), pentagonal prism (pentagonal base), hexagonal prism (hexagonal base), or an octagonal prism (octagonal base). Consequently, because a prism is a three-dimensional form, its volume likewise exists in a three-dimensional plane. Prisms are measured in terms of their volume in cubic meters, cubic millimeters, cubic inches, or cubic feet. Following are the steps to calculate the prism's volume:

Write down the prism's dimensions as specified in step one.

Step 2: Use the formula V = B H to calculate the prism's volume. V, B, and H stand for the prism's volume, base area, and height, respectively.

Step 3: After obtaining the volume of the prism's value, add the unit of prism volume at the conclusion (in terms of cubic units).

In the question, we have given that:

Prism is made up of 120 equal cubes;

The volume of the prism is 25, 920[tex]cm^{3}[/tex];

So, we can equate the volume of 120 equal cubes with the prism's volume;

⇒ 120 × [tex](a)^{3}[/tex] = 25, 920;

⇒[tex](a)^{3}[/tex] = [tex]\frac{25920}{120}[/tex]

⇒[tex](a)^{3}[/tex] = 216;

So, the value of a is 6 cm;

That is the side of the cube is 6 cm;

Hence, The side of the cube is 6 cm.

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Answer:  6  -3  

Step-by-step explanation: i just took the test

Answer:

(-6,3) (5,-9)

Step-by-step explanation:

Answer:

A- the slope is -4 and y-intercept is 3

Step-by-step explanation:

The standard form is y=mx+c (for straight line graph) while m is slope(gradient) and c is y-intercept.

So, slope is -4 and y-intercept is 3

Answer:

Step-by-step explanation:

A total of 640 cubes of 3cm size can fit into a box with internal dimensions of 54, 40, and 8 cm.

By using volume, et’s assume that ’n’ cubes can be cut out from the cuboid. The volume of n cubes will be equal to the total volume of the cuboid.

The volume of 1 cube of side 3 cm is (3)^3 = 27 c.c. [volume of a cube of side 'a' is (a)^3]

Now, the volume of cuboid from which the cubes will be cut is 54 X 40 X 8 = 17280 c.c. [volume of a cuboid is length X breadth X height].

Now, the number of cubes that can be cut out from the cuboid (n) = (volume of cuboid)/(volume of 1 cube) => n = 17280/27 = 640.

Hence, a total of 640 cubes of side 3cm can beput into a box which had internal measurement of 54cm 40cm and 8 cm

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The dimensions of the rectangle are length and width are 6 and 11.6      respectively.

L = 3w - 11 ,

where,

L = length of the rectangle and

W =width of the rectangle

A=LW

Here A is Area of the Rectangle which is product of its dimensions i.e., length and breadth.

LW = 42

substituting for l:-

(3W-11)W= 42

3W^2 - 11W - 42 = 0

(3W + 10)(W - 6) = 0

W = 6 or -10/3  (ignore the negative root)

So the width is 6 and the length is 70/6= 11.6

The rectangle's length and width are therefore 6 and 11.6, respectively.

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Answer:

25 & 37

Step-by-step explanation:

The option that could be the diameter of a baseball used by a professional baseball team is A. 2 7/8 inches.

From the information, the baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches.

In this case, 2 7/8 inches to decimal is 2.875

2 7/9 inches will be 2.778

2 8/10 will be 2.8

2 9/11 inches will be 2.818

Therefore, the correct option is A as it fits tye value given.

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Complete question

A baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches. which of the following could be the diameter of a baseball used by a professional baseball team?

A. 2 7/8 inches

B 2 7/9 inches

C 2 9/11 inches

D. 2 8/10 inches.

The equation, 4 - 0.25g + 0.5h, will be evaluated as equal to: 4.

To evaluate an equation, plug in the values of the variables in the equation and solve to get the simplified value.

Given the equation, 4 - 0.25g + 0.5h, where:

g = 10

h = 5

Substitute g = 10 and h = 5 into the equation 4 - 0.25g + 0.5h, then evaluate:

4 - 0.25(10) + 0.5(5)

Simplify

= 4 - 2.5 + 2.5

= 4 + 0

= 4

Therefore, if g = 10 and h = 5, the equation 4 - 0.25g + 0.5h, is evaluated as: 4.

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The Question:

Evaluate 4 - 0.25g + 0.5h when g = 10 h = 5.

a. The functions are classified as follows:

b. The functions are given as follows:

c. She should purchase Car 1, as it will have a higher value in nine years.

The functions are classified depending if there is an equal factor or an equal difference between consecutive terms, as follows:

Hence the functions in this problem are classified as follows:

Hence the functions are given as follows:

After nine years, the values are as follows:

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Answer:

That's right

Step-by-step explanation:

[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=6.4 \end{cases}\implies 6.4=ab^2\implies \cfrac{6.4}{b^2}=a \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} x=5\\ y=409.6 \end{cases}\implies 409.6=ab^5\implies \stackrel{\textit{substituting from the 1st equation}}{409.6=\left( \cfrac{6.4}{b^2} \right)b^5} \\\\\\ 409.6=6.4b^3\implies \cfrac{409.6}{6.4}=b^3\implies 64=b^3\implies \sqrt[3]{64}=b\implies \boxed{4=b} \\\\\\ \cfrac{6.4}{b^2}=a\implies \cfrac{6.4}{4^2}=a\implies \boxed{0.4=a}~\hfill {\Large \begin{array}{llll} y=0.4(4)^x \end{array}}[/tex]

The Simplify the expression is -10, when we use fraction.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=-5(∛27 *2)/3

=-5(3*2)/3

=-5(6)/3

=-10

Hence the answer will be -10 simplify the expression.

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The dimensions of the cylinder will be r = 8.92 cm and h = 17.86 cm.

What is dimensions ?

Dimensions refer to the length or width of an area, region, or space in one direction.

Main Body:

Volume of cylinder = πr²h

Surface area = 2πr² + 2πrh

Given surface area = 1500 cm²

1500 = 2πr²+2πrh

h= (750/πr)-r   ----(1)

V= πr²{(750/πr)-h}

V =750r - πr³

V' = 750- 3πr²

Put V' =0

0 = 750 - 3πr²

r≈ 8.92 cm

substituting the value of r in equation (1)

we get h= 17.86 cm

Hence the dimension of cylinder are r = 8.92 cm and h = 17.86 cm

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The side length of a single cube will be 6 centimeters.

The volume of the cube will be -

V = (a x a x a) cubic units

We have the volume of Prism as V[P] = 25920 cm³ which is made up of [n] = 120 cubes of the same volume.

The volume of a single cube will be -

V[c] = V[P]/n

V[c] =  25920/120

V[c] = 216 cm³

Volume of a cube = V[c] = (a x a x a)

Equating volume, we get -

a³ = 216

a = 6 cm

Therefore, the side length of a single cube will be 6 centimeters.

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the probability that each of the four players is dealt exactly one ace is about 0.11. this means that in a very large number of bridge deals, the percentage of deals on which each player has one ace will be very close to 11%

The probability of each of the four players is dealt exactly one ace is about 0.11

so,

the probability is always approximately the corresponding percent obtained for very large samples.

Hence it means that in a very large number of bridge deals, the percentage of deals on which each player has one ace will be very close to 11%

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Variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out to clustered together. The purpose for measuring variability is to obtain an objective measure of how the scores are spread out in a distribution

Variability also measure how accurately individual score or sample represent the entire population

When the standard deviation is 0 , the scores have no variability.

Variability describes how far the data points are from each other and from the center of the distribution. In addition to measures of central tendency, measures of variability provide descriptive statistics that summarize the data.

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