Janet is making chocolate chip cookies. One batch of chocolate chip cookies needs of a cup of sugar. Janet wants to make three batches of chocolate chip cookies.
Part A
How many total cups of sugar will Janet need to make three batches of chocolate chip cookies? Show your answer in lowest terms.

Part B:
Janet has 4 cups of sugar. How much sugar will she have left over after making three batches of chocolate chip cookies?

you should mix 4.5 quarts of 100% juice and 1.5 quarts of 20% juice. a=4.5, b= 1.5

The US liquid quart is equivalent to two liquid pints, or one-fourth US gallon (57.75 cubic inches, or 946.35 cubic centimetres), and the US dry quart is equivalent to two dry pints, or 1/32 bushels (67.2 cubic inches, or 1,101.22 cubic cm). 32 ounces, 2 pints, 4 cups, and 14 gallon are all equivalent to one US liquid quart. When converting any dry component, keep in mind that a dry quart is equivalent to 4.6546 cups. A quarter gallon is equal to one quart in English (symbol: qt). The liquid and dry quarts of the US customary system and the imperial quart of the British imperial system are the three types of quarts now in use. They all generally measure one litre.

Let you should mix a quarts of 100% juice and b quarts of 20% juice.

[tex]a+b=6[/tex]

100%a+20%b=6*8%

By solving the system of equation.

a=4.5

b= 1.5

So you should mix 4.5 quarts of 100% juice and 1.5 quarts of 20%.

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The slopes are :- -5, 1/3, -1/5, undefined, 1/4, -2/3, -1, -1, -2/3 and -5/2

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Given are the equations of the lines, we need to find the slope of the equation,

The general equation of a line is given by,

y = mx + c, where m is the slope and c is the y-intercept of the line.

So, finding slope of given equations by comparing them with the general equation,

1) y = -5x-1

m = -5, slope = -5

2) y = x/3-4

m = 1/3, slope = 1/3

3) y = -x/5-4

m = -1/5, slope = -1/5

4) x = 1,

Since, x=1 is a vertical line, the slope is undefined.

5) y = x/4+1

m = 1/4, slope = 1/4

6) y = -2x/3-1

m = -2/3, slope = -2/3

7) y = -x+2

m = -1, slope = -1

8) y = -x-1

m = -1, slope = -1

9) 2x+3y = 9

Converting into slope-intercept form,

2x+3y = 9

3y = -2x+9

y = -2x/3+3

m = -2/3, slope = -2/3

10) 5x+2y = 6

Converting into slope-intercept form,

5x+2y = 6

2y = -5x+6

y = -5x/2+3

m = -5/2, slope = -5/2

Hence, the slopes are :- -5, 1/3, -1/5, undefined, 1/4, -2/3, -1, -1, -2/3 and -5/2

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The expression is equivalent to 9250.

Scientific notation is a way of writing very large or very small numbers in the powers of 10.

Given is the expression -

92.5 x 10²

We can write the expression as -

92.5 x 10²

925/10 x 100

925 x 10

9250

Therefore, the expression is equivalent to 9250.

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{

Question in english -

what is 92.5 × 10 times the power of 2​

}

Answer:

Below

Step-by-step explanation:

y/40 = 5/8    multiply both sides of the equation by 40

y = 40 * 5/8 = 200/8 = 25

The total size downloaded for both versions was 3840 MB.

Number is a mathematical object used to count level and measure it is the fundamental concept in mathematics and used in many different way number can be used to represent anything from quantities of object to ideas and concept additionally number are used to describe relationship between different object or concept number are also used to represent position in space as well as represent the time graph of table.

Since the size of the high-quality version was 4.5 MB, the total size downloaded for the high-quality version was 4.5 MB x 3 = 13.5 MB. Therefore, the total size downloaded for the standard version was 3840 MB - 13.5 MB = 3826.5 MB. Since the size of the standard version was 2.5 MB, the number of downloads for the standard version was 3826.5 MB / 2.5 MB = 1530.6. Rounding to the nearest whole number, the number of downloads for the standard version was 1531.

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The percentage of the race he finished first is 40%

A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Glenn raced his motorcycle 30 times and he finished first 12 times.

So, 12/30 = 2/5 = x/40

by using cross multiplication we get,

⇒ 5 * x = 2 * 100

⇒ 5 * x = 200

divided both side by 5 we get,

⇒ 5 * x / 5 = 200 / 5

⇒ x = 40

So that the percentage of the race he finished first is 40%

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Answer:

Step-by-step explanation:

(2.75m / min) x 60

= 0.04359 gallons / hour

(sorry if im wrong xd)

Without the actual values of b0 and b1, it is not possible to determine the predicted explanatory value. The correlation coefficient alone does not give enough information to make this prediction.

To find the predicted explanatory value that gives an average response value of 150, you would need to use the regression equation.

The regression equation takes the form:

y = b0 + b1x

where y is the response variable, x is the explanatory variable, b0 is the y-intercept, and b1 is the slope.

To find the x value that gives you a y value of 150, you would rearrange the equation as follows:

x = (y - b0)/b1

Plug in 150 for y and the y-intercept and slope values from your regression analysis to find the predicted explanatory value.

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Answer:

5.625

Step-by-step explanation:

4.5/0.8 = 5.625

The equation P(t) = A - Bexp(-ct) can be used to model a worker's productivity after t hours on the job, where A, B, and c are positive constants.

We can then define the change in productivity over a brief period of time dt as

where P(t) is the productivity at time t. We can assume that dP(t) is negative because productivity is assumed to decrease over time.

As a result, the equation can be written as dP(t)/dt = -cP(t), or it can be rewritten as P(t) = Aexp(-ct), where A is a constant. P(t) = A - Bexp(-ct) can be obtained by adding a constant B to the right side of the equation to account for the fact that productivity can never be negative.

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Answer:

4

Step-by-step explanation:

1/2x + 8 ≤10 / ×2

x + 16 ≤ 20

x ≤ 20 - 16

x ≤ 4

[tex]\dfrac{1}{2} x+8\leq 10[/tex]

Subtract 8 from both sides:

[tex]\dfrac{1}{2} x+8-8\leq 10-8[/tex]

[tex]\dfrac{1}{2} x\leq 2[/tex]

Multiply both sides by 2:

[tex]2\times(\dfrac{1}{2} x)\leq 2\times(2)[/tex]

[tex]\boxed{x\leq 4}[/tex]

Answer:

24

Step-by-step explanation:

The equivalent expressions are:

a) 4*(x + 2) = 4x + 8

b) 4*(2x + 3) = 8x + 12

c) (6 + 8)*x = 14*x

d) 6*(x + y + z) = 6x + 6y + 6z

This is a property of the multiplication, and it says that we can distribute products in the following way:

A*(B + C) = A*B + A*C

So let's do that.

a) 4*(x + 2) = 4*x + 4*2 = 4x + 8

b) 4*(2x + 3) = 4*(2x) + 4*3

                    = 8x + 12

c) (6 + 8)*x = 6*x + 8*x = 14*x

d) 6*(x + y + z) = 6x + 6y + 6z

These are the equivalent expressions.

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Answer:

354.294 cu ft

Step-by-step explanation:

4*3*1.5 = 18 cube yard *27³ = 354.294 cu ft

you have to multiply 27 three times because every side of the shed 4, 3, 1.5 yards  equals to 4*27 ft, 3*27 ft, 1.5*27 ft

Answer:

229 Feet I think it is right just make sure

Step-by-step explanation:

x+125/255=x/165

cross multiply

255x=165x+20,625

90x=20,625

229=x

Assuming a binomial distribution for the number of auto accidents. If 7 in 10 auto accidents involve a single vehicle, the probability, p =[tex]\frac{7}{10}[/tex] = 0.7

Then the probability that the accident involved multiple vehicles is

q = 1 - p = 1 - 7/10 = 3/10 = 0.3

Since 14 accidents are randomly selected, n = 14

The formula for binomial distribution is expressed as

P(x = r) = nCr × q*(n - r) × p*r

a) we want to determine P(x = 4) =

P(x = 4) = 14C4 × [tex]0.3^{10}[/tex] × 0.7^4

P(x = 4) = 0.00142

b) we want to find P(x lesser than or equal to 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P( x = 4)

P(x = 0) = 14C0 × [tex]0.3^{14}[/tex] × 0.7^0 = 0.00000004783

P(x = 1) = 14C1 × [tex]0.3^{13}[/tex] × 0.7^1 = 0.00011

P(x = 2) = 14C2 × [tex]0.3^{12}[/tex] × 0.7^2 = 0.00002

P(x = 3) = 14C3 ×[tex]0.3^{11}[/tex]  × 0.7^3 = 0.00022

P(x = 4) = 0.00142

P(x lesser than or equal to 4) = 0.00000004783 + 0.00011 + 0.00002 + 0.00022 + 0.00142 = 0.00177

c) p = 0.7, q = 0.3

P(x = 5)= 14C5 × 0.7^(14 - 5) × 0.3^5 = 0.19631

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Answer:11x

Step-by-step explanation:

(−6x−2)+(6x2−5x−10)

first solve whats inside the brackets.

=-6x-2+(12-5x-10)

=-6x-2+(2-5x)

then open the brackets and solve the rest using order of operations.

=-6x-2+2-5x

=11x

There are 64 ways to choose a single class representative.

To find the total number of ways to choose a single class representative, we add the number of students in each college: 18 students from the College of Liberal Arts and Social Sciences, 19 students from the College of Education, and 27 students from the College of Science and Health.

This gives us a total of 18 + 19 + 27 = 64 students. To choose a single class representative, we can choose any one of these 64 students, so there are 64 ways to choose a single class representative.

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so hmmm let's call the points A(-10 , 5) and B(8 , 2) and the point "C" partitions them, so

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-10,5)\qquad B(8,2)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-10,5)=1(8,2)[/tex]

[tex](\stackrel{x}{-20}~~,~~ \stackrel{y}{10})=(\stackrel{x}{8}~~,~~ \stackrel{y}{2}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-20 +8}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{10 +2}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ -12 }{ 3 }~~,~~\cfrac{ 12}{ 3 } \right)\implies C=(-4~~,~~4)[/tex]

The solution is, the circumference of the circle with radius 14in. is  87.96 inch.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the radius = r = 14 inch.

we know,

circumference = 2*pi* r

so, calculating we get,

circumference = 87.96 inch.

Hence, The solution is, the circumference of the circle with radius 14in. is  87.96 inch.

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The domain and range of the relation is

Domain = {1, 2, 3, 4, 5}

Range = {3, 5, 7, 9}

Option D is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

{(1, 3), (2, 5), (3, 7), (4, 9), (5,9)}

It is in ordered paired as (x, y).

x-coordinate is the domain and the y-coordinate is the range.

So,

Domain = {1, 2, 3, 4, 5}

Range = {3, 5, 7, 9}

Thus,

Domain = {1, 2, 3, 4, 5}

Range = {3, 5, 7, 9}

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The graph of the function is added as an attachment

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

y = √x +3-6

Make y the subject

y =√(x + 3) - 6

The above equation is a square root function

The parent of a square root function is represented as

y = √x

This means that the parent function was translated to get the given function

Next, we plot the graph of the equation

See attachment for the graph

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Answer:

2.14x10^12=  Two and fourteen hundredths times ten to the second power

                  OR

14x10^2   = Fourteen times ten to the second power

Is that a 2.14 or 14?

This function satisfies the conditions given: it is an nth-degree polynomial with real coefficients, it has zeros at -1, 4, and 4 + 4i, and it has the value of -150 at x = 1.

A polynomial is a mathematical expression that is composed of variables and coefficients, which are combined using only addition, subtraction, and multiplication. The variables in a polynomial can be raised to whole number powers, and the highest degree of a polynomial (i.e., the highest power to which a variable is raised) is known as the degree of the polynomial. For example, the polynomial 3x^2 + 2x + 1 has a degree of 2. The terms in a polynomial are usually arranged in descending order of degree, so that the first term has the highest degree and the last term has a degree of zero. The sum or difference of two or more polynomials is also a polynomial.

To find an nth-degree polynomial function with real coefficients that satisfies the given conditions, we can use the following process:

1. Write the polynomial in factored form using the zeros:

p(x) = a(x-1)(x-4)(x-(4+4i))(x-(4-4i))

2. Use the value of f(1) to find the leading coefficient a:

f(1) = p(1) = a(0)(0)(0)(0) = -150

a = -150

3. Write the polynomial in expanded form:

p(x) = -150(x-1)(x-4)(x-(4+4i))(x-(4-4i))

The resulting polynomial function is:

p(x) = -150(x-1)(x-4)(x-(4+4i))(x-(4-4i))

This function satisfies the conditions given: it is an nth-degree polynomial with real coefficients, it has zeros at -1, 4, and 4 + 4i, and it has the value of -150 at x = 1.

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The cost of the car leasing for 1 month is $31.25.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of the car leasing for 24 months = $750

Cost of the car leasing for 1 month.

= 750 ÷ 24

= $31.25

Thus,

The monthly cost of car leasing is $31.25.

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The complete question:

Keely is looking at leasing a car for 24 months in order to lease the car she needs to give the dealership $750.

Find the monthly charge for leasing the car.

The rate is 150 square meters per hour. Then the area of the oil spill after 2 hours will be 300 square meters.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

An oil spill spreads 25 square meters every 1/6 hour. Then the number of square meters in each hour is given as,

Rate = 25 / (1/6)

Rate = 25 x 6

Rate = 150 square meters per hour

The area of the oil spill after 2 hours will be given as,

⇒ 150 x 2

⇒ 300 square meters

Thus, the area of the oil spill after 2 hours will be 300 square meters.

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the Probability of 0.04 and would warrant a refund.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.84mm and a standard deviation of 0.35mm.

probability = P(X<0.24)

= (Z<(0.24-0.84)/0.35)

= P(Z<(-1.7143)

= 0.0432 ~ 0.04

since the above probability is less than 0.05 ;

this event can be termed unusual

therefore, the Probability of 0.04 and would warrant a refund.

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Answer:

Step-by-step explanation:

35% of 255 = 89.25

255-89.25 =165.75