Patty rolls a six-sided number die 120 times. How many times should she expect to roll a
prime number?

Answer:

1. 4x(x + 1)(x + 4)

2. 2x²(3x + 8)(2x - 1)

3. 2(x + 5)(5x - 1)

Answer:

yes, 3:4

Step-by-step explanation:

The ratio of the side lengths is 6:8 and 18:24 both of which simplify to 3:4

Answer:

-21, -16, 4, 9

Step-by-step explanation:

-3: f(-3) = 5(-3)-6 = -15-6 = -21

-2: f(-2) = 5(-2)-6 = -10-6 = -16

2: f(2) = 5(2)-6 = 10 - 6 = 4

3: f(3) = 5(3)-6 = 15 - 6 = 9

The instantaneous rate of change at the left endpoint is f'(a) = cos(a), and at the right endpoint is f'(b) = cos(b).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the average rate of change of the function f(x) = sin(x) over a given interval, we need to determine the difference in the function values at the endpoints of the interval divided by the difference in their corresponding x-values.

Let's denote the left endpoint as "a" and the right endpoint as "b". The average rate of change (AROC) is given by:

AROC = (f(b) - f(a)) / (b - a)

Since the function is f(x) = sin(x), the AROC becomes:

AROC = (sin(b) - sin(a)) / (b - a)

To compare the average rate of change with the instantaneous rates of change at the endpoints, we need to calculate the derivative of the function and evaluate it at the endpoints.

The derivative of f(x) = sin(x) is f'(x) = cos(x).

Therefore, the instantaneous rate of change at the left endpoint is f'(a) = cos(a), and at the right endpoint is f'(b) = cos(b).

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Answer: 1. 64 | 2. 32

Step-by-step explanation:

Formula for a rectangle is Area = Length*Width

Therefore: 8*8 = 64

Formula for a triangle is Area = 1/2*Base*Height, which is also 1/2*length*width

Therefore: 1/2*8*8 = 32

Hope this helps :)

Answer:

40 quarts

Step-by-step explanation:

one gallon is 4 quarts, so ten gallons would be 40.

4(quarts) x 10(gallons) = 40(number of quarts in the 10 gallons)

d. cylinder a frozen juice can suggests the geometric solid of a cylinder due to its cylindrical shape with circular bases and a curved surface.

A frozen juice can typically has a cylindrical shape, characterized by its circular base and curved sides. The cylindrical shape is suggested by the can's structure, with a constant radius and height throughout.

To further explain, a cylinder is a geometric solid that has two congruent circular bases connected by a curved surface. The frozen juice can perfectly fits this description, as it has a circular lid and bottom, and its sides are formed by the curved surface connecting the two circular bases. The cylinder is known for its uniform cross-section, constant radius, and constant height, which are also present in the frozen juice can.

a frozen juice can suggests the geometric solid of a cylinder due to its cylindrical shape with circular bases and a curved surface.

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The type of problem being solved is an estimation problem. This is because the aim of the problem is to estimate the mean cookie weight. The mean weight will provide an estimate of the weight of cookies produced by the new baking machine. So, it's clear that the kind of problem being solved is an estimation problem.

What is an estimation problem?

An estimation problem is a problem that involves the estimation of a parameter based on a sample statistic. The objective of estimation problems is to calculate the most likely value of the population parameter by using the sample statistic. The sample statistic is a measurable attribute of a random sample from a population, whereas the population parameter is a numerical value that describes the population as a whole. The population parameter can be a mean, standard deviation, proportion, or any other numerical value of interest. Therefore, estimation problems are designed to make a prediction about a population by analyzing a sample.

Therefore, the kind of problem being solved here is an estimation problem.

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The solution to the inequality expression given as x + 2 < 5 is x < 3

Inequality expressions refer to statements in mathematics that use symbols like <, >, ≤, or ≥ to compare two values.

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

x + 2 < 5

Subtract 2 from both sides of the inequality expression

So, we have the expression below

x + 2 < 5 - 2

Evalaute the like terms

x < 3

This means that, the solution is x < 3

The graph of the inequality is added as an attachment

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The absolute deviation of the data set 7 10 14 and 20 is 4.25.

What is the mean deviation method?

When calculating the average departure from the mean value of a particular data set, statisticians employ a measure known as the mean deviation. Following the steps below will make it simple to determine the mean deviation of the data values.

In statistics, the term "deviation" refers to the discrepancy between the observed value of a data point and its expected value. As a result, mean deviation, also known as mean absolute deviation, is the typical departure of a data point from the mean, median, or mode of the data collection.

data set is 7, 10, 14, 20,

Mean = m = 51/4 = 12.75

So the MAD is 1/4 |7-12.75| |10-12.75| |14-12.75| 20-12.75|

MAD = 17/4 = 4.25

Hence the mean absolute deviation of the data set 7 10 14 and 20 is 4.25.

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Answer: 81

Step-by-step explanation: If you add all of the numbers, then you end up getting 81.35 and 81.35 estimated to the nearest whole number is 81 because that's the closest whole number to 81.35.

Answer:

We can use equivalent ratios to solve this problem.

We know that 3 pounds of potatoes makes 8 servings of mashed potatoes.

This can be expressed as a ratio: 3 pounds of potatoes : 8 servings of mashed potatoes

We can use this ratio to find the number of servings of mashed potatoes that 12 pounds of potatoes would make.

To do this, we'll keep the ratio of potatoes to servings of mashed potatoes the same, while scaling up the quantity of potatoes.

We can start by cross multiplying:

3 pounds of potatoes * x servings of mashed potatoes = 8 servings of mashed potatoes * 12 pounds of potatoes

3 * x = 8 * 12

Next, we'll solve for x by dividing both sides of the equation by 3

x = 8*12/3

x = 32

So, 12 pounds of potatoes would make 32 servings of mashed potatoes.

This answer is correct because the ratio of potatoes to servings of mashed potatoes is the same in both cases and we just scaled up the quantity of potatoes while keeping the ratio the same.

The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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Answer:

8/10

Step-by-step explanation:

The rise on the y axis is eight and the run on the x axis is 10

(Hope this helped)

The cartesian vector form of \(F\) is \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\). We call x + yi the Cartesian form for a complex number.

Given that \(i,j,p\) and \(q\) are unit vectors and the angle \(\alpha = 222\)°, we can express the cartesian vector form of \(F\) as \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\).

To calculate the components of \(F\) , we use the trigonometric functions \(cos(\alpha )\) and \(sin(\alpha )\) with the given angle \(\alpha = 222\)°.

\(cos(222) = -0.766\\sin(222) = -0.643\)

Substituting these values into the cartesian vector form, we have:

\(F = (-31cos(222)i + 102sin(222)j)\\F = (-31 * -0.766i + 102*-0.643j)\\F = (23.746i - 65.586j)\)

Therefore, the cartesian vector form of \(F\) is \(F = (23.746i - 65.586j)\).

The cartesian vector form of \(F = (23.746i - 65.586j)\)

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Answer:

193.5

Step-by-step explanation:

1 inch = 12 ft

0.5x48x2=48

48x1.5x2=144

0.5x1.5x2=1.5

144+48+1.5=193.5

Add up the areas of all four strips to get an estimate for the distance traveled by the car in the first 40 seconds: Distance traveled = Area of strip 1 + Area of strip 2 + Area of strip 3 + Area of strip 4.

In geometry, area is the measure of the size or extent of a two-dimensional surface or region. It is typically measured in square units, such as square meters or square feet. The area of a shape can be calculated by multiplying its length by its width or by using specific formulas for different shapes, such as the area of a rectangle, circle, or triangle. Area is an important concept in many fields, including mathematics, physics, engineering, and architecture.

by the question.

Assuming the graph shows the speed of the car in meters per second (m/s) on the y-axis and time in seconds on the x-axis, we can estimate the distance traveled by the car in the first 40 seconds by dividing the area under the graph for that time period into four equal strips and calculating the area of each strip using the trapezium rule.

To do this, we need to find the speed of the car at four different times during the first 40 seconds, which we can do by reading off the graph. Let's say we choose the times t = 0, 10, 20, and 30 seconds.

Then we can estimate the distance traveled by the car in the first 40 seconds as follows:

Calculate the area of the first strip (from t = 0 to t = 10 seconds) using the trapezium rule:

Area of strip 1 = (1/2) x (speed at t = 0 seconds + speed at t = 10 seconds) x 10 seconds

Repeat for the other three strips, using the appropriate speeds and time intervals:

Area of strip 2 = (1/2) x (speed at t = 10 seconds + speed at t = 20 seconds) x 10 seconds

Area of strip 3 = (1/2) x (speed at t = 20 seconds + speed at t = 30 seconds) x 10 seconds

Area of strip 4 = (1/2) x (speed at t = 30 seconds + speed at t = 40 seconds) x 10 seconds

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To prove that triangle FGE and triangle IJH we need information like the two sides of each triangle and the included angle to be congruent.

To prove two triangles are similar by the SAS is that you need to show that two sides of one triangle are proportional to two corresponding sides of another triangles, with the included corresponding angles being congruent.

For the SAS postulate you need two sides and the included angle in both triangles.

Side-Angle-Side (SAS) postulate:-

If two sides and the included angles of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. SAS postulate relate two triangles and says that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

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Using proportions, the costs are given as follows:

a) Total Labor Cost: $2,505,600.

b) Total Product Cost: $1,950,000.

c) Total Cost = $4,455,600.

d) Cost per home = $461.77.

e) Cost per week = $99,013.33.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item a, the labor cost is found using the earnings of the workers, as follows:

45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)

Hence:

Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.

For item b, the product cost is the cost of the boards, hence:

(175 + 150 + 50 boards) x 5,200

Total Product Cost = 375 x 5,200 = $1,950,000.

For item c, the total cost is the sum of the product cost and the labor cost, hence:

Total Cost = 2,505,600 + 1,950,000 = $4,455,600.

For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:

Cost per home = 4455600/9649 = $461.77.

For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:

Cost per week = 4455600/45 = $99,013.33.

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Answer:

3/8

Step-by-step explanation:

Answer:

slope is 4/5

Step-by-step explanation:

Answer:

\(m=\frac{4}{5}\)

Step-by-step explanation:

add y to both sides

\(2x+4y+y=6x\)

add 4y and y

\(2x+5y=6x\)

subtract 2x from both sides

\(5y=6x-2x\)

subtract 2x from 6x

\(5y=4x\)

divide each term by 5

\(\frac{5y}{5} =\frac{4x}{5}\)

cancel common factor

\(y=\frac{4x}{5}\)

reorder the term x

\(y=\frac{4}{5}x\)

using the slope-intercept form, the slope is \(\frac{4}{5}\)

Based on an equation, the weight of each train is as follows:

An equation is an algebraic statement of the equality of two or more mathematical expressions.

An equation uses the equation symbol (=) to differentiate it from a mathematical expression that combines values, variables, constants, and numbers with mathematical operands.

The total weight of Train A and Train B = 225 tons

Let the weight of Train B = x tons

Let the weight of Train A = x + 27 tons

2x + 27 = 225

2x = 198

x = 99

Train A = 126 tons (99 + 27)

Train B = 99 tons

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Answer:

8√2 in.

Step-by-step explanation:

The original square:

Perimeter = 16 in.

Side = 4 in.

New square:

Each side of the new square is the hypotenuse of an isosceles right triangle with legs of length 2 inches.

(2 in)² + (2 in.)² = s²

s² = √(8 in.²)

s = 2√2 in.

p = 4s = 4(2√2) in. = 8√2 in.

Answer:

Step-by-step explanation:

the total perimeter is 33 so all of the sides are equal to it.

33=3x+13+12

then combine like terms

33=3x+25

subtract from each side

(33)-25=(3x+25)-25

8=3x

divide by 3

x=2  2/3

Answer:

arc QS = 95°

Step-by-step explanation:

the inscribed angle QSR is half the measure of its intercepted arc RQ , then

arc RQ = 2 × 95° = 190°

the sum of the arcs in a circle = 360° , then

arc QS = 360° - arc SR - arc RQ = 360° - 75° - 190° = 95°

Answer:

√2π / 4

Step-by-step explanation:

Your answer should be:She can make 92 key chains with the yarns she has.

Step-by-step explanation

1. Let's add and see the total of yarns she has!

36 + 216 + 24 = 276

2. Let's divide the total we got in 1 by the yard she needs to make one key chain!

276 ÷ 3 = 92

3. Your answer should be 92.