how do i find x? geometry unit 4 homework 3

Step-by-step explanation:

a) To find the number of seconds that it takes for the rocket to reach the ground, we need to find the value of t when h = 0. We can set h = 0 and solve for t:

0 = 16t^2 + 96t + 10

To solve for t we need to use the quadratic formula:

t = (-b ± √(b^2 - 4ac))/2a

Where:

a = 16, b = 96 and c = 10

t = (-96 ± √(96^2 - 41610))/2*16

t = (-96 ± √(9216 - 640))/32

t = (-96 ± √(8576))/32

t = (-96 ± 92.8)/32

So the rocket will take approximately 2.89 seconds to reach the ground.

b) To find the number of seconds that it will take the rocket to be at its highest maximum height, we need to find the value of t when the derivative of h is equal to 0.

h' = 32t + 96

h' = 0

32t + 96 = 0

t = -3

So the rocket will take approximately -3 seconds to be at its highest maximum height.

c) To find the maximum height of the rocket, we need to substitute the value of t from part b into the equation for h:

h = 16(-3)^2 + 96(-3) + 10

h = 169 + 96(-3) + 10

h = 144 - 288 + 10

h = -134

So the maximum height of the rocket is approximately -134 feet.

2x + 5y =10.This is a equations is correctly written in Standard Form.

What is meant by Standard Form?

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Answer:

x = -4

y = 4

Step-by-step explanation:

2x + 5y = 12       Q1

4x + 3y = -4       Q2

Q1 * 2

4x + 10y = 24

-   Q2

7y = 28

y = 4

put y back into equation

2x + 5y = 12

2x + 5(4) = 12

2x + 20 = 12

2x = -8

x = -4

The radius of the sphere is, 3 inch.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A sphere has a volume of 36 π in³.

We know that;

⇒ Volume of sphere = 4/3 πr³

Here, A sphere has a volume of 36 π in³.

Hence, We get;

⇒ 4/3 πr³ = 36π

⇒ 4/3 r³ = 36

⇒ r³ = 36 × 3 / 4

⇒ r³ = 27

⇒ r = ∛ 27

⇒ r = 3 inch

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Therefore , the solution of the given problem of probability comes out to be  probability that the second marble will be red  = 0.5.

Calculating the likelihood that a statement is true or that an event will occur is the focus of the branch of mathematics known as probability theory. Any number from 0 to 1, where 1 represents certainty and 0 normally represents possibility, may be used to represent chance. The likelihood that a particular event will occur is depicted in a probability diagram. Probabilities can be represented by the numbers 0 and 1, percentages with a range of 0% to 100%, and a small number of extra characters. the proportion of incidents that occurred among a set of equally likely possibilities out of all potential outcomes

Here,

(p = 5/10) First Blue

Blue II (p = 4/9)

Red 2 (p = 5/9)

Primary Red (p = 5/10)

Blue II (p = 5/9)

Fourth Red (p = 4/9)

Interestingly, if you observe the first marble and then put it back in, the outcome will remain the same (sampling with replacement). The second draw doesn't depend on the first.

=> Pr(B, R) = Pr(B)*Pr(R)

=>  (5/10), (5/10), (1/2), (1/2), and 1/4.

and

=>Pr(R, R) = Pr(R)*Pr(R)

=> (5/10), (5/10), and (1/2).

(1/2) = 1/4

Pr

R, R, or (B, R) = (1/4) + (1/4) = 1/2

Therefore , the solution of the given problem of probability comes out to be  probability that the second marble will be red  = 0.5.

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Because the x and y coordinates are squared before being added together, the formula will always result in a positive number.

In math, what is a distance?

The length of the segment of the line that connects the supplied two points determines the distance between them.

                     The shortest segment of a line connecting a point to a line will have a length equal to the distance between them.

Why does the distance formula work?

The Pythagorean Theorem, which states that a side plus a side plus a side equals a side equals a side equals a side equals a side equals a side equals a side equals a side equals a side, is where the Distance Formula actually originates (known as the legs of a right triangle).

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No solution can be described as a situation in which there is no solution or outcome that meets the needs of all parties involved.

When no solution is present, it is often because the problem is too complex or the parties involved have conflicting interests.

This can lead to a stalemate between parties, leaving no one satisfied with the outcome.

No solution can also be the result of a lack of resources or other constraints. It is important to recognize when no solution is present in order to move forward and find a suitable alternative.

No solution can be defined as a problem or situation without a clear answer or resolution. It can be a complex issue that is difficult to solve or a situation with no path forward.

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Inferential statistics uses methods that take a result from a sample, extend it to a population, and measure the reliability of the result.

Inferential records use measurements from the pattern of topics within the experiment to examine the remedy agencies and make generalizations about the larger populace of subjects. there are numerous varieties of inferential facts and every one is suitable for a particular research design and sample characteristics.

Inferential statistics is a department of statistics that makes the usage of diverse analytical equipment to attract inferences approximately the population information from pattern facts. aside from inferential information, descriptive records form another branch of information.

Statistical inference is the procedure of the usage of facts evaluation to deduce houses of an underlying distribution of opportunity. Inferential statistical evaluation infers homes of a populace, for instance through testing hypotheses and deriving estimates.

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Complete Question:

_______ statistics uses methods that take a result from a sample, extend it to a population, and measure the reliability of the result.

Answer: 3052

Step-by-step explanation: 8250 - 5198 = 3052

Full-time worker minimum monthly income = US$ 7,846.40

Part-time worker minimum monthly income  = US$ 7,846.40

Full-time worker hourly wage = US$ 49.04

Part-time worker hourly wage = US$ 98.08

1.Review the information

Monthly costs of a 2-adult and 3-children family in the Modesto metro area = US$ 5841

Full-time worker = 4 weeks of 40-hour per month

Part-time worker = 2 weeks of 40-hour per month

2. Let's calculate the minimum monthly income and hourly wage per worker

Full-time worker hourly wage = Monthly costs/160

Part-time worker hourly wage = Monthly costs/80

Full-time worker hourly wage = 5841/160

Part-time worker hourly wage = 5841/80

Full-time worker hourly wage = US$ 36.5

Part-time worker hourly wage = US$ 73

Full-time worker minimum monthly income = Hourly wage * 160

Part-time worker minimum monthly income  = Hourly wage * 80

Full-time worker minimum monthly income = US$ 5840

Part-time worker minimum monthly income  = US$ 5840

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Answer:

3x5−4x4−x2+5

Simplify the expression.

The most realistic sampling method that represents the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area is Cluster Sampling technique.

In cluster sampling, the total population is divided into homogeneous groups known as clusters and a simple random sample of the groups is selected. The elements present in each cluster are then sampled like a sample. In other words we can say each cluster is represent a tiny population set. We have, geologists have an interest in the structure and the history of the earth. In this study, the whole population is divided into groups based on retrieving a core sample, estimating the ages of the various layers, and examining the composition. After that a timeline can be built of the entire area for drilling the core sample. So, each set work as small population i.e., clusters. The sampling technique which is used here to represent the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area is known as cluster sampling.

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Answer:

(- 4, - 5 )

Step-by-step explanation:

a vertical move down means subtract 10 from the y- coordinate

a horizontal move left means subtract 8 from the x- coordinate

(4, 5 ) → (4 - 8, 5 - 10 ) → (- 4, - 5 ) ← end point

If the mean number of people who attended three basketball games was 8,242, that means the sum of the number of people who attended all three games is equal to 8,242 multiplied by the number of games, which is 3.

What does math mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Total attendance = mean attendance * number of games

Total attendance = 8,242 * 3

Total attendance = 24,726

So the total attendance at the three games is 24,726 people.

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The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

The domain of a function is defined as the set of inputs accepted by the function. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Consider the function y = f(x), which has the independent variable x and the dependent variable y.

A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

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Answer:

  1.00

Step-by-step explanation:

You want to know the price of a cookie when 3 pizza slices and 2 cookies cost 6.50, while 1 pizza slice and 1 cookie costs 2.50.

We can write equations for the costs as ...

  3p +2c = 6.50

  p + c = 2.50

Multiplying the second equation by 3 and subtracting the first equation eliminates the variable p.

  3(p +c) -(3p +2c) = 3(2.50) -(6.50)

  3p +3c -3p -2c = 7.50 -6.50 . . . . . . . eliminate parentheses

  c = 1.00 . . . . . . . . . simplify

The cost of a cookie is 1.00.

The alcohol required to make 12 ounce vanilla extract is 7.42 ounces.

In the given question, we have to find how much water and alcohol he should use.

Given that vanilla extract requires a 60% alcohol solution and that Given that the pure alcohol content in 12 ounces of vanilla extract is 97%.

Let x denote the alcohol required in ounces.

Let y represent the needed water in ounces.

Then, we must find x and y such that

x + y = 12

Given the desired strength, the volume needed, and the pure alcohol percentage, the following formula can be used to determine the pure alcohol:

Required Pure Alcohol = Desired strength × Volume required Pure alcohol content

x = 60 × 12

97x = 7.42

Therefore the alcohol required to make 12 ounce vanilla extract is 7.42 ounces.

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Therefore the polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written in the form: ax^3 + bx^2 + cx + d = x^3 - 2x^2 + 4x - 6 where a = 1, b = -2, c = 4, and d = -2

The polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written as:

ax^3 + bx^2 + cx + d = (x - 2)(x^2 + 1) - x(x - 3)

To find the values of a, b, c, and d, we need to multiply out the binomials and combine like terms. Using the distributive property, we get:

ax^3 + bx^2 + cx + d = x^3 - 2x^2 + x^2 + x - x^2 + 3x - 2

Now we can combine like terms:

ax^3 + bx^2 + cx + d = x^3 - 2x^2 + 4x - 2

So we can see that:

a = 1, b = -2, c = 4, and d = -2

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The amount of wrapping paper, in square centimeters, needed to completely cover the cylinder is SA = 2π(1.2)² + 1.2π(3.8).

The lateral surface area of a cylinder is also called the curved surface area of the cylinder.

Suppose that Radius of the considered cylinder = 'r' units

Height of the considered cylinder = 'h' units

Then, the lateral surface area of that cylinder is:

[tex]S_L = 2\pi r h \: \rm unit^2[/tex]

We are given that a cylinder with the diameter labeled 2.4 centimeters and the height labeled 3.8 centimeters.

Therefore, we have;

Diameter = 2.4 cm

Height = 3.8 cm

Radius = 1.2 cm

So, The total area is;

SA = 2π(1.2)² + 1.2π(3.8).

The amount of wrapping paper,needed to completely cover the cylinder

SA = 2π(1.2)² + 1.2π(3.8).

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Answer: The answer you're looking for is A.

Step-by-step explanation: 7th-grade math exam used the answer from the person above and they were right!

Function is a relation where each input has exactly one output.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, co domain, and domain. The usual way to refer to a function is as f(x), where x is the input.

The link between INPUT and OUTPUT is demonstrated by the relation. A function, on the other hand, is a relation that yields one OUTPUT for each given INPUT.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co domain, respectively.

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From the graph, the following information is seen.

Team A speed is 4.17 meters per second.

Team B speed is 6.25 meters per second.

Team C speed is 8.3 meters per second.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph,

Pick two coordinates from each line.

Team A is the blue line.

(6, 50) and (10, 75)

Rate of change.

= (75 - 50) / (10 - 6)

= 25/6

= 4.17

Team B is the red line.

(6, 25) and (10, 50)

Rate of change.

= (50 - 25) / (10 - 6)

= 25/4

= 6.25

Team C is the green line.

(6, 25) and (12, 75)

Rate of change.

= (75 - 25) / (12 - 6)

= 50/6

= 8.3

Thus,

Team A runs about 4.17 meters per second.

Team B runs about 6.25 meters per second.

Team C runs about 8.3 meters per second.

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Answer:

Step-by-step explanation:

Total length = addition of the lengths of the two pipes

We know, 1cm= 10 millimeters

                Hence, 82 centimeters = 82*10 = 820 millimeters.

Total length therefore = 820 millimeters + 260 millimeters = 1080 millimeters.

The equivalent expression is 5b-0.9b.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

As per the given information in the question,

Discount on the price of bread = 18%

Total loaves of bread by Shanaya = 5

Let the price of bread is b.

Then, the expression for the statement will be,

=>5 (b - 0.18b)

The equivalent expression for the statement will be,

=>5b - 0.9b

Hence the equivalent expression is 5b-0.9b.

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Scatter plot is best for analyzing relationship between two variables.

What is scatter ?

In statistics and data visualization, a scatter plot (also called a scatter graph or scatter chart) is a type of graph used to display the relationship between two sets of data. It is a two-dimensional plot that uses Cartesian coordinates to display values for typically two variables for a set of data.

A scatter plot is a graph that uses dots to represent values for two numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are a useful tool for visualizing the relationship between two variables, such as how changes in one variable may be associated with changes in another variable.

Scatter plots can show the following types of relationships:

Positive correlation: as one variable increases, the other variable increases.

Negative correlation: as one variable increases, the other variable decreases.

No correlation: there is no relationship between the two variables.

Non-linear relationship: the relationship between the two variables is not linear.

Scatter plot is best for analyzing relationship between two variables.

Complete Question: Which of the following types of graph is the best kind to use for analyzing how two variables are related?

Line Graphs, Bar Graphs, Pie Charts, Scatter Plots

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It takes Cindy 1 hour to do the job alone and Bill 3 hours to do the job alone.

Let x be the time it takes Cindy to do the job alone, in hours. Then, it takes Bill x + 2 hours to do the job alone.

During the first 2 hours, when they worked together, they did 2/x + 2/(x + 2) = 1/2 of the job.

Bill finished the job in 1 hour after Cindy left, so he did 1/x + 2 = 1/3 of the job during that hour.

We can now set up a system of two equations to solve for x:

2/x + 2/(x + 2) = 1/2 (1)

1/x + 2 = 1/3 (2)

From equation (1), we can find x + 2:

2/x + 2/(x + 2) = 1/2

2x + 4 = x(x + 2)

2x + 4 = x^2 + 2x

x^2 - 2x + 4 = 0

(x - 4)(x - 1) = 0

x = 4 or x = 1

Since x represents the time it takes Cindy to do the job, we reject x = 4 and keep x = 1.

Substituting x = 1 into equation (2), we find:

1/1 + 2 = 1/3

3 = 3

So, it takes Cindy 1 hour to do the job alone and Bill 3 hours to do the job alone.

Therefore, It takes Cindy 1 hour to do the job alone and Bill 3 hours to do the job alone.

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It takes Cindy 1 hour to do the job alone and Bill 3 hours to do the job alone.

Let x be the time it takes Cindy to do the job alone, in hours. Then, it takes Bill x + 2 hours to do the job alone.

During the first 2 hours, when they worked together, they did 2/x + 2/(x + 2) = 1/2 of the job.

Bill finished the job in 1 hour after Cindy left, so he did 1/x + 2 = 1/3 of the job during that hour.

We can now set up a system of two equations to solve for x:

2/x + 2/(x + 2) = 1/2 (1)

1/x + 2 = 1/3 (2)

From equation (1), we can find x + 2:

2/x + 2/(x + 2) = 1/2

2x + 4 = x(x + 2)

2x + 4 = x² + 2x

x² - 2x + 4 = 0

(x - 4)(x - 1) = 0

x = 4 or x = 1

Since x represents the time it takes Cindy to do the job, we reject x = 4 and keep x = 1.

Substituting x = 1 into equation (2), we find:

1/1 + 2 = 1/3

3 = 3

So, it takes Cindy 1 hour to do the job alone and Bill 3 hours to do the job alone.

Therefore, It takes Cindy 1 hour to do the job alone and Bill 3 hours to do the job alone.

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The solution of the inequality is given by x < -1

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

The stages of resolving inequities are as follows:

The inequality is described as :

-2(3x - 5) > 16

⇒ -6x + 10 > 16

⇒ -6x > 6

⇒ x < -1

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Answer: The equation representing the position of the bug 8 seconds after passing the branch is given by:

x = -7t + 8, where x is the position in millimeters and t is the time in seconds.

Step-by-step explanation:

The number of ways to choose 32 candies is 58,905 ways.

A combination is a way of choosing items from a collection in which the order of selection does not matter.

The number of combinations of n items taken r at a time is determined by the following formula:

[tex]^{(n+r-1)} C_{(r-1)}[/tex]

where:

n represents the total number of items; and

r represents the number of items being chosen at a time.

In this case, a store is selling 5 types of candies, which means the number of types of items or r = 5. And being questioned the number of ways to choose 32 candies, which means the number of items or n = 32.

So, n = 5 and r = 32. Now, substitute both values into the formula:

= [tex]^{(n+r-1)} C_{(r-1)}[/tex]

= [tex]^{(32+5-1)} C_{(5-1)}[/tex]

= [tex]^{36} C_{4}[/tex]

= [tex]\frac{36!}{4!(36-4)!}[/tex]

= 58,905

Hence, the number of ways to select 32 candies is 58,905.

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Although part of your question is missing, you might be referring to this full question: A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How many ways are there to choose 32 candies?

There are 34560 ways can the 11 animals be placed in a row of 11 cages, such that all of the animals of each type are in adjacent cages.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

As per the question, the happy valley kennel has 4 chickens, 2 dogs, and 5 cats.

Now calculate the number of ways in which the animals are placed in a row in the adjacent cages is:

=4!*2!*5!*3!=4*3*2*1*2*15*4*3*2*1*3*2*1=34560 ways

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