Please help on 4 and 5

Step-by-step explanation:

step 1. the difference between x -> x' was 7

step 2. the difference between y -> y' was -2

step 3. the translation was 7 right and -2 down

step 4. the translation can be written (x + 7, y - 2)

step 5. the pre image was located in quadrant II.

1) The lower class limits: 100, 200, 300, 400, 500, 600 .

2) The upper class limits:  199, 299, 399, 499, 599, 699.

3) The class width: 100.

4) Class midpoints: 149.5, 249.5, 349.5, 449.5, 549.5, 649.5.

5) Class boundaries : 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5.

6) The number of individuals included in the summary : 155

The lower class limit in each class: 0,100, 200, 300, 400, 500, 600.

The upper-class limit is the biggest value in each class.

so the upper-class limit is:  99, 199, 299, 399, 499, 599, 699.

As we know the class width is the difference between the lower limit of one class and the lower limit of the previous class.

For example, 300 is the lower limit of one class and the lower limit of the previous class is 200 , so 300 - 200 = 100.

We know that, the class midpoints are the average of the limits of a class.

So, using midpoint formula the class midpoints are:

\(\frac{100+199}{2} = 149.5\\\\\frac{200+299}{2} = 249.5\\\\\frac{300+3199}{2} = 349.5\\\\\frac{400+499}{2} = 449.5\\\\\frac{500+599}{2} = 549.5\\\\\frac{600+699}{2} = 649.5\\\)

We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.

So, the class boundaries for the first class = (99.5, 199.5)

the class boundaries for the second class = (199.5, 299.5)

the class boundaries for the third class = (299.5, 399.5)

the class boundaries for the fourth class = (399.5, 499.5)

the class boundaries for the fifth class = (499.5, 599.5)

The total of individuals is equal to the sum of all the frequencies of each class: 3 + 54 + 76 + 21 + 0 + 0 + 1 = 155

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The complete question is:

Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Blood Platelet Count of Males ​(1000 ​cells/mu​L) Frequency 0​-99 3 100​-199 54 200​-299 76 300​-399 21 400​-499 0 500​-599 0 600​-699 1 Identify the lower class limits​ (in 1000 ​cells/mu​L).

Answer:

\(-x\:-\:1\:=\:221\:+\:2x\)

\(\hookrightarrow Answer:x=-74\)

-------------------------

hope it helps...

have a great day!!

A polynomial is an expression consisting of variables and coefficients and factoring is the process of breaking down a polynomial into simpler units

A polynomial is an expression consisting of variables and coefficients, which are combined using only addition, subtraction, and multiplication. For example, 3x^2 + 2x - 1 is a polynomial, where x is the variable, 3 and 2 are coefficients, and ^2 and ^1 are exponents.

Factoring is the process of breaking down a polynomial into simpler units, which can be multiplied together to obtain the original polynomial. The simplest units are usually linear expressions, which have the form ax + b, where a and b are coefficients. For example, the polynomial 3x^2 + 2x - 1 can be factored into (3x - 1)(x + 1) by identifying two linear expressions that when multiplied together produce the original polynomial.

Factoring is an important tool in algebra, as it can help to simplify expressions, solve equations, and identify the roots of a polynomial.

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Answer:

25

Step-by-step explanation:

3^2=9

-2^4=16

9+16=25

Answer: -7

Step-by-step explanation:

3 squared is 9. -2 to the fourth is negative 16. 9 minus 16 is -7. Hope this helps!

Answer: 79 degrees

Step-by-step explanation:

Answer:

79°

Step-by-step explanation:

Answer:

1.10

Step-by-step explanation:

1.79

0.67

1.12 rounded is 1.10 to the nearest tenth

Among the given options, the correct statement is: C. Var (X + Y) = Var (X) + Var (Y).

This statement is known as the addition rule for variance and holds true for all random variables X and Y, regardless of their specific distributions.

To understand why this statement is true, let's briefly discuss the concept of variance. Variance measures the dispersion or spread of a random variable's values around its expected value (mean). Mathematically, variance is defined as the average of the squared deviations of the random variable from its mean.

Now, let's prove statement C:

Var (X + Y) = E[(X + Y - E[X + Y])^2] (definition of variance)

= E[(X + Y - E[X] - E[Y])^2] (linearity of expectation)

Expanding the square term:

mathematica

Copy code

       = E[(X - E[X])^2 + 2(X - E[X])(Y - E[Y]) + (Y - E[Y])^2]

By linearity of expectation, we can split this expression into three parts:

scss

Copy code

       = E[(X - E[X])^2] + 2E[(X - E[X])(Y - E[Y])] + E[(Y - E[Y])^2]

       = Var(X) + 2Cov(X, Y) + Var(Y)     (definition of variance and covariance)

Note that Cov(X, Y) represents the covariance between X and Y, which measures the extent to which X and Y vary together. However, the given options do not mention anything about the covariance between X and Y, so we cannot determine its value.

Therefore, statement C is correct because it expresses the addition rule for variance, which states that the variance of the sum of two random variables is equal to the sum of their individual variances.

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Answer:

1.6

Step-by-step explanation:

12.8/8 = 1.6

15.2/9.5 = 1.6

Scale factor = 1.6

Using the t-distribution, as we have the standard deviation for the sample, it is found that there is a significant difference between the wait times for the two populations.

At the null hypothesis, we test if there is no difference, that is:

\(H_0: \mu_A - \mu_B = 0\)

At the alternative hypothesis, it is tested if there is difference, that is:

\(H_1: \mu_A - \mu_B = 0\)

For each sample, we have that:

\(\mu_A = 73, s_A = \frac{2}{\sqrt{100}} = 0.2\)

\(\mu_B = 74, s_B = \frac{4}{\sqrt{100}} = 0.4\)

For the distribution of differences, we have that:

\(\overline{x} = \mu_A - \mu_B = 73 - 74 = -1\)

\(s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.2^2 + 0.4^2} = 0.447\)

It is given by:

\(t = \frac{\overline{x} - \mu}{s}\)

In which \(\mu = 0\) is the value tested at the null hypothesis.

Hence:

\(t = \frac{\overline{x} - \mu}{s}\)

\(t = \frac{-1 - 0}{0.447}\)

\(t = -2.24\)

Considering a one-tailed test, as stated in the exercise, with 100 - 1 = 99 df, using a t-distribution calculator, the p-value is of 0.014.

Since the p-value is less than the significance level of 0.05, it is found that there is a significant difference between the wait times for the two populations.

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Answer:

a. $57.80

 $66.47

b. $122.46

   $140.829

Step-by-step explanation:

Mean = 110

Standard Deviation = 17

The solution is given below:A. What is the probability that X is greater than 138.05?We have, Mean (μ) = 110Standard Deviation (σ) = 17Let's first standardize X = 138.05: Z = (X - μ)/σZ = (138.05 - 110)/17 = 1.650Therefore, P(X > 138.05) = P(Z > 1.650)Using a standard normal table, the probability of Z being greater than 1.650 is:0.0495Probability = 0.0495B. What value of X does only the top 15% exceed?We have, Mean (μ) = 110Standard Deviation (σ) = 17We need to find the value of X such that only the top 15% exceed. In other words, we want to find X such that P(X > x) = 0.15.Using a standard normal table, we can find that the Z-value for the top 15% is 1.0364. We can write this as:P(Z > 1.0364) = 0.15We now standardize the equation:P(Z > 1.0364) = 0.15Z = invNorm(0.15) + 1.0364Z = -1.0364 + 1.0364Z = 0Therefore, we have:Z = (X - μ)/σ0 = (X - 110)/17X = 110Therefore, the value of X such that only the top 15% exceed is 110.

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A. The probability that X is greater than 138.05 is 0.0492.

B. The value of X does only the top 15% exceed is 127.57.

Given that X is normally distributed with mean 110 and standard deviation 17.

A. Probability= P(X > 138.05)

First, we need to calculate the z-score of 138.05 by using the formula;

z = (X - μ)/σ

Where

X = 138.05, μ = 110, and σ = 17z = (138.05 - 110)/17 = 1.649

Therefore, P(X > 138.05) = P(Z > 1.649)

Using a standard normal table, the probability P(Z > 1.649) = 0.0492

Thus, the probability that X is greater than 138.05 is 0.0492.

B. We know that the mean of the normal distribution is 110 and the standard deviation is 17, and we need to find the value of X such that only the top 15% exceed.

Therefore, we need to find the value of X such that P(X > x) = 0.15

Using a standard normal table, we find that the Z-value of 0.15 is 1.0364

Therefore, z = (x - μ)/σ = 1.0364

Solving for x, we get,

x = σz + μ = 17 × 1.0364 + 110 = 127.57

Thus, the value of X that only the top 15% exceed is 127.57.

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Answer:

Option D

Step-by-step explanation:

Given equation:

This equation can be solved by:

Subtracting 2 both sides of the equation (according to step 1):

Dividing -4 to both sides of the equation (according to step 2):

Therefore, Option D is correct.

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Answer:

d) 4

Step-by-step explanation:

Solving for the value of x,

→ -4x + 2 = -14

→ -4x = -14 - 2

→ -4x = -16

→ x = -16/-4

→ [ x = 4 ] {option d}

Verification of the value of x,

→ -4x + 2 = -14

→ -4(4) + 2 = -14

→ -16 + 2 = -14

→ -14 = -14

→ [ LHS = RHS ]

Hence, the value of x is 4.

Answer:

The answer is 3.9754976e+23

Answer:

3.9754976e+23

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Answer:

x = 33 , y = 82

Step-by-step explanation:

The sum of the 3 angles in Δ ACD = 180° , then

x = 180 - (40 + 107) = 180 - 147 = 33

x + 65 + y = 180° ( sum of angles on a straight line ) , then

33 + 65 + y = 180

98 + y = 180 ( subtract 98 from both sides )

y = 82

9514 1404 393

Answer:

  216 mi/h

Step-by-step explanation:

The time for the trip with the wind is ...

  (1080 mi)/(225 +45 mi/h) = 4 h

The time for the trip against the wind is ...

  (1080 mi)/(225 -45 mi/h) = 6 h

The average speed for the entire round trip is ...

  (2160 mi)/(4 +6 h) = 216 mi/h

Answer:

the slope is the rise over run so how ever many up it goes over how far side to side it goes these numbers are fractions and will very based on the rise over run.  

Step-by-step explanation:

The answer is D. Ben's statement is incorrect and Robert's cylinder will have a volume about 125 cubic units more than Ben's cylinder.

You use the formula V=πr²h, where r is the radius of the base and h is the height. If we plug in the values for Ben's cylinder, we get V=π(5²)(8)= 100π cubic units. If we do the same for Robert's cylinder, we get V=π(4²)(10)= 160π cubic units. Therefore, Robert's cylinder has a volume that is approximately 125 cubic units more than Ben's cylinder. This can also be calculated by subtracting the volume of Ben's cylinder from the volume of Robert's cylinder, which gives us (160π-100π) = 60π cubic units.

To determine this, we need to calculate the volumes of both cylinders. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. For Ben's cylinder with a 10-inch diameter, the radius is 5 inches, and the height is 8 inches. The volume is V = π(5^2)(8) = 200π cubic inches. For Robert's cylinder with an 8-inch diameter, the radius is 4 inches, and the height is 10 inches. The volume is V = π(4^2)(10) = 160π cubic inches.

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Answer:

5 gallons

Step-by-step explanation:

there were 5 gallons already in the tank before it started to get filled.

The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.

To understand this ratio, let's break it down using different units:

A. 1/3 part bleach and 2/3 part water:

If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.

B. 2 cups of bleach and 3 cups of water:

If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.

C. 3 cups of bleach and 2 cups of water:

If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.

Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

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Answer:False, true, true, false

Step-by-step explanation:

The first one is false because 2 & 5 equal 180 together. B is true because they equal the same thing. C is true because they equal 180 together. And D is false because those don’t equal 180.

The proof is shown below:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given:

CB || HE

Now using the property of parallel lines.

So,

<HAC = <ACB (alternate interior angles)

<EAB= <ABC (alternate interior angles)

Now, HAE is a straight line then

<HAC + <CAB + <EAB = 180 ( linear pair)

<ACB + <CAB + <ABC = 180

Hence, the sum of the three interior angles of a triangle is 180.

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Every line on the graph is 1/2 unit.

When y = 0, x would be -0.25 and 1.25

When y = 2, x would be -0.5 and 1.5

Blake needs to now at least 17 lawns in order to earn at least $200 to buy a new stereo system.

To solve this problem, we can set up an inequality that represents the situation. Let's let x be the number of lawns that Blake needs to mow. The inequality will be:
12x >= 200

This inequality states that the amount of money Blake earns from mowing lawns (12x) must be greater than or equal to the amount of money he wants to earn ($200).

To solve for x, we can divide both sides of the inequality by 12:
x >= 200/12

Simplifying the right side of the inequality gives us:
x >= 16.67

Since Blake cannot mow a fraction of a lawn, we need to round up to the next whole number. This means that Blake needs to now at least 17 lawns in order to earn at least $200 to buy a new stereo system.

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Answer:

23.4

Step-by-step explanation:

23/5+99/5-5/5= 23.4

hope this helps....

have a great day and i hope you pass al of your exams! <3

The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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Given expression is  \(x⁵/⁹\).

Recall to write the nth root of a number, we have to type root(n).

For example, to get\(³√4x\), type "\(root(3)(4x)\)".

We can write the expression x⁵/⁹ as follows:

\($$\frac{x^5}{9}$$\)

Let's rewrite the expression as:

\($$\frac{x}{\sqrt[9]{9}}^5$$\)

Let's write the nth root of a number by typing root(n).

Therefore, the final answer becomes:

\($$\frac{x}{root(9)(9)}^5$$\)

Therefore, the given expression in radical form is   \(\frac{x}{root(9)(9)}^5\)

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Answer:

\(\bold{2\cdot10^9}\)

Step-by-step explanation:

The given expression s are:

\(8 \cdot 10^4\) and

\(4\cdot10^{-5}\)

To find:

\(8 \cdot 10^4\) is how many times  as large as \(4\cdot10^{-5}\).

Solution:

Let \(8 \cdot 10^4\) is \(x\) times as large as \(4\cdot10^{-5}\).

So, we can say that:

\(8 \cdot 10^4\)  = \(4\cdot10^{-5}\)\(\times\) \(x\)

OR

\(x= \dfrac{8\cdot 10^4}{4\cdot 10^{-5}}\)

Let us have a look at the formula for exponents:

\(\dfrac{x^p}{x^q} = x^{p-q}\)

Here we have:

\(x=10\\p=4\ and\\q=-5\)

Solving the expression using above formula:

\(\Rightarrow x= \dfrac{8}{4}\cdot 10^{4-(-5)}} = \bold{2\cdot10^9}\)

So, Let \(8 \cdot 10^4\) is \(\bold{2\cdot10^9}\) times as large as \(4\cdot10^{-5}\)

Answer: 5 is your answer!

Step-by-step explanation:

Answer:

-288

Step-by-step explanation:

math