Which expression is a factored form of 816² - 25c²?

Answer:

B is correct. Angle 7 measures 125°.

Step-by-step explanation:

Parallel lines intersected by a transversal form congruent alternate interior angles. Therefore, angles 4 and 5 are congruent, meaning angle 5 measures 55°. Angles 5 and 7 are supplementary angles, so angle 7 measures 125°. B is the correct answer.

The volume of air of a sphere with diameter 9 centimeters is 381.51 cubic centimeters

The formula for the volume of a sphere is:

V = (4/3)πr³

where r is the radius of the sphere.

The diameter of the sphere is 9 cm, which means the radius is half of that:

r = 9/2 = 4.5 cm

Substituting this value into the formula, we get:

Volume = (4/3)π(4.5)³

Volume = (4/3)×3.14 × 91.125

Volume = 381.51 cubic centimeters

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This data does not provide sufficient evidence that the level of radon in the country is unsafe at the 0.05 level of significance.

We have taken a random sample of 32 homes and we have measured the radon level in each. The sample mean is 4.9 with a standard deviation of 2.1. Using a significance level of 5 %, we have to determine whether this data provides convincing evidence that the mean radon level in the country is too high.

State:

H1: mu = 4

H2: mu > 4 (unsafe radon level)

The parameter is an acceptably safe radon level.

The significance level (alpha) = 0.05.

We will do a one-sample t-test with a random sample, large sample size (> 30), and sample size of less than 10% of the population

t-stat = (sample mean - population mean)/(sample standard deviation/square root(sample size)

= (4.9 - 4)/(2.1/[tex]\sqrt{32}[/tex]) = 2.42

p-value = P(t > 2.42) with 31 degrees of freedom is just above 0.1 (using table value for DOF = 30).

We will not reject H1 at 0.05 level of significance as

p-value > level of significance.

Therefore, we do not have sufficient evidence that the level of radon in the country is unsafe at the 0.05 level of significance.

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g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.

Option C is the correct answer.

We have,

To find the transformation that maps f(x) to g(x), we need to determine how the points of g(x) relate to the points of f(x).

First, we can see that the two functions have the same x-coordinates (1 and 4). This means that the transformation only affects the y-coordinates of the points.

At x = 1,

f(x) has a y-value of 4, and g(x) has a y-value of 2.

This means that g(x) is f(x) after vertical compression by a factor of 1/2.

At x = 4, f(x) has a y-value of 8, and g(x) has a y-value of 4.

This means that g(x) is f(x) after vertical compression by a factor of 1/2.

Therefore,

g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.

i.e

g(x) = (1/2) f(x)

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The rational numbers are solved and the incorrect number is A = 3/0

Given data ,

Let the rational number be represented as A

Now , the value of A is

A)

The division 0/3 will be a rational number because any number divided by 0 is undefined, but in this case, the division is defined and the result is 0, which is a rational number.

B)

The division 3/0 will not be a rational number because any number divided by 0 is undefined, and therefore, the division is not defined.

C)

The division -3/8 will be a rational number because it can be expressed as a ratio of two integers (-3 and 8) and can be written in the form of a fraction -3/8

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Answer:

[tex]-\frac{9}{1}[/tex]

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

The value of angle x is 48.07 degree.

Given that,

ΔSTU is right angle triangle

TU = 7

SU = 9.4

Since sinx = opposite/hypotenuse

                 = TU/SU

                 = 7/9.4

                 = 0.744

⇒ sinix = 0.744

Take inverse of sinx both sides

⇒ x = 48.07 degree

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Answer:

Step-by-step explanation:

The true statement about the given ones is:

"The 4 is the x-coordinate and indicates movement parallel to the x-axis."

A general point in 2D is written as (x-coordinate, y-coordinate). The x-axis is the horizontal axis, and the y-axis is the vertical one. With information we can graph the point.

Here we have the point (4, 9), then:

4 = x-coordinate.

9= y-coordinate.

And to graph these, just move these number of units along (or parallel to) the correspondent axis.

The only true statement from the given one is:

"The 4 is the x-coordinate and indicates movement parallel to the x-axis."

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Answer:

7 schools have fewer than 50 classrooms.

The translation matrix is,

[tex]\left[\begin{array}{ccc}2&2&2\\-1&-1&-1\end{array}\right][/tex]

The coordinates of the triangle as a coordinate matrix is

-2 0 0

0 0 1.

Here the triangle has been translated 2 units right and 1 unit down.

Translating the triangle 2 units to the right means that each x -coordinate increases by 2.

Translating the triangle 1 unit down means that each y -coordinate decreases by 1.

So the translation matrix is,

[tex]\left[\begin{array}{ccc}2&2&2\\-1&-1&-1\end{array}\right][/tex]

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Answer:

the absolute value of 6 is just 6

Answer:

The answer is D

Step-by-step explanation:

8× the number

let the number be n

8×n=8n

Answer:

8n

Step-by-step explanation:

whenever a number is attached to a variable, that means multiplication. 8n is the correct answer.

have a great day and thx for your inquiry :)

Answer:

0 liters

Step-by-step explanation:

The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:

Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³

Since the tank was filled up to of its height, the volume of water in the tank at this point is:

Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³

To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):

Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height

= 384,000 cm³ - 1,200,000 cm³

= -816,000 cm³

Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.

Therefore, the answer to the problem is 0 liters or 0 cm³.

Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.

The total amount of paper required is 3π(3+√71)unit²

The equation for the surface area of a cone is given as follows:

A = πr²+πrs.

Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)

Substituting the values of r & h to determine s

s = √(8²+3²)

s = √71

Substituting the values to get Area,

A=π*3²+π*3*√71.

A=3π(3+√71)

Hence, the required paper will be A=3π(3+√71)unit²

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The hypothesis are

Null Hypothesis: The proportion of time the penny lands on heads 0.5

Alternative Hypothesis: The proportion of times the penny lands on heads in not 0.5.

We can denote the proportion of times the penny lands on heads as p.

If the null hypothesis is true, then p = 0.5. If the alternative hypothesis is true, then p is not equal to 0.5.

We can use a hypothesis test to determine if the sample data provides evidence to reject the null hypothesis in favor of the alternative hypothesis. One possible hypothesis test is the two-tailed z-test for proportions.

To perform this test, we would calculate the test statistic :

z = (p' - p) / √(p x (1-p) / n)

where p' is the sample proportion, p is the null hypothesis proportion (0.5), and n is the sample size.

In this case, we have a sample size of n = 50 and a sample proportion of p' = 30/50 = 0.6. We can calculate the test statistic:

z = (0.6 - 0.5) / √(0.5 x 0.5 / 50)

z ≈ 2.24

To determine if this test statistic is significant at the 5% level, we would compare it to the critical values from the standard normal distribution. For a two-tailed test at α = 0.05, the critical values are -1.96 and 1.96.

Since 2.24 falls outside of this range, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the proportion of times the penny lands on heads is not 0.5.

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The values with Charged Chip model are

9 + (-4) = 5.

9-(-4)=13

-9+4=-5

-9-(-4)=-5

To solve 9 + (-4), we start with 9 positive chips and take away 4 negative chips. We can represent this as:

[+][+][+][+][+][+][+][+][+]

[-][-][-][-]

When we combine the chips, we end up with 5 positive chips remaining:

[+][+][+][+][+]

Therefore, 9 + (-4) = 5.

To solve 9 - (-4), we start with 9 positive chips and add 4 negative chips. We can represent this as:

[+][+][+][+][+][+][+][+][+]

[-][-][-][-]

When we combine the chips, we end up with 13 positive chips remaining:

[+][+][+][+][+][+][+][+][+][+][+][+][+]

Therefore, 9 - (-4) = 13.

Similarly -9+4 value is -5

-9-(-4) value is -5

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The mean and standard deviation is x ~ N(76,3).

Given that a population has a mean = 76 and a standard deviation o = 24

We need to find the standard deviation of a sampling distribution of sample means with sample, n = 64.

The mean of the sampling distribution of sample means is =

x = μ

x = 76

Now,

SD = σ/√n

= 24/√64

= 24/8

= 3

Hence, x ~ N(76,3).

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Answer:

66 inches

Step-by-step explanation:

Every foot is twelve inches

Answer: 66 inch is in 5 1/2 feet

Step-by-step explanation: there is 12 inches in 1 foot so you do 12 x 5= 60 then there is 6 inches in a half of a foot so you add 60 and 6 and you get 66 inches

Step-by-step explanation:

'Find the product...'   just means multiply the two numbers together:

(use your calculator)    5602 x 17 =   95,234

Product means multiply them together. Please see image showing multiplication. You could also break this up into (5602 x 7) + (5602 x 10), which is basically what I did vertically.

The mistake done in the solution is while finding the distance from mean we have not taken the absolute value

To find the MAD (Mean Absolute Deviation), first find the mean of the data set:

mean = (2 + 3 + 4 + 7 + 9 + 11) / 6 = 6

Then, calculate the absolute deviation of each data point from the mean:

|2 - 6| = 4

|3 - 6| = 3

|4 - 6| = 2

|7 - 6| = 1

|9 - 6| = 3

|11 - 6| = 5

Next, find the average of these absolute deviations:

(4 + 3 + 2 + 1 + 3 + 5) / 6 = 2.67

While find the distance from mean we have to use the absolute value or positive value

Hemce, the MAD of the data set {2, 3, 4, 7, 9, 11} is 2.67.

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The logarithmic equation is equivalent to this exponential equation is x = log (8/25) (option c).

In this case, we are asked to find the logarithmic equation that is equivalent to the given exponential equation:

2,400 = 7,500(10)⁻ˣ

To solve for x, we need to isolate it on one side of the equation. We can start by dividing both sides by 7,500:

2,400/7,500 = (10)⁻ˣ

The choice of base for the logarithm doesn't matter, as long as we use the same base for both sides. Let's use base 10:

log(2,400/7,500) = log(10⁻ˣ)

Using the properties of logarithms, we can simplify the right-hand side:

log(2,400/7,500) = -x*log(10)

We know that log(10) = 1, so we can simplify further:

log(2,400/7,500) = -x

x = log(8/25) = log(8) - log(25) = 0.9031 - 1.3979 = -0.4948

So the only answer choice that gives us the same equation as the original exponential equation is (C) x = log (8/25).

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Complete Question:

Which logarithmic equation is equivalent to this exponential equation?

2,400 = 7,500(10)^(-x)

A. x= -log (25/8)

B. x = log(-25/8)

C. x = log (8/25)

D. x = -log (8/25)

We would need to randomly sample at least 1067 people to estimate the proportion of Americans who ate breakfast this morning with a margin of error of 3 percentage points and a 95% confidence interval.

The formula to calculate the sample size required to achieve a desired margin of error and confidence interval is:

n = (Z² x p x (1-p)) / E²

where n is the sample size, Z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated proportion of the population who ate breakfast, and E is the desired margin of error as a decimal (0.03 in this case).

To determine the estimated proportion of Americans who ate breakfast this morning, we could use data from previous studies or surveys. Let's assume that previous studies have found that approximately 60% of Americans eat breakfast regularly. Therefore, we can use p = 0.60 in our formula.

Substituting the values into the formula, we get:

n = (1.96² x 0.60 x 0.40) / 0.03²

n ≈ 1067

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The y-intercept represents the base price of $200 for airfare from NYC.

The slope represent a cost of $0.30 cents per mile traveled.

According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their fare.

According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles.

If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x.

In Mathematics, the slope-intercept form of the equation of any straight line is modeled by this mathematical equation;

y = mx + c

Where:

Based on the information provided about this trip, an equation that represents the situation is given by;

y = mx + c

y = 0.30x + 200

When x = 2000 miles, the price of airfare (y) can be calculated as follows;

y = 0.30(2000) + 200

y = $800.

When y = $500, the distance traveled (x) can be calculated as follows;

500 = 0.30x + 200

300 = 0.30x

x = 1000 miles.

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The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

The class has a cat and a dog = 9

Has a dog and does not have a cat = 2

Does not have a dog and has a cat = 4

Does not have dog and cat = 5

The total strength of the class is 20

The probability that a student is chosen randomly from the class has a cat or a dog =  Number of favorable outcomes / total number of outcomes

P(E) = 15 /20

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Answer:

Step-by-step explanation:

its 11/28

Step-by-step explanation:

At least twice means it could be   2  3  4  5  6  7  or  8 heads

 there is 8 chances of having only one TAIL

there are   2^8 outcomes = 256 outcomes possible

     take away the EIGHT with one tail

                  248 out of 256 have at least 2 heads

248/256 = 31/32

( Let me know if this is incorrect and I will re-evaluate !)

Answer:

[tex]\frac{247}{256}[/tex]

Pre-requisite Knowledge:

Permutations and Combinations

Elementary Probability

Step-by-step explanation:

Total number of outcomes (Cardinality of the sample space) = [tex]2^{8}[/tex]  

P(at least 2 heads show up) = 1 - [ P(no Head) + P(exactly 1 Head) ]

[tex]= 1-\frac{C(8,0)+C(8,1)}{2^8}\\\\=1-\frac{1+8}{256}\\\\ =1-\frac{9}{256}\\\\= \frac{247}{256}[/tex]

Answer:

Step-by-step explanation:

There are 10 bundles and 1 sticks in the Popsicle sticks

Given that  Sasha has 47 Popsicle sticks (4 bundles of 10 and 7 sticks)

4B+7S=47

Jose has 62 (6 bundles of 10 and 2 sticks).

6B+2S=62

We have to find B and S values

12B+21S=141

12B+4S=124

Subtract both the equations

21S-4S=141-124

17S=17

Divide both sides by 17

S=1

Now let us plug in the value of S

4B+7=47

4B=40

B=10

Hence, there are 10 bundles and 1 sticks in the Popsicle sticks

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The value of KL and LMJ in the pie chart are 54 degrees and 198 degrees respectively

The pie chart is an important type of data representation. It contains different segments and sectors in which each segment and sector of a pie chart forms a specific portion of the total(percentage). The sum of all the data is equal to 360°. The total value of the pie is always 100%.

To find the value of angle KL and LMJ, we can proceed as;

a. angle KL;

KL = 15 / 100 = x / 360

KL = 0.15 = x / 360

x = 360 * 0.15

x = 54°

KL = 54°

Let's find LMJ

LMJ = 24 + 31 = 55%

55 / 100 = x / 360

0.55 = x / 360

x = 360 * 0.55

x = 198°

LMJ = 198°

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