Which of the following numbers is not divisible by any positive integer except 1 and itself? A. 41 B. 49 C. 51 D. 57 E. 91​

Answer:

FE is not congruent to FG.

Step-by-step explanation:

FE is 49 and FG is 111.

So, because these two numbers are not equal,

FE is not congruent to FG.

Answer:

Step-by-step explanation:

1/3x+2/3x-2/3x: x equasion

3/4+(-1/4)

1/3x +  2/4(or 1/2)

1/3x+1/2

(note that positive 2/3 and -2/3 cancel out)

Cyber safety is the use of information and communication technologies in a responsible and safe manner. It involves protecting information and keeping it secure, but it also entails handling information responsibly, showing consideration for others online, and following proper internet etiquette.

The Essential Eight are a collection of eight mitigation techniques: application control, application patching, configuring Microsoft Office macro settings, user application hardening, limiting administrative rights, operating system patching, multi-factor authentication, and regular backups.

Best Cybersecurity Advice for 2023:

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Answer:

Using the banker's method, we can use the following formula to find the interest:

Interest = (Principal x Rate x Days) / 360

Where,

Principal = $16,400

Amount = $16,851

Days = 180

We know that the interest plus the principal equals the amount, so we can set up the following equation:

Interest + Principal = Amount

Substituting the values:

(16,400 x Rate x 180) / 360 + 16,400 = 16,851

Multiplying both sides by 360:

16,400 x Rate x 180 + 5,904,000 = 6,066,360

16,400 x Rate x 180 = 162,360

Rate = 162,360 / (16,400 x 180)

Rate = 0.055 or 5.5%

Therefore, the interest rate of the loan is 5.5%.

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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There were 17 students in the group, and each student paid the same whole number of dollars for the concert tickets.

To determine the number of students in the group, we need to find a whole number that is greater than 2 and less than 20, and when multiplied by another whole number, results in a product of $391.
First, let's list some factors of 391:
1 x 391 = 391
17 x 23 = 391

Since we are looking for a number of students, we can eliminate the factorization of 1 x 391 because that would mean there is only one student in the group, which contradicts the condition in the question.
Now, let's consider the factorization of 17 x 23. In this case, the number of students in the group would be the smaller factor, which is 17. Therefore, there were 17 students in the group.
To summarize, there were 17 students in the group, and each student paid the same whole number of dollars for the concert tickets.

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The range is 4.5, and it means that the data varies by a value of 4.5.

What is the data set?

A data set is an ordered collection of data. As we know, a collection of information obtained through observations, measurements, study, or analysis is referred to as data. It could include information such as facts, numbers, figures, names, or even basic descriptions of objects.

The range is the difference between the largest and smallest values in a data set.

In this case, the largest value is 8 and the smallest value is 3.5, so the range is 8 - 3.5 = 4.5.

This means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

Hence, The range is 4.5, and it means that the data varies by a value of 4.5.

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The multiplier to use in order to calculate the 92% confidence interval for a population proportion p, based on a sample of 250 individuals, is 1.75 (rounded to 2 decimal places).

A confidence interval is a statistical tool for estimating the possible range of values that a population parameter may take.

The process of constructing a confidence interval involves sampling a smaller subset of the population known as a sample, calculating a test statistic based on the sample data, and then using the test statistic to establish the interval limits.

A population is a group of individuals or objects that possess one or more characteristics of interest to the researcher and are under investigation in a study.

A sample is a subset of the population that is selected to participate in a study in order to obtain information that is representative of the population as a whole.

The formula for calculating the multiplier is as follows:

Multiplier = (1 - confidence level) / 2 + confidence level

Where the confidence level is the level of confidence expressed as a percentage divided by 100.

Therefore, for this question, we have:

confidence level = 92% = 0.92

Multiplier = (1 - 0.92) / 2 + 0.92= 0.04 / 2 + 0.92= 0.02 + 0.92= 0.94

Rounded to 2 decimal places, the multiplier to use in order to calculate the 92% confidence interval for a population proportion p, based on a sample of 250 individuals, is 1.75.

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The integration is as follow

Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.

Given:

first, \(\int\limits {e^{4x} / 19 - e^{8x}} \, dx\)

= \(\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx\)

let \(e^{4x}\) = z

4\(e^{4x}\) dx = dz

= 1/4 \(\int\limits {dz / \sqrt{19} ^2 -z^2} \,\)

= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C

= 1/8√19 log|(\(e^{4x}\) + √19)/ (\(e^{4x}\) - √19)| + C

Second,

\(\int\limits {33 sec^5 (x)} \, dx\)

= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]

= 33/4  tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]

=  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

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The equation in vertex form is y = 2(x+3)² + 1. The vertex is (-3,1), the axis of symmetry is x = -3, and the direction of opening is upwards.

The vertex form of the equation is y = a(x-h)^2 + k, where (h, k) is the vertex. The axis of symmetry is x = h, and the direction of opening is determined by the value of a.

Using this formula, let us write each equation in vertex form and then identify the vertex, axis of symmetry, and direction of opening.

1. y = x² + 8x + 18

To write this equation in vertex form, we need to complete the square. y = x² + 8x + 18 is equivalent to y = (x+4)² - 2. Therefore, the equation in vertex form is y = (x+4)² - 2.

The vertex is (-4,-2), the axis of symmetry is x = -4, and the direction of opening is upwards.2

. y = -x² - 12x - 36To write this equation in vertex form, we need to complete the square. y = -x² - 12x - 36 is equivalent to y = -(x+6)² - 12. Therefore, the equation in vertex form is y = -(x+6)² - 12.

The vertex is (-6,-12), the axis of symmetry is x = -6, and the direction of opening is downwards.3. y = 2x² + 12x + 13To write this equation in vertex form, we need to complete the square. y = 2x² + 12x + 13 is equivalent to y = 2(x+3)² + 1.

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Answer:

D=-64

Step-by-step explanation:

-10(d+56)=80

d+56=8

d=8-56

d=-64

The correct option is Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction

Emanuel did a mistake in her first step by taking negative sign twice.

Positive results are obtained if the sign are same. If the signs disagree, the outcome is adverse. Addition: Keep in mind that a signed number's magnitude and absolute value are the same.

Multiplication and division appear to be more difficult than addition and subtraction, but they are actually far less challenging. The result of multiplying two positive or two negative numbers with the same sign, according to the rule, will always be positive.

For instance:

According to question,

= \(\left(\frac{3}{5}\right)\left(\frac{4}{9}\right)\left(-\frac{1}{2}\right)\)

Emanuel found the solution, but she erred in the first step. She incorrectly distributes the negative sign with both 1 and 2, as she should. We can write negative sign with either 1 or 2 but not both.

Correct steps are:

Step 1:

\(\frac{(3)(4)(-1)}{(5)(9)(2)}\)

Step 2:

\(\frac{-12}{90}\)

Step 3:

\(-\frac{2}{15}\)

Therefore, the step 1 was miscalculated by Emanuel.

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The complete question is -

Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)

Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction Step 2 StartFraction negative 12 over negative 90 EndFraction

Step 3 StartFraction 12 over 90 EndFraction

Step 4 StartFraction 2 over 15 EndFraction

In which step did his first error occur?

Answer:

Height of the kite = 86.60 meter (Approx)

Step-by-step explanation:

The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.

Given:

Length of thread = 100 meter

Angle of elevation = 60°

Find:

Height of the kite.

Computation:

Using trigonometry application:

Height of the kite / Length of thread = Sin 60°

Height of the kite / 100 = √3 / 2

Height of the kite = [√3 / 2]100

Height of the kite = 50√3

Height of the kite = 86.60 meter (Approx)

Answer:2.7

Step-by-step explanation:

The average density of the rod is  0.704 kg/m.

For given question,

We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.

We need to find the

The length of rod is, L = 5 m.

The linear density of rod is, ρ = 10/( x + 4) kg/m

To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,  

The expression for the average density is given as,

⇒ ρ'

\(=\int\limits^5_0 {\rho} \, dx\\\\=\int\limits^5_0 {\frac{m}{L} } \, dx\\\\=\int\limits^5_0 {\frac{10}{5(x+4)} }\, dx\\\\=\int\limits^5_0 {\frac{2}{x+4} }\, dx\)                        ......................(1)

Using u = x + 4  

du = dx

u₁ = x₁ + 4

u₁ = 0 + 4

u₁ = 4

and

u₂ = x₂ + 4

u₂ = 5 + 4

u₂ = 9

By entering the values above into (1), we have:

⇒ ρ'

\(=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352]\)

= 0.704

Thus, we can conclude that the average density of the rod is  0.704 kg/m.

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Answer:

Option B

Step-by-step explanation:

By applying Pythagoras theorem in the given right triangle,

(Hypotenuse)² = (leg 1)² + (leg 2)²

Now substitute the measures of each side in the formula,

(13)² = x² + (12)²

169 = x² + 144

x² = 169 - 144

x² = 25

x = √25

x = 5

Therefore, Option B will be the correct option.

Answer: Look below :)

Step-by-step explanation:

I graphed the inequality below:

from that we can see:

a. Points on the line are combinations of US/Mexico minutes he can do where all of his prepaid money will be used, For example, he could do 50 USA minutes and 80 Mexico minutes, and there would be no money left to spend

b. Points above the line are combinations of US/Mexico minutes that will cost him more than the prepaid $50.

c. Points below the line are combinations of US/Mexico minutes that will leave him with money left over from his $50.

I hope this makes sense! ask questions if you have any :)

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Answer:

8

Step-by-step explanation:

100-3t=76

-3t=-24

t=8

Answer:

t=8

Step-by-step explanation:

100 - 3t = 76

-100        -100

-3t = -24

/-3    /-3

t = 8

Hope this helps!

Answer:

Part A: 5 miles per hour or 12 min per mile.

Part B: 30 min to get to his friends house.

Question 16 Part B: 30 minutes.

Step-by-step explanation:

Part A:

36 min for 3 miles so the unit is :

36/3 = 12 so: 1 mile per 12 min and 5 miles per hour.

Part B:

21/2 miles away so:

one mile per 12 min so 2.5 x 12 = he'll get there in 30 min.

Question 16 Part B:

just type in 30.

Disregarding intermediate, let's assume she has access to a letter that can be powerful or weak. Let's say she receives a persuasive letter. If she receives a strong letter, her chance of being hired is then increased.

P(J|S)

If, however, she receives a subpar letter, Considering since she received a subpar cover letter, her chances of landing the job are slim.

P(J|W)

Let's assume that we have some knowledge of such two numbers. I believe

In addition, we recognize how likely it is that she will receive either one or both letters: P(J|S)=0.8 P(J|W)=0.1

Note that P(S)+P(W)=1 since there are only two possibilities: P(S)=0.7 and P(W)=0.3.

P(J)=P(J|S) P(S)+P(J|W) P(W)

This is a representation of two distinct directions that could be taken. In one, we receive a compelling letter and ponder if she'll be hired in light of that compelling letter. As a result of the weak letter from the other, we are unsure if she will be hired. We give the pathway carrying the formal letter a higher weight because there is a substantially larger chance of receiving it compared to a weak letter.

The law of probability value is used in this situation.

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Answer:

  7

Step-by-step explanation:

You want the common difference of the arithmetic sequence that starts ...

  15, 22, 29, ...

The common difference is the difference between a term and the one before. It is "common" because the difference is the same for all successive term pairs.

  22 -15 = 7

  29 -22 = 7

The common difference is 7.

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Answer:

11/9,2

Step-by-step explanation:

Because we are doing this in school

Answer:

W) 1/18=10/180

N) 2/15=4/30

F) 7/12= 84/144

S) 9/25= 36/100

D) 7/20=35/100

T) 9/10=36/40

M) 19/20=95/100

Step-by-step explanation:

W) is 10/180 as you need to multiply the numerator as the denominator.

N) is 4/30 as you need to multiply the numerator as the denominator.

F) is 84/144 as you need to multiply the numerator as the denominator.

S) is 36/100 as you need to multiply the numerator as the denominator.

D) is 35/100 as you need to multiply the numerator as the denominator.

T) is 36/40  as you need to multiply the denominator as the numerator.

M) is 95/100 as you need to multiply the numerator as the denominator.

O sin(0.0005) ≈ 0.0005. The line tangent to the graph of f(x) = sin x at (0,0) is y = x.

The line y = x touches the graph of f(x) = sin x at exactly one point, (0,0). This means that the point (0,0) is on the line y = x and the slope of the line y = x is equal to the derivative of the function f(x) = sin x evaluated at x = 0. The slope of the line y = x is 1, so the derivative of f(x) = sin x evaluated at x = 0 is 1.

The line y = x is the best straight line approximation to the graph of f(x) = sin x for x near 0. This is because the first derivative of sin x evaluated at x = 0 is 1, which is the same as the slope of the line y = x. Therefore, the tangent line to the graph of f(x) = sin x at (0,0) is y = x.

Finally, O sin(0.0005) ≈ 0.0005. This is because sin x is approximately equal to x for small values of x. When x = 0.0005, sin x is approximately equal to 0.0005. Therefore, O sin(0.0005) ≈ 0.0005.

In summary, the line tangent to the graph of f(x) = sin x at (0,0) is y = x. The line y = x touches the graph of f(x) = sin x at exactly one point, (0,0). The line y = x is the best straight line approximation to the graph of f(x) = sin x for x near 0. O sin(0.0005) ≈ 0.0005.

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Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators.


Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators. These variables help measure and track progress towards a goal by providing a quantitative or qualitative measure of how far the target is from the desired level of achievement.

Performance metrics can be represented in various forms, such as distance covered, percentage completed, points earned, or even subjective evaluations. For example, in a fitness program, a performance metric could be the number of miles run or the number of push-ups completed.

These metrics enable individuals or organizations to assess their progress and make necessary adjustments to reach their desired outcomes.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

120

Step-by-step explanation:

20 x 6 = 120 which will be subtracted by his balance. hence the change.

Answer:

-$160

Step-by-step explanation:

20*6=160