find the interval on which the function is continuous

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

the answer is C mean absolute deviation

Answer:

4th graph (in bottom right corner)

Step-by-step explanation:

First, convert the given equation into slope-intercept form.

Given :-

1/2x - 2y > -6

-2y > -1/2x - 6

2y < 1/2x + 6

y < 1/4x + 3

As the < sign indicates, the line will be dotted and the solution set will be towards the origin in this case.

The correct option is the 4th graph (in bottom right corner)

=======================================================

Explanation:

A decrease of 17% means that he made 100% - 17% = 83% of what he did last year.

83% = 83/100 = 0.83

83% of $55,000 = 0.83*55000 = 45,650 dollars

Answer:

y = 2/3x+4

Step-by-step explanation:

Answer:

A. \(n=100\)
B. \(k=0\)

Step-by-step explanation:

A. The equation "110% n = 11" can be solved as follows:

110% n = 11

To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).

(110% n) / 110% = 11 / 110%

n = 11 / 0.110

n = 100

So, the solution for n in the equation "110% n = 11" is n = 100.

B. The given equation is:

(328 x 128) x k = 328 x (82 x 128) x k

To solve for k, we can simplify the equation using the properties of multiplication.

Step 1: Perform the multiplications inside the parentheses:

41984 x k = 328 x 10576 x k

Step 2: Rearrange the equation by applying the associative property of multiplication:

41984 x k = 328 x (10576 x k)

Step 3: Divide both sides of the equation by 328:

(41984 x k) / 328 = 10576 x k

Step 4: Cancel out the common factor of k on the left-hand side:

(41984 / 328) x k = 10576 x k

Step 5: Simplify the left-hand side:

128 x k = 10576 x k

Step 6: Subtract 10576 x k from both sides of the equation to isolate k:

128 x k - 10576 x k = 0

Step 7: Factor out k on the left-hand side:

k x (128 - 10576) = 0

Step 8: Simplify further:

k x (-10448) = 0

Step 9: Divide both sides of the equation by (-10448):

k = 0

So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.

For the first equation, we can complete the square to find its vertex form. Here's how we do it:

0 = x^2 - 18x + 1

0 = (x - 9)^2 - 80

So we have (x - 9)^2 = 80. This is in the form (x - p)^2 = q, where p = 9 and q = 80.

For the second equation, we can complete the square in a similar way:

x^2 + 26x + 167.5 = 0

x^2 + 26x = -167.5

x^2 + 26x + (26/2)^2 = -167.5 + (26/2)^2

(x + 13)^2 = 9.25

So we have (x + 13)^2 = 9.25. This is in the form (x - p)^2 = q, where p = -13 and q = 9.25.

I hope that helps!

The interest monthly is  1332.94(approx.)

Given,

You borrowed $ 1,892 for 9 years with compound interest rate of 5.94 %.

To find the how much interest you have to pay to the lender.

Now, According to the question:

Based on the given conditions,

Formulated:

We know that:

Formula of Compound Interest:

A = P\((1 + \frac{r}{n} )^n^t\)

P = $1,892

r = 5.94%

n = 12

t = 9 years

Put the values in above formula:

A = 1892.\((1+ \frac{5.94}{12} )^1^2^.^9\)

Evaluate the equation/ expression:

A = 1332.94(approx.)

Hence, The interest monthly is  1332.94(approx.)

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The z-score of a person who scored 330 on the exam is approximately 2.7.

To find the z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where:

z is the z-score

x is the raw score (330 in this case)

μ is the mean (195 in this case)

σ is the standard deviation (50 in this case)

Substituting the values into the formula, we get:

z = (330 - 195) / 50

z = 135 / 50

z = 2.7

The z-score of a person who scored 330 on the exam is 2.7.

The z-score measures the number of standard deviations a particular data point is away from the mean.

In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean score of 195.

The z-score is useful for comparing data points across different normal distributions or for determining the relative position of a data point within a distribution.

A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

In this context, a z-score of 2.7 suggests that the person's score is relatively high compared to the average performance on the exam.

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Answer/Step-by-step explanation:

Equation to represent the daily rental cost for each type of truck can be written as follows:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Where, m = Emily's mileage

To determine the number of miles for which the truck cost the same amount, set both equations equal to each other and solve for m.

\( 42 + 0.72m = 70 + 0.12m \)

Collect like terms

\( 0.72m - 0.12m = 70 - 42 \)

\( 0.6m = 28 \)

Divide both sides by 0.6

\( \frac{0.6m}{0.6} = \frac{28}{0.6} \)

\( m = 46.7 \)

At approximately 47 miles, both trucks would cost the same amount.

Check:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Plug in the value of x = 47

= 42 + 0.72(47) = $75.84 ≈ $76

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Plug in the value of x = 47

= 70 + 0.12(47) = $75.64 ≈ $76

Answer:

83.4

Step-by-step explanation:

16.2 x 2

=

32.4 +

1/2 x 8.5 x 12  

=

51 + 32.4 = 83.4

Hope this helps!

Answer:

the equation would be y = 3x +6

Answer:

y = 1/3x        y - 0 = 1/3 (x - 0)

Step-by-step explanation:

slope intercept: y = 1/3x

point slope: y - 0 = 1/3 (x - 0)

Answer:

How spread out are the values for perseverance among teenage boys?

Step-by-step explanation:

1. What is the most common value for the variable perseverance among teenage boys? - This deals with MODE. Hence, this option is not correct because the problem does not deal with a specific value of the perseverance variable but about the variability of the perseverance variable

2. What is the central tendency for the variable perseverance among teenage boys? - This deals with the MEDIAN. However, since the problem is about determining dispersion, and not a central tendency, it is incorrect.

3. What is the average value for the variable perseverance among teenage boys? - This deals with the MEAN. Hence, it is not correct either.

However, since the given situation deals with a measure of variability for the variable perseverance conveys, the correct answer is "How spread out are the values for perseverance among teenage boys?" Because it measures how far are the observation away from the center.

Answer:

Opal saves more

Step-by-step explanation:

Yes, the problem describes a valid simulation design.

We do sampling so that we don't have to work on entire population of items but only on that sample in a way that we can predict information about population.

Most of the times, it isn't possible in real world to work on entire populations. Samples come out for rescue by assumptions that they will have some properties of the population pertained in them.

Thus, the sample should be taken out such that it includes data of the population as much  as it can in unbiased way so as to imitate population. (assuming that we want the sample to contain the summary of the population).

We are given that;

A media report claims that 50% of U.S. teens with smartphones feel addicted to their devices.

A sample of 100 U.S. teens who have smartphones was taken.

Only 40 of the teens in the sample feel addicted to their devices.

The goal is to estimate the probability of getting 40 or fewer teens who feel addicted to their devices in a random sample of size 100 from a population of teens with smartphones in which 50% feel addicted to their devices.

A simulation is proposed where 1 represents feeling addicted and 2 represents not feeling addicted.

Now,

The simulation design involves randomly selecting a sample of 100 U.S. teens who have smartphones and then using a random number generator to simulate the proportion of teens who feel addicted to their devices. This is a valid simulation because it mimics the process of sampling from a large population, and the use of a random number generator ensures that the simulation is unbiased and reflects the randomness inherent in the sampling process.

By repeating this process many times and calculating the percent of trials on which the number of 1's (teens who feel addicted to their devices) was 40 or less, we can estimate the probability of getting such a result by chance. This will help us determine whether the sample of 40 teens who feel addicted to their devices is consistent with the media report's claim that 50% of U.S. teens with smartphones feel addicted to their devices.

Therefore, by sampling the answer will be yes

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Answer:

0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

20% of employees would like to move into management and be the boss.

This means that \(p  = 0.2\)

Sample of 75:

This means that \(n = 75\)

Mean and standard deviation:

\(\mu = E(X) = np = 75(0.2) = 15\)

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{75*0.2*0.8} = 3.4641\)

Find the probability that at least 18 of the 75 sampled employees would like to move into management.

Using continuity correction, this is \(P(X \geq 18 - 0.5) = P(X \geq 17.5)\), which is 1 subtracted by the p-value of X = 17.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{17.5 - 15}{3.4641}\)

\(Z = 0.72\)

\(Z = 0.72\) has a p-value of 0.7642.

1 - 0.7642 = 0.2358

0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.

Answer:

step explanation: 16+ 16 = 32

The polynomials in this problem that are in standard format are given as follows:

A. \(t^4 - 1\)

B. -2t² + 3t + 4.

C. 4t - 7.

The standard format of a polynomial is to write it in descending order of the exponents of the variable, with each term separated by a plus or minus sign.

For example, the standard format of a polynomial p(x) of the nth degree is given as follows:

\(p(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0\)

In which \(a_n, a_{n - 1}, \cdots, a_0\) are the coefficients.

For this problem, in all of the options a, b and c, the exponents are in decreasing order, hence the polynomials are in standard format.

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The value of {h} is equivalent to 6/5.

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

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 function takes.

Given is the function as follows -

(1/5) + h = (7/5)

We can write the function as -

(1/5) + h = (7/5)

h = 7/5 - 1/5

h = (7 - 1)/5

h = 6/5

Therefore, the value of {h} is equivalent to 6/5.

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The expressions that will correctly calculate what percent 19 is of 20 are:

A.19/20 .100

D.19.100/20

The concept that will be used here is percentage. A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

From the options we can see that to find the percentage of 19  of 20, iot can be expressed mathematically as :

(19/20) *100 and this can as well be expressed as (19*100)/20 becausethey will still give use the same value which is 95%

Therefore, option A and D are correct.

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Elements of following sets are

A = {1}

B = {-1, 1}

C = Q ∩ [0, 1]

Sets

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set. A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Given that

A = {n ∈ N : cos(nπ) greater than or equal to 0}

B = {cos(nπ) : n ∈ N}

C = {q + r : q, r ∈ Q ∩ [0, 1]}

Therefore elements of

A = {1}

as cos 2\(\pi\), cos 4\(\pi\), cos 6\(\pi\), cos 8\(\pi\) and so on is equal to 1.

B = {-1, 1}

as cos \(\pi\) , cos 2\(\pi\), cos 3\(\pi\), cos 4\(\pi\), cos 5\(\pi\) and so on is equal to -1 and 1.

C = Q ∩ [0, 1]

as q and r both belongs to Q ∩ [0, 1] and their sum will be also equal to Q ∩ [0, 1].

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Answer:

2.92 × 10⁹

Step-by-step explanation:

im not exactly sure if im right but this is what i know, lmk if its wrong

Answer:

2.92 x 10  12

Step-by-step explanation:

step one- make your number into a number 1-10

step two-write x10

step three- count how many times you moved your decimal :)

The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

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Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer: what is the answer

Step-by-step explanation:

TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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The distance from the pole at which the cable is anchored is about 25 feet from the pole .

Given that a 35-foot cable is run from the top of the pole and anchored to the ground at a distance from the pole. The problem is to determine about how far away from the pole would it be anchored.

Let AB be the pole of length 40 feet, and CD be the 35-foot long cable anchored to the ground at D and attached to the top of the pole at C. Let E be the point on the ground at which the cable is taut and is anchored. The distance ED is to be determined.

we can see that ∆CDE is a right-angled triangle with ∠CED = 90°.

Using Pythagoras Theorem, we have:CD² = CE² + DE²35² = (40 - ED)² + DE² .

Simplifying the above equation

1225 = 1600 - 80ED + ED²

1225 - 1600 + 80ED - ED² = 0ED² - 80ED + 375 = 0

Factorizing the above quadratic equation

ED² - 25ED - 15ED + 375 = 0ED(ED - 25) - 15(ED - 25)

  = 0(ED - 15)(ED - 25) = 0So, ED = 15 ft or ED = 25 ft.

The negative value of ED is extraneous since it represents a point below the ground, which is not possible. Therefore, the distance from the pole at which the cable is anchored is about 25 feet from the pole.

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