Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

Function Point
y = 8 + csc(x) / 7 - csc(x) (ㅠ/7, 2)

Answer:

1, 470

Step-by-step explanation:

4,200 * 0.35 = 1, 470

Answer:

2730 dollars

Step-by-step explanation:

35% of 4,200 is 1,470 so you want to subract 4,200 - 1470 = 2730

Answer:

y-intercept = 3

Step-by-step explanation:

The given equation is :

6x-5y=-15

We can rewrite it ib slope-intercept form as follows :

Dividing both sides by 5

\(\dfrac{6x}{5}-y=\dfrac{-15}{5}\\\\\dfrac{6x}{5}-y=-3\\\\\dfrac{6x}{5}+3=y\) .....(1)

The general equation of slope-intercept form is:

y = mx +c  ....(2)

On comparing equation (1) and (2) we get :

m = 6/5

c = 3

Hence, the y intercept of the graph of the equation is 3.

function is the answer of this question

Step-by-step explanation:

using the formula or so there a²+ b²= c²

so 18² + 80²= 82²

Answer:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

Step-by-step explanation:

Swap f(x) and x position of the function, thus:

\(\displaystyle{x=7f(x)+3}\)

Then solve for f(x), subtract 3 both sides and then divide both by 7:

\(\displaystyle{x-3=7f(x)}\\\\\displaystyle{\dfrac{x}{7}-\dfrac{3}{7}=f(x)}\)

Since the function has been inverted, therefore:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

And we can prove the answer by substituting x = 1 in f(x) which results in:

\(\displaystyle{f(1)=7(1)+3 = 10}\)

The output is 10, now invert the process by substituting x = 10 in \(f^{-1}(x)\):

\(\displaystyle{f^{-1}(10)=\dfrac{10}{7}-\dfrac{3}{7}}\\\\\displaystyle{f^{-1}(10)=\dfrac{7}{7}=1}\)

The input is 1. Hence, the solution is true.

The individual error rate for each of the 7 comparisons should be approximately 0.007 to maintain a family-wise error rate of 0.05. Option C is correct.

If there are 10 levels of one factor but only 7 comparisons are of importance, the total number of pairwise comparisons is given by the formula:

nC2 = (10 choose 2) = 45

Since only 7 of these comparisons are of importance, we need to adjust the individual error rate for multiple comparisons to maintain the overall family-wise error rate at 0.05.

Let α be the individual error rate for each of the 7 comparisons. Then, using the Bonferroni correction, the adjusted individual error rate for each comparison would be:

α' = α / m

where m is the number of comparisons of interest, which in this case is 7.

We want the family-wise error rate to be 0.05, so we have:

1 - (1 - α')^m = 0.05

Substituting α' = α / m, we get:

1 - (1 - α/m)^7 = 0.05

Solving for α, we get:

α ≈ 0.007

Option C is correct.

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The probability that the sample proportion is less than 0.27 with population mean 0.25 and sample size 107 is equals to 0.1844.

We have a historical data reports. Here claim is defined as, the manager believes that 25% of the company's orders come from first-time customers.

Sample size of orders, n = 107

We have to determine probability that the sample proportion is less than 0.27, i.e., P( X < 0.27). Now, 0.25 is the population proportion and sample proportion is

\(\hat p = 0.27 \). Calculate the

Standard deviations, σ \( = \sqrt{\frac{0.25 × (1 -0.25) } {107}} \)

= 0.0419

As we see the sample size is > 30, the normal distribution can be used. The Z-Score formula for sample proportion is written as \(Z = \frac{\hat p - p}{\sigma }\) , where, E --> standard error

Now, the required probability, P(p-hat< 0.27) = \(P (\frac{ \hat p - p }{ \sigma} < \frac{0.27 - 0.25}{0.0419})\)

= P ( Z < 0.48)

Using the distribution table value of P(Z< 0.48) is 0.1844. Hence, required probability value, P(p-hat < 0.27) is 0.1844.

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The result when dividing 2x + 5x³ + 7x² + 2x + 4 by -1 using synthetic division is -1. If there is a remainder, it is expressed as the sum of the quotient and the remainder, represented as g(x) + r(x).

To perform synthetic division, we set up the coefficients of the polynomial in descending order and divide them by -1:

```

    -1 |   5   7   2   2   4

       | -5   2  -2   0   -2

      -----------------------

       |   0   2   0   2    2

```

The result of the division is 2x² + 2. There is no remainder, so the expression is simply the quotient g(x) = 2x² + 2. In summary, when dividing 2x + 5x³ + 7x² + 2x + 4 by -1 using synthetic division, the result is 2x² + 2 with no remainder.

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Answer:

(2x + 4)^2 = -35200

....................

Answer:

97 degrees

Step-by-step explanation:

180 - 83 + 97

Answer:

∠? =97°

Step-by-step explanation:

because the 2 lines are paralel the 83° angle and the missing angle are suplementary angles so they add up to 180°

?= 180-83=97°

Given the velocity of an object, v(t) = 3t^2 - 12 m/s for t = 5 seconds. To find the distance travelled by the object in 5 seconds, we need to integrate the velocity function, v(t) with respect to time, t.

The integral of velocity with respect to time gives the distance travelled by the object.

So, the distance travelled by the object is given by d = ∫ v(t) dt, where v(t) = 3t^2 - 12 and the limits of integration are from 0 to 5 seconds

∴d = ∫ v(t) dt = ∫ (3t^2 - 12) dt (0 to 5)d = [(3/3)t^3 - (12)t] (0 to 5)d = [t^3 - 4t] (0 to 5)d = [5^3 - 4(5)] - [0^3 - 4(0)]d = (125 - 20) - (0 - 0)d = 105 m.

Therefore, the distance travelled by the object in 5 seconds is 105 m.

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Answer:

a= \(\frac{2}{5}\) or \(\frac{1}{2}\)

Step-by-step explanation:

Equate the equation to zero

\(10a^{2}\)-9a+2=0

\(10a^{2}\)-5a-4a+2=0

5a(2a-1)-2(2a-1)=0

Write out the factors

(5a-2)(2a-1)=0

Then equate each factor to zero

5a-2=0 OR 2a-1=0

5a=2  OR  2a=1

a= \(\frac{2}{5}\)   OR a= \(\frac{1}{2}\)

a=\(\frac{2}{5}\) or \(\frac{1}{2}\)

Answer:

\(m=1.5\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in the 2 coordinates into the slope formula to find slope m:

\(m=\frac{6.5-2}{7-4}\)

\(m=\frac{4.5}{3}\)

\(m=1.5\)

The length of h in the given parallelogram is 0.24

To help us solve this problem, please refer to the attached picture below for each corner annotation of the parallelogram.

First, we will try to focus on triangle AOD to find the length of OD.

We know that ABCD is a parallelogram and AD is parallel to BC; then AD = BC

AD = 5

To find the length of OD we will use the phytagoras theorem:

AD² = AO² + OD²

0.5² = 0.3² + OD²

0.25 = 0.9 + OD²

OD² = 0.16

OD = 0.4

Then, we will use the congruent triangle concept between triangle AOD and triangle CPD to find the length of h or PD.

Based on the congruent triangle concept; we know that AD and DC should be congruent; then:

AD / DC = AO / DP

0.5 / 0.4 = 0.3 / h

h = 0.24

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Answer:

1759.6

Step-by-step explanation:

8.3 multiplied by 212 i think

Remember that

P(A or B)=P(A)+P(B)-P(A and B)

In this problem, we have that

Event A and Event B are not independent

we have

P(A)=0.68

P(B)=0.32

P(A and B)=0.11

substitute

P(A or B)=0.68+0.32-0.11

P(A or B)=0.89

Answer:

For A, the confidence interval formula above cannot be applied because n is less than 30, so we use the t-score confidence interval value

C.I = Mean ± t score × Standard deviation/√n

Mean = 80

Standard deviation = 5

n = 25

Degree of freedom = 25 - 1 = 24

Hence, 95% confidence interval degree of freedom t score = 2.064

Hence, Confidence Interval =

80 ± 2.064 × 5/√25

80 ± 2.064 × 1

80 ± 2.064

Confidence Interval =

80 - 2.064

= 77.936

80 + 2.064

= 82.064

Confidence Interval: (77.936, 82.064)

The skeletons are 1056.474145 years old in 1989

Given:

Exponential decay model for carbon-14, A = A₀ e^(-0.000121 t)

The skeletons contained 88% of the expected amount of carbon-14 found in a living person

To determine how old the skeletons were, you will need to solve for t  in the exponential decay model:

A = A₀ e^(-0.000121 t)

A/A₀ = e^(-0.000121 t)          (Given: A/A₀ = 88%  = 0.88 )

0.88 = e^(-0.000121 t)

e^(-0.000121 t)  = 0.88

-0.000121 t = ln (0.88)

t = ln (0.88) / -0.000121

t = 1056.474145 years

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Therefore , the solution of the given problem of area comes out to be the picture's revised dimensions are 21 feet long and 15 feet wide.

What is scale factor?

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.

What exactly does an area mean?

Its total size can be determined by figuring out how much area would be required to completely enclose its exterior. When choosing a comparable product for the rectangular design, the surrounding area is taken into account. The total measurements of something are determined by its surface area. The volume of water a cuboid can contain depends on the number in sides between its four trapezoidal shapes.

Here,

The initial image's length and width must be multiplied by 3 in order to enlarge it by a scale factor of 3.

=>  7 feet in length at first.

=>  5 foot original diameter

=> New length = 7ft x 3 = 21ft

=>  New width = 5ft x 3 = 15ft

As a result, the picture's revised dimensions are 21 feet long and 15 feet wide.

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There is no statistical evidence of a prolonged lifetime of the stents.

Given data,

n (sample size) = 100

X (sample mean) = 9.3

s (sample standard deviation) = 3.8

Next, we need to define the null hypothesis and alternative hypothesis

Null hypothesis

\(H_{o}\) : u (mu) = 8.7

Alternative hyptohesis

\(H_{o}\) : u (mu) > 8.7

Next, we need to do hypothesis testing to get the claim about a population mean is tested under the null and the alternative hypotheses by using t-test and p-value.

t-test is a sampling test statistic and used when the population standard deviation is unknown.

the t-test can be calculated as follows:

= \(\frac{X-u}{s/\sqrt{n} }\)

= \(\frac{9.3-8.7}{3.8/\sqrt{100} }\)

= 1.578

Next, we need to calculate the p-value using Microsoft excel function. The p-value helps decide whether to reject the null hypothesis.

Enter the function below in excel to calculate p-value:

=TDIST(1.578,40-1,1)

= 0.061322.

The p-values is greater than the common threshold ( p<0.05), which means We can conclude that there is no statistical evidence of a prolonged lifetime of the stents.

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Answer:189 hours

Step-by-step explanation: 398 divided by 2 =199 -10 =189

The proof of the congruent sides RU and TS is given below.

What is congruent triangles?

In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

Let the given figure is a rectangle RSTU.

Since the all four angles of rectangle are of 90 degree.

So, each angle of rectangle RSTU is 90 degree.

Let, US divides the angle RUT and angle RST and form two new triangles, ΔSRU and ΔSTU.

Both the triangles having same measure of angles and sides.

⇒  ΔSRU ≅ ΔSTU

As the triangles are congruent so their sides are congruent.

Hence, RU is congruent to TS.

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The probability that the mean of a sample of 45 boards will be between 94.5 inches and 95.1 inches, given that the length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches, can be calculated using the Central Limit Theorem. The theorem states that the distribution of sample means will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean (μ) is 95 inches, the population standard deviation (σ) is 0.52 inches, and the sample size (n) is 45. The standard deviation of the sample mean is σ/√n = 0.52/√45 ≈ 0.0775.

To find the probability, we can use the Z-score formula:

Z = (X - μ) / (σ/√n)

For the lower limit of 94.5 inches, the Z-score is:

Z1 = (94.5 - 95) / 0.0775 ≈ -6.45

For the upper limit of 95.1 inches, the Z-score is:

Z2 = (95.1 - 95) / 0.0775 ≈ 1.29

Now, using a Z-table or calculator, find the probability for each Z-score:

P(Z1) ≈ 0 (since it is a very low Z-score)
P(Z2) ≈ 0.9015

The probability that the mean of the sample will be between 94.5 inches and 95.1 inches is the difference between these probabilities:

P(94.5 < X < 95.1) = P(Z2) - P(Z1) = 0.9015 - 0 ≈ 0.9015, or approximately 90.15%.

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Answer:

3,2

Step-by-step explanation:

Answer:

(3,1)

Step-by-step explanation:

If you moved two units left you would be at (3,2) the move one down you would be at (3,1)

The answer would be -49/18 after dividing 4 5/6 and -2 1/7, or in mixed fraction -2 13/18.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Divide 4 5/6 and -2 1/7

4 5/6 = 35/6

-2 1/7 = -15/7

= (35/6)/(-15/7)

= (35/6)(-7/15)

= -245/90

= -49/18

= -2 13/18

Thus, the answer would be -49/18 after dividing 4 5/6 and -2 1/7, or in mixed fraction -2 13/18.

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Answer:

-2x^2-2x

Step-by-step e-xplanation:

−2x2−4x+2−(−6x+2)

Distribute the Negative Sign:

=−2x2−4x+2+−1(−6x+2)

=−2x2+−4x+2+−1(−6x)+(−1)(2)

=−2x2+−4x+2+6x+−2

Combine Like Terms:

=−2x2+−4x+2+6x+−2

=(−2x2)+(−4x+6x)+(2+−2)

=−2x2+2x

The slope of the line is-7/6

The sampling Distribution of the sample proportion of people who answer yes to the question is normal with mean p = 0.6 and standard deviation σp = 0.049.

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading. We will take a random sample of 100 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is binomial.

The binomial distribution is appropriate since there are two possible outcomes: either a person believes that Martha Stewart is guilty of obstruction of justice and fraud related to insider trading or does not believe so. The sample size is n = 100.

The probability of a person believing that Martha Stewart is guilty is p = 0.6 and the probability of a person not believing is q = 1 - p = 0.4.

The mean of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:μp = p = 0.6

The variance of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:σ²p = pq/n = (0.6)(0.4)/100 = 0.0024

The standard deviation of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:σp = sqrt(σ²p) = sqrt(0.0024) = 0.049

This standard deviation measures how much the sample proportion is likely to vary from one sample to another. The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal by the Central Limit Theorem (CLT) if the sample size is sufficiently large, which is the case here since np and nq are both greater than or equal to 10: np = (100)(0.6) = 60 and nq = (100)(0.4) = 40.

Therefore, the sampling distribution of the sample proportion of people who answer yes to the question is normal with mean p = 0.6 and standard deviation σp = 0.049.

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Answer: 33/100, 33%

Step-by-step explanation:

I can't choose two answers if you don't give me the possible answers

67 days of homework = 100-67 or 33 days without homework.

33/100 or 33%

Step-by-step explanation:

100% = 100 days

1% = 100%/100 = 100/100 = 1 day

the student does NOT have homework on 100-67 = 33 days.

that is 33 out of 100 days or on 33/100 of days.

33 days are 33×1% = 33%