Evaluate. Write your answer as a fraction or whole number without exponents. 7^–1 =

Answer:

its its 12.

Step-by-step explanation:

=8÷4×6+2-2

=2×6+2-2

=12+2-2

=14-2

=12 is answer..

Answer:

12

Step-by-step explanation:

8÷4×6+2-2

=2×6+2-2

=12+2-2

14-2

=12

Answer:

4. ± 3.012

Step-by-step explanation:

Hello!

Assuming that for both variables X₁ and X₂ n₁= n₂ = 16

You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.

The hypotheses are:

H₀: β₁= 0

H₁: β₁≠ 0

α: 0.01

[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]

The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"

The rejection region for this test is two-tailed, the critical values are:

±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]

I hope this helps!

Answer:

85.4

Step-by-step explanation:

first you have to find the radius before you find the area. so given the height, the radius is 11.3 meters. then, you need to find the area behind the arc, which is 85.4 meters/

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

How large of a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to be within $2,000? The population standard deviation is assumed to be $10,500. z-value for 98% confidence level is 2.326.

Answer:

Sample size = n = 150

Step-by-step explanation:

Recall that the margin of error is given by

[tex]$ MoE = z \cdot (\frac{\sigma}{\sqrt{n} } ) $\\\\[/tex]

Re-arranging for the sample size (n)

[tex]$ n = (\frac{z \cdot \sigma }{MoE})^{2} $[/tex]

Where z is the value of z-score corresponding to the 98% confidence level.

Since we want mean salary to be within $2,000, therefore, the margin of error is 2,000.

The z-score for a 98% confidence level is 2.326

So the required sample size is

[tex]n = (\frac{2.326 \cdot 10,500 }{2,000})^{2}\\\\n = (12.212)^{2}\\\\n = 149.13\\\\n = 150[/tex]

Therefore, we need to take a sample size of at least 150 state employees to estimate with 98% confidence the mean salary to be within $2,000.

Answer:

[tex]3{x}^{3} + 2x + 5[/tex]

Step-by-step explanation:

Sorry if my notes weren't very clear.

Answer:B

Step-by-step explanation: got it right

Answer:

"30 years or less when, in reality, the average age is more than 30 years"

Step-by-step explanation:

Type I error is produced when conclusion rejects a true null hypothesis.

The null hypothesis is

"The average gamer is more than 30 years old"

(deduced from the wording, not explicitly stated).

Then if the conclusion is "the average gamer is less than or equal to 30 years old" when in reality the average age is more than 30 years, then there is a type I error, since the null hypothesis is rejected.

Answer is D:

"30 years or less when, in reality, the average age is more than 30 years"

Answer:

3(7) + 2* |7 - 8| - 12 = 11

Step-by-step explanation:

3(7) + 2* |7 - 8| - 12

21 + 2* |-1| - 12

21 + 2* 1 - 12

21 + 2 - 12

23 - 12 = 11

Hope this helps! :)

Answer:

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 28.983051

Chi-square value = χ² = 2.154239

Degree of freedom = 1

Critical value = 3.841

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Step-by-step explanation:

He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.

So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Data collected by Dr. Pagels:

                                              meadow voles     common voles      Row Total

apple slices                                     26                          32                      58

peanut butter-oatmeal                   35                          25                     60

Column Total                                   61                          57                     118

Where 118 is the grand total.

The expected number is given by

Expected = (row total)×(column total)/grand total

Expected meadow vole/apple slices = 58×61/118

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 58×57/118

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 60×61/118

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 60×57/118

Expected common vole/peanut butter-oatmeal = 28.983051

The chi-square statistic value is given by

χ² = Σ(Observed - Expected)²/Expected

χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051

χ² = 2.154239

The degrees of freedom is given by

DoF = (row - 1)×(col - 1)

For the given case, we have 2 rows and 2 columns

DoF = (2 - 1)×(2 - 1)

DoF = 1

The given level of significance = 0.05

The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be

Critical value = 3.841

Conclusion:

Reject H₀ If χ² > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

For the given case,

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Answer:

(A) 1199.168

(B) 1503.372

(C) 159.17728

Step-by-step explanation:

(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.

Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524

The formula for finding X (the number of items in a given percentile) is:

X = M + Z(S.D.)

Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.

So for the 30th percentile,

X = 1261 + (-0.524)(118)

X = 1261 - 61.832 = 1199.168

(B) The number of chocolate chips that make up the middle 98% of chips in the bag is

X = 1261 + (2.054)(118)

X = 1261 + 242.372 = 1503.372

(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.

This is within 1.34896 standard deviations of the mean.

IQR = (1.34896)(118)

IQR = 159.17728

Step-by-step explanation:

36 ÷ (4 x 3)

36 ÷ 12

= 3

54 - 48 - (16 ÷ 4)

54 - 48 - 4

= 2

So first one is greater

Answer:

segment I'm and segment ad

Answer:

The answer is B

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

If they were opposite, they would be equal.

But they are not, (on one of the spaces in between them is smaller and one is larger.)

Hope I have helped you, since it seems I haven't helped "other people" the last time :/

Answer:

No

Step-by-step explanation:

Answer:

y=15; y=5

Step-by-step explanation:

y=x2+2x

plug in x as 3:

y=3 2+ 2*3

y=9+6

y=15

Next problem:

y=x3-3

plug in x as 2:

y=2 3-3

y=8-3

y=5

Answer:

Step-by-step explanation:

There are 9 possible outcomes for (Bill, Ben)'s cards:

  (4, 4) total 8; (4, 5) total 9; (4, 6) total 10;

  (5, 4) total 9; (5, 5) total 10; (5, 6) total 11;

  (6, 4) total 10; (6, 5) total 11; (6, 6) total 12.

Of these 9 outcomes, 4 have an odd total; 6 are less than 11.

 P(odd) = 4/9

  P(sum < 11) = 2/3

Answer:

if the order of the digit matters, we have:

options: 1, 2, 3, 4.

We want to select two digits.

First selection: we have 4 options

Second selection: we have 3 options (because we already selected one in the first selection)

The total number of elements in the sample space, or the total number of combinations, is equal to the product of the number of options in each selection, this is:

P = 4*3 = 12

Answer:

d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle

Step-by-step explanation:

13 − 01 + 1 = 13

34 − 14 + 1 = 21

56 − 35 + 1 = 22

99 − 57 + 1 + 1 = 44

Answer:

15

Step-by-step explanation:

PEMDAS

3x3 = 9

3+3 = 6

9+6 = 15

By the BODMAS rule we get, 3 + 3 × 3 + 3 =​ 15

The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).

3 + 3 × 3 + 3 =​

3 × 3 = 9

3 + 9 + 3 = 15.

Therefore, the correct answer is 15.

Learn more about BODMAS rule here:

https://brainly.com/question/16738857

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The 4 angles need to add to 360.

2 of them are 70

The other two need to equal 360-140 = 220

They are both the same so one angle needs to equal 220/2 = 110

Now find x:

X + 60 = 110

Subtract 60 from both sides:

X = 50. The answer is D

Answer: 5/26

Step-by-step explanation: 6/13 x 5/12

Answer:

  5

Step-by-step explanation:

Substitute the given values and do the arithmetic.

  [tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]

Answer:

Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]

Step-by-step explanation:

Ratio of the areas of the given circles are 1 : 4 : 16

Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]

                                                                             = 1 : 2 : 4

If the radius of the smallest circle = x units

Then the radius of the middle circle = 2x units

and the radius of the largest circle = 4x units

Area of the smallest circle = πx²

Area of the middle circle = π(2x)² = 4πx²

Area of the largest circle = π(4x)²= 16πx²

Area of the region which is not shaded in the middle circle = πx²(4 - 1)

                                                                                                  = 3πx²

Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded

= 16πx² - 3πx²

= 13πx²

Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]

= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]

= [tex]\frac{13}{16}[/tex]

Answer:

[tex]sin(A+B)=-\dfrac{345}{377}[/tex]

Step-by-step explanation:

Given that:

[tex]sin(A)=-\dfrac{20}{29}\\cos(B)=\dfrac{12}{13}[/tex]

A is in 3rd quadrant and B is in 1st quadrant.

To find: sin(A+B)

Solution:

We know the Formula:

1. [tex]sin(A+B) = sinAcosB+cosAsinB[/tex]

2. [tex]sin^{2} \theta+cos^{2} \theta=1[/tex]

Now, let us find the values of cosA and sinB.

[tex]sin^{2} A+cos^{2} A=1\\\Rightarrow (\frac{-20}{29})^2+cos^{2} A=1\\\Rightarrow cos^{2} A=1- \dfrac{400}{941}\\\Rightarrow cos^{2} A=\dfrac{941-400}{941}\\\Rightarrow cos^{2} A=\dfrac{441}{941}\\\Rightarrow cos A=\pm \dfrac{21}{29}[/tex]

A is in 3rd quadrant, so cosA will be negative,

[tex]\therefore cos A=-\dfrac{21}{29}[/tex]

[tex]sin^{2} B+cos^{2} B=1\\\Rightarrow sin^{2} A+(\frac{12}{13})^2=1\\\Rightarrow sin^{2} B=1- \dfrac{144}{169}\\\Rightarrow sin^{2} B=\dfrac{169-144}{169}\\\Rightarrow sin^{2} B=\dfrac{25}{169}\\\Rightarrow sinB=\pm \dfrac{5}{13}[/tex]

B is in 1st quadrant, sin B will be positive.

[tex]sinB =\dfrac{5}{13}[/tex]

Now, using the formula:

[tex]sin(A+B) = sinAcosB+cosAsinB\\\Rightarrow -\dfrac{20}{29} \times \dfrac{12}{13}-\dfrac{21}{29}\times \dfrac{5}{13}\\\Rightarrow -\dfrac{20\times 12+21\times 5}{29\times 13} \\\Rightarrow -\dfrac{240+105}{29\times 13} \\\Rightarrow -\dfrac{345}{377}[/tex]

[tex]sin(A+B)=-\dfrac{345}{377}[/tex]

Answer:

Step-by-step explanation:

The independent variables are the input values which are not dependent on the other value.

The dependent variables are the output values whose values depends on the value of some other number.

The independent variable in this case is the data on the set of distances she measured out.

The dependent variable in this case is the the time (measured by the stopwatch) it takes for the ball to roll.

The control variable in this case study is the size of ball, slope of hill, weight of ball etc.

Answer:

0.56

Step-by-step explanation:

What is the probability that his mother returns just in time to catch Gabe stealing a cookie?

The probability of this is the same as 1 minus the probability that Gabe is NOT caught.

- Judy could return at anytime in the next 90 seconds

- Gabe spends the first 40 seconds pondering... time wasted=40secs

- It takes 30 seconds (out of the remaining 50secs) to finish eating a cookie without a trace

- The question says that Gabe was going to do it, so he probably did

Now we're looking for the probability that he gets caught. That is, probability that he does not "successfully" complete the 30secs task within the remaining 50secs.

Remember that each second has an equal probability of being the second that Judy comes back in. The latter of the 90 seconds does not carry a higher probability!

So the probability of catching Gabe (despite the 30secs it takes to complete his task) is 50/90 which is equal to 0.56

Answer:

A

Step-by-step explanation:

Two congruent chords in a circle have the same distance from the center.

If two chords in a circle are congruent, then they are the same distance from the center of the circle .

The properties of Equal Chords of a Circle are:

According to the question

If two chords in a circle are congruent, then they are

Now,

By properties of Equal Chords of a Circle

The equal chords will be equal distance from the center of the circle .

Hence, If two chords in a circle are congruent, then they are the same distance from the center of the circle .

To know more about  properties of equal chords of a circle here:

https://brainly.com/question/14539317

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Answer: (1 and 22/45)

Step-by-step explanation:

I guess that we are working with mixed numbers here, and we have the equation:

(8÷2 2/9) − (2 11/15)

first we solve: 8÷2 = 4.

Now, we can write this as:

(4 + 2/9) - (2 + 11/15)

(4 - 2) + (2/9 - 11/15)

now, 9*5 = 45

        15*3 = 45

then we can write the right side as: 2/9 - 11/5 = 10/45 - 33/45 = -23/45

2 - 23/45

But in mixed numbers we also need to work with a positive rational, then we have:

2 - 23/45 = 1 + 1 -23/45 = 1 + 45/45 - 23/45 = 1 + 22/45

then the solution is:

(1 and 22/45)

Answer:

  -5

Step-by-step explanation:

The value of x that gives f(x) = 3 is -5.

  [tex]f^{-1}(3)=-5[/tex]