Find the equation of the line that passes through the points (3, 4) and (-3, 2).

y(x) = tan(x + C) where C is an arbitrary constant of integration. Thus, the equilibrium solutions are y = 1 and y = -1. The non-equilibrium solutions are the values of y that make y' not equal to 0.

y(x) = tan(x + C)

Where C is an arbitrary constant of integration.

The solution y(x) = tan(x + C) is a family of functions indexed by the arbitrary constant C. The constant C cannot be determined from the information given in the problem, and so the general solution contains all possible specific solutions.

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The appropriate p-value for the given test statistic and hypotheses is approximately 0.0253.

Tο determine the apprοpriate p-value fοr the given hypοthesis test, we need tο use the t-distributiοn and the t-statistic value οbtained.

Given:

Null hypοthesis (H0): μ = 130 (pοpulatiοn mean)

Alternative hypοthesis (HA): μ > 130 (pοpulatiοn mean)

T-statistic: t = 2.73

Degrees οf freedοm: df = 5

Tο calculate the p-value, we cοmpare the t-statistic tο the t-distributiοn.

Since the alternative hypοthesis is μ > 130, it is a οne-tailed test, and we are interested in the right tail οf the t-distributiοn.

Using a t-table οr a statistical sοftware, we can determine the p-value assοciated with the t-statistic and the degrees οf freedοm.

Fοr a t-statistic οf 2.73 with 5 degrees οf freedοm, the p-value is apprοximately 0.0257 (assuming a twο-tailed test).

Since we have a οne-tailed test, the apprοpriate p-value is half οf the twο-tailed p-value:

p-value = 0.0257 / 2 = 0.01285

Therefοre, the apprοpriate p-value fοr the given hypοthesis test is apprοximately 0.01285.

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Answer:

9 2/12 more feet

Step-by-step explanation:

Answer:

5.8 lemme know if im wrong :)

Step-by-step explanation:

Answer:

5 4/5. ( decimal 5.8)

Step-by-step explanation:

21 1/2 -15 7/10

= 43/2 - 15 17/10

=43/2 - 157/10

=29/5

= 5 4/5

The distance between N and PS is 3.2.

What is the midpoint of the segment?

Take the distance between the two endpoints and divide it by two. This distance from either end is the line's midpoint. Alternatively, add the endpoints' x coordinates and divide by 2. Repeat for the y coordinates.

From the below figure,

N is the intersection of the red and blue circles.

I’ve drawn PQRS as the square (0,0), (4,0), (4,4), and (0,4).

Then the formula for the red circle is:

             (x-2)² + (y-4)² = 4.

The formula for the blue circle is

                  x² + y²- 16 = 0.

Solving for x and y yields intersections

               (0, 4) and (3.2, 2.4),

the first being S and the latter being N.

Hence, the distance between N and PS is 3.2.

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Answer: If each person tells 2 people each day, 1,024 people will know in 10 days.

Step-by-step explanation: Basically it is 2 to the 10th power. It is 2 to the 10th power because in 10 days 2 people each day are getting told this information and those same 2 people spread this information. So if 2 people each day for 10 days tell people about the product, 1,024 will know by the tenth day.

Nancy has a 1/256 chance of getting all the questions right, a 81/256 chance of getting at least one question right, a 255/256 chance of getting at least one question wrong, and a 255/256 chance of getting all the questions wrong.

The following parts can be solved by the concept of Probability.

(a) The probability of getting all four questions right is (1/4)^4 since there are four questions and four choices for each question. Therefore, the probability is 1/256.

(b) The probability of getting all four questions wrong is the complement of getting all the questions right, which is 255/256.

(c) The probability of getting at least one question right is the complement of getting all the questions wrong, which is 255/256. Therefore, the probability is 1 - (255/256) = 1/256.

(d) The probability of getting at least one question wrong is the complement of getting all the questions right, which is 255/256. Therefore, the probability is 1 - (1/256) = 255/256.

Therefore, Nancy has a very low chance of getting all the questions right or wrong, but a much higher chance of getting at least one question right or wrong..

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For the given figure, the area of the shaded region is obtained as 100 m².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The area of shaded region can be obtained as -

Area of shaded region =  Area of rectangular concrete path - Area of rectangular lawn

The formula for area of rectangle is -

Area of rectangle  =  Length × width

The area of rectangular concrete path is -

Length  =  (30+2) m  =  32 m

width  =  (18+2) m  =  20 m

Area of rectangular concrete path  =  32 × 20

Area of rectangular concrete path  =  640 m²------(1)

The area of rectangular lawn is -

Length  =  30 m and width  =  18 m

Area of rectangular lawn  =  30 × 10

Area of rectangular lawn  =  540 m²------(2)

To find the are of shaded region subtract equation (2) from (1) =

Area of shaded region = (1) - (2)

Area of shaded region =  (640 – 540) m²

Area of shaded region =  100 m²

Therefore, the total area of concrete is 100 m².

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A rectangular lawn 18 m by 30 m is surrounded by a concrete path 1 m wide. Draw a diagram of the situation and find the total area of concrete.

The answer to the given question is nominal and ordinal measurements. These two type measurements are used to group respondents or objects into groups or categories and also considered as categorical measures.

Nominal measurement is the least accurate and informative, because it only names the characteristic or identity which we are interested. In nominal variables, the numerical values just "name" the attribute differently. Thus, numerical value is simply a label.

Ordinal measurement reports the ranking and ordering of the data without chartering the degree of variation. Ordinal measurement includes statistical data type in which variables are in order or rank but without a degree of difference between categories. The ordinal measurement includes qualitative data. This measurement places variables in order or rank, and only allowing to measure the value as higher or lower in measurement.

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Answer:

the fraction would be \(\frac{1}{8}\)

Step-by-step explanation:

The computation of the fraction of the wall does annika paint blue is shown below:

\(= Wall \ in\ the\ yellow \times yellow\ part\ blue\\\\= \frac{1}{2}\times \frac{1}{4}\\\\= \frac{1}{8}\)

hence, the fraction would be \(\frac{1}{8}\)

The same would be considered and relevant too/

Answer:

We can conclude they are congruent

Step-by-step explanation:

Because of the vertical angles theorem

There is a slight possibility of 0.000240 that  5 card hand contains a four-of-a-kind, where the four-of-a-kind rank is a face card.

Total possible outcomes=⁵²C₅

                                        = 2598960

P( 4-of-a-kind) = ¹³C₁ * ⁴C₄

                        = 13

P( choosing one card from the rest of the deck) = ⁴⁸C₁

                                                                                 =48

P( 4-of-a-kind card with one different card)

= desired outcome / total number of outcomes.

= (13* 48) / 2598960

= 624/2598960

= 0.000240

Therefore, we get that the probability is 0.0240% .

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The mean and median next 12 months PE ratios of the group are the mean multiple followed by the median multiple, comma-separated with no spaces.

The mean and median next 12 months PE ratios of the group can be found by following these steps:
1. Gather next 12 months PE ratios for each company.
2. Calculate mean by summing the ratios and dividing by total number.
3. Arrange ratios in ascending order.
4. Find the middle value(s) to determine the median.
5. Write the mean multiple followed by the median multiple, comma-separated with no spaces.

Therefore, the mean and median next 12 months PE ratios of the group are the mean multiple followed by the median multiple, comma-separated with no spaces.

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Answer:

midpoint= x1+x2/2, y1+y2/2

5.5+2.25/2,-3.75,-2.25/2

=7.75/2,-6/2

=(3.875,-3)

Answer: Your answer is: (3 7/8, -1 3/4)

Step-by-step explanation:

Note/The midpoint WILL be the average of the endpoints.

coordinates:(5 1/2, -4 3/4)PLUS(2 1/4, 1 1/4)/2=(7 3/4, -3 1/2)/2 = (3 7/8, -1 3/4)

Hope this helps

The value of f(f^(-1)(4)) depends on the specific function f and its inverse f^(-1). Without knowing the function f, we cannot determine the exact value of f(f^(-1)(4)). Therefore, correct answer is option 5: Need to know f.

To evaluate the expression f(f^(-1)(4)), we would need to know the explicit form of the function f and its inverse f^(-1). Once we have the function f and its inverse, we can substitute f^(-1)(4) into f to find the corresponding output value. However, without this information, we cannot determine the result of f(f^(-1)(4)).

In summary, the value of f(f^(-1)(4)) cannot be determined without knowing the specific function f and its inverse.

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The percent increase in the cost of the coffee is 20%

percentage, a relative value indicating hundredth parts of any quantity.

Given that At a coffee shop, the price of a cup of coffee increased from $1.20 to $1.44

We need to find the  percent increase in the cost of the coffee

Original price-Change price/original price

1.20-1.44/1.20

0.20

Now multiply with 100 as it is hundredth part

0.20×100

20%

Hence,  the percent increase in the cost of the coffee is 20%

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Answer:

Step-by-step explanation:

To estimate the required sample size for estimating the true proportion of Americans who support gun control in 2018 with a 95% confidence level and a margin of error of 0.36, we need to use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (for 95% confidence level, Z ≈ 1.96)

p = estimated proportion (since we have no prior information, we can use p = 0.5, which gives the maximum sample size required)

E = margin of error

Substituting the values into the formula:

n = (1.96^2 * 0.5 * (1 - 0.5)) / 0.36^2

n = (3.8416 * 0.25) / 0.1296

n ≈ 9.6042 / 0.1296

n ≈ 74.0842

Rounding up to the nearest whole number, the required sample size is approximately 75. Therefore, you would need to survey at least 75 randomly selected Americans to estimate the true proportion of Americans who support gun control in 2018 with a 95% confidence level and a margin of error of 0.36.

The deposit is given as follows:

$7,502.

The amount of money earned, in compound interest, after t years, is given by:

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

In which:

The parameters for this problem are given as follows:

t = 4, A(t) = 10000, r = 0.0725, n = 4.

Hence the deposit is obtained as follows:

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

\(10000 = P\left(1 + \frac{0.0725}{4}\right)^{4 \times 4}\)

1.33296156P = 10000

P = 10000/1.33296156

P = $7,502.

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Answer:

≈  14.6

I'm assuming that says use 3.14 as radius, because it's cut off

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer:

12

Step-by-step explanation:

distribute the 2, turning the equation into 2x+12=36

subtract 12 from both sides, now resulting in 2x=24

then divide by 2

Step-by-step explanation:

2(x+6)=36

2x+12=36

collect like terms

2x=36-12

2x=24

divide both sides by 2

2x/2=24/2

x=12

Answer:

a = 60°, b = 40°, x = 30°

Step-by-step explanation:

The top half:

2x + x + 3x = 180° (angles on a straight line sum up to 180°)

6x = 180° (divide both sides by 6)

x = 30°

Bottom half:

2x is vertically opposite to 'a' which means they are equal: 2x = a = 60°

180 - 60 (a) = 120° (angles on a straight line sum up to 180°)

b + 2b = 120° (simplify)

3b = 120° (divide both sides by 3)

b = 40°

Hope this helps!

Answer:

the value of x is 30, so the angles in the upper are 60, 30 and 90 in that order, also a is 60 and b is 40, then the lower angles are 40, 80 and 60

If the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

As we know that,

Statustical significance refers to claim that a result from data generated by testing or experimentation is likely to be attributable to specific cause.

Sample size is the total number of individuals or items that comprise a sample.

And, the variance is a descriptive statistic, which falls under the category of a measure of spread.

The circumstance in which a very small treatment effect can be found to be significant is best described by option A: If the sample size big and the sample variance is small.

A large sample size will increase the probability that the results of a statistical test will yield significant results. This is why most statistical tests are accompanied by a measure of effect size. A statistically significant result associated with a very large sample size, will likely have a small effect size, an undesirable result for a researcher, as it implies one of the only reasons significant results were obtained was due to the large sample, not necessary the magnitude of the experimental effect.

Likewise, if variance is small, this will also increase the probability that the results of a statistical test will yield significant results. Variance is simply another word in statistics for the error. A decrease in error will lead to an increased probability of obtaining significant results, hence the idea that a small amount of variance will lead to an increased probability of significant results.

Hence, if the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

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Answer:

well time has to be on the X-axis because it is an independent variable

as a distance will be dependent variable Y-axis

Answer:

D

Step-by-step explanation:

is the correct answer i believe.

Answer:

B. 0,3

Step-by-step explanation:

I took the test and checked the answer, 0,3 is correct.

Answer:

26

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Shawna needs a mix of 4 cups of yoghurt and 6 cups of blueberries

Step-by-step explanation:

Here, we want to know the number of cups of yoghurt and smoothies Shawna needs to make;

We have 2 parts yoghurt and 3 parts blueberry, so we can say we have a ratio of 2:3

The total number of cups to be made is 10

So the number of cups of yoghurt will be;

2/(2+3) * 10

= 2/5 * 10 = 4 cups

The number of cups of blueberry would be;

3/5 * 10 = 6 cups

So a mix of 4 cups of yoghurt and 6 cups of blueberries is needed by Shawna