Sara's boss informed her she is getting a 5% raise. She currently makes $22 per hour. What is her new hourly wage?​

Answer:

12 yards

Step-by-step explanation:

Based on their given probabilities, e would expect the color blue or green to be spun approximately 75 times in this experiment.

To find the expected number of times the color blue or green will be spun, we first need to add their probabilities:

0.25 + 0.125 = 0.375

This means that, on average, we would expect to see blue or green spun 0.375 times for every spin. To find the expected number of times this will happen over 200 spins, we can multiply the probability by the number of spins:

0.375 x 200 = 75

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Answer:

Each term is a sum of the two previous terms like the fibonacci sequence, but the sum of the two starting terms of the lucas sequence is followed by 2 then 1, rather than 0 then 1 for the fibannaci sequence.

These are integer sequences.

The sum of the two previous terms can be represented by:

fn = fn-1 + fn-2.

These numbers can be obtained by adding the previous corresponding term of the fibonacci sequence by the next corresponding term to get the corresponding number of the lucas sequence.

Ln = { 2 if n = 0

1 if n = 1

Ln-1 + Ln-2 if n > 1

________________

Fn+1 + Fn-1 = Ln

___________________

f(0) = -1

f(1) = 2, f(2) = 1, f(3) = 3, f(4) = 4, f(5) = 7, f(6) = 11

________________________________

f(12) = 199

________

f(12) = f(11) + f(10) = (f(10) + f(9)) + (f(9) + f(8)) = .....

given f(n) = f(n-1) + f(n-2)

____________________

f(12) = f(1) + f(2) = f(2) + f(3) = f(3) + f(4) =

f(4) + f(5) = f(5) + f(6) = f(6) + f(7) =

f(7) + f(8) = f(8) + f(9) = f(9) + f(10) =

f(10) + f(11) = f(12) →

f(12) = 2 + 1 = 1 + [3] = 3 + [4] = 4 + [7] =

7 + [11] = 11 + [18] = 18 + [29] = 29 + [47] =

47 + [76] = 76 + [123] = 199

_____________________

Explicit formula

for n is an integer.

Nth term of the lucas sequence.

As you can see, the golden ratio

( 1 + √5 / 2) appears in here.

L(n) = ((1 + √5) / 2)ⁿ⁻¹ + ((1 – √5) / 2)ⁿ⁻¹

Answer:

Test statistic Z= 1.713

The calculated Z- value =  1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the  mean annual salary of all lawyers in a city is  different from $110,000

Step-by-step explanation:

Step(i):-

A researcher wants to test if the mean annual salary of all lawyers in a city is

different from $110,000

Mean of the Population  μ = $110,000

Sample size 'n' = 53

Mean of the sample x⁻ = $114,000.

standard deviation of the Population = $17,000,

Level of significance = 0.01

Null hypothesis :

There is no difference between the  mean annual salary of all lawyers in a city is  different from $110,000

H₀:  x⁻ =  μ

Alternative Hypothesis :  x⁻ ≠  μ

Step(ii):-

Test statistic

                 \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

                 \(Z = \frac{114000-110000}{\frac{17000}{\sqrt{53} } }\)

                Z =  1.7130

Tabulated value Z = 2.576 at 0.01 level of significance

The calculated Z- value =  1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the  mean annual salary of all lawyers in a city is  different from $110,000

Answer:

Step-by-step explanation:

Area formula for equilateral triangle with side a:

The base area is:

The three lateral surfaces have same sides of 10, 10 and 12.

Find each surface area using heron's formula:

Total surface area is:

Correct choice is C

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Answer:

Step-by-step explanation:

The expression 3s + s + 3 represents the total amount Alex and his family will spend to go to the movies. To simplify this expression, we can combine like terms.

The terms 3s and s are like terms because they both have the variable "s" raised to the power of 1. To combine them, we add their coefficients:

3s + s = (3 + 1)s = 4s

Therefore, the simplified expression is 4s + 3, which represents the total amount Alex and his family will spend to go to the movies.

Answer:

A. V + 18 < 30

Step-by-step explanation:

First of all, less than is the sign that points to the left,

Secondly, I'm guessing that y is actually V,

Before Ray gave Jan cards, she had 18,

so it is 18 plus V (the number of cards Ray gave her),

SO,

V + 18 < 30

Answer:

12 feet

Step-by-step explanation:

1 inch= 8 feet

1/2 inch= 4 feet

1/4 inch= 2 feet

(2x2)/2= 2  (one triangle)

2x4=8 (rectangle)

2+2=4 +8=12

^2 was added 2 times cause there are 2 triangles

(you did not need a 3rd measurement cause the triangle measurements were equal)

The measure of the obtuse angle with vertex P is 30 degrees.

We have,

If there is an acute angle with vertex Q measuring 60 degrees, then there must be a corresponding obtuse angle with vertex P that shares the same side as angle Q.

Let's call the measure of this obtuse angle x.

By the angle sum property of triangles, the sum of the measures of the three angles in any triangle is always 180 degrees.

Therefore, we can write the equation:

60 degrees + 90 degrees + x = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 60 degrees - 90 degrees = 30 degrees

Therefore,

The measure of the obtuse angle with vertex P is 30 degrees.

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Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

Answer: The dividends per share for 25000 shares of cumulative preferred 1% stock, $150 par, with a first-year dividend of $56300 per share, would be $2.252.

To calculate the dividends per share, we need to multiply the number of shares by the dividend rate and the par value.

The dividend rate is 1%, which means that for every $150 of par value, the company will pay $1.50 in dividends per year.

So, for 25000 shares with a par value of $150 each, the total par value would be $3,750,000 ($150 x 25,000).

Multiplying the total par value by the dividend rate gives us the total annual dividend payment:

$3,750,000 x 1% = $37,500

However, we know that in the first year, the company paid a higher dividend of $56,300 per share. Therefore, we need to adjust our calculation to reflect this higher amount.

Dividing the first-year dividend by the par value gives us the first-year dividend rate:

$56,300 / $150 = $375.33

Now we can calculate the dividends per share for subsequent years using this adjusted rate:

$3,750,000 x 0.01 = $37,500

$37,500 / 25000 = $1.50

$1.50 + $0.87533 = $2.252

Therefore, the dividends per share for 25000 shares of cumulative preferred 1% stock with a first-year dividend of $56300 per share would be $2.252.

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Answer:

Ok, when we have a point (x, y) and we do a rotation of 90° the new points will actually depend on the quadrant where we are, but it will always change the order to (y, x) but this does not end here, because depending on the quadrant where the point ends, the signs will change as follows.

1st quad (+y, +x)

2nd quad (-y, +x)

3rd quad (-y, -x)

4th quad (+y, -x)

So if we are in the second quadrant, the transformed point will be in the first quadrant

Now, we have that the points G and H are:

G = (-1, 3)

This point is in the second quadrant, so it moves to the first quadrant (where bot values must be positive).

The new point will be:

G´ = (3, 1)

And the other point is:

H = (-4, 0)

It also rotates to the first quadrant, so the new point will be:

H' = (0, 4)

Answer:

Because the person above already explained I’ll just give the answers.

Step-by-step explanation:

G = (-1,3) H = (-4,0) I = (3,-2)

Answer:

D= It is the total number of data points in the data set, which is also the sum of the row totals or the column totals.

Step-by-step explanation:

The number in the bottom right-hand corner of a two-way frequency table represents D. It is the total number of data points in the data set, which is also the sum of the row totals or the column totals.

When displaying frequencies or relative frequencies for two categorical variables, a two-way table is used. Columns indicate the second category, whereas rows represent the first.

The two-table displays frequencies for two categorical variables in terms of rows and columns.

The number in the bottom right-hand corner of a two-way frequency table represents the total number of data points in the data set, which is also the sum of the row totals or the column totals.

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Answer:

y = -8/5x + 7

Step-by-step explanation:

Step 1: Write equation

8x + 5y = 35

Step 2: Solve for y

Answer:

They are collinear if they are on the same line

Answer:

a. x = 6

b. x = 2

Step-by-step explanation:

a. \( 2^x = 64 \)

\( 2^x = 2^6 \)

\( x = 6 \) => the bases will cancel each other

b. \( 3^{2x + 1} = 243 \)

\( 3^{2x + 1} = 3^5 \)

\( 2x + 1 = 5 \) => the bases will cancel each other

\( 2x + 1 - 1 = 5 - 1 \)

\( 2x = 4 \)

Divide both sides by 2

x = 4/2

x = 2

Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

percentage is the quantitative way to express number of things out of 100 things.

For example : 20% of bananas are ripe.

it means that if there are 100 apples, 20 are ripe.

Let the  total number of cupcakes sold that day be X

20% of total number of cupcakes sold = 20% of X = (20/100) * X __1

It is given that 20% of total number of cupcakes sold is equal to 100

Thus the equation 1 should be equal to 100.

Writing it mathematically we have

(20/100) * X = 100

=> 0.2X = 100

=> X = 100/0.2 = 500

500  cupcakes did the bakery sell that day.

Answer:

\(x=98.13^\circ,135^\circ,278.13^\circ,315^\circ\)

Step-by-step explanation:

\(tan^2x+7tanx+8=0,[0^{\circ},360^\circ)\)

\(tan^2x+7tanx+8=0\)

\(u=tanx\) <-- U-substitution

\(u^2+7u+8=0\)

\((u+7)(u+1)=0\)

\((tanx+7)(tanx+1)=0\) <-- Replace u with tanx

\(tanx+7=0\)

\(tanx=-7\)

\(x=98.13^\circ,278.13^\circ\)

\(tanx+1=0\)

\(tanx=-1\)

\(x=135^\circ,315^\circ\)

Therefore, \(x=98.13^\circ,135^\circ,278.13^\circ,315^\circ\)

Answer:

y=4x+2

Step-by-step explanation:

To find the slope of a line, you would do y₂-y₁/x₂x₁

This would be 2-6/0-1...

So your answer would be -4/-1

After simplifying, your slope is 4.

To write this in slope-intercept form, that would be y=4x+2

The average weight of a male Florida panther rounded to the nearest whole number is 53 kg

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Average weight = 52.6 kg

52.6

The number after decimal point is 6 which is more than 5.

So add  1 to the 52, we get 53

Thus, the average weight of a male Florida panther rounded to the nearest whole number is 53 kg

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Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

I'm sorry but I rlly don't rember how I did it because I did this question on a quiz and the teacher said this was that answer but not how to get it.

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Answer:

Use the given functions to set up and simplify 2^4.

2^4=16

x⋅4^4=2^4=x=1/16

x⋅2^n=2^12==4096

Step-by-step explanation:

i think?

6 less than can be expressed mathematically in interval notation as:  s - 6 ≥ 78.

As the stated question;

The resulting formula in (1) is then s - 6 ---(1), which must be less than 78;

Thus, the mathematical equivalent of the expression in the question is:

s - 6 ≥ 78.

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When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.

A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.

The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.

When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.

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Answer: 1/3

Step-by-step explanation:

Here is the complete question:

machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 11.5 gallons per minute. Find the probability that between 9.0 gallons and 10.0 gallons are pumped during a randomly selected minute.

The Probability of the above question will be calculated as:

= (10-9) / (11.5 - 8.5)

= 1/3

The above is the easier way to solve this