A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model:
Salary = β0 +β1 Service + ε. The following ANOVA table below shows a portion of the regression results.
df SS MS F
Regression 1 555,420 555,420 7.64
Residual 27 1,962,873 72,699 Total 28 2,518,293 Coefficients Standard Error t-stat p-value
Intercept 784.92 322.25 2.44 0.02
Service 9.19 3.20 2.87 0.01
Which of the following is the monthly salary of an employee that has worked for 48 months at the bank?
rev: 11_17_2017_QC_CS-109762
$441.
$785.
$1,050.
$1,226.

Answer:

a = b = 3√2

Step-by-step explanation:

Use trigonometry:

\( \sin(45°) = \frac{a}{6} \)

Cross-multiply to find a:

\(a = 6 \times \sin(45°) = 6 \times \frac{ \sqrt{2} }{2} = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} \)

Use the Pythagorean theorem to find b:

\( {b}^{2} = {6}^{2} - {a}^{2} \)

\( {b}^{2} = {6}^{2} - ( {3 \sqrt{2}) }^{2} = 36 - 9 \times 2 = 36 - 18 = 18\)

\(b > 0\)

\(b = \sqrt{18} = 3 \sqrt{2} \)

Answer:

14

Step-by-step explanation:

c = -4, x = 2

Lets plug in the numbers!

-3(-4) + 2

Order of operations states that multiplication will be done before addition.

Step 1. Multiply -3 by -4, and the product is 12.

-3(-4) = 12. New expression: 12 + 2

Step 2. Add 12 and 2, and the solution is 14

12 + 2 = 14. Solution to initial question: 14

By answering the presented question, we may conclude that She spends equation 40% of her time at work and 15% of her time on other hobbies. She spends 20% of her time napping.

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion  \("2x + 3 = 9"\) states that the word  \("2x + 3"\) Corresponds to the number "9".

The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.

For example, in the equations \("x2 + 2x - 3 = 0\)  ," the variable x is lifted to the powercell. Lines are utilized in many areas of mathematics, include algebra, arithmetic, and geometry.

Abby, according to the picture, spent:

She spends 25% of her time in school.

She spends 40% of her time at work and 15% of her time on other hobbies.

Therefore, Furthermore, she spends  \(20\) of her time napping.

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Joshua was trying the subtract 8 – 4.13. He lays up the dilemma like this. 8-4.13 Joshua's issue therefore has a 3.87 as its solution.

Subtraction is a mathematical operation or procedure that involves calculating this same difference between two quantities or numbers.Whenever a number is removed from another, the phrase "taking away 1 integer from the other" is also used.

Part A: Joshua's setup is flawed since he did not align all decimal points during the subtraction.

Part B: In order to accurately subtract 4.13 off 8, we must first line up the decimal points before subtracting each digit as in columns going right to left. We can add a zero but after number 8 to align all decimal points as there are no digits beyond the decimal point in the number 8.

markdown

Code to be copied: 8.00 - 4.13 ———

Now, starting from the right, we can subtract the numbers from each column:

copy markdown 8.00

- 4.13

———

3.87

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The value of angle 1 given the value of angle 4 as 47° will be 133°

Parallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.

Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.

The value will be:

= 180° - 47°

= 133°

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9514 1404 393

Answer:

  7.5

Step-by-step explanation:

Corresponding sides are proportional, so ...

  UV/VW = LM/MN

  x/6 = 15/12

  x = 6(15/12) = 15/2

  x = 7.5

Answer:

0.006

Step-by-step explanation:

On the first draw, there are 52 cards, 4 of which are sevens.

On the second draw, there are 51 cards, 4 of which are nines.

The probability is:

(4/52) × (4/51)

= 4/663

≈ 0.006

Answer:

y=135

x=45

Step-by-step explanation:

x= 45

It is an isosceles so

180-90=90

90/2= 45  

y=135

angles on a straight line add up to 180 so

180-45=135

Hope this helps!

The two clocks will chime at the same time 96 times over the next 24 hours, based on the LCM of the intervals at which they chime.

To determine how many times both clocks will chime at the same time over the next 24 hours, we need to find the least common multiple (LCM) of the intervals at which the clocks chime.

The first clock chimes every 15 minutes, which means it chimes 24 times in a 24-hour period (24 hours × 60 minutes / 15 minutes = 96 intervals).

The second clock chimes every half hour, which means it chimes 48 times in a 24-hour period (24 hours × 60 minutes / 30 minutes = 48 intervals).

To find the LCM of 96 and 48, we can list the multiples of both numbers and find the smallest common multiple:

Multiples of 96: 96, 192, 288, 384, 480, ...

Multiples of 48: 48, 96, 144, 192, 240, ...

From the lists, we can see that the smallest common multiple is 96.

Therefore, both clocks will chime at the same time 96 times over the next 24 hours.

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The probability that the sum of the two dice is less than 4 is 3/36, which simplifies to 1/12.

Dice probability refers to the likelihood of a certain outcome when rolling one or more dice. The probability of rolling a particular number on a fair six-sided die, for example, is 1 in 6 or approximately 16.67%. The probability of rolling any number from 1 to 6 on a single die is always the same since each face has an equal chance of landing face up.

Given by the question.

To finds the probability that the sum of the two dice is less than 4, we need to list all the possible outcomes when Cindy throws one red and one blue dice, and then count the number of outcomes that satisfy the condition.

Possible outcomes when throwing two dice:

Red Blue

1 1

1 2

1 3

1 4

1 5

1 6

2 1

2 2

2 3

2 4

2 5

2 6

3 1

3 2

3 3

3 4

3 5

3 6

4 1

4 2

4 3

4 4

4 5

4 6

5 1

5 2

5 3

5 4

5 5

5 6

6 1

6 2

6 3

6 4

6 5

6 6

There are 36 possible outcomes when throwing two dice.

Outcomes where the sum of the two dice is less than 4:

Red Blue

1 1

1 2

2 1

There are 3 outcomes where the sum of the two dice is less than 4.

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There are no two Real numbers that add up to -2 and multiply to 10.

The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:

Equation 1: x + y = -2

Equation 2: x * y = 10

To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:

1. Solve Equation 1 for x:

  x = -2 - y

2. Substitute the value of x in Equation 2:

  (-2 - y) * y = 10

3. Simplify the equation:

  -2y - y^2 = 10

4. Rearrange the equation to standard form:

  y^2 + 2y + 10 = 0

5. Since the equation is a quadratic equation, we can apply the quadratic formula:

  y = (-b ± √(b^2 - 4ac)) / (2a)

  In this case, a = 1, b = 2, and c = 10.

6. Calculate the discriminant: b^2 - 4ac:

  2^2 - 4(1)(10) = 4 - 40 = -36

7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.

In conclusion, there are no two real numbers that add up to -2 and multiply to 10.

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The batch 3,5,7,9,11 represents items in set A which are the sums that are odd. For instance, rolling a 2 and a 3 leads to 2+3 = 5 which is an odd number sum.

The batch 4,8,12 represents the sums that are divisible by 4, ie they are multiples of 4. For instance: 2+6 = 8 is a multiple of 4.

The notation A U B means "A union B". Set union has us combine the two sets together to form one single set as indicated above. We toss out any duplicate entries. In this case, there are no duplicates because sets A and B have nothing in common. This means sets A and B are disjoint or mutually exclusive. If an item is in set A, then it cannot be in set B, and vice versa.

Optionally you can sort the items from smallest to largest getting A U B = {3,4,5,7,8,9,11,12}, but I chose to list 3,5,7,9,11 first to show that those items all belonged originally to set A, and kept 4,8,12 separate as well.

Answer:

sorry  dont't know  how  to  do  this  

Step-by-step explanation:

have a  nice day

No, the inference is not valid because it excluded those who were not online and so did not see the poll.

To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds

The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.

To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.

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

Explanation:

The unique digits are: 9, 6, 1

There are 1+3+3 = 7 digits with the repeats mentioned. If we could somehow tell the 6's apart and the 1's apart, then we'd have 7! = 7*6*5*4*3*2*1 = 5040 different permutations.

But because we can't tell the 6's apart, nor the 1's apart, this means we have to divide by (3!*3!). Each 3! represents the number of times the 6's show up and same goes for the 1's.

So (5040)/(3!*3!) = 5040/(6*6) = 5040/36 = 140 is the number of ways to rearrange the digits

After considering all the given data we conclude that the area of the given figure is 80, under the condition that the given figure is a rhombus.

Let us name the rhombus as ABCD, now looking at the figure we can detect that there are two diagonals crossing each other making a point  E, this allows the  two  diagonals to split in four smaller lines that are congruent in value
Then
Line AE = 5ft and Line ED = 5ft (because of congruency)
Line CE = 8ft and Line EB = 8ft(because of congruency)
Therefore,
Now we know that the diagonals
AD = 10ft
CB = 18 ft
The area of a rhombus can be evaluated applying the formula
Area = (d1 × d2) / 2,
Here,
d1 and d2 = lengths of the diagonals.
For this case, the diagonals are 10 ft and 16 ft.
Then, the area of the rhombus is
(10 × 16) / 2
= 80
Then, the area of the given figure is 80.
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The intervals in which the function is decreasing. \([-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ]\). Option 3

We're given a function f(x) = 2 sin x - x, which describes a curve on a graph. We want to find the intervals where this curve is decreasing (going down) within the range of -π to π.

To find when the function is decreasing, we look at its slope. The slope tells us if the curve is going up or down. We find the slope by taking the first derivative of the function: f'(x) = 2 cos x - 1.

We now have an equation for the slope, f'(x) = 2 cos x - 1. A negative slope means the function is decreasing. So, we want to find where f'(x) is less than 0 (negative).

We set up the inequality: 2 cos x - 1 < 0. We solve it to find the x-values where the slope is negative. The solution is cos x < 1/2.

From the inequality cos x < 1/2, we find the intervals within the range of -π to π where the function is decreasing. These intervals are [-π, -π/3] and [π/3, π].

The above answer is in response to the question below as seen in the picture.

Determine the interval(s) in \([-\pi, \pi ]\) on

which f(x) =  2 sin x - x

is decreasing.

1. \([-\frac{\pi }{3}, \frac{\pi }{3} ]\)

2. \([-\frac{\pi }{6}, \frac{\pi }{6} ]\)

3. \([-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ]\)

4. \([-\pi , -\frac{-2\pi }{3} ], [\frac{2\pi }{3}, \pi ]\)

5. \([-\pi , - \frac{5x}{6} ], [\frac{\pi }{6}, \pi ]\)

6. \([-\frac{\pi }{6}, \frac{5\pi }{6} ]\)

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Answer:

b

Step-by-step explanation:

Answer:

B thank you for doing that hard work

putting all that info in

Step-by-step explanation:

The answer to the question is 1/3.

There are three possible outcomes: 5, 6, or 7.

Out of these three outcomes, only two satisfy the condition of being odd or greater than 6: 7.

Therefore, the probability of picking a card that is odd or greater than 6 is 1/3, or approximately 0.333 or 33.3%.

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Answer:

d

Step-by-step explanation:

=-4

Which expression is equivalent to -11 - (-7)?

Answer

D. -11 + 7

Let's denote the length of the pool as L and the breadth as B.

According to the given information, the perimeter of the rectangular swimming pool is 154m. The formula for the perimeter of a rectangle is given by:

\(\displaystyle\sf P = 2(L + B)\)

Substituting the given value of the perimeter, we have:

\(\displaystyle\sf 154 = 2(L + B)\)

Dividing both sides of the equation by 2, we get:

\(\displaystyle\sf 77 = L + B\)

We are also given that the length of the pool is 2m more than twice its breadth. Mathematically, we can express this as:

\(\displaystyle\sf L = 2B + 2\)

Now we can substitute this value of L in terms of B into the equation we obtained earlier:

\(\displaystyle\sf 77 = (2B + 2) + B\)

Simplifying the equation, we have:

\(\displaystyle\sf 77 = 3B + 2\)

Subtracting 2 from both sides of the equation, we get:

\(\displaystyle\sf 75 = 3B\)

Dividing both sides of the equation by 3, we obtain:

\(\displaystyle\sf B = 25\)

Now we can substitute this value of B into the equation for L:

\(\displaystyle\sf L = 2(25) + 2\)

Simplifying the equation, we have:

\(\displaystyle\sf L = 52\)

Therefore, the length of the pool is 52m and the breadth is 25m.

Using the transpose method, we can rearrange the equation \(\displaystyle\sf 77 = L + B\) to solve for L:

\(\displaystyle\sf L = 77 - B\)

Then, substituting this expression for L in the equation \(\displaystyle\sf L = 2B + 2\), we have:

\(\displaystyle\sf 77 - B = 2B + 2\)

Adding B to both sides of the equation, we get:

\(\displaystyle\sf 77 = 3B + 2\)

Subtracting 2 from both sides of the equation, we obtain:

\(\displaystyle\sf 75 = 3B\)

Finally, dividing both sides of the equation by 3, we find:

\(\displaystyle\sf B = 25\)

By substituting this value of B back into the equation \(\displaystyle\sf L = 77 - B\), we get:

\(\displaystyle\sf L = 77 - 25 = 52\)

Hence, the length of the pool is 52m and the breadth is 25m.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

25 * 30= x

x= total number of candies

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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We have the system of equations:

Notice that in (equation 1) the variable x is already clear. Let's substitute in (equation 2), so we can find the value of y:

Notice that this is true for any value of y

Thereby, the system has infinite solutions

Answer:

Step-by-step explanation:

2/7 + 4/5 mixed forms

2/7 + 4/5 =

38/35 or 1 3/35

Answer:

38/35

Step-by-step explanation:

1. convert to like fractions

2/7-> 10/35

4/5-> 28/35

2. add fractions

10/35 + 28/35 = 38/35

There is approximately 130 centimeters of snow fell on the town last year.

Centimeters:

Centimeter means a metric unit for the measurement of length of objects and small distances. It is identified using the symbol cm. It also be defined as the unit of length in the International System of Units (SI).

Given,

A town in Alaska had 326 inches of snow last year.

Here we need to find the equivalent centimeters of snow fell on the town last year.

Through the given question, we know that,

One inch =  2.5 centimeters.

And we also know that, in last year, the amount of snowfall in inches is 326.

Now, we have to convert this inches into centimeter form,

For that we have to divide the inches value by the constant centimeter value, then we get,

=> 326/ 2.5

=> 130.4

Therefore, there are approximately 130 centimeters snowfall on the town in last year.

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y = Kx is required for direct variation, the constant of variation, k=-2.

A constant of variation (k) is a ratio that shows the relationship between the independent variable (x) and the dependent variable (y). If both variables have known values, divide y by x to find it.

When two variables are constant multiples of one other, they form a connection. r is directly proportional to Yr = K(y) k is constant.

It displays the degree of variation in reference to the population mean. The coefficient of variation should be determined only for data obtained on scales with a meaningful zero (ratio scales), allowing for relative comparison of two measurements (i.e., division of one measurement by the other). The coefficient of variation may be meaningless for data on an interval scale.

We have provided the following equation:  

-12 x = 6y

y = -12 x /6

y =  -2x

This is in the form of y = kx and k=-2

Therefore, the constant of variation, k=-2

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Answer:

-1/3

Hope this helps also I would appreciate brainliest is possible please :)

Answer:

c

Step-by-step explanation:

I need to deposit $1558.41 to have $2000 in the account in 5 years.

What is compound interest?

The interest charged on a debt or deposit is known as compound interest. It is the idea that we use the most regularly. Compound interest is calculated for a sum based on both the principal and cumulative interest.

    ∴ Compound interest = P(1 + \(\frac{r}{100*12}\))ⁿ  (∵ for monthly interest)

        P = Principal

        r = rate of interest per month

        n = number of months

Given:

r = 5% per month

n = 5 years = 5*12 = 60 months

  CI = P (1+5/(12 * 100))⁶⁰

2000 = P(1.0041)⁶⁰

2000 = P(1.2834)

      P = 1558.41

Therefore, the amount required to deposit is 1558.41 dollars to get 2000 dollars after 5 years with 5 percent interest per month.

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