The annual salaries of all employees at a financial company are normally distributed with a mean of $34,000 and a standard deviation of $4,000. What is the z-score of a company employee who makes an annual salary of $54,000?
–5
–3
4
5

Answer:

(0.5,3)

Step-by-step explanation:

Hi there!

We are given a line that has the endpoints of (5,9) and (-4,-3); we need to find the midpoint of the line.

The midpoint formula is given as (\(\frac{x_{1}+x_{2} }{2}\), \(\frac{y_{1}+y_{2}}{2}\)), where \(x_{1}\), \(x_{2}\), \(y_{1}\), and \(y_{2}\) are values of coordinate points

to avoid any confusion, we can label the values of the coordinates and then substitute them into the formula to find the midpoint

\(x_{1}\)=5

\(y_{1}\)=9

\(x_{2}\)=-4

\(y_{2}\)=-3

now substitute into the formula

so to find the value x in the midpoint, we'll use this part of the formula: \(\frac{x_{1}+x_{2} }{2}\)

substitute 5 and -4 into the formula

\(\frac{5+-4}{2}\)

do the addition on the numerator

\(\frac{1}{2}\) or 0.5

now let's find the value of y in the midpoint. we'll use this part of the formula: \(\frac{y_{1}+y_{2}}{2}\)

substitute 9 and -3 into the formula

\(\frac{9+-3}{2}\)

do the addition on the numerator

\(\frac{6}{2}\) or 3

Therefore the midpoint is (0.5,3)

Hope this helps! :)

Answer: The answer is A, $78.00

Step-by-step explanation: Hope it helps

The required cost of the item after 4% of sales tax is given as $78.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Let the total cost of the item be x,
According to the question,
x = cost + sales tax
X = 75 + 4% of 75
x = 75 + 3
x = $78

Thus, the required cost of the item after 4% of sales tax is given as $78.

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The first and third rectangular prisms have the same volume of 30 cubic units.

The second rectangular prism has a volume of 350 cubic units, and the fourth rectangular prism has a volume of 24 cubic units.

The volume of each of the rectangular prisms can be calculated as follows:

1.   length: 1; width: 10; height: 3

volume = 1 x 10 x 3 = 30

2.  length: 5; width: 10; height: 7

volume = 5 x 10 x 7 = 350

3.   length: 2; width: 5; height: 3

volume = 2 x 5 x 3 = 30

4.   length: 4; width: 2; height: 3

volume = 4 x 2 x 3 = 24

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Answer:

4

Hope that this helps!

Answer:

43°

Step-by-step explanation:

In a isosceles triangle, two angles HAVE to be equal.

This means that 94 can be one of the angles that are equal, or the angle that is not equal to another angle.

Let's start with the fact that 94 can be one of the angles that are equal. (Note: angles in a triangle add up to 180)

94+94+x=180

188+x=180

There is NOT a possible value for x in this situation, as you cannot have a negative value of an angle. Therefore we must try the other situation where 94 is the angle that is not equal to another angle.

x+x+94=180

2x+94=180

Subtract 94 from both sides

2x=86

Divide both sides by 2

x=43

Therefore the answer is 43°

Answer:

Number of people in a room

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The modeof the data is "Singing".

In statistics, the mode refers to the value or values that appear most frequently in a dataset. It represents the peak of the frequency distribution. In the given data, we have a list of talent show acts, and we are looking for the act(s) that occur most frequently.

To find the mode(s) of the given data, we look for the value(s) that appear most frequently. Let's count the occurrences of each act:

Singing - 7 times

Dancing - 6 times

Comedy - 3 times

Poetry - 2 times

Juggling - 1 time

Magic - 1 time

From the counts, we can see that "Singing" appears the most frequently, occurring 7 times. Therefore, the mode(s) of the data is "Singing".

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Answer:

1.59

Step-by-step explanation:

Divide 2,787 by 1,750

The equation is x √(x² + y²) = 7y x + y²

This equation describes a limacon, which is a type of polar curve.

Find a Cartesian equation for the curve and identify it. r 7tan() sec() circle O line O limaçon parabola O ellipse

The equation of the given curve is a limacon. A Cartesian equation for the curve r = 7tan(θ) sec(θ) is given by the following steps: First, make use of the identity  sec²(θ) = tan²(θ) + 1, by multiplying both sides of the equation by sec(θ) on both sides of the equation. So, we have the following:

r = 7tan(θ) sec(θ)r sec(θ) = 7tan(θ) tan²(θ) + tan(θ)Then, replace tan(θ) with y/x and sec(θ) with r/x to get a Cartesian equation.

xr = 7y x + y²We can further simplify this equation by eliminating the variable r using the fact that r² = x² + y².

This results in the equation x √(x² + y²) = 7y x + y²

This equation describes a limacon, which is a type of polar curve.

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Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Answer:

the answer is 23.

Step-by-step explanation: 20/15=1.5333333333......=1  1/2

The number is given by equation A = 1000

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as A

Now , the equation will be

15 is 1 1/2 % of the number A

Substituting the values in the equation , we get

15 = 1.5 % of A

On simplifying the equation , we get

15 = ( 1.5 / 100 ) x A

Multiply by 100 on both sides of the equation , we get

1.5A = 1500

Divide by 1.5 on both sides of the equation , we get

A = 1500/1.5

A = 1000

Therefore , the value of A is 1000

Hence , the number is 1000

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From the given values, the value of h'(x)= sin x(4x²+2x-3) - (-cos x)(8x+2) / (4x²+2x-3). The derivatives will help to solve the sum.

Given,

f(x)= -cos(x), g(x) = 4x²+2x-3,

h(x) = f(x)/g(x)

h(x) = \(\frac{-cos(x)}{4x²+2x-3}\)

h'(x)= \(\frac{d}{dx}\)(\(\frac{-cos(x)}{4x²+2x-3}\))

As an illustration, d/dx(tan(x))=(sin(x)cos(x))

=cos(x)(sin(x)))′sin(x)(cos(x))′ cos2(x)

=cos2(x)+sin2(x) cos2(x)

=1cos2(x)

=sec2(x).

Apply Quotient Rule:

To determine the derivative of a quotient of functions, use the quotient rule. Include negative exponent functions in the application of the power rule. To determine the derivative of a polynomial or rational function, combine the differentiation rules.

\(\frac{d}{dx}\)[f/g]'= (f'*g - g'*f)/ g^2

f'(x) = sin x

g'(x) = 8x+2

Therefore, the value of from the given data is h'(x)= sin x(4x²+2x-3) - (-cos x)(8x+2) / (4x²+2x-3).

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Answer:

StartFraction T Subscript h Baseline minus T Subscript C Baseline over T Subscript h Baseline EndFraction times 100

Step-by-step explanation:

could i have brainliest plz i so close to next rank

Answer:

its a

Step-by-step explanation:

Answer:

You take your current answer and simplify it to its lowest terms.

Step-by-step explanation:

Example: 32/4 is simplified to 8/1

I got that because I divided 4 from both sides. :)

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Using the formula for the CDF of the exponential distribution, we can calculate this probability as follows: P(X ≥ 5000) = 1 - P(X < 5000) = 1 - e^(-5000/10000) ≈ 0.3935. Therefore, there is approximately a 39.35% chance that the car will be able to complete the 5000-mile trip without replacing the battery.

To calculate the probability that a randomly chosen battery of this brand will need replacement within 4000 to 5000 miles of operation, we can subtract the CDF values at 4000 miles and 5000 miles. P(4000 ≤ X ≤ 5000) = P(X ≤ 5000) - P(X ≤ 4000) = e^(-5000/10000) - e^(-4000/10000) ≈ 0.1813. Hence, there is approximately an 18.13% probability that a randomly chosen battery of this brand will need replacement within the range of 4000 to 5000 miles.

For a random sample of 42 batteries, to find the probability that the average miles before replacement will be at most 12000, we can use the Central Limit Theorem. The average of the sample means follows a normal distribution with a mean equal to the population mean (10000 miles in this case) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (√42). We can calculate the z-score for 12000 miles, which is (12000 - 10000) / (standard deviation / √42). Using the z-table or a calculator, we can find the probability associated with this z-score, which represents the probability that the average miles before replacement will be at most 12000.

To determine the number of batteries out of the 1000 produced in the last month that will last for more than 20000 miles, we can use the cumulative distribution function (CDF) of the exponential distribution. The probability that a battery will last more than 20000 miles can be calculated as P(X > 20000) = 1 - P(X ≤ 20000) = 1 - e^(-20000/10000) ≈ 0.1353. Multiplying this probability by the total number of batteries produced (1000) gives an estimate of the number of batteries that will last for more than 20000 miles, which is approximately 135 batteries.

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The explicit solution of the initial value problem y′=y(y−1), y(0)=4 is y = 1/(1-3e^-x).

To find the explicit solution, we begin by separating the variables and integrating both sides:

dy/dx = y(y-1)

(dy/y(y-1)) = dx

Integrating both sides yields

ln|y-1| - ln|y| = -x + C

where C is a constant of integration.

We can simplify this expression by combining the logarithms using the identity ln(a/b) = ln(a) - ln(b):

ln|(y-1)/y| = -x + C

Taking exponential of both sides gives

|(y-1)/y| = e^(C-x)

Letting k = e^C, we can rewrite this as:

(y-1)/y = ± k e^-x

Rearranging and solving for y, we obtain:

y = 1/(1-k e^-x )

We can determine the value of k using the initial condition y(0) = 4:

4 = 1/(1-k)

Solving for k gives k = 3.

Substituting k=3 into the expression for y, we get:

y = 1/(1-3e^-x)

Therefore, the explicit solution of the initial value problem is y = 1/(1-3e^-x), where y(0) = 4.

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Answer:

35.6%

Step-by-step explanation:

31/87(100)

3100/87

35.6%

Answer:

35,6%

Step-by-step explanation:

31/87 = 0,35632184

As a percentage: 35,632184%

Rounded to one deciman place: 35,6%

Answer:The answer would be 28 the value of g would

be 2.8

Step-by-step explanation:

The equation that can be used to find the amount  of money that Sid and Dylan each have is 0.5E = $57

The following equations can be deduced from the question:

a + b + c =$90 equation 1

$33 + b + c = $90 equation 2

Where:

In order to determine the amount of money that Sid and Dylan have, make b and c the subject of the formula in equation 2

b + c = $90 - $33

b + c = $57

Since both people have the same amount of money, the equation becomes

0.5(b + c) = $57

0.5E = $57

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Malena's steps arranged sequentially are :

The first step :

2x + 5 = -10 - x

collecting like terms

2x + x = -10 - 5

step 2 : Using the appropriate numerical operator:

3x = -15

step 3 : divide both sides by 3 to isolate x

x = -5

Hence, the required steps as arranged above .

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the probability that in a randomly selected hour the number of calls is three is 0.18045, or about 18.045%.

Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes. Example: When rolling a die, an even number can occur in 3 different ways out of 6 possible. Being 3 the number of favorable outcomes and 6 the number of possible outcomes.

Knowing that:

Let's substitute the values into the formula and calculate the probability:

\(P(X = 3) = (e^(-2) * 2^3) / 3!\\P(X = 3) = (2.71828^(-2) * 2^3) / 3!\\P(X = 3) = (0.13534 * 8) / 6\\P(X = 3) ≈ 0.18045\)

Therefore, the probability that in a randomly selected hour the number of calls is three is approximately 0.18045, or about 18.045%.

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Answer:

4 is the smallest possible number of integers in the list.

Given:

Total number of curlers = 16

Pink Curlers = 1/4 of 16

Green Curlers = same with pink = 1/4 of 16

Soda Cans = 16 curlers minus pink and green curlers

To determine how many soda can curlers are in Carrie's head, let's determine first how many pink and green there are.

Since there are 1/4 of the curlers are pink, let's determine how many curlers exactly are pink by multiplying 1/4 to 16.

Therefore, there are 4 pink curlers. Similarly, there are also 4 green curlers since it is stated in the problem that they have the same count.

So, 16 curlers minus 4 pink and 4 green curlers, there are 8 soda cans curlers in Carrie's head.

Answer:The motel clerk has 33 $1 bills and 18 $10 bills.

Step-by-step explanation:

Let the number of $1 bills = x, so then number of $10 bills is 51-x.From the problem description, you can write:x($1)+(51-x)($10) = $213 Simplify and solve for x.x+510-10x = 213-9x+510 = 213 Add 510 to both sides.-9x = -297 Divide both sides by -9x = 33 and 51-x = 51-33 = 18.

Answer:

The answer is C. Hope this helps

Answer:

2/3

Hope that this helps!

Answer:

A kid leaping happily to home after school

The graph represents the relationship between height and time.

Given that,
A curve has been shown we have to explain the behavior of the curve.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The curve is shown, where the vertical axis represents the height above the ground and the horizontal axis represents the time. Let's assume a plane of paper is flying, the plane getting a rise and then a certain down and again rise and down as according to the height of the plane.

Thus, the graph represents the relationship between height and time.

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Answer:

v=10

Step-by-step explanation:

these 2 angles add up to 90 degrees bc of the right angle marker

6v-3 + 4v-7 = 90

combine like terms:  6v+4v  and  -3+-7

10v -10 = 90

isolate the variable by first adding 10 on both sides to get:

10v = 100

then divide 10 on both sides to get v

v=10

u can plug in the values to make sure it's right:

4(10)-7=33

6(10)-3=57

33+57=90