13. McKenzie gets a base pay of $1,800 per month. She also earns 12%
commission on the amount of car sales. If she sells $45,000 worth of cars,
how much money does she make in one month? *
$18,000
$45,000
$7,200
$5,400

Answer:

500

Step-by-step explanation:

Convert percent to decimal:

94%=

100

94

​

=0.94

Move decimal 2 places to the left

Multiplying the decimal by the whole gives us the part:

0.94x=

0.94x=

470

0.94

0.94x = 0.94

470

​

Divide both sides by 0.94x=

500

The sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function\(f(x) = 0\) on the interval \(I = [0, \infty)\).

To examine the uniform convergence of the sequence\(f_n(x) = e^{-nx}\) on the interval\(I = [0, \infty)\), we need to check if the sequence converges uniformly to a limit function on that interval.

For uniform convergence, we need the following condition to hold:

Given any\(\(\epsilon > 0\\)), there exists an \(\(N \in \mathbb{N}\\)) such that for all \(n > N\) and for all \(x \in I\), we have\(\(\left| f_n(x) - f(x) \right| < \epsilon\)\), where \(\(f(x)\)\) is the limit function.

Let's find the limit function\(\(f(x)\\)) of the sequence \(f_n(x) = e^{-nx}\) as \(n\) approaches infinity. Taking the limit as \(\(n\)\)goes to infinity

\(\[f(x) = \lim_{n \to \infty} e^{-nx}\]\)

We can rewrite this limit using the exponential function property:

\(\[f(x) = \exp\left(\lim_{n \to \infty} -nx\right)\]\)

Since the limit inside the exponential is\(\(-\infty\)\) as \(\(n\)\) goes to infinity, we have:

\[f(x) = \exp(-\infty) = 0\]

Therefore, the limit function \(f(x)\) is the constant function\(\(f(x) = 0\\)) on the interval \(I = [0, \infty)\).

To check for uniform convergence, we need to evaluate the difference \(\left| f_n(x) - f(x) \right|\) and see if it is less than any given \(\epsilon > 0\) for all \(n > N\) and for all \(x \in I\).

\(\[\left| e^{-nx} - 0 \right| = e^{-nx}\]\)

To make this expression less than\(\(\epsilon\),\) we need to find an \(N\) such that \(e^{-nx} \(< \epsilon\)\) for all\(n > N\) and for all\(\(x \in I\).\)

However, as \(\(x\)\) approaches infinity, \(e^{-nx}\) approaches 0. But for any finite \\((x\)\) in the interval \([0, \infty)\), \(e^{-nx}\)  will always be positive and never exactly equal to 0. This means we cannot find an\(\(N\)\)that satisfies the condition for uniform convergence.

Therefore, the sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function \(f(x) = 0\) on the interval \(I = [0, \infty)\).

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Answer:

It's actually 13 groups

4 students will be left over

Step-by-step explanation:

Add all the students together

134

Divide 10

13 and remainder 4

Answer:

13 ; 4

Step-by-step explanation:

Total students = 24 + 21 + 33 + 36 + 20 = 134

grups that will be made = 134 : 10 = 13,4 = 13

13 x 10 = 130

Students that will be left overs = 134 - 130 = 4

Answer:

regular price is $22.50

Step-by-step explanation: 22.50*.20=4.5 (discount)

The Wald test is a statistical test that can be used to test the significance of a group of coefficients in a multiple regression model.

The test statistic is calculated as the ratio of the estimated coefficient to its standard error. If the test statistic is significant, then the null hypothesis that the coefficient is equal to zero can be rejected.

Suppose we have a multiple regression model with three independent variables: age, gender, and education. We want to test the hypothesis that the coefficients for age and education are both equal to zero. The Wald test statistic would be calculated as follows:

Test statistic = (Estimated coefficient for age) / (Standard error of estimated coefficient for age) + (Estimated coefficient for education) / (Standard error of estimated coefficient for education)

If the test statistic is significant, then we can reject the null hypothesis that the coefficients for age and education are both equal to zero. This would mean that there is evidence that age and education are both associated with the dependent variable.

The Wald test is a powerful tool that can be used to test the significance of a group of coefficients in a multiple regression model. However, it is important to note that the test statistic is only valid if the assumptions of the multiple regression model are met. If the assumptions are not met, then the p-value of the Wald test may be inaccurate.

Here are some of the assumptions of the multiple regression model:

* The independent variables are independent of each other.

* The dependent variable is normally distributed.

* The errors are normally distributed.

* The errors have constant variance.

If any of these assumptions are not met, then the Wald test may not be accurate.

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The two numbers that add up to 158 are 99 and 59.

The equation of variables that have a maximum power of 1 is known as a linear equation.

Let the lesser number be x.

So, the greater number will be x+40.

And the sum of both the numbers is 158.

So, the resulting linear equation based on given conditions is,

x + x + 40 = 158

2x = 158 - 40

2x = 118

x = 118/2

x = 59

So, the lesser number is 59.

And the greater number is 59 + 40 = 99.

Hence, the two numbers that add up to 158 are 99 and 59.

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Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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Answer:

about 59 dogs

Step-by-step explanation:

helloo!

total: 493

percentage: 12%

to find this, you could divide by 100 to find one percent of it and multiply by 12

so, 493/100=4.93

this is 1% of dogs.

so, to find 12% we would do 4.93*12 which is 59.16

hope this helped you :)

Answer:

Step-by-step explanation:

c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.

__

d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.

If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.

This behavior most directly illustrates the concept of superstition in gambling. Gamblers may believe that throwing the dice a certain way will influence the outcome and affect the results they desire.

This is a common belief among gamblers, despite there being no scientific evidence to support it. In reality, the way the dice are thrown has no impact on the outcome, as the result is determined purely by chance and the laws of physics.

Nevertheless, the belief in superstition is widespread in gambling and can influence behavior and decision making.

Gamblers often pitch the dice gently for low numbers and hard for high numbers. This most directly adorned an illusion of control Regression towards the mean refers to the tendency for unusual events to be followed by more ordinary events.

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The mean time between requests is estimated to be 22.366 microseconds with a standard error of 2.248 microseconds.

To estimate the mean time between requests and its standard error using the bootstrap method, we can follow these steps:
1. Compute the sample mean of the given data. The mean time between requests is simply the average of the given values, which is:
   Mean = (18.77 + 28.81 + 11.87 + 15.92 + 23.2 + 21.12 + 22.79 + 39.99 + 21.86 + 15.33) / 10 = 22.366 microseconds
2. Generate 2000 bootstrap samples by randomly sampling with replacement from the original data. Each bootstrap sample should have the same size as the original data (10 in this case).
3. For each bootstrap sample, compute the mean time between requests.

4. Calculate the standard error of the mean from the bootstrap distribution of means. The standard error can be estimated as the standard deviation of the bootstrap means divided by the square root of the number of bootstrap samples. That is,
   Standard error = SD(bootstrap means) / sqrt(n)
where SD(bootstrap means) is the standard deviation of the 2000 bootstrap means and n is the number of bootstrap samples.
Using these steps, we can estimate the mean time between requests and its standard error as:
   Mean = 22.366 microseconds
   Standard error = 2.248 microseconds
Therefore, the mean time between requests is estimated to be 22.366 microseconds with a standard error of 2.248 microseconds.

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Answer:

3-2/6-3 =1/3

So the answer is 1/3'c'

The correct value that equates to this expression is 12‐³². Letter A

.

To solve this expression, just: eliminate the parentheses and multiply the exponents among themselves;\( \boxed{ \large \sf (a {}^{n} ) {}^{m} \rightarrow a {}^{n \times m} } \\ \\ \)

\({ = \large \sf (12{}^{-4} ) {}^{8} } \)

\({ = \large \sf 12{}^{-4 \times 8} } \)

\( \pink{ \boxed{ = \large \sf 12{}^{-32} } } \\ \)

Therefore, the answer will be 12‐³²

Answer:

Step-by-step explanation:

is 50

360-230=130

180-130=50

Answer:

10 gallons of paint

Step-by-step explanation:

First, find the surface area of the monument.

From inspection, this is made up of 4 congruent rectangles and 4 congruent triangles.

Area of a rectangle = width x length

Therefore, area of one rectangle of the monument:

13 x 40 = 520 ft²

Area of triangle = 1/2 x base x height

Therefore, area of one triangle of the monument:

1/2 x 13 x 11 = 71.5 ft²

Therefore, total surface area of the monument

= 4 x SA of rectangle + 4 x SA of triangle

= 4 x 520 + 4 x 71.5

= 2080 + 286

= 2366 ft²

We are told that one gallon of paint can cover 239 ft², and that paint can only be bought by the gallon.

Divide the total surface area of the monument by the area one gallon of paint can cover to calculate how many cans of paint are needed.

2366 ÷ 239 = 9.89958159...

Therefore, 10 gallons of paint must be bought (since we need to round up as paint can only be bought by the gallon).

The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.

The slope-intercept form is One of the most common ways to describe a line's equation. The general form of a slope-intercept form is given by

Where m is the slope and c is the y-intercept  

And the formula for Slope is given by

Here we have

Number of participants in 1st year = 26

Number of participants in 4th year = 89

Take number of years as x - coordinate

Number of participants as y - coordinate

As we know for 1 year, number of participants is 26

=>  The pair of coordinates = (1, 26)

For 4th year, number of participants is 89  

=>  The pair of coordinates = (4, 89)

Now we will find the slope-intercept form for the situation

using the coordinates (1, 26) (4, 89)

As we know slope m = (y₂ - y₁)/(x₂- x₁)  

Slope m = (89 - 26)/(4 - 1) = 63/3 = 21      

As we know slope intercept form, y = mx + c  

=> y = 21x + c --- (1)

As per the situation, Line (1) will pass through (1, 26)  

=> 26 = 21(1) + c  

=> c = 26 - 21

=> c = 5

=>  y = 21x + 5

Therefore,

The required Slope-intercept form is y = 21x + 5

To find the number of participants in the 6th year, take x = 6

=> y = 21(6) + 5

=> y = 126 + 5

=> y = 131

Therefore,

The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.

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Answer:

a = 5.07

Step-by-step explanation:

Here, we want to get the value of the side marked a

What we have is a right triangle

so, to find the value of a, we are to use the correct trigonometric ratio

The angle given faces a, which makes a the opposite

the side measure faces the right angle and that makes it the hypotenuse

The trigonometric ratio that connects the two is the sine

The sine is the ratio of the opposite to the hypotenuse

mathematically;

sine 25 = a/12

a = 12 * sine 25

a = 5.07

Fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line.

The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line

A line is shown connecting points on ordered pair (2, 12) and (4, 24) and (6, 36) and (8, 48)

m=24-12/4-2

m=12/2

Hence,  fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls

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Chance is 1/10

Given that the die has 20 different numbers, ranging from 1-20, we are to determine the chance that the top side will be either a 9 or a 10.When throwing a die with a different number of faces or sides, each face has an equal chance of showing up as the top side. Thus, to determine the chance that the top side will be either a 9 or a 10, we need to find the probability of rolling a 9 or 10.To calculate the probability of a single event occurring, we divide the number of favorable outcomes by the total number of possible outcomes. Thus, in this case, the probability of rolling a 9 or a 10 would be:Probability of rolling a 9 or a 10= number of favorable outcomes/ total number of possible outcomesNumber of favorable outcomes: 2 (since there are only 2 sides of the die that have a 9 or a 10)Total number of possible outcomes: 20 (since there are 20 different numbers on the die)Probability of rolling a 9 or a 10 = 2/20 = 1/10Therefore, the chance that the top side will be either a 9 or a 10 is 1/10.

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Answer:

The Point Form is: (-2,-1)

Equation form is x= -2, y = -1

Step-by-step explanation:

Answer:

(-2, -1)

Step-by-step explanation:

both equation form:  Ax + By = C

3x - 3y = -3 - 2×(3x - 3y = -3) =  6x + 6y = 6

2x - 6y = 2 - Terms opposite =   2x - 6y = 2

( Add) - 4x = 8

divide by -4 =  x = -2

Put X value in equations 3(-2) + 3 = 3y and solve -

-6 + 3 = 3y

-3  = 3y

-1 = y

Answer=  (-2, -1)

Answer:

x + 6 = -6

Step-by-step explanation:

Assuming x = -6

\(x+6=0\)

Subtract 6

\(x+6-6=0-6\)

Simplify arithmetic

\(x=0-6\)

Simplify arithmetic(again)

\(x=-6\)

we technically solved the equation right at the beginning when we assumed x was equal to -6 in order to group the constants to the right.

Hope this helps, have a great day!

Answer:

pi r^2 h/3, height =6, r=10, 100*6=600pi/3=200pi

Answer:

A would be a good form of the answer

Answer: x > -7, line b.

Step-by-step explanation:

3x - 6 < 4x + 1

-1x  < +7

x  > -7

The number of hours to stay within the budget of $100.60 is less than 7 hours

From the question, the parameters are:

Reservation fee = $32

Additional fee = $9.80

The linear equation that represents the total amount spent is represented as:

Total charges = Reservation fee + Additional fee * Number of hours

This can be represented as

y = Reservation fee + Additional fee * x

Where

x = Number of hours

y = Total charges

So, we have the following equations:

y = 32 + 9.80x

For the budget to be less than $100.60, we have the following inequality

32 + 9.80x < 100.60

Subtract 32 from both sides

9.80x < 68.6

Divide both sides by 9.80

x < 7

Hence, the hours is less than 7

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Answer:

The equation has 5 solutions and its real soluations are x=3, +sqrt2, -sqrt2, and -1

Step-by-step explanation:

Answer:

x = 3, -1, 2, -2

Step-by-step explanation:\(x^{2}\)

6(\(x\)-3)(\(x^{2}\)+4)(\(x\)+1) = 0

6(\(x\)-3)(\(x\)+2)(\(x\)-2)(\(x\)+1) = 0

Using the fact that (\(x^{2}\)+4) = (\(x\)-2)(\(x\)+2) - known as the difference of two squares rule

Thus solve by inserting values of \(x\) that will result in the equation equating to 0.

ie: if \(x\) = 3,

6(3-3)(3+2)(3-2)(3+1) = 0

0=0

RHS = LHS therefore true

Answer:

325 is the answer

Answer:

RQ=35.51 km

PR=34.62 km

Step-by-step explanation:

Bearing of Q from P = 72 degrees

Bearing of R from Q=320 degrees

320=270+50

Therefore, the second angle of Q is 50 degrees.

\(\angle P=72^\circ\\\angle Q=68^\circ\\\angle R=180^\circ-(72^\circ+68^\circ)=40^\circ\)

Using Law of Sines

\(\dfrac{r}{\sin R} =\dfrac{p}{\sin P} \\\dfrac{24}{\sin 40} =\dfrac{p}{\sin 72} \\p=\sin 72 \times \dfrac{24}{\sin 40}\\\\p=RQ=35.51$ km\)

Using Law of Sines

\(\dfrac{q}{\sin Q} =\dfrac{r}{\sin R} \\\dfrac{q}{\sin 68} =\dfrac{24}{\sin 40} \\q=\dfrac{24}{\sin 40}\times \sin 68\\\\q=PR=34.62$ km\)

Answer:

A) The factors are 5 & 6

B) There are 3 terms

C) the coefficient is 4

Step-by-step explanation:

I hope this helps <3