John Calvin sells children's clothing at a local specialty boutique. He is guaranteed a minimum salary of $1,350 per month plus commission of 4.45% of his total sales. What are John's total sales for a month in which his gross pay is $2,501.22?

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Answer:

Move all terms that don't contain  y  to the right side and solve.

y  =  3  +  4 x

The Hardy-Weinberg equation is a mathematical formula used to calculate the frequency of alleles (alternative forms of genes) in a population.

It states that the frequency of alleles and genotypes in a population will remain constant from generation to generation in the absence of other evolutionary influences.

The equation is expressed as: p² + 2pq + q² = 1

In this equation, p represents the frequency of the dominant allele in the population, and q represents the frequency of the recessive allele.

The superscripts 2 represent the proportion of individuals in the population that are homozygous for that allele (meaning they have two copies of the same allele), while the 2pq term represents the proportion of individuals that are heterozygous (meaning they have one copy of each allele).

The sum of these terms is always equal to 1, as it represents the entire population.

This equation assumes several conditions: that the population is large, randomly mating, with no mutations, migration, natural selection, or genetic drift.

In reality, these conditions are rarely met, and the Hardy-Weinberg equation serves as a useful model for understanding how allele frequencies can change over time due to various evolutionary influences.

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Answer:

See below

Step-by-step explanation:

Basically, when you have a product to two factors set equal to 0, you can use the Zero Product Property and make two separate equations, both set equal to 0, to find the roots for each factor:

\(2x+10=0\\2x=-10\\x=-5\)

\(x-7=0\\x=7\)

Notice that by plugging these roots back into the equation, either factor will be 0, making the whole expression 0:

\((2x+10)(x-7)=0\\(2(7)+10)(7-7)=0\\(24)(0)=0\\0=0\)

\((2x+10)(x-7)=0\\(2(-5)+10)(-5-7)=0\\(0)(-12)=0\\0=0\)

The first thing is to describe each interval on its own.

If you were to describe the left interval (x<-10) from left-to-right, you'd say, "It goes from negative infinity to -10, not including -10."  To put that into interval notation, you'd have:

     \(\big(-\infty, -10\big)\)

The right interval (x>-2) would be described as "from -2 to infinity, not including -2."  In interval notation, we'd write this as:

    \(\big(-2, \infty \big)\)

Now that we have each one individually, we need to glue them together to say, "You can pick a number from the left interval OR the right interval."  The way we do this, the way we write "or" with intervals is with the union symbol: \(\cup\)

    \(\big(-\infty,-10 \big) \cup \big (-2,\infty\big)\)

The probability represents the combination consists only of even numbers as per given condition is equal to 0.020.

Total numbers in combination lock = 38

Numbers from 0 to 37.

To find the probability that the combination consists only of even numbers,

Determine the total number of combinations that can be formed using only even numbers

And divide it by the total number of possible combinations.

Total number of even numbers in the lock

= 19 (since there are 19 even numbers from 0 to 37)

Calculate the total number of combinations using only even numbers,

Use the concept of combinations (nCr).

Since there are 19 even numbers to choose from,

Choose 4 numbers without repetition, the number of combinations is,

Number of combinations

= ¹⁹C₄

= 19! / (4!(19-4)!)

= (19 × 18 × 17 × 16) / (4 × 3 × 2 × 1)

= 3876

Now, calculate the total number of possible combinations without any restrictions.

Since we have 38 numbers to choose from,

and  choose 4 numbers without repetition, the number of combinations is,

Number of total combinations

= ³⁸C₄

= 38! / (4!(38-4)!)

= (38 × 37 × 36 × 35) / (4 × 3 × 2 × 1)

= 194,580

Finally, find the probability by dividing the number of combinations using only even numbers by the total number of combinations,

Probability

= Number of combinations using only even numbers / Total number of combinations

= 3876 / 194580

≈ 0.0199

≈ 0.020 Rounded to three decimal places.

Therefore, the probability that the combination consists only of even numbers is approximately 0.020.

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The range of the data is determined by the minimum and maximum values.

In this case, the minimum value is 102 (lower whisker) and the maximum value is 115 (upper whisker).  Therefore, the range of the data is 115 - 102 = 13.To determine where a number is in relation to another number on a number line, we need to compare their positions. If is seven units to the left of , we can represent this as: = - 7. Therefore, is to the right of on the number line. Similarly, if a number is to the left of another number, it means that it has a smaller value and its representation would have a negative sign. For example, if the number is three units to the left of , we can represent it as: = - 3.

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The point (16, -99) is not a perfect fit in the linear model, and the slope-intercept equation for the remaining four data points (-8, 9), (-6, -9), (-2, -18), and (8, -63) is y = (-15/2)x + 3; the y-intercept (3) represents the net approval rating for the president when there is no change in the Dow Jones, and the slope (-15/2) indicates that for every 1-point increase in the Dow Jones, the net approval rating is expected to decrease by 7.5 percentage points.

To determine which point is not a perfect fit in the linear model, we need to compute the slopes for each pair of consecutive data points.

The slope of a linear model represents the rate of change between the two variables.

Using the given data points:

Points: -8, -6, -2, 8, 16

Percentage Points: 9, -9, -18, -63, -99

Let's compute the slopes:

Slope between (-8, 9) and (-6, -9):

slope = (change in percentage points) / (change in points)

slope = (-9 - 9) / (-6 - (-8))

slope = -18 / 2

slope = -9

Slope between (-6, -9) and (-2, -18):

slope = (-18 - (-9)) / (-2 - (-6))

slope = -9 / 4.0

slope = -2.25

Slope between (-2, -18) and (8, -63):

slope = (-63 - (-18)) / (8 - (-2))

slope = -45 / 10

slope = -4.5

Slope between (8, -63) and (16, -99):

slope = (-99 - (-63)) / (16 - 8)

slope = -36 / 8

slope = -4.5

The slopes for the first three pairs of points (-9, -2.25, -4.5) match, indicating a consistent linear relationship.

However, the slope between the last two points is -4.5, not -4.25 like the others.

Therefore, the point (16, -99) is not a perfect fit.

Removing the point (16, -99), we have four remaining data points:

(-8, 9), (-6, -9), (-2, -18), and (8, -63).

To find the slope-intercept equation for the linear model that passes through these four points, we can use the formula:

y = mx + b

Using the slope formula with two of the remaining points:

-9 = m(-6) + b

-18 = m(-2) + b

Solving these two equations simultaneously, we find:

m = -9/4

b = 9/2

So the slope-intercept equation for the linear model is:

y = (-9/4)x + 9/2

The practical meaning of the y-intercept (9/2) is that when the previous day's change in the Dow Jones is 0 points, the net approval rating for the president of the United States is expected to be 9/2 percentage points, or 4.5 percentage points.

The practical meaning of the slope (-9/4) is that for every 1-point increase in the previous day's change in the Dow Jones, the net approval rating for the president of the United States is expected to decrease by 9/4 percentage points, or 2.25 percentage points.

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The height of the building is 71 meters.

We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:

(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)

Substituting the given values:

2.8 / 1.49 = (height of building) / 37.5

To find the height of the building, we can cross-multiply and solve for it:

(2.8 * 37.5) / 1.49 = height of building

Calculating the expression on the right side:

(2.8 * 37.5) / 1.49 ≈ 70.7013

Rounding to the nearest meter, the height of the building is approximately 71 meters.

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Answer:

a) green: 0.3

yellow: 0.1

b) 12

Step-by-step explanation:

Unfortunately, I cant write on the table. But, I CAN help you with this question.

Since all probabilities have to add up to one, we can for an equation like this

(where y is yellow)

0.35+0.25+3y+y=1

This simplified is

0.6+4y=1

4y=0.4

So, we now know that green is 0.3, and yellow is 0.1.

For b, we set 0.35x to 14. Dividing gives us:

14/0.35=1400/35=40.

Multiply 0.3 by 40, and you get 12.

Hope this helped!

Answer:

Moved the graph down by 4.

Step-by-step explanation:

By subtracting by 4 on the outside, you are moving it down 4.

The area of the figure is solved to be

The area of a kite is solved using the formula

= P * q / 2

Where

p = length of long diagonal

q = length of short diagonal

Using the figure the length can be traced to be

p = 3 - -5 = 3 + 5 = 5

q = 6 - 2 = 4

Area of the figure

= 5 * 4 / 2

= 20 / 2

= 10 square units

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Answer:

A

Step-by-step explanation:

Answer:

Since x (independent) is time and y (dependent) is temperature;

F(0)  =50 means; at the beginning which is 0 minutes, the temperature is 50F

f(120)>f(60) means the temperature after 120 min is bigger than the temperate after 60 min.

f(360) = f(345) means the temperature after 360 min and 345 min are the same  

f(390) < f(360) means the temperate after 390 min is less than the temperature after 360 min  

Step-by-step explanation:

Answer:

Since x (independent) is time and y (dependent) is temperature;

F(0)  =50 means; at the beginning which is 0 minutes, the temperature is 50F

f(120)>f(60) means the temperature after 120 min is bigger than the temperate after 60 min.

f(360) = f(345) means the temperature after 360 min and 345 min are the same  

f(390) < f(360) means the temperate after 390 min is less than the temperature after 360 min  

Step-by-step explanation:

Answer:

I don't know what the question is but there will be 9.25 pounds of apples?

Step-by-step explanation:

It will take 2 days for the car to cover the route.

To determine how many days it will take a car to cover a route of length M kilometers, we need to use the given formula:

Distance = Rate × Time

where distance is M kilometers, and rate is N kilometers per day.

We want to find the time in days.

Therefore, rearranging the formula, we have: Time = Distance / Rate

Substituting the given values, we get: Time = M / N

Therefore, the function days(n, m) that returns the number of days to cover the route can be defined as follows: def days(n, m):    return m / n

Now, let's use this function to calculate the number of days it will take for a car that covers a distance of 700 kilometers per day to cover a route of length 750 kilometers:

days(700, 750) = 1.0714...

Since the number of days should be a whole number, we need to round up the result to the nearest integer using the ceil function from the math module: import mathdef days(n, m):    return math.ceil(m / n)

Now, we can calculate the number of days it will take for a car that covers a distance of 700 kilometers per day to cover a route of length 750 kilometers as follows: days(700, 750) = 2

Therefore, it will take 2 days for the car to cover the route.

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Answer:23 /180

Step-by-step explanation:

−23/ 4 /5 /−9=  23 /180

Answer: 99/20

Step-by-step explanation:

-2 3/4 / 5/-9

-11/4/5/9

11/4*5/9

99/20

Answer:

eh its 12 because

Step-by-step explanation:

according to my calculations if there are 16 females therefore the ratio is 3 to 4 men to women 3x4=12 and 4x4=16 so the answer is 12

i might be wrong please let me know

This is the quarterly interest rate on the account. Rounded to four decimal places, the base of the exponential expression is 1.032.

To rewrite the function representing account C to reveal the quarterly interest rate on the account, we can rewrite the function in the form:

C(t) = C0\((1 + r)^{(nt)}\)

Where C0 is the initial amount of money in the account, r is the periodic interest rate, and nt is the number of periods over which the interest is compounded.

Substituting the values in the function,

3,000\((1.032)^{2t}\) = C0\((1 + r)^{(2t)}\)

Dividing both sides by C0, we get:

\((1.032)^{2t}\) = \((1 + r)^{(2t)}\)

Applying logarithms on both sides,:

2tln(1.032) = 2tln(1 + r)

Solving for r, we get:

r = ln(1.032)/2 = 0.0159/2 = 0.00795

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Answer:

LM corresponds to PQ

Angle R corresponds to angle N

*Hope this helped! : )*

I hope this helps, have a nice day!!

Answer:

Domain is all real numbers, x ≠ -5

Range is all real numbers, y ≠ 0

Step-by-step explanation:

Answer:

y=3/4. ×=-3/2

y-3/4=0

×+3/2=0

y-3/4=x+3/2

y=x+3/2+3/4

y=(2x+6+3)/4

4y=2x+9

4y-2x-9=0

The given expression of trigonometry is equivalent to cos(2θ).

trigonometry capability, in math, one of six capabilities (sine [sin], cosine [cos], digression [tan], cotangent [cot], secant [sec], and co-secant [csc]) that address proportions of sides of right triangles. These six geometrical capabilities comparable to a right triangle.

We have,

1 - tan^2(θ)/1 +  tan^2(θ)

Use 1 + tan^2(θ) = sec^2(θ)

1 - tan^2(θ)/ sec^2(θ)

1/ sec^2(θ) - tan^2(θ)/sec^2(θ)

Use tan(θ) = sin(θ)/cos(θ)

cos^2(θ) - sin^2(θ)×cos^2(θ)/cos^2(θ)

cos^2(θ) - sin^2(θ)

Using sin^(θ) + cos^2(θ) = 1

cos^2(θ) - (1 - cos^2(θ))

2cos^2(θ) - 1

Here we have 2cos^2(θ) - 1 = cos(2θ)

Then, simplification of given expression is cos(2θ).

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Correct question:

which expression is equivalent to 1 - tan^2(θ)/1 +  tan^2(θ) for all values of θ for which 1 - tan^2(θ)/1 +  tan^2(θ) is defined?

The probability of getting two consecutive yellow marbles in a row is 1/625.

Given that there are 38 red marbles, 23 green marbles, 11 blue and 3 yellow marbles in the bag.

We are required to find the probability of getting two consecutive yellow marbles in a row.

Probability is basically the calculation of chance of happening an event among all the events that are possible to happen.

Probability= Number of items/ Total number of items.

Number of red marbles=38

Number of green marbles=23

Number of blue marbles=11

Number of yellow marbles=3

Total number of marbles=75

Probability of getting two consecutive yellow marbles=Probability of getting yellow marble*Probability of getting yellow marble

Probability of getting yellow marble=3/75

Probability of getting two consecutive yellow marbles=3/75*3/75

=1/25*1/25

=1/625

Hence the probability of getting two consecutive yellow marbles in a row is 1/625.

Question is incomplete. The question should include the following:

Number of red marblesin the bag=38

Number of green marbles in the bag=23

Number of blue marbles in the bag=11

Number of yellow marbles in the bag=3

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Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Answer:

answer is x=-1/10 is the answer

Answer:

5.23

Step-by-step explanation:

78.45÷ 15 = 523/100

simplified is 5.23

Answer:

D.

Step-by-step explanation:

The car is going the same speed as its average speed over the interval 0 to 10 seconds at t = 5 seconds.

To find the time when the car is going the same speed as its average speed over the interval 0 to 10 seconds, we need to compare the instantaneous velocity of the car at a given time with its average velocity over the interval [0, 10].

The position equation is given by:

\(\mathrm{s(t) = \frac{1}{4} t^2 + 1}\)

To find the instantaneous velocity, we need to take the derivative of the position equation with respect to time:

\(\mathrm{v(t) = ds/dt = d/dt [\frac{1}{4} t^2 + 1]}\)

\(\mathrm{v(t) = \frac{1}{2} t}\)

The average velocity over the interval [0, 10] is the change in position divided by the change in time:

Average velocity = \(\mathrm{\frac{s(10) - s(0)}{(10 - 0)}}\)

\(= \frac{1/4 (10^2) + 1 - (1/4)(0^2) - 1}{10} \\\\ = \frac{(25 + 1 - 0 - 1)} {10}\\\\= 25 / 10\\\\= 2.5\)

Now we need to find the time when the instantaneous velocity (v(t)) is equal to the average velocity (2.5):

(1/2)t = 2.5

Solving for t:

t = 2.5 x 2

t = 5

Therefore, the car is going the same speed as its average speed over the interval 0 to 10 seconds at t = 5 seconds.

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