What is the answer for 3x + 9x?

Janet can customize a car in 630 different ways.

To determine the number of ways Janet can customize a car, we need to multiply the number of options for each customization choice.

Number of car models: 10

Number of exterior colors: 7

Number of interior colors: 9

To calculate the total number of ways, we multiply these numbers together:

Total number of ways = Number of car models × Number of exterior colors × Number of interior colors

= 10 × 7 × 9

= 630

Therefore, the explanation shows that Janet has a total of 630 options or ways to customize her car, considering the available choices for car models, exterior colors, and interior colors.

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The exact value of sin θ can be determined by using the Pythagorean identity and the given information that cos θ is equal to 3/4 in Quadrant IV. The simplified form of sin θ is -√7/4.

In Quadrant IV, the cosine value is positive (given as 3/4). To find the sine value, we can use the Pythagorean identity: sin^2 θ + cos^2 θ = 1.

Plugging in the given value of cos θ:

sin^2 θ + (3/4)^2 = 1.

Rearranging the equation and solving for sin θ:

sin^2 θ = 1 - (9/16),

sin^2 θ = 16/16 - 9/16,

sin^2 θ = 7/16.

Taking the square root of both sides:

sin θ = ± √(7/16).

Since we are in Quadrant IV, where the sine is negative, we take the negative sign:

sin θ = - √(7/16).

To simplify the radical, we can factor out the perfect square from the numerator and the denominator:

sin θ = - √(7/4) * √(1/4),

sin θ = - (√7/2) * (1/2),

sin θ = - √7/4.

Therefore, the exact value of sin θ, in simplest form, is -√7/4.

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Answer: 51,000 ; 111,000

Step-by-step explanation:

The formula to calculate the simple interest is: PRT/100

where,

P = principal = 60,000

R = rate = 8.5%

T = time = 10 years

Simple interest =(60000 × 8.5 × 10)/100

= 5100000/100

= 51,000

Total Amount Paid= Principal + Interest

= 60,000 + 51,000

= 111,000

Answer:

This proves that f is continous at x=5.

Step-by-step explanation:

Taking f(x) = 3x-1 and \(\varepsilon>0\), we want to find a \(\delta \) such that \(|f(x)-14|<\varepsilon\)

At first, we will assume that this delta exists and we will try to figure out its value.

Suppose that \(|x-5|<\delta\). Then

\(|f(x)-14| = |3x-1-14| = |3x-15|=|3(x-5)| = 3|x-5|< 3\delta\).

Then, if \(|x-5|<\delta\), then \(|f(x)-14|<3\delta\). So, in this case, if \(3\delta \leq \varepsilon\) we get that \(|f(x)-14|<\varepsilon\). The maximum value of delta is \(\frac{\varepsilon}{3}\).

By definition, this procedure proves that \(\lim_{x\to 5}f(x) = 14\). Note that f(5)=14, so this proves that f is continous at x=5.

The probability that at least one of the stocks will rise in price is 0.92. Rounded to 2 decimal places, the answer is 0.92.

To calculate the probability that at least one of the stocks will rise in

, we can use the complement rule of probability. The complement rule of probability states that the probability of an event occurring is equal to one minus the probability of the event not occurring. Therefore, the probability of at least one stock rising in price can be found by subtracting the probability that none of the stocks will rise in price from one.

Let P(A) be the probability that a stock will rise in price and P(A') be the probability that a stock will not rise in price.

The probability that none of the stocks will rise in price is:

P(A') * P(A') * P(A') = (0.2) * (0.5) * (0.8) = 0.08

The probability that at least one of the stocks will rise in price is:

1 - 0.08 = 0.92

Therefore, the probability that at least one of the stocks will rise in price is 0.92. Rounded to 2 decimal places, the answer is 0.92.

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The number 7,656,565 consists of seven digits. To calculate the number of ways these digits can be arranged, we can use the concept of permutations.

The total number of arrangements can be found by considering that each digit can occupy a different position, without repetition. Therefore, the number of ways to arrange the digits in 7,656,565 can be determined.To calculate the number of arrangements, we start by considering that there are seven digits in the number 7,656,565. Each digit can be placed in a different position, without repetition. In other words, we have seven choices for the first digit, six choices for the second digit (as one digit has already been placed), five choices for the third digit, and so on.

Using the concept of permutations, we can calculate the total number of arrangements by multiplying these choices together. Therefore, the number of ways to arrange the digits in 7,656,565 can be found as 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.Hence, there are 5040 different ways in which the digits in the number 7,656,565 can be arranged.

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For given six number cards, three pairs with the same total:

(8, -4), (6, -2) and (5, -1)

In this question, we have been given six number cards.

-4 -2 -1 5 6 8

We need to arrange the cards into three pairs with the same total in brackets.

Arranging cards with numbers  -4, -2, -1, 5, 6, 8 making pair with the same total.

i.e.  8 - 4 = 4

so the first pair is (8, -4)

6 - 2 = 4

so the second pair is (6,-2)

5 - 1 = 4

and the last pair is (5,-1)

Therefore, for given six number cards, three pairs with the same total:

(8, -4), (6, -2) and (5, -1)

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The average payment will be $611.64.

It should be noted that average means mean. This implies that we will add the numbers and then divide.

This will be:

= ($23.42 + $14.95 + $276.50 + $219.93 + $76.84) / 5.

= $611.64

Therefore, the average payment will be $611.64.

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Answer:

All these added amount to $611.64, yes.

However, to find average, you then divide by 6.

Which equals; $101.94.

That is the average payment.

Step-by-step explanation:

Hope it helps.

Answer:

It's still gonna equal 28

Answer:

Note that both the x and y coordinates are multiplied by the SAME value, k. Given ΔDEF with center of dilation the origin (0,0) and scale factor of 2, plot ΔD'E'F'. As shown in the formula above, multiply each x and y coordinate value by the scale factor of 2 to find the new coordinator

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Using 3 different methods, we can find that YZ = 25m

Method 1:

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations -

sin(θ) = (opposite side)/Hypotenuse

cos(θ) = (adjacent side)/Hypotenuse

tan(θ) = (opposite side)/(adjacent side)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent side

YZ = opposite side.

We want to find YZ, so with the known things, we can use the first relation:

sin(30°) = YZ/50m

YZ = sin(30°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 2:

We know that the sum of the measure of all the internal angles of a triangle is always equal to 180°.

In a right-angled triangle, we have an angle equal to 90°.

Then we can write -

Z + 90° + 30° = 180°

Z = 180° - 90° - 30°

Z = 60°

From this angle, the side YZ is the adjacent side, then we can use the second trigonometric relation:

cos (60°) = YZ/50m

YZ = cos(60°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 3:

With the same angle of 60° we could find side XY, the opposite side as follows:

sin(60°) = XY/50m

XY = sin(60°) * 50m

XY = √3/2 *50m

XY = 25m

Now that we know one of the sides, we can use the last trigonometric relation-

tan(60°) = XY/YZ

tan(60°) = 43.3m/YZ

YZ =  43.3m/tan(60°)

YZ = 25m

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The complete question is -

Describe three ways to determine the measure of segment YZ.

Triangle XYZ is shown. Angle XYZ is a right angle and angle ZXY is 30 degrees. The length of hypotenuse XZ is 50 meters.

The statement is false. The correct formula to find the size of the union of two sets is |a ∪ b| = |a| + |b| - |a ∩ b|. Substituting the values given in the question, we get |a ∪ b| = n + m - |a ∩ b|.

We don't know anything about the intersection of sets a and b, so we cannot directly calculate |a ∩ b|.

However, we do know that |a ∩ b| is less than or equal to the minimum of |a| and |b|, which is min(n,m). Therefore, we can say that |a ∩ b| ≤ min(n,m).

Substituting this inequality into the formula for |a ∪ b|, we get:

|a ∪ b| = n + m - |a ∩ b|
≥ n + m - min(n,m)

We can simplify this expression by observing that if n ≤ m, then min(n,m) = n. If n > m, then min(n,m) = m. Therefore:

|a ∪ b| ≥ n + m - n = m
or
|a ∪ b| ≥ n + m - m = n

In either case, we have shown that |a ∪ b| is greater than or equal to the larger of |a| and |b|. Therefore, the given formula, |a ∪ b| = nm - nm, cannot be correct. The correct answer is b. false.

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Using the binomial distribution, it is found that there is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that at least one commits an error is given by:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{30,0}.(0.3)^{0}.(0.7)^{30} = 0.000023\)

Then:

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.000023 = 0.999977\)

There is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.

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The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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It gradually decreases as alcohol is metabolized. The function C(t)=0.135 t e^{-2.802 t}models the mean BAC measured in g/mL.

The maximum average BAC during 3 hours is 0.0001358 g/mL.

f(t) = α t e−βt --(1)

Let's rewrite this in a simple form:

f(t)= α eˡⁿ ᵗ e⁻βt = αe^(ln t −βt)

Since e^x is strictly increasing and it will be maximized exactly when its argument is maximized, so we can maximize instead:

g(t)=ln t −βt

differentiating with respect to t , and g'(t) = 0

g′(t)=1/t − β = 0

=> t =1/β

we have given a function

C(t)=0.135 t e⁻²·⁸⁰²ᵗ

if we compare it with (1) we get

β = 2.802, 0.135 = α

For it's maximized we need to check the second order condition, and that of g will differentiate again , g′′(t)= −1/t² < 0

We have to compute the derivative of C(t):

C′(t) = 0.135 t⋅(−2.802)e⁻²·⁸⁰²ᵗ + 1.35e⁻²·⁸⁰²ᵗ

For optimum at t₀ if C′(t₀)=0 and C′′(t₀)≠0. Here, we have

C′(t₀) = 0.135t₀⋅(−2.802)e⁻²·⁸⁰²ᵗ₀+ 0.135e⁻²·⁸⁰²ᵗ₀ =e⁻²·⁸⁰²ᵗ₀(−0.135* 2.802t₀+ 0.135)=0

It is clear that e⁻²·⁸⁰²ᵗ₀ not equal to zero for all t₀∈R, so that

=> −0.135* 2.802t₀+0.135=0

=> t₀ = 1/2.802 ≈0.36

let us consider t is in hours, so that it makes t₀ =0.36h≈21.41min. This is the only optimum and one should verify it is indeed a maximum, i.e. C′′(t₀)<0.

Now, easily compute the maximum average BAC, which is C(t₀)=C(0.36) = 0.135 (0.36)e⁻²·⁸⁰²⁽⁰·³⁶⁾

= 0.0486(0.3678) = 0.01787508

Hence, the maximum average BAC, is 0.017 g/dL.

Maximum average BAC during the first 3 hours,

t = 3 , C(t)=C(3) = 0.135 (3)e⁻²·⁸⁰²⁽³⁾ = 0.0001358 g/mL

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The option B, "The adult male foot length of 23.8 cm is significantly low because it is less than 24.26 cm" is correct.

In the given question, a group of adult males has foot lengths with a mean of 26.84 cm and a standard deviation of 1.29 cm.

We have to find the adult male foot length of 23.8 cm significantly low or significantly​ high.

According to thumb rule, a value is significantly low if it is 2 standard deviations below mean and significantly high if it is 2 standard deviations above mean

Mean = 26.84 cm

Standard deviation = 1.29 cm

Significantly low value = 26.84 - 2*1.29 = 24.26 cm

Significantly high value = 26.84 + 2*1.29 = 29.42 cm

Significantly low values are 24.26 cm or lower.

Significantly high values are 29.42 cm or higher.

The adult male foot length of 23.8 is lower than the significant low value of 24.26.

So the option B, "The adult male foot length of 23.8 cm is significantly low because it is less than 24.26 cm" is correct.

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The researcher wants to determine if the number of calories burned during an hour is the same for running and walking. To conduct this investigation, the researcher would measure continuous scale data.

Continuous scale data is quantitative data that can take any numerical value within a certain range.

In this case, the researcher would measure the number of calories burned, which is a continuous variable that can have various values within a specific range (e.g., 0, 100, 200, etc.).

By measuring the calories burned for both running and walking, the researcher can compare and analyze the numerical data to determine if there is a significant difference between the two activities.

It is important to note that the type of statistical analysis required to evaluate the data would depend on the specific research design and the number of groups involved.

If the researcher is comparing only two groups (running and walking), an independent t-test may be appropriate.

On the other hand, if there are more than two groups or additional factors being considered, an analysis of variance (ANOVA) might be more suitable.

The choice of statistical analysis method would depend on the specific research question and study design.

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The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.

To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:

Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ

For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78

For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06

Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803

Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178

So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.

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Answer:10

Step-by-step explanation: dd

The required radius of the cylindrical can is 4 millimeters.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases.

Given that,

The height of the cylinder h  = 12 cm.

And volume of the cylinder v = 600 mL

Since, 1 mL = cm³

The volume v = 600 cm³.

Let radius of cylinder is r,

To find the radius, use formula,

Volume of cylinder V = π x r² x h

22/7 x r² x 12 = 600

22/7 x r² = 50

r² = 350 / 22

r² = 15.909

r = 3.98

or r =  4 millimeters.

The radius of the cylinder is 4 millimeters.

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Answer:

11

Step-by-step explanation:

Answer:

9 and -4

Step-by-step explanation:

Answer:

a = 9

Step-by-step explanation:

Step 1: Add 3 to both sides

2a – 3 = 15

2a – 3 + 3 = 15 + 3

Step 2: Simplify

add the numbers ( 2a = 18 )

Step 3: Divide both sides by the same factor

2a = 18

2a 18

––– = –––

2 2

Step 4: Simplify

l

Cancel the terms that are in both the numerator and the denominator

l

l

Divide the numbers

l

a = 9

Answer: a = 9

Answer:

A. 424.12 \(in^{2}\)

Step-by-step explanation:

The volume for a cylinder is (pi)(r^2)(h)

\(\pi r^{2} h\)

radius = 3

height = 15

(pi) (9) (15)

135pi = 424.1150082 = 424.12

hope this helps :)

Answer: 9 1/2 ==> D

Step-by-step explanation:

14 1/4 - 4 3/4 =

14 + 1/4 - (4 + 3/4) =

14 + 1/4 - 4 - 3/4 =

56/4 + 1/4 - 16/4 - 3/4 = ==> make each term share common denominators

(56+1-16-3)/4=

(57-19)/4=

38/4=

(36+2)/4=

36/4 + 2/4=9 1/2 ==> D

Answer:

c) 74.052 in Expanded form with decimal form =

7 × 10 + 4 × 1 + 0 × 0.1 + 5 × 0.01 + 2 × 0.001

b) 74.052 in Expanded form with fractions =

7 × 10 + 4 × 1 + 0 × 1/10 + 5 × 1/100 + 2 × 1/1000

Step-by-step explanation:

We are given the number 74.052

The place value of each of the numbers is given as follows:

7 = Tens

4 = units

0 = Tenth

5 = Hundredth

2 = Thousandth

We are asked to write 74.052 in Expanded form of Decimals and fractions.

74.052 in Expanded form with decimal form =

7 × 10 + 4 × 1 + 0 × 0.1 + 5 × 0.01 + 2 × 0.001

74.052 in Expanded form with fractions =

7 × 10 + 4 × 1 + 0 × 1/10 + 5 × 1/100 + 2 × 1/1000

Here, we are required to write the number 74.052 in expanded form using fractions and decimals to express the decimal place value units.

The answer in fractions is;

(7×10) + (4×1) + (0×1/10) + (5×1/100) + ( 2× 1/1000)

The answer in decimal form is;

(7×10) + (4×1) + (0×0.1) + (5×0.01) + ( 2× 0.001).

From the number:

(a) Therefore, to write the number in expanded form using fractions;

(7×10) + (4×1) + (0×1/10) + (5×1/100) + ( 2× 1/1000)

(b) Therefore, to write the number in expanded form using decimals;

(7×10) + (4×1) + (0×0.1) + (5×0.01) + ( 2× 0.001).

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Answer:

C

Step-by-step explanation:

subtract

Nadia has constructed a pentagonal prism

We know that, a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.

If we consider the bottom view of  pentagonal prism then it would be pentagon in shape.

If we consider the side view of  pentagonal prism then it would be rectangular in shape.

If we consider the front view of  pentagonal prism then it would be rectangle.

Therefore, Nadia has constructed a pentagonal prism

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When something decreases by 15.7%, the growth factor is about 1.182 and when something decreases by 0.12%, the growth factor is about 1.00012.

In math, what is the definition of multiplying?

Multiplication is a mathematical process that shows the amount of times a number has been added to itself. It is represented by the multiplication symbols (x) or (*). Division is a mathematical process that shows how many equal amounts add up to a given quantity.

If something decreases by 15.7%, the increase in the factor is 100 / (100 - 15.7) Equals 1.182.

As a result, when something decreases by 15.7%, the growth factor is about 1.182.

When something falls by 0.12%, the expansion factor is 100 / (100 - 0.12) = 1.00012.

As a result, when something decreases by 0.12%, the growth factor is about 1.00012.

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