What would the height need to be for this curve to be a density curve?
-1/6
1/6
1/5
1
​

Answer:

The coordinates of A would be (-1, 2)

Step-by-step explanation:

In order to find this, use the mid-point formula.

(xA + xB)/2 = xM

In this, the xA is the x value of point A, xB is the x value of point B, and xM is the x value of M. Now we plug in the known information and solve for xA.

(xA + 5)/2 = 2

xA + 5 = 4

xA = -1

Now we can do the same using the midpoint formula and the y values.

(yA + yB)/2 = yM

(yA + 10)/2 = 6

yA + 10 = 12

yA = 2

This gives us the midpoint of (-1, 2)

Answer:

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Step-by-step explanation:

The graph is not a direct variation because the line does not go through the origin; option C.

A direct variation is a relationship between two or more quantities in which as one quantity increases, the other quantity also increases. Similarly, if the other quantity decreases, the other decreases as well.

For the graph of a direct variation, the line must pass through the origin.

Therefore, the graph does not represent a direct variation because the line does not go through the origin.

In conclusion, direct variation involves a corresponding increase or decrease in two related quantities.

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Answer:

there are 63360 inches in 1 mile. if you divide 2 into 63360 and add that with it, that should give you the accurate answer

Using the binomial distribution, it is found that the variance of the number that pass inspection in one day is 5.7.

For each component, there are only two possible outcomes, either it passes inspection, or it does not. The probability of a component passing inspections is independent of any other component, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability, and has variance given by:

\(V(X) = np(1 - p)\)

In this problem:

The variance is given by:

\(V(X) = np(1 - p) = 120(0.95)(0.05) = 5.7\)

The variance of the number that pass inspection in one day is 5.7.

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The required total number of grams is 13.5 gram.

From figure we have,

The masses of 4 samples are the masses are 1.5 gram, 3.5 gram , 5 gram and 5 gram respectively.

To calculate the total number of grams of salt in the 3 samples with the most mass,

Add the masses of the three largest samples.

In this case,

The three largest samples are 3.5 grams, 5 grams, and 5 grams.

We have: 3.5 grams + 5 grams + 5 grams = 13.5 grams

Therefore, the total number of grams of salt in the 3 samples with the most mass is 13.5 grams.

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Answer:

b

Step-by-step explanation:

Answer:

$32.50

Explanation:

Let the cost price of the bicycle = x

The harmonized sales tax is 13%.

We can then subtract from the sales price to find the harmonized sales tax.

The harmonized sales tax on the price is $32.50.

The volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

To calculate the volume of the tree stump, we can use the formula for the volume of a cylinder, which is given by:

Volume = π * r^2 * h

Given:

Radius (r) = 20 inches

Height (h) = 0.7 feet

First, let's convert the height from feet to inches since the radius is already in inches. There are 12 inches in 1 foot, so:

Height (h) = 0.7 feet * 12 inches/foot = 8.4 inches

Now, we can substitute the values into the volume formula:

Volume = π * (20 inches)^2 * 8.4 inches

Calculating the volume:

Volume = 3.14159 * (20 inches)^2 * 8.4 inches

≈ 3.14159 * 400 inches^2 * 8.4 inches

≈ 1005.3096 cubic inches

Rounding the volume to the nearest tenth:

Volume ≈ 1005.3 cubic inches

Therefore, the volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

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The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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Answer: 138 inches

Step-by-step explanation:

We can use proportions here, let h = height of the statue

height/height = shadow/shadow

\(\frac{h}{69} = \frac{94}{47}\)

h/69 = 2

*69 (h/69 = 2) *69

h = 138 inches

Answer:

Step-by-step explanation:

Hello,

We know that

\(|x|=\begin{cases}x & \text{if } x\geq 0 \\ -x & \text{if } x<0 \end{cases}\)

So we need to take into account two cases

Case 1 - \(x-3\geq 0<=> x\geq 3\)

Then, |x-3|=x-3

||x-3|-2|=|x-3-2|=|x-5|

Either x-5 is positive and then |x-5|=x-5 and

\(|x-5|\leq 1<=>x-5\leq 1<=>x\leq 6\)

Or x-5 is negative and then, |x-5|=-x+5

\(|x-5|\leq 1<=>-x+5\leq 1<=>4\leq x\)

So the solution is [4;6]

Case 2 - \(x-3< 0<=> x< 3\)

Then, |x-3|=-x+3

||x-3|-2|=|-x+3-2|=|-x+1|

Either -x+1 is positive and then |-x+1|=-x+1 and

\(|-x+1|\leq 1<=>-x+1\leq 1<=>0\leq x\)

Or -x+1 is negative and then, |-x+1|=x-1

\(|-x+1|\leq 1<=>x-1\leq 1<=>x\leq 2\)

So the solution is [0;2]

Conclusion

The solution is [0;2]∪[4;6]

Thanks

The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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Answer:

false

Step-by-step explanation:

its not correct

Answer:

the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days

Step-by-step explanation:

Given that :

Mean  = 265

standard deviation = 14

The formula for calculating the z score is \(z = \dfrac{x -\mu}{\sigma}\)

x = μ + σz

At middle of 50% i.e 0.50

The critical value for \(z_{\alpha/2} = z_{0.50/2}\)

From standard normal table

\(z_{0.25}=\) + 0.67  or -0.67  

So; when z = -0.67

x = μ + σz

x = 265 + 14(-0.67)

x = 265 -9.38

x = 255.62

when z = +0.67

x = μ + σz

x = 265 + 14 (0.67)

x = 265 + 9.38

x = 274.38

the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days

Answer:

96

Step-by-step explanation:

Surface area=2*Area of triangle+Area of different rectangular strips

Surface area=2*(1/2)*(48)+2*8+2*6+2*10=48+48=96

Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

Using ratios to find the value of MK in the similar triangle, MK is equal is 24

Similar triangles are triangles that have the same shape but not necessarily the same size. Two triangles are similar if and only if their corresponding angles are congruent (equal in measure) or in other words, if the ratio of any two corresponding sides of the triangles is equal.

In the given problem;

MJ / ML = MK / KL

Substituting the values into the ratios and solving for MK;

30 / 40 = MK / 32

MK = (30 * 32) / 40

MK = 960 / 40

MK = 24

The value of MK is 24

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Answer:

90

Step-by-step explanation:

(let x be his 3rd test grade)

\(88=\frac{83+91+x}{3} \\264=83+91+x\\264=174+x\\x=90\)

Answer:

D. The number of students enrolled each year in school 1 is generally lower than the number of students enrolled in school 2.

Step-by-step explanation:

I got it right on the test :)

Answer:

I would say that answer is proportional

Step-by-step explanation:

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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A constant term that makes the equation have infinite solutions include the following: C. 20

In Mathematics, an equation is said to have an infinitely many solutions when the left hand side and right hand side of the equation or inequality are the same and equal.

This ultimately implies that, an equation or an inequality would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and y-intercept for the two lines are the same.

By applying the rule for an infinitely many solutions, we have:

5x + 20 = 5x + 20

5x - 5x = 20 - 20

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The polynomial expression that represents the perimeter is (3x^3 +3x -148)ft and the value is 182ft

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

Perimeter of the triangle is the sum of the sides of the triangle which is = 2x^2 -120 + x^2 -5x +8x -28

Perimeter = (3x^2 +3x -148)ft

when x = 10

Perimeter = 3(10)^2 +3(10) -148 = 182ft

In conclusion the expression  (3x^2 +3x -148)ft is the expression for the perimeter of the triangle and the value is 182ft

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5 is the measure of the value of x from the diagram

The given diagram is a triangle with the following parameters

Opposite = 5

Adjacent  = x

Using the trigonometry identity

tan theta = opp/adj

tan45 = 5/x

x = 5/tan45

x = 5/1

x = 5

Hence the measure of the value of x is 5.

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