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The probability density function for a normal distribution N(68, 5) reaches its maximum height at x = 68, which is the mean of the distribution. The function does not touch the x-axis at μ±30.

The probability density function (PDF) for a normal distribution is bell-shaped and symmetrical around its mean. In this case, the mean (μ) is 68, and the standard deviation (σ) is 5.

(a) To find the x value at which the PDF reaches a maximum, we look at the mean of the distribution, which is 68. The PDF is highest at the mean, and as we move away from the mean in either direction, the height of the PDF decreases. Therefore, the x value at which f(x) reaches a maximum is x = 68.

(b) The PDF of a normal distribution does not touch the x-axis at μ±30. The x-axis represents the values of x, and the PDF represents the likelihood of those values occurring. In a normal distribution, the PDF is continuous and never touches the x-axis. However, the PDF becomes close to zero as the values move further away from the mean. Therefore, the probability of obtaining values μ±30, which are 38 and 98 in this case, is very low but not zero. So, the PDF does not touch the x-axis at μ±30, but the probability of obtaining values in that range is extremely small.

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The probability of randomly selecting a player with a sprint speed larger than Mookie Betts is 0.2119.

To find the probability that a randomly-selected player will have a sprint speed larger than Mookie Betts (28.2 ft/sec), we can use the standard normal distribution.
First, we need to calculate the z-score for Mookie Betts' sprint speed. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation.
z = (x - μ) / σ
z = (28.2 - 27) / 1.5
z = 1.2 / 1.5
z = 0.8
Next, we need to find the area to the right of the z-score (0.8). This represents the probability that a randomly-selected player will have a sprint speed larger than Mookie Betts.
Using a standard normal distribution table or calculator, we can find the corresponding probability. The probability is approximately 0.2119.
Therefore, the probability that a randomly-selected player will have a sprint speed larger than Mookie Betts is 0.2119.
Conclusion: The probability of randomly selecting a player with a sprint speed larger than Mookie Betts is 0.2119.

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The product of (−21)(19)(−5) is 1995.

What is product?

In mathematics, the product is the result of multiplying two or more numbers or expressions together. The product is an important concept in mathematics and is used in many areas, including arithmetic, algebra, calculus, and geometry.

The problem asks us to find the product of (−21)(19)(−5). To solve this problem, we can multiply the three numbers together in any order because multiplication is associative.

So, let's multiply the numbers from left to right:

(−21)(19)(−5) = (−399)(−5)

We then simplify this expression by multiplying -399 and -5 together:

(−399)(−5) = 1995

Therefore, the product of (−21)(19)(−5) is -1995.

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Answer:

x = 7

Step-by-step explanation:

Parallel sides have to be the same length

5x+3 = 38

Subtract 3 from each side

5x+3-3 = 38-3

5x = 35

Divide by 5

5x/5 = 35/5

x = 7

Answer:

First Picture: Right side- 5 Left side- 3 Second Picture: Top- 26.5 Bottom- 41

Step-by-step explanation:

Hope this helps!

A transversal is a third line that crosses two other lines.

Lines on a plane that do not intersect are considered parallel lines in geometry. It is referred to as being parallel when two straight lines in a plane do not cross at any point.

Eight distinct angles may be obtained by drawing two parallel lines, a line across them, and then another line through that.

A key mathematical ability that calls for conceptual comprehension and clarity is the angles form. Worksheets on angles generated by parallel lines and transversals provide a variety of activities and problems based on angles that can aid students in learning about angles.

Correct question: What is the angles formed by a transversal called?

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Answer:

expanded form: 7+0.08+0.009+0.0003

Step-by-step explanation:

7 = the ones place

0.08 = hundredths place

0.009 = thousandths place

0.0003= ten thousandths place

y-y1 = m(x-x1) — point-intercept form

Given both x1 and y1 = coordinate point.

First​ we have to find the slope by using rise over run. (y2-y1)​/(x2-x1)​ = m

The slope should be m = -4 then we substitute m-value in point-slope form.

y-y1=-4(x-x1) — new equation. After substituting slope in, we need to find the coordinate point that is part of the graph. You can use any points that are given in the picture. I will use point F or (5,0).

Then we substitute x1 = 5 and y1 = 0 in the point-slope form

y-0=-4(x-5) — point-slope form

y=-4x+20 — slope-intercept​ form..

How about we change to another coordinate point to substitute in? We can check if these points also give same equation (slope-intercept).

Let's substitute (4,4) in the equation.

y-4=-4(x-4)

y=-4x+16+4

y=-4x+20

Same answer. Meaning that all these points that are shown can be substituted in the equation and get the same slope intercept form.

Therefore, point-slope form for the graph can be

y-4=-4(x-4)

you can also change the coordinate point value.

Answer:

B, C, D

Step-by-step explanation:

Hope this helped ^-^

Hi there!

Hope this helps!

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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The equations equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are;

The correct answer is option B and C

2.3p – 10.1 = 6.5p – 4 – 0.01p

collect like terms

2.3p - 6.5p + 0.01p = -4 + 10.1

-4.19p = 6.1

p = 6.1/-4.19

p = -1.46

2.3p – 10.1 = 6.5p – 4 – 0.01p

= 2.3p – 10.1 = 6.49p – 4

Given options:

2.3p – 10.1 = 6.4p – 4

False

2.3p – 10.1 = 6.49p – 4

True

230p – 1010 = 650p – 400 – p

divide through by 100

= 2.3p – 10.1 = 6.5p – 4 – 0.01p

True

23p – 101 = 65p – 40 – p

False

2.3p – 14.1 = 6.4p – 4

False

Therefore, 2.3p – 10.1 = 6.49p – 4; 230p – 1010 = 650p – 400 – p are equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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Answer:

TS

Step-by-step explanation:

QT≅TS because QS is bisected by PR

Answer: It will have to pay $36 in fees.

Step-by-step explanation: Hope this helps:) please mark me brainliest.

Answer:

y=3x (squared) -30x+79 and y-intercept is 79

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given equation:

Make c the subject:

Divide all terms by 0.9:

Now make r the subject:

Divide all terms by 1.89:

Confirmed that both equations are equivalent with the initial one.

These are helpful when finding one of the variables if the value of another variable is given.

Answer:. r = - 10/21 c + 9

Step-by-step explanation:

Answer: B

Step-by-step explanation:

9.62112750.....

area = πr²

3.5 ÷ 2 = 1.75

1.75² × π = 9.6211250....

= 9.6 ft²

7x + 3y + 2z

Answer: Can't be simplified

Answer: option b. 71%

Step-by-step explanation:

The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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Answer:

23.9

Step-by-step explanation:

(75 - 32) x 5/9 = 23.888888888888888888

Answer:

6x-3

Step-by-step explanation:

4x+6x-3-4x

6x-3

Answer:

6x -3

Step-by-step explanation:

4x + 3(2x - 1) - 4x

4x + 6x - 3 - 4x

Combine same values

6x -3

Answer:

The bag costs 1500, while the umbrella cost 500

Step-by-step explanation:

Let the cost of the bag be b and the cost of the umbrella be u

Total cost is;

b + u = 2,000 •••••(i)

From the second part of the question;

b = 5u-1000 ••••••(ii)

Substitute ii into i

5u-1000 + u = 2000

6u = 2000 + 1000

6u = 3000

u = 3000/6

u = 500

To get b, substitute the value of u into equation ii

b = 5(500)-1000

b = 2500-1000

b = 1500

Answer:

8x+8

Step-by-step explanation:

-9x-x+3+5

-9x-1x+3+5

9x-1x+3+5

8x+3+5

8x+8

HAVE A GREAT DAY!! HOPE THIS HELPS!! :))

Answer:

76

Step-by-step explanation:

Not sure what you mean by the second half, but I'll answer the first question. Since the number is two digits, you can represent it as 10x + y. If you reverse the digits, it becomes 10y + x. So, 11x + 11y = 143, and 9x - 9y = 9. Solving for x and y, you find x = 7 and y = 6.

Answer:

1.35 kg

Step-by-step explanation:

450/ 6= 75

75 x 18= 1350 grams

1.35 kg

Hassan needs 1.35 kg of rice for 18 people.

"It is a method of finding the value of a single unit."

For given question,

Hassan needs 450 grams of rice for 6 people

Let he needs 'x' grams of rice for 1 person.

By unitary method,

\(\Rightarrow x=\frac{450}{6}\\\\\Rightarrow x=75~~grams\)

So, the amount of rice for 18 people would be,

⇒ 18x

= 18 × 75

= 1350 grams

= 1.35 kg                                  ......................(1000 grams = 1 kg)

Therefore, Hassan needs 1.35 kg of rice for 18 people.

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