Height of 10th grade boys is normally distributed with a mean of 63. 5 in. And a standard deviation of 2. 9 in. The area greater than the z-score is the probability that a randomly selected 14-year old boy exceeds 70 in. What is the probability that a randomly selected 10th grade boy exceeds 70 in. ?Use your standard normal table.




Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard deviation of 2. 9 in. Find the z-score associated with the 96th percentile. Find the height of a 16-year-old boy in the 96th percentile. State your answer to the nearest inch

If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find (f/g)(x), we need to divide f(x) by g(x) as follows:

f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2

f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)

To simplify this expression, we can factor the numerator and denominator:

f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]

Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:

f(x) / g(x) = (x - 3) / (x + 2)

Therefore, (f/g)(x) = (x - 3) / (x + 2).

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Answer:

22% of 86

Step-by-step explanation:

22% = 0.22

0.22 × 86

The probability that at least one of the two adults believes most famous people make good role models be 0.436.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

A) The likelihood that both adults believe that most famous people make good role models would be = (199/800) × (198/799) = 39402/639200 = 0.062

B) We're looking for the likelihood that neither adult believes that most famous people make good role models.

Today that 199 people out of 800 believe that most famous people make decent role models.

The percentage of people who disagree that most celebrities make for good role models = 800 - 199 = 601

The probability that neither adult thinks most celebrities exists good role models. would be = (601/800) × (600/799)= 180300/319600 = 0.564

C) We're looking for the likelihood that at least one of the two adults believes that most celebrities make for positive role models.

Now that we know that neither of them believes that the majority of famous people are good role models, we can simply deduct that probability from 1.

The likelihood that at least one of the two adults believes most famous people make good role models = 1 - 0.564 = 0.436

The complete question is;

​In a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​adults, complete parts​ (a) through​ (c).

(a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as​ needed.)

​(b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is _______?(Round to three decimal places as​ needed.) ​

(c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models ______? (Round to three decimal places as​ needed.)

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By the radius-tangent theorem, the radius is equal to 39/10 units.

In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

Since CB is tangent to OA at point C and line segment CB is perpendicular to line segment AC by the radius-tangent theorem, we would determine the radius by applying Pythagorean's theorem as follows;

r^2 + 8^2 = (r + 5)^2

r^2 + 64 = r^2 + 10r + 25

r^2 - r^2 = -10r + 64 - 25

10r = 39

r = 39/10 units.

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Kindly, check below

1) As we can see, this is a piecewise function. So, let's plot that accordingly to each interval.

2) So, we can represent that this way:

Note that the open dot does not include the endpoint. And closed dots include the endpoints.

Thus, this is the answer.

The value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. The fraction is defined as the division of the whole part into an equal number of parts.

The given fractions 34/9, 43/9, and 32/5 can be written in the form of the mixed fraction as below:-

To write the fractions in the form of the mixed fraction first divide the fraction by the complete number and put the remainder on the numerator.

34/9 = 3(⁷/₉)

43/9 = 4(⁷/₉)

32/5 = 6(²/₅)

Therefore, the value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

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Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

Answer: Figure D

Figure D is a 180 degree rotation of figure A.

if the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, then 20,281 collections of 50 coins can be chosen.

what are quarters?

Given that:

25 quarters and only 40 dimes

No. of. Ways with at least 26 quarters and 41 dimes.

26 + 41 = 67 coins, but we have only 50 coins.

There are 0 ways to select at least 26 quarters and 41 dimes.

\(A_{1}\) = at least 26 quarters

\(A_{2}\) = at least 41 dimes

Using inclusion / exclusion rule for the two sets:

N(\(A_{1} U A_{2}\)) = N ( \(A_{1}\)) + N ( \(A_{2}\))- N (\(A_{1}\) ∩ \(A_{2\))

                = 2925 + 220 - 0

                = 3145

Therefore, no . of . ways with at most 25 quarters and at most 40 dimes are

= 23426 - 3145

= 20,281 ways

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Answer:

For A, the confidence interval formula above cannot be applied because n is less than 30, so we use the t-score confidence interval value

C.I = Mean ± t score × Standard deviation/√n

Mean = 80

Standard deviation = 5

n = 25

Degree of freedom = 25 - 1 = 24

Hence, 95% confidence interval degree of freedom t score = 2.064

Hence, Confidence Interval =

80 ± 2.064 × 5/√25

80 ± 2.064 × 1

80 ± 2.064

Confidence Interval =

80 - 2.064

= 77.936

80 + 2.064

= 82.064

Confidence Interval: (77.936, 82.064)

Using conversion from fraction to decimal and rational numbers, we have that:

7. The fraction that has a corresponding decimal greater than 1 is 4/3.

8. One rational number between 7 and 8 is given by option a, which is 7.83838383...

A fraction is converted to decimal dividing the numerator by the denominator.

In item 7, we consider fraction 4/3, for which:

Hence the corresponding decimal is given as follows:

4/3 = 1.333, which is the result of the division of 4 by 3, and is greater than 1.

The set of rational numbers is composed by all numbers that can be represented by fractions, such as integer, terminating decimals and repeating decimals.

In item 8, option a, we have the number 7.83, with the bar at 83. This means that 83 is the repeating decimal part, that is, the rational number is 7.83838383...

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The value of t would be,

⇒ t = 1.761

Using a table or calculator, we can find the value of t that corresponds to an area of 0.05 in the right tail of the t-distribution with 14 degrees of freedom.

The table or calculator will provide us with the t-value and its corresponding area in the right tail of the distribution.

Since we want an area of 0.05 in the right tail, we need to look for the t-value that has an area of 0.05 to the left of it.

Hence, Using a t-table, we find that the t-value with 14 degrees of freedom and an area of 0.05 in the right tail is approximately 1.761.

Therefore, t = 1.761 rounded to 3 decimal places.

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The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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For the given width length ratio and perimeter of rectangle, the length of rectangle is 80 cm.

The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Let the width of the rectangle be 3x, and the length be 4x (since the ratio of the width to the length is 3:4).

The perimeter of a rectangle is the sum of the lengths of all four sides, so we have:

Perimeter = 2(length + width)

Substituting the expressions for the length and width, we get:

280cm = 2(4x + 3x)

Simplifying the right-hand side, we get:

280cm = 14x

Dividing both sides by 14, we get:

x = 20

Therefore, the length of the rectangle is 4x = 4(20) = 80 cm

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Answer:

the answer for under n would be 14

Answer:

n + 4

Step-by-step explanation:

For this problem, we must simply determine the operation that is occurring between each input and each output.

Let's start with the first input, 1, and the first output, 5.  Notice 5-1 = 4.  Let's assume that this difference holds.  We need to check the next option.

The second input, 5, and the second output, 9.  Notice 9-5 = 4.  It would seem that our assumption holds.  Let's check the next case to ensure the validity of our assumption.

The third input, 7, and the third output, 11.  Notice 11 - 7 = 4.  Since all three cases match our assumption, we will apply our assumption to the generalized input, n.

When the input is n, our output will be n + 4, as we have determined with our assumption from the previous inputs and outputs that we analyzed.

Thus, when input in n, output is n+4.

Cheers.

The sample space for genders from two births would include four possible outcomes: two boys, two girls, one boy and one girl (in either order).

 The sample space for the genders from two births includes all the possible outcomes of genders for two children. In this case, there are four possible combinations:

1. Male (M) - Male (M)
2. Male (M) - Female (F)
3. Female (F) - Male (M)
4. Female (F) - Female (F)

So, the sample space for the genders from two births is {MM, MF, FM, FF}.

In probability theory, the sample space is the set of all potential outcomes or results of an experiment or random trial. It is also referred to as the sample description space, possibility space, or outcome space. The potential ordered outcomes, or sample points, are listed as elements in a set that is used to represent a sample space. A sample space is frequently referred to as S,, or U (for "universal set"). A sample space may contain symbols, words, letters, or numbers as its components. They may also be uncountably infinite, countably infinite, or finite.

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it is true big brain

The figure shows three types of unconformities: an angular unconformity (A - A) with tilted and eroded layers, a non-conformity (B- B) between uplifted and underlying rocks, and a paraconformity (C - C ) with a smooth transition between sedimentary layers indicating a potential time gap.

Based on the information provided, the figure shows three different unconformities

(A - A) represents an angular unconformity:

This occurs when horizontally layered rocks (A) are tilted or folded, eroded, and then overlain by younger, undeformed rocks (A). The angular discordance between the older and younger layers indicates a significant period of deformation and erosion.

(B- B) represents a non-conformity:

A non-conformity occurs when igneous or metamorphic rocks (B) are uplifted and eroded, exposing the underlying, usually sedimentary, rocks (B). The boundary between the two types of rocks represents a significant time gap and a change in the geological history of the area.

(C - C) represents a paraconformity:

A paraconformity is a type of unconformity where there is a relatively smooth transition between parallel layers of sedimentary rocks (C - C). Unlike angular unconformities and non-conformities, paraconformities do not show significant tilting, folding, or erosion. The time gap between the two layers may still exist, but it is often difficult to distinguish due to the lack of obvious discontinuities.

In summary, an angular unconformity (A - A) shows significant tilting and erosion, a non-conformity (B - B) indicates an uplift and erosion of older rocks, and a paraconformity (C - C) represents a relatively smooth transition between parallel sedimentary layers with a potential time gap.

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--The given question is incomplete, the complete question is given below " List and explain three different unconformities shown on this

figure. Explain your answer (15 points) "--

Answer:

(1,0)&(0,-3)

Step-by-step explanation:

might be not sure..

the expression 15*3y with all perfect squares removed is 9 * 5y, or simply 45y if you prefer not to factor it further.

In mathematics, a factor is a number or expression that divides another number or expression exactly, leaving no remainder. For example, 2 and 3 are factors of 6, because 6 can be divided by 2 and by 3 without any remainder. Similarly, (x - 3) is a factor of the expression x^2 - 9, because if we divide \(x^{2}\)- 9 by (x - 3), we get x + 3 with no remainder. Factoring is the process of breaking down a number or expression into its factors. Factoring is an important concept in many areas of mathematics, including algebra, number theory, and calculus.

by the question.

Remove all the perfect squares from 15*3y

The expression 15*3y can be simplified as follows:

15*3y = 45y

To remove all perfect squares from this expression, we need to find the perfect squares that divide into 45.

The prime factorization of 45 is:

45 = \(3^{2}\) * 5

So, the perfect squares that divide into 45 are\(3^{2}\) = 9.

To remove the perfect squares from 45y, we can factor out 9 from 45, and get:

45y = 9 * 5y

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Answer:

36

Step-by-step explanation:

As the triangle ABC is isosceles so A and B has the same measures

And, the sum of the angles is 180°.

Therefore 2 times the measure of angle

B plus  120° = 180°,

So, the equation:

2x + 120 = 180

So x = 30

Now we have to apply the law of sin on the triangle BMC as shown below:

\(\frac{12}{\sin30} = \frac{BC}{\sin 60}\)

Now calculate for BC

BC = 20.7

We use the law of sin again i.e

\(\frac{AB}{\sin 120} = \frac{20.7}{\sin 30}\)

So AB is 36

Answer:

36

Step-by-step explanation:

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Answer:

y = 168

Step-by-step explanation:

y = 3(14) x 4

y = 42 x 4

y = 168

Answer:

Taylor got 8 gallons of candy.

Step-by-step explanation:

I. As you can see jug is greater than gallon

So the ratio is  \(\frac{jug}{gallon} = \frac{3}{2}\)

II. If Taylor got 12 jugs that means

                3x = 12

                  x = 4

III. So make it equa by multiply 4 in jug and gallon

              =  \(\frac{3}{2} * \frac{4}{4}\)

              = \(\frac{12}{8}\)

So Taylor got 12 jugs and 8 gallons

Ask me anything.

Answer: its 2/6 is the answer the choices don't make cense

Step-by-step explanation:

The turtle's average velocity in the x-direction is approximately 0.00707 m/s, while in the y-direction it is approximately -0.00650 m/s. The magnitude of its average velocity, which represents the overall speed, is approximately 0.00955 m/s.

To find the components and magnitude of the turtle's average velocity, we can use the following formulas:

Average velocity components:

\(v_{av,x}\) = Δx / Δt

\(v_{av,y}\) = Δy / Δt

Magnitude of average velocity:

|\(v_{av}\)| = √(\((v_{av,x})^2\) + \((v_{av,y})^2\))

where:

Δx is the change in the x-coordinate (r2,x - r1,x)

Δy is the change in the y-coordinate (r2,y - r1,y)

Δt is the time taken for the excursion (323 s)

Given the position vectors:

r1,x = 1.07 m

r1,y = -2.69 m

r2,x = 3.35 m

r2,y = -4.79 m

Δt = 323 s

We can calculate the average velocity components and magnitude as follows:

Δx = r2,x - r1,x = 3.35 m - 1.07 m = 2.28 m

Δy = r2,y - r1,y = -4.79 m - (-2.69 m) = -2.10 m

\(v_{av,x}\) = Δx / Δt = 2.28 m / 323 s ≈ 0.00707 m/s

\(v_{av,y}\) = Δy / Δt = -2.10 m / 323 s ≈ -0.00650 m/s

|\(v_{av}\)| = √(\((v_{av,x})^2\) + \((v_{av,y})^2\)) = √\(((0.00707 m/s)^2 + (-0.00650 m/s)^2\)) ≈ 0.00955 m/s

Therefore, the components of the turtle's average velocity are approximately:

\(v_{av,x}\)≈ 0.00707 m/s

\(v_{av,y}\) ≈ -0.00650 m/s

And the magnitude of the turtle's average velocity is approximately:

|\(v_{av}\)| ≈ 0.00955 m/s

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After the dilation, the coordinates will become (- 9, 12).

Given is the coordinate of point (- 3, 4).

The given coordinate is -

(-3, 4)

After the dilation, the coordinates will become -

(x, y) → (Kx, Ky)

The coordinates after the dilation will be -

(3 x - 3, 3 x 4)

(- 9, 12)

Therefore, after the dilation, the coordinates will become (- 9, 12).

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