The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.2 years, with a standard deviation of 3.5 years. The winner in one recent year was 23 years old.

(a) Transform the age to a z-score.

(b) Interpret the results.

(c) Determine whether the age is unusual.

Answer:

(A) Add the two equations.

Step-by-step explanation:

Solved by addition/elimination method.

Let me know if I'm wrong.

<3

Answer:

Step-by-step explanation:

From the given right angle triangle,

the hypotenuse of the right angle triangle is 6

With m∠x as the reference angle,

the adjacent side of the right angle triangle is the unknown side.

the opposite side of the right angle triangle is 4

To determine m∠x, we would apply

the sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin x = 4/6 = 0.67

x = Sin^-1(0.67)

x = 42.1° to the nearest tenth.

Answer: 12,045 boxes

Step-by-step explanation:

120,450 divided by 10

= 12,045

Answer:

12,045

Step-by-step explanation

If you need to ship 120,450 soda divide that by 10 (the number of cans in a box) and that gives you 12,045.

The unknown number was found from the equation to be -30.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the unknown number. Two thirds of a number is negative Twenty, hence:

(2/3)x = -20

Multiply both sides of the equation by 3/2, hence:

(2/3)x * 3/2 = -20 * 3/2

x = -30

The unknown number was found from the equation to be -30.

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Answer:

slope = 5/2

Step-by-step explanation:

This equation is written in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = 5/2x -3

The slope is 5/2 and the y intercept is -3

Answer:

Slope: 5/2

Y Intercept: -3

Step-by-step explanation:

[tex]8y - 72 = 8 \times y - 8 \times 9 = \\ = 8 \times (y - 9) = 8(y - 9)[/tex]

Answer:D.y=94x

Step-by-step explanation:

Final answer:

The relationship between time and distance for the cheetah can be modeled by y = 94x.

Explanation:

The relationship between the time, x, and distance, y, for the cheetah can be modeled by the equation y = 94x. This equation corresponds to the pattern shown in the table where the distance traveled increases by 470 feet as the time increases by 5 seconds.

Answer:

1/30

Step-by-step explanation:

Answer:

1.2

Step-by-step explanation:

(simplified)

Answer:

A= 1/2 Bh

1/2 (12)(10.4)

A=62.4

V= 62.4x19= 1185.6

Final answer is 1185.6

Step-by-step explanation:

You first need to find the area of the Prism than multiply with the height.

The solution is, Correct option D) 1,185.6 inches cubed, is the volume of the triangular prism.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

given that,

A triangular prism. The triangular base has a base of 12 inches and height of 10.4 inches. The height of the prism is 19 inches.

We need to find  the volume of the triangular prism .

Let's find out:

We have following parameters :

b = 12

h = 10.4

l = 19

now, we know,

A= 1/2 Bh

so, we have,

A = 1/2 (12)(10.4)

A=62.4

We know that , Volume of triangular prism is :

⇒ V = 1/2 * bh* l

       = A * l

so, we get,

V= 62.4x19

  = 1185.6

Final answer is 1185.6

Hence, The solution is, Correct option D) 1,185.6 inches cubed, is the volume of the triangular prism.

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Answer:

3 miles

Step-by-step explanation:

The circumference of a circle can be found using:

c=[tex]\pi d[/tex]

We know the circumference is [tex]3\pi[/tex], so we can substitute that in for c

[tex]3\pi[/tex]=[tex]\pi d[/tex]

We want to find the diameter. To do this, we need to get d by itself. It is being multiplied by pi. To undo this, divide both sides by pi. This will cancel pi, and leave d by itself.

[tex]3\pi /\pi =\pi d/ \pi[/tex]

3=d

So, the diameter is 3 miles

Answer:

Diameter is 3

Step-by-step explanation:

C=2πr

3π = 2πr

3π / 2π = r  (Divide each side by 2π)

3/2 = r   (Simplify π)

3/2 *2 = d  (d = 2r)

d = 6/2 = 3

Answer:

37.68

Step-by-step explanation:

C=2[tex]\pi[/tex]r

C=2*6*3.14

C=12*3.14

C=37.68

Answer:

C = 2 π r

Step-by-step explanation:

2*3.14*6=37.69911=37.7

the answer is 37.7

Answer:

0.256 or 0.26

Step-by-step explanation:

The common ration is being multiply by 0.4

Answer:

7/9

Step-by-step explanation:

There are 9/9 in one whole, so if we have 2/9 now, we need another 7/9 to make 9/9: 2/9 + 7/9 = 9/9 = 1

Answer:

7/9

Step-by-step explanation:

1-2/9=7/9

Answer:

there are infinite many solutions.

Step-by-step explanation:

i have taken this before

Answer:

D

Step-by-step explanation:

Answer:

Wheres the diagram?

Step-by-step explanation:

A Venn Diagram is commonly used in probability theory to visualize and calculate probabilities. The probability of two conditions being met can be found by taking a sum of the probabilities of both conditions and their intersection, and subtracting the probabilities of each condition occurring separately. A Tree Diagram is another tool used to easily represent and calculate probabilities of multiple outcomes.

The use of a Venn Diagram is a common strategy in probability theory to help visualize and calculate probabilities effectively. To begin solving these problems, label each piece of the Venn Diagram clearly and note the probability or frequency of each part. Start by labeling the overlapping section first.

In the case of calculating the probability that a student belongs to a club and works part-time, identify the overlapping section of the Venn Diagram that represents both these conditions. The probability of this will be the sum of the probabilities of the student belonging to a club, working part-time, and both these conditions minus the probabilities of each of these conditions occurring separately.

Another tool that can be useful for visualizing and calculating probabilities is a Tree Diagram. A tree diagram uses branches to represent the possible outcomes of a scenario, which makes it easier to visually work through and solve probability problems. For instance, to visualize the probability of a man developing cancer in his lifetime and having at least one false-positive test, a tree diagram could be used where one branch represents the man developing cancer and the other branch represents the man having a false-positive.

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Answer:

13 years

first calculate interest and use formula

SI=ptr/100.

Answer:

13

Step-by-step explanation:

Answer:

0.02 (rational)

2 (rational)

Square root of 2 (irrational)

Square root 1/2 (irrational)

Step-by-step explanation:

Rational numbers are numbers that can be in form of a/b such that a and b are not zeros. In other words, a and b are integers ranging from 1 to infinity.

Conversely, irrational numbers are numbers that are endless and are non repeating digits after decimal point.

Thus, from the questions above;

[tex]0.02 = \frac{2}{100} = rational \: number[/tex]

[tex]2 = \frac{2}{1} = rational \: number[/tex]

[tex] \sqrt{2} = 1.41421356 = irrational \: number[/tex]

[tex] \sqrt{ \frac{1}{2} } = 0.70710678 = irrational \: number[/tex]

Answer: 6/12

Step-by-step explanation:

You have a 50% percent chance of landing on the shaded area

V= (3.14)x(2²)x(24)= 301.592 ft³

Answer:

96π ft^3 or  301.59 ft^3 to the nearest hundredth.

Step-by-step explanation:

Volume =  π r^2 L         (r = radius L = length).

=  π * 2^2 * 24

= 96π ft^3.

Answer:

The cost to rent a snorkel is 9$

(espanol) el costo de un snorkel es de 9$

Step-by-step explanation:

(English)Given that the group of tourists have spent $153 in renting snorkels and fins and there are 12 snorkels and 15 pairs of fins being rented, allow x to be the amount paid for the rent of the snorkels and y to be the rent for pairs of fins then 12x + 15y = 153. Given also that the rent for a snorkel is three times the rent of a pair of fins then x = 3y then, 12(3y) + 15y = 153. Simplify the equation, 36y + 15y = 153. 51y = 153. Solve for y by dividing both sides of the equation by 51 then, y = 153/51 = 3. Therefore, renting a pair of fins costs $3. To compute for the rent of a snorkel, use the equation x = 3y then, x = 3($3) = $9.

(Espanol) Dado que el grupo de turistas han gastado $153 en el alquiler de snorkels y aletas y hay 12 snorkels y 15 pares de aletas que se alquilan, permitir x para ser la cantidad pagada por el alquiler de los snorkels y y para ser el alquiler para pares de aletas entonces 12x + 15y 153. Dado también que el alquiler para un snorkel es tres veces el alquiler de un par de aletas y luego x a 3y, entonces, 12 (3y) + 15y a 153. Simplifique la ecuación, 36y + 15y a 153. 51y a 153. Resuelva para y dividiendo ambos lados de la ecuación por 51 entonces, y á 153/51 a 3. Por lo tanto, alquilar un par de aletas cuesta $3. Para calcular el alquiler de un snorkel, utilice la ecuación x á 3y, a continuación, x a 3($3) a $9.  

Answer:

x < -6

Step-by-step explanation:

-2x -4 > 8

-2x +4 >+4

-2x >12

/-2 > /-2

x < -6

remember to flip the inequality sign whenever you divide by a negative number :)

Answer:

I =2000(0.075)4= $600

Step-by-step explanation:

Answer:

£6000

Step-by-step explanation:

Given:

Phillip Cage played, £21,000 was split at a ratio of 2:5 between the arena and Phillip Cage.

Question asked:

How much money did the arena make from Phillip Cage's concert?

Solution:

Ratio Arena and Philip cage in which money distributed = 2 : 5

Let ratio be [tex]x[/tex]

Money earned by Arena = [tex]2x[/tex]

Money earned by Phillip Cage = [tex]5x[/tex]

Phillip Cage played total for =  £21,000

Money earned by Arena + Money earned by Phillip Cage = £21,000

[tex]2x+5x=21000\\7x=21000\\[/tex]

Dividing both sides by 7

[tex]x=3000[/tex]

Money earned by Arena = [tex]2x[/tex] = [tex]2\times3000=6000[/tex]

Thus, Arena made  £6000 from Phillip Cage's concert.

Answer:

P(X<65)=0.9452

Step-by-step explanation:

This is a normal distribution problem.

-Given the mean age is 53 years and the standard deviation is 75, the probability of dying before age 65 is calculated as:

[tex]z=\frac{\bar x-\mu}{\sigma}\\\\\\=\frac{65-53}{7.5}\\\\=1.60[/tex]

#We check the value of z=1.60 on the z table:

[tex]P(X<65)=0.5+0.4452\\\\=0.9452[/tex]

Hence, the probability of dying before 65 is 0.9452

the probability that the person will die before the age of 65 is 0.9452.

[tex]P(X<65 ) = P[(X- \mu ) \div \sigma < (65 -53) \div 7.5][/tex]

= P(z <1.6 )

Now here we Using z table

So,  

= 0.9452

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Answer:

Yes, it is possible

Step-by-step explanation:

In a triangle, the length of the longest side of the triangle cannot be larger than the sum of the lenghts of the two shortest sides.

In formula, this means that:

[tex]c\leq a+b[/tex]

where

c is the length of the longest side

a, b are the lengths of the shortest side

In this problem, we want to build a triangle using 3 pieces of lumber, each of length:

a = 3 ft

b = 7 ft

c = 8 ft

We can verify that the length of the longest piece of lumber is less than the sum of the lengths of the other two sides, so:

[tex]8\leq 3+7 = 10[/tex]

Therefore, yes, it is possible to build a closed triangular pen.

The question is about the Triangle Inequality Theorem in Geometry. It asks if a triangle can be formed with given lengths of 3 ft, 7 ft, and 8 ft. By verifying with the theorem, we can confirm that a triangle can be formed.

The subject of the question is determining if a triangle can be formed with three given lengths. This topic belongs to Geometry, a branch of Mathematics. To form a triangle, the lengths must satisfy the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. In this case, we can plug our given lengths into this theorem:

All these inequalities hold true, so yes, Mrs. Barto can build a closed triangular pen for her pet rabbit with the three pieces of lumber.

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Answer:

  C.  -4n+8+9n-2 and 5n+6

Step-by-step explanation:

The equivalent expression is found by combining like terms:

  -4n +8 +9n -2 = n(-4+9) +(8-2)

  -4n +8 +9n -2 = 5n +6 . . . . . matches choice C

__

The other answer choices have flaws in the work:

  A. 3v -9v ≠ 6v

  B. +3 +2 ≠ +6

  D. 10n -2n ≠ 5n

Answer:

C. -4n+8+9n-2 and 5n+6

Step-by-step explanation:

Hope this helps, and holy cow! the person above me deserves brainliest!

To solve the equation -3/13 - 2/5, find the common denominator, convert both fractions and then subtract them. The answer is -41/65.

The question asks to solve the equation -3/13 - 2/5. To solve this, we need to find a common denominator for the fractions, which in this case is 65. We then convert each fraction to have this common denominator and subtract them.

Here is the step-by-step solution:

The answer to the equation is -41/65.

Given that the functions [tex]f(x)=x+4[/tex] and [tex]g(x)=x^{3}[/tex]

We need to determine the value of the function [tex](g \ {\circ} f)(-3)[/tex]

First, we shall determine the composition of the function [tex](g \circ f)(x)[/tex]

Function [tex](g \circ f)(x)[/tex]:

Let us determine the function [tex](g \circ f)(x)[/tex]

Thus, we have;

[tex](g \circ f)(x)=g[f(x)][/tex]

               [tex]=g[x+4][/tex]

               [tex]=(x+4)^3[/tex]

[tex](g \circ f)(x)=x^3+3x^2(4)+3x(4)^2+(4)^3[/tex]

[tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]

Thus, the function is [tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]

Value of the function [tex](g \ {\circ} f)(-3)[/tex]:

The value of the function can be determined by substituting x = -3 in the function [tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]

Thus, we have;

[tex](g \circ f)(-3)=(-3)^3+12(-3)^2+48(-3)+64[/tex]

Simplifying the terms, we get;

[tex](g \circ f)(-3)=-27+12(9)+48(-3)+64[/tex]

[tex](g \circ f)(-3)=-27+108-144+64[/tex]

[tex](g \circ f)(-3)=1[/tex]

Thus, the value of the function [tex](g \ {\circ} f)(-3)[/tex] is 1.

Answer:

x = 8

Step-by-step explanation:

The axis of symmetry for graph is always set up as "x="

So, if the x in this ordered pair is 8, then the axis of symmetry is also 8.

(I have posted a picture below as proof...)

Answer:

Part A. [tex]\frac{84.3y}{12} = 7 +\frac{0.1\cdot y}{4}[/tex]

Part B. The correct quotient is (3 × 4)

Step-by-step explanation:

Part A.

To divide 84.36 by 12 we look for the Highest Common Factor of the whole number and the decimal portions of the numerator and the denominator individually as follows;

[tex]\frac{84.36}{12} = \frac{84+0.3636}{12} = \frac{2 \times 2 \times 3 \times 7+0.01\times 12\times 3}{12} = \frac{12 \times 7+0.03\times 12}{12}[/tex]

Therefore, dividing 84.36 by 12 gives [tex]\frac{12 \times 7+0.03\times 12}{12} = 7+0.03[/tex] = 7.03

When dividing 84.3·y by 12, therefore, we have;

[tex]\frac{12 \times 7+0.3\times y}{12} = 7 +\frac{0.1\cdot y}{4}[/tex]

Part B.

The correct quotient should have factors of the numerator

Therefore the divisor 12 should be represented as follows

[tex]\frac{12 \times 7+0.3\times y}{12} =\frac{12 \times 7+0.3\times y}{3 \times 4}[/tex]

The correct quotient therefore = (3 × 4)

Elena divided the decimal 84.36 by the whole number 12 to get the correct quotient of 7.03. The division process is similar to dividing whole numbers but includes placing the decimal point correctly in the quotient.

To answer the question, Elena divided a decimal by a whole number. Specifically, the division problem is 84.36 ÷ 12. Dividing a decimal by a whole number follows the same process as dividing two whole numbers, with the additional step of placing the decimal point in the quotient.

Set up the division problem with 84.36 inside the division bracket and 12 on the outside.

Start dividing from the left. 12 goes into 84 seven times (12 x 7 = 84), so put 7 above the 84 in the quotient.

Subtract 84 from 84, which leaves 0, and bring down the next digit, which is 3 (from the decimal part).

Since 12 does not go into 3, we place a 0 in the quotient above the 3 and bring down the next digit, which is 6.

Now we have 36. 12 goes into 36 three times (12 x 3 = 36), so place a 3 in the quotient above the 36.

Again, we subtract 36 from 36, leaving 0, with no more digits to bring down, so we have our answer.

The correct quotient is 7.03. Multiplying or dividing by powers of ten, as seen when working with decimals, involves shifting the decimal point. For example, when multiplying 45.86 by 100, you would move the decimal point two places to the right, giving 4586. Conversely, dividing 1.9436 by powers of 10 shifts the decimal point to the left. The significance of this process is underlined by the fact that in scientific fields, calculations often require adjusting the decimal by powers of ten to maintain precision and correct significant figures.

It should be noted that a calculator provides the raw numerical result of a division and doesn't account for the significant figures involved; therefore, it's essential to consider how many decimal places are appropriate for the situation.