The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test. What percent of students scored below Jake? Include a step by step description of the process you used to find that percentage. (Round your answer to the nearest whole number.)

Answer:

[tex](2a-b)(a-2b) = 0[/tex]

Step-by-step explanation:

We can use the quadratic formula to factor this expression

For a quadratic function of the form:

[tex]na ^ 2 + ma + c[/tex]

Whe have:

[tex]2a^2 + 2b^2 - 5ab[/tex]

Then:

[tex]n = 2\\\\m = -5b\\\\c = 2b^2[/tex]

The quadratic formula is:

[tex]a =\frac{-m\±\sqrt{m^2-4nc}}{2n}[/tex]

Then the solutions are:

[tex]a= \frac{-(-5b)\±\sqrt{(-5b)^2 -4(2)(2b^2)}}{2(2)}\\\\a = \frac{5b\±\sqrt{25b^2-16b^2}}{4}\\\\a = \frac{5b\±3b}{4}\\\\a_1=2b\\\\a_2 =\frac{b}{2}[/tex]

Finally The factored expression is:

[tex]a-\frac{b}{2} = 0\\\\2a -b = 0\\\\[/tex]

and

[tex]a-2b= 0[/tex]

Then

[tex]2a^2 + 2b^2 - 5ab = (2a-b)(a-2b) = 0[/tex]

Answer:

163/500 = 0.326

Step-by-step Explanation:

Drawing a Venn diagram for this, we will have 3 circles.  One will represent rock, one will represent country, and one will represent jazz.

There are 11 students that like all 3 types of music.  This means the number 11 goes in the intersection of all 3 circles.

There are a total of 30 students that like rock and country; taking out the 11 that like all 3, this leaves 30-11 = 19 students in the intersection of just rock and country.

There are a total of 27 students that like rock and jazz; taking out the 11 that like all 3, this leaves 27-11 = 16 students in the intersection of just rock and jazz.

There are a total of 22 students that like country and jazz; taking out the 11 that like all 3, this leaves 22-11 = 11 students in the intersection of just country and jazz.

There are 206 students that like rock; taking out the 11 that like all 3, the 19 that like rock and country, and the 16 that like rock and jazz, we have

206-(11+19+16) = 206-(46) = 160 in just rock.

There are 161 students that like country; taking out the 11 that like all 3, the 19 that like rock and country, and the 11 that like country and jazz, we have

161-(11+19+11) = 161-(41) = 120 in just country.

There are 118 students that like jazz; taking out the 11 that like all 3, the 16 that like rock and jazz, and the 11 that like country and jazz, we have

118-(11+16+11) = 118-38 = 80 in just jazz.

This leaves

500-(80+120+160+11+11+19+16) = 500-417 = 83 students that like none of the 3 types of music.

This means for the probability that a student likes neither rock nor country, they either like just jazz or none of the 3; this is (83+80)/500 = 163/500 = 0.326.

The probability that a randomly selected student likes neither rock nor country is;

P(R' ∩ C') = 0.326

Let us denote them as follows;

Number that like rock music be R

Number that like Country music be C

Number that like Jazz music be J

Thus, as we are given we have;

R = 206

C = 161

J = 118

R ∩ C = 30 - 11 = 19

R ∩ J = 27 - 11 = 16

C ∩ J = 22 - 11 = 11

R ∩ C ∩ J = 11

n(only jazz) = J - [(R ∩ J) + (C ∩ J) + (R ∩ C ∩ J)]

n(only jazz) = 118 - (16 + 11 + 11)

n(only J) = 80

n(only Rock) = R - [(R ∩ C) + (R ∩ J) + (R ∩ C ∩ J)]

n(only Rock) = 206 - (19 + 16 + 11)

n(only R) = 160

n(only country) = C - [(R ∩ C) + (C ∩ J) + (R ∩ C ∩ J)]

n(only country) = 161 - (19 + 11 + 11)

n(only C) = 120

Now, the number of students that like neither of the 3 music is;

A' ∩ B' ∩ C' =  500 - [(R ∩ C) + (R ∩ J) +  (C ∩ J) + (R ∩ C ∩ J) + n(only J) + n(only R) + n(only C)]

⇒ 500 - (80 + 120 + 160 + 19 + 16 + 11 + 11)

⇒ A' ∩ B' ∩ C' = 83

Thus, number of students that likes neither rock nor country is;

n(A' ∩ B') = (A' ∩ B' ∩ C') + n(only C)

n(A' ∩ B') = 83 + 80

n(A' ∩ B') = 163

Thus, probability that a randomly selected student likes neither rock nor country = 163/500 = 0.326

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Answer:

It is a right triangle because if it contains a 90 degree angle (a right angle), it's  a right triangle.

Step-by-step explanation:

It would be a right angled triangle because all triangles with a 90 degree angle are right angle triangles : 90 degrees is a right angle

umm ok then its 2...

Answer:

A = (x^2 - 2x - 8) m^2

Second option

Step-by-step explanation:

Area of rhombus = 1/2 d1 * d2

= 1/2(2x+4)(x-4)

= 1/2 (2x^2 -8x + 4x - 16)

= 1/2 (2x^2 - 4x - 16)

= x^2 - 2x - 8

Final answer:

A biconditional statement regarding Alaska's size is 'Alaska is the biggest state in the United States of America if and only if no other state in the United States has more territory than Alaska.' This statement clarifies that Alaska's status as the largest state is based on a measurable, verifiable fact.

Explanation:

A biconditional statement is a logical assertion that combines two statements into one, where one statement implies the other, and vice versa. In this context, the statement 'Alaska is the biggest state in the United States of America' can be written as a biconditional statement as follows:

'Alaska is the biggest state in the United States of America if and only if no other state in the United States has more territory than Alaska.'

This biconditional statement emphasizes the fact that Alaska's status as the largest state is contingent on the condition that all other states must have less territory. This is a fact that is verifiable and not subject to opinion, underscoring the importance of factual accuracy in research and the careful use of evidence.

Answer:

[tex] R = 10.39^\circ [/tex]

Step-by-step explanation:

Since you have the lengths of all the sides, you can use sine, cosine, or tangent to find the answer. Let's use the tangent ratio.

For angle C, AB is the opposite leg, and BC is the adjacent leg.

[tex] \tan C = \dfrac{opp}{adj} [/tex]

[tex] \tan C = \dfrac{22}{120} [/tex]

[tex] C = \tan^{-1} \dfrac{22}{120} [/tex]

[tex] C = 10.39^\circ [/tex]

Applying the tangent ratio (tan ∅ = opposite length/adjacent length), the measure of angle C, to the nearest hundreth, is: 10.39°

In a given right triangle, the tangent ratio is given as, tan ∅ = opposite length/adjacent length.

Given the following:

Applying the tangent ratio:

tan C = 22/120

m∠C = tan^(-1)(22/120)

m∠C = 10.39° (nearest hundreth)

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Answer:

Option A. 36

Step-by-step explanation:

Let

x-------> the number of boys

y------> the number of girls

we know that

[tex]x+y=42[/tex] -----> equation A

[tex]y=\sqrt{x}[/tex] -----> equation B

using a graphing tool to solve the system of equations

Remember that the solution is the intersection point both graphs

The solution is the point (36,6)

see the attached figure

therefore

The number of boys is 36

I think it's possibly a rhombus

Answer:

11 %

Step-by-step explanation:

Percent = Amount deducted/original amount × 100 %

               = 213.84/1944 × 100 %

               = 11.00 %

Paige has 11.00 % of her paycheck deducted for her 401(k).

Answer:

11%

Step-by-step explanation:

Answer:

The length is [tex]8\frac{1}{4}\ ft[/tex]

Step-by-step explanation:

we know that

The area of a rectangle is equal to

[tex]A=LW[/tex]

In this problem we have

[tex]A=53\frac{5}{8}\ ft^{2}[/tex]

[tex]W=6\frac{1}{2}\ ft[/tex]

convert to an improper fraction

[tex]A=53\frac{5}{8}=\frac{53*8+5}{8}=\frac{429}{8}\ ft^{2}[/tex]

[tex]W=6\frac{1}{2}=\frac{6*2+1}{2}=\frac{13}{2}\ ft[/tex]

substitute in the formula and solve for L

[tex]\frac{429}{8}=L\frac{13}{2}[/tex]

[tex]L=\frac{429*2}{8*13}=\frac{858}{104}\ ft[/tex]

Convert to mixed number

[tex]L=\frac{858}{104}=\frac{832}{104}+\frac{26}{104}=8\frac{1}{4}\ ft[/tex]

The length of the bathroom floor in this case is 8 1/4 feet.

The area of a rectangle is calculated by multiplying its length by its width. In this case, with the bathroom floor having an area of 53 5/8 square feet and a width of 6 1/2 feet, we can find the length as follows:

Area = Length x Width

53 5/8 = Length x 6 1/2

Length = 53 5/8 / 6 1/2

Length = 8 1/4 feet

Therefore, the length of the bathroom floor is 8 1/4 feet.

Answer:

Prime

Step-by-step explanation:

Since none of the other answers work. Your answer is Prime.

Answer:

Prime

Step-by-step explanation:

(x + 4y)(x + 4y)  

Appy FOIL method to multiply it

x^2 +4xy + 4xy +16y^2

x^2 + 8xy +16y^2

(x + 4y)(x − 4y)  

Appy FOIL method to multiply it

x^2 -4xy + 4xy -16y^2

x^2 - 16y^2

(x − 4y)(x − 4y)

Appy FOIL method to multiply it

x^2 -4xy - 4xy +16y^2

x^2 - 8xy +16y^2

the options does not gives us x^2 +16y^2

So it is not factorable , It is prime

Answer:

Step-by-step explanation:

U+b=15

7+8=15

Answer:

-6,0,2

Step-by-step explanation:

f(x)=x(x−2)(x+6)

To find the zeros of the function, set the function equal to zero

0 =x(x−2)(x+6)

Using the zero product property

x=0  x-2 =0   x+6=0

Solve each equation

x=0  x=2    x=-6

There are three zero's

-6,0,2

Answer:

The diameter of the circle is [tex]3,600\ units[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

where

D is the diameter

In this problem we have

[tex]C=11,304\ units[/tex]

assume [tex]\pi=3.14[/tex]

substitute the values and solve for D

[tex]11,304=(3.14)D[/tex]

[tex]D=11,304/(3.14)=3,600\ units[/tex]

Answer: 3,600 units

Step-by-step explanation:

The pic will help you

Good luck:))

Answer:

1:  z = 1.96

2:  t = 2.552

Step-by-step explanation:

1:  When you don't know the population standard deviation and the sample size is large, you can still use a z test because many large samples are relatively normally distributed.  A 95% confidence interval uses a z-score of 1.96

2.  We are told that n < 30, so we use t distribution.  Use the degrees of freedom, which is one less than the population, and the column that has 0.02 in the area of 2 tails.

In constructing a confidence interval, if the standard deviation is unknown and the population appears skewed, we typically use the t-distribution. However, without enough information given, the answer to the first problem tends towards 'Neither normal nor t distribution applies'. For the second problem, the standard deviation is given and the population appears normally distributed, hence answer is 'zα/2 = 2.33' from the z-table.

The relevant subject matter here is Statistics, specifically, confidence intervals. The construction of a confidence interval depends on the knowledge of the standard deviation and whether the population is normally distributed or not.

For the first problem, since the standard deviation (σ) is unknown and the population appears to be skewed, student's t-distribution applies here. This would involve using tα/2 with degree of freedom (n-1) in place of the unavailable standard deviation. However, without enough data provided in the question, it is difficult to correctly compute tα/2. The answer therefore likely tends towards option E: 'Neither the normal nor the t distribution applies'.

For the second problem, the standard deviation (σ) is given and the population appears to be normally distributed. This suggests the normal distribution applies, hence you would compute zα/2, the critical value for the z-score at a 98% confidence level. Referring to a standard z-table at a 98% confidence level gives a z-score of approximately 2.33. So, the answer for this scenario is A: zα/2 = 2.33.

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Answer:

38°

Step-by-step explanation:

One side length is 34cm and the hypotenuse is 55cm. Used SOH-CAH-TOA to find what trig function to use. You have the opposite side and the hypotenuse, so use sine. SinC = 34/55. You can input this into a calculator as 34/55 and press sin^-1 to get the angle value, which is approximately 38°.

Answer:

△ABC is a right triangle with right angle at ∠B.

AB=34 cm  

AC=55 cm

What is the measure of ∠C, to the nearest degree?

Enter your answer in the box.

38°

Step-by-step explanation:

As given,

Number of sheets of paper put in the binder 8 days ago = 50 sheets

Current number of sheets left after 8 days = 2 sheets

So, number of sheets used in 8 days = [tex]50-2=48[/tex] sheets

As it is stated that the same number of sheets are used each day, so number of sheets used per day = [tex]\frac{48}{8}=6[/tex] sheets.

Hence, 6 sheets of paper were used each day.

Answer:

6

Step-by-step explanation:

Answer: the one that is not a magor epense catgortuy is c : transportation

Step-by-step explanation:

the answer is: C) transportation

For the given sets, the domain of set C is {2}, and its range is {5, 6, 7}. Set E has both domain and range as {3, 4, 5, 6}.

A set of ordered pairs is defined as a relation. The domain of a relation is the set of all the first elements of the ordered pairs, and the range is the set of all the second elements. Let's look at the listed sets and determine their domains and ranges.

A function is a special type of relation where each element of the domain is associated with exactly one element in the range. This condition is also known as the vertical line test when graphing the relation on a coordinate plane.

Answer: 10,472.36 feet

Step-by-step explanation:

- Observe the diagram attached (It is not drawn to scale).

- Calculate the height between helicopter and airplane (h), as following:

[tex]tan\alpha=\frac{opposite}{adjacent}\\\\tan(71\°)=\frac{h}{3,055}[/tex]

Solve for h:

[tex]h=(3,055)(tan(71\°))\\h=8,872.36ft[/tex]

- Therefore, the altitude of the plane is:

[tex]altitude=1,600ft+8,872.36ft\\altitude=10,472.36ft[/tex]

You can use the tangent ratio to find the airplane's altitude.

The altitude of the airplane in the given condition is 10,471.72 ft

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

In a right angled triangle(triangle with one of the angles as right angle which is 90 degrees), seeing from perspective of an angle, the tangent ratio is the ratio of the side opposite to that angle and the side which is perpendicular to that opposite side.

Refer to the attached figure.
The altitude of the plane is the length of the line segment CE.

We have the rectangle ABDE, thus, AD = BE in terms of length.

(remember that |AB| means length of line segment AB).

Thus,
|CE| = |CB| + |BE| = |CB| + 1600 ft

Using the tangent ratio for triangle ABC from angle A, we get:

[tex]tan(A) = \dfrac{|CB|}{|AB|} = \dfrac{|CB|}{3055}\\\\tan(71) \approx 2.904 = \dfrac{|CB|}{3055}\\\\|CB| = 3055 \times 2.904 = 8.871.72 \: \rm ft[/tex]

Thus,

|CE| = |CB| + 1600  = 8871.72 + 1600 = 10,471.72 ft.

Thus,

The altitude of the airplane in the given condition is 10,471.72 ft

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Answer:

Nine

Step-by-step explanation:

The smallest number of buns is one pack or 9 buns.

If there is one hot dog per bun, the smallest number of hot dogs is nine.

Answer:

36 hotdogs

Step-by-step explanation:

Mathematically, we say that 36 is the least common multiple of 12 and 9. In math notation this looks like:

lcm of 9 and 12 is 36

The smallest total number of hot dogs that Yadira's mom can purchase is , 36.

The equations are shown in the top of the tables,

Replace x in the equations with the values of x given:

a = 4^-0 = 1

b = 4^-2 = 1/16

c = 4^-4 = 1/256

d = (2/3)^0 = 1

e = (2/3)^2 = 4/9

f = (2/3)^4 = 16/81

The value of a, b, c, d, e, and f are 1, 1/16, 1/256, 1, 4/9, and 16/81 after plugging the values of x.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×

where a is a constant and a>1

We have:

y = 4⁻ˣ

x = 0

a = 4⁻⁰ = 1

x = 2

b = 4⁻² = 1/16

x = 4

c = 4⁻⁴ = 1/256

y = (2/3)ˣ

x = 0

d = (2/3)⁰ = 1

x = 2

e = (2/3)² = 4/9

x = 4

f = (2/3)⁴ = 16/81

Thus, the value of a, b, c, d, e, and f are 1, 1/16, 1/256, 1, 4/9, and 16/81 after plugging the values of x.

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Answer:

After 7 years it will have a value of $13.946 to the nearest dollar.

Step-by-step explanation:

As it depreciates by 8% (0.08) a year the value of the car after each year is

1 - 0.08 = 0.92 of the previous year's value.

So we have the formula:

Value =  25,000(0.92)^7

= $13,946.17 (answer).

Answer:

The rounded answer is equal to 14000

Step-by-step explanation:

Answer:

your 3rd option because 3^3 is 27

I agree because when you do prime factorization you get 27 by doing it

[tex]\bf \begin{array}{ccll} miles&\stackrel{gas}{gallons}\\ \cline{1-2}\\ 23\frac{1}{8}&1\\\\ x&17 \end{array}\implies \cfrac{23\frac{1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{23\cdot 8+1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{185}{8}}{x}=\cfrac{1}{17} \\\\\\ \cfrac{\frac{185}{8}}{\frac{x}{1}}=\cfrac{1}{17}\implies \cfrac{185}{8}\cdot \cfrac{1}{x}=\cfrac{1}{17}\implies \cfrac{185}{8x}=\cfrac{1}{17} \\\\\\ 3145=8x\implies \cfrac{3145}{8}=x\implies 393\frac{1}{8}=x[/tex]

Answer:

Equation 3

Step-by-step explanation:

An identity is, simply put, an equation that is always true. 1 = 1, 2 = 2, and x = x are all examples of identities, as there's no case in which 1 ≠ 1, 2 ≠ 2, and x ≠ x. Essentially, if we can manipulate and equation so that we end up with the same value on either side, we've found an identity. Let's run through and try to solve each of these equations to see which one fulfills that condition:

8 - (6v + 7) = -6v - 1

8 - 6v - 7 = -6v - 1

1 - 6v = -6v - 1

1 = -1

This is clearly untrue. Moving on to the next equation:

5y + 5 = 5y - 6

5 = -6

Untrue again. Solving the third:

3w + 8 - w = 4w - 2(w - 4)

2w + 8 = 4w - 2w + 8

2w + 8 = 2w + 8

If we created a new variable z = 2w + 8, we could rewrite this equation as

z = z, which is always true. We can stop here, as we've now found that equation 3 is an identity.

The identity among the given equations is 3w + 8 - w = 4w - 2(w - 4), as it simplifies to a true statement 2w + 8 = 2w + 8 for all values of w.

The student asked which equation is an identity. To find the identity, we simplify and solve each equation:

8 – (6v + 7) = –6v – 1: When we simplify, we get 8 - 6v - 7 = -6v - 1, which further simplifies to 1 - 6v = -6v - 1. Adding 6v to both sides, we have 1 = -1, which is not true, so it's not an identity.

5y + 5 = 5y – 6: Simplifying this we simply subtract 5y from both sides, and we are left with 5 = -6, which is not true, so this is not an identity either.

3w + 8 – w = 4w – 2(w – 4): Simplifying we get 2w + 8 = 4w - 2w + 8, which reduces to 2w + 8 = 2w + 8. This is true for all values of w, therefore, this is an identity.

6m – 6 = 7m + 9 – m: Simplifying gives us 6m - 6 = 6m + 9. Subtracting 6m from both sides, we get -6 = 9, which is not true and thus not an identity.

The identity is the equation 3w + 8 – w = 4w – 2(w – 4) because it simplifies to a true statement regardless of the value of w.

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Answer:

25.95

Step-by-step explanation:

Answer:

Roughly $396.71

Step-by-step explanation:

Chuck starts the month with $268.23 balance on his card

He makes a $125 and $98 purchase, add those two together to get $223, and then add that to the total starting balance of $268.23 to get $491.23.

At the end of the month, he made a $100 payment, subtracting $100 from the balance to get $391.23. $391.23 times 1.014 (Adding 1.4% converted into decimal form, to convert a percent into decimal form move the decimal left two places) equals $396.71