In a certain year, when she was a high school senior, Idonna scored 671 on the mathematics part of the SAT. The distribution of SAT math scores in that year was Normal with mean 509 and standard deviation 115 . Jonathan took the ACT and scored 24 on the mathematics portion. ACT math scores for the same year were Normally distributed with mean 21.1 and standard deviation 5.3 . Find the standardized scores (±0.01) for both students. Assuming that both tests measure the same kind of ability, who had the higher score?
Idonna's standardized score is ____ Jonathan's standardized score is _____
A.) Idonna's score is higher than Jonathan's
B.) Idonna's score is less than Jonathan's
C.) Scores are equal

Answer:

The right triangular pyramid volume is given by the formula V = 1 3 × B × h , where B is the area of the triangular base and h is the height (the distance from the apex to the base).

Step-by-step explanation:

Answer:

192 cubic feet

Step-by-step explanation:

The volume V of a triangular pyramid is given by the formula:

V = (1/3) * base area * height

where base area is the area of the triangular base.

In this case, the triangular base has a length of 8 ft and a width of 8 ft, so it is a square with area:

base area = length * width = 8 ft * 8 ft = 64 sq ft

Substituting the given values into the formula, we get:

V = (1/3) * 64 sq ft * 9 ft

V = 192 cubic feet.

Therefore, the volume of the triangular pyramid is 192 cubic feet.

= -4,-8 I think

Solve for x by simplifying both sides of the equation, then isolating the variable.

The mathemematical sum of the three numbers 1+1+1 would give 3

Addition of numbers can involve 2 or more values using the additive sign '+'. For any given sum of values, the result obtained would be greater than any of the individual value in the sum.

Here, 1 + 1 + 1 means that we are adding 1 in three places. The value obtained would be 3.

Therefore, the sum of the 1+1+1 is 3

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Enlarged area = x^2 + 11x + 24 ft²

Original area =

a + 24 ft^2 = x^2 + 11x + 24 ft²

a = x^2 + 11x + 24 ft² - 24 ft^2

a = x^2 + 11x

Factored:

a = x (x + 11 )

Dimensions before the increase

x ft by (x-11) ft

\(~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 2500\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}\)

\(A=2500\left[ \cfrac{\left( 1+\frac{0.035}{1} \right)^{1 \cdot 10}-1}{\frac{0.035}{1}} \right]\left(1+\frac{0.035}{1}\right)\\\\\\ A=2500\left[ \cfrac{0.4106}{0.035} \right](1.035)\implies A \approx 30354.98\)

Answer:

4/52

Step-by-step explanation:

The value of the limit lim n → ∞ [4/n + 4/n³]/[ 1 + 6/n² + 1/n^4] is 0.

We need to find the value of limit.

lim n → ∞ ((n+1)^4 - (n-1)^4)/((n+1)^4 + (n-1)^4)

We can write an expression [(n+1)^4 - (n-1)^4]/[(n+1)^4 + (n-1)^4] as

[(n+1)^4 - (n-1)^4]/[(n+1)^4 + (n-1)^4] =  [4n³ + 4n]/[n^4 + 6n² + 1]

This means, we need to find the value of limit lim n → ∞ [4n³ + 4n]/[n^4 + 6n² + 1]

Divide numerator and denominator by n^4.

lim n → ∞ [4/n + 4/n³]/[ 1 + 6/n² + 1/n^4]

Consider the numerator,  

lim n → ∞ [4/n + 4/n³] = 0

for denominator,

lim n → ∞ [ 1 + 6/n² + 1/n^4] = 1

So, limit becomes,

lim n → ∞ [4/n + 4/n³]/[ 1 + 6/n² + 1/n^4]

= 0/1

= 0

Therefore, the value of the limit lim n → ∞ [4/n + 4/n³]/[ 1 + 6/n² + 1/n^4] is 0.

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Answer:

Ok I might misunderstand this but this is what I got ( in order )

Answer:

420 = 4.2 x 100 = 4.2 × 102

Step-by-step explanation:

Answer:

-9/10

Step-by-step explanation:

Yw, me!

Answer:

Real, irrational/ R, I

Sidenote: Mark me brainliest? Do you agree that anime girls are cute?

Answer:

  14 units

Step-by-step explanation:

The two given points have the same y-coordinate, so lie on the horizontal line y = -8. The distance between the points will be the difference of their x-coordinates.

  distance = 10 -(-4) = 10 +4 = 14

The distance between the points is 14 units.

Answer:

14 units

The two given points have the same y-coordinate, so lie on the horizontal line y = -8. The distance between the points will be the difference of their x-coordinates.

Step-by-step explanation:

The two given points have the same y-coordinate, so lie on the horizontal line y = -8. The distance between the points will be the difference of their x-coordinates.

 distance = 10 -(-4) = 10 +4 = 14

The distance between the points is 14 units.

Answer:

The counter in the drawing is 8 in. wide.

Step-by-step explanation:

Divide each term by 8 and simplify.

exact form should be

1/12

Decimal form should be

0.083

Answer:

bru

Step-by-step explanation:

bru

Answer:

Provide the picture needed for in order to get this question answerd

Step-by-step explanation:

the 25th, 50th, and 75th percentile from the following list of 32 data are 25th percentile: 13 , 50th percentile: 21 , 75th percentile: 29.

To find the 25th percentile:

25th percentile: 25% of 32 = 8th number = 13

Count the total number of values in the data set, which is 32

Calculate 25% of 32, which is 8

Count 8 numbers from the beginning of the list and the 25th percentile is the 8th number, which is 13

To find the 50th percentile:

50th percentile: 50% of 32 = 16th number = 21

Count the total number of values in the data set, which is 32

Calculate 50% of 32, which is 16

Count 16 numbers from the beginning of the list and the 50th percentile is the 16th number, which is 21

To find the 75th percentile:

75th percentile: 75% of 32 = 24th number = 29

Count the total number of values in the data set, which is 32

Calculate 75% of 32, which is 24

Count 24 numbers from the beginning of the list and the 75th percentile is the 24th number, which is 29

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The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.

We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.

We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;

Now solving for p,

2 (p+ 7) = 4 - 8

Open the bracket,

2p+ 14 = 4 - 8

Combine the like terms,

2p = -4 - 14

2p = -18

p = -18/2 = -9

Therefore, the equation has only one solution which is -9.

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Answer:   t=24−i

Step-by-step explanation:

Answer:

Yes it its!!! It goes on for a long time!! Keep that in mind when you are doing problems like this!  

:)

Step-by-step explanation:

The coordinates of B are (-7,-2).

What do you mean by x and y coordinates?

The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.

According to the given data in the question,

if M is the location where line segment AB meets its midpoint.

Then, we will using the midpoint formula,

\((-5,2)=(\frac{-3+x}{2},\frac{6+y}{2})..............(1)\)

Putting the x-coordinates in (1),

\(-5=\frac{-3+x}{2}\\ -10=-3+x\\-10+3=x\\x=-7\)

Similarly, putting the y-coordinates in (1),

\(2=\frac{6+y}{2} \\4=6+y\\4-6=y\\y=-2\)

Hence, the coordinates of B are (-7,-2).

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Answer:

Hence, total surface area of the pyramid is 360 cm².

Step-by-step explanation:

We first calculate slant height L of the pyramid with base s=10 cm and height 12 cm:

L²=H²+(s/2)²=122+(10/2)²=122+5²

=144+25=169⇒

L=(169)^1/2=13

The perimeter of the base is P=4s, since it is a square, therefore, 

P=4×10=40 cm

The general formula for the lateral surface area of a regular pyramid is LSA=1/2Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=40 cm and the slant height is l=13 cm, therefore, the lateral surface area is:

LSA=1/2Pl=1/2×40×13=260 cm²

Now, the area of the base B=s² with s=10 cm is:

B=s²=10²=100 cm²

The general formula for the total surface area of a regular pyramid is TSA=1/2Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA=1/2Pl=260 cm² and area of the base is B=100 cm², therefore, the total surface area is:

TSA=1/2Pl+B=260+100=360 cm²

Hence, total surface area of the pyramid is 360 cm².

Answer:

60%

Step-by-step explanation:

\(\frac{12}{20}\)×\(\frac{100}{1}\)= 60%

You put 12 over 20 and multiply it by 100 over 1 and you cancel and multiply to find your answer.

(when you are trying to find the percentage you multiply by 100)

Answer:

B

Step-by-step explanation:

x cannot have any negative value, or the sum with -4 will create -5 or lower, and the corresponding absolute value is therefore larger than 3.

so, A and C are automatically out.

D can't be right, because it is an "or" condition, so, we could violate one of the conditions (like "x greater than 1"), and it would still be OK, as long as we keep the second. but that is not true, as we just ruled out negative x values.

so, only B includes the "and" condition.

it means 1 has to be less than x AND x has to be less than 7.

and that is correct.

Answer:

b

Step-by-step explanation:

Answer:

It is a possible explanation of events using prior knowledge

Step-by-step explanation:

The family spent $2004 per month on groceries and eating out.

The amount spent in five months is given as follows: $10,020.

The amounts are obtained applying the proportions in the context of this problem.

The monthly budget is given as follows:

$6012.

1/3 of that is spent in groceries and eating out, hence the amount is of:

1/3 x 6012 = $2004.

Hence in five months the amount spent is going to be of:

5 x 2004 = $10,020.

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Answer:

\(-x^2 +18x -16\)

Step-by-step explanation:

First we must apply the distributive property to expand \((x -4)^2\):

\((x -4)^2 \\ (x -4)(x -4) \\ x(x -4) -4(x -4) \\ x^2 -4x -4x +16 \\ x^2 -8x +16\).

Now we can subtract the result from \(10x\).

\(10x -(x^2 -8x +16) \\ 10x -x^2 +8x -16 \\ -x^2 +10x +8x -16 \\ -x^2 + (10 +8)x -16 \\ -x^2 +18x -16\)

Answer:

9x^2 + 8x - 16

Step-by-step explanation:

By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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Answer

The Answer is: 29/300

SOLUTION

Problem Statement

We are asked to express 48 1/3 cm as a fraction of 5m.

Method

To solve this question, we should follow these steps:

1. Convert 48 1/3 cm to an improper fraction.

2. Convert 5m to centimeters

3. Divide the result from step 1 by the result from step 2.

Implementation

1. Convert 48 1/3 cm to an improper fraction:

To convert a mixed fraction to an improper fraction, we need to:

i. Multiply the denominator of the fraction and whole number

ii. Add the result from step i to the numerator of the fraction.

iii. The Improper fraction is the result from step (ii) divided by the original denominator

Let us apply these steps to convert 48 1/3 cm to an improper fraction:

2. Convert 5m to centimeters

3. Divide the result from step 1 by the result from step 2:

Final Answer

The Answer is: 29/300

Part 1) The probability of selecting all Republicans is 0.0877,

Part 2) The probability of selecting all Democrats is 0.1212, and

Part 3) The probability of selecting 1 Democrat, 1 Republican, and 1 Independent is 0.0695.

Now, let's apply probability to the given problem. We are asked to find the probability of selecting 3 senators at random from the Senate of the 107th Congress to head a committee on arts in education. The Senate is composed of 45 Republicans, 50 Democrats, and 5 Independents.

For Part 1, we are asked to find the probability of selecting all Republicans. This means we need to choose 3 senators from the 45 Republicans. The total number of ways to choose 3 senators from 100 (excluding the 5 Independents) is given by the combination formula: C(100,3) = 161,700. The number of ways to choose 3 Republicans from 45 is given by C(45,3) = 14,190. Therefore, the probability of selecting all Republicans is:

P(all Republicans) = 14,190/161,700 = 0.0877 (rounded to 3 decimal places)

For Part 2, we are asked to find the probability of selecting all Democrats. This means we need to choose 3 senators from the 50 Democrats. Using the same combination formula, we get C(50,3) = 19,600. Therefore, the probability of selecting all Democrats is:

P(all Democrats) = 1,9600/161,700 = 0.1212 (rounded to 3 decimal places)

For Part 3, we are asked to find the probability of selecting 1 Democrat, 1 Republican, and 1 Independent. This means we need to choose 1 senator from each party. The number of ways to choose 1 Democrat from 50, 1 Republican from 45, and 1 Independent from 5 is given by the product of the individual combinations: C(50,1) * C(45,1) * C(5,1) = 11,250. Therefore, the probability of selecting 1 Democrat, 1 Republican, and 1 Independent is:

P(1 Democrat, 1 Republican, 1 Independent) = 11,250/161,700 = 0.0695 (rounded to 3 decimal places)

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