Use the range rule of thumb to identify the values that are significantly​ low, the values that are signficantly​ high, and the values that are neither significantly low nor significantly high.
A test is used to assess readiness for college. In a recent​ year, the mean test score was 19.7 and the standard deviation was 5.3. Identify the test scores that are significantly low or significantly high.
What test scores are significantly​ low? Select the correct answer below and fill in the answer​ box(es) to complete your choice.

First it is needed to find the slope with the following equation

We take two points of the line. (10,50) and (3,15)

Then you substitute them on the equation

The answer would be 5 gal/min

Answer:

Step-by-step explanation:

B) the stone hits the water within the first 2 seconds. Because the stone drops at the speed of 88 feet/second, and 88 x 2 is 176. but the bridge is only 135 feet tall.

so,

88 feet/second

176 feet/2 seconds

135 feet means that it reached the river within 2 seconds. it reached the river in 1.545 seconds

a) The formula that models the height of the stone after t seconds is: s(t) = 135 + 88t + 16.1t²

b) No, the stone does not hit the water within the first 2 seconds.

(a) The formula for the height of an object thrown downward with an initial velocity and under the influence of gravity is expressed as:

s(t) = s₀ + v₀t + ¹/₂gt²

where:

s(t) is the height of the stone at time t,

s₀ is the initial height

v₀ is the initial velocity

g is the acceleration due to gravity

We are given:

s₀ = 135 ft

v₀ = 88 ft/s

g = 32.2 ft/s²

Thus:

s(t) = 135 + (88)t + ¹/₂(32.2)t²

s(t) = 135 + 88t + 16.1t²

(b) To check if the stone hits the water within the first 2 seconds, we need to find s(2) and determine if it is less than or equal to 0 (water level).

s(2) = 135 + 88(2) + 16.1(2)^2

s(2) = 135 + 176 + 64.4

s(2) = 375.4 ft

Since the height at t = 2 seconds is 375.4 feet, and this height is above the water level (which is 0 feet), the stone does not hit the water within the first 2 seconds.

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Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect

The points are given as:

(3,6.5) and (4,17.55)

An exponential equation is represented as:

\(y = ab^x\)

Using the given points, we have the following equations:

\(ab^3 = 6.5\)

\(ab^4 = 17.55\)

Divide both equations:

\(ab^4 \div ab^3 = 17.55 \div 6.5\)

Evaluate

b = 2.7

Substitute b = 2.7 in \(ab^3 = 6.5\)

\(a * 2.7^3 = 6.5\)

Solve for a

\(a = \frac{6.5}{2.7^3}\)

Substitute \(a = \frac{6.5}{2.7^3}\) and b = 2.7 in \(y = ab^x\)

\(y = \frac{6.5}{2.7^3} * 2.7^x\)

His point (5,28.6) means that:

x = 5 when y = 28.6

Substitute x = 5 in \(y = \frac{6.5}{2.7^3} * 2.7^x\)

\(y = \frac{6.5}{2.7^3} * 2.7^5\)

Evaluate

y = 47.385

y = 47.385 and y = 28.6 are not the same

Hence, Mike's claim is incorrect

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Answer:

(1) the whole is the sum of its parts

Step-by-step explanation:

This isn't using a property of equality. Instead, it's stating that the whole (MP) is the sum of its two parts (MN and NP).

Answer:

Step-by-step explanation:

Leon visited Chicago, which is located on the shore of

Lake Michigan. The lake has a volume of about 4,920

km cubed. Chicago was a major gateway to the west in

1825 when the Erie Canal was completed. When built,

the Erie Canal was 680 long and only 100 or

10 deep. While in Chicago, Leon visited the Sear

Tower. One of the tallest buildings in the world, the

Sears Tower is 443 tall

during Leon's visit was about 7

Answer:

5 is your answer

Step-by-step explanation:

The \(\sqrt{25}\) will equal to 5, because \(5^2\) = 25

Answer:

5

Step-by-step explanation:

5 x 5 =25, so it is the square root of 25

Answer:

7:11

Step-by-step explanation:

Hope this helps! God bless.

Answer:

A is ST, PR, and UV

B is rays SQ and QT

C is point Q

D is Points S, Q, and T

The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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9514 1404 393

Answer:

Step-by-step explanation:

The angles of a linear pair are supplementary. That is, they total 180°. The angle marked x° and the one marked 72° are a linear pair:

  x° +72° = 180°

  x = 180 -72 = 108 . . . . . . . divide by °, subtract 72

__

Vertical angles are congruent. Angles y° and 72° are vertical angles, so ...

  y = 72

__

Angles z° and 72° together make a right, which has a measure of 90°.

  z° +72° = 90°

  z = 90 -72 = 18 . . . . . . . divide by °, subtract 72

__

  (x, y, z) = (108, 72, 18)

_____

Additional comment

Angles 72° and x° form a linear pair, as do angles x° and y°. That is, angles 72° and y° are both supplementary to angle x°. Angles that are supplementary to the same angle are congruent. This will be the case for any vertical angles: they are supplementary to the same angle.

Answer:

  m = 1 + 2log(x)/log(y)

Step-by-step explanation:

Taking logarithms, you have ...

  log(x) +m·log(y) = log(y) +3log(x)

  m·log(y) = log(y) +2·log(x) . . . . subtract log(x)

  m = (log(y) +2·log(x))/log(y) . . . divide by the coefficient of m

  m = 1 +2·log(x)/log(y) . . . . . . . simplify a bit*

_____

* The "simplified" form will depend on your preference. Here, I like the integer 1 brought out because most logs are irrational. The result may be very slightly more accurate if we add 1, rather than log(y)/log(y)--depending on your calculator.

Answer:68

Step-by-step explanation:

You can first subtract 104-36=68 so,68+36=104

Answer:

  68

Step-by-step explanation:

You want to know the number of marbles Chloe originally had in her collection if adding 36 marbles gave her a total of 104.

You can let a variable (o) represent the original number of marbles. You would choose this because the original number of marbles is what you're asked to find. It never hurts to use a variable name that reminds you of what it stands for.

The problem statement tells you that adding 36 to the original number gives a total of 104. As an equation, this looks like ...

  o + 36 = 104 . . . . . . adding 36 to o gives 104

The properties of equality tell you that you can subtract the same number from both sides of the equation without changing the value of the variable.

Here, we want the variable by itself, so we want to get rid of the added number 36. We do that by subtracting 36 from both sides of the equation:

  o +36 -36 = 104 -36 . . . . . subtract 36 from both sides

  o = 68 . . . . . . . . . . simplify

This solution tells us that Chloe originally had 68 marbles.

__

Additional comment

The way to solve this, or any, "word problem" is to read and understand the relationships the words are telling you, and what the words are asking for. Then write those relationships as math expressions, choosing variables and a procedure that will give you what the question is asking for.

Here, we could choose a variable that represents the quantity we want to find. That is not always the case.

Sometimes, you have to find an "intermediate" value that you need in order to be able to answer the ultimate question. You're not done when you find that intermediate value; you're only done when you are able to answer the question asked.

Answer:

See below ~

Step-by-step explanation:

Unit Conversion :

1 quart = 2 pints

1 quart = 4 cups

He wants the 3 quart birdbath to be 3/4 filled.

Hence,

He can fill it with 4.5 pints and using cups :

Answer:

x = - 6

Step-by-step explanation:

x² + 12x + 36 = 0 ( subtract 36 from both sides )

x² + 12x = - 36

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(6)x + 36 = - 36 + 36

(x + 6)² = 0 ( take square root of both sides )

x + 6 = \(\sqrt{0}\) = 0 ( subtract 6 from both sides )

x = - 6

Each person will get 1.2 of the Blueberry muffins

The number blueberry muffins in 5

6 people wants to share the 5 blueberry muffins

Therefore the number of blueberry muffins each person will get can be calculated by dividing 6 by 5

= 6/5

= 1.2

Hence each person will get 1.2 blueberry muffins if the muffins are shared equally.

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We cannot conclude that there are more than 70,000 defined words in the dictionary.

To test the claim that there are more than 70,000 defined words in the dictionary, we can set up the null and alternative hypotheses as follows:

Null Hypothesis (H0): The mean number of defined words on a page is 48.0 or less.

Alternative Hypothesis (H1): The mean number of defined words on a page is greater than 48.0.

So, sample mean

= (59 + 37 + 56 + 67 + 43 + 49 + 46 + 37 + 41 + 85) / 10

= 510 / 10

= 51.0

and, the sample standard deviation (s)

= √[((59 - 51)² + (37 - 51)² + ... + (85 - 51)²) / (10 - 1)]

≈ 16.23

Next, we calculate the test statistic using the formula:

test statistic = (x - μ) / (s / √n)

In this case, μ = 48.0, s ≈ 16.23, and n = 10.

test statistic = (51.0 - 48.0) / (16.23 / √10) ≈ 1.34

With a significance level of 0.05 and 9 degrees of freedom (n - 1 = 10 - 1 = 9), the critical value is 1.833.

Since the test statistic (1.34) is not greater than the critical value (1.833), we do not have enough evidence to reject the null hypothesis.

Therefore, based on the given data, we cannot conclude that there are more than 70,000 defined words in the dictionary.

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The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1  using synthetic division is x³ +  2x² - 2x  + 7  and the remainder is 13

From the question, we have the following parameters that can be used in our computation:

x⁴ - 3x³ + 9x + 6 ÷ x + 1

The synthetic set up is

-1  |   1  3  0   9   6

    |__________

Bring down the first coefficient, which is 1 and repeat the process

-1  |   1  3  0   9   6

    |__-1_-2_-2_7____

       1  2  -2  7  13

This means that the quotient is

x³ +  2x² - 2x  + 7  

And the remainder is 13

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Complete question

Find the quotient and remainder using synthetic division.

x^4-3x^3+9x+6/x+1

The quotient is

The remainder is

Answer:

Step-by-step explanation:

To use synthetic division, we need to set up the coefficients of the dividend polynomial in decreasing order of powers of x, including any missing terms with zero coefficients.

So we have:

Dividend: x^4 - 3x^3 + 9x + 6

Divisor: x + 1

We can represent the divisor as (x + 1) and set up the synthetic division table as follows:

-1 | 1 -3 9 0 6

| -1 4 -13 13

|___________________

| 1 -4 13 -13 19

The numbers on the first row of the table are the coefficients of the dividend polynomial in decreasing order of powers of x. The -1 on the left of the table is the opposite of the divisor, x + 1.

The first number in the second row is always 0, and we get it by bringing down the first coefficient, which is 1. To get the next number in the second row, we multiply the divisor, -1, by 1, and add the result to the second coefficient, which is -3. This gives us -1 x -3 = 3, which we write under -3 in the first row.

We repeat this process for the next numbers in the second row, always multiplying the divisor by the last number in the second row, and adding the result to the next coefficient in the first row. We continue until we reach the last coefficient in the first row.

The last number in the second row, 13, is the remainder of the division. The other numbers in the second row are the coefficients of the quotient polynomial in decreasing order of powers of x. So the quotient is:

x^3 - 4x^2 + 13x - 13

And the remainder is:

13

Therefore, the quotient is x^3 - 4x^2 + 13x - 13, and the remainder is 13.

Answer:

P(X < 1) = 0.5

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 1 L and standard deviation of 0.05 L.

This means that \(\mu = 1, \sigma = 0.05\)

Find P(X < 1).

This is the p-value of Z when X = 1. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1 - 1}{0.05}\)

\(Z = 0\)

\(Z = 0\) has a p-value of 0.5. Thus

P(X < 1) = 0.5

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The value of R500 decrease to ratio 9:8 is x = 400.

By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.

Given that, decrease R450 in the ratio 9:8.

Let 9 = 450

Then 8 will have the value = x.

That is,

9 = 450

8 = x

Using cross multiplication we have:

9x = 450(8)

x = 50(8)

x = 400

Hence, the value of R500 decrease to ratio 9:8 is x = 400.

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The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answer:

6x - 3 y = 6

6x + 8y = -16

multiply equation 2 by -1

-6y -8y = 16

6x - 3y = 6

-11y =22

y = -2

substitute the value of y in 1

6x - 3(-2) = 6

6x + 6 =6

6x =0

x = 0

(x;y)

[0; -2]

9) 4x + 3y = 19

6x + 3y =33

multiply equation 2 by -1

4x + 3y = 19

-6x - 3y = -33

eliminate one variable by adding the equations

-2x =-14

x = 7

substitute the value of x in the equation

4(7) +3y = 19

28+ 3y = 19

3y =-9

y = -3

(x;y)

[7 ; -3]

10 ) 2x + 6y = 17

2x - 10y = 9

multiply by -1 in equation2

2x +6y = 17

-2x + 10 y = -9

eliminate one variable by adding the equations

16 y = 8

y = 1/2

substitute the value of y in the equation.

2x +6 (1/2) = 17

2x + 3 = 17

2x = 14

x = 7

x:y

[7 ; 1/2 ]

Answer:

750 peices of mail

Step-by-step explanation:

150 times 5 is 750

The completed statement with regards to the area of the square and the rectangle are;

The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.

The area of a square is the product of the side lengths which are congruent, therefore;

Area of a square = Side length, s × Side length, s = s²

The possible figure in the question includes;

A shaded square that is 125 square inches

An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches

Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.

Therefore;

The side length of the square = √(125) inches =  5·√5 inches

The estimated value of the side length of the square is; 5·√5 inches

The area of a rectangle = Length × Width

The length of the rectangle = 7·√5 inches

The width of the rectangle = 5·√5 inches

Therefore;

The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175

The estimated area of the unshaded rectangle is 175 square inches

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Answer:

12 pounds of tea-1 and 8 pounds of tea-2 should be used.

Step-by-step explanation:

distance = y-coordinate for the school - y-coordinate for the house

distanc=6

ExplanatIon

Step 1

to go from Jean's house to the school, we move up, only in vertical, so the change is in the y-coordinate, so the subtraction is

replacing

I hope this helps you

The probability that an ace is drawn is 4/52, or 1/13 and the probability that a heart is drawn is 13/52, or 1/4.

Since, one of the aces is the ace of hearts

P(an ace or heart is drawn)=4/52+13/52-1/52

P=16/52=4/13

or look at it this way...

P=13/52+3/52=16/52 because one of the aces, the ace of hearts, is already include in the 13/52

you add the probabilities because of the word "or"

the odds (in favor) of an ace or a heart is the ratio of the probability that the event will occur to the probability that the event will not occur

odds=(16/52)/(36/52)=16/36=4/9, or simply look at 4/13, 13-4=9, and the ratio is 4/9

the event cannot happen in 36 ways: 13 diamonds+13 spades+13 clubs-ace of diamonds-ace of spades-ace of clubs=39-3=36, so 16(ways it can happen)/36(ways it cannot happen)=16/36=4/9

note: don't be mislead looking at 4/9, it is not probability but odds; the event can happen in 4 ways and cannot happen in 9 ways, so the event can happen in 4 ways out of a total of 4+9=13 ways

Hence, the probability that an ace is drawn is 4/52, or 1/13 and the probability that a heart is drawn is 13/52, or 1/4.

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Using a graph of the unitary circle,

Every point on the unitary circle can be expressed as (cosθ,sinθ).

In our case, since θ=pi/3,

Then,

Thus, the answer is (1/2,sqrt(3)/2)