Question
What numbers are a distance of 23 unit from 12 on a number lineQuestion
What numbers are a distance of 23 unit from 12 on a number line

The number you should multiply 3 1/3 to get a product of 4 is 1 1/5

From the question, the statement is given as

What number should you multiply 3 1/3 to get a product of 4

Let the number be x

So, we have the following representation

3 1/3 * x = 4

Express 3 1/3 as an improper fraction

So, we have the following representation

10/3 * x = 4

Multply both sides by 3

So, we have

10 * x = 12

Divide both sides by 10

This gives

x = 12/10

Express as mixed numbers

x = 1 1/5

Hence, the number is 1 1/5

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Let's call the amount of lugagge the first men had as x, and the amount of lugagge the second men had as y.

Since both had to pay for excess of luggage, both had the permitted amount of luggage plus an extra amount. Let's call the permitted amount as a, the extra the first men had as z, and the extra the second man had as w. Then, our total amounts of luggage can be rewritten as

Since their total amount of luggage added together was 135 kg, this gives to us the following equation

The charge for the extra luggage is a flat rate, let's call it r, then, the price you pay for the extra luggage is given by the product between this rate and the amount of extar luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage, therefore

If we divide one equation by the other, we can write the excess of luggage of one as a function of the other.

If all of the luggage belonged to one person, this person would have to pay $8.10 for the excess. If we call the excess of this person as p, the amount of luggage this person had would be

Using the "rate formula" we created before, we can also write p as a function of z.

Rewritting all the total amounts, we have

If we add the equations for x and y together, we have

From the first equation, we know that the sum between both total amounts of luggage is equal to 135.

Now, we have two equations for our two variables.

If we multiply the first equation by 2, and subtract the second equation, we're going to get a new equation only for a(the amount in kilograms of permitted luggage).

The amount of luggage permitted to bring onto the plane for free is 45 kilograms.

Water used in three minutes in the shower is 12.6 gallons.

An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Given Data

Elyse uses 42 gallons of water for a 10-minute shower,

Let

the time in minutes at position x

y=the quantity of water in gallons

The fact that

[tex]\frac{y}{x}[/tex] = [tex]\frac{42}{10}[/tex] = 4.2x

The unit price equals

The slope of the linear equation is equal to the unit rate.

then

y=4.2x

Problem

How much water will Elyse use in her shower for three minutes?

x = 3 minutes

substituting in the previous equation

y = 4.2x

y = 4.2(3)

y = 12.6

Water used in three minutes in the shower is 12.6 gallons.

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Answer: (4) [tex]y=2x[/tex]

When you look at the table, you can see that the y values are double the x values they are associated with. Therefore, to get to the y value, the x values must be multiplied by 2, which would be the equation [tex]y=2x[/tex]

The value obtained for z-score for the given sample mean is 0.5.

For the given question;

The formula for finding the z-score is;

z = (x - μ)/σ

x = sample size

μ = population mean

σ = standard deviation population.

The given values are-

Put the value in the z-score.

z = (35 - 25)/20

z = 10/20

z = 0.5

Therefore, the value obtained for z-score for the given sample mean is 0.5.

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The correct question is-

Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the z-score for the of the sample means for the sample less than 35?.

Answer:

x = 5/3, 1/3

Or

x=1.6 repeating ,0.3 repeating

Answer:

(2[tex]b^{2}[/tex] - 5) (3b + 8)

Step-by-step explanation:

First factor out 2[tex]b^{2}[/tex] from the first set of parentheses and -5 from the second

2[tex]b^{2}[/tex] ( 3b + 8)  - 5 (3b + 8)

Next factor out (3b + 8)

(2[tex]b^{2}[/tex] - 5) (3b + 8)

The estimate of the average rate of change f is -2

The possible graph that completes the question is added as an attachment

The interval is given as

-1 ≤ x ≤ 0

This can be rewritten as

x = -1 to x = 0

This can also be represented as

(a, b) = (-1, 0)

From the attached graph, we have

f(-1) = 7

f(0) = 5

The estimate (to one decimal place) of the average rate of change f is

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(-1) - f(0)]/[-1 - 0]

So, we have

Rate = [7 - 5]/[-1 - 0]

Evaluate

Rate = -2

Hence, the average rate of change f is -22

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Answer:

x = 12

Step-by-step explanation:

Be the 8 consecutive numbers like this:

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) =  124

8x + 28 = 124

8x = 124 - 28

8x = 96

x = 12

Answer:

$3,690

Explanation:

The shipping charge for all 3 TVs =$90

Cost of a TV = $1200

Therefore, the cost of 3 TVs = 3 x $1200 =$3,600

The total amount paid by Gordon will be:

=$3600+90

=$3,690

Answer:

I believe it would be "A population of 200 bacteria quintuples every week"

Step-by-step explanation:

If it is quintupling each week then the number is getting larger and larger exponentially.

The number 150 is 0.0000455 % out of 329.5 million

The statement is given as

the percentage of 150 out of 329.5 million

The percentage can be calculated as

Percentage = 150 out of 329.5 million *100%

Express as fraction

So, we have

Percentage = 150/329.5 million *100%

Rewrite as

Percentage = 150 *100/329.5 million %

Evaluate the product

Percentage = 15000/329.5 million %

Evaluate the quotient

Percentage = 0.0000455 %

Hence, the percentage of 150 out of 329.5 million is 0.0000455 %

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The area of the land is 289/4 square units

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The given parameters are

Shape = Square

Side length = 17/2

The area of a square shape is

Area = Side length^2

So, we have

Area = (17/2)^2

Evaluate the exponent

Area = 289/4

Hence, the area of square plot of land whose each side measures 17/2 is 289/4 square units

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Answer:108 inches

Step-by-step explanation:

to find the area of one of the right triangles you do.

base = 6/2 =3

3x6=18

18/2=9

there are 8 right triangles so you would do

9x8 = 72.

then you would add 72 and the area of the square in the middle

6x6=36

36+72= 108

so Area of SA = 108 inches ^2

Based on the model that shows the altitude of Mr. Mole relative to the ground, the rate at which Mr. Mole was digging was 2.3 meters down per minute.

When given a linear function, the rate that the model progresses is given by the slope. The slope in a linear function can be found as:

y = mx + b

m =  slope

b = y-intercept

In the model given for Mr. Mole's digging, which is -2.3t - 7, the slope is -2.3.

This means that Mr. Mole is digging downwards at 2.3 meters per minute.

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The maximum number of miles Julie can drive the car is 272 miles.

Let's check how:

Julie's budget for renting a car is $200.

number of days she'll rent a car is 3.

car rental per day is $44 + $0.25 per mile.

so to know maximum no. of miles she can drive

we'll first subtract the 3 days rent from Julie's budget = $200 - ( 3 x $44 )

= $200 - $132

= $132

Now, the left money is $68.

so, we will divide $68 by $0.25 to know how much miles she can drive.

= $68 ÷ $0.25

= 272 miles

Hence, the maximum number of miles Julie can drive the car for 3 days is 272 miles.

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Answer:

Step-by-step explanation:

Answer:

x+46

Step-by-step explanation:

Distribute

Combine like terms

Answer:

3

Step-by-step explanation:

Absolute value is how far away the value is from 0. The only value of x that would make this equation true is 3.

Answer:8.7:1.2

Step-by-step explanation: divide both by 3

Answer:

length = 6m

Step-by-step explanation:

H=5m

V=180m^3

Here

V=l^2 ×H ( being a square)

180=a^2×5

a^2=36

a=6m

Answer:

86

Step-by-step explanation:

average is calculated as

average = [tex]\frac{sum}{count}[/tex]

given her average was 70 in 3 tests , then

[tex]\frac{sum}{3}[/tex] = 70 ( multiply both sides by 3 )

sum = 210

let the score she must get in test 4 be x for an average of 74 , then

[tex]\frac{210+x}{4}[/tex] = 74 ( multiply both sides by 4 )

210 + x = 296 ( subtract 210 from both sides )

x = 86

she must score 86 in her next test

Answer:

[tex]\frac{x}{3}[/tex]= 70

x=210

[tex]\frac{210+x}{4}[/tex] = 74

210+x=74x4

210+x=296

x=296-210

x=86

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The number that fills in the blank to make a perfect square trigeminal of the given expression is 81.

Given expression:

[tex]x^2+18x +[/tex] _

We have to find the number that will fill the blank.

A perfect square trigeminal is an algebraic expression that is of the form ax 2 + bx + c, which has three terms. It is obtained by the multiplication of a binomial with itself.

Let the number that fills the blank be a.

Hence, the expression becomes:-

[tex]x^2+18x +a[/tex]

To make it a perfect square geminal, the expression must be a perfect square of a binomial.

We know that,

[tex](x+y)^2=x^2+2xy+y^2[/tex]

Comparing it with given expression, we get

2xy = 18x and,

[tex]y^2=a[/tex]

Hence,

y = 9

a = [tex]9^2[/tex] = 81

Hence, the number that fills the blank is 81.

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Yes , ∠WGR is congruent ∠GHR because both angles are on one line.

What does the word "congruent" mean in math?

a) No, ∠PHG is not congruent  ∠MGH because both angles are not equal.

b) No, ∠RHG and ∠MGH are not supplementary angle because in   supplementary angle is equal to 180° .

c) No, ∠SGW  is not congruent   ∠PHV.

d)  Yes , ∠WGR is congruent ∠GHR because both angles are on one line.

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[tex] = 2^{3} \\ = 2 \times 2 \times 2 \\ = (2 \times 2) \times 2 \\ = 4 \times 2 \\ = 8[/tex]

ATTACHED IS THE SOLUTION

LAST OPTION IS THE ANSWER.

Answer:

Step 4

Step-by-step explanation:

Mia made a mistake in step 4.

Step3:  x(x + 6) -2(x + 6)

In both terms, (x + 6) is common.

Step 4: When we take (x + 6) out, it will be (x + 6 ) (x - 2)

The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]. The evaluated expression is  3a+4.5b+c=40.5

Given that,

The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]

We have to evaluate the expression

Evaluating an algebraic expression involves determining its value when a particular integer is substituted for a variable. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.

Take,

0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]

0.5×81=a×3+b×4.5+c

40.5=3a+4.5b+c

The expression can be written in 4 ways

1st- 3a+4.5b+c=40.5

2nd- a=[tex]\frac{40.4-4.5b-c}{3}[/tex]=13.4-1.5b-c (this is the expression with subject a)

3rd- b= [tex]\frac{40.5-3a-c}{4.5}[/tex]=9-1.6a-c (this is the expression with subject b)

4th- c= 40.5-3a-4.5b (this is the expression with subject c)

Therefore, The evaluated expression is 3a+4.5b+c=40.5

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a) The minimum number of dogs that could have a mass of more than 27 kg is 4.

b) The maximum number of dogs that could have a mass of more than 27 kg is 17.

The given table shows information about the masses of some dogs.

a) Because we need the minimum number of dogs,

Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the minimum value out of 13 and 4 is 4.

b) Because we need the maximum number of dogs,

Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17

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Answer:

Step3

-by-step explanation:

After evaluating the given expression -(8⁻²), the resultant expression is - 1/64.

So, -(8⁻²):

Now, evaluate -(8⁻²) as follows:

Therefore, after evaluating the given expression -(8⁻²), the resultant expression is - 1/64.

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Answer:

2(x - 2) = 8

x = 6

Step-by-step explanation:

2(x - 2) = 8

2(x - 2) = 8

2x - 4 = 8

     +4   +4

-----------------

2x = 12

÷2   ÷2

----------

x = 6

I hope this helps!