Greg and Max left Ottawa for Toronto in their old jalopy to see the Grey Cup football game
The mileage gauge on the car was not working but the speedometer was. Their jalopy
averaged 40 mph from Ottawa to Toronto and 35 mph on the return trip. The total
traveling time for the round trip was 15 hours. Being good mathematics students, Greg and
Max were able to determine the distance between the two cities. What is this distance?

Answer: 132.5

Step-by-step explanation:

Answer:

132.75

Step-by-step explanation:

*in picture below*

Answer:

y = 3x + 2

Step-by-step explanation:

The slope is the rate of change.  The y intercept is the y value when x is 0.

Answer:

red cubes = 99, plastic cubes = 462

Step-by-step explanation:

total number of cubes/total ratio

= 560/17

= 33 (approximately)

red cubes

= 33 × 3

= 99

plastic cubes

= 33 × 14

= 462

Though 462 + 99 equals 561 rather than 560, I had to approximate the values because if not, the result will be 461 which is a prime number.

The height of the large boxes is 36 inches when the volume of box is 3456 cubic inches.

According to the question,

We have the following information:

A cereal company packs cereal boxes into large cardboard boxes. The large boxes are 12 inches long and 8 inches wide.

Volume of box = 3456 cubic inches

We know that the box is in the shape of cuboid.

Following formula is used to find the volume of cuboid:

Volume = length*width*height

12*8*height = 3456

96*height = 3456

Dividing both sides by 96:

Height = 3456/96

Height of the box = 36 inches

Hence, the height of the large boxes is 36 inches when the volume of box is 3456 cubic inches.

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Let's say we have blue and red balls

Blue : Red

3 : 5

Now we can add another ratio for the whole.

Blue : Red : Total

Total is Blue + Red = 3 + 5 = 8

So

Blue : Red : Total

3 : 5 : 8

Then the part : whole ratio for Blue is...

Blue : Total

3 : 8

Traingle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

The sum of the three angles is equal to 180 degrees.

The value of angle W is 47.67

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

In this triangle:

angle W = (3x-24) degrees.

angle C = (4x-11) degrees.

angle T = 2x degrees.

Now,

The sum of the three angles is equal to 180 degrees.

3x - 24 + 4x - 11 + 2x = 180

9x - 35 = 180

9x = 215

x = 215/9

Now,

The angle W.

= 3x - 24

= (3 x 215/9) - 24

= 215/3 - 24

= 71.67 - 24

= 47.67

Thus,

The value of angle W is 47.67

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Answer: Yes

Step-by-step explanation:

An equilateral triangle has three equal sides and angles, therefore all of the sides are congruent.

Answer: The answer to this question is: the mass of the metal in pounds is 1.5 grams.

Step-by-step explanation: Search a free gram to pounds calculator and input your given input or output into there for further help if needed.

Hope this helps

The mass of the metal in pounds is 1.5 pounds.

A unit conversion expresses the same property as a different unit of measurement.

Given that, a scientist measures the mass of a metal to be 682 grams

682 grams = 0.682 kg

0.682 kg = 0.682*2.2 = 1.5 pounds.

Hence, The mass of the metal in pounds is 1.5 pounds.

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Her situation can be modeled by the linear equation (in standard form):

x*$0.25 + y*$0.79 = $2.50

The variables that we will use here are:

x =  number of apples that she can buy.

y = number of bananas that she can buy.

We know that she has $2.50 to spend, that each apple costs $0.25 and each banana costs $0.79, then the cost of the x apples and y bananas is:

x*$0.25 + y*$0.79

and that must be equal to the amount she has to spend, then we can write the linear equation:

x*$0.25 + y*$0.79 = $2.50

That is the linear equation in standard form that represents her situation.

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Answer:

======================

(a) f(-7)

(b) f(0)

(c) f(4)

Answer:

Step-by-step explanation:

a) f(-7) = ?

→ f(x) = 8 - 4x

→ f(-7) = 8 - 4(-7)

→ f(-7) = 8 + 28

→ f(-7) = 36

Hence, f(-7) = 36.

b) f(0) = ?

→ f(x) = 8 - 4x

→ f(0) = 8 - 4(0)

→ f(0) = 8 - 0

→ f(0) = 8

Hence, f(0) = 8.

c) f(4) = ?

→ f(x) = 8 - 4x

→ f(4) = 8 - 4(4)

→ f(4) = 8 - 16

→ f(4) = -8

Hence, f(4) = -8.

The measure that will be captured by approximately 9000 of the confidence intervals is given as follows:

(E) The Population Median.

The interpretation of a x% confidence interval is that it is x% likely that the population parameter(mean/proportion/standard deviation/median) is between a and b, which are the bounds of the confidence interval.

The bounds of the confidence interval are obtained by the estimate plus/minus the margin of error.

The measure for which the confidence intervals are calculated in this problem is given by:

Median.

The sample median for each sample is used for the estimes, and then these estimates are inferred for the population median, which is the population parameter, hence option e is correct.

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Answer:

x-intercept: -([tex]\frac{35}{9}[/tex],0)

y-intercept: (0,-3)

Step-by-step explanation:

The total segment AE is 46.

"SAS" is when we know two sides and the angle between them.

To solve an SAS triangle we use "The Law of Cosines" to calculate the unknown side.

The Law of Cosines = a² = b² + c² − 2bc cosA

where

'b' and 'c' are two given sides

'A' is the angle between side 'b' and 'c' and

a' is the unknown side which we have to find.

In ΔABC , b=21, c=20, a= AC

By the Cosine law

a² = 21²+20² - 2*21*20 cos90°

a² =441 + 400 - 0 (∵cos 90° =0)

a² = 841

a=√841

a=29= AC.

Now, in ΔCDE, b=8, c=15 and a = CE

By the Cosine law

a² = 8² + 15²- 2*8*15cos90°

a² = 64 + 225 - 0 (∵cos 90° =0)

a²= 289

a = 17 = CE.

AE = AC + CE

AE = 29+17= 46.

Therefore, the total segment AE is 46.

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 y = -3/5x - 123/5 is slope-intercept form .

What is an explanation of the slope-intercept form?

Point = ( 1,24 )

slope = -3/5

the equation in standard form of the line that passes through the point

               y - y₁ = m ( x - x₁)

                y - 24 = -3/5 ( x - 1)

             5 (y - 24) = -3( x - 1 )

                5y -    120 = -3x + 3

                 5y = -3x + 3 + 120

                 5y = -3x + 123

                 y = -3/5x - 123/5

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Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

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Inequality represented by the given graph is equal to 5x -3y > 9.

As given in the question,

For the given graph,

Consider two points on the line represented on the graph ,

( x₁ , y₁) = (0,-3)

(x₂ , y₂) = ( 3,2)

Equation of the line given by two points on the graph,

( y - y₁)/ (x -x₁) = ( y₂ - y₁)/ (x₂ -x₁)

⇒(y +3)/(x-0) = ( 2 + 3)/(3 -0)

⇒(y + 3) / x = 5/3

⇒3(y+ 3) = 5x

⇒3y + 9 = 5x

⇒5x -3y = 9

As per shaded region inequality of the graph is given by,

5x -3y > 9

Therefore, inequality represented by the given graph is equal to 5x -3y> 9.

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The equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0 which can be found out from slope intercept formula.

It is given to us that -

The point is P(-8,0)

The line is represented as y=-3

The point P is perpendicular to the given line.

We have to find out the equation of the line passing through P which is perpendicular to the given line.

We know that the equation of a line is given by -

y = mx + c

where, (x, y) = coordinates of the point

m = slope of the line

c = a constant

Comparing this with the equation of the given line, we have

m=0 and c =-3

This implies that the slope of the perpendicular is also equal to 0.

The slope intercept formula for the perpendicular line can be represented as -

y = mx + c

Using the coordinates of P(-8,0), we have

0 = 0*(-8) +c

=> c = 0.

Thus, the equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0.

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Answer:

26x/7

Step-by-step explanation:

The effect of the sample size on the mean of the sampling distribution is that it effects the variations .

In the question ,

If the sample size is increased ,

that is if the number of sample is increased then the errors in the sampling distribution becomes less .

and if the sample size is decreased then it will lead to the increase in the errors  of the distribution .

The formula for relationship between variation and sample size is given as ,

σx = σ / sqrt (n)

we can see that variation and sample size are inversely proportional .

that means increase in the sample size results in reduction of variation.

Therefore , The effect of the sample size on the mean of the sampling distribution is that it effects the variations .

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The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

In the question ,

it is given that ,

the initial point of the vector = (1 , -1)

the terminal point of the vector = (4,2)

we know that the vector with initial point (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

V = (x₂ - x₁)i + (y₂ - y₁)j

Substituting the values from the point ,

we get the vector as

V = (4 - 1)i + (2 -(-1))j

V = 3i + (2 + 1)j

V = 3i + 3j

Therefore , The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

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well, we know the first $25,000 is taxed at 8%, wait a second!!!!! Chris didn't make 25,000 bucks, he only made $17,000, so he'd be in the range of $0 - $25,000 because $17,000 is in that range, that means he owes 8% of 17,000

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 17000}}{\left( \cfrac{8}{100} \right)17000}\implies 1360[/tex]

The amount Chris owes in tax is $1360.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The first $25,000 is taxed at 8%.

This means,

Amount from 0 to $25000 is taxed at 8%.

Now,

Chris earned = $17,000

Tax amount.

= 8% of 17,000

= 8/100 x 17,000

= 8 x 170

= $1360

Thus,

The tax amount is $1360.

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By using Binomial Distribution  of probability, it is obtained that

Probability  that the number of heads is 13 or more =  [tex]137980(\frac{1}{2})^{20}[/tex]

What is Binomial Distribution?

Binomial distribution is a discrete type probability distribution whose probability mass function is

P(X = k) = [tex]{n \choose k} p^k(1 - p)^{n-k}[/tex]

p is the probability of success.

Here Binomial distribution of probability is used

P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + ........ + P(X = 20)

P(X = 13) = [tex]{20 \choose 13} (\frac{1}{2})^{13}( 1 - \frac{1}{2}})^{20-13}[/tex]

              = [tex]{20 \choose 13} (\frac{1}{2})^{13}( \frac{1}{2}})^{7}[/tex]

              =[tex]{20 \choose1 3} (\frac{1}{2})^{20}[/tex]

P(X = 14) = [tex]{20 \choose14} (\frac{1}{2})^{20}[/tex]

P(X = 20) = [tex]{20 \choose20} (\frac{1}{2})^{20}[/tex]

Total Probability = [tex]({20 \choose 13} + {20 \choose 14} + .... {20 \choose 20})(\frac{1}{2})^{20}[/tex]

                  = (77520 + 38760 + 15504 + 4845 + 1140 + 190 + 20 + 1)[tex](\frac{1}{2})^{20}[/tex]

                   = [tex]137980(\frac{1}{2})^{20}[/tex]

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The number of dimes and nickels that Johnny has are 6 and 3 respectively.

The following should be noted:

Nickel = 5 cent = 0.05

Dime = 10 cents = 0.10

Let the number of nickels = n

Let the number of dimes = 2n

Total worth = $0.75

This will be illustrated as:

0.05(n) + 0.10(2n) = 0.75

0.05n + 0.20n = 0.75

0.25n = 0.75

Divide

n = 0.75/0.25

n = 3

Number of nickels = 3

Number of dimes = 2n

= 2 × 3

= 6

Number of dimes = 6

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It will take 300 days to get to 2000 dollars.

According to the question,

We have the following information:

One gets paid every 12 days and one puts back $80 every 12 days.

Now, the total amount of dollars is $2000.

Now, we have the following progression:

80, 160, 240, ...

This is an arithmetic progression.

an = a+(n-1)d where a is the first term and d is the common difference

2000 = 80+(n-1)80

2000 = 80+80n-80

2000 = 80n

n = 2000/80

n = 25

Now, the number of days one is paid is after 12 days.

So, the number of days to get 2000 dollars:

25*12

300 days

Hence, it will take 300 days to get to 2000 dollars.

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Answer:

Hundreds: 6 Tenths: 2 Ten Thousands: 5

Step-by-step explanation:

Hundreds are 2 decimal places (0.02)

Tenths are 1 decimal place (0.1)

Ten Thousands are 4 decimal places (0.0004)

Hope this helped!

Answer:

It says right there that he bought a pound of turkey for $5.50.

One pound of turkey is $5.50?

Step-by-step explanation:

This is extremely confusing

Percentage of bags that weigh more than 9.25 ounces is 19.3%.

Given:

Mean μ = 9.12

standard deviation σ = 0.15

z = x - μ / σ

= 9.25 - 9.12 / 0.15

= 0.13/0.15

= 0.867

P(x>Z)  = 0.193

= 0.193/100

= 19.3%

Therefore Percentage of bags that weigh more than 9.25 ounces is 19.3%.

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The slope of the line -1 and the y-intercept is 3.

From the question, we have

x+y = 3

y = -x+3

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

m = -1

c = 3

Slope of a Line :

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.

where "m" represents a line's slope. The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

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