Bill Gutierrez drove 130 miles at a speed of 65 miles per hour on an expressway for 2 hours. He drove 67.5 miles for 1.5 hours at 45 miles per hours on a state highway. What is his average speed?

The width of the plywood = 23/8 ft

The two rectangular pieces of plywood had equal widths.

The length of first rectangular piece = 6 ft

The length of second rectangular piece = 5 1/2 ft = 11/2 ft

The two pieces are joined to make a single rectangular stage.

Then the total length of the stage = 6 + 11/2 = 23/2 ft

Now area of the rectangular stage = 66 1/8 = 529/8 square feet.

⇒ length x width = 529/8

⇒ 23/2 x width = 529/8

⇒ width = 529/8 x 2/23 = 23/4 ft

Let 'x' be the width of a rectangular plywood.

Then 2x = width of the stage

⇒ 2x = 23/4

⇒ x = 23/8 ft

Hence width of the plywood = 23/8 ft

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The probability of getting an even number is 1/2 while the probability of getting a factor of 6 is 1/6

The probability of an even number

From the question, the sample space of the number cube is given as

Space = 1, 2, 3, 4, 5, and 6

The above means that

Sample size, n = 6 ---- i.e. the number of observations

Number of even numbers, x = 3

The probability of getting an even number is then calculated as

P(Even) = Number of even numbers/Sample size

This gives

P(Even) = 3/6 = 1/2

The probability of a factor of 6

From the question, the sample space of the number cube is given as

Space = 1, 2, 3, 4, 5, and 6

The above means that

Sample size, n = 6 ---- i.e. the number of observations

Number of factor of 6, x = 1

The probability of getting a factor of 6 is then calculated as

P(factor) = Number of factor of 6/Sample size

This gives

P(factor) = 1/6

Hence, the probability is 1/2 and 1/6

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character character character

Answer:

See below

Step-by-step explanation:

[tex]\frac{1}{a+b}[/tex] ([tex]\frac{1}{a}[/tex] + [tex]\frac{1}{b}[/tex])

[tex]\frac{1}{a+b}[/tex] ([tex]\frac{b}{ab}[/tex] + [tex]\frac{a}{ab}[/tex])

[tex]\frac{1}{a+b}[/tex] ([tex]\frac{b+a}{ab}[/tex])

[tex]\frac{(a+b)}{(a+b)(ab)}[/tex]

[tex]\frac{1}{ab}[/tex]

[tex]ab^{-1}[/tex]

Answer:

I believe it's " a study that collects data on every subject in sample"

Answer:

Explanation:

Terry bought 2 shirts for $14 each.

That is $28 on shirts

2 pair of socks for $2.99

That is $5.98 on socks

A pair of slacks for $25

The sales tax rate is 6.5% or 6.5/100 or 0.065

We want to know how much he paid.

Adding all the items he bought together, we have:

$28 + $5.98 + $25

= $58.98

Next, we apply the sales tax rate.

Take 6.5% of $58.98

This is: $58.98 * 0.065

= $3.83

Finally, add the sales tax with the amount we got

$58.98 + $3.83

= $62.81

He paid $62.81 in total

The tunnel measures 225 meters in length.

Velocity is the measure of how quickly an object's position changes over time and in relation to a frame of reference. A body moves across space with uniform velocity when it does so with an equal displacement per unit of time.

Velocity is equal to the product of distance and time.

It measures in m/s.

In response to the query, we are provided with the-

150m is the length of the train.

s m is the tunnel's length.

90 km/hr is the train's speed.

= 90 × 5/18 m/sec

= 25m/sec

Total distance equals (train length plus tunnel length).

[tex]Speed = \frac{Distance}{Time}[/tex]

⇒ 25 = (150 + s) / 15

⇒ 25 × 15 = 150 +s

⇒ 375 = 150 + s

⇒ 375 - 150 = s

⇒ s = 225

⇒ s = 225m

Hence, the length of the tunnel is 225 m.

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Answer:

  18

Step-by-step explanation:

You want to know the number of pencils in a box when 7 more than 4 boxes totals 79 pencils.

Let b represent the number of pencils in a box. Then the total number of pencils Mr. Ridley has is ...

  4b +7 = 79

This 2-step linear equation is solved in the usual way:

Step 1: isolate the variable term

  4b +7 -7 = 79 -7 . . . . . . add the opposite of the left-side constant

  4b = 72 . . . . . . . . . simplify

Step 2: isolate the variable

  4b/4 = 72/4 . . . . . . . . . . divide by the coefficient of the variable

  b = 18 . . . . . . . . . . simplify

There were 18 pencils in each of Mr. Ridley's pencil boxes.

Answer:

I will assume that 2√√/2 is actually 2[tex]\sqrt{2}[/tex]

Vab = 8

Step-by-step explanation:

ab

([tex]\sqrt{8}[/tex])*( 2[tex]\sqrt{2}[/tex])

2*[tex]\sqrt{16}[/tex]

2*4

Vab = 8

Answer: k>8.14

Step-by-step explanation: just do math.

Answer:

1,897,055

Step-by-step explanation:

1,381,069+515,986​=1,897,055

Answer:

A

Step-by-step explanation:

With the concepts of percentages and calculations, the percent decrease in the number of people who went to the pool over these four weeks is 10%

Take the base as 100 and convert the percentage to numbers and then proceed with the same.

Now, the initial number of people in the local swimming pool is 1020, after which 100 fewer went, hence 920 people

Now, 135 people more people need to be added, thus 1055 people.

Now, 137 fewer people went, so 918 people went to the pool in the four weeks.

Therefore percent decrease = Difference/No. of people in the first week * 100

Thus, the percent decrease =  102/1020*100=10%

Hence 10% of people went less in the fourth week as compared to the first week.

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Answer:

5/6

Step-by-step explanation:

Step 1: Find the GCD (greatest common denominator)

12

Step 2: multiply your factions to represent this

[tex]\frac{2x3}{4x3} = \frac{6}{12} \\[/tex] , [tex]\frac{1x4}{3x4} = \frac{4}{12}[/tex]

Step 3: add the numerators:

[tex]\frac{6}{12} + \frac{4}{12} = \frac{10}{12}[/tex]

Step 4: reduce your fraction

[tex]\frac{10}{12} = \frac{5}{6}[/tex]

Hope that helps

Fraction multiplication

2/4 x 1/3

We reduce the fraction 2/4 to its lowest expression by extracting and canceling 2.

1/2 x (1/3)

Multiply 1/2 by 1/3 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

1 x 1/2 x 3 =====> Multiply

1/6  ====> Answer

the coordinates of point c is (9/2, -3/2)

The original coordinate = C(6, -2)

scale factor r =3/4

New coordinate (c) = scale factor × the original coordinate

c = 3/4(6, -2)

c = (3/4×6, -2×3/4)

c = (18/4, -6/4)

c = (9/2, -3/2)

Hence, the coordinates of point c is (9/2, -3/2)

Given:

The linear equations are,

The objective is to solve by elimination method.

The equations can be rearranged as,

To solve the equation, multiply equation (1) b

The given inequality is,

The graph of the inequality will be shown below

Answer:

Slope is -2!

y= -2x

Step-by-step explanation:

Based on the 2 points given: (3, -6) (-3, 6)

Answer:

The well-desgined graph has an appropriate scale for the y-axis. By appropriate we mean that the scale is such that all points on the graph can be discerned easily. In other words, the scale is not too wide or too narrow.

For graph A, the scale is such that the data points are at such a distance from each other that their values can be easily read off. On the other hand, for graph B, there isn't enough vertical distance between the data points for them to be easily read.

The distance between Noor's house and her grandparent's house is 37.40 miles or if rounded off to the nearest tenth, it will be 40 miles using the estimation concept.

As per the question statement, Noor’s family is meeting her grandparents at a restaurant and the restaurant is 24.5 miles from Noor’s house but this is 65.5% of the distance from Noor’s house to her grandparents’ house.

We are supposed to find the distance between Noor's house and her grandparent's house. We will use the concept of estimation.

Distance between Noor's house and restaurant = 24.5 miles

Let distance between Noor's house and her grandparent's house be "x" miles.

So the distance between grandparent's house and restaurant = x - 24.5

Now it is given that 24.5 miles is 65.5% of the distance from Noor’s house to her grandparents’ house.

So, 65.5% of x = 24.5

(65.5*x)/100 = 24.5

65.5*x = 2450

x = 2450 / 65.5

x = 37.40 miles

If rounded off to the nearest tenth mile, we get

x = 40 miles.

So, the distance between Noor's house and her grandparent's house is 37.40 miles or if rounded off to the nearest tenth, it will be 40 miles.

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Answer:

y = 6.75x

Step-by-step explanation:

$33.75 ÷ 5 = $6.75

$47.25 ÷ 7 = $6.75

So we have y = 6.75x.

Answer:

130 miles

Step-by-step explanation:

65×2=130 So if I am driving at a rate of 65 mph then in one hour I drive 65 miles. Since it is in 2 hours I will have driven 130 miles.

Answer:

130 miles.

Step-by-step explanation:

so it said that the car is traveling 65 miles per hour and it wants to know how far it would go in 2 hours. so if 1 hour is 65 miles if we multiply it by two then we will get

65 miles = 1 hour

130 miles = 2 hours

The result of the expression 3x-(2x+10) for x = [tex]7\frac{5}{13}[/tex] is -2.61

The expression is

3x-(2x+10)

The expression is the mathematical sentence with a minimum of two variables and at least one math operation.

The value of the x = [tex]7\frac{5}{13}[/tex]

Convert the mixed fraction to the simple fraction

[tex]7\frac{5}{13}[/tex] = 96/13

Convert the simple fraction to the decimal form

96/13 = 7.39

Substitute the value of x in the given expression 3x - (2x + 10)

= 3 × 7.39 - (2×7.39 + 10)

Multiply the terms first

= 22.17 - (14.78 + 10)

= 22.17 - (24.78)

= -2.61

Hence, the result of the expression 3x-(2x+10) for x = [tex]7\frac{5}{13}[/tex] is -2.61

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Answer:

True

Step-by-step explanation:

Matching sides of two or more polygons are titled corresponding sides,and matching angles are titled corresponding angles . If two figures are lookalike,then the measures of the corresponding angles are similar and the ratios of the lengths of the corresponding sides are proportional .

Answer:

2

Step-by-step explanation:

So to get the answer we need to figure out what x is

2×2=4

so x has to be 2

Using properties of exponents, it is found that Mia's first mistake is described as follows:

Mia made a mistake in Step 3. She simplified the exponents 16 and -8 incorrectly. She should have subtracted them.

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, as follows:

3^0 x 3^(16) = 3^(0 + 16) = 3^16.

Hence the Step 1 is correct.

For the power of power rule, we keep the base and multiply the exponents, hence:

(3^(-4))² = 3^(-4 x 2) = 3^(-8).

Hence the Step 2 is correct.

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, as follows:

3^16/(3^(-8)) = 3^(16 - (-8)) = 3^(16 + 8) = 24.

Which is Mia's mistake, as she did not subtract the exponents.

The steps are missing and are given by the image at the end of the answer.

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