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Using proportions, it is found that the speed of the sports car is of 85 miles per hour.

A proportion is a fraction of a total amount.

The cars are moving in the same direction, hence their relative speed is the difference of them.

The sports car is 0.5 miles faster over one minute, hence over one hour the difference is:

60 x 0.5 = 30 miles per hour.

Considering that the utility vehicle has a speed of 55 mph, the speed of the sports car is given by:

55 + 30 = 85 miles per hour.

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Answer:

............

Step-by-step explanation:

Answer:

x = a/7

Step-by-step explanation:

Area is length x width, so let's call our unknown, the length, x

So the total area is 7 (the width) times x

If the total area is a, then we can write the equation a = 7(x)

Next, we have to isolate the variable for the length, x

To do this, we divide both sides by 7, leaving a/7 = x, or x = a/7

Answer:

Did this at school today… the answer is F. 7(1+5x)

Step-by-step explanation:

rewrite 35 as 7x5

Rewrite 7 as 7x1

That will be 7(5x+7x1) factor out the 7 and the answer will be 7(5x+1)

The length of arc ABC with center O and radius of 9 units is 13π.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let r represent the radius of the circle. Hence:

arc ADC = (100 / 360) * 2πr

5π = (100 / 360) * 2πr

r = 9 units

arc ABC = (260 / 360) * 2π(9) = 13π

The length of arc ABC with center O and radius of 9 units is 13π.

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Answer: 58.33%

Step-by-step explanation:

So, Liz flipped the coin a total of 60 times

Let this be the denominator.

Probability of coin landing up: 35/60

Probability of coin landing down: 24/60

We need the probability of the coin landing up.

So, convert 35/60 into a percentage

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1003560 × 100100= (35 × 10060) × 1100 = 58.33/100

So, the probability is 58.33%

The two common retirement accounts that allow people to minimize their tax bills are tax-deferred and tax-exempt accounts. Just to be clear, both types of retirement account minimize the amount of lifetime tax expenses someone will incur, which provides incentives to start saving for retirement at an early age.

Hope this helps :)

The pints of ice cream for the students is an illustration of metric units

Nadia needs 12 pints of ice cream for the 24 students

The given parameter is:

Students = 24

She needs one cup for each student in the class.

So, the number of cups needed is:

Cups = 24

1 cup makes 1/2 pint.

So, we have:

Pint = 1/2 * 24

Pint = 12

Hence, Nadia needs 12 pints of ice cream for the 24 students

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Answer: x=99.54

Step-by-step explanation:

Answer:

94.2

Step-by-step explanation:

We are given a reference angle of 34, we are also given opposite and hypotenuse side of the triangle, following SOHCAHTOA, We know that to solve this question, we have to use sine.

sin(34) = x/178

Get x alone

178sin34 = x

178sin34 is equal to 94.17, since we are looking for one decimal, we can round to the tenths place. The number next to the tenths is seven so we round up.

Our answer is 94.2

Answer:

Mean is 73.2. Median is 85. Mode is 85. Range is 47.

Step-by-step explanation:

First order the numbers. 46, 58, 72, 85, 85, 93. The mode is all of these numbers added up to get 439. divided by the amount of numbers there are. there are 6. so 439 divided by 6 is 73.166 or 73.2. Median is the middle of the data set which is 85. the mode is the number that appears the most in a data set which is also 85. the range is the highest number minus the lowest number so we get 93 - 46 to get 47.

Answer:

Step-by-step explanation:mode 85

mean 73.2

median 85

range 47

Distance measure how far an object have gone. The length of the line segment that has the endpoints A (-3,2) and B (1,0) is 2√5.

The formula for calculating the distance between two coordinates is expressed as:

D = √(x2-x1)²+(y2-y1)²

Given the coordinate points A (-3,2) and B (1,0), the length of the line segment that has the endpoint is given as:

D = √(0-2)²+(1+3)²
D = √(2)²+(4)²
D = √16+4
D=√20
D = 2√5

Hence the length of the line segment that has the endpoints A (-3,2) and B (1,0) is 2√5

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Answer: Plant A

Step-by-step explanation: In the graph for plant A, the X axis is the months and the Y Axis is the inches. You can compare the data for Plant B in the graph for Plant A and see that Plant A has a larger number of inches for each number of months. For example, if you look at 6 months. The chart for Plant B says Plant B is 3 inches, while if you look at 6 months on the graph for Plant A, Plant A is at 10 inches.

Answer:

k=10

Step-by-step explanation:

The reason is that we should solve the following equation:

4k+5 + 6k+10 + (180-115) = 180

by doing some basic algebra we get:

10k = 100

thus: k=10

Answer:

  x = 13

Step-by-step explanation:

The relevant fact about vertical angles is that they are congruent, their measures are equal. This lets you write an equation relating the expressions for the measures of angles A and B.

__

  ∠A = ∠B

  (8x -12)° = (6x +14)° . . . . . substitute given expressions

  2x = 26 . . . . . . . . . . . divide by °, add 12-6x

  x = 13 . . . . . . . . . . divide by 2

Answer:

Answer to question 1 is 18

Answer to question 2 is 4/5

Step-by-step explanation:

Question one simply asks how much one controller is

Being that both controllers = 36$

And to find one controller price you would just divide the price by the number of units

36/2= 18

The second question asks how much pizza would be more .6, 4/5 or .8, or .75

Since .8 has the most value or in this case pizza 4/5ths is the answer

Answer:

Step-by-step explanation:

x1= -3

y1= -4

m=5

y-y1=m(x-x1)

y-(-4)=5(x-(-3))

y+4=5(x+3)

y+4=5x+15

y=5x+15-4

y=5x+11

Answer:

426.16

Step-by-step explanation:

v=r^2h π

π =3.14

v=6^2*4*3.14

v=426.16

The Net profit margin is 22.41%

Rusty's Tool experienced $67550 in net sales, creating a gross profit of $50338.

If Rusty had a total operating expense of $35200 then we have to find the net profit margin.

Since profit $50338 includes the operating expense of $35300 then net profit will be

= $50338 - $33500

= $15138

Now the selling price is given as $67550.

Profit margin = (Net profit/selling price) 100

Profit margin =151.38/675.50=22.41 %

Therefore, the answer is profit margin = 22.41%.

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Answer:

  37°

Step-by-step explanation:

Angle ECF is vertical to angle ACG, so has the same measure. Angle ACG is the second acute angle in right triangle ACG, so is complemetary to angle CAG. It has measure ...

  ∠ECF = ∠ACG = 90° -∠CAG = 90° -53°

  ∠ECF = 37°

Answer:

40/2 = 20

20/2 = 10

10/2 = 5

5/2 = 2.5

2.5/2 = 1.25

Answer:x^2-9y^2

Step-by-step explanation:

x timesx +x(-3y)+3yx+3y(-3y)

Then simplify

X^2-9y^2

Step-by-step explanation:

the answer shoukd be 324

because in cube there are 6 sides

and one side contain 54 box

so... 54 × 6 = 324

Answer:

Hi mate!

[tex] \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} } = \sec( \theta) - \tan( \theta) [/tex]

Step-by-step explanation:

By taking LHS,

[tex] \maltese \: \: \large \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} } [/tex]

[tex] : \longrightarrow \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} \times \frac{1 + \sin( \theta)}{1 + \sin( \theta)} } \\ \\ : \longrightarrow \frac{ {( \sqrt{1 + \sin\theta }) }^{2} }{( \sqrt{1 - \sin( \theta)})(\sqrt{1 + \sin( \theta)}) } \\ \\ : \longrightarrow \frac{ {( \sqrt{1 + \sin\theta }) }^{2} }{ \sqrt{ {1}^{2} - { \sin}^{2} \theta } } \: \\ \\ : \longrightarrow \: \frac{1 + \sin \theta}{ \cos \theta } \\ \\ \longrightarrow \: \frac{1}{ \cos \theta } + \frac{ \sin \theta}{ \cos \theta} [/tex]

[tex] \: \: \: \: \: \bigg\lgroup \because \: \frac{1}{ \cos \theta }\: = \sec \theta \: \\ \: \: \: \: \: \: \: \: \: \: \: \frac{ \sin \theta}{ \cos \theta} = \tan \theta \bigg \rgroup[/tex]

[tex] \implies \boxed{\pink{ \sec \theta + \tan \theta }}[/tex]

Now taking RHS

[tex] \sf \sec \theta + \tan \theta [/tex]

[tex]\implies \: \: \frac{1}{ \cos \theta } + \frac{ \sin \theta}{ \cos \theta} \\ \\ \implies \frac{1 + \sin \theta }{ \cos \theta } [/tex]

Hence, proved

Answer:

[tex]\large{\pink{\underline\textsf{To Prove :-}}}[/tex]

[tex] \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } = \sec \theta + \tan \theta[/tex]

[tex] \huge{\orange{\underline{\textsf{Solution :-}}}}[/tex]

[tex] \sf \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } [/tex]

[tex] \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } \times \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } \\ \sqrt{ \frac{ {(1 + \sin \theta) }^{2} }{(1 + \sin \theta)(1 - \sin \theta) } } \\ \sqrt{ \frac{ {(1 + \sin \theta) }^{2} }{1 - { { \sin}^{2} \theta } } }[/tex]

[tex] \sqrt{ \frac{( {1 + \sin \theta })^{2} }{ { \cos}^{2} \theta} } \\ \frac{1 + \sin \theta }{ \cos \theta } \\ \frac{1}{ \cos \theta} + \frac{ \sin \theta }{ \cos \theta } [/tex]

[tex]\sf{\red { \sec \theta + \tan \theta}}[/tex]

[tex] \sf \huge \purple {HENCE \: \: PROVED! }[/tex]

Answer:

Step-by-step explanation:

pi = 3.14

h = 2.60 m

d = 160.0 cm

Radius

r = d/2

r = 160.0 / 2

r = 80.0 cm

height

There are 100 cm in 1 meter. The units have to agree.

2.6 m * 100 cm / m

2.6 * 100 = 260 cm

Formula

V = pi * r^2 * h

V = 3.14 * 80^2 * 260

V = 5224960 cm^3

If you want a more manageable number, you could convert this into m^3

That's done by

V = 5224960 / 1000000 = 5.22 m^3

Answer:

x = ± [tex]\sqrt{3}[/tex]

Step-by-step explanation:

3x² - 9 = 0 ( add 9 to both sides )

3x² = 9 ( divide both sides by 3 )

x² = 3 ( take square root of both sides )

x = ± [tex]\sqrt{3}[/tex]

or

3x² - 9 = 0 ← factor out 3 from each term

3(x² - 3) = 0

equate x² - 3 to zero and solve for x

x² - 3 = 0 ( add 3 to both sides )

x² = 3 ( take square root of both sides )

x = ± [tex]\sqrt{3}[/tex]

The correct statements about the two-way frequency table are:

Option A, Option C, and Option E.

In Mathematics and statistics, A two-way frequency table is a tabular method for displaying relative data for two categories of variables. (See the attached).

The question (attached) shows that:

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Answer:

The answer is a,c, e

Step-by-step explanation:

31°

hope it helps......!!!!!

where are u from and why u need thes answer

Answer:

C

Step-by-step explanation:

Step 1

Step 2