22 miles in 20 minutes 38 miles in 30 minutes

Given:

A model of a famous statue is [tex]3\dfrac{1}{2}[/tex] inches tall. The actual statue is [tex]5\dfrac{1}{4}[/tex] feet tall.

To find:

The the ratio of the height of the model to the height of the actual statue in simplest form.

Solution:

We have,

Height of the model = [tex]3\dfrac{1}{2}[/tex] inches

Height of the actual statue = [tex]5\dfrac{1}{4}[/tex] feet.

Now, the ratio of the height of the model to the height of the actual statue is:

[tex]\text{Ratio}=\dfrac{\text{Height of model}}{\text{Height of actual statue}}[/tex]

[tex]\text{Ratio}=\dfrac{3\dfrac{1}{2}\ in.}{5\dfrac{1}{4}\ ft}[/tex]

[tex]\text{Ratio}=\dfrac{\dfrac{3(2)+1}{2}\ in.}{\dfrac{5(4)+1}{4}\ ft}[/tex]

[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{\dfrac{21}{4}\ ft}[/tex]

We know that 1 ft = 12 in.

[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{\dfrac{21}{4}\times 12\ in.}[/tex]

[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{21\times 3\ in.}[/tex]

[tex]\text{Ratio}=\dfrac{7}{2\times 21\times 3}[/tex]

[tex]\text{Ratio}=\dfrac{1}{2\times 3\times 3}[/tex]

[tex]\text{Ratio}=\dfrac{1}{18}[/tex]

Therefore, the ratio of the height of the model to the height of the actual statue in simplest form is [tex]\dfrac{1}{18}[/tex].

Answer:

15 miles

Step-by-step explanation:

They both ran a total of 9 laps and 9 laps = 27 miles

This means each lap is 3 miles.

So Luigi ran 15 miles cause he ran 5 lap and each lap is 3 miles

Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

[tex]1)\, XY=XZ[/tex]                                              Given

[tex]2) \text{ $ m\angle Y= m\angle Z$}[/tex]                                        Isosceles Triangle Theorem

[tex]\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}[/tex]                  Angle Addition

[tex]\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}[/tex]                               Given

[tex]5) \text{ $m\angle XYQ=m\angle QYZ$}[/tex]                           Definition of Bisector

[tex]\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}[/tex]                               Substitution

[tex]7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}[/tex]              Angle Addition

[tex]8)\text{ $ZP$ bisects $\angle XZY$}[/tex]                              Given

[tex]\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }[/tex]                          Definition of Bisector

[tex]\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}[/tex]                            Substitution

[tex]11)\text{ } 2m\angle QYZ=2m\angle PZY[/tex]                    Substitution

[tex]12)\text{ }m\angle QYZ=m\angle PZY[/tex]                        Division Property of Equality

[tex]13)\text{ } YZ=YZ[/tex]                                         Reflexive Property

[tex]14)\text{ } \Delta YZP\cong\Delta ZYQ[/tex]                             Angle-Side-Angle Congruence*

[tex]15)\text{ } YQ=ZP[/tex]                                         CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

Answer:

this is your answer. look at this once.

Answer:

A

Step-by-step explanation:

We are given:

[tex]\cos(22f-1)=\sin(7f+4)[/tex]

Recall the co-function identity:

[tex]\sin(\theta)=\cos(90-\theta)[/tex]

Let θ = 7f + 4. So:

[tex]\sin(7f+4)=\cos(90-(7f+4))[/tex]

Substitute:

[tex]\cos(22f-1)=\cos(90-(7f+4))[/tex]

Remove the cosine:

[tex]\displaystyle 22f-1=90-(7f+4)[/tex]

Distribute:

[tex]22f-1=90-7f-4[/tex]

Subtract:

[tex]22f-1=-7f+86[/tex]

Add 7f and 1 to both sides:

[tex]29f=87[/tex]

Therefore:

[tex]f=3[/tex]

Answer:

explanation below

Step-by-step explanation:

f(x) = 3x + 2

f(8) : replace x with 8    f(8) = 3 * 8 + 2 = 26

g(x) = 5x

g(a+2) : replace x with a+2    g(a+2) = 5 (a+2) or 5a + 10

Answer:

-1x or -x

Step-by-step explanation:

4 divided by -4

Answer:

19

Step-by-step explanation:

46x0.84=38.64

That means you have to score at least a 39 to pass.

19 students have 39 or better.

Answer:

9.33333 inches.

Step-by-step explanation:

700 / 75?

Answer: The answer is a > 50.45 since the amount of A is larger than 50.45

Step-by-step explanation:

Answer: 710,000 kg

Step-by-step explanation:

There are 100 pence in one pound.

The number of two pence coins in 1 pound is therefore:

= 100 / 2

= 50 coins

In 2 million pounds therefore, there will be:

= 50 * 2,000,000

= 100,000,000 two pence coins

If one coin weighs 7.1g, weight is:

= 100,000,000 * 7.1

= 710,000,000 g

A kg is 1,000 grams so the weight in kg is:

= 710,000,000/1,000

= 710,000 kg

Answer:

i think  

3 ,  

12

12 ,  

48

48 ,  

192

192  ,  

768

768

Answer:

A line that crosses the y-axis but not the x must be horizontal. Therefore, it has no slope.

Answer:

See step by step

Step-by-step explanation:

The student found the cosine of angle A not the sine. Sine is Opposite/Hypotenuse. This student found Adjacent/Hypotenuse. The correct answer is Sin A= 12/13.

first of all it is not in the form of A. P because d=a2-a1=9-5=4,a3-a2=14-9=4,a4-a3=18-14=4,a5-a4=5-18= -13,a6-a5=23-5=18

Answer:

35

Step-by-step explanation:

Please look at the attachment down below.

Hope this helped! :)

The  sum of three number is 35.

A square number is the result when a number has been multiplied by itself.

For example, 25 is a square number because it's 5 lots of 5, or 5 x 5.

Given:

if the number given is 9

9² - (9 - 1)² = 9² - 8²

                 = 81-64

                  = 17.

if the number given is 6.

6² - (6 - 1)² = 6² - 5²

                 = 36-25

                 = 11.

if the number given is 4.

4² - (4 - 1)²= 4² - 3²

                = 16-9

                = 7.

Thus, the sum of three number is

=17 + 11 + 7

= 35

Learn more about square here:

https://brainly.com/question/14198272

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Answer:

The answer is 6.

Step-by-step explanation:

This is how I do it, there are other ways too but,

add up the ratio 5+7=12

36 (students total) divided by 12 = 3

find the difference between the ratio, which is 2.

multiply 2 by 3 and you get 6.

Answer:

Step-by-step explanation:

b hbbjnhbjjnh

Answer:

y- intercept = 30

Step-by-step explanation:

The y- intercept is the value on the y- axis (vertical) where the graph crosses

Each square on the vertical has a value of 10

The graph crosses the vertical axis 2 squares below 50.

Then y- intercept = 30

Answer: 4x+8<120

x<28

Step-by-step explanation:

As per the statement in the question, the inequality will be 4x + 8 < 136.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the instructions given in the question,

The length (l) of the rectangle = x+4

The width (w) of the rectangle = x

As per the formula of the perimeter, P:

P = 2 (l + w)   (i)

Put the values in (i)

P = 2 (x + 4 + x)

P = 2x + 8 + 2x

P = 4x + 8

Then the inequality as per the statement in the question will be,

4x + 8 < 136.

To know more about inequality:

https://brainly.com/question/28823603

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Answer:

no solution

Step-by-step explanation:

the lines are parallel, they never intersect.

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

Answer:

slope is m= y_2-y_1/x_2-x_1 and the y-intercept is where the line crosses over the x-axis

Step-by-step explanation:

fill in the points and do the equation m= rise(y points)/ run(x points)

m=slope

(x_1, y_1) =coordinates of first point in the line

(x_2, y_2)=coordinates of second point in the line

Answer:

2x+5=5x-1​ =2 so it sould be one soulution

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

Here, we want to get the domain

The domain refers to the possible x values of the function

As we can see, the plot extends thoroughout the entirety of the graph

This extends from positive infinity to negative infinity

This means that the domain is all real

numbers

9514 1404 393

Answer:

  33 ft²

Step-by-step explanation:

Each triangle's area is given by the formula ...

  A = (1/2)bh

  A = (1/2)(3 ft)(4 ft) = 6 ft²

The square base area is given by ...

  A = s²

  A = (3 ft)² = 9 ft²

__

The total area of the pyramid is the area of the base plus the area of four triangular faces.

  Total Area = (9 ft²) + 4(6 ft²) = (9 +24) ft²

  Total Area = 33 ft²

Answer:

a+c=27

195a+320c=6515

Step-by-step explanation:

adult (a): 195

children (c): 320

total $: $6515

child $: 27

a+c=27 --> c=-a+27

195a+320c=6515

sub the first equation into the 2nd equation to get a=17

sub a=17 into c=-a+27 to get c=10

so, an adult ticket is $17 and a child ticket is $10.

Answer:

Option 3

Step-by-step explanation:

SAS Triangle Congruence Theorem

Answer:

option- 3 which is sas theorum

1c is equal

1d not equal

1b is equal

1a is not equal