A map is drawn using the scale 2 cm:100 mi. On the map, Town B is 3.5 centimeters from Town A, and Town C is 2 centimeters past Town B. How many miles apart are Town A and Town C?
A.) 275 miles
B.) 200 miles
C.) 550 miles
D.) 1,100 miles​

Answer:

The solution is:

Part A. [tex]\sqrt{5}^{\frac{7k}{3}})[/tex] which is sqrt(5)^7k/3[/tex]

Part B. k = 18/7

Step-by-step explanation:

Part A.

To solve this part, we're going two use THREE important properties of exponents:

1. [tex](x^{n})^{m} = x^{nm}[/tex]

2. [tex]\frac{x^{n}}{x^{m}} = x^{n-m}[/tex]

3. [tex]\sqrt[n]{x^{m}} = x^{\frac{m}{n} }[/tex]

Let's work the numerator using the properties 1, 2 and 3:

[tex](\sqrt{5}^{3} )^{\frac{k}{9} } }  = (\sqrt{5}^{3\frac{k}{9}}) = (\sqrt{5}^{\frac{k}{3}})[/tex]

Let's work the denominator using the properties 1, 2 and 3:

[tex](\sqrt{5}^{6} )^{-\frac{k}{3} } }  = (\sqrt{5}^{6\frac{k}{3}}) = (\sqrt{5}^(2k))[/tex]

Now dividing the numerator by the denominator:

[tex]\sqrt{5}^{\frac{k}{3}-(-2k)})=\sqrt{5}^{\frac{7k}{3}})[/tex]

Part B

if [tex]5^{\frac{3}{2} } 5^{\frac{3}{2}} = \sqrt{5}^{\frac{7k}{3}})[/tex]

Then:

[tex]5^{3} = 5^{\frac{7k}{6}})[/tex]

So [tex]\frac{7k}{6}} = 3[/tex]

Solving for k, we have:

k = 18/7

Answer:

translated left by 2 units

Step-by-step explanation:

Given y = f(x) then

y = f(x ± a) represents a horizontal translation of a units

• If + a then a shift of a units to the left

• If - a then a shift of a units to the right

Hence

g(x) is the graph of f(x) translated 2 units to the left

The function g(x) = (x+2)^2 + 1 is a transformation of the function f(x) = x^2 + 1. It represents a translation of the graph of f(x) to the left by 2 units.

The function g(x) = (x+2)^2 + 1 is a transformation of the function f(x) = x^2 + 1. Particularly, it's a horizontal shift, not a compression or stretching of the graph. By comparing coefficients, we infer that the +2 inside the parentheses on g(x) represents a shift of the graph of f(x) to the left by 2 units. This is because the rules of transformations dictate that h(x) = (x - h)^2, where h represents a shift to the right, and h(x) = (x + h)^2 represents a shift to the left. Therefore, the correct statement is that the graph of g(x) is translated left 2 units compared to the graph of f(x).

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Answer:

y=1 + [tex]\frac{4x}{5}[/tex]

x=-[tex]\frac{5}{4}[/tex] + [tex]\frac{5y}{4}[/tex]

ANSWER

The correct answer is A.

EXPLANATION

The given triangle is a right isosceles triangle because one angle is 90° and the base angles will be 45° each.

This means that:

[tex]a = b[/tex]

Using, the Pythagorean Theorem, we have

[tex] {a}^{2} + {a}^{2} = {(9 \sqrt{2} )}^{2} [/tex]

We simplify to get:

[tex]2{a}^{2} = 81 \times 2[/tex]

[tex]{a}^{2} = 81[/tex]

Take positive square root,

[tex]a = \sqrt{81} [/tex]

This implies that

[tex]a = 9[/tex]

Therefore b is also equal to 9

The correct answer is A.

Answer: option a

Step-by-step explanation:

You can use these identities:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

Then, to find "a" you know that:

[tex]\alpha=45\°\\adjacent=a\\hypotenuse=9\sqrt{2}[/tex]

Substituting:

[tex]cos(45\°)=\frac{a}{9\sqrt{2}}[/tex]

Now you must solve for "a":

[tex]a=cos(45\°)(9\sqrt{2})\\\\a=9in[/tex]

To find  "b", you know that:

[tex]\alpha=45\°\\opposite=b\\hypotenuse=9\sqrt{2}[/tex]

Substituting:

[tex]sin(45\°)=\frac{b}{9\sqrt{2}}[/tex]

Now you must solve for "b":

[tex]b=sin(45\°)(9\sqrt{2})\\\\b=9in[/tex]

Answer:

Step-by-step explanation:

(2x-6)(2x-5)

2(x-3)(2x-5)

^ fully factored

x-3=0       2x-5=0

x=3          2x=5

                 x=5/2

Answer: This series would have no last term. The general form of the infinite geometric series is a1+a1r+a1r2+a1r3+... , where a1 is the first term and r is the common ratio.

Step-by-step explanation:

Answer:

[tex]S_{\infty}=\frac{80}{3}[/tex]

Step-by-step explanation:

The sum of an infinite geometric series is given by:

[tex]S_{\infty}=\frac{a}{1-r}[/tex],

The given geometric series is

[tex]\sum_{n=1}^{\infty}32(-\frac{1}{5})^{n-1}[/tex]

The constant ratio for this series is

[tex]r=-\frac{1}{5}[/tex]

The first term of the series is [tex]a=32(-\frac{1}{5})^{1-1}=32[/tex]

The sum to infinity is [tex]S_{\infty}=\frac{32}{1--\frac{1}{5}}[/tex]

[tex]\implies S_{\infty}=\frac{32}{\frac{6}{5}}=\frac{80}{3}[/tex]

Answer:

y = x + 3

y = 3x²

y = [tex]3^{x}[/tex]

Step-by-step explanation:

Relationship1

y = x + 3

y = (0) + 3 = 3

y = (1) + 3 = 4

y = (2) + 3 = 5

Relationship 2

y = 3x²

y = 3(0)² = 0

y = 3(1)² = 3

y = 3(2)² = 3(4) = 12

Relationship 3

y = [tex]3^{x}[/tex]

y = [tex]3^{0}=1[/tex]

y = [tex]3^{1}=3[/tex]

y = [tex]3^{2}=9[/tex]

Answer:

C

Step-by-step explanation:

Use the formula for the volume of a cylinder.

[tex]V=\pi r^2h[/tex]

Plug in the height, the radius, and 3.14 for [tex]\pi[/tex].

[tex]V=3.14(15^2)(5) \\ \\ V=3.14(225)(5) \\ \\ V=3.14*1125 \\ \\ V=3532.5[/tex]

If you round that number you'll get [tex]V=3533[/tex].

So the answer is answer choice C.

Answer:

Choices are:

p>30

p<30

p=30

not enough information to tell

Answer is p>30

Step-by-step explanation:

Since there are more boys than girls, there must be at least 9 boys.  Plug into equation:  (b+8) represents number of students.  If they each have at least 2 pencils we would use 2(b+8).  Plugging in  9 for the boys we have: 2(9+8)=?

2(17)=34.  So with the minimum number of boys there would be at least 34 pencils, so the answer is p>30

Final answer:

By calculating that p equals 2 times the sum of boys and girls, and that there are at least 9 boys, we find that p (the total number of pencils) must be greater than 30.

Explanation:

To compare the expressions p and 30, let us first define p as the total number of pencils. Since there must be more boys than girls and there are 8 girls, let b represent the number of boys. We can say that b > 8, since there are more boys than girls.

It's also given that each student has at least 2 pencils. Therefore, the minimum total number of pencils p can be calculated by multiplying the total number of students by 2.

This gives us p = 2(b + 8). Because b > 8, let's substitute the minimum number for boys (9), so p = 2(9 + 8) = 34.

Therefore, p > 30.

Answer:

478 people

Step-by-step explanation:

All you need to do for this problem is simply multiply 239 by 2. If the first 6 rows are 239 people, and so are the next 6, that's all you need to do.

239*2=478

Answer:

28

Step-by-step explanation:

Using PEMDAS (or something similar) start off with the exponent.

5^2 would equal 25 since it is multiplying 5 by itself.

Then, you would add 3 to 25 making the answer 28.

For this case we must find the value of the following expression:

[tex]3 + 5 ^ 2 =[/tex]

We have that, replacing in a calculator:

[tex]5 ^ 2 = 5 * 5 = 25[/tex]

Rewriting the expression we have:

[tex]3 + 25 =[/tex]

Equal signs are added and the same sign is placed:

[tex]3 + 25 = 28[/tex]

Answer:

[tex]3 + 5 ^ 2 = 28[/tex]

Subtract x from both sides

2x + 3 - x = -4

Simplify 2x + 3 - x to x + 3

x + 3 = -4

Subtract 3 from both sides

x = -4 - 3

Simplify -4 - 3 to -7

x = -7

2x+3=x-4

2x-x= -4-3

x= -7

Check answer by using substitution method

2(-7)+3= -7-4

-14+3=-11

-11=-11

Answer is x=-7

Answer:

The answer is x=2

Step-by-step explanation:

Answer:

B x = 2

Step-by-step explanation:

As you can see you have to find out what equals 4 AND what equals 12 and to make sure:

Do 2x2 is 4 because 4 times 1 yes but 6 times 1 is not 12 its 26 therefore C is INCORRECT

A Is Also wrong because 6 x 1 is 6 sure yes 4 x 1 is for but they both have to be equal so A is INCORRECT

And Is wrong because 8 x 4 is 32 but we are looking for what equals 4 not 32 and 6 x 8 is 48 we are looking for a 12 so D is INCORRECT

Now what leaves is B well 2 x 2 =4 and 2 x 6 = 12 Therefore B is Correct! Another way you can do this is to divide 12 ÷ 6 = 2 and 4 ÷ 2 = 2

Hope this helps!

Answer:

a. 0.25

b. 0.4

c. 0.66 repeating

d. 0.75

Step-by-step explanation:

a. 1/4 is equal to one quarter which is 0.25

b. 2/5 is equal to 4/10 which equals 0.40 or 0.4

c. 2/3 is 0.6666666 and goes on forever so we would call that a repeating decimal

d. 3/4 is equal to three quarters which would be 0.75

i hope this helps :)

1/4=0.25 2/5=0.4 2/3=0.666666666666667 3/4=0.75

ANSWER

The car moves at 32 mi/hr

EXPLANATION

This question is asking us to determine how fast is a train that makes 330 mile trip in 4 hours.

This is the same as calculating the speed of the train:

Speed = distance covered/time taken

The distance covered is 330 mile

The time taken is 4 hours.

Speed =330/4 =82.5 mi/hr

Answer:

$0.75

Step-by-step explanation:

$0.35+$0.40=$0.75

Answer:

Step-by-step explanation:

.75 cents

Answer:

[tex]\large\boxed{q\geq-8}[/tex]

Step-by-step explanation:

[tex]7q-5\leq10q+19\qquad\text{add 5 to both sides}\\\\7q\leq10q+24\qquad\text{subtract 10q from both sides}\\\\-3q\leq24\qquad\text{change the signs}\\\\3q\geq-24\qquad\text{divide both sides by 3}\\\\q\geq-8[/tex]

Answer:

1. same standard deviation, different means

2. same mean, different standard deviation

3. median is higher than the mean

4. mean is higher than the median

Step-by-step explanation:

Answer:

51.3

Step-by-step explanation:

This is a right triangle (because of the 90° angle).  For any right triangle, you can use the following:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

You can remember this as SOH-CAH-TOA.

We want to find the angle y.  We know that the opposite side is 10 and the adjacent side is 8.  So we can use tangent:

tan y = 10 / 8

y ≈ 51.3°

Answer:

Where are the answer choices?

Step-by-step explanation:

Answer:

C: f(x) = (x - 5)(x + 1)

Step-by-step explanation:

Answer

90 degrees , it's a right angled triangle

Step-by-step explanation:

180 - 65 - 25 = 90

The sum of all the interior angles of a triangle equals 180 degrees

a right angled triangle has one 90 degree angle and two different angles

Answer:

The measurement of the third angle is 90 degrees

Step-by-step explanation:

There are 180 degrees in a triangle.

180 - 65 = 115 - 25 = 90

It is a right angled triangle

Answer:

The short leg is 7 because half of 14 is 7 and the hypotenuse is always twice as long as the shortest one.

The required short leg is 7inches.

Given that,

Hypotenuse = 14 inches,

In triangle 30-60-90

We have to determine,

By using figure find the short leg.

According to the question,

A 30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º.

The triangle is special because its side lengths are always in the ratio of 1: √3:2.

The 30-60-90 triangle rule is for finding the the lengths of two sides when one side is given.

The shorter side is opposite the 30 degree angle, the longer side is opposite the 60 degree angle, and the hypotenuse is opposite the 90 degree angle.

Therefore,

The hypotenuse is always twice as long as the shortest one.

Where, Hypotenuse = 14inches

Then,

[tex]Hypotenuse = 2 \times short \ leg \\\\14 = 2 \times short \ leg\\\\short\ leg = \dfrac{14}{2}\\\\short \ leg = 7[/tex]

Hence, The required short leg is 7inches.

To know more about Pythagoras theorem click the link given below.

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Answer: 14/25 = 56/100

               11/20 =  55/100

               14/25 > 11/20

Step-by-step explanation:

The least common multiple of 20 and 25 is 100.

(100 = 20*5, 25*4)

So we can take the common denominator 100.

14*4/25*4 =56/100. ∴14/25 = 56/100

11*5/20*5  =55/100. ∴11/20  = 55/100

56>55

∴56/100 > 55/100

∴14/25 > 11/20

Hope it's good;)

Answer: 48

Step-by-step explanation:

336/7=48

Answer:

48

Step-by-step explanation:

Well, 336/7 is 48

There are 13 shoppers aged 20 or older. Calculated by summing frequencies of age groups 20-24 through 35-39. Answer: (c) 13.

Of course, I'm happy to help! To find out how many shoppers are at least 20 years old, we need to add up the frequencies of the age groups that are 20 years old and older. Here are the steps:

1. Identify the age groups that are 20 years old and older.

2. Add up the frequencies (the number of shoppers) for those age groups.

Let's assume the histogram provides age groups in 5-year intervals, starting from 0 to 4 years old, then 5 to 9 years old, and so on.

Let's look at the age groups that are at least 20 years old:

1. 20-24 years old

2. 25-29 years old

3. 30-34 years old

4. 35-39 years old

5. 40-44 years old

We add up the frequencies for these age groups:

1. Frequency for 20-24 years old: 5

2. Frequency for 25-29 years old: 4

3. Frequency for 30-34 years old: 3

4. Frequency for 35-39 years old: 1

5. Frequency for 40-44 years old: 0 (since it's not specified in the histogram, we assume it's 0)

Adding these frequencies together:

5 + 4 + 3 + 1 + 0 = 13

So, there are 13 shoppers who are at least 20 years old.

The answer is (c) 13.

[tex]f^{-1} (x)=3+\frac{x}{2}[/tex]

Answer:

f(x)^-1 = 1/2x +3

Step-by-step explanation:

f(x) = 2x-6

y =2x-6

Exchange x and y and solve for y

x = 2y -6

Add 6 to each side

x+6 = 2y

Divide by 2

(x+6)/2 = 2y/2

(x+6)/2 =y

1/2x +3 =y

This is the inverse of f(x)

f(x)^-1 = 1/2x +3

Answer: C. Mode

Step-by-step explanation:

Qualitative data applies to observable data such as reoccurring patterns (mode)

Quantitative data applies to numbers and numerical calculations (Mean, Median)

Mode is the best way to analyze qualitative data as it makes the analysis easier.

Mode is the most frequently occurring value in the data.

Qualitative data is the descriptive and conceptual findings collected through questionnaires, interviews, or observation. Analyzing qualitative data allows us to explore ideas.

For example

Each child’s gender

His or her favorite color

Whether he or she owns at least one pet

How he or she gets to and from school

In order to analyze the above data,  Mode is the best method because the mode is the most frequently occurring value in data and one can easily analyze the data.

Therefore,  Mode is the best way to analyze qualitative data.

To get more about mode refer:

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Answer:25%

Step-by-step explanation:

Because 2 is only a quarter of 8 and 25%=quarter from 100%

Answer:

25%

Step-by-step explanation:

Answer:

E = 3(62)

E = 3(36)

E = 108

Answer:

See below  

Step-by-step explanation:

This question is about estimation of volumes. Think of a 2 L bottle of pop or a 2 L carton of milk. Could its contents fit inside