Which choices are equivalent to the expression below? Check all that apply. (3/8)^3

A. (3^3/8^3)
B. 27/512
C. 24
D. 3^18
E. 3^5
F. 9/7

Please answer I would really appreciate it.​

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:

10/20 for green, then 4/19 for blue. 10/20 * 4/19 = 2/19

Step-by-step explanation:

Explanation is above. If you need any more help let me know.

Answer:

The smaller number is 240.

Step-by-step explanation:

The question says that the larger number is 300, so 5 has to be 300.

4:5

?:300

You can use cross-multiplication or find the scale factor to find the answer.

Cross-multiplication:

4 × 300 ÷ 5 = 240

Finding the scale factor:

300 ÷ 5 = 60

4 × 60 = 240

The smaller number is 240.

Answer:

Step-by-step explanation:

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▹ Answer

(x₁, y₁) = (-2, 0)

(x₂, y₂) = (1, -3)

▹ Step-by-Step Explanation

y = x² - 4

y = -x - 2

x² - 4 = -x - 2

x = -2

x = 1

y = -(-2) - 2

x = 1

y = 0

y = -1 - 2

y = 0

y = -3

(x₁, y₁) = (-2, 0)

(x₂, y₂) = (1, -3)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

(-2,0) (1,-3)

Step-by-step explanation:

The solution to the system is where the two graphs intersect.

The two graphs intersect at two different points  (-2,0) and at (1,-3)

Answer: 2/3

Step-by-step explanation:

First you multiply both numerators which equals 8

Then, you multiply the denomerators which is 24

This gives you 8/24

Since both 8 and 24 are divisible by 8, you divide them by 8 and you get 1/3

Since two negative numbers equal a positive one, the answer is positive

The minimum number of bricks Salah will have to buy is 4050 bricks

Given that the

So, the length of walkway plus garden, L = 40 ft + 18 ft = 58 ft. The width of walkway plus garden, W = 17 ft + 18 ft = 35 ft.

We now need to find the area of the walkway.

Area of walkway, A" = area of walkway plus garden - area of garden

= LW - lw

= 58 ft × 35 ft - 40 ft × 17 ft

= 2030 ft² - 680 ft²

= 1350 ft²

Now, since each brick is 6 inches wide and 8 inches long, the area of each brick is A' = 6 in × 8 in  = 48 in²

So, the number of bricks required, n = area of walkway/area of brick

= 1350 ft²/48 in²

= 1350 × 144 in²/48 in²

= 194400 in²/48 in²

= 4050 bricks

So, the minimum number of bricks Salah will have to buy is 4050 bricks

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FALSE. The number of dots in a dotplot of a bootstrap distribution is equal to the size of the bootstrap sample, not the original sample.

In a bootstrap analysis, multiple samples of the same size are drawn from the original sample with replacement, creating a distribution of sample statistics. The dotplot of this distribution represents the frequency of the sample statistics and can help us understand the variability of the original sample.

The number of dots in the dotplot reflects the number of bootstrap samples, which can be much larger than the original sample size. Therefore, the number of dots in the bootstrap distribution can be different from the size of the original sample.

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Step-by-step explanation:

"times" is always the indication for multiplication. we do things over and over again so and so many times.

like when adding the same number several times.

e.g.

3+3+3+3+3

then I added the number 3 five times.

now, I could do all the basic additions, or I could simply say 3×5.

a multiplication is simply the short form of doing the same addition multiple times.

of course, in such a simple example we could easily do both, but it really gets annoying to do e.g. 3256 × 635 as single additions ...

so, the original question was : how many times as many dimes does he have than quarters?

he has 10 dimes and 2 quarters.

so, the numbers in play are 10 and 2.

therefore, the question really is, how many times is 10 of 2 ? or nicer : how many times of 2 is 10 ?

how often, how many times do I need to add 2 to get 10 ?

so, what do I need to multiply with 2 to get 10 ?

I am sure, you see the answer already.

formally in math we try to express such "riddles" as equations with the unknown and to be determined element as a generic variable named most of the time by a single letter like "x".

so, or problem here looks like

2*x = 10

"x" is what I have to multiply 2 with to get 10.

what value is that "x" ?

well, the beauty of such an equation is - we simplify it by performing the same operation on both sides of the "=" sign without changing its meaning.

so, we can divide both sides by 2 and get

x = 10/2 = 5

and that is our solution and answer.

he has 5 times as many dimes as he has dollars.

Answer: A solution to an equation is a number that can be plugged in for the variable to make a true number statement. Example 1: Substituting 2 for x in.

Step-by-step explanation:

,11

Step-by-step explanation:

let's face it.

100-45=55. 55/5=11

therefore,The maxium number is 11

The value of x is 7/3, which can be rounded to two decimal places as approximately 2.33.

To solve the equation 2x + 8 + 4x = 22, we need to combine like terms and isolate the variable x.

Combining like terms, we have:

6x + 8 = 22

Next, we want to isolate the term with x by subtracting 8 from both sides of the equation:

6x + 8 - 8 = 22 - 8

6x = 14

To solve for x, we divide both sides of the equation by 6:

(6x) / 6 = 14 / 6

x = 14/6

Simplifying the fraction 14/6, we get:

x = 7/3

Therefore, the value of x is 7/3, which can be rounded to two decimal places as approximately 2.33.

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The plane EFG  in the rectangular prism is parallel to plane ABC.

In this question, we have been given the rectangular prism ABCDEFGH

We need to find the plane which is parallel to plane ABC.

We can observe that in given rectangular prism,

plane ABH is parallel to the plane CDF

plane BCE is parallel to the plane AGF

plane EFG is parallel to plane ABC.

Therefore, the plane EFG  in the rectangular prism is parallel to plane ABC.

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Answer:

what

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the identity

sin²x + cos²x  = 1 then

sin²x = 1 - cos²x

sin x = ± \(\sqrt{1-cos^2x}\)

Given cos θ = \(\frac{2}{3}\) , then

sinθ = ± \(\sqrt{1-(\frac{2}{3})^2 }\) = ± \(\sqrt{1-\frac{4}{9} }\) = ± \(\sqrt{\frac{5}{9} }\) = ± \(\frac{\sqrt{5} }{3}\)

Also

tanθ = \(\frac{sin0}{cos0}\)

       = \(\frac{\frac{\sqrt{5} }{3} }{\frac{2}{3} }\)

       = \(\frac{\sqrt{5} }{3}\) × \(\frac{3}{2}\) = ± \(\frac{\sqrt{5} }{2}\)

Answer & Step-by-step explanation:

In this problem, we are given two functions.

s(x) = 2x + 1

r(x) = -x² + 3x

We are asked to find the difference between s(x) and r(x).

(2x + 1) - (-x² + 3x)

Distribute the negative to the second parentheses.

2x + 1 + x² - 3x

Combine like terms and put the equation in standard form. This means the exponents should be in descending order.

x² - x + 1

So, (s - r)(x) equals x² - x + 1

Answer:

(2x-1) - (-x^2 +3x)

THEN

x^2  - x + 1

Step-by-step explanation:

Since youre subtracting r from s...

s(x) = 2x + 1

r(x) = -x^2 + 3x

you subtract the two to get an equation for the first step.

(s-r)(x) = (2x+1) - (-x^2 +3x)

for the next step, you're simplifying...

distribute the minus: (2x+1) + x^2 - 3x

combine like terms: x^2 + 1 - 1x

which gives you the answer of...

x^2  - x + 1

Hope this helps!!

Answer:

B

Step-by-step explanation:

B is the only one that has only 2 sides of the same length and one that doesn't match the other 2.

A doesn't have any of the lengths being the same

C. is a right triangle, although there can be isosceles right triangles they still need to have only 2 lengths that are the same and in this one, all the values are different

D. This is an equilateral triangle, this has more than 2 lengths that are the same

For 160 calories and 20 grams of carbohydrates 0.61 cups are required.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of carbohydrates.

For 160 calories the number of cups will be calculated as,

1 cup = 260 calories

160 calories = ( 160 ) / 260 cups

160 calories = 0.61 cups

Therefore, for 160 calories and 20 grams of carbohydrates 0.61 cups are required.

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The standard error for the estimate of the proportion of all persons aged 65 and over with osteoarthritis is 0.0092.

The subset chosen from the larger set to make assumptions is known as a random sample. Standard Error can be defined as the term that measures the accuracy of the sample distribution which represents the population.

We know that,

                   Standard Error   =   √ ( P ( 1 - P ) / n )    → 1

As per the given question,

Substitute the values in 1,

Standard Error ( SE )   =   √ ( P ( 1 - P ) / n )

                                    =   √ ( 0.115 ( 1 - 0.115 ) / 1200 )

                                    =   √ ( 0.115 ( 0.885 ) / 1200 )

                                    =   √ ( 0.101775 / 1200 )

                                    =   √ ( 0.0000848125)

Standard Error ( SE )   =   0.0092093702   ≅   0.0092

Therefore, 0.0092 is the standard error for the estimate of the proportion of all persons aged 65 and over with osteoarthritis.

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Answer:9.64

Step-by-step explanation:

smart :!

Answer:

each pencil costs 11 cents

Step-by-step explanation:

1.35 divided by

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

i.) x=4 and y=8

ii.) x=9 and y=4

iii.) x=4 and y=9

b.)  -36

Step-by-step explanation:

i.)

Since the coefficient of x is 2 times greater then that of y, we know that the value of y must be 2 times greater than x so that they total 0. This means that x=4 and y=8.

4x - 2y = 0

4(4) - 2(8) = 0

16 - 16 = 0

0 = 0

ii.)

To make the equation the greatest value possible, you want x to be the greatest value possible and for y to be the least possible value, so the least amount is subtracted. This will mean that x=9 and y=4.

3x - 2y

3(9) - 2(4)

27 - 8

19

iii.)

To make the equation the least value possible, you want x to be the smallest value possible and for x to be the greatest possible value, so the most amount is subtracted. This will mean that x=4 and y=9.

3x - 2y

3(4) - 2(9)

12 - 18

-6

b.)

4 ( a - 3b )  

4 ( -8 - 3(1/3) )

4 ( -8 - 1 )

4 ( -9 )

-36

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The last digit  of \(196^{213}*213^{196\) is 6.

What is Number theory?

The characteristics and connections of integers are studied in number theory, a subfield of mathematics. The study of numbers' structures, characteristics, and patterns, as well as how they relate to other mathematical ideas, are the main topics.

Numerous subjects fall under the broad category of number theory, such as prime numbers, divisibility, modular arithmetic, congruences, diophantine equations, number patterns, and many more.

It examines fundamental ideas including prime factorization, prime number distribution, principles for divisibility, and characteristics of integer arithmetic operations.

Focusing on the final digits of each phrase and looking for any patterns will help us determine the final digit of the formula \(196^{213}*213^{196\).

First, let us examine the last digit of \(196^{213}\).

Six is the 196th and final digit. Every time we increase 6 by any power, the final digit repeats itself in a cycle: 6,

\(6^2 = 36\) (the last digit is 6),

\(6^3 = 216\) (the last digit is 6),

and so on.

The final digit of \(196^{213\) will also be 6, as 213 is an odd exponent.

Let us now think about \(213^{196}\) final digit.

213 has a final digit of 3. Any time we multiply 3 by a power, the last digit always has a consistent pattern: 3,

\(3^2 = 9,\)

\(3^3 = 27\) (last digit is 7),

\(3^4 = 81\) (last digit is 1),

\(3^5 = 243\) (last digit is 3),

and so on.

The final digit of \(213^{196\) will be 1, as 196 is an even exponent.

By multiplying the final digits of each phrase, we can now get the expression's final digit: 6(1) = 6.

The last digit of \(196^{213}*213^{196\) is therefore 6.

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Answer:

  cylinder, has the least surface area

Step-by-step explanation:

We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.

__

We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.

The relevant formulas are ...

  V = LWH

  A = 2(LW +H(L +W))

for length L, width W, and height H.

a) prism 1

The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...

  V = (8 in)(8 in)(5 in) = 320 in³

  A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²

b) prism 2

The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...

  V = (10 in)(8 in)(4 in) = 320 in³

  A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²

__

The relevant formulas are ...

  V = πr²h

  A = 2πr(r +h)

for radius r and height h.

c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...

  V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³

  A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²

__

The relevant formulas are ...

  V = 1/3s²h

  A = s(s +2H)

for base side dimension s, vertical height h, and slant height H.

d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...

  V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³

  A = (10 in)(10 in + 2×14 in) = 380 in²

__

The proposed figures have volume and area (rounded to the nearest unit) as follows:

  \(\begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}\)

The proposed cylinder requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.

_____

Additional comment

For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.

Answer:

-1(-4)=-5

Step-by-step explanation:

as h = -1