Which equation justifies why seven to the one third power equals the cube root of seven?

seven to the one third power all raised to the third power equals seven to the one third plus three power equals seven
seven to the one third power all raised to the third power equals seven to the three minus one third power equals seven
seven to the one third power all raised to the third power equals seven to the one third times three power equals seven
seven to the one third power all raised to the third power equals seven to the one third minus three power equals seven

The number of nickels and the number of dimes that Violet has is 10 nickles and 11 dimes.

Given:

Violet has $1.60 worth of nickels and dimes. She has a total of 21 nickels and dimes altogether.

Let nickles be n and dimes be d.

From statement given:

n + d = 21

n = 21 - d

1 dimes = 10 cents , 1 nickle = 5 cents and $1 = 100 cents.

n + d = $1.60

convert into cents

5n + 10d = 160

divide by 5 on both sides

n + 2d = 32

n = d - 21 substitute in n + 2d = 32

21 - d + 2d  = 32

d + 21 = 32

d = 11

Hence number of dimes = 11

substitute d = 11 in n = 21 - d

n = 21 - 10

n = 10

Hence number of nickles = 10

Therefore the number of nickels and the number of dimes that Violet has is 10 nickles and 11 dimes.

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Answer:

12 answer

Step-by-step explanation:

(8x-34)=(5x+2) (correspounding angle)

8x-5x=34+2

3x=36

x=36/3

x=13

Answer:

38

Step-by-step explanation:

:) hope this helps

a) An example of a countably infinite set that is not a subset of R is the set of all natural numbers (N).

b) It is impossible to have an uncountable set with a countable subset.

a) An example of a countably infinite set that is not a subset of R (the set of real numbers) is the set of all natural numbers (N). The set N = {1, 2, 3, 4, ...} is countably infinite because it can be put into a one-to-one correspondence with the set of positive integers. However, N is not a subset of R because it only contains whole numbers and does not include any fractional or decimal values.

b) It is impossible to have an uncountable set with a countable subset. This is known as Cantor's theorem, which states that the cardinality of a power set (the set of all subsets) of a given set is always strictly greater than the cardinality of the original set. In other words, the number of subsets of an uncountable set is always larger than the number of elements in any countable subset. Therefore, it is not possible to have an uncountable set that contains a countable subset.

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Probability is nothing but the ratio of favorable cases to all possible cases or in simple terms it is the ratio of sample set to all set

We are required to find all the cases in which sum of any two bills is 20$ or more

The total number of bills are two $ 1 bills, two $ 5 bills, two $ 10 bills, and two $ 20 bills.

The total case of drawing any two bills will be =

2 for $ 1 bill x two for 5$ bill x two for 10$ bill x two 20$ bills

=2 x 2x2x2 =16

Hence 16 ways in which two bills can be drawn at random

Cases in which bill can be greater than 20$= (1,20)(20,1)(5,20)(20,5)(10,10)(20,10)(10,20) (20,20)= 8 cases

Hence, total number of possible outcomes = 8

Hence the probability of bill to be 20$ or more= favorable outcome/total outcome

=8/16 =1/2

Hence the probability is 1/2

Disclaimer: the fraction sign is missing in question options

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Answer:

then babies babies babies

Step-by-step explanation:

thats what huhh

Answer: 67 babies

Step-by-step explanation:

10 babies + 1000 more babies = 110 babies

110 babies crying - 53 babies not crying = 67 babies crying

67 babies crying = a retired nanny

Answer:

24.5 m/s

Because this acceleration is attributable to gravity, G into T, it turns out to be zero plus 9.8 into 2.5, which is 24.5 m/s.

Step-by-step explanation:

Hope this helps

Answer: y = 3

Step-by-step explanation:

4(-1)+8y=20

negative * positive = negative

-4+8y=20

add 4 on both sides to isolate 8y

8y = 24

divide each side by 8

y = 3

Answer:

\(y=3\)

Step-by-step explanation:

Step-By-Step on how to solve for y is in the attached picture.

Hope this helps! :)

\(\sin^2\alpha-\cos^2\alpha=2\sin^2\alpha-1\\\sin^2\alpha+\cos^2\alpha=1\)

This is the Pythagorean identity, therefore \(\alpha\in\mathbb{R}\).

Step-by-step explanation:

please mark me as brainlest

To solve the problem, we used the distance formula and the midpoint formula. Distance formula is used to find the distance between two points in a coordinate plane. Whereas, midpoint formula is used to find the coordinates of the midpoint of a line segment.

The distance between p and q is 13, and the midpoint of the line segment pq has coordinates (1, -7/2). The given points are p(-5, -6) and q(7, -1).

Therefore, we have:$$d = \sqrt{(7 - (-5))^2 + (-1 - (-6))^2}$$

$$d = \sqrt{12^2 + 5^2}

= \sqrt{144 + 25}

= \sqrt{169}

= 13$$

Thus, the distance between p and q is 13.

The distance between p and q was found by calculating the distance between their respective x-coordinates and y-coordinates using the distance formula. The midpoint of the line segment pq was found by averaging the x-coordinates and y-coordinates of the points p and q using the midpoint formula. Finally, we got the answer to be distance between p and q = 13 and midpoint of the line segment pq = (1, -7/2).

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Answer:28

Step-by-step explanation:

Break it up! 6x3 is 18. Then 18 + 10 is 28 :P

Hope this helps :D

Answer:

The value is -3

Step-by-step explanation:

Here in this question, we are interested in making the expressions on both sides of the equation equal. But we seek a particular value or number which when placed in front of the quadratic expression on the right hand side makes the equations equal.

To get this done with, we will need to factorize the expression on the left hand side of the equation.

Thus, we can write;

-27x^2 + 9x + 12 as 3(-9x^2 + 3x + 4)

What do we notice? we can see that the now factored quadratic expression resembles what we have on the right hand side asides there fact that we are not there yet in terms of sign.

Thus, we can finally write ;

-27x^2 + 9x + 12 as -3(9x^2 -3x -4)

This exactly gives the expression on the right hand side

Thus the value to place in the blank is -3

Answer:

225

Step-by-step explanation:

(- 15)² = - 15 × - 15 = 225

Answer:

Step-by-step explanation:

You plug in the number of lawns mowed for "n"

So 1 lawn would be 15(1)  (15 times 1)

15(1)=15

15(2)=30

15(3)=45

15(4)=60

15(5)=75

15(6)=90

15(7)=105

15(8)=120

15(9)=135

15(10)=150

and so on

Answer:

increase

Step-by-step explanation:

if your number gets bigger it's increase

if it gets smaller it's decrease

Step-by-step explanation:

Hope this helps, happy learning!!!

The diagram of translatation FGH 3 units down and 2 units left followed by a rotation counterclockwise 90° is attached below.

Dilation is the process of increasing the size of an item without affecting its form.

Depending on the scale factor, the object's size can be raised or lowered.

The translate FGH 3 units down and 2 units left followed by a rotation counterclockwise 90°.Then followed by a dilation by a scale factor of 2.

F ( -1, 0)

G (1, 0)

H ( -1, 1)

Thus, counterclockwise 90°

F' ( 0, 1)

G' (0, -1)

H' ( -1, -1)

Scale factor = 2

Then

F'' ( 0, 2)

G'' (0, -2)

H'' ( -2, -2)

The diagram of translatation FGH 3 units down and 2 units left followed by a rotation counterclockwise 90° is attached below.

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A: Two proportions from independent samples would be used to answer this question.

After comparing the percentage of runners that typically wear sunscreen on a run to the percentage of bikers that typically wear sunscreen on a bike ride. The survey is comparing the percentage of runners who wear sunscreen to the percentage of bikers who wear sunscreen, which is a comparison of two proportions. The samples of runners and bikers are independent since they are two separate groups being compared, and the design is not matched or paired in any way. Therefore, option A is the correct choice.

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According to Siegler, the pattern of learning math concepts involves a gradual development and refinement of strategies. Siegler's theory, known as the overlapping waves model, suggests that learners use multiple strategies simultaneously and gradually shift towards more efficient ones over time. This process allows for a better understanding and application of math concepts, ultimately leading to improved problem-solving skills.

According to Siegler, the pattern of learning math concepts involves a gradual progression from using counting strategies to more efficient and accurate strategies. Children initially rely on counting strategies to solve math problems, such as counting fingers or objects. As they progress, they begin to use more advanced strategies, such as decomposition or mental math, which allow them to solve problems more quickly and accurately. Siegler also emphasizes the importance of practice and repetition in developing math skills and the role of feedback and instruction in promoting learning. Overall, Siegler's theory suggests that children's math skills develop through a combination of innate abilities and environmental factors, including exposure to math concepts and opportunities for practice and instruction in time.

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The average speed of the train and the bus is 50 miles per hour.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

The average speed is defined as the total distance travelled by the object in the total time.

Given that valentine travels 70 miles to Rome by train and then takes a bus 30 miles to the coliseum. the bus travels 24 miles per hour slower than the train. The total time travelling on the bus and train is 2 hours.

The average speed is calculated as,

Average speed= Total distance / total time

Average speed = (70 + 30) / 2

Average speed = 100 / 2

Average speed = 50 miles per hour

Therefore, the average speed of the train and the bus is 50 miles per hour.

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Answer:

The highest common factor of 21 and 6 is 3

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Because there are 4 different trim levels, 5 different colors, and 3 different interiors, you have to multiply 4 x 5 x 3.

4 x 5 x 3= 60

Answer:

7/8

Step-by-step explanation:

3/8 + 4/8 = 7/8

While the measurement of the individual angles in a triangle can vary depending on the size and shape of the triangle, their sum is always 180 degrees.

This fundamental concept is known as the Triangle Sum Theorem and is true for all types of triangles, including equilateral, isosceles, and scalene. This theorem is essential in geometry and plays a significant role in solving various mathematical problems related to triangles. By knowing the sum of the angles, it is possible to calculate the measurement of one missing angle if the other two are known. Additionally, it helps in proving congruence and similarity of triangles and finding various geometric properties of triangles.

While the measurement of the individual angles in a triangle can vary, their sum is always constant. This constant sum is 180 degrees. This principle is known as the Triangle Sum Property, which states that the three interior angles of any triangle will always add up to 180 degrees, regardless of the triangle's shape or size. To find the sum of the angles, you simply add the three angle measures together. For example, if a triangle has angles of 60, 70, and 50 degrees, the sum would be 60 + 70 + 50 = 180 degrees. This property holds true for all triangles, ensuring that their interior angles always have a constant sum.

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Answer:

9)  C = 6\(\pi\) units

standard form : (x + 7)² +(y + 5)² = 9²

12) C = 8√5 \(\pi\) units

standard form : (x + 3)² +(y + 2)² = ( \(\sqrt{80}\))²

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

interior angle + exterior angle = 180°

162° + exterior angle = 180° ( subtract 162° from both sides )

exterior angle = 18°

the sum of the exterior angles of a polygon = 360° , then

number of sides = 360° ÷ 18° = 20

Answer: It is either 0.13 or 13/100

For given function the rule obtained when finding f^(-1) is ±√[(x + 4)/3]

In this question, we have been given a function f(x) = 3x² - 4

We need to write the rule obtained when finding f^(-1)

Le f(x) = y          ........(1)

y =   3x² - 4

We find the value of x.

3x² = y + 4

x² = (y + 4)/3

x = ±√[(y + 4)/3]

From (1),

f^{-1}(y) = ±√[(y + 4)/3]

Since the choice of the variable is arbitrary, we can write this as ,

f^{-1}(x) = ±√[(x + 4)/3]

Therefore, for given function the rule obtained when finding f^(-1) is  ±√[(x + 4)/3]

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Based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

Chebyshev's Theorem states that for any given number k greater than 1, at least (1 - 1/k²) of the data values in a dataset will fall within k standard deviations of the mean.

In this case, we have a sample size of 225 bags and a mean weight of 353 gm with a standard deviation of 6 gm.

To find a lower bound for the number of bags that weigh between 335 and 371 gm, we need to calculate the range within k standard deviations of the mean.

First, let's find the number of standard deviations for the given range:

Lower range: (335 - 353) / 6 = -3

Upper range: (371 - 353) / 6 = 3

Since we want to find the lower bound, we consider the lower range and use its absolute value: |-3| = 3.

Now, we can use Chebyshev's Theorem to find the lower bound:

(1 - 1/k²) ≤ (1 - 1/3²) = 1 - 1/9 = 8/9

This means that at least 8/9 of the bags will fall within 3 standard deviations of the mean.

To find the lower bound for the number of bags, we multiply this probability by the sample size:

Lower bound = (8/9) * 225 = 200

Therefore, based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

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Answer:

5/12, $10

Step-by-step explanation:

Lea earned $24 babysitting. She spent ⅔ of that amount on a gift for her bestie, ¼ on snacks. What fraction of her earning is left? How much money does she have left?

Let the total amount earned be 1

Given

Amount on snacks = ¼

Amount on babysitting = ⅔

Required

Fraction left

Fraction left = Total -(snacks+babysitting)

Fraction left = 1-(1/4+2/3)

Fraction left = 1-(3+4/12)

Fraction left = 1-7/12

Fraction left = 5/12

Amount of money she has left = 5/12 × 24 = 5×2 = $10

Hence she has $10 left

Answer:

1st one

Step-by-step explanation:

spinner colours: green, blue, red

card colours: purple, green

possible outcomes:

green + purple

green + green

blue + purple

blue + green

red + purple

red + green

Answer:

A.

Step-by-step explanation:

Match the table units.

If you look at each inside cell, it matches what your result is.

Hope this helps. Have a nice day.

(Make sure that each cell matches with each color.)