2/9( 9/4x - 9)
Simplify

The expression with rational exponents as a radical expression by extending the properties of integer exponents is, [tex]\sqrt[6]{3}[/tex]

The exponents that should be integers are those that are. It may be an integer that is either positive or negative. It specifies how many times the base number should be multiplied by itself using positive integer exponents.

Given:

The given expression is,

[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6} } }[/tex]

We know that,

[tex]\frac{x^{a} }{x^{b}}= x^{a-b}[/tex]

[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}} = 3^{\frac{1}{3}-\frac{1}{6}}[/tex]

[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}=3^{\frac{1}{6} }[/tex]

Therefore,

[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}=\sqrt[6]{3}[/tex]

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Answer: 12 free throws

Step-by-step explanation:

40 * 7/10=

280/10=28 free throws made

40-28=12 free throws missed

If boy can mow a lawn in 90 minutes and his sister can mow the same lawn in 60 minutes, then it will take 36 minutes to mow the lawn if both mowing at the same time

Given,

The time taken for the boy to mow a lawn= 90 minutes

The time taken for the sister to mow a lawn= 60  minutes

Work done by the boy in one minute= [tex]\frac{1}{90}[/tex]

Work done by the sister in one minute= [tex]\frac{1}{60}[/tex]

When both mowing at the same time

[tex]\frac{1}{90}+\frac{1}{60}=\frac{1}{36}[/tex]

Then, the time taken when both mowing at the same time = 36 minutes

Hence, if boy can mow a lawn in 90 minutes and his sister can mow the same lawn in 60 minutes, then it will take 36 minutes to mow the lawn if both mowing at the same time

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Answer:

Step-by-step explanation:

A composite number is a whole number greater than 1 that has more than two factors

Given,

The conditions,

We know, composite number is a number that has more than 2 factors

Prime number is a number that has two factors, one and itself.

Here, number is a whole number greater than 1 that has more than two factors

So, the given number is composite number

Hence, a composite number is a whole number greater than 1 that has more than two factors

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Answer:

-3<x<1

(-3,1)

Step-by-step explanation:

it is shown as (-3,1) because x is anything inbetween -3 and 1 and those numbers are not included so you use ( ) as opposed to [ ]

3/4 a number b divided by 5 is 15b/4

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction).

3/4 a number b:

=3b/4

Divided by 5:

=3b/4/5

We have to multiply numerator with the dominator by 5 to remove the double fraction:

=3b*5/4

=15b/4

3/4 a number b divided by 5 is 15b/4

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The value of a and the value of b is 6 and 5.

We can solve this problem by few steps, If we change the representation of power by replacing all powers according to √x or [tex] {x}^{1/2} [/tex]. We know that, [tex] {x}^{m/n × n/b } = {x}^{m/b} [/tex]

So, using this we can write, [tex] {4x}^{1/2 \times 6} + {x}^{1/2 \times 10/2} = {4 \sqrt{x} }^{6} + { \sqrt{x} }^{5} [/tex]..............(1)

Now if we compare the value of ( 1 ) with

[tex] {4 \sqrt{x} }^{a} + { \sqrt{x} }^{b} [/tex], we can easily find out the value of a and b and it is, a = 6 and b = 5

Thus, the value of a and b is 6 and 5.

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The complete question is -

Driven that 4x^ 3+x^ (5/2) all over √x can be written in the form 4√x^a+√x^ b, write down the value of a and the value of b.

Step-by-step explanation:

well, the starting equation and the target format have been given.

let's do the multiplications and compare the target with the starting information.

from there we see what is different or missing.

x² + 14x + 13 = 0

and

(x - p)² = q

x² - 2px + p² = q

x² - 2px + (p² - q) = 0

now let's compare the different parts :

x² = x²

-2px = 14x

-2p = 14

p = -7

p² - q = 13

-7² - q = 13

49 - q = 13

36 - q = 0

q = 36

so, the square (x - p)² = (x + 7)² is completed when

x² + 14x + 49 = 0

but we have only "+ 13". so we need to add 36 to get 49. but we need to do it on both sides, to keep the equation true :

x² + 14x + 13 + 36 = 36

x² + 14x + 49 = 36

(x + 7)² = 36

just as we calculated already above.

and now this can be solved by pulling the square root on both sides (a quadratic equation has always 2 solutions)

x + 7 = ±6

x1 = 6 - 7 = -1

x2 = -6 - 7 = -13

The mass of the biscuit and fruit are 20 and 64 grams respectively.

A ratio indicates how many times one number contains another.

Therefore, the ratio of fruits and biscuit the zoo fed the monkeys is 7:5.

let's find the total number of the items.

Hence, using the table and ratio,

number of fruits = 7 / 12 × x

number of fruits = 28

Therefore,

28 = 7x / 12

cross multiply

12 × 28 = 7x

336 = 7x

divide both sides by 7

336 / 7 = 7x / 7

x = 48

Hence,

mass of biscuit = 5 / 12 × 48

mass of biscuit = 20

The second missing value of the table,

mass of biscuit = 5 / 12 × x

45 = 5x / 12

5x = 504

x = 504 / 5

x = 108

Hence,

mass of fruit = 7 / 12 × 108

mass of fruit = 756 / 12

mass of fruit = 63

Therefore, the mass of the biscuit and fruit are 20 and 64 grams respectively.

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Answer:yes

Step-by-step explanation:fact

The probability of scoring a goal exactly 8 times by Jon is given by 0.0234. It is obtained using the prerequisite knowledge of binomial distribution and probability.

What is Binomial Distribution in Probability?

When each trial has a probability of occurring equally likely, then the number of trials or observations is outlined using the binomial distribution. The chance of observing a specific number of successful outcomes in a specific number of trials is determined by using the binomial distribution.

Calculation of the probability of the given event

Total no. of possible outcomes, n = 11

The probability that Jon will kick the ball in the net, p(x) = 0.4

The probability that Alex will kick the ball in the net, q(x) = 0.6

Using Binomial Distribution, we get,

P(x = r) = C(n,r) × (p)r × q(n - r)

where x is the score made by Joe

P(x = 8) = C(11,8) × (0.4)8 × (0.6)3

             = 0.0234

Hence, the probability that Jon will score exactly 8 times is 0.0234.

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Answer:

Hope this helps :)

19/20 = 95/100 = 95%

9/16 = 0.5625 = 56.25%

0.4 = 4/10 → 40/100 = 40%

0.22 = 22/100 = 22%

There are 3 whole number with different values of x.

All positive integers from 0 to infinity are included in the group of numbers known as whole numbers. The number line has these numbers. They are all genuine numbers as a result. Although not all real numbers are whole numbers, we may argue that all whole numbers are real numbers. As a result, the set of natural numbers plus zero may be used to define whole numbers. The category of whole numbers and the negative of natural numbers is known as integers. Thus, integers can be either positive or negative, including 0. Natural numbers, whole numbers, integers, and fractions all fall under the category of real numbers.

Whole numbers refer to all natural numbers, including '0,' in their entirety. Examples include: 0, 11,1,2,3,4 etc

As stated in the question,

Then, in order to determine which values of "x" the given fraction is a square for, we must first locate them.

We are aware that the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Now, from the above factors of 48 only (3,12 & 48) of can give us a square number.

Therefore,

Hence, There are 3 whole number with different values of x.

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The equation of the perpendicular bisector of the line segment whose endpoints are (-8,-1) and (-4,5) is y = 3/2x + 7

First we have to find the midpoint of the line

endpoints are (-8,-1) and (-4,5).

midpoint = -8 + -4/2 , -1 +5/2

= -6, 2

slope = -1 - 5 / -8 - -4

= -6 /-4

= 3 / 2

Equation for the line

y - 2 = 3/2(x + 6)

y = 3/2(x + 6)-2

y = 3/2x + 7

Hence the equation of the perpendicular bisector of the line segment whose endpoints are (-8,-1) and (-4,5) is y = 3/2x + 7

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Sample correlation B  = R in output = 0.7 The above data is calculated from parameter estimation.

The Pearson correlation coefficient (PCC) is a statistical measure of linear correlation between two data sets. It is also referred to as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or simply the correlation coefficient. It is a normalised covariance measurement, with the result always falling between 1 and 1. It is the ratio between the covariance of two variables and the product of their standard deviations. The measure, like covariance itself, can only account for linear correlations between variables and ignores numerous other kinds of connections or correlations.

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Answer: -6 7/8

Step-by-step explanation:

-2 1/4 - 4 5/8=

(-2 1/4 - 4 5/8)*8/8=     ==> Multiply by 8 since it is the LCM of 4 and 8 and will get rid of denominators

(-16 8/4 - 32 40/8)/8=

(-(16+2)-(32+5))/8=

(-18-37)/8=

-55/8=

-(48+7)/8=-6 7/8

The image after the composition is X''(9, -1), Y'(13, -5), and Z''(14, -3)

The vertices of the triangle are given as:

X(2, 4), Y(6, 0), and Z(7, 2)

The compositions of translations are given as:

Translation: (x, y) → (x + 12, y + 4)

Translation: (x, y) → (x − 5, y − 9)

So, we have:

Translation: (x, y) → (x + 12, y + 4)

X'(2 + 12, 4 +4), Y'(6 + 12, 0 + 4), and Z'(7 + 12, 2 + 4)

Evaluate

X'(14, 8), Y'(18, 4), and Z'(19, 6)

Translation: (x, y) → (x − 5, y − 9)

X''(14 - 5, 8 - 9), Y'(18 - 5, 4 - 9), and Z'(19 - 5, 6 - 9)

Evaluate

X''(9, -1), Y'(13, -5), and Z''(14, -3)

Hence, the image after the composition is X''(9, -1), Y'(13, -5), and Z''(14, -3)

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The equation representing the inequality is 2·x² + 16·x + 32 ≥ 254

The width of the photo on the cake is x.

The dimensional relationship mentioned between the dimensions of the cake & the photo on the cake mentioned in the question are:

Width of cake = Width of photo + 4 inches

i.e., W = x + 4

And, Length of the Cake is twice the Width of the cake

i.e., L = 2*W

Also, It is mentioned that the Area of the Cake is 254 sq inches.

We know Formula to calculate the Area of a rectangle is :

          =>   Area = Length * Width

          =>   254  ≤ 2*W * (x+4)     =>   254 ≤ 2(x+4)*(x +4)

          =>   2·x² + 16·x + 32 ≥ 254

Hence, The inequality representing this case is 2·x² + 16·x + 32 ≥ 254

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Kurt organized a bike race that was 84 miles long. All 469 riders completed the race. 39,396 miles were biked in all

Kurt organized a bike race = 84 miles long

All 469 riders completed the race

miles were biked in all :

Total miles =84 Multiply By 469

=39,396 miles

39,396 miles were biked in all

Miles :

A mile is a unit of distance equal to 1760 yards or approximately 1.6 kilometers

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A 84-mile cycling race that Kurt planned took place. The race was completed by all 469 cyclists. All told, 39,396 miles were pedaled

Kurt planned an 84-mile cycling race.

The race was completed by all 469 cyclists.

total number of miles cycled:

Miles total = 84; multiply by 469.

=39,396 miles

All told, 39,396 miles were pedaled

Miles:

Approximately 1.6 kilometers or 1760 yards make up a mile as a unit of measurement.

Answer:

x = 7

y = 3

Step-by-step explanation:

Because the opposite side, Line segment QR, is 11. So, you need to find a number that when multiplied by 2 and then subtracted by 3 is equal to 11.

First, I just guessed, that 7 times 2 is 14, and then minus 3 is equal to 11

Here is how I worked it out:

2x-3=11

2x=14

x=7

8y+5=6y+11

2y=6

y=3

The value of the variable x and y will be 7 and 3, respectively.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

The rectangle PQRS is shown.

From the rectangle PQRS, the side PQ and RS are congruent. And the side PS and QR are also congruent.

PQ = SR

6y + 11 = 8y + 5

2y = 6

y = 3

PS = QR

2x - 3 = 11

2x = 14

x = 7

The value of the variable x and y will be 7 and 3, respectively.

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la 2. es multiplicand 20 por 18 da 360 y ese número se multiplicand por 500 da 180000 . 3se suma y da 1025 la.4 se reparte en 9625 a cada amigo

Mathematicians use multiplicand to calculate the merchandise of two or more numbers.  it's a fundamental operation in mathematics that is frequently utilized in everyday life.  once we need to combine groups of similar sizes, we utilize multiplicand. On this page, let's study more about multiplicand.

The fundamental concept of repeatedly adding the same number is represented by the process of the multiplicand. The results of multiplying two or more numbers are referred to as the product of those numbers,  and therefore the factors that are multiplicand are referred to as the factors. Repeated addition of the identification number is made easier by multiplying the numbers.

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Answer:

1/4*6/2=6/8

3/4

Step-by-step explanation:

The equation of line is y= -1/4x  + 2

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis.

The general form is [tex](y- y_1)= m(x - x_1)[/tex]

given:

line that is perpendicular to y = 4x + 8 and passes through (−8, 4).

Here the slope of given line is 4.

So, the slope of perpendicular lines is

m = -1/4

Now, as the line passes through (-8, 4)

Then using

(y - y1) = m (x- x1)

y- 4= -1/4(x- (-8))

y-4 = -1/4 ( x+8)

y-4 = -1/4 x - 2

y= -1/4x  + 2

Hence, the equation of line is y= -1/4x  + 2.

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Answer: y= -1/4x  + 2

Step-by-step explanation: chose the answer and got it right on my test

Answer:

4.12

Step-by-step explanation:

Step-by-step explanation:

what do you mean by "rule" ?

the line equation (in slope-intercept form ? or any other ?) ?

or only the slope of the line ?

I assume you need the slope-intercept line equation.

this looks like

y = ax + b

"a" is the slope of the line, "b" is the y-intercept (the y value when x = 0).

"b" we know already from the specified intercept points : 5.5

the slope of a line is simply the ratio

(y coordinate change / x coordinate change)

when going from one point on the line to another.

and the axis-intercept points are points on the line too. so, we can use them.

so, we see

x changes by +3.667

(= 3 2/3 = 3×3/3 + 2/3 = (3×3 + 2)/3 = 11/3)

from -3.667 to 0.

y changes by +5.5

(= 5 1/2 = 5×2/2 + 1/2 = (5×2 + 1)/2 = 11/2)

from 0 to 5.5

the slope is therefore

5.5 / 3.667 = 11/2 / 11/3 = 11/2 × 3/11 = 3×11 / 2×11 = 3/2

and so, the line equation is

y = 3/2 x + 5.5

or

y = 3/2 x + 11/2 = 1/2 × (3x + 11)

Answer:

170 minutes

Step-by-step explanation:

Weekly gym sessions:

Therefore, the total time for all sessions is:

[tex]\begin{aligned}\implies \sf Total\:time & = \sf 2 \times 45 + 4 \times 30\\& = \sf 90 + 120 \\& = \sf 210 \:\:minutes\end{aligned}[/tex]

If Judy attended all sessions, yet

[tex]\begin{aligned}\implies \sf Total\:time\:Judy\:lost& = \sf 2 \times 10 + 4 \times 5\\& = \sf 20 + 20 \\& = \sf 40\:\:minutes\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies \sf Total\:time\:Judy\:worked\:out & = \textsf{Total time of sessions}-\textsf{Total time Judy lost}\\& = \sf 210-40\\& = \sf 170\:\:minutes\end{aligned}[/tex]

So Judy worked out for a total of 170 minutes for the week

Answer:

74 , 138

Step-by-step explanation:

12 + 2 = 14

14 + 4 = 18

18 + 8 = 26

26+16 = 42

42+32= 74

74+64 =138

please make my answer as brainelist

Answer: $5.25

Step-by-step explanation:

Brianna bought 1 3/4 pounds of cheese

Each pound cost $3.00

1 3/4 x $3

Turn this into an improper fraction, you get 7/4

7/4 x $3

$21 over 4

Do the division, you get $5.25

Answer:

Step-by-step explanation:

1 pound price= 3 dollars

Then she has to pay= (7/4)*3 = 5.25 dollars

Answer:

Transformation that result in a change in the size of a figure are called dilations.

Answer:

x=4

Step-by-step explanation:

We can see that points A,E, and D form a triangle.

Points A, C, and C also form a triangle.

These two triangles are similar, while [tex]\triangle ACB[/tex] has side lengths twice as long as [tex]\triangle ADE[/tex]. this means that

[tex]2x+2=4x-6\\2x=8\\x=4[/tex]