simplify the expression involving rational exponents 1( ( -64) 2/3

Step-by-step explanation:

we have the 2 numbers x and (x+2).

x × (x + 2) = 143

x² + 2x = 143

x² + 2x - 143 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case this is

x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =

= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =

= (-2 ± 24)/2 = (-1 ± 12)

x1 = -1 + 12 = 11

x2 = -1 - 12 = -13

so, we have 2 solutions : 11 and 13, -13 and -11

11× 13 = 143

-11×-13 = 143

Answer:38

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

try 150 divided by 9. It doesn’t work. We then round up by 1 week to get us to 17 weeks

We must first find the equation that describes the problem:

• P = postal clerks

• T = time

• L = Letters

Where C is a constant of proportionality. Then we use the initial values to calculate C

The equation that will help us to calculate the number of letters is

We replace the values of the number of people and the time they had_

Answer: 14π

Step-by-step explanation: The formula for circumference is 2 * pi * the radius. However, we are looking for the terms of pi, so we will multiply 2 times pi to get 2 pi. then we get 2 pi x 7 which gives us 14pi, the answer.

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

Answer:

Probability that 32 or more from this sample used Internet Explorer as their browser is 0.9015.

Step-by-step explanation:

We are given that according to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market.

A random sample of 70 users was selected.

Let \(\hat p\) = sample proportion of users who used Internet Explorer as their browser.

The z score probability distribution for sample proportion is given by;

                            Z  =  \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\)  ~ N(0,1)

where, p = population proportion of users who use internet explorer = 53.4%

           \(\hat p\) = sample proportion = \(\frac{32}{70}\) = 0.457

           n = sample of users = 70

Now, probability that 32 or more from this sample used Internet Explorer as their browser is given by = P( \(\hat p\) \(\geq\) 0.457)

      P( \(\hat p\) \(\geq\) 0.457) = P( \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) \(\geq\) \(\frac{0.457-0.534}{\sqrt{\frac{0.457(1-0.457)}{70} } }\) ) = P(Z \(\geq\) -1.29)

                            = P(Z \(\leq\) 1.29) = 0.9015

The above probability is calculated by looking at the value of x = 1.29 in the z table which has an area of 0.9015.

Answer:

B

Step-by-step explanation:

x + 3y = 2 → (1)

4x - 3y = 23 → (2)

adding (1) and (2) term by term will eliminate y

(x + 4x) + (3y - 3y) = 2 +  23

5x + 0 = 25

5x = 25 ( divide both sides by 5 )

x = 5

Step-by-step explanation:

Plug your x and y values into the equation. y = 3(0); y = 0; y = 3(-1); y = -3; y = 3(2); y = 6.

Answer:

Around 150.72

Step-by-step explanation:

The formula for Circumference is \(2\pi r\).

The radius is down in the question as 24yd. (Radius is the distance from the center of the circle to a point on the circle)

Now we now the radius equals 24, simply substitute it into the formula.

2(3.14)(24)

Around 150.72.

Answer:

Circumference ≈ 150.8yd

Step-by-step explanation:

The formula for the circumference of a circle is 2πr. Since we know the radius is 24 yards, plug it into the formula.

C = 2π(24)

C = 150.796

C ≈ 150.8yd

Answer:

1.56 hours

Step-by-step explanation:

300 gal × 1 min 3.2 gal × 1 hr 60 min = 1.56 hr.

Answer:

i thought the question said a 'HORSE' fills a hot tub...

Step-by-step explanation:

lol dont mind me i just want points :D

The roots of the quadratic function are given as,

Sum of roots is calculated as,

The product of roots is calculated as,

The required quadratic function is given as,

A required quadratic function is calculated as,

Thus the required quadratic function is,

The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Formula of force,

F = ma

Given that,

A man pulled a cart filled with stones that had a total mass of 60 kg

He increased the amount of force used to pull the cart from 60 N to 90 N

New acceleration of cart = ?

F  = ma

Old acceleration,

60  = 60a

a   =  1 m/s²

New acceleration,

90 = 60a

a   = 90/60

a   =  3/2

a   =  1.5 m/s²

Hence, the new acceleration is 1.5 m/s²

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Answer:

The equation of a straight line is:

y = mx + b

m is the slope, and that is -2.

All of that bit about simplifying and ... is just a smokescreen to make you think the answer might not be so simple.

Step-by-step explanation:

Given:

let u = x+5

so, the equation will become:

so, the equation is quadratic in form because the substitution u = x+5

The answer is the first statement

Note:

the second statement is wrong, because when the equation expanded, it will be a second degree polynomials not fourth degree

Also, the last 2 statements are wrong, because it is quadratic equation.

Answer:

No it is D.52

Step-by-step explanation:

The angle has to equal 180 degrees.

180-76=104

52 time 2 equals 104

104=104

Answer:

\(\boxed {\tt D. \ x=52}\)

Step-by-step explanation:

The 2 angles are 2x and 76. They are on a straight line together. Therefore they are supplementary and add to 180 degrees.

\(2x+76=180\)

Solve for x by isolating x on one side of the equation.

76 is added to 2x. The inverse of addition is subtraction. Subtract 76 from both sides of the equation.

\(2x+76-76=180-76\\2x=180-76\\2x=104\)

x is multiplied by 2. The inverse of multiplication is division. Divide both sides of the equation by 2.

\(2x/2=104/2\\x=104/2\\x=52\)

x is equal to 52 and D is the correct answer.

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

Answer:

The correct answer for this question is D

The finance charge for a credit card that has given the average daily balance and interest rate is 11.170$.

The finance charge is the cost of credit in dollars. It is calculated on a credit card's unpaid balance. A finance charge, the cost of having the debt a longer time, is added to the outstanding credit card balance.

Given:

Average daily balance: $118.18,

monthly interest rate: 1.15%

According to given question we have

A common way of calculating a finance charge on a credit card is to multiply the average daily balance by the annual percentage rate (APR) and the days in your billing cycle. The product is then divided by 365 .

i.e

\(\frac{118.18*1.15*30}{365} \\=11.170\)

Therefore, the finance charge for a credit card that has given the average daily balance and interest rate is 11.170$.

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Answer:

The number is 26

Step-by-step explanation:

Since decreasing means subtracting and addition is the opposite of subtraction you just add 6 to 20.

that was a terrible explaination but hopefully you understand.

Answer:

Step-by-step explanation explain :

Answer:

This relation is a function

Step-by-step explanation:

The vertical line test is drawing an imaginary vertical line through the graph. If more than one point is on the line, the relation would not be considered a function.

In this relation, no points have the same x coordinate, which means that they will not appear on the same line of the vertical line test. So, this relation is a function.

At the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.

The idea of proportionality can be applied. The time it would take Nathan Adrian to complete one lap in a 25-meter pool is known to be 47.52 seconds for the 100-meter freestyle. Since the tempo is constant while the distance varies, we can establish a ratio:

100 meters / 47.52 seconds = 25 meters / x seconds

where x is the unknown time for one lap in the 25-meter pool.

To solve for x, we can cross-multiply:

100 meters * x seconds = 47.52 seconds * 25 meters

100x = 1188

Dividing both sides by 100, we get:

x = 11.88 seconds

Therefore, at the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.

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The sum of the internal angles of the polygons are

a) The sum is A = 540°

b) The sum is A = 360°

c) The sum is A = 1800°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the sum of the internal angles of a polygon be represented as A

Now , the value of A is

The sum of exterior angle of n polygon is = 360°

Now ,

a)

The number of sides of the polygon = 5 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 5 in the equation , we get

nθ = 180° ( 5 - 2 )

nθ = 180° x 3

nθ = 540°

b)

The number of sides of the polygon = 4 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 4 in the equation , we get

nθ = 180° ( 4 - 2 )

nθ = 180° x 2

nθ = 360°

c)

The number of sides of the polygon = 12 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 12 in the equation , we get

nθ = 180° ( 12 - 2 )

nθ = 180° x 10

nθ = 1800°

Hence , the sum of the internal angles of the polygon is solved

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Answer:

x: (1,0)

y: (0,-2)

Step-by-step explanation:

Given the function:

if we have h(x)=-20, we can find the value of x by matching both equations:

therefore, x=8

The number of elements in the Q complement set, n(Q') is 7

From the question, we are to determine the number of elements that are in the given set.

To find n(Q'),

First, we will determine the elements in Q'

NOTE: Q' means Q complement, that is, the elements that are present in the universal set but not in Q

The universal set is

ξ = {numbers between 3 and 19}

That is,

ξ = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}

From the given information,

Q = {3, 5, 6, 7, 9, 10, 12, 13, 17, 18}

Therefore,

Q' = {4, 8, 11, 14, 15, 16, 19}

The value of n(Q') is the number of elements in the q' set

That is,

n(Q') = 7

Hence, n(Q') = 7

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Answer:

please write it more clearly or take a pic

The alternative hypothesis is a two-tailed hypothesis because it examines whether there is a difference in effectiveness, which can be positive or negative.

A null hypothesis is a type of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Sample data is used to assess the viability of theories. H0 represents what is referred to as "zero" on occasion. The researchers make the assumption that there may be a relationship between the factors. The null hypothesis, on the other hand, claims that no such relationship exists. Although it may not appear to be significant, the null hypothesis is an important part of research.

The following hypotheses would be appropriate for testing the difference in effectiveness between brand-name and generic ibuprofen:

The null hypothesis (H0) states that there is no difference in the mean effectiveness of brand-name and generic ibuprofen.

Alternative hypothesis (Ha): The mean effectiveness of brand-name ibuprofen and generic ibuprofen differs.

These hypotheses can be expressed symbolically as follows:

H0: _generic = _brand-name\\

Ha: _trademark _generic

Where _brand-name denotes the population mean efficacy of brand-name ibuprofen and _generic denotes the population mean efficacy of generic ibuprofen. The alternative hypothesis is a two-tailed hypothesis because it examines whether there is a difference in effectiveness, which can be positive or negative.

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Answer:
H0: μ1 – μ2 = 0

Ha: μ1 – μ2 ≠ 0

Step-by-step explanation:

took the quiz :)

Answer:

The test statistic to test the null hypothesis equals 1.059

Step-by-step explanation:

From the given information; we have:

Treatment               Observations

A                                20        30         25       33

B                                22         26        20       28

C                               40         30         28       22

The objective is to find the  test statistic to test the null hypothesis; in order to do that;we must first run through a series of some activities.

Let first compute the sum of the square;

Total sum of squares (TSS) = Treatment sum of squares \((T_r SS)\)  +    Error sum of squares   (ESS)

where:

(TSS) = \(\sum \limits ^v_{i=1} \sum \limits ^{n_i}_{j-1}(yij- \overline {y}oo)^2\)  with (n-1)   df

\((T_r SS)\)   \(= \sum \limits ^v_{i=1} n_i( \overline yio- \overline {y}oo)^2\)   with (v-1)  df

\((ESS) = \sum \limits ^v_{i=1} \sum \limits ^{n_i}_{j-1}(yij- \overline {y}io)^2\)   with (n-v) df

where;

v= 3

\(n_i=\)4

i = 1,2,3

n =12

\(y_{ij}\) is the \(j^{th\) observation for the \(i^{th\) treatment

\(\overline{y}io\) is the mean of the  \(i^{th\) treatment  i = 1,2,3 ;  j = 1,2,3,4

\(\overline y oo\)   is the overall mean

From the given data

\(\overline y oo = \dfrac{1}{12} \sum \limits ^3_{i=1} \sum \limits ^{4}_{j=1}(yij)^2= 27\)

\(TSS = \dfrac{1}{12} \sum \limits ^3_{i=1} \sum \limits ^{4}_{j=1}(yij- 27)^2 = 378\)

\(T_r SS= \sum \limits^3_{i=1}4 (\overline y io - \overline yoo)^2\)

\(=4(27-27)^2+4(24-27)^2+4(30-27)^2 = 72\)

Total sum of squares (TSS) = Treatment sum of squares \((T_r SS)\)  +    Error sum of squares   (ESS)

(TSS) =  378 - 72

(TSS) =  306

Now; to the mean square between treatments (MSTR); we use the formula:

MSTR = TrSS/df(TrSS)

MSTR = 72/(3 - 1)

MSTR = 72/2

MSTR = 36

The mean square within treatments  (MSE) is:

MSE = ESS/df(ESS)

MSE = 306/(12-3)

MSE = 306/(9)

MSE = 34

The test statistic to test the null hypothesis is :

\(T = \dfrac{ \dfrac{TrSS}{\sigma^2}/(v-1) }{ \dfrac{ESS}{\sigma^2}/(n-v) } = \dfrac{MSTR}{MSE} \ \ \ \approx \ \ T(\overline {v-1}, \overline {n-v})\)

\(T = \dfrac{36}{34}\)

T = 1.059