Calculate the unit rate for each option and determine which one is the BEST buy.
$160 for 10 books
$114 for 6 books

The equation used to determine the value of x for the length of a square side is:  4 x = 3 (x 1).

The given condition are-

Perimeter of square = 4x

Equilateral triangle perimeter = 3(x 1)

Equating both by the condition-

4x = 3(x 1)

Thus, the equation used to determine the value of x for the length of a square side is:  4 x = 3 (x 1).

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The additive counterpart of given expressions are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

When two numbers may be added together or multiplied, regardless of the order in which they are entered, the result is said to be commutative. There are different formulas available for the conversion of multiplicative expressions to their additive counterparts.

a) The first expression is a²b³. This expression is written as aabbb. This is of the form ab and its corresponding additive counterpart is of the form a+b.

Then, a+a+b+b+b=2a+3b.

b) The second expression is a⁻²(b⁻¹c)². This expression is of the form a⁻¹ and its corresponding additive counterpart is of the form -a.

Then,

[tex]\begin{aligned}a^{-2}(b^{-1}c)^2&=a^{-1}a^{-1}(b^{-1}c)(b^{-1}c)\\&=-a-a-b+c-b+c\\&=-2a+2(-b+c)\end{aligned}[/tex]

c) The third expression is (ab²)⁻³c²=e. This expression is first expanded as, (ab²)⁻¹(ab²)⁻¹(ab²)⁻¹c²=e. Using property, (xy)⁻¹=y⁻¹x⁻¹.

Then,

[tex]\begin{aligned}((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})c^2&=e\\(b^{-2}a^{-1})(b^{-2}a^{-1})(b^{-2}a^{-1})c^2&=e\end{aligned}[/tex]

Also, the additive identity to e is zero. And, aⁿ=na.

Then,

(-2b-a)+(-2b-a)+(-2b-a)+2c=0

Simplifying we get,

-3(a+2b)+2c=0.

The answers are  (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

The complete question is -

Translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative

a. a²b³

b. a⁻²(b⁻¹c)²

c. (ab²)⁻³c²=e

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Answer:85%

Step-by-step explanation:

51 is what percent of 60 is equal to (51 / 60) x 100 = 85%. So if you buy an item at $60 with $51 discounts, you will pay $9 and get 85% discount cashback rewards. So 51 out of 60 as a percentage is 85%

Step-by-step explanation:

If there are 2 points (a,b) and (c,d),

then the slope = (d - b)/(c - a) = (b - d)/(a - c)

Therefore slope = (10 - 4)/(4 - 2) = 6/2 = 3

The point-slope form of a line is

y = mx + b, where m is the slope and b is the y-intercept Substituting either point (2,4) or (4,10) into the equation is fine.

(4) = (3)(2) + b

4 = 6 + b

b = 4 - 6 = -2

y = 3x - 2

Or

(10)=(3)(4) + b

10 = 12 + b

b = 10 - 12 = -2

y = 3x - 2

Answer: -9

Step-by-step explanation: To find the value of u, we can use the slope formula to calculate the slope of the line that goes through the points (9, u) and (10, -1). The slope formula is: slope = (y2 - y1)/(x2 - x1). In this case, we have: slope = (-1 - u)/(10 - 9) = (-1 - u)/1. Since the slope of the line is given as 8, we can set this equal to the value we calculated above and solve for u. This gives us: 8 = (-1 - u)/1. Multiplying both sides by 1 gives us: 8 = -1 - u. Adding 1 to both sides gives us: 9 = -u. Finally, negating both sides gives us: u = -9. Therefore, the value of u is -9.

The equation that represents the proportional relationship in this graph is y = 2 / 7 x.

Two variables have a proportional relationship if all the ratios of the variables are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x if:  

for some constant k , called the constant of proportionality .

Therefore, the variables in this case are y and x.

Hence, let's find k using the coordinates on the graph

(0.7, 0.2)

0.2 = k (0.7)

k = 0.2 / 0.7

k = 2 / 7

Hence,

y = 2 / 7 x

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The number of bacteria in the petri dish after 24 hours will be y = 125 + 24x

Given is Gina was working in the laboratory on an experiment involving the population of bacteria. Her initial starting amount in a petri dish was 125 bacteria.

Assume that each hour the bacteria rises by [x] bacteria per hour. Then,

the number of bacteria in the petri dish after 24 hours will be -

y = 125 + 24x

Therefore, the number of bacteria in the petri dish after 24 hours will be y = 125 + 24x.

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The total proportion of shirts between two prices is 0.9431, which is obtained using the knowledge of proportion and statistics.

What is proportion?

In mathematics, a proportion is defined as the comparison between two numerical quantities. If both possess the same nature, they are called directly proportional, or else called inversely proportional.

Calculation of the proportion based on the problem

The mean and standard deviation are given to be 45 and 5 respectively

Calculate standard normal variate using the formula, z = (x - 45) / 5

Taking x = 37, we get,

z1 = (37 - 45) / 5

= -1.6

Using the z table, we get the value, z1 = 0.0548

Now, taking x = 59.35, we get,

z2 = (59.35 - 45) / 5

= 2.87

Using the z table, we get the value, z2 = 0.9979

The proportion between two prices is given by z = z2 - z1

z = 0.9979 - 0.0548

= 0.9431

Hence, the proportion of shirts between the two prices is 0.9431.

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Blank 1: Corresponding because All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

Blank 2:

Blank 3: x= 46 as 180-134 = 46

Check the picture below.

bearing in mind that the ratio of the sides of similar figures is the same as the ratio of their perimeters

[tex]\stackrel{\textit{\Large perimeters}}{21.3\hspace{5em}p}\hspace{5em}\stackrel{\textit{\Large areas}}{16\hspace{5em}25} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(21.3)^2}{(p)^2}~~ = ~~\cfrac{16}{25}\implies \left( \cfrac{21.3}{p} \right)^2=\cfrac{16}{25}\implies \cfrac{21.3}{p}=\sqrt{\cfrac{16}{25}}\implies \cfrac{21.3}{p}=\cfrac{\sqrt{16}}{\sqrt{25}} \\\\\\ \cfrac{21.3}{p}=\cfrac{4}{5}\implies 106.5=4p\implies \cfrac{106.5}{4}=p\implies {\Large \begin{array}{llll} 26.625=p \end{array}}[/tex]

Answer:

85%

Step-by-step explanation:

Hope it helps!

Answer:

85%

Step-by-step explanation:

51/60=.85=85%

Step-by-step explanation:

y=Mx+b

M- slope

B- y intercept

1. find slope by choosing 2 point(any 2)

Once you’ve picked 2 point- (X1, y1) (x2, y2) set up the equation to calculate slope

y2-y1 / x2-x1 = m

2. Solve for b

Take any point and plug in the x and y value

Plug in y= (the slope you solved for)(x intercept) + b

3. then write the equation

Y= (slope)x + b

Answer:

53

Step-by-step explanation:

The average speed is 54 miles per hour.

What is average ?

In plain English, an average is one number chosen to represent a list of numbers. It is often calculated by dividing the total number of numbers in the list by the number of numbers in the list. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.

The definition of the average is the mean value, which is the ratio of the sum of the values in a given set to the total number of values in the set.

The formula for distance is

Distance = Rate × Time

Total distance = 50 × 3 + 60 × 2 = 270

Total time = 3 + 2 = 5

Using the formula:

[tex]Speed = \frac{Distance}{Time}[/tex]

       = 270 / 5

       = 54

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The required answer are according to the following order,

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

What do you mean by sum of angles?

We know that the sum of angles in a triangle is 360°. The question requires us to find the angle that corresponds to each of the given holiday destinations. We shall now proceed as follows:

The angle subtended is obtained from number of people that chose a particular location.

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

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The solution to the quadratic equation using quadratic formula is X has a negative value x is undefined with no real solution.

    x= [tex]\frac{4 + 3.41i}{4}[/tex]  or  x=  [tex]\frac{4 - 3.14i}{4}[/tex]

Using quadratic formula to solve the equation

[tex]x = \frac{-b +or - \sqrt{b^{2}-4ac } }{2a}[/tex]

2x^2-4x +3 = 0

All equations of the form ax^2+bx+c=0 can be solved using the quadratic formula:  

The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

we need to identify a, b and c

from the quadratic equation a = 2, b= -4 and c=3

[tex]x = \frac{-b +or - \sqrt{b^{2}-4ac } }{2a}[/tex]

Substitute the value of a, b and c into the equation

[tex]x = \frac{-(-4) ± \sqrt{(-4^{2} - 4(2)(3)} }{2(2)}[/tex]

[tex]x=\frac{ 4 ± \sqrt{16 -28} }{4}[/tex]

x= [tex]\frac{4+\sqrt{-12} }{4}[/tex] or  x= [tex]\frac{4-\sqrt{-12} }{4}[/tex]

x= [tex]\frac{4 + 3.41i}{4}[/tex]  or  x=  [tex]\frac{4 - 3.14i}{4}[/tex]

Since X has a negative value x is undefined with no real solution.

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Answer:

[tex]x=\dfrac{2+\sqrt{2}\: i}{2}, \quad x=\dfrac{2-\sqrt{2}\: i}{2}[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]2x^2-4x+3=0[/tex]

When completing the square for a quadratic equation in the form ax²+bx+c=0, first move the constant to the right side of the equation:

[tex]2x^2-4x=-3[/tex]

Divide both sides of the equation by the coefficient of x²:

[tex]x^2-2x=-\dfrac{3}{2}[/tex]

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]x^2-2x+\left(\dfrac{-2}{2}\right)^2=-\dfrac{3}{2}+\left(\dfrac{-2}{2}\right)^2[/tex]

Simplify:

[tex]x^2-2x+1=-\dfrac{3}{2}+1[/tex]

[tex]x^2-2x+1=-\dfrac{1}{2}[/tex]

Factor the perfect square trinomial on the left side:

[tex](x-1)^2=-\dfrac{1}{2}[/tex]

Square root both sides:

[tex]\sqrt{(x-1)^2}=\sqrt{-\dfrac{1}{2}}[/tex]

[tex]x-1=\pm\sqrt{-\dfrac{1}{2}}[/tex]

Simplify:

[tex]x-1=\pm\sqrt{\dfrac{1}{2} \cdot -1}[/tex]

[tex]x-1=\pm\sqrt{\dfrac{1}{2}} \sqrt{-1}[/tex]

[tex]x-1=\pm\dfrac{1}{\sqrt{2}} i[/tex]

[tex]x-1=\pm\dfrac{\sqrt{2}}{2} i[/tex]

Add 1 to both sides:

[tex]x=1\pm\dfrac{\sqrt{2}}{2} i[/tex]

[tex]x=\dfrac{2}{2}\pm\dfrac{\sqrt{2}}{2} i[/tex]

[tex]x=\dfrac{2\pm\sqrt{2}\: i}{2}[/tex]

Therefore, the solutions of the given quadratic equation using the method of completing the square are:

[tex]x=\dfrac{2+\sqrt{2}\: i}{2}, \quad x=\dfrac{2-\sqrt{2}\: i}{2}[/tex]

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A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.

The problem can be solved using the average value approach.

Average value = total amount or sum of data / number of data

In the given problem,

total amount = total coffee served last year

total amount = 40,000

number of data = number of hours in a year

number of data = 365 day/year x 24 hours/day = 8760 hours

Hence,

Average value = total amount or sum of data / number of data

                         = 40000 / 8760

                         = 4,6 ≈ 5 (round to the nearest whole cup)

Hence, the average coffee served is 5 cups per hour.

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The Null hypothesis and alternative hypothesis for the given sample of cell phone spent time data of 32 randomly selected adults during lockdown and pre-pandemic times are,

                           H₀ : μd = 0 and Hₐ : μd > 0

Correct option is option (d).

To decide whether a hypothesis should be accepted or rejected, statisticians utilize formal, planned procedures known as hypothesis testing. Hypothesis testing is the process of choosing hypotheses for a specific probability distribution based on observable evidence.

Given:

A study obtained time data of 32 randomly selected young adults spent on their cell phones pre-pandemic and then during the lockdown phase of the pandemic. let us consider,

L --> time spent on cell phone by adults during lockdown

P --> time spent on cell phone by adults at pre pandemic time

and                       d = L- P

we want to perform a hypothesis testing on this sample .

The samples are dependent because same adults are being sampled before and after the lockdown.

Also, we need to test if mean time after is higher than mean time before so this is a right tailed test. Hence,

The correct hypotheses will be:

                                   H₀ : μd= 0

                                     Hₐ : μd> 0

Hence, option D is the correct option.

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The correct option is . D) Her IQ score is above the majority of the population types of intelligence.

IQ is an abbreviation for intelligence quotient. IQ tests are used to assess people's intellectual abilities and potential. They are intended to test a wide range of cognitive abilities, including reasoning, logic, and problem-solving.

It's a test of intelligence, which you're born with. It is not a test of knowledge that represents what you learn in school or through life experience.

Amber's mental age = 14

Amer's age = 10

Then her IQ can be calculated by

[tex]IQ=\frac{mental\ age}{chronological\ age}*100=\frac{14}{10}*100=140[/tex]

Average IQ of majority of population is between 85 to 115.

Only small percentage of population has IQ score higher than 130.

It means Amber's IQ score is above the majority of the population.

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The polygon ABCD and polygon EFGH are congruent polygons.

A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons, etc

Here,
Consider two polygons,
ABCD and EFGH,
As given in the figure,
AB = EF,
AD = EH
∠A = ∠E
∠D = ∠H
ABCD ≅ EFGH,

Thus, Congruent polygons are polygons ABCD and EFGH.

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The account balance after 3 years will be $218.

The crediting of cash flows connected with an investment or deposit is referred to as "simple" interest.

Given that you deposit $200 in an account that earns simple interest at an annual rate of 3%.

The formula to calculate the simple interest is given below,

SI = ( P x R x T ) / 100

SI = ( 200 x 3 x 3 ) / 100

SI = 2 x 3 x 3

SI = $18

Total account balance = 200 + 18 = $218

Therefore, the account balance after 3 years will be $218.

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Answer:

C -5 + (-15)

Step-by-step explanation:

-5 - 15 = -20

A -15 - (-5) = -15 + 5 = -10

B -5 + 15 = 10

C -5 + (-15) = -20

D -15 + 5 = -10

Answer:

c; -5+(-15)

Step-by-step explanation:

-5-15=-20

adding a negative number is subtraction, which means;

-5+(-15)=-20

therefore

-5-15=-20=-5+(-15)

The degrees of freedom here is 5.

Given,

A grocery store company wanted to know how well some of their local stores were doing.

The number of sample reviewers they hired to rate 15 local stores = 6

We have to find the degrees of freedom;

Degrees of freedom;-

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the number of items in the data sample.

Here,

Degrees of freedom = n - 1

n = 6

Then,

Degrees of freedom = 6 - 1 = 5

That is,

5 is the degrees of freedom in this case.

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Answer:

h = -3y + 2x

Step-by-step explanation:

Add 4x to both sides of the equation.

2h = −6y + 4x

Divide each term in 2h = −6y + 4x by 2 and simplify.

Divide each term in 2h = −6y + 4x by 2.

2h/2 = -6y/2 + 4x/2

Simplify the left side.

h = −6y/2 + 4x/2

Simplify the right side.
Simplify each term.
Cancel the common factor of −6 and 2.

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

Cancel the common factors.
Factor 2 out of 2.

h = -3y+2(2x)/2(1)
Cancel the common factor

h = -3y+2(2x)/2(1)
Rewrite the expression
h = -3y + 2x/1

Divide 2x by 1.
h = -3y + 2x

hopefully its right LOLZ

There is no sufficient evidence to indicate the true standard deviation is less than 4000

What is standard deviation ?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

given that n = 16

x = 60139.7

s = 3718.06

∝ = 0.05

To test the hypothesis

H0 : = 4000

H1 :  < 4000 (claim)

test statistics

x² = ((n-1)s²) / H0²

   = (15 * 13823970.16) / (16000000)

   = 12.96

P- value = P [x² < 12.96]           DF = n-1 = 15

             = 0.3946

0.1 < P-value <0.5

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The predicted amount of an unstable element that is left after 6 years is 5.46 grams.

For the stated question-

The equation for the least-squares regression line, is;

In(Element) = 2.305 -0.101(Time)

Amount of unstable element left after time t = 6 years.

In (Element) = 2.305 -0.101(6)

ln (Element) = 1.699

(Element) = e¹°⁶⁹⁹

(Element) = 5.46

Thus, the predicted amount of an unstable element that is left after 6 years is 5.46 grams.

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The equivalent form of the function is [tex]Q(t)=4000(64)^t[/tex]

The equation of the function, according to the question is given as

Q(t)=4000(4)3t

This equation can be properly rewritten as

Q(t)=4000(4)³⁺

Express 4 as a radical expression

So, we have the following representation

Q(t)=4000(4³)⁺

Evaluate the exponent in the above expression

Q(t)=4000(64)⁺

The above expression cannot be further simplified

Hence, the solution to the exponential expression is Q(t)=4000(64)⁺

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Complete question

Q(t)=4000(4)3t.

Write an equivalent function of the form Q(t)=ab^t.

[tex] \frac{2}{5} + \frac{2}{3} = \\ lcm \: of \: 5 \: and \: 3 \: is \: 15 \: so \\ \frac{6 + 10}{15} = = \: \frac{16}{15} [/tex]

Therefore, the answer is

[tex]{ \red{ \sf{ \frac{16}{5}}}}[/tex]

[tex]\colorbox{pink}{\blue{ \boxed{ \tt{ hope \: it \: helps \: you}}}}[/tex]

Step-by-step explanation:

[tex]{ \blue{ \sf{ \frac{2}{5} + \frac{2}{3}}}}[/tex]

If you take the Lowest Common Multiple (L.C.M.) you will get 15.

[tex]{ \blue{ \sf{ \frac{6+10}{15}}}}[/tex]

[tex]{= \blue{ \sf{ \frac{16}{15}}}}[/tex]