The temperature outside is 15°F. If the
temperature drops 20°, will the outside temperature be represented
by a positive or negative integer? Explain your reasoning.

The equation of the circle with diameter endpoints of (17, -3) and(-13,3) is (x-2)²+y²=936

A circle is a form made up of all points on a plane that are at the same distance from the center. In other words, it is the curve that a moving point in a plane creates to keep its distance from a specific point constant. The radius is the separation between any point on a circle and its center. The radius must typically be a positive integer. Degenerate cases include circles with displaystyle r=0 and r=0. Unless otherwise stated, this article discusses circles in Euclidean geometry, specifically the Euclidean plane.

A circle is a straight forward closed curve that splits the plane into its inner and outside. In regular use, the

The equation of a circle is given as,

(x-a)²+(y-b)=r²

Here, the center of the circle is (a ,b) and r is the radius of the circle

The circle's center can be located first. The middle point of the line segment serves as the center of the circle since the two locations from the issue are the endpoints of a diameter.

Given two end points, how do you calculate a line's midpoint? You may use the formula below.

M=((x1+x2)/2, (y1+y2)/2)

Here, M denotes the mid-point

The points are taken as (x1, y1), (x2, y2)

M=((17-13)/2, (-3+3)/2)

M=(2,0)

Now, the center of the circle is (2,0)

We have to calculate the distance

d= √(x₁-x₂)²+(y₁-y₂)²

d= √(17+13)²+(-3-3)²

d=√900+36

d=√936

Therefore, the radius of the circle is √936

Now, the equation of the circle is,

(x-2)²+(y-0)²= (√936)²

(x-2)²+y²=936

Therefore, the equation of the circle with diameter endpoints of (17, -3) and(-13,3) is (x-2)²+y²=936

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Answer:

[tex]y=2x+4[/tex]

Step-by-step explanation:

The slope of the given line is [tex]\frac{-2-4}{-2-1}=2[/tex].

Parallel lines have the same slope, so the equation is:

[tex]y-6=2(x-1) \\ \\ y-6=2x-2 \\ \\ y=2x+4[/tex]

The value of prime numbers c in the equation is c = 2.

What is prime numbers?

Those greater than one are known as prime numbers. They simply have two variables, the number itself and factor 1.

We have given that a - b = c requires all of the integers to be positive prime numbers,

c can only have one outcome, which is 2.

                 [tex]e.g., 13 - 11 = 7 - 5 = 2.[/tex]

Hence in the given prime numbers c in the equation is c = 2.

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The sum of even numbers between 105 and 351 is 28,044 .

An additive or arithmetic sequence is a sequence of numbers such that the difference between  consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.

even numbers between 105 and 351

the series will start like

106 , 108 , 110 , .................................. , 346 , 348 , 350

this is a arithmetic progression

a = 106 d  = 2 l = 350

we need to find n

350 = 106 + ( n - 1 ) 2

350 - 106 = (n -1 ) 2

244/2 = n -1

n = 123

now sum = 123/2 ( 106 + 350)

               = 28,044

so the sum of even numbers between 105 and 351 is 28,044 .

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The simplified expression is 2187.

Given expression:

expression 3 with the exponent 4 multiplying  3 with the exponent of 3.

= [tex]3^{4} *3^{3}[/tex]

we know that,

if base are equal exponents are added.

= [tex]3^{4+3}[/tex]

= [tex]3^{7}[/tex]

= 3*3*3*3*3*3*3

= 9*3*3*3*3*3

= 27*3*3*3*3

= 81*3*3*3

= 243*3*3

= 729*3

= 2187.

Therefore the simplified expression is 2187.

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Answer:

1,070 g

Step-by-step explanation:

Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 15 minutes. After 45 minutes, then, the amount of radioactive atoms is halved three times. Therefore:

1st half-life: 8,560 ÷ 2 = 4,280 g

2nd half-life: 4,280 ÷ 2 = 2,140 g

3rd half-life: 2,140 ÷ 2 = 1,070 g

To produce five constructive batches of salsa, 2.5 cups of onion will be needed.

What is unitary method of problem solving?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.

Given, the number of onions required to produce one batch = 0.5 cup(s)
∴ The number of onions required to produce five batches = 0.5×5
= 2.5 cup(s)
Thus, to produce five constructive batches of salsa, 2.5 cups of onion will be needed.

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Answer:

see image

Step-by-step explanation:

Use new exponent rules like:

A power raised to a power is the product of the powers. (power to a power, times the exponents)

and,

Square root is a half power. (Converting radicals to fractional exponents)

Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)

see image.

Here's the plan:

Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.

see image.

The proof of the equation  (√5)³ = √(5³) is given below.

Exponentiation is one of the mathematics operation.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a times to itself.

So, a is the exponent of m.

Given:

A radical equation,

(√5)³ = √(5³).

LHS =  (√5)³

Simplifying,

(√5)³ = {(5[tex])^{1/2}[/tex]}³

        = [tex]5^{3/2}[/tex]

        = √(5³)

        = RHS.

Therefore,  (√5)³ = √(5³).

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The complete question:

Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.

An equation relating W to T is given by W = 700 + 25T. Also, a graph of this linear equation is shown in the image attached below.

In order to write an equation relating W to T, we would define the variables that represents the amount of water in the pond (in liters) and the number of minutes this water has been added as follows:

The initial volume of water is given by:

700

The volume of water added to this pool would be given by:

25T

Therefore, the total volume of water added to this pool is given by:

W = 700 + 25T

Next, we would determine the points for the graph of this equation:

At T = 0, we have:

W = 700 + 25(0)

W = 700   ⇒ (0, 700)

At T = 1, we have:

W = 700 + 25(1)

W = 725   ⇒ (1, 725)

At T = 2, we have:

W = 700 + 25(2)

W = 750   ⇒ (2, 750)

At T = 3, we have:

W = 700 + 25(3)

W = 775   ⇒ (3, 775)

At T = 4, we have:

W = 700 + 25(4)

W = 800   ⇒ (4, 800)

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The coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) is; (x, y) = (-1, 2)

Centroid of a Triangle states that  the center of the triangle can be calculated as the point of intersection of all the three medians of that same triangle, and that this median is a line drawn right from the midpoint of one side to the opposite vertex.

We are given the coordinate of the vertices of the triangle as;

X(−4, 0) , Y(−1, 4) , and Z(2, 2)

Now, the formula to find the coordinates of the centroid of the triangle is; (x, y) = (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3

Thus, the coordinates of the Centroid is;

(x, y) = (-4 + (-1) + (2))/3, (0 + 4 + 2)/3

(x, y) = (-1, 2)

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The quadratic equations are solved and answered below -

An equation is a mathematical statement showing the equivalence of two mathematical expressions. Example -

3x + 5 = 8

Given is -

3x² - 7 = 31

2x² + 18 = 0

4x² - 26 = - 50

2x² + 36 = x²

We have -

3x² - 7 = 31

3x² = 38

x² = 38/3

x² = 12.67

x = ±3.56

2x² + 18 = 0

2x² = - 18

x² = -9

x = ±3i

4x² - 26 = - 50

4x² = - 24

x² = -6

x = ±√6i

2x² + 36 = x²

x² = - 36

x = ±√6 i

Therefore, the quadratic equations are solved above.

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The Number of ways that four people can be seated on the bench so that john is not next to paul is 12

In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.

The arrangement of n items in r ways is given by

Here we have

4 people (John, Paul, George, and Ringo) are seated in a row on a bench

Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24

The number of ways of seating the four people so that john is next to paul is 12

Then the number of ways the four people on the bench so that john is not next to paul can find as given below

= Total No of ways, 4 can be seated - No of ways that john next to paul  

= 24 - 12 = 12        

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The number of randomly selected employers that would have to be contacted is 9604

The confidence level is 95%

1 - 0.95 = 0.05

We have to get the z value at 0.05

0.05/2 = 0.025

Using the standard normal table, the critical value at 0.025 = 1.96

We have to define the probability as P = 50% = 0.5

we have to define q = 1 - 50% = 0.5

The formula that would be used to find the value of n is given as

[tex]n = pq\frac{Zc}{E} ^2[/tex]

These variables used are:

pq = variance of population

E = margin of error = 0.01

critical value = Zc = 1.96

[tex]n = 0.5*0.5 (\frac{1.96}{0.01})^2[/tex]

= 0.25 * 38416

= 9604

Hence the sample space is given as 9604

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The equation  y = 4x - 8 is discrete

Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.

While complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.

The main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.

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The end behavior of given polynomial function f(x) = 5 + 7x - 9x^2 + 4^3,

as x → -∞, f(x) → -∞

as x → ∞, f(x) → -∞

In this question, we have been given a polynomial function

f(x) = 5 + 7x - 9x^2 + 4^3

We need to  state the end behavior of f(x).

The graph of f(x) is as shown below.

We can observe that as x tends to -∞, f(x) → -∞

Also, as x → ∞, f(x) → -∞

We know that the end behavior of polynomial function is determined by the degree of the polynomial and the leading coefficient.

For given polynomial function, the degree of this polynomial is 2.

The leading coefficient is -9

We know that for polynomial function of even degree, the ends of the function graph point in the same direction.

Therefore, the end behavior of given polynomial function f(x) = 5 + 7x - 9x^2 + 4^3,

as x → -∞, f(x) → -∞

as x → ∞, f(x) → -∞

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The probability that the next spin will land on red or green or purple is 75%

Given , A spinner is divided into five colored sections that are not of equal size

Color      Frequency

Red            18

Blue            11

Green          8

Yellow         4

Purple          19

Total spin recorded = 18+11+8+4+19

=60

Let "A" be the event when spinner land on Red , "B" be the event when spinner land on Green and "C" be the event when spinner land on Purple

P(A) = 18/60 = 0.3

P(B) = 8/60 = 0.134

P(C) = 19/60 = 0.32

Probability that the next spin will land on red or green or purple will be P(A∪BC) = P(A) + P(B) + P(C)

P(A∪BC)  = 0.3 + 0.134 + 0.32 =0.754

= 0.754 × 100 = 75%

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The correct option ; Quadrilateral, has the given information describing quadrilateral UVWX.

For the given values in the question;

In the quadrilateral UVWX

As, none of the sides are equal to other and none of the angles are equal to the other.

Thus, the this information shows the values are given for quadrilateral.

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Answer:

Step-by-step explanation:

3 as the x axis and -5 for the y axis

6 integers that satisfy the given condition are 10,11,12,13,14,15.

Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size

we have the number X

Of which the square root is greater than 3 and less than 4

so,

[tex]3 < \sqrt{X} < 4[/tex]

on squaring both sides

[tex]3^2 < (\sqrt{X})^{2} < 4^2[/tex]

[tex]9 < X < 16[/tex]

so the integer that satisfies the condition is 10,11,12,13,14,15.

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Answer:

6

Step-by-step explanation:

Because 4 > √x > 3, we know that 16 > x > 9. Thus, the integers from 10 to 15 inclusive satisfy this inequality, which means 6 integers satisfy the condition in the problem.

Option B is the correct choice

A marine biologist measured the size of each barnacle in twenty 10 by 10 square inch areas that were chosen at random. Cluster sampling is illustrated by this.

For a study that is a population into clusters, such as districts or schools, researchers will divide the population into multiple groups (clusters) and will then randomly select some of these clusters as your sample. Ideally, each cluster should be a miniature reflection of the population as a whole.

In order to determine the average size of the barnacles Semibalanus balconies along a section of rocky shoreline, a marine biologist is conducting this study. To do this, he measured the size of every barnacle in each of the twenty 10 by 10 square inch plots that were randomly chosen. Cluster sampling is illustrated by this. (Option B)

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COMPLETE QUESTION:

A marine biologist wants to estimate the mean size of the barnacle Semibalanus balconies on a stretch of rocky shoreline. To do so, he randomly selected twenty 10 by 10 square inch plots and measured the size of every barnacle in each selected plot. This is an example of  

a. convenience sampling.

b. cluster sampling.

c. stratified random sampling.

d. simple random sampling.

e. voluntary sampling.

Answer:

The answer is 18 hours

Step-by-step explanation:

3 hours x 6 days

3x6 = 18

The coordinates of the preimage given in the image below and the composition of a rotation 180 about the origin and a translation 3 units up are: (2, -3), (3, 1), and (-5, 0).

In Geometry, the rotation of a geometric figure 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

From the graph of the image of triangle A'B'C', we have the following coordinates and they would be reversed to obtain the coordinate of triangle ABC before a translation:

(-x, -y)                              →               (x, y)

Points at A' = (-2, 5)        →              Points at A = (2, -5)  

Points at B' = (-3, 1)          →             Points at B = (3, -1)

Points at C' = (5, 2)           →             Points at C = (-5, -2)

Next, we would apply a translation of 3 units up:

Points at A = (2, -5)      →     (2, -5 + 2) = (2, -3)

Points at B = (3, -1)       →     (3, -1 + 2) = (3, 1)

Points at C = (-5, -2)     →     (-5, -2 + 2) = (-5, 0)

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76263

Step-by-step explanation:

[tex] \: \: \: 20005[/tex]

[tex] + 56258[/tex]

___________

[tex] = 76263[/tex]

Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.

Permutation and Combination

Combination is a mathematical way to arranging the set of values randomly.

ⁿCᵣ = n! / r! (n-r)!

we have given that ,

total number of farms for lead contamination = 50

Number of farms have dangerously high level of lead = 8

so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42

We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .

Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28

Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈

= 42! / 8! 34! = 42×41×---×35/8×7×----×1

= 118013185

The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .

= 118030185× 28 = 3,304,845,180

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Answer: 696.511

Step-by-step explanation:

84,250 = b(1.008)120

84250 = 120.96b

b = 696.511

The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).

Given that:

Enrique predicts that he can make additional money from sales of accessories and services for computer products sold by his store.

The store makes x dollars selling computer products, Enrique predicts the store will make 0.05x dollars ($0.05) from selling accessories.

The following steps can be used in order to determine the equation that represents the predicted amount y:

Step 1 - According to the given data, the store makes x dollars selling computer products.

Step 2 - It is also given that, in January and February of this year, the store made $2,500 from sales of accessories and services.

Step 3 - So, the linear equation that represents the given situation is:

y = 0.05x + 2500

Hence the answer is The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).

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well, there's no great mystery when it comes to getting a product from decimals.  Now, we have 611.2 and 0.0061, let's for a second take off the decimal point and simply multipy 6112 times 00061

6112 * 00061 = 372832

ok....... hmmm now let's see 611.2 had 1 decimal, whilst 0.0061 had hmm 4 decimals, let's add them up, that's 1 + 4 = 5 decimals total from both amounts, that simply means that our 372832 needs to have 5 decimals as well, so that makes it 3.72832.

The solution to the inequality 4x + 6 ∠ -6 is x ∠ -3

inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value.

4x + 6 ∠ -6

taking 6 to the right hand side of the inequality

4x < -6 -6

4x < -12

divide both sides by 4

x < -12/4

x < -3

In conclusion, x < -3 is the solution to the Algebraic expression above.

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In order to a breakpoint or the total cost = total investment company must need to sell 100 grams of links.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's suppose the number of links that are needed to solve for a breakpoint is x.

Cost of x number of links with the rate of $2/gram = 2x

Total cost = total selling

100 + 2x = 3x

3x - 2x = 100

x = $100

Hence "In order to break even point or the total cost = total investment company must need to sell 100 grams of links".

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