Use the box method to distribute and simplify (3x – 1)(-5x + 1)

The average rate of change is D. 2.

The average rate of change simply means the measure of how the function will change let unit of time.

In this case, it is important to look at the input and the output that wee given. It can seen that the difference between the output is given as:

13 - 11 = 2

15 - 13 = 2

In this case, the average change is 2.

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Answer:

96, 84, 72, 60, 48, 36

Step-by-step explanation:

The 6 arithmetic means are the terms of an arithmetic sequence between 108 and 24

let the means be a, b, c, d, e, f , then sequence is

108, a, b, c, d, e, f, 24

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 108 , and n = 8

24 = 108 + 7d ( subtract 108 from both sides )

- 84 = 7d ( divide both sides by 7 )

- 12 = d

Then

a = 108 - 12 = 96

b = 96 - 12 = 84

c = 84 - 12 = 72

d = 72 - 12 = 60

e = 60 - 12 = 48

f = 48 - 12 = 36

The 6 arithmetic means are 96, 84, 72, 60, 48, 36

Answer:

a = 5

Step-by-step explanation:

3(a+3)+6 = 30

subtract 6 from both sides

3(a+3) = 24

divide both sides by 3

a+3 = 8

subtract 3 from both sides

a = 5

Answer:

The answer is definitelly B.(Area of 1) + (Area of 2) = (Area of 3)

Step-by-step explanation:

A because they are all surrounding the triangle

Answer:

She made an average of 145$ per day.

Step-by-step explanation:

If she earned 725$ in 5 days, just divide 725 by 5 for your average a day.

Step-by-step explanation:

change the angle to radian

then use formula 1/2 × π × radius square

The number if the number is even, less than -12 and the absolute value of the number is between 9 and 15 is 14

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Number is even

Number is less than -12

Number is between 9 and 15

Now,

If the number is even and less than -12, the only possibility within the given constraints is -14.

Since the absolute value of -14 is 14, which is between 9 and 15, it satisfies the additional condition that the absolute value of the number is between 9 and 15.

Therefore, by algebra the answer will be 14.

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Answer:  x=55, y=65

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Since 9 and 11 do not factor 35, they are not the answer.

5 is a factor of 35, but not the largest. So, the answer is 7.

Answer:

the largest prime factor of 35 is 5

Answer:

Addition Property of Equality

If a, b, and c are any real numbers, and a(b + c) = ab + ac, then (b = c) a = ba + ca.

If the degree of freedom is 24, your sample size when conducting a t-test for dependent means must be 25. Option C is the correct answer.

The sample size when conducting a t-test for dependent means depends on the specific study design and the level of significance desired, and cannot be determined solely based on the degrees of freedom.

However, if we assume that the sample size is equal for both groups, then the formula to calculate the degrees of freedom for a t-test for dependent means is:

df = n - 1

Where "n" is the number of pairs of observations in the sample.

Therefore, if the degree of freedom is 24, then the number of pairs of observations in the sample would be:

n = df + 1 = 24 + 1 = 25

Hence, the answer is 25.

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Answer:

answer is -1/2

have a nice day

Answer:

Step-by-step explanation:

a=55  (180-125)

b= 65 (180-55-60)

d= 30    (90-60)

 c=  60 (180-30-90)

Answer:

Step-by-step explanation:

If the corners of the kitchen are (8, 4), (−3, 4), (8, −8), and (−3, −8), the area of the kitchen is 132 square feet. So, the correct option is C.

To find the area of the rectangular kitchen, we need to use the formula for the area of a rectangle, which is A = L x W, where A is the area, L is the length, and W is the width.

From the given ordered pairs, we can determine the length and width of the rectangle. The length is the distance between the points (8,4) and (-3,4), which is 8 - (-3) = 11 feet. The width is the distance between the points (8,4) and (8,-8), which is 4 - (-8) = 12 feet.

Now that we know the length and width, we can find the area by multiplying them together:

A = L x W = 11 x 12 = 132 square feet

Therefore, the correct answer is C.

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Answer    C. 132 fT2  

Step-by-step explanation:

The answer is (b) getting 50 twos after 600 separate rolls of a single die. The law of large numbers states that as the sample size increases, the sample mean approaches the population mean.

In other words, the more times you roll the die, the closer you should get to the expected value of each number on the die (which is 1/6 for a fair die). Option (a) of getting 200 threes and option (c) of getting 100 sixes are both too far away from the expected value to be consistent with the law of large numbers. Option (b) of getting 50 twos is closer to the expected value and thus consistent with the law of large numbers.

Therefore, the  law of large numbers predicts that over a large number of trials, the frequency of an event should approach its probability of occurrence. In this case, the probability of rolling a two on a fair die is 1/6, so getting 50 twos after 600 rolls is consistent with the law of large numbers.

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The value of γ is greater than 1 for any v > 0, greater than 10 for v > 0.995c, and greater than 100 for v > 0.99995c.

To determine for what speed (in terms of c) the value of γ is greater than 1, 10, and 100, we'll use the formula for the Lorentz factor (γ):
γ = 1 / √(1 - v²/c²)
where v is the speed and
c is the speed of light.

(a) For γ > 1:
Since γ is always greater than 1 for any speed v greater than 0, we can say that γ is appreciably greater than 1 for any v > 0.

(b) For γ > 10:
We need to solve the equation 10 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 100 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/100 = 99/100.
So, v/c = √(99/100), which implies v > 0.995c for γ > 10.

(c) For γ > 100:
Similar to (b), solve the equation 100 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 10000 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/10000 = 9999/10000.
So, v/c = √(9999/10000), which implies v > 0.99995c for γ > 100.

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Answer: Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).

Step-by-step explanation:

To find all values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x:

-x² + 5 = -2x + 2

Expanding the right-hand side:

-x² + 5 = -2x + 2

-x² + 2x + 3 = 0

Solving for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 2, and c = 3

x = (-2 ± √(2² - 4(1)(3))) / 2(1)

x = (-2 ± √(4 - 12)) / 2

x = (-2 ± √(-8)) / 2

Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).

To decide whether it is sensible for Stacy to utilize the ordinary show for the inspecting conveyance of the test extent, we got to check whether the conditions for utilizing the typical conveyance estimation are met. The conditions are:

The test estimate is expansive sufficient

The test information is autonomous

The populace is at slightest 10 times bigger than the test

The test estimate, in this case, is 50. To check whether it is expansive sufficient, ready to utilize the run the show of thumb that the test measure ought to be at the slightest 10% of the populace estimate.

Hence, based on these conditions, it is sensible for Stacy to utilize the ordinary demonstration for the inspecting conveyance of the test extent. She can accept that the testing dispersion is roughly typical with a cruel of p = 0.11 and a standard deviation of sqrt[(p(1-p))/n] = sqrt[(0.11(0.89))/50] = 0.05.

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The coordinates of the point that partitions the segment into a ratio of 4 to 3 are approximately (-7.76, -3.63) and (8.58, -1.01).

To discover the coordinates of the factor that walls the directed line phase from (−10, 2) to (−3, −5) right into a ratio of 4 to 3, we will use the following steps:

step 1: discover the total distance of the phase

to find the full distance of the segment, we are able to use the distance formula:

d = √ ((x2 - x1)² + (y2 - y1)²)

plugging within the given coordinates, we get:

d = √ ((-3 - (-10))² + (-5 - 2)²)

d = √ (49 + 49)

d = √ (98)

therefore, the overall distance of the phase is √ 98.

Step 2: find the coordinates of the partition point

to permit the partition points to be (x, y). We can set up the subsequent equation based on the ratio of 4 to 3:

√ ((x - (-10))² + (y - 2)²) / √ ((x - (-3))² + (y - (-5))²) = 4/3

simplifying this equation, we get:

3√ ((x + 10)² + (y - 2)²) = 4√ ((x + 3)² + (y + 5)²)

squaring both facets and simplifying, we get:

25x² - 242x - 75y² + 200y + 1859 = zero

fixing for y in terms of x, we get

y = (4x - 319) / 75

substituting this into one of the coordinates of the authentic section, we will remedy for x:

-5 = (3(x + 3) + 4(2x - 319)/75) / 7

simplifying this equation, we get:

25x² - 913x + 16728 = 0

the use of the quadratic system, we get:

x = (-(-913) ± √ ((-913)² - 4(25)(16728))) / (2(25))

x ≈ -7. 76 or x ≈ 8. 58

substituting these values back into the equation for y, we get:

y ≈ -3. 63 or y ≈ -1. 01

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Answer:

The coordinates of X,Y,Z are given below as

The coordinates of X',Y',Z' are given below as

To figure out the translation between this two points, we will have

The coordinates of X'',Y'',Z'' are given below as

180 Degree Rotation

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.

Hence,

The final answer is

B) Translation: (x,y) → (x – 2,y + 1); 180° rotation about the origin

Answer:

Nemani has paid $1250 for a TV on hire purchase. The cash price was $1250, so the total cost to Nemani was $1300. Nemani has paid $450 deposit and 12 monthly instalments of $95, for a total of $1445.

So, Nemani has paid an interest rate of 10% on his total payment.

Answer:

55 degrees

Step-by-step explanation:

well, x is on the same line as 125, and a line is always a straight 180 degrees, so you subtract 180-125=55, and angle x and angle y are corrisponding angles, so y also equals 55 degrees.

hope that helps!

Answer:

97.5

Step-by-step explanation:

In my eyes I think we are talking about perimeter...

So then we would have to add up all the sides giving us the result.

30.25+30.25+18.5+18.5 = 97.5

And I am terribly sorry if it was incorrect I feel like i messed up on the "Disregard" part.. Anyways

Hope this helps! :)

we randomly select two people, drawing without replacement , the  probability of getting 2 females: a) = 1/7 ( = 0.1429) , b) = 9/49 ( = 0.1837 ).

a)  Without replacement,

2 female can be selected from 3 female by \(3C_{2}\) ways.

P(2 female) = \(3C_{2} / 7C_{2}\)

= 1/7 ( = 0.1429)

b)  With replacement,

P(female) = n(female) / total people.

= 3 / 7

P(2 female) = 3/7 * 3/7

= 9/49 ( = 0.1837 )

Probability is basically the way that logical something is to occur. Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific outcomes — how likely they are. The investigation of occasions administered by probability is called statistics.

By and large, the probability is the proportion of the quantity of positive outcomes to the absolute outcomes in that example space. It is communicated as, Probability of an occasion P(E) = (Number of good outcomes) ÷ (Test space).

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Solving by the system of linear equations, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.

What do you mean by system of linear equations?

A system of linear equations consists of two or more equations, each of which has two or more variables, and all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy each of the system's linear equations is necessary to identify the system's unique solution.

Let, the cost per pound of peanut be $x and for M&M's be y

so, according to the question, we are getting two linear equations,

$8x + $5y = $55.27..................(i)

$6x + $4y = $42.70....................(ii)

Solving this two systems of linear equations , x=$3.79 and y=$4.99

Hence, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.

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