Help please, i need to check this FAST

Answer:

ya it's the same thing I guess

Answer:

WHAT!? THEY BOTH GOT BANNED?! HOW

The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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Answer:

95

Step-by-step explanation:

To find the average you take the sum of the scores and then divide it by the number of exams. Let x equal the score Lucy must obtain on the next math test.

\(\frac{85+64+76+x}{4} =80\)

Add the scores and multiply both sides by 4

225 + x = 320

Subtract 225 from both sides

x = 95

Answer:

n-35=40

n=75 (the amount she started with)

Step-by-step explanation:

Number of ways to roll 5 distinct dice and get 3 of a kind is 7200

To find the number of ways to roll 5 distinct dice and get 3 of a kind:

Choose which number appears three times. There are 6 possible choices.

Choose which three dice will show the chosen number. There are 5 ways to choose the first die, 4 ways to choose the second die, and 3 ways to choose the third die, for a total combinations 5 x 4 x 3 = 60 ways.

Choose the numbers that the remaining two dice will show. There are 5 choices for the first die and 4 choices for the second die, but the order in which we choose them doesn't matter, so we need to divide by 2 to correct for overcounting. This gives us (5 x 4) / 2 = 10 ways.

Choose which of the two remaining dice will show the first chosen number. There are 2 choices.

Multiply all of the choices together: 6 x 60 x 10 x 2 = 7,200.

Therefore,  there are 7,200 ways to roll 5 distinct dice and get 3 of a kind.

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Answer:

A) -4, -2

Step-by-step explanation:

The translation vector is the distance

point A: (3, 1)

point A': (-7, -3)

3 + (-7) = -4

1 + (-3) = -2

Answer:

12

Step-by-step explanation:

its a square all sides of the square are the same so 48 divided by 4 is 12

5 points is not a lot of points

The region bounded by the given curves is a triangle with vertices at (0,0), (1,1), and (1,0). When this region is revolved around the line y=3, we obtain a solid with a hole in the middle.
To find the volume of this solid, we can use the method of cylindrical shells. Imagine slicing the solid into thin cylindrical shells with radius r and height Δy. The volume of each shell is approximately 2πrΔy times the thickness of the shell.

The distance between the axis of rotation (y=3) and the line y=1 is 2 units. Therefore, the radius of each cylindrical shell is r = 3 - y. The height of each shell is Δy = dx, where x is the distance from the y-axis.

To set up the integral, we need to express x in terms of y. Since the region is bounded by y=x and y=1, we have x=y for 0<=y<=1. Therefore, the integral for the volume of the solid is:
V = ∫[0,1] 2π(3-y)x dx
 = 2π ∫[0,1] (3-y)y dx

Evaluating this integral, we get:
V = 2π [3y^2/2 - y^3/3] from 0 to 1
 = 2π (3/2 - 1/3)
 = 2π/3

Therefore, the volume of the solid obtained by rotating the region bounded by y=x, y=1 about y=3 is (2/3)π cubic units.

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Answer:

I'm pretty sure it's b but I'm not 100% sure

Answer:

B

Step-by-step explanation:

The equation of the line is that passes through (1,4) and (3, -6) is

y = -5x + 9

First, write the equation in slope-intercept form:

y = mx + b

(the m is the slope, and b is the y-intercept)

Now, Lets find the slope(m) of the line by using the formula:

y2-y1/x2-x1

(-6 - 4)/ (3 - 1) = -10/2 = -5

Next, find the y-intercept (b) by using the slope-intercept form equation and substituting -5 in for m and one of the ordered pairs in for x and y:

4 = (-5)(1) + b

b = 9

-OR-

-6 = (-5)(3) + b

b = -6 + 15 = 9

b = 9

Now, we can write the full equation of the line:

y = -5x + 9 is the answer

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Answer: I hope you understand, just mutiply whatever x is by 11 to get Y

Step-by-step explanation:

x = unknown number

9x+2x= 11x

Y=11x

Answer:

the 12th term of the geometric sequence is approximately 9,559,938.

Step-by-step explanation:

Given that a₄ = 54 and a₇ = 1,458, we can use these values to find the common ratio:

a₇ = a₄ * r³

1,458 = 54 * r³

r³ = 1,458 / 54

r³ ≈ 27

Taking the cube root of both sides:

r ≈ ∛27

r ≈ 3

Now that we have the common ratio (r = 3), we can find the 12th term using the formula for the nth term of a geometric sequence:

aₙ = a₁ * r^(n-1)

In this case, we have a₁ = 54, n = 12, and r = 3:

a₁₂ = 54 * 3^(12-1)

a₁₂ = 54 * 3^11

Calculating this expression:

a₁₂ = 54 * 177,147

a₁₂ ≈ 9,559,938.

Answer:

The 12th term is 354294

Step-by-step explanation:

A geometric sequence has the from,

f(n) = f(n-1)(r)

where r is the common ratio

in our case, f(4) = 54

and f(7) = 1458

we have to find f(12)

now, since f(4) = 54, then f(5) must be,

\(f(5) = r(f(4))\\so,\\f(5) = r(54)\\similarly,\\f(6) = r(f(5))\\but f(5) = r(54) \ so,\\f(6) = r(r(54))\\f(6) = r^{2} (54)\\finally, \\f(7) =rf(6)\\f(7)=r(r^{2} (54))\\but f(7) = 1458\\so\ we \ get\\1458=r^{3}(54)\\ == > \ 1458/54=r^{3}\\ 27=r^{3}\\so,\\r=3\)

Hence we have found the ratio,

now we just keep going till we get to the 12th term

\(f(8) = 3(f(7))\\f(8) = 3(1458)\\f(8) = 4374\\f(9) = 3(4374)\\f(9) = 13122\\\\Similarly,f(10) = 39366\\f(11) = 118098\\f(12) = 354294\)

Hence the 12th term is f(12) = 354294

or a sub 12 = 354294

Step-by-step explanation:

5x-4=-3-x

5x+x=4+(-3)

6x=1

x=1/6

Answer:

Step-by-step explanation:

\( \sf{5x - 4 = - 3 - x}\)

Move constant to R.H.S and change it's sign

Similarly, Move variable to L.H.S and change it's sign

⇒\( \sf{5x + x = - 3 + 4}\)

Collect like terms

⇒\( \sf{6x = - 3 + 4}\)

Calculate

⇒\( \sf{6x = 1}\)

Divide both sides of the equation by 6

⇒\( \sf{ \frac{6x}{6} = \frac{1}{6} }\)

Calculate

⇒\( \sf{x = 0.16}\)

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

A is called a subset of B if every element of A is contained in set B.

The equation that shows the cost of salsa is (c) d = 5p

From the question, we have the following parameters that can be used in our computation:

p  4      6     8

d  20   30   40

The equation that shows the cost of salsa. is calculated as

p : d = 4 : 20

Express the ratio as fraction

So, we have the following representation

p/d = 4/20

Take the inverse of both sides

d/p = 20/4

Evaluate

d/p = 5

So, we have

d = 5p

Hence, the equation is (c) d = 5p

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7.071 is the length, in inches, of each side of the square.

What is meant by "square"?

The term "square" refers to a regular quadrilateral having four equal-length sides and angles. Angles in the square are at right angles or are separated by 90 degrees. The diagonals of the square are also equal and meet at a 90-degree angle.

                             Having equal length sides and right angles on all four, a square is a quadrilateral. Due to the fact that a square's sides are all the same length, it may be distinguished from other types of rectangles. Every square consequently becomes a rectangle since it is a quadrilateral with right angles at all four of its angles.

If the side od=f a square is s, the diagonal is  s√2

  This comes from Pythagoras as diagonal is

   √s² + s²  = √2s² = s√2

 as such s√2 = 10

           s = 10/√2

        = 10 * √2/√2  * √2

         = 5√2

    5 * 1.4142  = 7.071

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Answer:

Angle L= 53 degrees. Side ML = 4.521 and Side NL= 7.513

Step-by-step explanation:

The appropriate hypotheses for testing if the proportion of each color of Froot Loops by using chai test is the same are:

H0: The proportion of each color of Froot Loops is the same.

HA: The proportion of at least one color of Froot Loops is different.

To test if the proportion of each color of Froot Loops is the same, we can formulate the following hypotheses:

Null Hypothesis (H0): The proportion of each color of Froot Loops is the same.

Alternative Hypothesis (HA): The proportion of at least one color of Froot Loops is different.

With these hypotheses, we can perform a chi-square test of independence to analyze the distribution of colors in Charise's morning bowl of Froot Loops. This test will help us determine if the observed distribution significantly deviates from what would be expected if the proportions were the same.

The chi-square test will compare the observed counts of cereal pieces for each color with the expected counts under the assumption of equal proportions. If the chi-square test statistic is significant, it suggests evidence of a difference in the proportion of colors.

To perform the chi-square test, we will calculate the expected counts assuming equal proportions for each color. We will then compare the observed counts with the expected counts using the chi-square test statistic. The degrees of freedom for the test will be (number of colors - 1).

In conclusion, the appropriate hypotheses for testing if the proportion of each color of Froot Loops by using  chi-square tests is the same are:

H0: The proportion of each color of Froot Loops is the same.

HA: The proportion of at least one color of Froot Loops is different.

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Answer:

1/8

Step-by-step explanation:

Amount of pan of brownies that Mike has = 1/2

Amount he will eat= 1/4 of the amount he has

Amount he will eat = 1/4 of 1/2

Amount he will eat = 1/4×1/2

Amount he will eat = 1/8

Hence he will eat 1/8 of the pan of brownies

The probability of selecting two women and one man in that order is 0.036 (rounded to three decimal places).

To find the probability of selecting two people at random from a group of thirteen women and fifteen men, we first need to determine the total number of people in the group.

Total number of people = 13 women + 15 men = 28 people

(a) To find the probability that all three selected people are men, we need to determine the number of ways we can select two men out of the 15 men in the group:

Number of ways to select two men = 15C2 = (15*14)/(2*1) = 105

Since we need all three selected people to be men, we can only select one more person from the remaining 13 women:

Number of ways to select one woman = 13C1 = 13

Therefore, total number of ways to select three people where all three are men = 105 * 13 = 1365

The probability of selecting all three men = (number of ways to select three men) / (total number of ways to select three people) = 1365 / 32760 = 0.042

So the probability of selecting all three men is 0.042 (rounded to three decimal places).

(b) To find the probability that the first two selected people are women and the third is a man, we need to determine the number of ways we can select two women out of the 13 women in the group:

Number of ways to select two women = 13C2 = (13*12)/(2*1) = 78

Since we need the third selected person to be a man, we can only select one more person from the 15 men in the group:

Number of ways to select one man = 15C1 = 15

Therefore, the total number of ways to select three people where the first two are women and the third is a man = 78 * 15 = 1170

The probability of selecting two women and one man in that order = (number of ways to select two women and one man in that order) / (total number of ways to select three people) = 1170 / 32760 = 0.036

So the probability of selecting two women and one man in that order is 0.036 (rounded to three decimal places).  

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With probability we can predict that, Bennet will select a red marble about 60 times in 200 draws, which corresponds to option C.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

The probability of selecting a red marble on any given draw is the number of red marbles divided by the total number of marbles in the bag:

P(Red) = 15 / (8 + 7 + 15 + 20) = 15 / 50 = 0.3

Since Bennet is replacing the marble after each selection, each draw is independent and has the same probability of selecting a red marble. Therefore, the number of red marbles selected in 200 draws follows a binomial distribution with n = 200 (the number of trials) and p = 0.3 (the probability of success on each trial).

The expected value of the number of red marbles selected can be found using the formula:

E(X) = np

where X is the number of red marbles selected, n is the number of trials, and p is the probability of success on each trial.

Substituting the values we get:

E(X) = 200 * 0.3 = 60

Therefore, we can predict that Bennet will select a red marble about 60 times in 200 draws, which corresponds to option C.

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The probability of at most 1 person leaving the elevator on each floor when assuming that every person is equally likely to leave the elevator on any floor depends on the number of floors in the building and can be calculated using the binomial distribution formula.

Assuming that every person is equally likely to leave the elevator on any floor, the probability that on each floor at most 1 person leaves the elevator can be calculated using the binomial distribution.

Let's say there are n floors in the building. The probability of at most 1 person leaving the elevator on each floor is the probability that 0 or 1 person leaves the elevator on each floor. This can be calculated as follows:

P(at most 1 person leaves the elevator on each floor) = P(0 people leave on floor 1) x P(0 or 1 people leave on floor 2) x P(0 or 1 people leave on floor 3) x ... x P(0 or 1 people leave on floor n)

Now, since we are assuming that every person is equally likely to leave the elevator on any floor, the probability of 0 people leaving the elevator on any floor is (n-1)/n and the probability of 1 person leaving the elevator on any floor is 1/n. Therefore, we can calculate the probability of at most 1 person leaving the elevator on each floor as:

P(at most 1 person leaves the elevator on each floor) = (n-1)/n * (1/n + (n-1)/n)^(n-1)

Simplifying this expression, we get:

P(at most 1 person leaves the elevator on each floor) = (n-1)/n * (2/n)^(n-1)

For example, if there are 5 floors in the building, the probability of at most 1 person leaving the elevator on each floor is:

P(at most 1 person leaves the elevator on each floor) = 4/5 * (2/5)^4
P(at most 1 person leaves the elevator on each floor) = 0.08192

Therefore, the probability of at most 1 person leaving the elevator on each floor when assuming that every person is equally likely to leave the elevator on any floor depends on the number of floors in the building and can be calculated using the binomial distribution formula.

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The formula for an exponential function is y = 45/8x + 57/8.

Here we have to find the formula for an exponential function that passes through the points.

Given data:

The two points are (-1, 3/2) and (3, 24).

We need to find the slope of the line. So,

Slope(m) = (y2 - y1) / (x2 - x1)

m = (24 - 3/2) / ( 3+ 1)

   = 45/ 8

The general equation of a line:

y = mx + c

Now putting the value of x and y as -1 and 3/2 and m = 45/8.

3/2 = -1 × 45/8 + c

c = 57/8

Now we get the equation:

y = 45/8x + 57/8

Therefore the equation is y = 45/8x + 57/8.

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The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.

1. Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems.
maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

Now, To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 3/4), (0, 0), and (3, 0).

        z = x₁ + 2x₂ = (0) + 2(3/4)

                    = 1.5z = x₁ + 2x₂ = (0) + 2(0) = 0

                        z = x₁ + 2x₂ = (3) + 2(0) = 3

The maximum value of the objective function z is 3, and it occurs at the point (3, 0).

Hence, the optimal solution is (3, 0), and the optimal value of the objective function is 3.2.

maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

To find the optimal solution and the optimal value of the objective function,

        evaluate the objective function at each corner of the feasible region:

                                (0, 0), (3, 0), and (2, 5).

                          z = x₁ + x₂ = (0) + 0 = 0

                          z = x₁ + x₂ = (3) + 0 = 3

                           z = x₁ + x₂ = (2) + 5 = 7

The maximum value of the objective function z is 7, and it occurs at the point (2, 5).

Hence, the optimal solution is (2, 5), and the optimal value of the objective function is 7.3.

maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 1), (2, 0), and (5, 1).

                         z = 3x₁ + 4x₂ = 3(0) + 4(1) = 4

                      z = 3x₁ + 4x₂ = 3(2) + 4(0) = 6

                      z = 3x₁ + 4x₂ = 3(5) + 4(1) = 19

The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.

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The area of the shaded region cannot be determined without additional information about the dimensions of the square.

To determine the area of the shaded region, we need additional information about the dimensions of the square. The length of AD alone is not sufficient to calculate the area.

We need either the length of one side of the square or the radius of the outer circle. With the length of one side of the square, we can calculate the area by squaring the side length. If we have the radius of the outer circle, we can calculate the area by subtracting the area of the square from the area of the circle.

However, without this information, we cannot accurately determine the area of the shaded region.

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Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.

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Answer:

Your final grade will be 78.67 %

Step-by-step explanation:

67% of your grade will be from your test average which is 79 (higher)

33% of your grade will be from your homework average which is 78.

Calculating:

(67×79+33×78) / (67+33) = 7867 / 100 = 78.67

The values of all sub-parts have been obtained.

(a). The value of bₙ = ((-1)ⁿ 2n) / (n + 2).

(b). The value of limit is Lim bₙ = 2.

What is series for convergence or divergence?

The term "convergent series" refers to a series whose partial sums tend to a limit. A divergent series is one whose partial sums, in contrast, do not approach a limit. The Divergent series often reach, reach, or don't reach a particular number.

As given series is,

-(2/3) + (4/4) - (6/5) + (8/6) - (10/7) + ...

Assume b₁ = (-2/3), b₂ = (4/4), b₃ = (-6/5), b₄ = (8/6), and b₅ = (-10/7).

Since mod-bi < mod-b(i + 1) for all i implies that mode of the series.

(a). Evaluate the value of bₙ:

From given series,

-(2/3) + (4/4) - (6/5) + (8/6) - (10/7) + ...

Then, b₁ = (-2/3), b₂ = (4/4), b₃ = (-6/5), b₄ = (8/6), and b₅ = (-10/7).

So, bₙ = alpha ∑ (n = 1) {(-1)ⁿ 2n) / (n + 2)}

Thus, bₙ = {(-1)ⁿ 2n) / (n + 2)}.

(b). Evaluate the value of Limit:

lim (n = alpha) mod- bₙ = lim (n = alpha) {(2n) / (n + 2)}

                                      = lim (n = alpha) {(2n) / n(1 + 2/n)}

                                      = 2

Since, lim (n = alpha) bₙ = 2.

Hence, the values of all sub-parts have been obtained.

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Applying the definition of exterior angle, the measure of angle B is: c. 33°

When a side of a triangle is extended through an interior angle, the angle formed is called the exterior angle of a triangle.

The angle to the exterior angle of the triangle, when added to the exterior angle will have a sum of 180 degrees, which means their supplementary angles.

Therefore:

4x - 15 + 14x - 21 = 180

4x + 14x - 15 - 21 = 180

18x - 36 = 180

18x = 180 + 36

18x = 216

18x/18 = 216/18

x = 12

m∠B = 4x - 15 = 4(12) - 15 = 33°

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Answer:

its B. 33

Step-by-step explanation: