Help me please When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.

The mean and median of the given data is 84 and 84, in order to have 85% as average, Alyssa should score 89 marks and we cannot say anything about how the median is affected.

Part A: Finding the mean of the data,

Mean = (74 + 86 + 94 + 82) / 4 = 336 / 4 = 84

Therefore, the mean score is 84. To find the median, we first need to put the scores in order from smallest to largest, 74, 82, 86, 94. Since we have an even number of scores, the median is the average of the two middle scores. In this case, the two middle scores are 82 and 86, so we take their average,

Median = (82 + 86) / 2 = 168 / 2 = 84

Therefore, the median score is 84.

Part B: Let x be the score Alyssa needs to earn on her fifth test. To find the score she needs to maintain an 85% average, we can set up the following equation,

(74 + 86 + 94 + 82 + x) / 5 = 85

Multiplying both sides by 5, we get,

74 + 86 + 94 + 82 + x = 425

Adding up the first four scores, we get,

74 + 86 + 94 + 82 = 336

Substituting in equation,

336 + x = 425

Subtracting 336 from both sides, we get,

x = 89

Therefore, Alyssa needs to earn at least an 89 on her fifth test to maintain an 85% average.

Part C: The median is the middle score when the data is arranged in order. Since the fifth test score has not yet been added, the median is still 84. So, we cannot really say anything about the median.

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Answer:

1. true

2. false

3. true or false

Answer:

[tex]j = 7 \pm \sqrt{44}[/tex]

Step-by-step explanation:

First, move the constant term to the other side of the equation.

[tex]j\² + 14j + 5 = 0[/tex]

[tex]j\² + 14j = -5[/tex]

Next, add the coefficient of the first degree j term divided by 2, then squared to both sides.

[tex]j^2 + 14j + (14/2)^2 = -5 + (14/2)^2[/tex]

[tex]j^2 + 14j + (7)^2 = -5 + (7)^2[/tex]

[tex]j^2 + 14j + 49 = -5 + 49[/tex]

[tex]j^2 + 14j + 49 = 44[/tex]

Now, we can factor the left side as a square.

[tex](j+7)(j+7) = 44[/tex]

[tex](j+7)^2 = 44[/tex]

Finally, we can take the square root of both sides to solve for j.

[tex]\sqrt{(j+7)^2} = \sqrt{44[/tex]

[tex]j+7=\pm\sqrt{44}[/tex]

[tex]\boxed{j = 7 \pm \sqrt{44}}[/tex]

Note that there are two solutions, as [tex]\sqrt{44[/tex] could be positive OR negative because of the even root property:

if [tex]x^2 = a^2[/tex],

then [tex]x = \pm a[/tex]

because both [tex](+a)^2[/tex] and [tex](-a)^2[/tex] equal [tex]a^2[/tex].

You will end up at the point (-1, -5).

We have,

Starting at the point (-1,-2), moving down 3 units means moving 3 units in the negative y-direction.

Now,

The endpoint will have the same x-coordinate as the starting point but a y-coordinate that is 3 less than the starting y-coordinate.

This means,

The endpoint is (-1, -5).

Thus,

You will end up at the point (-1, -5).

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Answer:

-------------------------

Given two legs of a right triangle and we need to find the hypotenuse.

Use Pythagorean theorem:

The matching choice is C.

the solutions of the equation [tex]x^{2} -6x+10=0[/tex] in terms of a+ib are given by x=3-i and x=3+i.

The given equation is [tex]x^{2} -6x+10=0[/tex]. To find the solution to the equation, we use the quadratic formula.

The expression [tex]ax^{2} +bx+c=0[/tex] is the quadratic equation of the second degree, where a, b, and c are coefficients, then the quadratic formula is given by, [tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex].

Here, [tex]a=1[/tex], [tex]b=-6[/tex], and [tex]c=10[/tex]. Substitute all the values in the above formula, and we get

[tex]$x=\frac{-6\pm\sqrt{(-6)^2-4(1)(10)}}{2(1)}$[/tex]

[tex]$x=\frac{-6\pm\sqrt{36-40}}{2}$[/tex]

[tex]$x=\frac{-6\pm\sqrt{-4}}{2}$[/tex]

The squares of the negative real number give an imaginary unit 'i'.

So, the value of [tex]\sqrt{-4}[/tex] is [tex]2i[/tex]. Then,

[tex]x=\frac{-6\pm2i}{2}[/tex]

[tex]x=\frac{2(3\pm i)}{2}}[/tex]

[tex]x=3\pm i[/tex]

Therefore, the solutions of the equation [tex]x^{2} -6x+10=0[/tex] in terms of a+ib are given by [tex]x=3-i[/tex] and [tex]x=3+i[/tex].

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Answer:

Yes

Step-by-step explanation:

1  3/4    x 3   =   7/4 x 3 = 21/4 = 5 1/4 cups

The probability that a randomly selected points falls within the red-shaded square is given as follows:

p = 9/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The area of the red-shaded square is given as follows:

3² = 9 units².

The total area is given as follows:

4² = 16 units².

Hence the probability that a randomly selected points falls within the red-shaded square is given as follows:

p = 9/16.

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Answer:

40 cm²

Step-by-step explanation:

The surface area of a square-based pyramid is made up of:

The area of a square is the square of its side length.

Given the side length of the square base is 4 cm, the area of the base is:

[tex]\begin{aligned}\implies \sf Area\;of\;square\;base&=4^2\\&=4 \cdot 4\\&=16\;\sf cm^2\end{aligned}[/tex]

The area of a triangle is half the product of its base and height.

Given the base of the triangular side is 4 cm and its height is 3 cm, the area of one triangular side is:

[tex]\begin{aligned}\implies \sf Area\;of\;one\;triangular\;side&=\dfrac{1}{2}\cdot 4 \cdot 3\\&=2 \cdot 3\\&=6\;\sf cm^2\end{aligned}[/tex]

Therefore, the total surface area of the square pyramid is:

[tex]\begin{aligned}\implies \sf Total\;surface\;area&=\sf square\;base+ 4\; triangular\;sides\\&=\sf 16\;cm^2+4 \cdot 6\; cm^2\\&=\sf 16\; cm^2+24\;cm^2\\&=\sf 40\;\sf cm^2\end{aligned}[/tex]

Answer:

Step-by-step explanation:

Reflecting a point across the x-axis results in changing the sign of the y-coordinate, but keeping the x-coordinate the same. Reflecting a point across the y-axis results in changing the sign of the x-coordinate, but keeping the y-coordinate the same.

Reflecting (5,2) across the x-axis gives (5,-2), and reflecting it across the y-axis gives (-5,2).

Reflecting (-6,12) across the x-axis gives (-6,-12), and reflecting it across the y-axis gives (6,12).

Reflecting (2,-7) across the x-axis gives (2,7), and reflecting it across the y-axis gives (-2,-7).

Reflecting (-4,-2) across the x-axis gives (-4,2), and reflecting it across the y-axis gives (4,-2).

Reflecting (0,-2) across the x-axis gives (0,2), and reflecting it across the y-axis gives (0,-2).

Answer: A

Step-by-step explanation:

Well when we use a calculator to determine the square root of 158 we get= 12.56980509.

And so option A woud be closest, smallest difference between all.

Answer: A

Step-by-step explanation: Square root of 158 simplified is 12.5698

The difference quotient for the function f(x)=-3x²+6x-6 is -3h+6.

Now, let's move on to finding the difference quotient for the function f(x)=-3x²+6x-6. The difference quotient is a formula used to find the average rate of change of a function between two points.

The formula for the difference quotient is:

f(x+h) - f(x)

So, to find the difference quotient for the function f(x)=-3x²+6x-6, we first need to find f(x+h) and f(x):

f(x+h) = -3(x+h)² + 6(x+h) - 6

= -3(x² + 2xh + h²) + 6x + 6h - 6

= -3x² - 6xh - 3h² + 6x + 6h - 6

f(x) = -3x² + 6x - 6

Now we can plug these values into the difference quotient formula:

f(x+h) - f(x)

= [-3x² - 6xh - 3h² + 6x + 6h - 6] - [-3x² + 6x - 6]

= [-3x² - 6xh - 3h² + 6x + 6h - 6 + 3x² - 6x + 6] / h

= [-3h² + 6h] / h

= -3h + 6

This tells us the average rate of change of the function between x and x+h is -3h+6.

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The keyword that best describes the OF SERVICE is a. None of the above

A keyword is a term in information retrieval that captures the essence of a document's topic. Index terms make form a regulated vocabulary for usage in bibliographic data.

None of the preceding keywords correctly describe the term "of service" as it is a preposition used to denote the sort or character of a particular service being delivered. It does not refer to any statistical or mathematical concept.

The right answer is A based on the information.. It is not a statistical or mathematical term.

Based on the information, the correct option is A.

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y= x+1/x-8  has a diagonal asymptote. Therefore, the correct option is option A among all the given options.

A line that, in analytical geometry, is an asymptote either a curve is one where, when either or both of the x and y coordinates go to infinity, the distance among the curve as well as the line approaches zero. An asymptote on a curve appears a line that is tangential with the curve at an angle at infinity in projection geometry and similar contexts. y= x+1/x-8 has a diagonal asymptote.

Therefore, the correct option is option A.

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Answer:

2464

Step-by-step explanation:

Parallelogram Area Formula: A=bh

Length is the same as base or b.

H is height

B =88 H=28

A=88•28=2464 m^

The statement that could be true for function g b) g(-13) = 20.

Since g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, it is possible that g(-13) = 20. The fact that g(0) = -2 and g(-9) = 6 does not provide enough information to determine the value of g at x = -13.

Statement (a) is not possible since g(7) is outside the domain of g. Statement (c) is not possible since g(0) was given as -2. Statement (d) is not possible since -11 is outside the range of g.

Correct Question :

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.

a) g(7) = -1

b) g(-13) = 20

c) g(0) = 2

d) g(-4) = -11

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The probability of randomly selecting a blue jelly bean from the first bag and then randomly selecting a green jelly bean from the second bag is 1/15 (option a).

Firstly, we need to determine the total number of jelly beans in both bags.

The first bag contains 15 jelly beans (3+5+2+5) and the second bag contains 10 jelly beans (1+7+2).

Therefore, the total number of jelly beans in both bags is 25.

Next, we need to determine the probability of randomly selecting a blue jelly bean from the first bag.

Since there are 5 blue jelly beans out of a total of 15 jelly beans in the first bag, the probability of selecting a blue jelly bean is 5/15 or 1/3.

After selecting a blue jelly bean from the first bag, we move on to the second bag to select a green jelly bean.

Since there are 2 green jelly beans out of a total of 10 jelly beans in the second bag, the probability of selecting a green jelly bean is 2/10 or 1/5.

To determine the probability of both events occurring, we use the multiplication rule of probability.

Therefore, the probability of randomly selecting a blue jelly bean from the first bag and then randomly selecting a green jelly bean from the second bag is (1/3) x (1/5) = 1/15.

Hence, the answer is option (a) 1/15.

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Answer:

the equilibrium output (Y) is (gA-b(10))Mo + 2520/25 = 1076 and the equilibrium interest rate (i) is -176.

Step-by-step explanation:

(a) Writing the IS-LM system in matrix form:

IS equation: Y = 1 - b(10) + gA

LM equation: Y = (Mo/k) - (/k)i

We can rewrite the equations in matrix form as:

| 1 - b(10) -gA | | Y | | 0 |

| 1/k /k | | i | = | Mo/k |

(b) Solving for Y and i by matrix inversion:

| Y | | (1/k) (gA-b(10))/k | | 0 |

| i | = | (1/k) (-1/k) | | Mo/k |

Multiplying the inverse matrix by the right-hand side:

| Y | | (1/k) (gA-b(10))/k | | 0 | | (gA-b(10))Mo/k |

| i | = | (1/k) (-1/k) | | Mo/k | = | -Mo/k |

Solving for Y and i:

Y = (gA-b(10))Mo + 2520

25

i = -176

Therefore, the equilibrium output (Y) is (gA-b(10))Mo + 2520/25 = 1076 and the equilibrium interest rate (i) is -176.

[tex]{\boxed{\sf tan\Theta=\dfrac{sin\Theta}{cos\Theta}}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{11}{60}=\dfrac{sin\Theta}{\dfrac{60}{11}}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{11}{60}\times \dfrac{60}{11}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{121}{3600}[/tex]

The slope of the line that contains the points (-2,-20) and (3,30) is 10

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope of the line that contains the points (-2,-20) and (3,30)

Slope= 30-(-20)/3-(-2)

=30+20/3+2

=50/5

=10

Hence, the slope of the line that contains the points (-2,-20) and (3,30) is 10

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Answer:

if you are asking for an angle it's either 180° or 0°

Answer:

your answer is D. 1,0 & -3,0

Step-by-step explanation:

have a nice day.

The correct statement is,

D) The median is less than the mean.

E) The mode and the mean are equal.

Given that;

Data set is,

⇒ {60, 5, 18, 20, 37, 37, 11, 90, 72}

Hence, We can formulate;

Mean = {60 + 5 + 18 + 20 + 37 + 37 + 11 + 90 + 72} / 9

Mean = 38.89

Arrange data set into ascending order,

⇒ 5, 11, 18, 20, 37, 37, 60, 72, 90

Hence,

Median = (9 + 1)/2

            = 5th term

            = 37

Mode = 37

Thus, The correct statement is,

D) The median is less than the mean.

E) The mode and the mean are equal.

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Answer: its the first one

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Volume = 27.2

⅓ × base area × height = 27. 2

Base area × height = 81.6

Base area = ½ bh = 1/2 × 3.2 × 8.5 = 13.6

13.6 × height = 81.6

Height = 81.6 ÷ 13.6 = 6 inches

The values of the matrices operations are [tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex] and [tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]

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

[tex]G = \left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right][/tex]

Also, we have

[tex]F = \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]

Using the above as a guide, we have

[tex]4G + 2F = 4\left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right] + 2 \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]

Evaluate the sum

[tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex]

Next, we have

[tex]D = \left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right][/tex]

Also, we have

[tex]B = \left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]

The matrix expression is then represented as

[tex]4D - 3B= 4\left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right] - 3\left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]

Evaluate

[tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]

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Answer: $150

Step-by-step explanation:

250 x 0.60

=$150

The equation y = -x - 2 and y = 2x + 13 has the coordinate a solution (-5, 3).

From the given coordinate plane, the solution is (-5, 3).

A linear equation is in the form: y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept.

When (x, y)=(-5, 3)

The linear equation y = -x - 2 satisfies this this equation because 3 = -(-5) -2

Also, the linear equation y = 2x + 13 satisfies this this equation because 3 = 2(-5) + 13

Therefore, the equation y = -x - 2 and y = 2x + 13 has the coordinate a solution (-5, 3).

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Answer:

By copying the given statements from the original problem

No. D

I hope it helped you.

Please Mark me the brainliest

Answer:

Hey, when writing a proof, the first statement should be based on the given information or assumptions, and it should be written in the left column of the proof. To get started, it's best to look at the "given" statements from the original problem and use those as your starting point. This first statement sets the foundation for the logical progression of the proof.

It's important to remember that each subsequent statement should be logically connected to the previous ones, and should lead towards the final statement or conclusion that you're trying to prove. To make your proof convincing, you should also include a justification for each statement that you make, which goes in the right column of the proof.

Overall, constructing a proof can take some time and effort, but by following a clear and logical progression, you can create a solid and convincing argument for your claim.

Step-by-step explanation: