88) 4 times a number decreased by 8 equals 40
A) x=80 B) x = 40 C) x=8
D) x = 12

First you have to draw points A and M and the line between them. Add two lines, one paralel to X and one paralel to Y to form a triangle.

Since M is the midpoint between A and B, this means that the distance between A and M, is equal to the distance between M and B.

Following the same inclination of the line, you have to draw another triangle starting from M with the same heigth and base as the one drawn under segment AM. The hypotenuse of this second triangle will be segment MB.

Now that you know were point B stand in the cartesian system, you can read the coordinates from the graphic.

X-coordinate is -6

Y-coordinate is 1

The coordinates for B are (-6,1)

Answer: a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The appropriate test is a t-test for slope. The test statistic is t = 2.68 and the p-value is 0.005. Because the p-value, 0.005, is less than α=0.05 we have convincing evidence that there is a positive linear relationship between the amount of water received and how tall the sunflower plants grew.

Answer:

B is the answer

Step-by-step explanation:

The money he would have after 20 years is $29,102.87

Compounding occurs when both the principal and the interest already accrued earns interest.

The formula for calculating future value:

FV = P (1 + r)^nm

$8000 x (1.0667)^20 = $29,102.87

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Answer:

Well, it's the perimeter, so...40.

You just calculate the perimeter of a rectangle with the lenght of 12 and width of 8, by the formula

\(P = 2L+2W\)

or you can factor it out.

Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Answer:

= 9/8     = 1.125

Step-by-step explanation:

y = 1.125x + 2.625

or

y =  9/8 x 21/8

When x=0, y = 2.625

When y=0, x = -2.3333333333333

Answer:

The second integer is greater than the first.

Step-by-step explanation:

Since the first integer is the leftmost out of the two, this means that the second one must be greater than the first since it is to the right of it.

Answer:

c

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

Answer:

12 km

Step-by-step explanation:

16km + 12 = 204

Subtract 12 from both sides:

⇒ 16km = 192

Divide both sides by 16:

⇒ km = 12

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

-2jdjdididjjdjdkdjhd

The volume of cylinder is 84.82 cubic feet

In this question, we have been given for a cylinder the diameter equals 3 feet and the length equals 12 feet.

We need to find  the volume of a cylinder.

From given data,

diameter d = 3 feet

So, radius r = d/2

                r = 1.5 ft

length of cylinder (h) = 12 ft

The formula for the  volume of a cylinder is,

V = π * r² * h

V = π * 1.5² * 12

V = π * 2.25 * 12

V = 84.82 cubic feet

Therefore, the volume of cylinder with the diameter equals 3 feet and the length equals 12 feet is 84.82 cubic feet

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The transformations applied to the graph of f(x)=x2 to produce the graph of g(x)=2x2−28x+3 is f(x) shifting right 7 units

This is further explained below.

Generally, the equation for vertex form is  mathematically given as

g(x) = 2(x – 7)2 – 95

Using the translations rule:

The conclusion that can be drawn from the vertex form " 2(x – 7)2 – 95" is that the parent function f(x) has been relocated 7 units to the right and 91 units upward.

In conclusion, we can say that f(x) shifted right 7 units

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A linearly independent set that generates the subspace of diagonal matrix in M2x2(F) is {[1,0;0,0], [0,0;0,1]}.

A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a, b∈F.

A linearly independent set of vectors that generate this subspace is {[1,0;0,0], [0,0;0,1]}. Any diagonal matrix can be written as a linear combination of these two vectors.

A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a,b∈F. This means that all the diagonal entries in the matrix must be non-zero. To find a linearly independent set that generates this subspace, we can start by considering the simplest form of a diagonal matrix, which is [1,0;0,0]. This vector is linearly independent, as it cannot be expressed as a linear combination of any other vector in the space. Similarly, [0,0;0,1] is also linearly independent, as it can't be expressed as a linear combination of any other vector.

These two vectors form a linearly independent set that generates the subspace of diagonal matrices in M2x2(F). Any diagonal matrix can be written as a linear combination of these two vectors. For example, the matrix [2,0;0,3] can be expressed as 2[1,0;0,0]+3[0,0;0,1]. Thus, this set of vectors is sufficient to generate the entire subspace.

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Answer:

It should be 90

Step-by-step explanation:

Because 270 divided by 3 is 90

Answer:

6

Step-by-step explanation:

All the steps are in the photo I attached

Answer:

Q.1.

Sum of angles of a triangle = 180°

∠A + ∠B + ∠c = 180

(3x - 9) + (4x + 15) + 90 = 180

3x - 9 + 4x + 15 + 90 = 180

7x + 96 = 180

7x = 84

x = 12

∠A = 3x - 9 = 3(12) - 9 = 36 - 9 = 27°

∠B = 4x + 15 = 4(12) + 15 = 48 + 15 = 63°

∠A = 27°

∠B = 63°

Q.2.

\(using \ pythagoras \ theorem \\x^2 = 7^2 + (7\sqrt{3} )^{2} = 49 + 49(3) = 196\\x = \sqrt{196} = 14\)

\(sin y = \frac{opposite}{hypotenuse} = \frac{7\sqrt{3} }{14} = \frac{\sqrt{3} }{2} \\\\y = sin^{-1} (\frac{\sqrt{3} }{2} ) = 60\)

x = 14

y = 60°

Answer:

The smallest 5 digit number is 10,000 and the greatest 5 digit number is 99,999. There are 90,000 five-digit numbers in all.

Answer:

6/25

Step-by-step explanation:

its a probability  out of all the odd numbers such as 1,3,5,7,9,11,13,15,17,19,21,23,25

The unknown number, represented by the variable b, is 1/2, which satisfies the equation "Five more than the product of a number and 8 equals 9."

To solve the equation "Five more than the product of a number and 8 equals 9" using the variable b for the unknown number, we can express this statement as an equation:

8b + 5 = 9

To solve for b, we need to isolate the variable on one side of the equation. Let's simplify the equation step by step:

Subtract 5 from both sides to get rid of the constant term:

8b + 5 - 5 = 9 - 5

8b = 4

Divide both sides of the equation by 8 to solve for b:

8b/8 = 4/8

b = 1/2

Therefore, the solution to the equation is b = 1/2. This means that when we substitute b = 1/2 into the equation, the equation will hold true:

8(1/2) + 5 = 9

4 + 5 = 9

Both sides of the equation are equal, confirming that b = 1/2 is the solution.

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Given inequality:

The steps for solving the problem are outlined below:

Step1 : solve the inequality by factorizing:

Step 2: Identify the intervals:

The possible intervals of solution are:

Using the given inequality we can confirm if the solution range satisfies the given inequality

The valid intervals of solutions are:

Hence, the solution set in interval notation is:

Based on the coldest temperature in Buffalo and the difference in the temperature of Chicago, the equation that can be used to find the coldest temperature in Chicago is C. C - 12 = -39; -27°

When temperatures are warmer, it means that they are higher. This means that to find the coldest temperature in Chicago, you need to add 12°F to the temperature of Buffalo.

The formula would therefore be:

C = -39 + 12

Making the Buffalo temperature the subject gives;

C - 12 = -39

The coldest temperature in Chicago is:

= -39 + 12

= -27°F

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Answer:228m

Step-by-step explanation: 19m x 12m = 228m

Answer: 228m

Step-by-step explanation: Just multiply 19m by 12m. That's how you find area.

Answer:

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is 0.0537.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is 0.0023.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is 0.1101.

Step-by-step explanation:

We are given that according to an NRF survey conducted by BIG research, the average family spends about $237 on electronics in back-to-college spending per student.

Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54.

Let X = back-to-college family spending on electronics

SO, X ~ Normal(\(\mu=237,\sigma^{2} =54^{2}\))

The z score probability distribution for normal distribution is given by;

                                 Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = population mean family spending = $237

           \(\sigma\) = standard deviation = $54

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is = P(X < $150)

        P(X < $150) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{150-237}{54}\) ) = P(Z < -1.61) = 1 - P(Z \(\leq\) 1.61)

                                                             = 1 - 0.9463 = 0.0537

The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9463.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is = P(X > $390)

        P(X > $390) = P( \(\frac{X-\mu}{\sigma}\) > \(\frac{390-237}{54}\) ) = P(Z > 2.83) = 1 - P(Z \(\leq\) 2.83)

                                                             = 1 - 0.9977 = 0.0023

The above probability is calculated by looking at the value of x = 2.83 in the z table which has an area of 0.9977.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is given by = P($120 < X < $175)

     P($120 < X < $175) = P(X < $175) - P(X \(\leq\) $120)

     P(X < $175) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{175-237}{54}\) ) = P(Z < -1.15) = 1 - P(Z \(\leq\) 1.15)

                                                         = 1 - 0.8749 = 0.1251

     P(X < $120) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{120-237}{54}\) ) = P(Z < -2.17) = 1 - P(Z \(\leq\) 2.17)

                                                         = 1 - 0.9850 = 0.015

The above probability is calculated by looking at the value of x = 1.15 and x = 2.17 in the z table which has an area of 0.8749 and 0.9850 respectively.

Therefore, P($120 < X < $175) = 0.1251 - 0.015 = 0.1101

For this exercise, we must use the binomial theorem. The formula of this theorem is described as follows

Where nCi represents the combinatory of n between i. For our case,

Replacing the values you have in the formula

Thus,the expansion and simplification is as follows

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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