Can someone please help me with this problem. And educate me on how to get the answer.

The final interval notation is  F ∩ H = [7, 4] &  F ∪ H = [-∞, ∞].

What is the interval notation?

A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.

We have,

F and H are sets of real numbers defined as follows.

F = { v l v < 4}

H = { v l v ≥ 7}

F is the set of all real numbers that are less than or equal to 4.  H is the set of real numbers greater than 7.

F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:

F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets.  Hence the answer is the empty set, Ø:

F ∩ H = Ø

F ∩ H = [7, 4]

F ∪ H = [-∞, ∞]

Hence, the final interval notation is  F ∩ H = [7, 4] &  F ∪ H = [-∞, ∞].

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Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Divide the area of the square by the area of the triangle.

[tex]\dfrac{A_{\textrm{square}}}{A_{\textrm{triangle}}} = \dfrac{3^2}{(9\times 6)\div 2}[/tex]

And simplify.

[tex]= \dfrac{9}{54 \div 2}[/tex]

[tex]= \dfrac{9}{27}[/tex]

[tex]=\dfrac{1}{3}[/tex]

Answer:

the answer would be x=3.

Step-by-step explanation:

when the x is supplemented for the 3, it comes out to 30. by then taking 5 from that, it brings the the number to 25.

Answer:

Step-by-step explanation:

25 = 10x - 5

What’s the solution?

25 = 10x - 5

30 = 10x

x = 30 : 10

x = 3

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

Check

25 = 10 x 3 - 5

25 = 30 - 5

25 = 25

the answer is good

Answer:

0.783

Step-by-step explanation: got it right :)

Answer:

Step-by-step explanation:

= 604800

Answer: d = -8

Step-by-step explanation: look at the attached link

Answer:210 miles

Step-by-step explanation:Gary walking in opposite directions will calculate how long it takes for him to be a given distance apart.

start by plugging them in to thr problem

Step-by-step explanation:

1). Red

x² = 98² - 44² = 9604 - 1936 = 7668

x =√7668 = 6√213

2) orange

X² = 31²+30² = 1861

x = √1861

Answer:

€20 for Sharon

€25 for Louise

Step-by-step explanation:

For a ratio of 4:5, you add 4+5 = 9.

You need 4 out of 9 parts for Sharon, and 5 out of 9 parts for Louise.

4/9 × €45 = €20 for Sharon

5/9 × €45 = €25 for Louise

The missing angle RPQ between the intersected chord is 115 degrees.

The intersecting chords theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175 degrees

arc angle SA = 55 degrees

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115 degrees.

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let's consider two numbers for this case, hmmm say

x = 13

y = 17

so yes, 13 < 17

also true, 13 + 2 < 17 + 2

also true that 2(13) < 2(17)

now, -13 < -17?  well, not quite

reason being, the on the negative side of the number line, the closer to 0, the larger the number, for that case, -1 is much much larger than -1,000,000.

Answer:

-2

Step-by-step explanation:

1. Identify two points with integer (not fraction or decimal) coordinates:

  Ex: (0,5) and (3,-1)

2. subtract the y-coordinates: -1-5 = -6

   and the x- coordinates (IN THE SAME ORDER): 3-0 = 3

3. divide the difference in y (-6) by the difference in x (3): -6/3 = -2

a. The trigonometric ratio sin(Ф/2) = +√(3/10)

b. The trigonometric ratio cos(Ф/2) = +√(7/10)

Trigonometric ratios are the ratios of the sides of a right-angled triangle. They include

where Ф is the angle between the sides

Given that cosФ = 2/5, we use the trigonometric identity

cosФ = 1 - 2sin²(Ф/2)

Making sin(Ф/2) subject of the formula, we have

sin(Ф/2) = ±√(1 - cosФ)/2

So, susbstituting the value of cosФ = 2/5 into the equation, we have

sin(Ф/2) = ±√(1 - cosФ)/2

sin(Ф/2) = ±√(1 - 2/5)/2

sin(Ф/2) = ±√[(5 - 2)/5]/2

sin(Ф/2) = ±√(3/[5 × 2])

sin(Ф/2) = ±√(3/10)

Since Ф is in the first quartile, sin(Ф/2) = +√(3/10)

Given that cosФ = 2/5, we use the trigonometric identity

cosФ = 2coss²(Ф/2) - 1

Making sin(Ф/2) subject of the formula, we have

coss(Ф/2) = ±√(1 + cosФ)/2

So, susbstituting the value of cosФ = 2/5 into the equation, we have

coss(Ф/2) = ±√(1 + cosФ)/2

cos(Ф/2) = ±√(1 + 2/5)/2

cos(Ф/2) = ±√[(5 + 2)/5]/2

cos(Ф/2) = ±√(7/[5 × 2])

cos(Ф/2) = ±√(7/10)

Since Ф is in the first quartile, cos(Ф/2) = +√(7/10)

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Answer:

18 R26

Step-by-step explanation:

[tex]\ \ \ \ \ \ \,\,\, 18 \textrm{ R}26\\{34\ \overline{\smash{)}\ 638}}\\\textrm{ } \ \ \ \underline{-34}\\\textrm{ } \ \ \ \ \ \, 298\\\textrm{ } \: \, \ \ \underline{-272}\\\textrm{ } \ \ \ \ \ \ \: \, 26[/tex]

The lines passing through points A (- 3, 10) and (1, 2) , B (- 1, 6) and (0, 2) , and C (1, 2) and (3, 4) has positive y-intercept.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

As we know, the slope formula is:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

A (- 3, 10) and (1, 2)

m = (2-10)/(1+3)

m = -8/4 = -2

y = mx + c

y = -2x + c

Plug (- 3, 10)

10 = -2(-3) + c

c = 10 - 6 = 4 (positive y-intercept)

Similarly, for the other points:

B (- 1, 6) and (0, 2)

y = -4x + 2 (positive y-intercept)

C (1, 2) and (3, 4)

y = x + 1 (positive y-intercept)

D (0, - 4) and (3, - 2)

y = 0.667x - 4 (negative y-intercept)

E (3, 1) and (5, 2)

y = 0.5x -0.5 (negative y-intercept)

Thus, the lines passing through points A (- 3, 10) and (1, 2) , B (- 1, 6) and (0, 2) , and C (1, 2) and (3, 4) has positive y-intercept.

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The score that Avery must get on Exam B is given as follows:

470.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.

For exam A, the mean and the standard deviation are given as follows:

[tex]\mu = 350, \sigma = 20[/tex]

She scored 310, hence the z-score of her grade is given as follows:

Z = (310 - 350)/20

Z = -2.

For exam B, the mean and the standard deviation are given as follows:

[tex]\mu = 550, \sigma = 40[/tex]

To do as well as on exam A, she needs a z-score of -2, hence the grade X is obtained as follows:

-2 = (X - 550)/40

X - 550 = -80

X = 470.

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The constraints to represent the incoming students at the college are -

0 < x ≤ 100 and 0 < y ≤ 400

We have a college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students

Now -

[x] = the number of out-of-state students

[y] = the number in-state students

y = 4x

0 < x ≤ 100

and the range of [y] will be -

0 < y ≤ (4 x 100)

0 < y ≤ 400

Therefore, the constraints to represent the incoming students at the college are -

0 < x ≤ 100 and 0 < y ≤ 400

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Answer:

The pattern is a repeated triangle and circle.

So, the next shape would be a triangle and a circle.

Step-by-step explanation:

Answer:

The required number lies between 41 and 46 and has prime factors of 2, and 11 is 44.

Step-by-step explanation:

The number lies between 41 and 46 are 42, 43, 44, and 45. From the straightforward observation and according to the condition that must be divisible by 2 and 11 there is only one number that is divisible by both 2 and 11 is 44.

Check the picture below.

Step-by-step explanation:

[tex] \sqrt{180 } = 6 \sqrt{5} [/tex]

because 6² = 36 and 36×5 = 180

I don't think there's any simple way to do it

Answer: 29

Step-by-step explanation: your welcome

Based on the four scenarios of statistical studies given, a study which uses a sample statistic is: D. As part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election, 39 said yes.

In Mathematics and Statistics, a sample statistic can be defined as a small piece of statistical information that is obtained by a researcher or scientist from the sample of a population.

This ultimately implies that, a sample statistic simply refers to any numerical quantity (figure) or data that is generated from the sample of a population by a researcher or scientist.

In this context, we can reasonably infer and logically deduce that 84 of Kaisa's classmates represent the sample of the total population while the 39 classmates who answered yes represent the sample statistic.

In conclusion, the statistical study that was conducted by Kaisa is a study that represent the sample statistic.

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Complete Question:

Four scenarios of statistical studies are given below. Decide which study uses a population parameter.

The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time time of 4:14.

Lakeside Family Dentistry reported that 6 of the 15 patients who came in for a regular cleaning one day had at least one cavity.

Of 351 dog owners who were surveyed, 70 reported owning two dogs.

As part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election, 39 said yes.

The common ratio of given geometric sequence is r = - (1/2)

A geometric sequence is a set of integers that follows a pattern where each term is multiplied by a fixed number called the common ratio, or r, to find the following term.

solution:

a3 = - (3/8)

a8 = 3/256

common ratio = a3 / a8

                        = - (3/8) / 3/256

common ratio = - (1/32)

a8/a3 = (ar^7) / (ar^2)

          = r^5

r^5 = - (1/32)

    r = - (1/2)

Hence the common ratio of given geometric sequence is r = - (1/2)

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The amount of money after 18 years when the interest is compounded continuously is $15725.

The process of calculating interest and reinvesting it in an account's balance over an infinite number of periods is known as continuous compounding.

Given that Levi invested $8,500 in an account paying an interest rate of 3.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars?

The compound interest will be calculated as

[tex]P(t) = P_oe^{rt}[/tex]

[tex]P(t) = 8500\times e^{0.034\times 18}[/tex]

P(t) = 8500 x 1.85

P(t) = $15725

Therefore, the amount of money after 18 years when the interest is compounded continuously is $15725.

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Answer:15670

Step-by-step explanation:

Since only the lengths increase by scale factor,  B'C' on the same line as its corresponding side segment BC​ .

What is the Dilation?

Math definition of dilation Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.

The following are the properties of dilation of the triangle:

1)measures of the angles will not change

2)The sides  of the image of the triangle are multiplied  by the scale factor 2.

So,

A'B'=2AB

B'C'=2BC

A'C'=2AC

Since only the lengths  increase by scale factor,  B'C' on the same line as its corresponding side segment BC​ .

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Answer: IT can have simultaneous solutions

Step-by-step explanation:

You need to go through the cubic units and count them to get the answer

Answer:

2 solutions

Step-by-step explanation:

The solutions of the system of equations are the points of intersection of the two graphs, the red line and the blue parabola. Since there are two points of intersection, there are 2 solutions.

Answer: 2 solutions

Answer:

Step-by-step explanation:

No because the deepness of an pool doesnt affect how fast you will swim during the race

No because the deepness of an pool doesnt affect how fast you will swim during the race.

What is the depth?

Depth refers to a type of vertical distance, where vertical distance is the difference between two vertical positions. One of the most common everyday examples of depth is its use in reference to water.

Here given that,

Your friend says that when the pool in Exercise [tex]19[/tex] is more than [tex]8[/tex] feet deep, you will win the race.

Our swimming speed will never change it does not depend on the depth of the pool.

Hence, depth of the pool does not effect the speed of swimmer.

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Answer:

The quickest answer is to take the number 72 and divide it by the rate of interest. In this case, it would take approximately 72/6, or 12 years to double.

Step-by-step explanation: