b. How should she co I 4. (2 points) Solve the equation for n to determine the term number. (SHOW WORK!) 32 = 2 + 3(n-1) C

To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.

The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:

I₁ U I₂ = (-2, 2] U [1, 5)

To find the union, we combine the intervals while considering their overlapping points:

I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)

So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).

Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:

I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)

To find the intersection, we consider the overlapping range between the two intervals:

I₁ ∩ I₂ = [1, 2]

Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].


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Answer:

Step-by-step explanation:

You are looking for 1/2 of an unknown number minus 19.  It will equal -13.

                                                                                                  1/2x - 19 = -13

Get x isolated, so add 19 on left to cancel, then add on right)     +19    +19                                                                                                

                                                      And you now are down to   1/2 x      =   6  

Now, let's simplify the fraction (1/2).  Since it is 1 divided by 2, you reverse division with multiplication. Multiply 1/2 by the denominator (2) and you get 1. So, you're down to 1x, or just x.   Then multiply the number on the other side of the equal sign (the 6) by 2 and you get 12.

So x = 12.

Now, let's go back to our original equation and plug in the x and see if it works.

1/2x - 19 = -13

becomes 1/2 (12) - 19 = -13

becomes 6 - 19 = -13

Voila! Our missing number (x) is 12.

Answer:

1289155 golf balls

Explanation:

The total volume of all the balls equals to the storage unit space volume.

Let the number of total balls in the storage be b.

Conversion:

1 ft³ = 1728 in³

For the ball:

diameter = 1.6 in

radius = diameter/2 = 1.6/2 = 0.8 in

Equation created:

\(\sf \rightarrow volume \ of \ all \ balls = volume \ of \ storage\)

\(\sf \rightarrow b\left(\dfrac{4}{3} \pi r^3\right) = length \times width \times height\)

\(\sf \rightarrow b\left(\dfrac{4}{3} \pi (0.8)^3\right) =20 \times 10 \times 8 \times 1728\)

\(\sf \rightarrow b =\dfrac{20 \times 10 \times 8 \times 1728}{\left(\dfrac{4}{3} \pi (0.8)^3\right)}\)

\(\sf \rightarrow b =1289155\)

Answer:

2

Step By Step Explanation:

= 2*(8+3*3-4^2)

= 2*(8+3*3-16)

= 2*(8+9-16)

= 2*(17-16)

= 2*(1)

= 2*1

= 2

Answer: 2

Step-by-step explanation:

2/(8+9-16)

2/1 = 2

Answer:

Expected Payoff ⇒ $ 1.50 ; Type in 1.50

Step-by-step explanation:

Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;

\(100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars\)

Thus, Solution ; Expected Payoff ⇒ $ 1.50

The function dependency A -> B for relation schema R(A,B,C,D) implies that:
d. Any two tuples in R that have the same value for A must have the same value for B

The correct answer is option d. This is because the function dependency A -> B means that the value of B is functionally dependent on A.  The productivity function X → Y is called trivial if Y is part of X. In other words, the FD:X → Y dependency means that the value of Y is determined by the value of X. Two bunches of X values ​​that share the same thing must have the same Y value where Z = U - XY is the residue. In simple terms, if the values ​​of the X attributes are known (assuming they are x), then the values ​​of the Y attributes corresponding to x can be determined by looking at them in an R tuple containing x.

Therefore, any two tuples in R that have the same value for A must have the same value for B. This ensures that the relationship is functional and follows the rules of normalization. Tuples are individual rows in a relation and value refers to a specific entry in a tuple for a particular attribute.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

{4, 5, 6}, {64, 65, 66}, {124, 125, 126}

Step-by-step explanation:

x = 1st number

x + 1 = 2nd number

x + 2 = 3rd number

{4, 5, 6}, {64, 65, 66}, {124, 125, 126}

The possible set of numbers are {4,5,6}, {64,65,66} and {124,125,126}

Consecutive numbers are the numbers which follow each other in order from small to greater number.

Let three consecutive numbers are, x ,x+1 and x+2.

According to given condition,

The first number is a multiple of 4,

The second number is a multiple of 5,

And The second number is a multiple of 6.

Start from 4 and then try to find out sequence,

The numbers can be 4, 5 and 6.

Further, the number can be 64,65 and66

And The numbers can be 124,125 and 126

So, three sets of numbers are {4,5,6}, {64,65,66} and {124,125,126}

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The antiderivative of a function f will be the integral of differentiated  value of the function i.e. the function itself.

What is Antiderivative of a function?

A function is said to be antiderivative if its derivative equals the original function. The antiderivative function is the same as an indefinite integral. The limit of a sum of terms f (x) x in the limit that approaches zero, where is the integrand function, is known as a definite integral.

Considering a function f(x) = Sin x

                                  dy/dx = Cos x

 Now, the integral of Cos x would be known as Anti derivative.

here, ∫ Cos x = Sin x

thus, Anti derivative of Cos x is equal to the function itself.

hence, proved.

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gradient is 2

Step-by-step explanation:

hhhhhhhhfhdd

Answer:

See below.

Step-by-step explanation:

(-3,1) and (-1,5)

The formula for finding slope is (y²- y¹)/(x²- x¹).

(5-1)/(-1-(-3))

(4)/(2)

2

The slope would be 2.

-hope it helps

Hi! I hope you're enjoying your day!

Use the Slope formula:

\(\bold{\displaystyle\frac{y2-y1}{x2-x1}}\)

\(\bold{\displaystyle\frac{5-1}{-1-(-3)}}\)

\(\bold{\displaystyle\frac{4}{-1+3} =\frac{4}{2} =2}\)

Hence, the slope is

\(\boxed{\boxed{\bold{2}}}\)

Hope everything is clear.

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\(\rule{250}{2}\)

The correct simplification would be \(18x^4 - 36x^3 + 9x^2\) (option a).

To simplify the expression \(9x^2(4x - 2x^2\) - 1), we need to perform the multiplication and combine like terms.

1. Start by distributing the 9x^2 to each term inside the parentheses:

  \(9x^2 * 4x = 36x^3 9x^2 * (-2x^2) = -18x^4 9x^2 * (-1) = -9x^2\)

2. Now we can combine the terms obtained from the distribution:

\(36x^3 - 18x^4 - 9x^2\)

3. Rearranging the terms in descending order of exponents:

\(-18x^4 + 36x^3 - 9x^2\)

4. However, we can simplify this expression further by factoring out a common factor of \(-9x^2\):

\(-9x^2(2x^2 - 4x + 1)\)

5. Thus, the final simplified expression is:

\(18x^4 - 36x^3 + 9x^2\)

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Answer:

the answer is b I know this because I'm a very young person but I'm a very young man who has been a great person for the last two decades so I'm not really into this

Step-by-step explanation:

I just don't want you back in here and you know this because I know this because you are a good friend of yours but you have no reason for me not knowing that I was in love and you are a great man but you have no idea how to do this 6AM 6AM I know this because you have to be with him to be a great person to be able and be able and be happy and you will have a great time

PERIOD BOO

70 simple random samples of size 4 can be selected from a population of size 8

According to the question, samples of size 4 have to be selected from a population of size 8. The selection can be made in

8C4 ways.

Selection=8C4=8!(8−4)!4!

Selection=8!(8−4)!4!

Selection=8×7×6×5×4!4!×4×3×2

Selection=2×7×5

Selection=70

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The theoretical probability that the coin lands on tails and you roll a 5 is equals to the 1 over 12, i.e., 1/12.

Probability is calculated by ratio of the number of ways it could happen the total number of possible outcomes. We have, a cube with six sided and each side is labeled with numbers 1, 2, 3, 4, 5, and 6. So, total possible outcomes on rolling six sided cube = 6 = { 1,2,3,4,5,6 }

Total number of outcomes when a coin is fillped = 2 = { H, T}

A coin is flipped and a cube is rolled.

Favourable outcomes to result a 5 on rolling cube = 1

So, probability of occurrence 5 on rolling = 1/6

Similarly, favourable outcomes for lands tail on flipping a coin = 1.

That is probability of landing tails on filpping= 1/2.

Since these are independent events, the collective probability is equals to multiplication the results of each event. The probability of rolling a 5 and flipping tails = 1/2 x 1/6 = 1/12. Therefore, The required probability is 1/12.

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The probability that an outcome of 5 appears before an outcome of 7 is 1.

The probability of getting a 5 or a 7 in one roll of two fair dice is 6/36 = 1/6. The probability of getting a 5 before a 7 is equal to the sum of the infinite geometric series with the first term being 1/6 and common ratio 5/6:

1/6 + (5/6) * (1/6) + (5/6)² * (1/6) + ... = 1/6 / (1 - (5/6)) = 1/6 / (1/6) = 1.

So, the answer is 1.

The method used here is called the Geometric Series formula. It is used to calculate the sum of an infinite geometric series, which is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed constant called the common ratio. The formula for the sum of an infinite geometric series is:

S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.

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Answer:

The area will decrease by 9%.

Step-by-step explanation:

The area of a rectange is given by the formula below.

\(\boxed{\text{Area of rectangle}= \text{length}×\text{width}}\)

Let the original length and width of the rectangle be L and W respectively.

Start by finding the original area:

Original dimensions

Length= L= 100%L

Width= W= 100%W

Original area= LW

Let's find the dimensions of the new rectangle in terms of L and W.

New dimensions

Length= (100% +30%)L= 130%L

Width= (100%-30%)W= 70%W

New area

\( = \frac{130}{100} L \times \frac{70}{100} W\)

\( = \frac{91}{100} LW\)

= 91% LW

Comparing the new area with the original area:

100% LW- 91% LW= 9% LW

∴ The area will decrease by 9%.

*Note that percentage is equivalent to dividing a number by 100.

Answer:

25

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

E2021

Answer:

yesss

Step-by-step explanation:

Answer:

y=2

Step-by-step explanation:

I am assuming you meant "solve for y."

You first multiple the 6 into the parenthesis: 12y-24=0

You add 24 both sides: 12y=24

You divide both sides by 12: y=2

Check: 6(2(2)-4)=0=6(0)=0=0=0.

Answer:  B  

Step-by-step explanation:

They've given you two functions  f(x) = x^2 + 1 and g(x) = 3x +1  And they are you to find 2 * f(4) then g(x) is not needed so input in  4 for the function f(x) and multiply the output by 2.

F(4) = 4^2 + 1

F(4) = 16 +1

f(4) =  17  

   17  * 2 = 34

Answer:

Step-by-step explanation:

\(f( x ) = x^ 2 + 1 \\ g( x ) = 3 x + 1\\\\f(4) \times 2 = ?\\f(4) = 4^2 +1\\\\=( 16+1) \times 2\\\\= 17\times 2\\\\= 34\)

Answer:

\(d=\sqrt{58}\approx7.6\)

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Our first point, A, is at (1, 1) and our second point, B, is at (-2, 8).

Let's let A(1, 1) be (x₁, y₁) and B(-2, 8) be (x₂, y₂). Substitute this into the distance formula:

\(d=\sqrt{(-2-1)^2+(8-1)^2\)

Subtract:

\(d=\sqrt{(-3)^2+(7)^2\)

Square:

\(d=\sqrt{9+49}\)

Add:

\(d=\sqrt{58}\)

This cannot be simplified.

So, the distance between the two points is √58 or about 7.6 units.

And we're done!

So... where's my cookie :)?

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Case 1 - The equations of the lines that contains the four sides of the trapezoid are y = - 2, y = 1, y = - 3 · x - 5 and y = 3 · x - 5

Case 2 - The equation of the line is y = - (1 / 4) · x - 1.

Case 3 - The equation of the line is y = (7 / 5) · x + 4.

In this question we find three cases where equations of lines related to three figures. Lines are defined by equations of the form:

y = m · x + b

Where:

And the slope is calculated by secant line formula:

Case 1 - We need to determine the equations of the lines that contain the four sides of the trapezoid:

The two horizontal sides are represented by equations y = - 2 and y = 1. Now we proceed to determine the two remaining lines:

Line 1:

Slope

m = (- 2 - 1) / [- 1 - (- 2)]

m = - 3

Intercept

b = y - m · x

b = 1 - (- 3) · (- 2)

b = 1 - 6

b = - 5

Equation of the line

y = - 3 · x - 5

Line 2:

Slope

m = [1 - (- 2)] / (2 - 1)

m = 3

Intercept

b = y - m · x

b = 1 - 3 · 2

b = - 5

Equation of the line

y = 3 · x - 5

Case 2 - Now we determine the equation of the line:

Slope

m = [- 2 - (- 1)] / (4 - 0)

m = - 1 / 4

Intercept

b = - 1

Equation of the line

y = - (1 / 4) · x - 1

Case 3 - Now we determine the equation of the line:

Slope

m = [4 - (- 3)] / [0 - (- 5)]

m = 7 / 5

Intercept

b = 4

Equation of the line

y = (7 / 5) · x + 4

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Answer:

y intercept is -2.

Step-by-step explanation:

Convert the equation to slope-intercept form, or in other words, isolate the y variable. You should get y=(7/4)x-2. the -2 is the y intercept.

Hope this helped!