Write the absolute value equations in the form |x−b|=c (where b is a number and c can be either number or expression) that have the following solution sets: One solution: x=23.

Answer:

Hemisphere radius = 3 inch

Sphere volume = 4/3 • π • radius^3

Sphere volume = 4/3 • π • 27

Sphere volume = 113.0973355292 cubic inches

Cylinder Volume = π • radius^2 • height

Cylinder Volume = π • 9 * 10

Cylinder Volume = 282.7433388231 cubic inches

TOTAL VOLUME = 113.10 + 282.74 cubic inches

TOTAL VOLUME = 395.84 cubic inches

Step-by-step explanation:

Answer: 126π in.³

Step-by-step explanation:

Answer:

Largest Median: Same

Largest Range: Castro

Largest IQR: Castro

Step-by-step explanation:

With a box-and-whisker plot, the box represents the upper and lower quartiles, the vertical line inside the box represents the median, and the lines on either side of the box show the high and low of the range.

Largest Median: Medians are the same because the verticle line inside the boxes is at 7 for both

Largest Range: Ms Castro's Class- the lines on either side of the box for Ms Castro go from 1-10 while the other class only goes from 4-10.

Largest IQR (interquartile range) Ms. Castro's class: their IQR goes from 5-8 while the other class only goes from 6-8

Answer:

same median and CASTRO CASTRO just took the TYS on algebra nation

Step-by-step explanation:

Answer:

1. y = 4n -1

2. y = 9n -2

Step-by-step explanation:

1. For some integer n, numbers that are congruent to 2 mod 4 are ... 4n+2. Then you have ...

y + 3 = 4n +2 . . . . next, subtract 3 from both sides

y = 4n -1 . . . . values of y are natural numbers for all natural numbers n

___

2. Similarly, ...

3 - y = 9n +5

3 - 9n - 5 = y . . . . . add y-9n-5

-9n -2 = y . . . . . . . . collect terms

For every integer n, there is also an integer -n. For our purpose, we're only interested in those values of n that make -9n be positive. Rather than require n be negative so -9n is positive, we can require n be positive and use the expression 9n for the multiple of 9.

We want y a natural number, so we can write this as ...

y = 9n -2 . . . . for natural numbers n

To find the natural number solutions for congruences, we use algebraic manipulation to simplify the equation and find values that satisfy the congruence. For the given congruences, the natural number solutions are y = 3, 7, 11, 15, ... and y = 7, 16, 25, ..., respectively.

1. To find the natural number solutions for the congruence y + 3 ≡ 2 mod 4, we need to find all values of y that satisfy the given congruence.

Subtracting 3 from both sides of the congruence, we have y ≡ -1 mod 4. Since we are looking for natural number solutions, we can rewrite this as y ≡ 3 mod 4.

The natural number solutions for this congruence are y = 3, 7, 11, 15, ...

2. For the congruence 3 - y ≡ 5 mod 9, we need to determine the natural number solutions for y that make the congruence true.

Subtracting 3 from both sides, we have -y ≡ 2 mod 9. Multiplying both sides by -1, we get y ≡ -2 mod 9. Rewriting this as y ≡ 7 mod 9, the natural number solutions for y are y = 7, 16, 25, ...

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Answer:

25m + 10b = 400

Step-by-step explanation:

Total amount that can be earned = $ 400

Amount earned on mowing a lawn = $ 25

Amount earned per hour on babysitting = $10

Amount earned for mowing one lawn is $ 25, so amount earned for mowing m lawns will be $ 25m

Amount earned for one hour of babysitting is $ 10, so amount earned for babysitting for b hours will be $ 10b

Total amount earned = Amount earned from mowing m lawns + Amount earned from babysitting for b hours

Using the values from above, we can set up the equation as:

400 = 25m + 10b

or

25m + 10b = 400

This equation represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.

a cube would be formed as ABCD form a square when graphed

Answer:

y=3/4 *x

Step-by-step explanation:

1. the given equation is the equation of line in slope-interception form (y=kx+b), where 3/4 is 'k' and (-4) is 'b'.

2. if the system of the two equations has no solution, it means, the 2d line is parallel to the given one, then 'k' of the 2d line is the same value.

3. common view of the equation of the 2d line is y=3/4 *x+b, where 'b' is number. For example, y=3/4x; y=3/4 *x+1; y=3/4 *x-5/8, etc.

One example of a linear function that generates a system without a solution is given by:

[tex]y = \frac{3}{4}x + 5[/tex]

A linear function is modeled by:

y = mx + b

In which:

If two equations have the same slope but different intercepts, they never  intersect each other, that is, a system without solutions is generated. Hence, one possible example in this problem is given by:

[tex]y = \frac{3}{4}x + 5[/tex]

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When writing rational expressions, you need to be aware that ...

  1/4x = (1/4)x ≠ 1/(4x)

Parentheses around the denominator are required, unless you're typesetting the expression and can use a fraction bar for grouping.

The derivative of the curve expression is ...

  y' = x - 1/(4x) . . . . . parentheses added to what you wrote

and the expression (1 -(y')^2) can be written ...

  1 -(y')^2 = x^2 +1/2 +1/(16x^2) . . . . . parentheses added to what you wrote

The first and last terms of this trinomial are both perfect squares, so you might suspect the whole trinomial is a perfect square. You recall that ...

  (a +b)^2 = a^2 + 2ab + b^2

This is a good "pattern" to remember. Using it is a matter of pattern recognition, as is the case with a lot of math.

Here, you have ...

  a = x

  b = 1/(4x)

In order for your trinomial to be a perfect square, the product 2ab must equal the middle term of your trinomial. (Spoiler: it does.)

  2ab = 2(x)(1/(4x)) = (2x)/(4x) = 1/2 . . . . . matches the middle term of 1 -(y')^2

Hence your trinomial can be written as the square ...

  1 -(y')^2 = (x +1/(4x))^2

_____

This is convenient because you want to integrate the square root of this. Your integral then becomes ...

[tex]\displaystyle\int\limits_{2}^{4}{\left(x+\frac{1}{4x}\right)\,dx[/tex]

Answer:

perimeter = (18 +9π) cm

area = (81 -20.25π) cm^2

Step-by-step explanation:

The perimeter of the shaded area is the circumference of the circle added to two sides of the square. The circumference of the circle is π times the diameter, so the perimeter is ...

p = 2(9 cm) + π(9 cm) = (18 +9π) cm

___

The area of the shaded portion is the difference between the area of the square and the area of the circle. The area of the square is the square of the diameter. The area of the circle is π/4 times that value.

A = (9 cm^2) + (π/4)(9 cm^2) = (81 +20.25π) cm^2

_____

Comment on circle area

The formula you often see is ...

A = πr^2 . . . . r is the radius

since r = d/2, where d is the diameter, this can also be written as ...

A = π(d/2)^2 = (π/4)d^2

Here, the diameter of the circle is the same as the side length of its enclosing square, so the area of the circle is π/4 times the area of the enclosing square.

Answer:

Area= [tex]81-\frac{81}{4}\pi[/tex]

Perimeter= [tex]9\pi +18[/tex]

Answer:

58 at the point (9,8)

7 at the point (1, 1)

Step-by-step explanation:

The maximum points will be found in the vertices of the region.

Therefore the first step to solve the problem is to identify through the graph, the vertices of the figure.

The vertices found are:

(1, 10)

(1, 1)

(9, 5)

(9, 8)

We look for the values of x and y belonging to the region, which maximize the objective function [tex]f(x, y) = 2x + 5y[/tex]. Therefore we look for the vertices with the values of x and y higher.

(1, 10), (9, 5), (9, 8)

Now we substitute these points in the objective function and select the one that produces the highest value for f (x, y)

[tex]f(1, 10) = 2(1) + 5(10) = 52\\\\f(9, 5) = 2(9) + 5(5) = 43\\\\f(9, 8) = 2(9) + 5(8) = 58[/tex]

The point that maximizes the function is:

[tex](9, 8)[/tex] with [tex]f(9, 8) = 58[/tex]

Then the value that produces the minimum of f(x, y) is (1, 1)

[tex]f(1, 1) = 2(1) + 5(1) = 7[/tex]

Seven thousand sixty-five fifty six

Answer:

seven hundred sixty-five thousand fifty-six

Step-by-step explanation:

Your Welcome

When dealing with numbers, we find the LCM by factoring the numbers, and then choosing all the primes appearing, with the highest exponent possible.

Similarly, we will factor the polynomials first:

[tex] x^4+3x^3 = x^3(x+3)[/tex]

[tex]x^2-9 = (x+3)(x-3)[/tex]

[tex]x^3+6x^2+9x = x(x^2+6x+9) = x(x+3)^2[/tex]

The following factors emerged:

So, the LCM is

[tex]x^3(x-3)(x+3)^2[/tex]

Answer:

Option D. minimum value at −38

Step-by-step explanation:

we have

[tex]x^{2}-12x-2[/tex]

Let

[tex]y=x^{2}-12x-2[/tex]

Complete the square

[tex]y+2=x^{2}-12x[/tex]

[tex]y+2+36=(x^{2}-12x+36)[/tex]

[tex]y+38=(x^{2}-12x+36)[/tex]

[tex]y+38=(x-6)^{2}[/tex]

[tex]y=(x-6)^{2}-38[/tex] ------> equation of a vertical parabola in vertex form

The vertex is the point [tex](6,-38)[/tex]

The parabola open upward-----> the vertex is a minimum

therefore

minimum value at −38

Answer:

The answer A

Step-by-step explanation:

B: You need a side that is longer than 2 equal sides. B is incorrect.

A: Try

9^2 + 12^2 = 15^2 if that works, A will work.

81 + 144 = 225

This works. I used these numbers because they were easier to see.

0.9^2 + 1.2^2 = 1.5^2

0.81 + 1.44 = 2.25

2.25 = 2.25

That is the answer A

But we have to check the  other two.

C:

0.9^2 = 0.81

1.2^2 = 1.44

1.8^2 = 3.24   This won't work. 3.24 is just too big.

D:

0.9^2 = 0.81

0.6^2 = 0.36

1.5^2 = 2.25   It's too far away.

Answer:

C. 6.683

Step-by-step explanation:

Answer:

3 - 2√5

-------------  

      2

Step-by-step explanation:

These two expressions have different denominators, and thus use of the LCD is necessary.  The LCD is 4.

Thus, we have:

6/4 - (4/4)√5, or

6 - 4√5

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

      4

This can be reduced to:

3 - 2√5

-------------   (answer)

      2

I’m pretty sure it’s A

Answer: A

Step-by-step explanation:

Compare [tex]\dfrac1{\sqrt{n^2+1}}[/tex] to [tex]\dfrac1{\sqrt{n^2}}=\dfrac1n[/tex]. Then in applying the LCT, we have

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac1{\sqrt{n^2+1}}}{\frac1n}\right|=\lim_{n\to\infty}\frac n{\sqrt{n^2+1}}=1[/tex]

Because this limit is finite, both

[tex]\displaystyle\sum_{n=1}^\infty\frac1{\sqrt{n^2+1}}[/tex]

and

[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]

behave the same way. The second series diverges, so

[tex]\displaystyle\sum_{n=0}^\infty\frac1{\sqrt{n^2+1}}=1+\sum_{n=1}^\infty\frac1n[/tex]

is divergent.

The limit comparison test is used to determine the convergence or divergence of a series by comparing it to a known convergent or divergent series.

The limit comparison test is used to determine the convergence or divergence of a series by comparing it to a known convergent or divergent series. The test states that if the limit of the ratio between the terms of the given series and the terms of a known convergent series is a finite positive number, then both series behave in the same way. Here is how you can use the limit comparison test step by step:

For example, if we have the series ∑(n^2)/(2^n), we can use the limit comparison test with the series ∑(1)/(2^n). Taking the limit of the ratio (n^2)/(2^n) / (1)/(2^n) as n approaches infinity, we get:

lim(n→∞) [(n^2)/(2^n)] / [(1)/(2^n)] = lim(n→∞) (n^2)/(1) = ∞

Since the limit is infinite, the result is inconclusive. Therefore, the given series does not converge or diverge using the limit comparison test.

Answer:

60

Step-by-step explanation:

∑[i=1,5] 4i = 4·1 + 4·2 + 4·3 + 4·4 + 4·5

= 4 + 8 + 12 + 16 + 20

= 60

Let

[tex]\theta=\sin^{-1}\dfrac x2\implies\sin\theta=\dfrac x2[/tex]

Recall that

[tex]\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\dfrac{x^2}4}[/tex]

Then

[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}\implies\tan\left(\sin^{-1}\dfrac x2\right)=\dfrac{\frac x2}{\sqrt{1-\frac{x^2}4}}[/tex]

[tex]\implies\tan\left(\sin^{-1}\dfrac x2\right)=\dfrac x{\sqrt{4-x^2}}[/tex]

Final answer:

To find tan(sin⁻¹(x/2)), we use the relationship between the sides of a right triangle, leading to the solution tan(θ) = x/√(4 - x²).

Explanation:

The question "what is tan(sin-1(x/2))" involves understanding inverse trigonometric functions and their properties. To solve this, we can create a right-angled triangle where the angle θ has a sine value of x/2. According to the Pythagorean theorem, if one side (opposite) is x and the hypotenuse is 2, the adjacent side can be calculated as √(4 - x²). Thus, tan(θ) = opposite/adjacent = x/√(4 - x²).

Answer:

a = 12

Step-by-step explanation:

Multiply the equation by the inverse of the coefficient of "a".

4·(1/4)a = 4·3

1·a = 12 . . . . . . simplify

a = 12

Answer:

The equation of the line is y = 3/4x - 1/4

Step-by-step explanation:

To find the equation of this line, start by using the two points with the slope formula to find the slope.

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

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

m = (3/2)/2

m = 3/4

Now that we have the slope, we can use that and either point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 2 = 3/4(x - 3)

y - 2 = 3/4x - 9/4

y = 3/4x - 1/4

Answer:

b) 15

Step-by-step explanation:

Given that,

Total people = 100

% of people prefer vanilla = 25%

Number of people prefer vanilla out of 100 = 25% of 100

=> 25/100 * 100 = 25

% of people prefer swirl = 35%

Number of people prefer swirl out of 100 = 35% of 100

=> 35/100 * 100 = 35

% of people prefer chocolate = 40%

Number of people prefer chocolate out of 100 = 40% of 100

=> 40/100 * 100 = 40

The number of more people preferring chocolate over vanilla =  40 - 25

=> 15 so option b is correct

Answer:

The answer is B (15)

Step-by-step explanation:

Answer:

  3.  P(R1|Q) = 3/19 ≈ 0.16

Step-by-step explanation:

The desired probability is the ratio of P(Q·R1) to P(Q). The probability P(Q) is not given, but there is sufficient information to find it.

  P(Q·R1) = P(Q|R1)·P(R1) = 0.40·0.15 = 0.06

  P(Q·R2) = P(Q|R2)·P(R2) = 0.20·0.55 = 0.11

  P(Q·R3) = P(Q|R3)·P(R3) = 0.70·0.30 = 0.21

Since R1 and R2 and R3 are mutually exclusive and have a joint probability of 1, this means ...

  P(Q) = P(Q·R1) +P(Q·R2) +P(Q·R3) = 0.06 +0.11 +0.21 = 0.38

Then the desired probability is ...

  P(R1|Q) = P(Q·R1)/P(Q) = 0.06/0.38

  P(R1|Q) = 3/19 ≈ 0.16

Final answer:

To plot a graph of the amount Betsy earns against the time she works, we'll put the hours worked on the x-axis and the amount earned on the y-axis. Betsy is paid $11.50 per hour and the equation for Betsy's earnings is Y = 11.50X.

Explanation:

To plot a graph of the amount Betsy earns against the time she works, we'll put the hours worked on the x-axis and the amount earned on the y-axis. In this case, Betsy worked an 8 hour shift and was paid $92.00. So, the point on the graph would be (8, 92). To find how much Betsy is paid per hour, we can divide the total amount earned by the number of hours worked. In this case, $92.00 divided by 8 hours equals $11.50 per hour.

Using the equation Y = MX + B, where Y is the amount earned, M is the rate per hour, X is the number of hours worked, and B is the y-intercept, we can write the equation for Betsy as Y = 11.50X + 0, since she doesn't have a one-time fee.

this is an isosceles triangle two sides are the same

so there are 180° in a triangle

180-58= 122 now divide this by two because the last two angles are equal

122/2=61° =x°

Answer:

  A.  216 cm³

Step-by-step explanation:

The volume of a cube is the cube of the side length:

  V = s³ = (6 cm)³ = 216 cm³

Answer:

The difference is that the simple interest gives you interest only on the deposited amount in the account while the compound interest is calculated over the deposited amount and the previous interest amount added to the deposited amount.

Step-by-step explanation:

The difference between simple and compound interest is that simple interest is calculated only on the principal amount, while compound interest is earned on past interest.

The difference between simple and compound interest in a savings account is that simple interest is an interest rate calculation only on the principal amount, while compound interest is interest that is earned on past interest. This means that with compound interest, the total amount of savings will grow dramatically over time. To illustrate this, consider the example of putting $1,000 in a savings account with 10% interest. With simple interest, after one year, you will have $1,100. But with compound interest, if you leave the $1,100 in the account and continue to earn 10% interest, you will have $1,210 at the end of year two.

Solve for x in 5x - 3y = 18

x = 3(6 + y)/5

Substitute x = 3(6 + y)/5 into 3x + 3y = 30

9(6 + y)/5 + 3y = 30

Solve for y in 9(6 + y)/5 + 3y = 30

y = 4

Substitute y = 4 into x = 3(6 + y)/5

x = 6

Therefore,

x = 6

y = 4

The solution to the system of equations is x = 6 and y = 4.

Step 1: Add the two equations.

5x - 3y = 18

3x + 3y = 30

8x = 48

Step 2: Solve for x.

8x = 48

x = 6

Step 3: Substitute x = 6 into one of the original equations to solve for y.

5(6) - 3y = 18

30 - 3y = 18

-3y = -12

y = 4

Answer:

both are

Step-by-step explanation:

A number, or a polynomial, is "divisible" by a "factor." Since (k+5) is a factor of (k^2-25), (k^2-25) is divisible by (k+5). Both Eleanor and Isabel are correct in their description.