1) The base of a solid is the region enclosed by y=√25- and the v-avis. All parallel cross-sections
perpendicular to the x-axis are squares. Find the volume of the solid

The value of angle S and angle R is 95⁰ and 110⁰ respectively.

The value of angle S and angle R is calculated as follows;

11y + 7y = 180 (opposite angles of cyclic quadrilateral are supplementary)

18y = 180

y = 180/18

y = 10

(3x - 5) + (3x + 5) = 180 (opposite angles of cyclic quadrilateral are supplementary)

6x = 180

x = 180/6

x = 30

Angle S = 3x + 5

= 3(30) + 5

= 95⁰

Angle R = 11y

= 11 x 10

= 110⁰

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The measures of the angles add up to 180°, using that we can see that x = 10.

Here we can see that the two vertical lines are parallel, thus, the angles in both intersections are equal.

Now, notice that the 75° angle would be an adjacent angle to (11x - 5)°, then their measures add up to 180°, then we can write:

75° + (11x - 5)° = 180°

We can solve that for x.

75 + 11x - 5 = 180°

70 + 11x = 180

11x = 180 - 70 = 110

x = 110/11

x = 10

That is the value of x.

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Answer:

answer is 0.25

Step-by-step explanation:

2.50/10

there is only one zero in 10 so we move the decimal one digit towards left.

which then the decimal ends up in front of 2.

The calculated value of the number of different outcomes in the sample space is 24

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

Using the above as a guide, we have the following:

Colors = 3

Clasps = 2

Locations = 4

So, we have

Outcomes = Colors * Clasps * Locations

Substitute the known values in the above equation, so, we have the following representation

Outcomes = 3 *2 * 4

Evaluate

Outcomes = 24

Hence, the number of different outcomes in the sample space is 24

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By completing squares, we can rewrite the quadratic equation as:

(x + 9)^2 = -9

Remember the perfect square trinomial:

(a + b)^2 = a^2 + 2ab + b^2

Here we have the quadratic equation:

x^2 + 103 = -18x + 13

We can rewrite this as:

x^2 + 18x = 13 - 103

x^2 + 18x = -90

x^2 + 2*9*x = -90

We can add 9^2 and subtract 9^2 to get:

x^2 + 2*9*x + 9^2 - 9^2= -90

(x^2 + 2*9*x + 9^2) - 9^2= -90

(x + 9)^2 - 81 = -90

(x + 9)^2 = -90 + 81

(x + 9)^2 = -9

That is the equation we wanted to get.

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The domain of the function is, (-4, +∞) - {6}

And the range of the function is, R - [-2,0).

Since, The domain of a function is the set values of x for which the function is defined.

And, The range of a function is the set values of y for which the function is defined.

As we can see that the graph of the function can be defined everywhere except on 6 at the x-axis, and between 0 to -2 on the y-axis. therefore,

Domain = (-4, +∞) - {6}

Range = R - [-2,0)

Hence, the domain of the function is (-4, +∞) - {6} and the range of the function is R - [-2,0).

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The probability by the given data is 1%.

We are given that;

set α=0.01

Now,

The probability of making a type I error is the significance level, or alpha (α), which is the threshold we set for rejecting the null hypothesis124. It is also known as the false positive rate3.

If we set α=0.01, it means that we are willing to accept a 1% chance of making a type I error. Hence, the probability that we reject the null hypothesis when it was in fact true is 0.01 or 1%.

Therefore, by probability the answer will be 1%.

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the equivalent expression of 5^-4 is 1/625

Index forms are defined as mathematical forms that are used in the representation of numbers or variables that are too large or too small.

They are also called scientific notation or standard forms.

They are represented as a number or variable that is raised to an exponent.

Examples of index forms are;

a³, c²

5², 6³

From the information given, we have;

5^-4

Note that equivalent expressions are described as expressions that have the same solution but different arrangement of values

Then, we have;

1/5⁴

Find the fourth root

1/625

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If you choose the baseball workshop, you will need to know the kind of beverage that would be better for the participants after playing baseball, and if we ask participants it is likely they choose water or soda.

Information about the workshop is limited; however, it is likely the participants have to play baseball and they will need to drink and eat something after this.

We want to know the beverage and snack that would be better for hydration. Moreover, it can be expected the participants choose common options such as soda or water.

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Steven ran more distance, and the difference is 5.6 units.

Rebbeca ran 3 times across the center of a circle whose diameter is 40 units, then the distance that she ran is 3 times that:

distance for Rebbeca = 40*3 = 120 units.

While Steven ran one time across the circumference, remember that the circumference is 3.14 times the diameter, so the distance that he ran is:

Distance for Steven = 3.14*40 = 125.6 units.

So Steven ran more, and the difference is:

125.6 - 120 = 5.6 units.

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The angle formed between this vector and the positive x-axis measures around 61.26° and goes in a counterclockwise direction.

First, we calculate the components:

u = (80cos(30°), 80sin(30°)) ≈ (69.28, 40.00)

v = (60cos(60°), 60sin(60°)) ≈ (30.00, 51.96)

w = (50cos(120°), 50sin(120°)) ≈ (-25.00, 43.30)

Now, let's find the resultant vector (u+v+w):

u+v+w = (69.28 + 30.00 - 25.00, 40.00 + 51.96 + 43.30) ≈ (74.28, 135.26)

The magnitude of the resultant vector ||u+v+w|| can be found using the Pythagorean theorem:

||u+v+w|| = √(74.28² + 135.26²) ≈ 152.44

To find the direction, we calculate the angle θ:

θ = atan2(135.26, 74.28) ≈ 61.26°

The total size of the composite vector, obtained by adding u, v, and w, amounts to a value close to 152.44.

The angle formed between this vector and the positive x-axis measures around 61.26° and goes in a counterclockwise direction.

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The three vectors are in two-dimensional space and have the following components:

u = (80cos(30°), 80sin(30°))

v = (60cos(60°), 60sin(60°))

w = (50cos(120°), 50sin(120°))

What are the magnitude and direction is u+v+w? ||v|= 60 ||w||=50 ||u||= 80

The measure of the missing vaule of x in the diagram is 43

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

The circle

Using the theorem of sum of angles on a circumference, we have

2x + 122 + 152 = 360

Evaluating the like terms, we have

2x = 360 - (122 + 152)

So, we have

2x = 86

Divide by 2

x = 43

Hence, the missing vaule of x in the diagram is 43

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Answer:

(1/2)(x + 4 + 100) = 3x

x + 104 = 6x

5x = 104, so x = 20.8

The local maximum of f is at (-5/3, 128/27), and the local minimum is at (4/3, -64/27).

To find the neighborhood maxima and minima of the capability f(x) = (x-3)(x+1)(x+4), we really want to take its subordinate:

f'(x) = (x+1)(x+4) + (x-3)(x+4) + (x-3)(x+1)

f'(x) = [tex]3x^2 + 6x - 20[/tex]

Setting f'(x) equivalent to nothing and settling for x, we get:

[tex]3x^2 + 6x - 20 = 0x^2 + 2x - 20/3 = 0(x+5/3)(x-4/3) = 0[/tex]

Thusly, the basic focuses are x=-5/3 and x=4/3.

To decide the time periods and diminishing, we can utilize the principal subsidiary test. Since f'(x) is a quadratic capability with a positive driving coefficient, it is dependably certain for x < - 5/3 and x > 4/3, and consistently negative for - 5/3 < x < 4/3.

Thusly, f(x) is expanding on the spans (- ∞, - 5/3) and (4/3, ∞), and diminishing on the stretch (- 5/3, 4/3).

To find the nearby maxima and minima, we can utilize the subsequent subsidiary test. Taking the subordinate of f'(x), we get:

f''(x) = 6x + 6

Subbing x=-5/3 and x=4/3, we get:

f''(- 5/3) = - 2 < 0, so f has a neighborhood greatest at x=-5/3.

f''(4/3) = 10 > 0, so f has a neighborhood least at x=4/3.

Thusly, the neighborhood limit of f is at (- 5/3, 128/27), and the nearby least is at (4/3, - 64/27).

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Answer:

The cost of one share of the stock on Friday is $41.45

Step-by-step explanation:

The initial cost of one share of the stock on Monday is $41.45.

On Tuesday, the cost goes up by $0.58, so the cost becomes:

$41.45 + $0.58 = $42.03

On Wednesday, the cost goes down by $0.26, so the cost becomes:

$42.03 - $0.26 = $41.77

On Thursday, the cost also goes down by $0.26, so the cost becomes:

$41.77 - $0.26 = $41.51

Finally, on Friday, the cost goes down by $0.06.

So the expression to represent the cost of one share of the stock on Friday is:

$41.51 - $0.06

To evaluate this expression, we simply subtract $0.06 from $41.51:

$41.51 - $0.06 = $41.45

Therefore, the cost of one share of the stock on Friday is $41.45

The amount of commission Mr. A received last month is C = $ 417.62

Given data ,

Let the amount of commission earned be C

Now , the equation is

The first $1,500 in sales are eligible for a commission rate of 21%, so the commission on this portion of his sales is:

0.21 x $1,500 = $315

The remaining portion of his sales is:

$2,233 - $1,500 = $733

This amount is eligible for a commission rate of 14%, so the commission on this portion of his sales is

On simplifying the equation , we get

0.14 x $733 = $102.62

To find Mr. A's total commission, we add the commission on the first $1,500 to the commission on the remaining $733

$315 + $102.62 = $417.62

Hence , Mr. A earned a commission of $417.62 last month

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The number of days the family were on vacation is 20 days.

The number of days the family were on vacation is calculated as follows;

Let's consider morning and afternoon as a half day.

From the question we will have the following equation;

12 mornings +  13 afternoons = 25  half days.

25 - 15 days of raining = 10  half days

10  half days = 5  mornings and 5 afternoons with no rain.

The number of days they stayed is calculated as;

15 + 5 = 20  days.

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Answer:

Step-by-step explanation:

The sum of angles in a quadrilateral is 360 degrees. So, we have:

x + 2x + 3x + fourth angle = 360

6x + fourth angle = 360

fourth angle = 360 - 6x

To find the value of x, we can use the fact that the angles in a quadrilateral add up to 360 degrees:

x + 2x + 3x + (360 - 6x) = 360

6x + 360 - 6x = 360

360 = 360

This equation is true for any value of x, so we cannot solve for x.

To find the size of the largest angle, we can substitute any value of x into the expression for the fourth angle and then find the largest of the four angles. For example, if we choose x = 30, then the angles are:

x = 30 degrees

2x = 60 degrees

3x = 90 degrees

fourth angle = 360 - (x + 2x + 3x) = 180 degrees

So the largest angle is 180 degrees.

Answer:

80 miles per hour.

Step-by-step explanation:

120 - 80 = 40 Because 40 is half than 80.

A function f(x) = (x⁴ - 5x² + 4) / (x² + x - 2) is discontinuous at  x = 1 and x = -2. And it is a removable discontinuity.

Consider function f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)

We factorise denominator as,

x² + x - 2

= x² + 2x - x - 2

= x(x + 2) - 1(x  + 2)

= (x  + 2)(x - 1)

So, the function f(x) becomes,

f(x) = (x⁴ - 5x² + 4) / ((x  + 2)(x - 1))

A function f(x) is discontinuous when the denominator of f(x) is zero.

i.e.,  (x  + 2)(x - 1) = 0

i.e., x = 1 or x = -2

Also, the factors of the polynomial x⁴ - 5x² + 4 are (x - 2), (x  + 2), (x - 1) and (x + 1)

We can write function f(x) as,

f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)

f(x) = ((x - 2) (x  + 2) (x - 1) (x + 1)) / ((x  + 2)(x - 1))

f(x) = (x - 2)(x + 1)

Now, the function f(x) is continuous.

Therefore, the type of discontinuity is removable discontinuity.

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Answer:

The new shape has a base of 35 cm and a height of 20 cm.

Step-by-step explanation:

Since the shape is five times larger than the shape it is similar to, we can simply multiply everything by 5.

7×5=35

4x5=20

The new shape has a base of 35 cm and a height of 20 cm.

Hope this helps (and is correct)! Good luck on your homework!

Jada will receive a prize and what prize she will receive depends on the specific details of the prize allocation process.

If there are exactly 36 prizes available and they are being allocated in sequential order, then Jada will receive a prize because she is the 36th customer.

However, if there are fewer than 36 prizes available or if they are being allocated randomly, then Jada may or may not receive a prize.

It is possible that Jada will receive a specific prize designated for the 36th customer, or she may receive a prize that is randomly allocated to any customer.

It is also possible for Jada to receive more than one prize if the prizes are being allocated in a way that allows customers to receive multiple prizes.

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The smaller of the triangle’s two acute angles is 34 degrees

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

In a right triangle, cos(7x) = sin(5x−6)

As a general rule in a right triangle,

if cos(a) = sin(b), then

a + b

Using the above as a guide, we have the following:

7x + 5x - 6 = 90

So, we have

12x = 96

Divide

x = 8

Next, we have

Angles = 7x and 5x -  6

So, we have

Angles = 7 * 8 and 5 * 8 -  6

Evaluate

Angles = 56 and 34

Hence, the smaller of the triangle’s two acute angles is 34 degrees

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The value of C(11, 0) is 1.

We have to find C(11, 0)

Using the definition of Combination

C(n, r) = n!/ r1 (n-r)!

Here, n =11 and r= 0

So, C( 11, 0)

= 11! / 0! (11-0)!

= 11! / 1 x 11!

= 1

Thus, the value of C(11, 0) is 1.

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The total distance El had biked when he finally reached the library is 119/20 miles

Given that Eli biked for [tex]1\frac{1}{10}[/tex] miles two times extra as he missed a book at home.

The distance between the Elis house and library is [tex]3\frac{3}{4}[/tex] miles

We have to find the total distance Eli biked

Total distance  = [tex]1\frac{1}{10} +1\frac{1}{10} +3\frac{3}{4}[/tex]

=11/10+11/10+15/4

20 is LCM of 10, 10 and 4

= 22+22+75/20

=119/20 miles

Hence, the total distance El had biked when he finally reached the library is 119/20 miles

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The ratio of the cost price and the printed price of the book is 1.2444.

We have,

Let's assume the printed price of the book = P.

As per the problem, the shopkeeper is selling the book at a discount of 10% on the printed price. So the selling price of the book.

= (P - 0.1P)

= 0.9P.

The shopkeeper earns a profit of 12% on selling the book.

So, the selling price of the book is also 112% of the cost price.

That is,

0.9P = 1.12C

where C is the cost price of the book.

Now, let's find the ratio of the cost price and the printed price of the book:

C/P

= (C/0.9P)/(P/0.9P)

= 1.12/0.9

= 1.2444

Therefore,

The ratio of the cost price and the printed price of the book is 1.2444.

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Answer:

12

Step-by-step explanation:

The square root of 144 is 12. This is because when a number is squared, it means it is multiplied by itself. So, 12 multiplied by 12 is equal to 144. Therefore, the square root of 144 is the value that, when multiplied by itself, gives the result of 144. This value is 12. The square root of 144 is also a perfect square, which means it is a whole number that can be generated by multiplying two equal integers.

An equation for the line that passes through (-14, 14) and whose slope is undefined is x = -14.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-14, 14) and an undefined slope, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 14 = undefined(x - (-14))

y - 14 = undefined(x + 14)

x = -14

In conclusion, the equation of a line that has an undefined slope represents a vertical line that crosses the x-axis only i.e x = -14.

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