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The volume of the sphere is [tex]\frac{4}{3}\pi (x-1)^3[/tex]. It can be obtained by using the formula of the volume of the sphere.

What is the formula of the volume of the sphere?

Volume of any object is the amount of 3 dimentional space occupied by that object. Volume of the sphere is given by the following expression:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Here, V is the volume of the sphere and r is the radius of the sphere.

Substitute x-1 for r in the above formula.

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (x-1)^3[/tex]

This is the simplest form.

In the above equation, you can apply the formula [tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex] but that will make the equation difficult and lenthy. Hence, there is no need to apply this formula.

Hence, the volume of the sphere is [tex]\frac{4}{3}\pi (x-1)^3[/tex].

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Yes, the points are the vertices of a right triangle and we will prove that by using the Pythagorean theorem.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)² + (b - d)²)

The distance between (-4, 8) and (8, 8) is:

d₁ = √( (-4 - 8)² + (8- 8)²) = 12

The distance between (8, 8) and (-4, 3) is:

d₂ = √( (8 + 4)² + (8- 3)²) = 13

The distance between (-4, 8) and (-4, 3) is:

d₃ = = √( (-4 + 4)² + (8 - 3)²) = 5

if the Pythagorean theorem is true, then the sum of the squares of the two shorter sides must be equal to the square of the larger side, then we must have that:

5² + 12² = 13²

Solving that we get:

25 + 144 = 169

169 = 169

This is true, so yes, the vertices are the vertices of a right triangle.

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For the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to

7 : 3.

As given in the question,

Probability of any particular event occurring is equal to 7 /10

Probability of any particular event not occurring is = 1- (7/10)

                                                                                    = (10 -7) /10

                                                                                    = 3/10

Probability of the odds favoring the events which are not occurring

= (7 /10) / (3/10)

= ( 7 × 10) / (3 × 10)

= 7 /3

Odds favoring the events which are not occurring in the form a: b

= 7 : 3

Therefore, for the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to 7 : 3.

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The percent change of the worth is 3.26%.

Apples were for sale from a fruit vendor. He has 420 apples and sells 40% of them. How many apples did he have in total when he first started?

Solution: Assume a fruit vendor had x apples in stock.

According to the query,

(100 – 40%) of x = 420

60% of x = 420

60/100 x = 420

X = 700

The fruit vendor, therefore, had 700 apples in all.

Let , the worth is $x.

according to the question, $x + $5 =$158

∴ $x= $153

∴ percent change= (5/153)×100

                             =3.26%

The percent change of the worth is 3.26%.

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The correct option is, Mickey should have added –4 and 2 when combining the coefficients of the x terms.

Given,

The expression;  2x² - 4x - 9 - x² + 2x + 3

We have to simplify the expression;

To group and arrange an expression in such a way that it is easier to understand and solve is to simplify the expression.

We first group and find like terms and then add and cancel out

2x²-x²- 4x+2x - 9+ 3

=x²-2x-6

Mickey did not add the coefficients -4 and +2 for x terms in the expression, instead it looked like he added 4+2 as the coefficients

Therefore the correct option is

Mickey should have added –4 and 2 when combining the coefficients of the x terms.

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Answer:

Step-by-step explanation:

D

Jessica bought [tex]2\frac{1}{4}[/tex] yards of fabric more than Derek.

According to the question,

We have the following information:

Jessica bought 5 yards of fabric, plus 20% extra fabric. Derek bought 3 yards of fabric, plus 25% extra.

Now, we will find first the extra fabric they both bought:

For Jessica, we have:

20% of 5

20*5/100

1 yard

Now, the total fabric Jessica has:

5+1

6 yards

For Derek, we have:

25% of 3

25*3/100

3/4 yards

Now, the total fabric Derek has:

3 + 3/4

Taking 4 as the least common factor and adding the fractions:

15/4 yards

Now, we will subtract the fabric Derek has from the fabric Jessica has:

6 - 15/4

(24-15)/4

9/4

Converting this into mixed fraction:

[tex]2\frac{1}{4}[/tex] yards

Hence, the correct option is B.

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Camel can drink 21 gallons of water in 14 minutes.

Given in question,

Gallons of water camel can drink in 10 minutes = 15

 Gallons of water camel can drink in 1 minutes = 15/10

                                                                              = 1.5

Gallons of water camel can drink in 14 minutes = 1.5 * 14

                                                                              = 21

Hence, camel can drink 21 gallons of water in 14 minutes.

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The solution to the linear equation is (-1, 3).

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.

2x + y = 1 …… (1)

3x - y = -6 …… (2)

To solve the linear equations in two variables

By adding both the equations

5x = -5

x = -1

Substitute the value of x in equation (1)

2 (-1) + y = 1

-2 + y = 1

y = 1 + 2 = 3

y = 3

Therefore, the solution to the linear equation is (-1, 3).

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The confidence interval for the proportion of left-handed golfers is of:

(0.12, 0.18).

A confidence interval is calculated as the sample mean plus/minus the margin of error, hence the bounds of the confidence interval are given as follows:

In the context of this problem, these parameters are given as follows:

Hence the lower bound of the confidence interval for the proportion of left-handed golfers is:

0.15 - 0.03 = 0.12.

The upper bound of the confidence interval for the proportion of left-handed golfers is:

0.15 + 0.03 = 0.18.

Then the interval is:

(0.12, 0.18).

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The probability that at least one person will receive the correct letter is 2/3.

Given data,

Let's say that the letter matching to the envelope is A, B, and C.

Each envelope has exactly one letter inside it once the letters are randomly placed inside.

Aa, Bb, Cc, Aa, Bc, Cb, Ab, Ba, Cc, Ab, Bc, Ca, Ac, Bb, Ca, Ac, Ba, Cb, are all possible combinations.

Thus, the total number of scenarios is 6 (n(S)).

A=(Aa, Bb, Cc), (Aa, Bc, Cb), (Ac, Bb, Ca), (Ab, Ba, Cc), n(A)=4

let A be an event that at least one letter is in its right envelope.

So,

The probability that at least one letter is in the right envelope P(A) = n(S) / n(A) = 4 / 6

= 2 / 3

​

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The flowrate of decreasing water is 3.98 cm/min after the water reaches 5cm of its height.

We need to know about the flowrate to solve this problem. The rate can be described as how much water flows in a unit of time. It can be represented by this equation

Q = V / t

where Q is flowrate, V is volume and t is time.

From the question above, the given parameters are

Inverted cone with

Q = 50 cm³/min

R = 4 cm

h = 5 cm

Hence, the rate of decreasing water is

Q = V / t

50 = A . h / t

50 = π . R² . h / t

50 = 22/7 . 4 . h / t

h/t = 3.98 cm/min

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The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.

The area of the right-angle triangle is given as

A = 1/2 x B x H

Where B is the base and H is the height of the right triangle.

The length of PT is 10 and the angle ∠TPS is 60°.

The length of PR is given as,

PR = PT + TR

PR = 10 + 10

PR = 20

And the length of QS is given as,

QS = QT + TS

QS = 10 + 10

QS = 20

The area of the rectangle is given as,

A = Area of triangle ΔPQR + Area of triangle ΔPSR

A = 2 [(1/2) x (20 cos 60°) x (20 sin 60°)

A = 173.21 square units

The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.

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Answer:

[tex]3( - 7x - 3) + 4x = - (x - 3)[/tex]

[tex] - 21x - 9 + 4x = - x + 3[/tex]

[tex] - 21x + 4x + x = 9 + 3[/tex]

[tex] - 16x = 12[/tex]

[tex] - 16 \div ( - 16x = 12)[/tex]

[tex]x = - \frac{3}{4} [/tex]

Step-by-step explanation:

it is negative 3/4 not positive 3/4

This is an incomplete question and the complete question is in the image attached.

Both circles A and F have the same radius and diameter.

What is the center of the circle?

It is possible to define a circle as the locus of a point moving in a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its center. The fixed point is referred to as the center of the circle.

Given:

We have,

Two circles are named A and F.

The radius of circle A is 4cm

So, the diameter of Circle A is 4 x2 = 8 cm

The Diameter of Circle F is 8 cm

Hence, Both circles A and F have the same radius and diameter.

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The correct statement that regarding the angles of triangle is option (C)  m∠C > m∠A > m∠B

The value of p ≥ 3

Consider the value p = 3

The length of the side AB = 4p - 1

= 4×3 - 1

= 12 - 1

= 11 units

The length of side BC = 3p

= 3×3

= 9 units

The length of the side AC = p + 4

= 3 + 4

= 7 units

Then length of AB > length of BC > length of AC

The angles opposite to the side AB, BC and AC are m∠C , m∠A and m∠B

Then  m∠C > m∠A > m∠B

Hence, the correct statement that regarding the angles of triangle is option (C)  m∠C > m∠A > m∠B

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Answer:

17 = 5 + b

b = 12

y = x + 12

If a mixed fraction, 6(3/4) is divided by another fraction 1(2/3), then the quotient will be 4.05.

As per the question statement, a mixed fraction, 6(3/4) is divided by another fraction 1(2/3),

And we are required to calculate the quotient of the above mentioned division.

To solve this question, we will first convert the mixed fractions, into improper fractions, and then use the reciprocal rule to obtain our desired answer, that is,

[{6(3/4)}/1(2/3)]

= [{(4 * 6) + 3}/4]/[{(3 * 1) + 2}/3]

= [{(24 + 3)/4}/{(3 + 2)/3}]

= [(27/4)/(5/3)]

= [(27/4) * (3/5)]

= [(27 * 3)/(4 * 5)]

= (81/20)

= 4.05

Hence, when a mixed fraction, 6(3/4) is divided by another fraction 1(2/3), then the quotient will be 4.05

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Answer 2

Step-by-step explanation and no not writing out how to do it.

Answer:

12.5 hours a week

Step-by-step explanation:

So far this week, you have worked 10 hours at your part-time job. This is 80% of the number of hours you work each week. How many hours do you work each week?

10 hours = 80%

80% = 0.8

10/0.8 = 12.5 hours a week

75÷100=0.75

0.75×5=3.75

3.75×4=15

75+15=90

Depreciation expense in year 2 = 2/4 x $225,000 = $112,500.

acc to our question-

hence,Depreciation expense in year 2  = $112,500.

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Answer:

1018.25

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

hope you do well on the quiz/test/assignment!

Answer:

76.93

Step-by-step explanation:

As the area of circle is πr^2

The area of semi-circle is

1÷2×πr^2

0.5×3.14×7×7

76.93

The value of [m] will be 2.

Given is the median of the ordered set of observations 2, 3, (4m-3), (3m + 1), 11 and 13 in ascending order is 6.

We have the following data as -

2, 3, (4m-3), (3m + 1), 11, 13

N = 6

So median will be -

{(4m - 3) + (3m + 1)}/2 = 6

(4m - 3) + (3m + 1) = 12

4m + 3m - 3 + 1 = 12

7m - 2 = 12

m = 2

Therefore, the value of [m] will be 2.

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Answer:

y= 1/4x+5

Step-by-step explanation:

y=mx+c

to calculate gradient: change in y/change in x

-3/-12 = 0.25

y = 1/4x+c

4 * 1/4 = 1

6-1 = 5

c= 5

Totally:
y= 1/4x+5

The value of x in complementary angle is 12.5⁰.

We need to know about complementary angles to solve this problem. The complementary angle is the angle that can make another angle has a value of 90⁰. It can be written as

A + B = 90⁰

where A and B are the complementary angles.

From the question above, the given parameters are

A = 18⁰

B = (8x - 28)⁰

By substituting the given parameters, we can calculate the x value

A + B = 90⁰

18⁰ + (8x - 28)⁰ = 90⁰

8x = 90 - 18 + 28

8x = 100

x = 12.5⁰

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Answer: 12.5

Step-by-step explanation:

18+8x-28=90

18-18

90-18

8x-28=72

28+28

72+28

8x=100

8x/8

100/8

x=12.5

The base of the triangle is 15 meters.

Here, we are given that the height of a triangle is 5 m longer than the base.

Let the height of the triangle be h

Then, the base of the triangle will be = h - 5

Further, we are given that area of the triangle = 150 meter square

We know that area of a triangle = 1/2 × base × height

⇒ 150 = 1/2 × h × (h-5)

150 × 2 = h(h-5)

300 = [tex]h^{2}[/tex] - 5h

[tex]h^{2}[/tex] - 5h - 300 = 0

Now, we solve the above quadratic equation by splitting the middle term.

[tex]h^{2}[/tex] + 15h - 20h - 300 = 0

h( h + 15) - 20( h + 15) = 0

(h - 20) (h + 15) = 0

Thus, h = 20 or -15

But since height cannot be negative, h = 20

⇒ base = h - 5

= 20 - 5

= 15 meters

Thus, the base of the triangle is 15 meters.

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