Geometry B
Spheres
The volume of a sphere is given by the following formula:
V =
4
3
V = = πr³
3
Page #6
Example Cros
What is the volume of the sphere in the diagram?
Find the volume of the sphere by entering the given radius into
the volume formula for a sphere.
4
V=X π X 3³
V = __________π cubic units
PEH
13

Answer: 0.286

Step-by-step explanation:

1.657−2.397(5.968x−0.27)=4.193x−3

Use the distributive property to multiply −2.397 by 5.968x−0.27.

1.657−14.305296x+0.64719=4.193x−3

Add 1.657 and 0.64719 to get 2.30419.

2.30419−14.305296x=4.193x−3

Subtract 4.193x from both sides.

2.30419−14.305296x−4.193x=−3

Combine −14.305296x and −4.193x to get −18.498296x.

2.30419−18.498296x=−3

Subtract 2.30419 from both sides.

−18.498296x=−3−2.30419

Subtract 2.30419 from −3 to get −5.30419.

−18.498296x=−5.30419

Divide both sides by −18.498296.

x=

−18.498296

−5.30419

Expand  

−18.498296

−5.30419

​by multiplying both the numerator and the denominator by 1000000.

x=

−18498296

−5304190

Reduce the fraction  

−18498296

−5304190

 to lowest terms by extracting and canceling out −2.

x=

9249148

2652095

​

and then round

The ratio of boys to girls of the junior members of a tennis club is  1 : 3.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, Three-quarters of the junior members of a tennis club are boys.

Assuming the total no. of boys and girls is 1.

∴ 3/4 members are boys and (1 - 3/4) = 1/4 are girls.

So, the ratio of boys to girls is 1/4 : 3/4 which is equal to 1 : 3.

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If we compute a 92% confidence interval in  excel command the critical value will be 1.750686.

Level of confidence c = 0.92

level of significance α = 1 - c = 0.08

A 92% confidence interval has goes from  8/2 = 4% to 100%–(8/2)% = 96%

Leaving 92% in the middle (96%–4%) = 92 %

So look up z-score for 96% or p =0.96

The two closest value in a z-table are

P(z< 1.75) = 0.95994

P(z< 1.76) = 0.96080

Based on this online table

( https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf )

So critical value Z = 1.75 is the closest value , but just barely.

But if you want a more accurate , use the normal function on Excel or from an online calculator or interpolate

If you interpolate

1.75 + (0.96–0.959954)*0.01/ (0.9608–0.95994)

Critical value Z= 1.750535

If you round to four digits,  critical value Z = 1.7505

So the interpolation isn’t that much more accurate

Excel function says critical value Z= 1.750686

=normsinv(0.96)

= 1.750686 which is probably more accurate.

By using the word interval, you have implied you are talking about a two-sided test.

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Answer:

jenny earned a total of $103.05.

Step-by-step explanation:

jenny charges 9.15 an hour to babysit todllers and 7.4 an hour to babysit school -aged children. if jenny babysat toddlers for 9 hours and school -aged childrenfor 6, she earned in all 83.55.

Answer:

(3,2)

Step-by-step explanation:

-5+8=3

6-4=2

(3,2)

The absolute value of change in the predicted value of dependent variable Y is 18.

Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.

Slope = b = -4

Intercept = a = -2.8

So, the equation of the regression line is

y  =  a + bx

y = -2.8 - 4x              ...Equation 1

Now suppose the value of x is changed by adding 4.5

i.e. put x = x + 4.5

So,

y = -2.8 - 4(x + 4.5)

y = -2.8 -4x - 18         ...Equation 2

Comparing 1 and 2 ,

We get the predicted value of dependent variable Y as 18

Therefore The absolute value of change in the predicted value of dependent variable Y is 18

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Answer:

  x = -0.5, -3.5

Step-by-step explanation:

You want the solution to 4x² +16x +7 = 0 using the quadratic formula.

Comparing the given equation to the standard form quadratic, you can identify the coefficients as ...

Substituting these values into the quadratic formula, you find the solutions to be ...

  [tex]x=\dfrac{-16\pm\sqrt{16^2-4(4)(7)}}{2(4)}=\dfrac{-16\pm\sqrt{144}}{8}\\\\x=\dfrac{-16\pm12}{8}=\dfrac{-4\pm3}{2}\\\\x=\left\{-\dfrac{7}{2},\ -\dfrac{1}{2}\right\}[/tex]

The possible values of x are -3.5 and -0.5.

A line that intersects two or more lines at a distinct point is known as a transversal line.

A transversal is a line in geometry that connects two lines in the same plane at two different places. When determining whether two or more other lines in the Euclidean plane are parallel, transversals are important. Consecutive interior angles, consecutive exterior angles, corresponding angles, and alternate angles are only a few examples of the several pairings of angles that can be formed when a transversal intersects two lines. Euclid’s parallel postulate states that if two lines are parallel, then comparable interior angles are equal, alternate interior angles are equal, and successive interior angles are supplementary.

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Answer:

182 [tex]in^{2}[/tex]

Step-by-step explanation:

Bottom:

12 x 4 = 48

Left side:

5x4= 20

Front:

[tex]\frac{12x5}{2}[/tex]= 30

Back

[tex]\frac{12x5}{2}[/tex] = 30

Top

13x4 =54

Add together:

48+ 20+ 30+30+54 = 182

When chromosomal DNA replication occurs, two identical copies of a chromosome that are linked by a common centromere form a sister chromatid.

DNA, commonly referred to as deoxyribonucleic acid, is the genetic material carried by humans and virtually all other organisms. A person's cells have almost the same DNA.

DNA are made molecular building blocks which are known as the nucleotides. These building blocks consist of a phosphate group, a sugar group, and one of four distinct nitrogen bases. To build DNA strands, nucleotides are linked together into chains with the phosphate and sugar groups swapping positions.

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The line m passing through the points (2, -7) and (4, -9) is parallel to the line y = -x + 2 , the correct option is (c) .

In the question ,

it is given that ,

the Line m passes through the points (2,-7) and (4,-9),

So , the slope of the line will be = (-9 + 7)/(4 - 2)

= -2/2

= -1

We know that the if two lines are parallel then they will have same slope ,

the slope of the line should be -1,

from the given options , we can see that only option (c) has the slope = -1

on comparing equation y = -x + 2 with the general equation of the line y = mx + c , we get

slope(m) = -1

hence , the line m is parallel to y = -x + 2 .

Therefore , the line m passing through the points (2, -7) and (4, -9) is parallel to the line y = -x + 2 .

The given question is incomplete , the complete question is

Line m passes through the points (2, -7) and (4, -9). Line m is parallel to which line?

(a) 8x + 2y = -10

(b) x = 5

(c) y = -x + 2

(d) y = x - 9

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The dimensions x and x+50 are 150 ft by 200 ft. When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them.

When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.

If you draw a diagonal, you have 2 right triangles, each with leg lengths of x and x + 50.

The diagonal is the hypotenuse, h = 250

Using Pythagorean theorem:

X² + (x+50)² = 250²

x² + x²+ 100x + 2500 = 62500

2x²+ 100x - 60000 = 0

All are even, so factor out a 2:

x² + 50x - 30000 = 0

From quadratic equation:  x = [-50±√(50²-4(1)(-30000))]/(2(1))

x = (-50 ± 350)/2

We can disregard the negative so

x = (-50 + 350)/2 = 300/2 = 150 ft

The dimensions x and x+50 are 150 ft by 200 ft

The complete question is: A rectangular parking lot is 50ft longer than it is wide. Determine the dimensions of the parking lot if the diagonal distance from corner to corner of the lot is 250ft.

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The number is 115.

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = [tex]\frac{a}{b}[/tex] x 100

We have,

Number = M

40% of M = 46

[tex]\frac{40}{100}[/tex] x M = 46

M = (46 x 100) / 40

M = 115

Thus,

The number is 115.

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Answer: ∠1 = 90°

Step-by-step explanation:

      There are a few steps we will take to solve this problem. In each step, I will write an equation to help us solve, then use inverse operations to solve.

      First, we will use the exterior angles theorem to find the measurement of ∠3 (this will help us solve for ∠2, then for ∠1).

89° = 51° + ∠3

∠3 = 38°

      Next, we will find the measurement of ∠2 since we know ∠2 plus ∠3 is 90 degrees, as shown by the perpendicular lines and the box.

90° = ∠3 + ∠2

90° = 38° + ∠2

∠2 = 52°

      Lastly, we will solve for ∠1. We know that there are 180 degrees in a triangle.

180° = 38° + ∠1 + ∠2

180° = 38° + ∠1 + 52°

180° = 90° + ∠1

∠1 = 90°

Answer:

90

Step-by-step explanation:

I started by finding angle 5

180 - 89 = 91  Supplemental angles

Then I found angle 3

The sum of the interior angles of a triangle is 180

180-89-91 = 38

Angle2 and 3 are complementary angles

90- 38 =52

the sum of the interior angles of a triangle is 180

Angle 1

180 - 52 - 38 = 90

The length of the other leg of the right angles triangle is 3. Option D

The Pythagorean theorem states that the square of the hypotenuse side is equal to the square of the other two sides in a right angled triangle.

We have;

a² = b² + c²

Where;

Now, substitute the values

4² = (√7)² + c²

Find the square values

16 = 7 + c ²

collect like terms

c² = 9

Find the square root of both sides

c = 3

Hence, the value is 3

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Answer:The length of the other leg of the right angles triangle is 3. Option D

Step-by-step explanation:

The correct algebraic form is b. k/-9 + 7 = 17

There are four components in division namely divisor, dividend, quotient and remainder. The significance and meaning of each is evident from their name. The dividend is the number that is being divided. And the number which is used to divide the dividend is divisor. The result of dividing the dividend by divisor is termed as quotient. Remainder is the left over amount.

So, multiplying the divisor and quotient and adding the product with remainder will give us the desired algebraic expression. Seven is remainder. The quotient of k and negative nine implies k is dividend and negative nine is divisor. So, algebraic expression -> k/-9 + 7 = 17

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The total amount that the band earns when the concert  sells out is $18566.50

Given,

Number of seats in The Playhouse Concert Hall = 523

The cost for one ticket charged by The Pink Ladies rock band who holds a concert = $35.50

We have to find the total amount that the band earns when the concert  sells out;

Total amount = Number of seats x Cost for one ticket

Total amount = 523 x 35.50

Total amount that the band earn = $18566.5

That is,

The total amount that the band earns when the concert  sells out is $18566.50

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Answer:

r≈1.13ft

Step-by-step explanation:

hope this helps <333

Answer:

y=1.5x-3

Step-by-step explanation:

(0,-3) => x=0, y=-3

(2,0) => x=2, y=0

y=ax+b

-3=a*0+b

0=2*a+b

-3=b

0=2a+b

2a-3=0

2a=3

a=1.5

b=-3

y=1.5x-3

Answer:

[tex]y = \dfrac{3x}{2} -3[/tex]

Step-by-step explanation:

Before we identify the equation of the line in slope intercept form, we must identify the slope intercept form equation. The slope intercept form equation is y = (m)x + (b) ⇒ m = slope of line; b = y-intercept of line.

To identify the equation of the line shown in slope intercept form, according to the slope intercept form equation, we need to identify the slope of the line and the y-intercept of the line. The slope of a line is the rate of a line, which advances up/down/side-to-side at a constant rate. The y-intercept of a line is the intersection of the line at the y-axis.

There is a specific formula for identifying the slope:

[tex]\boxed{\text{Slope} = \dfrac{\text{y coordinate of 2nd point - y coordinate of 1st point}}{\text{x coordinate of 2nd point - x coordinate of 1st point}}}[/tex]

Some facts about slope: The slope of a line will also depend on the graph. If the graph ascends upward to somewhere in Quadrant 1 or 2, the slope of the line will be positive. If the graph descends downward to somewhere in Quadrant 3 or 4, the slope will be negative. If the line horizontal and it passes perfectly through the x-axis, the slope of the line is 0. If the slope of the line is vertical, then the slope will be undefined.

Location of plotted points: First point: (0, -3); Second point: (2, 0)

Let us now identify the x and y coordinates of the plotted points:

[tex]\boxed{\text{y-coordinate of 2nd point = 0; y-coordinate of 1st point = -3}} \\ \boxed{\text{x-coordinate of 2nd point = 2; x-coordinate of 1st point = 0 }}[/tex]

Plug the coordinates into the slope formula to determine the slope:

[tex]\implies {\text{Slope} = \dfrac{\text{0 - (-3)}}{\text{2 - 0}}} = \dfrac{0 + 3}{2} = \dfrac{3}{2}[/tex]

Plug the slope of the line into the slope intercept form equation:

[tex]\implies y = (m)x + (b)[/tex]

[tex]\implies y = \huge\text{(}\dfrac{3}{2} \huge\text{)}x + (b)[/tex]

[tex]\implies y = \dfrac{3(x)}{2} + b[/tex]

Let us plug any point (that is on the line) for x and y. This will help us find the y-intercept (b). I will plug in the first point because it is my preference.

[tex]\implies y = \dfrac{3(x)}{2} + b[/tex]

[tex]\implies -3 = \dfrac{3(0)}{2} + b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{First point: (0, -3)} \implies x = 0; y = -3]}[/tex]

[tex]\implies -3 = 0 + b[/tex]

[tex]\implies -3 = b[/tex]

Finally, let us substitute the slope of the line and the y-intercept of the line into the slope-intercept form equation. Then, we can simplify both sides of the equation and isolate the y-variable completely on the other side.

[tex]\implies y = (m)x + (b)[/tex]

[tex]\implies y = \huge\text{(}\dfrac{3}{2} \huge\text{)}x + (-3)[/tex]

[tex]\implies y = \dfrac{3x}{2} -3[/tex]

Therefore, the equation of the line in slope intercept form is y = 3x/2 - 3.

The rectangular coordinate form of a complex number is represented by the formula z=a+bi. The real axis is the horizontal one, and the imaginary axis is the vertical one. In terms of r and, where r is the vector's length and is the angle it makes with the real axis, we determine the real and complex components.

Rectangular form;-

Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides.

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Answer: A: x=4

Step-by-step explanation:

5(4)-5=15

20-5=15

15=15

Answer:

The expression "2(x + 6) + x" would make the equation unsolvable (i.e., no solution),

Step-by-step explanation:

This initially appears to be an odd question, since one might imagine that there would always be a solution for x, no matter what is put into the "box."  But lets take a look and see what the possible solutions look like when compared to the original equation.  First, rearrange the reference equation so that we can better compared it to the answer options:

3 (x + 1) + 9 = box

3x + 3 + 9 = box

3x + 12 = box

3(x + 4) = box

Now look through the answer options and evaluate how, or if, they may be able to prevent us from finding an actual value or x::

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

     Option[Box]    Reformatted     Complete Equation   Unsolvable?

                                                            3x + 12 = 3x +12    

                                                               0 = 0                        YES*

                                                              3x + 12 = 11x - 12

                                                               -8x = -24

                                                                   x = 3                        NO

                                                               2(x+4) = 0

                                                                 2x = -8

                                                                    x = -4                      NO    

*  The YES answer means that this expression would make the answer unsolvable.  Note that the expressions on both sides of the equation are equal.  So there is no one answer.  Any choice of a value for x will always be a valid solution.  A singkle value is not possible with this equation.

The value of the expression (2/3)4 is 8/3.

Expression:

An expression also known as algebraic expression consists of unknown variables, numbers and arithmetic operators. And it does not contain any equality or inequality symbols.

Given,

Here we have the expression (2/3)4

Now, we have to evaluate the expression to find the solution for this one.

In order to get the solution for this expression,

We have to rewrite the given expression like the following form,

=> (2/3) x 4

Now, we have to multiply 4 with the numerator, then we get,

=> 8/3

Therefore, the solution of this expression is 8/3.

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Answer: A. Yes, their slopes are negative reciprocals

Step-by-step explanation:

x=3 is a vertical line where every y value lands on x=3. (Undefined slope)

y=5 is a horizontal line where every x value lands on y=5 (Zero slope)

Even though the slopes are not numbers they can still be negative reciprocals. The lines are indeed perpendicular and thus the slopes are negative reciprocals. The relationship between undefined slopes and zero slopes is negative reciprocals because 0/1 cannot be inversed because anything divided by 0 is undefined.

There are in total 1.04 x 10^6 bacteria that are growing in the petri dish.

Given that, there are 5.2 x10^4 bacteria in each 20 petri dish, we have to multiply 5.3x10^4 by 20, get the total bacteria in all 20 petri dish.

5.2 x10^4x 20

= 1,040,000

We have to write this in scientific notation.

The goal of scientific notation is to make it simple for scientists to write extremely large or extremely small numbers.

Since it always follows this notation, calculating scientific notation for a positive integer is straightforward:

a x 10^b

1.040000

1 is a, there are 6 digits right to the decimal point.

a=1.04

b=6

The scientific notation for total bacteria in 20 petri dish is 1.04 x 10^6.

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Answer:

....

Step-by-step explanation:

....

....

....

....

...

The expression (√z√y√x)^8 is simplified to zyx

Square root of a number can be defined as a value, which by multiplying itself, gives the original number.

It is represented with the symbol " √ ".

The square root of a number is the direct opposite of squaring a number.

Given the expression;

Find the square root of z

[tex]{\sqrt{z\sqrt{y\sqrt{x} } }}^8[/tex]

Square root can be expressed as the power of 1/2

Then, we have'

[tex]z\sqrt{y\sqrt{x} } ^ 4[/tex]

Find the square root of y

[tex](zy\sqrt{x} )^2[/tex]

Find the square root of x

zyz

Hence, the expression is xyz

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