The viewing room at a planetarium is in the shape of a hemisphere. The diameter of the hemisphere is 48 feet. What is the volume of the viewing room?

The correct option is d. [tex]\( \frac{40}{870} \)[/tex]

To find the probability of selecting a green gum ball followed by a yellow gum ball, we first calculate the total number of gum balls and then determine the number of ways to select a green gum ball followed by a yellow gum ball.

[tex]\text{Total number of gum balls} = 9 (red) + 5 (green) + 8 (yellow) + 8 (blue) = 30[/tex]

Number of ways to select a green gum ball followed by a yellow gum ball:

There are [tex]5[/tex] green gum balls and [tex]8[/tex] yellow gum balls.

Therefore, the number of ways to select a green gum ball followed by a yellow gum ball is [tex]\(5 \times 8 = 40\)[/tex]

The probability of selecting a green gum ball followed by a yellow gum ball is the number of ways to select them divided by the total number of gum balls:

[tex]\[ P(\text{green, then yellow}) = \frac{40}{30 \times 29} \][/tex]

[tex]\[ P(\text{green, then yellow}) = \frac{40}{870} \][/tex]

Answer:

C.  3(2x+1)(x-2)

Step-by-step explanation:

To factor the trinomial 6x² - 9x -6, we will follow the steps below;

First, 3 is common among the three numbers, so we will start by factoring out 3, so that the expression becomes;

3(2x² -  3x - 2)

We will now proceed to factorize; 2x² -  3x - 2  

Find two numbers such that its product gives -4 and its sum gives -3.

Such number is -4 and 1

-4 × 1 = -4

-4 + 1 = -3

We will replace -3x by -4x + x in the above expression

2x² -  4x + x - 2

(2x² -  4x) (+x - 2)

In the first parenthesis, 2x is common, so we will factor out 2x while in the second parenthesis 1 is common, so we will factor out 1. Hence;

2x(x - 2)  + 1(x-2)

(2x+1)(x-2)

3(2x² -  3x - 2)  = 3(2x+1)(x-2)

6x² – 9x – 6 = 3(2x+1)(x-2)

Therefore the factorized form of 6x² – 9x – 6  is   3(2x+1)(x-2)

The machine will take 2.5 minutes to clean 1 car.

To find the number of minutes it will take the machine to clean 1 car, we can use the concept of ratios. If the machine cleaned 20 cars in 50 minutes, we can set up a ratio:

20 cars / 50 minutes = 1 car / x minutes

Using cross-multiplication, we can solve for x:

20x = 50

x = 50 / 20 = 2.5 minutes

Therefore, it will take the machine 2.5 minutes to clean 1 car.

The area of the rectangle that was transformed from a square by increasing the length by 5 units and the width by 3 units is given by the expression (a + 5)(a + 3), or when expanded a² + 8a + 15.

Given that the original shape was a square, the length and width of the square are the same. Let's denote this common length as 'a'. When transformed into a rectangle, the length was increased by 5 units and the width increased by 3 units. Therefore, the new length and width of the rectangle are 'a + 5' and 'a + 3' respectively.

The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the rectangle in square units is represented by the expression (a + 5)(a + 3), which when expanded gives a² + 8a + 15.

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The area of a new rectangle formed from a square by increasing the length by 5 units and the width by 3 units is represented by the mathematical expression (side+5) * (side+3) in square units. This equation stems from the basic geometric formula of calculating the area by multiplying the length by the width.

The area of a shape, such as a square or rectangle, is calculated by multiplying its length by its width. In the case of a square, where all sides are equal, the formula for area can be represented as side² or side * side. If we know the side of the square, and it is increased in length by 5 units and width by 3 units, we are essentially creating a rectangle now. The formula for the rectangle area changes to (side+5) * (side+3). So, if you have a square and you increase the length by 5 units and the width by 3 units, the expression that represents the area of the new rectangle in square units would be (side+5) * (side+3). For example, if side of the square was 5 units originally, upon modification, length of rectangle will be [tex]5+5 = 10[/tex] and width will be [tex]5+3 = 8[/tex]. So, area of rectangle becomes [tex]10*8 = 80[/tex] square units.

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Final answer:

Calculate the number of terms in the arithmetic sequence 6, 2, -2, ..., -102 using the provided formula to find it is 28.

Explanation:

In mathematics, an Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference, denoted by d.

Arithmetic sequence: 6, 2, -2, ..., -102

Formula: an = a1 + d(n - 1)

Therefore, the number of terms in the arithmetic sequence is 28.

The diameter of the roll of streamers after the circumference decreases to 7 inches is approximately 2.23 inches.

To find the diameter after the circumference decreases, we can use the formula for the circumference of a circle, which is C = πd, where C is the circumference and d is the diameter.

Therefore, the diameter after the decrease is approximately 2.23 inches.

It is 3500

Carla sells hot coffee, cider and tea from a sidewalk cart near wall street in new york city. last month she sold $4,500 worth of product to 1,000 customers. she spent $800 on buying her beverages in bulk. her monthly costs

Answer:

-1

Step-by-step explanation:

I got this correct on my quiz

i^38 = -1

The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. Hence the required coordinate point is (9/4, 11/4).

Suppose that there is a line segment [tex]\overline{AB}[/tex] such that a point P(x,y) lying on that line segment [tex]\overline{AB}[/tex] divides the line segment [tex]\overline{AB}[/tex] in m:n, then, the coordinates of the point P is given by:

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]

where we have:

the coordinate of A is[tex](x_1, y_1)[/tex]

and the coordinate of B is [tex](x_2, y_2)[/tex]

The coordinate point between two points P and G divided between ratios a and b is expressed as;

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]

Given the coordinate points F(3, 5) and G(0, –4) divided within the ratio 1:3

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{1(0) + 3(3)}{1+3} , \dfrac{1(-4)+ 3(5)}{1+3} \right)\\\\(x,y) = \left( \dfrac{9}{4} , \dfrac{11}{4} \right)[/tex]

Hence the required coordinate point is (9/4, 11/4).

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Answer:

0.32

Step-by-step explanation:

The ration of gallons to cost is 1:$5.12

We want to know the ratio of ounce to cost.

We need to convert gallons to ounces.

There are 128 ounces in 1 gallon.

So, if one Moo Milk costs $5.12, then 128 ounces also cost $5.12

The ratio of ounces to cost is 128:$5.12

Now, we can find an equivalent ratio to find the cost for 1 ounce.

Then we can multiply by 8 to find the cost of 8 ounces

Ounces ---------> Cost

128 ------------> 5.12 (Both divided by 128)

1 -------------> 0.04 (Both times 8)

8 ------------> 0.32

An 8 ounce of Moo Milk costs $0.32

Answer: C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A residual value of 1.3, when referring to the line of best fit of a data set, means that,

⇒ a data point is 1.3 units above the line of best fit.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

To find a residual value of 1.3 mean when referring to the line of best fit of data set.

Since, A residual is defined as the difference between the observed value of a dependent variable and the predicted value of that variable using the regression equation.

Hence, In this case, the residual value of 1.3 indicates that the observed value of the dependent variable is 1.3 units above the predicted value, or the line of best fit.

Thus,

A residual value of 1.3, when referring to the line of best fit of a data set, means that,

⇒ a data point is 1.3 units above the line of best fit.

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Answer:

The answer is 2,765.85 dollars. Thanks.

Step-by-step explanation:

Answer:

a is correct on edege

Step-by-step explanation:

The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here A card is drawn from a standard deck of cards. Now There are some events that can impact each other or that are overlapping. They have one or more outcomes in common. When events have outcomes in common, they are said to be overlapping events, also known as mutually inclusive events. Thus this event is defenitely inclusive.

Now the probability that a red card or a queen is =( 26 red cards + 2 black queens ) /52                        

= 28/52

=7/13

Hence, The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13

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Answer:

1/4

Step-by-step explanation:

Hope this helped :)

Final answer:

A square is the quadrilateral with congruent consecutive sides. It is an equilateral rectangle and a special type of parallelogram with equal-length sides and right angles.

Explanation:

The type of quadrilateral in which consecutive sides are congruent is a square. A square is a special type of parallelogram where all sides are equal in length and all angles are right angles. When considering a square as a rectangle (which technically it is), its diagonals (which are equal in length) bisect one another at right angles, suggesting the property of being an equilateral rectangle. Furthermore, in a larger context, if we treat the sides of any parallelogram symmetrically, such as in a notation [PQRS], the order can change to [QRSP], [QPSR], and [PRQS] without affecting its properties, which aligns with the symmetric nature of a square's sides.