To find the volume of a prism, Frank multiplies the area of the base by the height. Frank finds the area of the base of a rectangular prism is 24 square inches.
How many inch cubes are needed to fill the bottom layer of the prism?

The event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Option D

To determine which event is most likely to occur, we need to compare the probabilities of each event happening.

Rolling a multiple of 4 on an eight-sided die:

There are 8 possible outcomes when rolling an eight-sided die, and 2 of them are multiples of 4 (4 and 8). So, the probability of rolling a multiple of 4 is 2/8, or 1/4.

Spinning a spinner and landing on pink:

There are 4 possible outcomes when spinning the spinner, and only one of them is pink. So, the probability of landing on pink is 1/4.

Winning a raffle that sold a total of 100 tickets, if you buy 53 tickets:

The total number of possible outcomes is the total number of tickets sold, which is 100. The number of favorable outcomes is the number of tickets the person bought, which is 53. So, the probability of winning the raffle is 53/100.

Reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew:

The total number of possible outcomes is the total number of candies in the bag, which is 50 + 10 = 60.

The number of favorable outcomes is the number of strawberry chews in the bag, which is 50. So, the probability of pulling out a strawberry chew is 50/60, which simplifies to 5/6.

Comparing the probabilities, we can see that the event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Therefore, this event is the most likely to occur.

Learn more about probabilities at:https://brainly.com/question/13604758

#SPJ1

Answer:

The rule for reflection along the x axis (x;y) to (x; -y)

A' (x ; -(y) )

A' (4 ; -(5) )

A' (4 ; -5 )

The point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).

As a line has length but no width, it is a one-dimensional figure in geometry. A line is constructed from a collection of points that can be stretched indefinitely in opposite directions. In a two-dimensional plane, it is determined by two points. In a two-dimensional coordinate plane, there are various ways to express line equations. The general or standard form of the equation of a line, the slope-intercept form, and the point-slope form are the three most often used ways. The point-slope form, as its name implies, combines a line's point with the straight-line slope. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line.

The point slope equation with the point (x1, y1) is given by the formula:

(y - y1) = m (x - x1)

Here, (x1, y1) are the coordinates of the point on the graph.

m is the slope of the line.

Hence, the point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).

Learn more about slope here:

https://brainly.com/question/16941905

#SPJ1

Answer:

[tex]S_n= n^2+4n[/tex]

[tex]n=11[/tex]

Step-by-step explanation:

The given arithmetic series is 5 + 7 + 9 + ...

From inspection of the given series, we can see that the first term is 5.

The common difference is the difference between consecutive terms. Therefore, the common difference of the given series is 2.

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

To determine an equation for the sum of the first n terms of the given series, substitute a = 5 and d = 2 into the formula.

[tex]\implies S_n=\dfrac{1}{2}n\left[2(5)+(n-1)(2)\right][/tex]

[tex]\implies S_n=\dfrac{1}{2}n\left[10+2n-2\right][/tex]

[tex]\implies S_n=\dfrac{1}{2}n\left[2n+8\right][/tex]

[tex]\implies S_n= n^2+4n[/tex]

To find the value of n, substitute Sₙ = 165 into the formula and solve for n:

[tex]\implies n^2+4n=165[/tex]

[tex]\implies n^2+4n-165=0[/tex]

[tex]\implies n^2+15n-11n-165=0[/tex]

[tex]\implies n(n+15)-11(n+15)=0[/tex]

[tex]\implies (n-11)(n+15)=0[/tex]

Apply the zero product property:

[tex](n-11)=0 \implies n=11[/tex]

[tex](n+15)=0 \implies n=-15[/tex]

Therefore, as the value of n is positive, the value of n for which the series has a sum of 165 is 11.

As we discovered in chapter, there is a 1/12 chance of getting a 3.

By reducing the number of successful effects by the total amount of possible outcomes, probability—the chance that a will occur—is determined. A coin toss serves as the most fundamental example. There are just two results when users flip a coin: either it shows up heads or tails.

There are 12 potential results in total because the die has 12 sides.

(1) Since there is only one side of the die with a 3 on it and all sides are equally probable, the chance of rolling the die and having the 3 face on top is 1/12.

(2) The likelihood that the die will fall on top with a 3 or a 7 is calculated as the product of the odds of rolling a 3 and a 7 minus the likelihood of simultaneously rolling a 3 and a 7. (which is zero, since the die has only one side).

As we discovered in chapter, there is a 1/12 chance of getting a 3. (1). Given that the dice only has a 7 on one side, the likelihood of getting a 7 is also 1/12. The likelihood of tossing the dice and having the 3 or 7 face up is therefore:

1/12 + 1/12 - 0 = 1/6

(3) Since the die doesn't have a face marked "15," there is no chance that tossing the die will result in a 15 face landing on top.

To know more about Probability visit:

https://brainly.com/question/25839839

#SPJ1

Answer:

Error refresh.

Step-by-step explanatithanksforfreepointlolon:

Answer:

a. The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of b.

b. Approximately 8.

b. Enter the approximate slope of the estimated line of best fit in the second box. slope=24 (Enter your estimate to the nearest tenth.)

Approximately 2.4.

The required point slope of the line shown in the graph is y + 4 = 2(x - 3).

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
From the graph, we have two points on the line (3, -4) and (6, 2)

The slope of the line, with the help of the two-point, is given as,

m = (y₂ - y₁) /  (x₂ - x₁)

m = 2 + 4 / 6 - 3
m = 6/3
m = 2

Now,
The equation of the line having a slope of m = 2 and passing through (3, -4) is given as

y - y₁ = m (x - x₁)

y + 4 = 2(x - 3)
y = 2x - 6 - 4
y = 2x - 10

Thus, the required point slope of the line shown in the graph is y + 4 = 2(x - 3).

Learn more about slopes here:

https://brainly.com/question/3605446

#SPJ1

Quadrilateral R'S'T'V' is smaller than Quadrilateral RSTV because a scale factor is less then 1.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Quadrilateral RSTV is dilated with the origin as the center of dilation using the rule (x, y) = (3/2x, 3/2y) to create quadrilateral R'S'T'V'.

Here, All the coordinates of vertex of Quadrilateral RSTV are,

R = (- 3, - 2)

S = (- 2, 3)

T = (2, 2)

V = (3, - 1)

Hence, By applying rule we get;

All the coordinates of vertex of Quadrilateral R'S'T'V' are,

R' = (- 3 × 3/2, - 2× 3/2) = (- 9/2. - 3)

S' = (- 2 × 3/2, 3 × 3/2) = (- 3, 9/2)

T' = (2 × 3/2, 2× 3/2) = (3, 3)

V' = (3 × 3/2, - 1 × 3/2) = ( 9/2. - 3/2)

Now, Distance between R and S;

RS = √ (- 3- (- 2))² + (- 2 - 3)²

     = √1 + 25

     = √26

And, Distance between R' and S';

R'S' = √ (- 3- (- 9/2))² + (- 3 - 9/2)²

     = √(3/2)² + (15/2)²

     = √9/4 + 225/4

    = √234/4

Hence, The scale factor is,

⇒ RS / R'S' = √26 / (√234/4)

                  = 2√26/ √234

                  = 2/3

                  = 0.67 < 1

Thus, Quadrilateral R'S'T'V' is smaller than Quadrilateral RSTV because a scale factor is less then 1.

Learn more about the transformation visit:

https://brainly.com/question/2689696

#SPJ1

Answer:

The answer is A my friend! Good luck on your test Mr Rush.

Answer:

f(x)-g(x)

= [tex](x^{2} - 13x + 36) - ( x -4)[/tex]

= [tex]x^{2} -13x+36-x+4[/tex]

= [tex]x^{2} -14x-40[/tex]

Therefore , the solution of the given problem of probability comes out to be the required probability is 0.05 or 1/20 and the correct option is c.

Probability theory is an area of mathematics that focuses on calculating the probability that a claim is valid or that a specific event will occur. Chance can be represented by any number between zero and 1, where range 1 is typically used to convey certainty and 0 is frequently used to denote possibility. The probability that a specific event will occur is displayed in a probability diagram.

Here,

The probability of randomly selecting an umbrella and a shaving kit in that order is equal to the probability of selecting an umbrella (with probability 1/5) multiplied by the probability of selecting a shaving kit from the remaining gifts (with probability 1/4,

since one gift has already been chosen and removed from consideration).

Therefore, the probability of selecting an umbrella and a shaving kit in that order is:

=>(1/5) x (1/4) = 1/20 or 0.05

So if you purchased Allure, the probability of randomly selecting an umbrella and a shaving kit in that order as your two free gifts is 1/20 or 0.05.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Note that where you have a square with a side of 20dm is inscribed in a circle, the area of the shaded region is At = [tex]\approx[/tex] 257.08dm²

A square is a geometrical shape with four equal sides and four equal angles, each measuring 90 degrees.

In the figure we will determine the area of the shade:

The formula is given as follows:

1/2(Area of the Square) + ∡AB + ∡DC

Note that the above equation subsists because:

i)  the shaded region comprises of two congruent or similar triangles since the diagonals of a Square will bisect each other equally creating 4 congruent triangles.

ii) A square in a circle will always create 4 equal Chords.

Thus, imputing the figures we have:
(20dm)²/2 + [π ((20√2)/2)² - (20dm)²]/4

= 200 + [200π -400]/4
= 200 + (50π -100)
= 100 + 50π

= 257.079632679

[tex]\approx[/tex] 257.08dm²

Learn more about Square in Circles:
https://brainly.com/question/16592747
#SPJ1

Full Question:

A square with a side of 20 dm is inscribed in a circle. Determine the shaded area shown in the figure.

The value of expression 50% of 36 is,

⇒ 50% of 36 = 18

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The expression is,

⇒ 50% of 36

Now, We can simplified as;

The expression is,

⇒ 50% of 36

By definition of percent we get;

⇒ 50/100 × 36

⇒ 1/2 × 36

⇒ 36/2

⇒ 18

Thus, The value of 50% of 36 is,

⇒  50% of 36 = 18

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ9

The system of inequalities that can be used to find the possible original prices of a laptop, x, and of a printer, y is: x + y ≥ 1050 and 0.8x + 0.9y > 860

Let x be the original price of the laptop and y be the original price of the printer.

So, the discounted price of the laptop is 0.8x and the discounted price of the printer is 0.9y

If the two are purchased together, the total discounted price is:

0.8x + 0.9y

This exceeds $860

0.8x + 0.9y > 860

The original prices of the two together is at least $1,050.

This can be written as:

x + y ≥ 1050

So, we have

x + y ≥ 1050 and 0.8x + 0.9y > 860

Read more about inequalities at

https://brainly.com/question/30673825

#SPJ1

Using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.

What is meant by Pythagoras' theorem?

The Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse. In essence, Pythagoras' theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.

The given figure is a right triangle.

The length of road A = 16.01 km

The length of road B = 10 km

a) The length of road C can be found using Pythagoras' theorem.

From figure,

A² = B² + C²

16.01 ² = 10² + C²

C² = 156.32

C = 12.5 km

b) Speed of bike = 19.5 km/h

   Length of road C = 12.5 km

Time = Length/speed = 12.5/19.5 = 0.64 hours

 Length of road B =10 km

Time = Length/speed = 10/19.5 = 0.51 hours

c) Length of road A = 16.01

Time taken = Length/speed = 16.01/19.5 = 0.82 hours.

Therefore using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.

To learn more about Pythagoras' Theorem, follow the link.

brainly.com/question/343682

#SPJ1

Answer:

x= 45°

Step-by-step explanation:

They are angle on a straight line

85+2x+5 = 180

2x+ 90 = 180

2x = 180-90

2x = 90

dividing both sides of the equation by 2

x = 45

The x and y values are x=5 and y= -2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=4x-22 ----(1)

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

Substitute (1) into (2)

=> 2x+3(4x-22)=4

=> 2x+12x-66 = 4

=> 14x = 4+66

=> 14x = 70

=> x=70/14 = 5

(1) => y=4*5-22 = 20 - 22 = -2

So, the x and y values are x=5 and y= -2

To learn more about the solution of an equation from the given link

https://brainly.com/question/22688504

#SPJ1

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the Pythagorean theorem to find the value of z:

[tex]AC^2 = AD^2 + DC^2[/tex]

Since BD is perpendicular to AC, we know that DC = BC. We can also use the fact that AB and BD are altitudes of triangle ABC to find the area of the triangle in two different ways:

Area of triangle ABC = 1/2 * AB * BD = 1/2 * AC * AD

Substituting the given values, we get:

1/2 * 10 * BD = 1/2 * z * 8

Simplifying this equation, we get:

BD = 4z/5

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

To know more about expression visit:

brainly.com/question/24242989

#SPJ1

The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.

Let 'a' is the leading coefficient and 'b' is the factor.

The exponent is given as,

y = a(b)ˣ

Some points regarding the exponent function:

The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.

More about the exponent link is given below.

https://brainly.com/question/5497425

#SPJ1

Answer:

7.25

Step-by-step explanation:

Divide 8.99 by 1.24

Answer:

translation point a cross the coordinator

Southeast Washington State has a long history of seasonal dust storms. In October 1991, levels of dust particles in the air were six times greater than the Environmental Protection Agency's standard.

Several researchers conducted studies at three community hospitals to examine the relationship between the amount of dust particles in the air during the storms and the number of emergency room visits for respiratory disorders. Using the methods of correlation and regression, they were able to determine the effect of these dust storms on local residents.

In this module, you will write a short statistical report based on your linear regression analysis of data collected for two interesting variables that you believe could be linearly correlated. Your report should be supported by a scatter plot of the data and a least squares regression line.

To begin, you should collect your own data or use data that has already been collected. You may find data in the exercises at the end of sections 10.2 and 10.3 of your course text. Use at least 5 pairs of data.

Once you have collected your data, you should create a scatter plot of the data and a least squares regression line. You should also calculate the correlation coefficient and the equation of the regression line.

In your report, you should discuss the relationship between the two variables and the strength of the correlation. You should also discuss the equation of the regression line and how it can be used to make predictions.

Finally, you should conclude your report by discussing the implications of your findings and any limitations of your study.

Overall, your statistical report should be factually accurate, professional, and concise. You should also be sure to cite any sources that you use in your report.

https://brainly.com/question/14313391

#SPJ1

The Accurate Prediction of the data:

In a group of 120 students, it is expected that 16 of them are taking electronics.

About 25% of the students in the school are taking art.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Total students = 60

let x% of students chose Arts

So, x% of 60 = 15

x/ 100 (60) = 15

x = 1500 / 60

x = 25%

and, if there 120 students then number of students choose electronics

= 8/60 x 120

= 16

Learn more about Percentage here:

https://brainly.com/question/29306119

#SPJ9

Answer:

Step-by-step explanation:

a) The slope of the line passing through the points (5,6) and (-1,6) can be calculated using the formula:

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

where (x1, y1) = (5,6) and (x2, y2) = (-1,6).

m = (6 - 6) / (-1 - 5) = 0 / -6 = 0

Therefore, the slope of the line is 0.

b) The slope of the line passing through the points (3,-2) and (3,-1) cannot be calculated using the previous formula since the points have the same x coordinate. This means that the line is vertical and therefore its slope is infinite (or undefined).

c) The slope of the line passing through the points (2,2) and (-5,2) can be calculated using the formula:

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

where (x1, y1) = (2,2) and (x2, y2) = (-5,2).

m = (2 - 2) / (-5 - 2) = 0 / -7 = 0

Therefore, the slope of the line is 0.

d) The slope of the line passing through the points (9,-2) and (-7,-2) can be calculated using the formula:

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

where (x1, y1) = (9,-2) and (x2, y2) = (-7,-2).

m = (-2 - (-2)) / (-7 - 9) = 0 / -16 = 0

Therefore, the slope of the line is 0.

e) The slope of the line passing through the points (-8,22) and (1,4) can be calculated using the formula:

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

where (x1, y1) = (-8,22) and (x2, y2) = (1,4).

m = (4 - 22) / (1 - (-8)) = -18 / 9 = -2

Therefore, the slope of the line is -2.

f) Since we know the slope m = 2 and one of the points is (3,6), we can use the formula:

y - y1 = m(x - x1)

where (x1, y1) = (3,6). Substituting m and (x1, y1) into the formula, we get:

y - 6 = 2(x - 3)

Expanding the formula and solving for y, we get:

y = 2x - 6 + 6

y = 2x

Therefore, the y-coordinate of the second point is y = 2(4) = 8. The second point is (4,8).

Answer:

66.67

Step-by-step explanation:

8 people stayed home, 8/12=2/3=66.67(approx)

Answer: f=756

Step-by-step explanation:

f/28=7

multiply both sides of the equation by 28

28 x f/28=28 x 27

cancel out the greatest common factor 28

f=28 x 27

multiply 28 x 27

f=756

Answer:

180 + t = 267

Step-by-step explanation:

180 and t more is the same as adding t to 180.

"is" means equals

The number of each denomination is: 13 of the $10-dollars bills.

Let x be number of the $20 dollars bills. Then, the number of the $10 dollars bills is (x+2), according to the condition.

The money equation will then be:

20x + 10*(x+2) = 350

Now, solve for x.  

20x + 10x + 20 = 350

30x = 350 -20

30x = 330

x = 330/30

x = 11

So, 11 of the $20 dollars bills and 11 +2 = 13 of the $10-dollars bills.

Full question "Part of the proceeds from a garage sale was ​$350 worth of ​$10 and ​$20 bills. If there were 2 more $10 bills than $20 bills, find the number of each denomination.

Read more about denomination

brainly.com/question/1023816

#SPJ1

The triangle whose sides are √13, 6, and 7, is a right triangle.

What is the right triangle?

A right triangle is defined as a triangle with one right angle or two perpendicular sides. The longest side of a right triangle is called the hypotenuse.

Pythagorean Theorem :

The square on the hypotenuse is equal to the total of the squares on the legs of a right triangle.

Mathematically, let r be the length of the hypotenuse of a right triangle. Again let p, q be the lengths of other sides of this triangle. By the Pythagorean Theorem,

r² = p² + q².

How to solve this problem?

We just check which triangle's sides follow the above theorem.

Option A (Triangle with sides √13, 6, and 7 ):

13 + 36 = 49

i.e. (√13)² + 6² = 7²

This triangle's sides follow the Pythagorean Theorem.

So, the triangle with sides √13, 6, and 7 is a right triangle.

Option B (Triangle with sides 7, 8, and 13 ):

49 + 64 ≠ 169

i.e. 7² + 8² ≠ 13²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides 7, 8, and 13 is not a right triangle.

Option C (Triangle with sides 10, 11, and 12 ):

100 + 121 ≠ 144

i.e. 10² + 11² ≠ 12²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides 10, 11, and 12 is not a right triangle.

Option D (Triangle with sides √10, 9, and 8 ):

10 + 64 ≠ 81

i.e. (√10)² + 8² ≠ 9²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides √10, 9, and 8 is not a right triangle.

Therefore the triangle whose sides are √13, 6, and 7, is a right triangle. So, option A is correct.

Learn more about right triangles here -

brainly.com/question/481046

#SPJ1

When two-proportion z-test if you're evaluating the populations parameter against a single proportion statistic.

Relationships generally regarded to as symmetrical when they continuously maintain a similar ratio. For instance, the number of trees in a vineyard and the number of apples in a yield of apples depend upon that average number of apples delivered by each tree. A linear relationship among two quantities or variables is described to as being proportional in mathematics. If the initial quantity doubles, the other amount does do so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two quantities be proportional, it means that if one grows, the other climbs as well, and their connection is constant at all values. The size and circumference of a sphere are used as an example.

given

To compare a proportion of replies or values in a sample of data to a (hypothesized) proportion in the population .

from which our sample data are obtained, one can use the single proportion (or one-sample) binomial test.

We rarely have access to statistics for a whole population, so this is significant.

when two-proportion z-test if you're evaluating the populations parameter against a single proportion statistic.

To know more about proportionality visit:

https://brainly.com/question/29126727

#SPJ1