Find the volume of each rectangular prism. Round to the tenths.

Find The Volume Of Each Rectangular Prism. Round To The Tenths.

Answers

Answer 1

Answer:

To find the volume of the given cuboid.

Length of the cuboid = 6.8 yd

Breadth of the cuboid = 4.5 yd

Height of the cuboid = 3.4 yd

We get,

Volume of a cuboid is,

[tex]=l\times b\times h[/tex]

where l,b and h are the length, breadth and height respectively.

Substitute the values we get,

[tex]=6.8\times4.5\times3.4[/tex][tex]=104.04\text{ yd}^3[/tex]

Answer is: Volume of the cuboid is 104.04 cubic yards.


Related Questions

8y = 0.2(3x - 5) answer in slope intercept and y-intercept

Answers

The slope of the given equation is 0.075 and  y-intercept is 0.125

What is slope of line ?

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The point with coordinate having same slope as with given coordinates can be plotted on the same line.

First writing the given equation in standard slope intercept form :

y = mx + c.........(1)

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• c is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function

8y = 0.2(3x - 5)

8y = 0.6x - 1

y = 0.6/8x - 1/8

y = 0.075x - 0.125

Now, comparing it with equation (1) we get :

m = 0.075 and c = - 0.125

hence the slope of the given equation is 0.075 and  y-intercept is 0.125

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what is the equation of the line with x-intercept (6,0) and y-intercept (0, 2)

Answers

Answer:

3y=6-x

Explanation:

The slope-intercept form of a line is y=mx+b.

First, we determine the slope(m) of the line.

[tex]\begin{gathered} m=\frac{2-0}{0-6} \\ =-\frac{2}{6} \\ m=-\frac{1}{3} \end{gathered}[/tex]

Since the y-intercept, b=2

The equation of the line is:

[tex]\begin{gathered} y=-\frac{1}{3}x+2 \\ y=\frac{-x+6}{3} \\ 3y=6-x \end{gathered}[/tex]

In which quadrant is the terminal side of 115° located?+Y43-2+-XX+3 -111841.2IV3.4

Answers

ANSWER

Quadrant II

EXPLANATION

• All angles between 0° and 90° are in the first quadrant.

,

• All angles between 90° and 180° are in the second quadrant.

,

• All angles between 180° and 270° are in the third quadrant.

,

• All angles between 270° and 360° are in the fourth quadrant.

115° is an angle measure that is between 90° and 180°. Therefore its terminal end is in the second quadrant.

3. Find the value of the function h(x) = 2 when x = 10=

Answers

[tex]h(x)=2[/tex]

In order to find the value of h(x) when x=10, we replace the value of x along with the function by 10, however, since there are not any variables the function is constant for all variables

[tex]h(10)=2[/tex]

the cake is regular price at $9 and is on sale for 25%. how much would you save with the discount

Answers

Let be "x" the amount of money (in dollars) you would save with the discount.

By definition, a percent can be converted to a Decimal number by dividing it by 100. Then, since the cake store is having 25% off sale on all cakes, this can be written as:

[tex]\frac{25}{100}=0.25[/tex]

According to the information given in the exercise, the regular price of the cake you want is $9. Based on this, you can set up the following expression for price of the cake with the discount (in dollars):

[tex]9-(9)(0.25)[/tex]

Evaluating, you get:

[tex]=6.75[/tex]

Knowing this value, you can set up that:

[tex]x=9-6.75[/tex]

Finally, evaluating, you get:

[tex]x=2.25[/tex]

The answer is: You would save $2.25 with the discount.

PLEASE PLEASE HELP

5. Renae Walters is paid a salary of $15,000 per month.



a. How much has she earned for the year after being paid at the end of January? _______________________________


b. How much is deducted in January for Social Security? For Medicare?

Social Security _____________________ Medicare _______________________


c. How much has she earned for the year after being paid at the end of November? ___________________________________

d. How much is deducted in November for Social Security? For Medicare?

Social Security _____________________ Medicare _______________________

e. How much has she earned for the year after being paid at the end of December? ___________________________________

f. How much is deducted in December for Social Security? For Medicare?

Social Security _____________________ Medicare _______________________

Answers

The amount for social security for all 3 months will $930 and the contribution for Medicare will be $217.5.

How to estimate the amount for social security for all 3 month?

Given that the salary exists paid in US dollars, we can consider that Renae Walters falls under the social security and Medicare tax rates for the United States. These rates, as of 2020, fall at 6.2% for social security and 1.45% for Medicare.

Social security contribution = Social security tax rate × Income earned

January for example Social Security = 0.062 × $15,000 = $930    

Medicare contribution = Medicare tax rate × Income earned

January for example Medicare = 0.0145 × $15,000= $217.5

The above method will apply through the months without changes.

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Given a and b are the first-quadrant angles, sin a=5/13, and cos b=3/5, evaluate sin(a+b)1) -33/652) 33/653) 63/65

Answers

We know that angles a and b are in the first quadrant. We also know this values:

[tex]\begin{gathered} \sin a=\frac{5}{13} \\ \cos b=\frac{3}{5} \end{gathered}[/tex]

We have to find sin(a+b).

We can use the following identity:

[tex]\sin (a+b)=\sin a\cdot\cos b+\cos a\cdot\sin b[/tex]

For the second term, we can replace the factors with another identity:

[tex]\sin (a+b)=\sin a\cdot\cos b+\sqrt[]{1-\sin^2a}\cdot\sqrt[]{1-\cos^2b}[/tex]

Now we know all the terms from the right side of the equation and we can calculate:

[tex]\begin{gathered} \sin (a+b)=\sin a\cdot\cos b+\sqrt[]{1-\sin^2a}\cdot\sqrt[]{1-\cos^2b} \\ \sin (a+b)=\frac{5}{13}\cdot\frac{3}{5}+\sqrt[]{1-(\frac{5}{13})^2}\cdot\sqrt[]{1-(\frac{3}{5})^2} \\ \sin (a+b)=\frac{15}{65}+\sqrt[]{1-\frac{25}{169}}\cdot\sqrt[]{1-\frac{9}{25}} \\ \sin (a+b)=\frac{15}{65}+\sqrt[]{\frac{169-25}{169}}\cdot\sqrt[]{\frac{25-9}{25}} \\ \sin (a+b)=\frac{15}{65}+\sqrt[]{\frac{144}{169}}\cdot\sqrt[]{\frac{16}{25}} \\ \sin (a+b)=\frac{15}{65}+\frac{12}{13}\cdot\frac{4}{5} \\ \sin (a+b)=\frac{15}{65}+\frac{48}{65} \\ \sin (a+b)=\frac{63}{65} \end{gathered}[/tex]

Answer: sin(a+b) = 63/65

A red maple sapling was 3 feet tall when planted in 2010. Six years later, the tree was 24 feet tall. The growth rate of the tree is constant over time. Find a linear model for the height H (in ft) of the red maple t years after 2010. Let t = 0 represent 2010.H = __________What is the expected height (in ft) of the red maple in 2020?________ ft

Answers

Since the growth rate is linear and constant over time, it means that the sequence formed is an arithmetic sequence. The formula for finding the nth term of an arithmetic sequence is expressed as

an = a1 + d(n - 1)

where

a1 is the first term of the sequence

n = number of terms

d = common difference

In this case, n would be t(number of years

From the information given,

a1 = 3

Since the first term is at t = 0 and it represents 2010, six years letter would be represented by t = 7. Thus, we would took for d given that a7 = 24

We have

24 = 3 + d(7 - 1)

24 = 3 + 6d

6d = 24 - 3 = 21

d = 21/6 = 3.5

The linear model would be

an = 3 + 3.5(t - 1)

Substituting H for an, the linear model is

H = 3 + 3.5(t - 1)

At 2020, t = 11

H = 3 + 3.5(11 - 1) = 3 + 35

H = 38

Simplify the following expression 6 + (7² - 1) + 12 ÷ 3

Answers

You have to simplify the following expression

[tex]6+(7^2-1)+12\div3[/tex]

To solve this calculation you have to keep in mind the order of operations, which is:

1st: Parentheses

2nd: Exponents

3rd: Division/Multiplication

4th: Addition/Subtraction

1) The first step is to solve the calculation within the parentheses

[tex](7^2-1)[/tex]

To solve it you have to follows the order of operations first, which means you have to solve the exponent first and then the subtraction:

[tex]7^2-1=49-1=48[/tex]

So the whole expression with the parentheses calculated is:

[tex]6+48+12\div3[/tex]

2) The second step is to solve the division:

[tex]12\div3=4[/tex]

Now the expression is

[tex]6+48+4[/tex]

3) Third step is to add the three values:

[tex]6+48+4=58[/tex]

Find the missing number so that the equation has no solutions.
5x + 12 =
- 2
Submit

Answers

By solving the equation 5x + 12 = -2, the value of x in is -2.8

Solution

Bring 12 to the other side of the equation. 12 becomes -12

5x = -2-12

Add -2 and -12.

5x = -14

We get -14

Bring 5 to the other side of the equation and divide -14 and 5

x = -14 ÷ 5

Hence the value of  x is -2.8

x = -2.8

Hence, by solving the equation 5x + 12 = -2, the value of x in is -2.8

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What is the exact surface area of the right rectangular pyramid below? Leave your answer in simplified radical form.

Answers

Usually, to calculate the area of a solid we need to calculate the area of every face. Here we have a rectangle down, and four triangles. Our desired area (TA) will be the sum of those areas. Let's calculate those areas:

Area of the rectangle) The area of the rectangle (R) is

[tex]R=(leng\ldots)(wid\ldots)=(10cm)\cdot(4cm)=40\operatorname{cm}^2[/tex]

Area of the front triangle and the back tringle) Note that the front triangle and the back triangle are the "same". So the area of each of them is equal (this simplifies our work...). The area of each of them (FB) is

[tex]FB=\frac{(base)\cdot(high)}{2}[/tex]

What is their high?

The triangle with red, blue, and green edges is a right triangle... Its hypotenuse is the blue edge. We know the red edge, its length is 6cm, but what is the length of the green edge? Because our solid is a rectangular pyramid, we can say that the green edge is half of the length of the rectangle. that is, 5cm (10cm/2). Now, we know the red and green edges; so we can apply The Pythagoras theorem to get

[tex](blue)^2=(red)^2+(green)^2[/tex][tex](blue)^2=(6cm)^2+(5cm)2=36\operatorname{cm}+25\operatorname{cm}=61\operatorname{cm}^2[/tex][tex]undefined[/tex]

find the circumstances of the circle. use 3.14 for pi.

Answers

Given:

The radius of the circiel is 4.2 in.

The value of π is 3.14.

The objective is to find the circumference of the circle.

The formula to find the circumference of the circle is,

[tex]\begin{gathered} C=2\cdot\pi\cdot r \\ =2\cdot3.14\cdot4.2 \\ =26.376\text{ inches} \end{gathered}[/tex]

Hence, the circumference of the circle is 26.376 inches.

The one-to-one functions 9 and h are defined as follows.g={(0, 5), (2, 4), (4, 6), (5, 9), (9, 0)}h(x)X +811

Answers

Step 1: Write out the functions

g(x) = { (0.5), (2, 4), (4,6), (5,9), (9,0) }

[tex]h(x)\text{ = }\frac{x\text{ + 8}}{11}[/tex]

Step 2:

For the function g(x),

The inputs variables are: 0 , 2, 4, 5, 9

The outputs variables are: 5, 4, 6, 9, 0

The inverse of an output is its input value.

Therefore,

[tex]g^{-1}(9)\text{ = 5}[/tex]

Step 3: find the inverse of h(x)

To find the inverse of h(x), let y = h(x)

[tex]\begin{gathered} h(x)\text{ = }\frac{x\text{ + 8}}{11} \\ y\text{ = }\frac{x\text{ + 8}}{11} \\ \text{Cross multiply} \\ 11y\text{ = x + 8} \\ \text{Make x subject of formula} \\ 11y\text{ - 8 = x} \\ \text{Therefore, h}^{-1}(x)\text{ = 11x - 8} \\ h^{-1}(x)\text{ = 11x - 8} \end{gathered}[/tex]

Step 4:

[tex]Find(h.h^{-1})(1)[/tex][tex]\begin{gathered} h(x)\text{ = }\frac{x\text{ + 8}}{11} \\ h^{-1}(x)\text{ = 11x - 8} \\ \text{Next, substitute h(x) inverse into h(x).} \\ \text{Therefore} \\ (h.h^{-1})\text{ = }\frac{11x\text{ - 8 + 8}}{11} \\ h.h^{-1}(x)\text{ = x} \\ h.h^{-1}(1)\text{ = 1} \end{gathered}[/tex]

Step 5: Final answer

[tex]\begin{gathered} g^{-1}(9)\text{ = 5} \\ h^{-1}(x)\text{ = 11x - 8} \\ h\lbrack h^{-1}(x)\rbrack\text{ = 1} \end{gathered}[/tex]

Sue wants to plant 545 acres of wheat. She has planted a 128 acre field near the river. Whatpercent of her wheat crop has she planted?

Answers

Percentage of the wheat crop planted = 128/ 545 x 100

= 12800/545

= 23.4 percent

Find an equation of the line. Write the equation using function notation.Through (4, - 7); perpendicular to 6y=x- 12The equation of the line is f(x)=..

Answers

To determine the equation of the line you need to determine its slope first.

You know that the line 6y=x-12 is perpendicular to the line you have to determine, two lines that are perpendicular, their slopes are opposite reciprocals. For example, let "m" represent the slope of one of the lines and "n" represent the slope of the perpendicular line, you can express their relationship as follows:

[tex]m=-\frac{1}{n}[/tex]

To determine the slope of the given line, you have to write it in slope-intercept form:

[tex]y=mx+b[/tex]

Where

m represents the slope

b represents the y-intercept

Given the line:

[tex]6y=x-12[/tex]

-Divide both sides by 6

[tex]\begin{gathered} \frac{6y}{6}=-\frac{x}{6}=-\frac{12}{6} \\ y=-\frac{1}{6}x-2 \end{gathered}[/tex]

The slope of this line is the coefficient of the x-term, n=-1/6

Its opposite reciprocal is:

[tex]\begin{gathered} m=-\frac{1}{n} \\ m=-(-\frac{1}{\frac{1}{6}}) \\ m=-(-1\cdot6) \\ m=-(-6) \\ m=6 \end{gathered}[/tex]

The slope of the line you have to determine is m=6

Now that you have the slope of the line, using the point-slope form, you can determine the equation of the line:

[tex]y-y_1=m(x-x_1)[/tex]

Where

m represents the slope of the line

(x₁,y₁) represent the coordinates of one point of the line

Replace the formula with m=6 and (x₁,y₁)=(4,-7)

[tex]\begin{gathered} y-(-7)=6(x-4) \\ y+7=6(x-4) \end{gathered}[/tex]

The next step is to write the equation in slope-intercept form:

-Distribute the multiplication on the parentheses term:

[tex]\begin{gathered} y+7=6\cdot x-6\cdot4 \\ y+7=6x-24 \end{gathered}[/tex]

-Pass "+7" to the right side of the equation by applying the opposite operation "-7" to both sides of it:

[tex]\begin{gathered} y+7-7=6x-24-7 \\ y=6x-31 \end{gathered}[/tex]

Finally, write the equation of the line using function notation:

[tex]f(x)=6x-31[/tex]

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

Answers

The required equation has the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 – p.

What is an equivalent expression?

Equivalent expressions are even though they appear to be distinct, their expressions are the same. when the values are substituted into the expression, both expressions produce the same result and are referred to be equivalent expressions.

We have the given expression below:

⇒ 2.3p – 10.1 = 6.5p – 4 – 0.01p

Convert the decimal into a fraction to get

⇒ (23/10)p – (101/10) = (65/10)p – 4 – (1/100)p

⇒ (23p – 101)/10 = (650p – 400 – p) /100

⇒ 230p – 1010 = 650p – 400 – p

As a result, the equation that has the same answer as 230p – 1010 = 650p – 400 – p.

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An angle bisector is a ray that divides an angle into two angles with equal measures. If OX bisects ZAOB and mZAOB 142, what is the measure of each of the
angles formed? (Note: Round your answer to one decimal place).

Answers

Measure of each of the angles formed between ZAOB is 71° using angle bisector theorem.

What is the angle bisector?

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

m(ZAOB)=142°

OX will bisect ZAOB in equal angel both side.

So m(ZAOX) is 71°

And also, m(ZAOB) is 71°

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A city has a population of 230,000 people. Suppose that each year the population grows by 4.25%. What will the population be after 12 years?

Answers

Answer:

379,001.

Explanation:

The population of the city grows by 4.25%.

This is a constant factor and models an exponential function.

An exponential population function is of the form:

[tex]\begin{gathered} P(n)=P_0(1+r)^t \\ P_o=\text{Initial Population} \\ r\text{ = growth rate} \\ t\text{ =time in years} \end{gathered}[/tex]

From the given problem:

[tex]P_0=230,000,r=4.25\%=0.0425,t=12years[/tex]

This then gives us:

[tex]\begin{gathered} P(12)=230000(1+0.0425)^{12} \\ =230000(1.0425)^{12} \\ =379,001 \end{gathered}[/tex]

The population after 12 years will be approximately 379,001.

Use the following data set to answer the question below.8 12 15 9 101212 18 14 1510 11 12 9 17What is the range for the data set?

Answers

Given the following set of data:

8 12 15 9 10 12 12 18 14 15 10 11 12 9 17

We will find the range of the data.

We need to find the maximum and the minimum

The maximum = 18

The minimum = 8

So, the range = maximum - minimum = 18 - 8 = 10

So, the answer will be The range = 10

There are 360° in a circle graph. If 50° of the graph represents rent and 7" of the graph represents savings, what fractional portion of the whole graph is not represented by rent and savings?​

Answers

The fractional portion of the whole graph is not represented by rent and savings? is 101/120.

How to illustrate the information?

From the information, there are 360° in a circle graph and 50° of the graph represents rent and 7" of the graph represents savings.

The part that isn't savings or rent will be:

= 360° - (7° + 50°)

= 360° - 57°

= 303°

Therefore, the fractional part will be:

= Part that isn't savings or rent / Entire degree

= 303/360

= 101 / 120

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A resort rented 62 cabins during its first season in operation. Based on the data for a similar resort, management estimated the equation of the line of best fit for the number cabins rented as y= 4x + 62, where x is the number of seasons since the first season of operation, and y is the number of cabins rented during that season. In reality, unusually bad weather for several years beginning in the first season led to the number of rentals for each season decreasing at the rate they were expected to increase. Which is the best choice for the equation for the line of best fit for the cabin rentals?A) y = 1/4 + 62B) y = - 4x + 62C) y = - 1/4x + 62D) y = 4x - 62

Answers

In the equation y = 4x + 62, the increasing rate is 4

If the actual rate decreases at the rate they were expected to increase, then it is -4 instead of 4.

Then, the equation of the line is:

B) y = - 4x + 62

See photo for problem

Answers

The distance, x, from one corner to another corner three corners away is 4. 70cm

The distance, y, from one corner to another corner two corners away is 4. 07cm

How to determine the value

It is important to note that the image shown is a hexagon and each of the interior angles of a hexagon has a value of 120 degrees

Also note that the have the trigonometric identities;

sinecosinetangentcotangentsecantcosecant

Using the cosine identity, we have;

sin θ = adjacent/ hypotenuse

substitute the values

cos 60 = 2.35/x

cross multiply

x = 2. 35/cos 60

x = 2. 35/ 0. 5

x = 4. 7 cm

Then, we have,

sin 60 = y/ 4. 7

y = sin 60 × 4.7

y = 0. 8660 × 4. 7

y = 4. 07cm

Hence, the values are 4. 7cm and 4. 07cm

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Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 3 years?

Answers

Answer:

The amount of interest she will be paid in the first 3 years is;

[tex]\text{ \$90}[/tex]

Explanation:

Given that Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. for the first 3 years;

[tex]\begin{gathered} \text{ Principal P = \$500} \\ \text{rate r = 6\% = 0.06} \\ \text{time t = 3 years} \end{gathered}[/tex]

Recall the simple interest formula;

[tex]i=P\times r\times t[/tex]

substituting the given values;

[tex]\begin{gathered} i=500\times0.06\times3 \\ i=\text{ \$90} \end{gathered}[/tex]

Therefore, the amount of interest she will be paid in the first 3 years is;

[tex]\text{ \$90}[/tex]

Write the equation of this line in point-slope form: The line passes through (−2,22) and (4,-8).

Answers

Write the equation of this line in point-slope form: The line passes through (−2,22) and (4,-8).

step 1

Find the slope of the line

m=(-8-22)/(4+2)

m=-30/6

m=-5

step 2

Find the equation in point slope form

y-y1=m(x-x1)

substitute the given values

we have

m=-6

(x1,y1)=(4,-8)

substitute

y+8=-6(x-4)

please show and explain this please

Answers

only answer ;( c.

Step-by-step explanation:

so hope it help

There are four roots: -2, 1, 1, and 3 [1 is repeated as it is a local maximum]
f(x) = (x + 2)(x - 3)(x - 1)(x - 1)
so the correct answer is C

Complete the description of the piece wise function graphed below

Answers

Analyze the different intervals at which the function takes the values provided by the graph. Pay special attention on the circles, whether they are filled up or not.

From the graph, notice that the function takes the value of 3 when x is equal to -4, -2 or any number between them. Therefore, the condition is:

[tex]f(x)=3\text{ if }-4\leq x\leq-2[/tex]

If x is greater (but not equal) than -2 and lower or equal to 3, the function takes the value of 5. Therefore:

[tex]f(x)=5\text{ if }-2Notice that the first symbol used is "<" and the second is "≤ ".

Finally, the function takes the value of -3 whenever x is greater (but not equal) to 3 and less than or equal to 5. Then:

[tex]f(x)=-3\text{ if }3In conclusion:[tex]f(x)=\mleft\{\begin{aligned}3\text{ if }-4\leq x\leq-2 \\ 5\text{ if }-2

Which of the following functions has an amplitude of 3 and a phase shift of pi over 2 question mark

Answers

Remember that f(x) = A f(Bx-C) +D

Where |A| is the Amplitude and C/B is the phase Shift

Options

A, B C all have amplitudes of |3| so we have just eliminated D with the amplitude

We need a phase shift of C/B = pi/2

A has Pi/2

B has -Pi/2

C has pi/2 /2 = pi/4

Choice A -3 cos ( 2x-pi) +4 has a magnitude of 3 and and phase shift of pi/2

(b) The area of a rectangular painting is 5568 cm².If the width of the painting is 58 cm, what is its length?Length of the painting:

Answers

Step 1: Problem

The area of a rectangular painting is 5568 cm².

If the width of the painting is 58 cm, what is its length?

Length of the painting:

Step 2: Concept

Area of a rectangle = Length x Width

Step 3: Method

Given data

Area = 5568 cm square

Width = 58 cm

Length = ?

Area of a rectangle = Length x Width

5568 = 58L

L = 5568/58

L = 96cm

Step 4: Final answer

Length of the painting = 96cm

A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with spicy italian sausage, banana peppers and beef. Express your answer as a fractionPizza toppings: Green peppers, onions, kalamata olives, sausage, mushrooms, black olives, pepperoni, spicy italian sausage, roma tomatoes, green olives, ham, grilled chicken, jalapeño peppers, banana peppers, beef, chicken fingers, red peppers

Answers

First, we need to find out how many possible combinations of pizza toppings there would be.

To do this, we will use the formula for Combination.

Combination is all the possible arrangements of things in which order does not matter. In our example, this would mean that a pizza topped with spicy Italian sausage, banana pepper, and beef is the same as a pizza topped with banana pepper, beef, and Italian sausage.

The formula for combination is

[tex]C(n,r)=^nC_r=_nC_r=\frac{n!}{r!(n-r)!}[/tex]

From our given, n would be 17, since there are a total of 17 toppings (including spicy Italian sausage, banana peppers, and beef) and r would be 3 since there are three toppings that you chose.

Substituting it in the formula,

[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex][tex]C(17,3)=\frac{17!}{3!(17-3)!}[/tex][tex]C(17,3)=680[/tex]

Now, since we know that there are a total of 680 combinations of pizza toppings, we can now solve the probability of the first winner selecting a pizza topped with Italian sausage, banana peppers, and beef.

A special deck of cards has 4 blue cards, and 4 red cards. The blue cards are numbered 1, 2, 3, and 4. The red cards are numbered 1, 2, 3, and 4. The cards are well shuffled and you randomly draw one card.A = card drawn is blueB = card drawn is odd-numbereda) How many elements are there in the sample space? b) P(A) = c) P(B) =

Answers

Answer

• a) 8

,

• b) 4/8

,

• c) 4/8

Explanation

Given

• Blue cards: 4, {B1, B2, B3, B4}

,

• Red cards: 4 {R1, R2, R3, R4}

,

• A = card drawn is blue

• B = card drawn is odd-numbered {B1, R1, B3, R3}

Procedure

• a) elements in the sample space

There are: S = {B1, B2, B3, B4, R1, R2, R3, R4}

Thus, the number of elements in the sample space is n(S) = 8.

• b) P(A)

Can be calculated as follows:

[tex]P(A)=\frac{n(A)}{n(S)}=\frac{4}{8}[/tex]

• c) P(B)

Can be calculated as follows:

[tex]P(B)=\frac{n(B)}{n(S)}=\frac{4}{8}[/tex]

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