shoe box = 1 cubic foot = 1 * 1 * 1
1 Layer: 6 shoe boxes -> Layer lenght = 6 feet, layer depht = 1 foot
Box height = 4 feet
Box volume = 6*4*1 = 24 feet
in the sophomore class at Summit High School the number of students taking French is 2/3 of the number taking Spanish. how many students are studying each language if the total number of students in French and Spanish is 310 ?This is Homework
From the information given in the statement let be
[tex]\begin{gathered} f=\frac{2}{3}s\text{ (1)} \\ f+s=310\text{ (2)} \end{gathered}[/tex]Where
*f: number of students taking a French class
*s: number of students taking a Spanish class
So, you have a system of linear equations, which you can use the substitution method.
To do this, replace the value of the first equation in the second equation and solve for s
[tex]\begin{gathered} f+s=310\text{ (2)} \\ \frac{2}{3}s+s=310 \\ \frac{5}{3}s=310 \\ \text{ Multiply by }\frac{3}{5}\text{ on both sides of the equation} \\ \frac{3}{5}\cdot\frac{5}{3}s=310\cdot\frac{3}{5} \\ s=186 \end{gathered}[/tex]Now,
Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 7.25x − 36.25, where x is the number of bracelets he sells. What is the value of Q(5), and what is its interpretation?
Q(5) = 0; If Quincy sells 0 bracelets, he will earn $5.
Q(5) = 0; If Quincy sells 5 bracelets, he will earn $0.
Q(5) = 5.69; If Quincy sells 5.69 bracelets, he will earn $5.
Q(5) = 5.69; If Quincy sells 5 bracelets, he will earn $5.69.
The value of Q(5) is zero and represents the zero profit on selling 5 bracelets thus option (B) is correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given,
Daily profit function Q(x) = 7.25x − 36.25 where x is the number of bracelets he sells.
At x = 5 ( selling 5 bracelets)
Q(5) = 7.25(5) - 36.25
Q(5) = 36.25 - 36.25 = 0
It means selling 5 bracelets doesn't give any profit.
Hence "The value of Q(5) is zero and represents the zero profit on selling 5 bracelets".
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a bottle of juice is 2/3 full the bottle contains 4/5 cup of juice write division problem that represents the capacity of the bottle
Answer:
x = ( 6 / 5 )y
Step-by-step explanation:
Identify the equaiton.
let x = bottle;
let y = cups;
( 2 / 3 )x = ( 4 / 5 )y;
Multiply both sides by ( 3 / 2 ).
( 3 / 2 )( 2 / 3 )x = ( 3 / 2 )( 4 / 5 )y;
x = ( 12 / 10 )y;
Write the fraction in its simplest form.
x = ( 6 / 5 )y;
It takes 1 + ( 1 / 5 ) of a cup to fill the bottle.
Today's previewYou can solve this by rearranging to create asituation to use the method from the previouslesson, or you can solve this by thinking a littledifferently about how the variables below mightalso be described.... so solve it.y = 2x + 4x + y = 7
A hummingbird's brain has a weight of approximately 2.94 x 10- ounces. An elephant's brain has a weight ofapproximately 1.76 x 102 ounces.Approximately how many times heavier is the elephant's brain than the hummingbird's brain?A) 60B) 600C) 6,000D) 60,000
Given the information on the problem,we have to divide the weight of the elephant's brain by the weight of the bird's brain, then, using the rules of exponents, we have the following:
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The observed values are given in the table shown in the question. The line of best fit is given to be:
[tex]y=-1.1x+90.31[/tex]where x is the average monthly temperature and y is the heating cost.
A residual is a difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line). The formula will be:
[tex]Residual=Observed\text{ }y\text{ }value-Predicted\text{ }y\text{ }value[/tex]QUESTION A
The average monthly temperature is 24.9:
[tex]x=24.9[/tex]Observed cost:
[tex]y=51.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(24.9)+90.31=-27.39+90.31 \\ y=62.92 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=51.00-62.92 \\ R=-11.92 \end{gathered}[/tex]QUESTION B
The average monthly temperature is 35.9:
[tex]x=35.9[/tex]Observed cost:
[tex]y=67.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(35.9)+90.31=-39.49+90.31 \\ y=50.82 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=67.00-50.82 \\ R=16.18 \end{gathered}[/tex]Answer: Hl
Step-by-step explanation:
–2(1 – 5x) = 4 – 4(-2x)
-2(1 - 5x) = 4 - 4(-2x)
First, we eliminate the parentheses and solve the multiplications
-2*1 - 2*(-5x) = 4 + 8x
-2 + 10x = 4 + 8x
Now, we subtract 8x from both sides and add 2 to both sides
-2 + 10x - 8x + 2 = 4 + 8x - 8x + 2
2x = 6
Then, we divide both sides by 2
2x/2 = 6/2
x = 6/2
x = 3
Let MF = 3x - 4 and BM = 5x - 5
Answer:
Explanation:
a)Here, we want to get the value of x
Mathematically, we know that for a triangle with median M, the length of one of the sides is two times the length of the other side of the median
We have this as:
[tex]BM\text{ }=\text{ 2MF}[/tex]Using the side lengths given, we have it that:
[tex]\begin{gathered} 5x-5\text{ = 2(3x-4)} \\ 5x-5\text{ = 6x-8} \\ 6x-5x=8-5 \\ x\text{ = 3} \end{gathered}[/tex]b) We want to find the length of MF. We just have to substitute the value of x in the expression for MP
Mathematically, we have this as:
[tex]MF\text{ = 3(3)-4 = 9-4 = 5}[/tex]c) We want to find the length of BM
[tex]5x-5\text{ = 5(3)-5 = 15-}5\text{ = 10}[/tex]d) Here, we want to find the length of BF
[tex]\begin{gathered} BF\text{ = BM + MF} \\ BF\text{ = 10 + 5 = 15} \end{gathered}[/tex]write each decimal in word form 302.78 and 15.023
Answer and Explanation:
302.78 can be written as THREE HUNDRED AND TWO AND SEVENTY EIGHT HUNDREDTHS or THREE HUNDRED AND TWO POINT SEVEN EIGHT.
15.023 can be written in word as FIFTEEN AND TWENTY THREE THOUSANDTHS or FIFTEEN POINT ZERO TWO THREE.
(a) The perimeter of a rectangular garden is 312 m.If the length of the garden is 89 m, what is its width?Width of the garden: ]וח(b) The area of a rectangular window is 6205 cm?If the width of the window is 73 cm, what is its length?Length of the window: 7 cm
EXPLANATION
Let's see the facts:
Perimeter = P = 312 m
Length = l = 89m
Width = w = unknown
The perimeter of a rectangle is given by the following relationship:
[tex]P=2(w+l)[/tex]Replacing terms:
[tex]312=2(w+89)_{}[/tex]Applying the distributive property:
[tex]312=2w\text{ + 178}[/tex]Subtracting 178 to both sides:
[tex]312-178=2w[/tex][tex]134=2w[/tex]Dividing 2 to both sides:
[tex]\frac{134}{2}=w[/tex]Simplifying:
[tex]67=w[/tex]Switching sides:
[tex]w=67[/tex]The width of the garden is 67 meters.
A car wheel has a radius of 35 cm.(a) What is the circumference of the wheel? Give your answer correct to 2 decimal places.(b) If the wheel rotates 100 000 times, how far does the car travel?
Explanation
(a) The formula for the circumference of a circle is as follows:
[tex]C=2\pi r[/tex]Where r is the radius of the circle. So, we have:
[tex]X=2\pi r=2\cdot3.1415\ldots\cdot35=219.9114\ldots\approx219.91[/tex]So, the circumference is approximately 219.91 cm.
(b) Assuming the wheel is always in contact and every rotation make sthe exact same length of travel, every rotation will make the car travel approximately 219.91 cm.
If the wheel rotates 100,000 times, the car will travel 100,000 times as many, so it will travel:
[tex]100,000\cdot219.91=21,991,000[/tex]So, the car will travel approximately 21,991,000 cm which is equivalente to 219.91 km.
Answer
(a) the circumference is approximately 219.91 cm
(b) the car will travel approximately 21,991,000 cm or 219,91 km.
set up a trigonometric ratio for angle H and solve for X
According to the picture, it is necessary to use cosine, which is the ratio between the side that is adjacent to a given angle and the hypotenuse.
In this case, the angle would be H, the adjacent side to it would be x and the hypotenuse 14. It means that cos H is the ratio between x and 14:
[tex]\cos H=\frac{x}{14}[/tex]If f(x) = -3 and g(x) = 4x + 2x - 4, find (* + )(x).O A. 4x2 + x +1OB. 432 + x ->C.X2-12OD. 4x2+2x-7
You have the following functions:
[tex]\begin{gathered} f(x)=\frac{x}{4}-3 \\ g(x)=4x^2+2x-4 \end{gathered}[/tex]In order to find (g + f)(x) add like terms of each function. Remind that like terms are those terms with the same variable and same exponent.
Then, you have:
[tex]\begin{gathered} (f+g)(x)=4x^2+2x+\frac{x}{4}-3-4 \\ (f+g)(x)=4x^2+\frac{9}{4}x-7 \end{gathered}[/tex]Hence, the answer is
4x^2 + 9/4 x - 7
Find the rate of change of each linear function 1. y = x - 7
Rate of change = 1
Explanations:The given linear function is:
y = x - 7
The rate of change of the function is gotten by finding the derivative (dy/dx) of the function
dy/dx = 1
The rate of change = 1
Suppose medical records indicate that the length of newborn babies (in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6. Find the probability that a given infant is longer than 20 inches. [? ]%
To find the probability we need to use the z score formula, given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the value we like, mu is the median and sigma is the standard deviation.
Then the z score is:
[tex]z=\frac{20-20}{2.6}=0[/tex]Then we have to look for the proability:
[tex]P(z>0)=0.5[/tex]Therefore the probability that a given infant is longer than 20 inches is 0.5 or 50%.
A Ferris wheel at a carnival has a diameter of 72 feet. Suppose a passenger is traveling at 5 miles per hour. (A useful fact: =1mi5280ft.)
(a) Find the angular speed of the wheel in radians per minute.
(b) Find the number of revolutions the wheel makes per hour. (Assume the wheel does not stop.)
a) The Ferris wheel has an angular speed is 12.222 radians per minute.
b) The Ferris wheel makes 116.712 revolutions in an hour.
How to understand and analyze the kinematics of a Ferris wheel
Kinematics is a branch of mechanical physics that studies the motion of objects without considering its causes. In other words, kinematics studies displacements, velocities and accelerations in translation, rotation and combined motion. In this case we find a Ferris wheel rotating around its axis at constant rate.
a) Then, the angular speed (ω), in radians per minute, is determined by the following product:
ω = v / R
Where:
v - Linear velocity at the rim of the Ferris wheel, in feet per second.R - Radius of the Ferris wheel, in feet.Please notice that the length of the radius is the half of the length of the diameter.
If we know that v = 5 mi / h and R = 36 feet, then the angular speed of the wheel is:
ω = [(5 mi / h) · (1 h / 60 min) · (5280 ft / 1 mi)] / [(0.5) · (72 ft)]
ω = 12.222 rad / min
The angular speed is 12.222 radians per minute.
b) A revolution is equal to an angular displacement of 2π radians and an hour is equal to 60 minutes. Then, we can derive the number of revolutions in an hour by dimensional analysis:
n = (12.222 rad / min) · (1 rev / 2π rad) · (60 min / h)
n = 116.712 rev / h
There are 116.712 revolutions in an hour.
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a test has 20 Questions worth 100 points the test consists of true or false questions worth 3 points each and multiple choice questions worth 11 points each how many multiple choice questions are on the test
A test is to be conducted with certain types of questions and each type of question weighs certain number of points.
A test would consist of two types of questions. These two types will be assigned variables that will denote the number of questions respectively as follows:
[tex]\begin{gathered} \text{True and False: x} \\ \text{MCQS : y} \end{gathered}[/tex]We are given that the entire test will consits of 20 questions. We can express the total number of questions on the test in terms of number of True and False questions ( x ) and number of MCQS ( y ) as follows:
[tex]\begin{gathered} \text{Total number of Questions = True and False + MCQS} \\ \textcolor{#FF7968}{20}\text{\textcolor{#FF7968}{ = x + y }}\textcolor{#FF7968}{\ldots Eq1} \end{gathered}[/tex]Further information is given to us in the questions regarding the number of points aloted to each type. The total weightage of each type of question on the test can be expressed as a product of ( number of each type * point weight of each type ).
The point weights for each type of questions are:
[tex]\begin{gathered} \text{True and False ( x ) : 3 points each} \\ \text{MCQs ( y ) : 11 points each} \end{gathered}[/tex]The total weights of each types of questions are:
[tex]\begin{gathered} \text{True and False ( points ) = 3}\cdot x \\ \text{MCQS ( points ) = 11}\cdot x \end{gathered}[/tex]We are given that the entire test is worth ( 100 points ). We express the total number of points of the test in terms of total weight of each type of question as follows:
[tex]\begin{gathered} test\text{ points = True and False ( points ) + MCQS ( points )} \\ \textcolor{#FF7968}{100}\text{\textcolor{#FF7968}{ = 3}}\textcolor{#FF7968}{\cdot x}\text{\textcolor{#FF7968}{ + 11}}\textcolor{#FF7968}{\cdot y\ldots}\text{\textcolor{#FF7968}{ Eq2}} \end{gathered}[/tex]We have two equations that express the total number of questions ( Eq 1 ) and total points ( Eq2 ) of the test in terms of number of True and False questions ( x ) and number of MCQs on the test ( y ).
[tex]\begin{gathered} \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ + y = 20 }}\textcolor{#FF7968}{\ldots Eq1} \\ \textcolor{#FF7968}{3x}\text{\textcolor{#FF7968}{ + 11y = 100 }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq2}} \end{gathered}[/tex]We will solve the above two equations simultaneously using Elimination method.
Step1: Multiply Eq1 with ( -3 )
[tex]\begin{gathered} -3\cdot\text{ ( x + y ) = -3}\cdot20 \\ \textcolor{#FF7968}{-3x}\text{\textcolor{#FF7968}{ - 3y = -60 }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq3}} \end{gathered}[/tex]Step2: Add Eq 3 into Eq 2
[tex]\begin{gathered} -3x\text{ - 3y = -60 } \\ 3x\text{ + 11y = 100} \\ =========== \\ 8y\text{ = 40 } \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 5}} \\ =========== \end{gathered}[/tex]Step3: Back susbtitue the value of ( y ) into ( Eq1 )
[tex]\begin{gathered} x\text{ + ( 5 ) = 20 } \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 15 }} \end{gathered}[/tex]Therefore, the number of each type of questions that must be put on the test should be.
[tex]\begin{gathered} \text{\textcolor{#FF7968}{True and False ( x ) = 15}} \\ \text{\textcolor{#FF7968}{MCQs ( y ) = 5}} \end{gathered}[/tex]Solve the system by substitution:y=-6x-77x+y=-3(__ , __)
Substitute -6x-7 for y in the equation 7x+y=-3 to obtain the value of the of x.
[tex]\begin{gathered} 7x-6x-7=-3 \\ x=-3+7 \\ =4 \end{gathered}[/tex]Substitute 4 for x in the equation y=-6x-7 to obtain the value of the y.
[tex]\begin{gathered} y=-6\cdot4-7 \\ =-24-7 \\ =-31 \end{gathered}[/tex]So solution of the equation is (4,-31).
Suppose theta is an angle in the standard position whose terminal side is in quadrant 1 and sin theta = 84/85. find the exact values of the five remaining trigonometric functions of theta
we know that
The angle theta lies in the I quadrant
[tex]sin\theta=\frac{84}{85}[/tex]step 1
Find out the value of the cosine of angle theta
Remember that
[tex]sin^2\theta+cos^2\theta=1[/tex]substitute given value
[tex]\begin{gathered} (\frac{84}{85})^2+cos^2\theta=1 \\ \\ cos^2\theta=1-\frac{7,056}{7,225} \\ \\ cos^2\theta=\frac{169}{7,225} \\ \\ cos\theta=\frac{13}{85} \end{gathered}[/tex]step 2
Find out the value of the tangent of angle theta
[tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]substitute given values
[tex]\begin{gathered} tan\theta=\frac{\frac{13}{85}}{\frac{84}{85}}=\frac{13}{84} \\ therefore \\ tan\theta=\frac{13}{84} \end{gathered}[/tex]step 3
Find out the cotangent of angle theta
[tex]cot\theta=\frac{1}{tan\theta}[/tex]therefore
[tex]cot\theta=\frac{84}{13}[/tex]step 4
Find out the value of secant of angle theta
[tex]sec\theta=\frac{1}{cos\theta}[/tex]therefore
[tex]sec\theta=\frac{85}{13}[/tex]step 5
Find out the value of cosecant of angle theta
[tex]csc\theta=\frac{1}{sin\theta}[/tex]therefore
[tex]csc\theta=\frac{85}{84}[/tex]2) seperate 90 into two parts (the sum of two numbers is 90)so that one part Cone number) is four times the other part (the other number)
The sum of two parts equal 90.
Also,
one part is 4 times the other part.
Let the normal part be "x", so the 4 times part would be "4x".
Their sum is 90, thus we can write:
[tex]x+4x=90[/tex]Solving for x (a part):
[tex]\begin{gathered} x+4x=90 \\ 5x=90 \\ x=\frac{90}{5} \\ x=18 \end{gathered}[/tex]The other part is:
90 - 18 = 72
So,
The two parts we separate 90 into are "18 and 72".
Determine the probability of the given opposite event.What is the probability of rolling a fair die and not getting an outcome less than 3?
The Opposite Event rule is the probability that event A happens is equal to one minus the probability that A does not happen.
If P(A) is the probability of A happening, and N(A) is the probability of A don't happen, we can write:
[tex]P(A)=1-N(A)[/tex]Now we can see:
[tex]N(A)=1-P(A)[/tex]This, we if we calculate the probability of getting less than 3, ve can calculate the probability of not getting less than 3.
Then, what are the results that are less than 3? Those are 1 and 2. Thus are the favorable outcomes, and since is a fair dice, there are 6 total possible outcomes.
The probability of A = getting less than 3, is:
[tex]\begin{gathered} P(A)=\frac{2}{6} \\ P(A)=\frac{1}{3} \end{gathered}[/tex]
Now we can calculate the probability of not getting less than 3:
[tex]\begin{gathered} N(A)=1-\frac{1}{3} \\ \end{gathered}[/tex][tex]N(A)=\frac{2}{3}[/tex]
The probability of not getting less than 3 is:
[tex]Probability=\frac{2}{3}\approx0.666[/tex]Or in percentage:
[tex]Probability=66.67\%[/tex]Amy's cookie shop had expenses of the following: flour $45.00sugar $92.00butter $53 she earns $12 per dozen. what is her profit,if she sells 9 dozen?what is the total dollar amount for expenses?what is the total dollar amount for earnings or revenue?
If she earns $12 per dozen, the following will be the profit if she sells 9 dozen:
[tex]9\cdot12=108[/tex]Profit would be $108.
*The dollar amount of expenses would be:
[tex]e=\frac{190\cdot108}{12}\Rightarrow e=1710[/tex]The expenses would be $1710 if she were to sell 9 dozen.
*The total amount of revenue would be $108 for the 9 dozen sold.
write the expression using exponents 7•7•7•7•7•7• (–3)•(–3)•(–3)•(–3)
We have the number 7 multiplying itself 6 times, and the number (-3) multiplying itself 5 times, so writing the expression using exponents, we have:
[tex]\begin{gathered} 7\cdot7\cdot7\cdot7\cdot7\cdot7=7^6 \\ (-3)\cdot(-3)\cdot(-3)\cdot(-3)\cdot(-3)=(-3)^5 \\ \\ 7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot(-3)\cdot(-3)\cdot(-3)\cdot(-3)\cdot(-3)=7^6\cdot(-3)^5 \end{gathered}[/tex]So the final expression is 7^6 * (-3)^5
“ Judy has a bag with 12 DVD’s, 12 marbles, 11 books, and 1 orange. What is the ratio of books to marbles? What is the ratio of DVD’s to the total number of items in the bag? What percentage of the items in the bag are DVD’s? “
First, let's calculate the total number of items:
[tex]12+12+11+1=36[/tex]The ratio of books to marbles is calculated by dividing the number of books by the number of marbles:
[tex]ratio=\frac{books}{\text{marbles}}=\frac{11}{12}[/tex]The ratio of DVD's to the total number of items is:
[tex]\text{ratio}=\frac{\text{dvds}}{\text{total}}=\frac{12}{36}=\frac{1}{3}[/tex]The percentage of dvd's from the total is:
[tex]\frac{1}{3}=0.3333=33.33\text{\%}[/tex]A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. The equation that give the height (h) of the ball at any time (t) is: h(t)= -16t^2 + 40t + 1.5. Find the maximum height attained by the ball. I need a clear explanation because I have to expose this
The height of the ball at any time t is given by
[tex]h(t)=-16t^2+40t+1.5[/tex]This is a quadratic equation, which attains its maximum value at time:
[tex]t=\frac{-b}{2a}[/tex]In the given equation, a = -16 and b = 40. substitute these values in the formula:
[tex]t=\frac{-40}{-16\times2}=\frac{-40}{-32}=\frac{5}{4}[/tex]Therefore, the ball attains its maximum height at t=5/4 seconds which is given below:
[tex]\begin{gathered} h(\frac{5}{4})=-16(\frac{5}{4})^2+40(\frac{5}{4})+1.5 \\ =-25+50+1.5 \\ =26.5 \end{gathered}[/tex]Thus, the maximum height attained by the ball is 26.5 feet.
1. The price for a new iPhone today is $829. In 2010 it was $299 for the new iPhone. What is the percent of change in the price of an iPhone from 2010 to today?
Given:
a.) The price for a new iPhone today is $829.
b.) In 2010 it was $299 for the new iPhone.
To be able to determine the percent change of price, we will be using the following formula:
[tex]\text{ Percent of Change = }\frac{Price\text{ today - Price in 2010}}{\text{Price in 2010}}\text{ x 100}[/tex]We get,
[tex]\text{ = }\frac{\text{ \$829 - \$299}}{\text{ \$299}}\text{ x 100}[/tex][tex]\text{ = }\frac{\text{ \$530}}{\text{ \$299}}\text{ x 100}[/tex][tex]\text{ = 1.77257525084 x 100 = 1.77 x 100}[/tex][tex]\text{ Percent of Change = 177\% ; an increase}[/tex]Therefore, the percent of change in the price from 2010 and today is an increase of 177%.
Consider the following data. The expected value is -2.1.Find the variance, standard deviation, P(X ≥ -1), and P(X ≤ -3).
Given
The data,
To find:
The variance, standard deviation, P(X ≥ -1), and P(X ≤ -3).
Explanation:
It is given that,
Then,
The variance is,
[tex]\begin{gathered} Var[x]=(-4-(-2.1))^2\times0.2+(-3-(-2.1))^2\times0.3+(-2-(-2.1))^2 \\ \times0.1+(-1-(-2.1))^2\times0.2+(0-(-2.1))^2\times0.2 \\ =(-4+2.1)^2\times0.2+(-3+2.1)^2\times0.3+(-2+2.1)^2\times0.1+(-1+2.1)^2 \\ \times0.2+(2.1)^2\times0.2 \\ =3.61\times0.2+0.81\times0.3+0.01\times0.1+1.21\times0.2+4.41\times0.2 \\ =0.722+0.243+0.001+0.242+0.882 \\ =2.09 \end{gathered}[/tex]And the standard deviation is,
[tex]\begin{gathered} SD=\sqrt{Var[x]} \\ =\sqrt{2.09} \\ =1.45 \end{gathered}[/tex]Also,
[tex]\begin{gathered} P\left(X≥-1\right)=P(X=-1)+P(X=0) \\ =0.2+0.2 \\ =0.4 \\ P\left(X≤-3\right)=P(-4)+P(-3) \\ =0.2+0.3 \\ =0.5 \end{gathered}[/tex]Hence, the answers are,
Variance is 2.09
Standard deviation is 1.45
P(X ≥ -1) is 0.4
P(X ≤ -3) is 0.5.
Mario ordered a pizza for dinner. WHEN IT Came Mario quickly ate 1/8 of the pizza. While Mario was getting napkins, his pet poodle ate 1/3 of the pizza.
Mario ordered a pizza for dinner. when pizza came, Mario quickly ate 1/8 of the pizza and his pet ate 1/3 of the pizza, then the remaining fraction of pizza left is 13/24
The fraction of pizza that Mario eat = 1/8
The fraction of pizza that his pet eat = 1/3
Total fraction = (1/8) + (1/3)
= 11/24
The remaining fraction of pizza = 1 - 11/24
= 13/24
Hence, Mario ordered a pizza for dinner. when it came, Mario quickly ate 1/8 of the pizza and his pet ate 1/3 of the pizza, then the remaining fraction of pizza left is 13/24.
The complete question is :
Mario ordered a pizza for dinner. When it Came Mario quickly ate 1/8 of the pizza. While Mario was getting napkins, his pet poodle ate 1/3 of the pizza. What is the fraction of pizza that left?
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Solve the equation for y in terms of x. After that, replace y & solve with function notation f(x). Once you solve that, find f(4).y+3x^2=4f(x)=____f(4)=____
Given:
[tex]y+3x^2=4[/tex]We have that y f(x), so solve for f(x):
[tex]\begin{gathered} y+3x^2-3x^2=4-3x^2 \\ y=4-3x^2 \\ f(x)=4-3x^2 \end{gathered}[/tex]And for f(4):
[tex]f(4)=4-3(4)^2=4-3(16)=4-48=-44[/tex]Answer:
[tex]\begin{gathered} f(x)=4-3x^{2} \\ f(4)=-44 \end{gathered}[/tex]Simplify.8(10 m)ANSWER CHOICES:80 m18 m810 m80 + m
To simplify this, we need to apply distributive property.
Given: 8(10 m)
Expand the parenthesis:
[tex]\begin{gathered} 8\text{ }\ast\text{ 10m} \\ =\text{ 80m} \end{gathered}[/tex]ANSWER:
[tex]80m[/tex]