Level L>X.15 Find probabilities using the addition rule UKVYou have prizes to reveal! Go to yourOver a weekend, Sue counted the number of single scoop ice creams ordered at her store.She tracked the flavors and the day on which it was ordered.The probability that an ice cream was vanilla is 0.85, the probability that it was ordered on aSunday is 0.96, and the probability that it was vanilla and was ordered on a Sunday is 0.82.What is the probability that a randomly chosen ice cream was vanilla or was ordered on aSunday?od.HESIouSubmit
Answers
We have the following data:
P(V) = 0.85
P(S) = 0.96
P(V and S) = 0.82
We can use the rules of addition to find P(V or S) as:
[tex]\begin{gathered} P(V\cup S)=P(V)+P(S)-P(V\cap S) \\ P(V\cup S)=0.85+0.96-0.82 \\ P(V\cup S)=0.99 \end{gathered}[/tex]Answer: The probability that a randomly chosen ice cream was vanilla or was ordered on a Sunday is 0.99.
Related Questions
23=1/3b-2+4/3bwhat is the value of b?
Answers
Next, we multiply throughout by the L.C.M of the denominators ( 3b)
[tex]23\text{ ( 3b ) = ( 3b ) }\frac{1}{3b\text{ }}\text{ - 2 ( 3b ) + }\frac{4\text{ ( 3b )}}{3b}[/tex][tex]\begin{gathered} 69b\text{ = 1 - 6b + 4 } \\ 69b\text{ + 6b = 5} \\ 75b\text{ = 5} \\ b\text{ = }\frac{5}{75}\text{ = }\frac{1}{15} \end{gathered}[/tex]Thus the value of b is
[tex]\frac{1}{15}[/tex]compare the two numbers 1/8 or 0.086 is bigger witch is bigger
Answers
To compare this numbers we need to have them both in a decimal form.
0.086 is already in decimal form.
We need to convert 1/8 to decimal by making the division between 1 and 8:
[tex]\frac{1}{8}=0.125[/tex]So we have to compare 0.086 and 0.125
The bigger number is 0.125 because when we compare 125 to 086, 125 is bigger.
Answer: 1/8
1.6.AP-13 Question: On a recent trip, Jeremy and Frank drove 790 miles on 33 - gallons of gas. How many miles per gallon did their car get on this trip? T(Type a whole number, proper fraction, or mixed number.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All Check Answer Review progress
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Answer:
[tex]23.7\frac{miles}{\text{gallon}}[/tex]Explanation: Their Car drove a certain distance on the gas that it had, which is as follows:
[tex]\begin{gathered} \text{ Distance }\rightarrow790miles \\ \text{Gas }\rightarrow33\frac{1}{3}gallons=\frac{100}{3}gallons\rightarrow\approx33.34gallons \end{gathered}[/tex]We need to find the miles per gallon that car had:
Miles per Gallon:
We can find the miles per gallon by simply dividing the total distance by the total amount of gas, which is done as follows:
[tex]\frac{M}{G}=\frac{790miles}{\frac{100}{3}\text{gallons}}=\frac{790\times3}{100}\frac{miles}{\text{gallon}}=23.7\frac{miles}{\text{gallon}}[/tex]Therefore their car got 23.7 miles/gallon on this trip!
Question 5, Pre calc, Make answer bold, I have bad WiFi, finish question if I get disconnected please.
Answers
Given the functions
[tex]\begin{gathered} f(x)\text{ = x+2} \\ g(x)=x^2 \end{gathered}[/tex]
To find (g o f)(x):
(g o f)(x) is evaluated as g(f(x)).
This implies that the function f(x) is substituted into the g(x) function.
Thus,
[tex]\begin{gathered} \text{Substitute f(x) into g(x)} \\ g(f(x))=(x+2)^2 \\ open\text{ brackets} \\ g(f(x))=x^2+4x+4 \\ \end{gathered}[/tex]Hence, the function (g o f)(x) is given as
[tex](g\circ f)(x)=x^2\text{ + 4x + 4}[/tex]
Suppose the triangles shown are similar with angle A = angle D, angle B = angle E, and angle C = angle F. Answer the question.
Answers
Similar triangles have the same ratio between corresponding sides:
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}[/tex]We have the sizes of the sides:
• AB = 17
,• BC = 22
,• CA = 2x-7
,• DE = 34
,• EF = 44
,• FD = 2x+4
We use the ratio property to find x:
[tex]\begin{gathered} \frac{BC}{EF}=\frac{CA}{FD} \\ \frac{22}{44}=\frac{2x-7}{2x+4} \\ \frac{1}{2}=\frac{2x-7}{2x+4} \end{gathered}[/tex]And now we clear x:
[tex]\begin{gathered} \frac{1}{2}=\frac{2x-7}{2x+4} \\ 2x+4=2(2x-7) \\ 2x+4=4x-14 \\ x(2-4)=-14-4 \\ x=\frac{-14-4}{2-4}=\frac{-18}{-2}=9 \end{gathered}[/tex]Now that we have x = 9, we can find the lenght of side DF (DF and FD are the same side):
[tex]FD=2x+4=2\cdot9+4=18+4=22[/tex]The answer is option C, FD = 22
At the movie theater, a largecylindrical container of popcorncosts $5.00, and a smallcylindrical container costs $2.50.Nicole thinks that the heights ofthe containers are about thesame and that the radius of thelarge container is about twicethe radius of the small container.Should she buy two smallcontainers or one large to getmore for her money? *
Answers
Let the radius of the small cylindrical container be r and the height be h. Then the radius of the large cylindrical container is 2r.
Volume of the small cylinder
[tex]=\pi r^2h[/tex]Volume of the large cylinder
[tex]\begin{gathered} =\pi(2r)^2h \\ =4\pi r^2h \end{gathered}[/tex]So, the volume of popcorn contains in the large cylindrical container is 4 times the volume contains in the small popcorn.
Hence buying one large container is profitable.
if f(x)=2x+7 and g(x)=3-, find (f-g)(5)
Answers
Answer:
(f-g)(5) = 14
Explanation:
Given the functions;
f(x) = 2x+7
g(x) = 3
f(x) - g(x) = 2x+7 -3
f(x)-g(x) = 2x+4
Substitute x = 5 int the result
(f-g)(x) = 2x +4
(f-g)(5) = 2(5) + 4
(f-g)(5) = 10+4
(f-g)(5) = 14
Which table or graph shows the value of y going up as the value of x goes up? ОА. ху 120 2 17 3 14 Ов. х у 1 5 2 4 3 3 42 7 6 Ос. 5
Answers
the only graph that increases in y as a function of the increase in x is option D
What percent of 25 is 24?
Answers
To compute the percentage that x represents from y we will use the following expression:
[tex]\frac{x}{y}\times100.[/tex]Therefore, the percentage that 24 represents from 25 is:
[tex]\frac{24}{25}\times100.[/tex]Simplifying the above result we get:
[tex]\frac{2400}{25}=96.[/tex]Answer: 96%.
Which of the following will have a unit rate of 50 miles per hour?F 210 miles in 4 hours G 300 miles in 5 hours H 250 miles in 4 hours I 175 miles in 3.5 hours
Answers
ANSWER
175 miles in 3.5 hours
EXPLANATION
We want to find the option that has a unit rate of 50 miles per hour.
To find the unit rate, we have to divide the distance travelled by the time taken.
OPTION F
Unit rate = 210 / 4 = 52.5 miles per hour
OPTION G
Unit rate = 300 / 5 = 60 miles per hour
OPTION H
Unit rate = 250 / 4 = 62.5 miles per hour
OPTION I
Unit rate = 175 / 3.5 = 50 miles per hour]
The correct option is the last one.
Given the following translated function , state the translations that have occurred and write the translated equation Toolkit function :y=x^2
Answers
Solution
Step 1
Write the function:
[tex]y\text{ = x}^2[/tex]Step 2
The function is reflected over the x-axis
f(x) to −f (x) reflects the function in the x-axis (that is, upside-down).
[tex]y\text{ = -x}^2[/tex]Step 2
Rule for vertical shift
When you shift f(x) vertically upward by b units, it becomes f (x) + b shifts the function b units upward.
[tex]y\text{ = -x}^2+1[/tex]y is shift 1 unit upward.
Final step
The finally the function is shift 2 units right using the rule below
f(x) shifted b units to the right to form f (x − b) shifts the function b units to the right.
[tex]y\text{ = -\lparen x-2\rparen}^2+1[/tex]Final answer
[tex]y\text{ = -\lparen x-2\rparen}^2+1[/tex]Angie opened a bank account. She deposited $225 each month for 4 months. Her bank charged her $5 each monthto use the account. How much money is in Angie's account after 4 moniths?
Answers
Answer:
$880
Explanation:
Angie deposited $225 for 4 months.
The total amount deposited will be = 4 x $225 = $900
Since her bank charged her $5 each month to use the account
The total charge for 4 months =4 x $5 = $20
Therefore, the amount in Angie's account after 4 months
=900-20
=$880
Question 17 of 25According to the fundamental theorem of algebra, how many zeros does thepolynomial below have?f(x)=x²-12x³ + 7x-5Answer hereSUBMIT
Answers
Solution:
The polynomial is given below as
[tex]x^5-12x^3+7x-5[/tex]Concept:
Fundamental theorem of algebra:
It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero.
Hence,
Using the fundamental theorem of algebra,
The number of zeros the polynomial is going to have will be
[tex]\Rightarrow5[/tex]Consider function f, where 8 is a real number.J(=) = tan(Br)Complete the statement describing the transformations to function fas the value of B is changed.As the value of B increases, the period of the functionV, and the frequency of the functionWhen the value of B is negative, the graph of the function (reflects over the y-axis
Answers
ANSWER:
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the x-axis
STEP-BY-STEP EXPLANATION:
The period of a trigonometric function is given by the following equation:
[tex]\begin{gathered} T=\frac{\pi}{k} \\ \\ \text{ let k be the constant number that is the coefficient of the angle x} \end{gathered}[/tex]In this case, k is equal to B, if B increases then the period decreases, and since the frequency is inversely proportional to the period it would increase.
If the value of B is negative we would have the following:
[tex]f(x)=\tan(-Bx)=-\tan(Bx)[/tex]Therefore, there is a reflection on the x-axis.
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the x-axis
Answer the following.(a) The signal from a certain satellite takes approximately 0.0037 seconds to reach Earth. Write this number in scientific notation.(b) The total surface area of Asia is approximately 1.72 x 10 ^7 square miles. Write this number in standard notation.(a) seconds(b) square miles
Answers
Explanation: Working with scientific notation all we need to do is to move the point to the left or to the right.
Letter a. Let's Illustrate below
As we can see above, we just needed to move the point 3 times to the right which represents the
[tex]10^{-3}[/tex]at the end of the scientific notation.
Letter b. Let's represent it as below
As we can see above we are doing the inverse representation so we needed to move the point 7 timer to the right.
you are converting 8 cm to meters. How will the number of meters compare to 8? Explain.
Answers
Solution:
100 cm is equivalent to 1 m then the conversion factor to convert centimeters to meters is:
[tex](\frac{1m}{100\text{ cm}})[/tex]then, 8cm is equivalent to
[tex]8cm(\frac{1m}{100\text{ cm}})\text{ = 0.08m}[/tex]We can conclude that the correct answer is:
[tex]0.08\text{ m}[/tex]on the other hand, notice that the comparison between the NUMBERS/CONSTANTS (not units) is:
[tex]0.08\text{ < 8}[/tex]10 mThe area of this rectangle is 30 m2.Which is the perimeter of the rectangle?O A 3 m0B. 13 mOC 20 mD. 26 mE. 30 m
Answers
Answer:
Step-by-step explanation:
The area of a rectangle is represented by the following expression:
[tex]\text{Area}=\text{length}\cdot\text{width}[/tex]Then, if we have that the area is 30 square meters and the length is 10 meters.
To determine the perimeter, we need to know the width, solve for the variable width:
[tex]\begin{gathered} 30=10\cdot\text{width} \\ \text{width}=\frac{30}{10} \\ \text{width}=3\text{ meters} \end{gathered}[/tex]Now, the perimeter of a rectangle is defined by the following expression:
[tex]\text{Perimeter}=2\cdot\text{width}+2\cdot\text{length}[/tex]Therefore, the perimeter of this rectangle would be:
[tex]undefined[/tex]The perimeter of a triangle is 93 It. Side a of thetriangle is twice as long as side b. Side c is 3 Itlonger than side a. Find the length of each side.
Answers
Step 1: Concept
The perimeter of a Triangle: A perimeter of a shape is the length of its boundary or the total length around the shape.
The perimeter of a triangle is the sum of the length of it boundary.
Step 2:
Draw the triangle
Step 3
Given data
Perimeter of a triangle = 93 ft
a = 2x
b = x
c = 3 + 2x
[tex]\begin{gathered} \text{Perimeter of a triangle = a + b + c} \\ 93\text{ = 2x + x + 3 + 2x} \\ \text{Collect similar terms} \\ 93\text{ - 3 = 2x + x +2x} \\ 90\text{ = 5x} \\ \frac{5x}{5}\text{ = }\frac{90}{5} \\ x\text{ = 18} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} a\text{ = 2x = 2}\times\text{ 18 = 36 ft} \\ \\ b\text{ = x = 18 ft} \\ \\ c\text{ = 3 + 2x = 3 + 36 = 39 ft} \end{gathered}[/tex]a = 36 ft , b = 18 ft , c = 39 ft
Which of the following answer choices shows the negation of the statement below?Statement: If Liz is in eighth grade, then she takes Spanish.
Answers
Given:
If Liz is in eighth grade, then she takes Spanish.
Required:
We need negation of the given statement.
Explanation:
There are some rules for then negation statement and one of those rules is
"if A, then B" negation of this is "A and not B"
Final answer:
Liz is in eighth grade and she does not take Spanish.
Sophia has $17,250 in a savings account that earns 11% annually. The interest is not compounded. How much will she have in 4 years?
Answers
To determine how much she will have in her account after 4 years you have to calculate the simple interest using the following formula:
[tex]A=P\mleft(1+rt\mright)[/tex]Where
A: total amount accured
P: principal investment
r: interest rate → you have to express it as a decimal number not as a percentage
t: time of the invesment → normally expressed in years
For
P= $17.250
r=11%→ 11/100=0.11
t=4years
The simple interest will be
[tex]\begin{gathered} A=17250(1+0.11\cdot4) \\ A=17250(1+0.44) \\ A=17250\cdot1.44 \\ A=24840 \end{gathered}[/tex]The school field trip for December is to the local Holiday Festival where there are horse drawn carriage and sleigh rides. Every student gets to take the horse drawn carriage or the sleigh ride. In the first hour 4 horse drawn carriage rides and 5 sleigh rides took a total of 132 students. In the second hour 6 horse drawn carriage rides and 4 sleigh rides took a total of 156 students. If the same number of students rode on each horse drawn carriage ride and the same number of students rode on each sleigh ride, how many students rode on each horse drawn carriage ride? How many students rode on each sleigh ride?
Answers
Let us formulate a system of equations to solve this problem.
Let x represent the number of students rode on each horse drawn carriage.
Let y represent the number of students rode on each sleigh ride.
4x + 5y = 132 Equation 1
6x + 4y = 156 Equation 2
We are going to use the elimination method to solve the system.
12x + 15y = 396 (Multiplying the first equation by 3)
12x + 8y = 312 (Multiplying the second equation by 2)
-------------------------------
7y = 84 ( Subtracting last form of equation 2 from last form of equation 1)
y=12 (Dividing on both sides of the equation by 7)
Replacing y=12 in the original form of Equation 1
4x + 5(12) = 132
4x + 60 = 132 (Multiplying)
4x = 72 (Subtracting 60 from both sides of the equation)
x= 18 (Dividing on both sides of the equation by 4)
The answer is 18 students rode on each horse drawn carriage and 12 students rode on each sleigh ride.
Use the graph of the parabola to fill in the table(1) Does the parabola open upward or downward(2) Find the intercept(s), make sure to do the following. if there is more is more than one, separate them with commas. If there are None put None.(3) Find the equation of the axis of symmetry. (4) Find the coordinates of the vertex.
Answers
x-intercepts = (2,0), (6,0)
y-intercepts = (0,3)
axis of simmetry x = 4
Vertex = ( 4, -1)
Question 1 Multiple Choice Worth 2 points(05.05)A boat's value over time is given as the function to and graphed below. Use A(x) = 400(b) + 0as the parent function. Which graph shows the boat's value decreasing at a rateof 40% per year?
Answers
Solving for the function for which the boat's value decreases 40% per year, we have
[tex]\begin{gathered} A(x)=400(b)^x \\ \text{Since it will decrease by 40\%, }b\text{ is equal to} \\ A(x)=400(1-0.4)^x \\ A(x)=400(0.6)^x \end{gathered}[/tex]Graphing our new function that is decreasing over time and we get
Mario is buying a number of hamburgers from the local store that cost $2.90 each. He is also buying one packet of hamburger rolls at a cost of $4.75. He has $39.55 to spend at the store. Write and solve an inequality that shows how many hamburgers, Mario can afford to buy.
Answers
ANSWER
[tex]\begin{gathered} 2.90b+4.75\le39.55 \\ b\le12 \end{gathered}[/tex]EXPLANATION
Each hamburger costs $2.90 and the hamburger roll costs $4.75
Let the number of hamburgers bought be b.
This means that b hamburgers cost:
[tex]2.90b\text{ dollars}[/tex]Mario has $39.55 to spend.
Therefore, the total cost of hamburgers and the hamburger roll must be less than or equal to $39.55.
That is:
[tex]2.90b+4.75\le39.55[/tex]Now, solve for b in the inequality:
[tex]\begin{gathered} 2.90b\le39.55-4.75 \\ 2.90b\le34.8 \\ \Rightarrow b\le\frac{34.8}{2.90} \\ b\le12 \end{gathered}[/tex]This means that Mario can afford to buy at most 12 hamburgers.
The weight of an object on Earth varies directly with its weight on the moon. The table below shows different weights of objects on Earth,X, compared to their weights on the moon, y. All weights are in pounds.Weight onEarth(X)Weight onMoon(y)1060201202403604060Which equation will calculate the weight, in pounds, of an object on the moon when its weight on Earth is x pounds?
Answers
Since we are told that the weight of an object on the moon varies directly with its weight on earth this means that we can express the equation like a linear one, with the form:
y=mx
We can find the value of m with the values from the table by means of this formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]For example, Let's us the pairs of x-y values (60,10) and (120,20), like this:
[tex]m=\frac{20-10}{120-60}=\frac{10}{60}=\frac{1}{6}[/tex]Then, the equation is:
[tex]y=\frac{1}{6}x[/tex]
Complete the square to write f(x) = x2 + 6x + 14 in vertex form. a. f(x) = (x + 3)2 + 5 b. f(x) = (x - 3)2 + 14 C. f(x) = (x + 3)2 + 23 d. f(x) = (x + 6)2 + 14
Answers
f(x) = x^2 + 6x + 14
Equation is written in ax^2 + bx + c form
where:
a= 1
b= 6
c=14
Consider the vertex:
a (x+d) ^2 + e
d= b/2a = 6 / 2 (1) = 3
e = c- b^2/4a = 14 - [6^2/4(1) ] = 5
Substitute d and e in the vertex form:
f(x)= 1 (x + 3 ) ^2 + 5
f(x) = (x+3)^2 + 5
option a
What is the sum of the first eight terms of the series 3 - 12+48-192+ ...
Answers
Given the series:
3 - 12 + 48 - 192 + ...
It can be identified as a geometric series because the common ratio is constant:
[tex]r=\frac{-12}{3}=-4[/tex]Now calculate the following terms:
a5 = (-192) * (-4) = 768
a6 = 768 * (-4) = -3072
a7 = -3072 * (-4) = 12288
a8 = 12288 * (-4) = -49152
The sum of the first eight terms is:
3 - 12 + 48 - 192 + 768 - 3072 + 12288 - 49152 = -39321
Sum = -39321
The sum of the first eight terms of the series 3 - 12+48-192+ ... will be -39321.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that the series is, 3 - 12+48-192+...
Given that the common ratio is constant, it is obvious that this series is geometric:
The common ratio for the sequence is,
r= -12/3
r= -4
The sum of the n term of the geometric sequence is,
Sₙ=a(rⁿ-1)/(r-1)
S₈=3((-4)⁸-1)/(-4-1)
S₈= -39321
Thus, the sum of the first eight terms of the series 3 - 12+48-192+ ... will be -39321.
Learn more about the sequence here:
brainly.com/question/21961097
#SPJ2
An air traffic controller locates an airplane on her radar display. The plane is moving in a diagonal directionAccording to the radar, the plane moves 5 miles east and 1 mile north over the course of a minute. There are noother planes to the north of the plane on the controller display, but there is an airport to the east of t. The airtraffic controller is not concerned with the plane's northeriy velocity, but she quicy calculates the plane'seasterty velocity. What does she find the easterty velocity of the airplane to be? Please answer in miles perhour.
Answers
The plane moves 5 miles east over the course of a minute. Then, the easterly velocity is:
[tex]\begin{gathered} \text{velocity}=\frac{\text{distance}}{\text{time}} \\ \text{velocity}=\frac{\text{5 miles}}{\text{1 minute}} \\ \text{velocity}=5\frac{\text{miles}}{\text{minute}} \end{gathered}[/tex]60 minutes is equivalent to 1 hour, then
[tex]5\frac{\text{miles}}{\text{minute}}\cdot\frac{60\text{ minutes}}{hour}=300\text{ mph}[/tex]Describe the graph of the quadratic function f(x)=2(x+2)^2-1 by stating which way the parabola opens and whether it is stretched taller or compressed shorter when compared to the quadratic parent function? A. The parabola opens downward and is stretched by a factor of 2.B. The parabola opens downward and is compressed by a factor of 2.C. The parabola opens upward and is stretched by a factor of 2.D. The parabola opens upward and is compressed shorter by a factor of 2.
Answers
EXPLANATION
Given the function:
f(x) = 2(x+2)^2-1 (Applying distributive property)
f(x) = 2X^2+2*4X+2*4-1
f(x) = 2x^2+8x+7
The parabola opens upward and is stretched by a factor of 2.
The table below shows the number of grapes and cups of water used to make fruit punch according to a certain recipe. Grapes 52 and 39 water cups 16 and 12 How many cups of water are needed for every 1 grape?
Answers
To find the number of cups of water needed for every 1 grape, divide the difference between the 2 values of cups of water by the difference between the 2 values of grapes, just as if you were finding a slope:
[tex]m=\frac{16-12}{52-39}=\frac{4}{13}=0.31[/tex]It means that 0.31 cups of water are needed for every grape.