Apple be A and blueberries be B
So
As per Venn diagram
n(A)=12n(B)=7n(A$\cap$B)=3#1
n(A)+n(B)12+719P(A)=12/24
P(B)=7/24
Add
12+7/2419/24#2.
n(AUB)
n(A)+n(B)-n(An B).19-316E=8+16=24
P(AUB)=16/24=2/3
Answer:
[tex]\sf a) \quad P(contains\:apple)+P(contains\:blueberry)=\dfrac{5}{6}[/tex]
[tex]\sf b) \quad P(contains\:apple\:or\:blueberry)=\dfrac{11}{15}[/tex]
c) Not mutually exclusive events
Step-by-step explanation:
From inspection of the Venn diagram:
Total number of smoothies = 12 + 3 + 7 + 8 = 30Number of smoothies containing Apple = 12 + 3 = 15Number of smoothies containing Blueberry = 3 + 7 = 10Number of smoothies containing both Apple and Blueberry = 3Number of smoothies not containing Apple or Blueberry = 8[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Let A = contains apple
Let B = contains blueberry
[tex]\implies\sf P(A)=\dfrac{15}{30}=\dfrac{1}{2}[/tex]
[tex]\implies\sf P(B)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]
Part (a)
[tex]\begin{aligned} \implies \sf P(A)+P(B) & =\sf \dfrac{1}{2}+\dfrac{1}{3}\\\\ & = \sf \dfrac{3}{6}+\dfrac{2}{6}\\\\ & = \sf \dfrac{5}{6}\end{aligned}[/tex]
Part (b)
[tex]\textsf{Addition Law}: \quad\sf P(A\:or\: B) = P(A)+P(B)-P(A\:and\:B)[/tex]
Given:
[tex]\sf P(A)+P(B)=\dfrac{5}{6} \quad \textsf{(from part a)}[/tex]
[tex]\sf P(A\:and\:B)=\dfrac{3}{30}\quad \textsf{(where the circles overlap)}[/tex]
[tex]\begin{aligned}\implies \sf \sf P(A\:or\: B) &= \sf P(A)+P(B)-P(A\:and\:B)\\\\& =\sf \dfrac{5}{6}-\dfrac{3}{30}\\\\ & =\sf \dfrac{25}{30}-\dfrac{3}{30}\\\\ & =\sf \dfrac{22}{30}\\\\ & = \sf \dfrac{11}{15}\end{aligned}[/tex]
Or, we can simply read P(contains apple or blueberry) from the Venn diagram.
P(A or B) is the total of the numbers inside the circles divided by the total number of smoothies:
[tex]\sf P(A\:or\:B) = \dfrac{12+3+7}{30}=\dfrac{22}{30}=\dfrac{11}{15}[/tex]
Part (c)
For two events, A and B, where A and B are mutually exclusive:
[tex]\sf P(A \: or \: B)=P(A)+P(B)[/tex]
Given:
[tex]\sf P(A)+P(B)=\dfrac{5}{6} \quad \textsf{(from part a)}[/tex]
[tex]\sf P(A\:or\:B)=\dfrac{11}{15} \quad \textsf{(from part b)}[/tex]
[tex]\sf As\:\dfrac{11}{15}\neq \dfrac{5}{6} \implies P(A \: or \: B)\neq P(A)+P(B)[/tex]
Therefore, choosing a smoothie containing apple and choosing a smoothie containing blueberry are NOT mutually exclusive events.
Quadrilateral abcd is a parallelogram if both pairs of opposite angles are congruent. prove that quadrilateral abcd is parallelogram by finding the measure of the opposite angle pairs?
Answer:
you how are doing please study and work hard
880$ at 5.25% for 2 years
Answer:
$977.20
Step-by-step explanation:
We will use the compound interest formula to solve this: A = P(1 + R) ^ T
Using this formula we plug-in the values that we already have:
A = 880(1 + .0525) ^ 2
Now if we solve this, we end up with 977.20. That is your answer.
2.5 lbs of apples for $3.25 or 35oz for $3.50?
Answer:
2.5 lbs of apples for $3.25
Step-by-step explanation:
16 oz in one pound, 2.5 pounds is 40 oz. 40 oz is bigger than 35 and it costs less.
HI GIVING BRAINLIESST CAN SOMEONE PLEASE EXPLAIN IM SORRY ITS SO LATE
Answer:
100°
Step-by-step explanation:
[tex] In\:right\:\triangle GHI \:\&\: \triangle GJI[/tex][tex]\angle GHI\cong\angle GJI[/tex] (Each 90° given)[tex]Hypotenuse \:GI \cong\: Hypotenuse GI[/tex] (Common side)[tex] side\: GH\cong\:side GJ[/tex] (Given)[tex]\implies \triangle GHI\cong\triangle GJI[/tex] (By HST postulate)[tex]\implies \angle GIH \cong \angle GIJ[/tex] (corresponding angles of congruent triangles or cact)[tex]\implies m\angle GIH = m\angle GIJ[/tex][tex]\implies 2z = z+25\degree[/tex][tex]\implies 2z-z = 25\degree[/tex][tex]\implies \red{\bold{z = 25\degree}}[/tex][tex]m\angle HIJ =m\angle GIH +m\angle GIJ[/tex] (By angle addition postulate)[tex]\implies m\angle HIJ = (2z) + (z + 25\degree)[/tex][tex]\implies m\angle HIJ = 3z + 25\degree[/tex][tex]\implies m\angle HIJ = 3(25\degree) + 25\degree[/tex][tex]\implies m\angle HIJ = 3(25\degree) + 25\degree[/tex][tex]\implies m\angle HIJ = 75\degree+ 25\degree[/tex][tex]\implies\huge{\purple{\boxed{ m\angle HIJ =100\degree}}}[/tex]The base of a solid is bounded by the curve y = sqrt (x+1) the x-axis and the line x = 1. the cross sections, taken perpendicular to the x-axis, are squares. find the volume of the solid.
a. 1
b. 2
c. 2.333
d. none of these
(will vote brainlest, like and rate)
See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
[tex]\displaystyle \int_{-1}^1 (x+1) \, dx = \left(\frac{x^2}2 + x\right) \bigg|_{-1}^1 = \boxed{2} ~~~~ (B)[/tex]
Helppppppppppp meeeeeeeeee pleaseeeeeee
graph this sin equation
Answer:
I graphed it on desmos:
What's the answer!!!!! ASAP
The number of hits the player that most outperformed the predicted number of home runs based on the model is: 163 hits.
What is a Model?A model can be represented by an equation in slope-intercept form which can be used to make predictions between the association or relationship between two variables.
From the details about the predictions given in the table above, 7 players outperformed the predicted number of home runs.
However, the player that outperformed the predicted number of home runs the most is the player that had 31 home runs with a predicted home run of 23.
The number of hits the player had was 163.
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The following set of ordered pairs represents y as a function of x.
{ (9,8), (-2, -14), (6, 2), (-3, -16), (______)}
Which of the following could be the missing ordered pair?
A (9,-8)
B (-3, 9)
C (-9, 8)
D (6,-2)
============================================================
Explanation:
The point (9,8) is in the original set of ordered pairs.
We cannot include (9,-8) since x = 9 is already listed. We can't have repeated x values. If x repeats, then we don't have a function.
This rules out choice A.
Choices B and D are eliminated for similar reasoning.
Choice C can be included because x = -9 hasn't been mentioned yet.
Note: A function is when any given x value leads to exactly one y value.
A container holds 4800 cubic inches of waste. The dimensions of the container are tripled. How many cubic feet
of waste does the new container hold?
This is a 3-D container and the dimensional factor is F=3. The volume increases by a factor of 33 = 27.
The answer is 4608 x 27 / 123 = 72
1.Judy put 50 cents and 1 quarter into a vending machine to buy a bottle of fruit juice. She got 2 dimes and 1 nickel back from the vending machine. How much did the bottle of fruit juice cost
Nickel - 5 cents
Dime - 10 cents
Quarter - 25 cents
Judy put in: 50 + 25 = 75 cents
The machine gave back: 10 + 10 + 5 = 25
Subtract the two numbers to find the difference (what the fruit juice cost): 75 - 25 = 50 cents
Answer:
Nickel - 5 cents
Dime - 10 cents
Quarter - 25 cents
Judy put in: 50 + 25 = 75 cents
The machine gave back: 10 + 10 + 5 = 25
Subtract the two numbers to find the difference (what the fruit juice cost): 75 - 25 = 50 cents
Step-by-step explanation:
HURRY 100 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which number line shows the solution to the inequality? y minus 2 less-than negative 5 A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. A closed circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 7. Everything to the left of the circle is shaded.
Answer:
3.
Step-by-step explanation:
Answer: the square root of 54 x IDC x i don't even want to help x haha no help for you x points for me not you
Step-by-step explanation:
find the volume of the compound shape
[tex]v = \frac{2}{3} \pi {r}^{3} [/tex]
[tex]v = \frac{2}{3} \times \pi \times {1.5}^{3} [/tex]
[tex]v = 7.07 \: {cm}^{3} [/tex]
Volume of the cylinder:[tex]v = \pi {r}^{2} h[/tex]
[tex]v = \pi \times {1.5}^{2} \times 4[/tex]
[tex]v = 28.27 \: {cm}^{3} [/tex]
Total volume:[tex]v = 7.07 + 28.27[/tex]
[tex]v = 35.34 \: {cm}^{3} [/tex]
Hence, the volume of the given compound shape is 35.34 cubic centimeters.
v of hemisphere:
2/3 pi r^3
v of cylinder:
pi r^2 h
total:
add both the value
apply the formula and try
Please help with the 4/5 problems:) I completely forgot how to do this! *please show work on how you got your answer!**
Rotate RST 90° counterclockwise around the origin.
The image of the triangle RST when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)
The coordinates of RST are given as:
R = (5,15)
S = (15,15)
T = (10,5)
The rule of 90° counterclockwise around the origin is:
(x,y) -> (-y,x)
So, we have:
R' = (-15,5)
S' = (-15,15)
T' = (-5,10)
Hence, the image of the triangle when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)
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NEED HELP PLEASE ANSWER ASAP! (42)
Answer:
(1) (4x - 5y)(4x + 5y)
Step-by-step explanation:
Question 42
16x² - 25y²The identity to be used is : a² - b² = (a - b)(a + b)(1) (4x - 5y)(4x + 5y)Answer:
(1) (4x - 5y)(4x + 5y)
Step-by-step explanation:
Difference of Two Squares: [tex]a^2-b^2=(a-b)(a+b)[/tex]
Therefore, we can use The Difference of Two Squares to factor this expression quickly.
Given expression: [tex]16x^2-25y^2[/tex]
[tex]16=4^2 \implies 16x^2=4x \cdot 4x=(4x)^2[/tex]
[tex]25=5^2 \implies 25y^2=5y \cdot 5y=(5y)^2[/tex]
Therefore:
[tex]16x^2-25y^2=(4x)^2-(5y)^2[/tex]
Using The Difference of Two Squares:
[tex](4x)^2-(5y)^2=(4x-5y)(4x+5y)[/tex]
The number 22 is multiplied by a 22-digit number that contains only "2"s. What is the
sum of the digits of the product?
Answer:
I don't know it is actually pretty hard! But is this part of the rsm mcp contest
Step-by-step explanation:
The sum of digits of the products is given by S = 176
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The number 22 multiplied by a 22-digit number that contains only "2"s would result in a number that consists of a string of "4"s.
This is because 2 multiplied by 2 results in 4. Since all the digits in the 22-digit number are "2"s, each digit would multiply by 2 and result in "4".
Therefore, the product of 22 multiplied by a 22-digit number that contains only "2"s would be a 44-digit number consisting of "4"s.
The sum of the digits of a 44-digit number consisting of only "4"s can be calculated by multiplying the digit "4" by the total number of digits, which in this case is 44.
Sum of digits = 4 × 44 = 176
Hence , the sum of the digits of the product would be 176
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The point P = (-3, y) lies on the unit circle shown below. What is the value of y
in simplest form?
The equation of the circle is given as (x-h)² + (y-k)² = r². Then the value of y will be ± √5/3.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at (h, k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x-h)² + (y-k)² = r²
The equation of the circle has the center at the origin and the radius is one unit. Then we have
x² + y² = 1
The point P = (-2/3, y) lies on the unit circle. Then the value of y will be
(-2/3)² + y² = 1
y² = 1 - 4/9
y² = 5/9
y = ± √5 / 9
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A runner ran a 400 m race in 1 min 35 sec. Calculate his average speed in m/sec.
Step-by-step explanation:
distance = 400m
time taken = 1 min 35 sec = 95 sec
average speed = 400m / 95 sec = 4=2105 m/ sec
Answer:
4.21 m / sec.
Step-by-step explanation:
1 min 35 sec.
= 60 + 35
= 95 sec.
So average speed = 400/95
= 4.21 m / sec.
Three coins are tossed. Find the probability that 2 land on heads
Answer:
1/8
Step-by-step explanation:
Probability denotes the possibility of something happening. It is a field of mathematics that studies the probability of a random event occurring. From 0 to 1.
the value is expressed.
When a coin is tossed, the chance of it landing on heads is 1/2, and vice versa.
So, we divide 1/2 by the number of times it lands on heads to get 1/4. However, when the second one landed on tails, we must multiply it by 1/2 again, making 1/4 x 1/2 = 1/8.
hope this helps:)
Pls someone
In this diagram, what is the BEST description of the transformation shown?
Answer: B) Rotation
Explanation:
The preimage has been rotated 180 degrees to land on the image.
Proof of this is to note that a point like (2,2) maps to (-2,-2)
The 180 degree rotation rule is [tex](x,y) \to (-x,-y)[/tex]. We flip the signs of each coordinate.
You can accomplish the same thing with two reflections: one over the x axis and the other over the y axis. However, a rotation is more direct.
Can you guys help me solve this equation with step-by-step help, please...
-2x -5y = 16
2x -3y = -16
-5x + 2y = 11
-3x + 4y = -13
Step-by-step explanation:
-2x - 5y = 16___(1)
2x - 3y = -16___(2)
(1) + (2) ==> -2x -5y = 16
(+) 2x -3y = -16
-8y = 0
y = 0/-8
y = 0
y=0 in (1)
(1)---> -2x-5y =16
-2x - 5(0) = 16
-2x - 0 = 16
-2x = 16
x = 16/-2
x = -8
x = -8 , y = 0
-5x + 2y = 11__(1) ; -3x + 4y = -13___(2)
multiply eqn(1) with 2
2 × (1) : -10x + 4y = 22___(3)
(3) - (2) :. -10x + 4y = 22
(-) -3x + 4y = -13
-7x = 35
x = 35/-7
x = -5
x=-5 in (1)
(1) : -5x + 2y = 11
-5(-5) + 2y = 11
25 + 2y = 11
2y = 11 - 25
2y = -14
y = -14/2
y = -7
x = -5 , y = -7
Find all the zeros of f(x).
f(x) = 3x4 + 11x3 + 11x2 + x - 2
Arrange your answers from smallest to largest.
If there is a double root, list it twice.
Answer:
-2, -1, -1, 1/3
Step-by-step explanation:
A graphing calculator can find the real roots of a polynomial pretty easily. The attached graph of this function shows its zeros to be ...
-2, -1, -1, 1/3
__
The rational root theorem tells you that rational roots will be from the set ...
{±1/3, ±2/3, ±1, ±2}
Descarte's rule of signs tells you there will be 1 positive real root. The sum of coefficients is 24 (a relatively large positive number), so it is certain the positive root will be less than 1.
The sum of coefficients of odd-degree terms (11+1) is equal to the sum of coefficients of even-degree terms (3+11-2), telling you that -1 is a root. Synthetic division gives the cubic factor as 3x³ +8x² +3x -2, which has the same characteristics as the original quartic. That is, there is one positive real root, and -1 is a root of the cubic (hence a double root of f(x)).
Another round of synthetic division reveals the quadratic factor to be 3x² +5x -2, which can be factored as (x +2)(3x -1) to reveal the remaining roots.
(-3+7i)(1-2i) can you help me with the answer to this
Answer:
11 + 13i
Step-by-step explanation:
A must know is that
[tex] \sqrt{i} = - 1[/tex]
Complex numbers
1st: foil the equations
[tex] - 3(1 - 2i) + 7i(1 - 2i)[/tex]
[tex] - 3 + 6i + 7i- 14 {i}^{2} [/tex]
2nd Combine like terms and substitute
[tex]i ^{2} for \: - 1[/tex]
[tex] - 3 + 14 + 13i[/tex]
[tex]11 + 13i[/tex]
PLEASEEEEE
Match the expressions with their simplified versions.
Answer:
1. [tex]\normalsize \boxed{\textsf{$4\sqrt{2}\cdot\sqrt{2}$}} \implies \boxed{8}[/tex]
2. [tex]\normalsize \boxed{\textsf{$3\sqrt{7}-2\sqrt{7}$}} \implies \normalsize \boxed{\textsf{$\sqrt{7}$}}[/tex]
3. [tex]\normalsize \boxed{\textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}} \implies \normalsize \boxed{\textsf{$\dfrac{1}{2}$}}[/tex]
4. [tex]\normalsize \boxed{\textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}} \implies \boxed{20}[/tex]
Step-by-step explanation:
The Radical Rules by Lial et al. (2017) state that:
Product rule: [tex]\large \textsf{$\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$}[/tex]
"The product of two roots is the root of the product."Quotient rule: [tex]\large \textsf{$\sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$}\ \ \textsf{$(b \neq 0)$}[/tex]
"The root of a quotient is the quotient of the roots."1.
[tex]\implies \normalsize \textsf{$4\sqrt{2}\cdot\sqrt{2}$}\\\\\normalsize \implies \textsf{$4\sqrt{2\cdot2}$}\\\\ \implies \normalsize \textsf{$4\sqrt{4}$}\\\\ \implies\normalsize \textsf{$4\cdot 2 = 8$}[/tex]
[tex]\normalsize \boxed{\textsf{$4\sqrt{2}\cdot\sqrt{2}$}} \implies \boxed{8}[/tex]
2.
[tex]\implies \normalsize \textsf{$3\sqrt{7}-2\sqrt{7}$}\\\\ \implies\normalsize \textsf{$(3-2)\sqrt{7}$}\\\\ \implies\normalsize \textsf{$1\sqrt{7}$}\\\\ \implies\normalsize \textsf{$\sqrt{7}$}[/tex]
[tex]\normalsize \boxed{\textsf{$3\sqrt{7}-2\sqrt{7}$}} \implies \normalsize \boxed{\textsf{$\sqrt{7}$}}[/tex]
3.
[tex]\implies \normalsize \textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}\\\\\\ \implies\normalsize \textsf{$\dfrac{1\sqrt{7}}{2\sqrt{7}}$}\\\\\\ \implies\normalsize \textsf{$\dfrac{1}{2}$}\\\\[/tex]
[tex]\normalsize \boxed{\textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}} \implies \normalsize \boxed{\textsf{$\dfrac{1}{2}$}}[/tex]
4.
[tex]\implies \normalsize \textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}\\\\ \implies\normalsize \textsf{$2\cdot2\sqrt{5\cdot5}$}\\\\ \implies \normalsize \textsf{$4\sqrt{25}$}\\\\ \implies \normalsize \textsf{$4\cdot5=20$}\\\\[/tex]
[tex]\normalsize \boxed{\textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}} \implies \boxed{20}[/tex]
Reference:
Lial, M., Hornsby, J., Schneider, D., & Daniels, C. (2017). College Algebra and Trigonometry, Global Edition (6th ed., p. 94).
The radius of a circle is 4 feet. what is the angle measure of an arc pi feet long?
Answer:
Step-by-step explanation:
A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company has access to 24 different vehicles. Each vehicle will receive four tires with the new tread and four with the original tread. The position, front or back, will be randomly determined for a pair of each type of tread. For example, a vehicle will have the new type of tread on the front tires and the original tread on the back tires. After six months, the pairs of unused tires will be used with the position switched on the car. The vehicles will be driven for six more months. At the end of one year, the depths of the remaining tread will be measured for each tire and the average differences between the new and original tread types will be determined. The average differences will then be used to determine if the new tread does last longer.
Is this a matched pairs design for this experiment?
Yes, the company used 24 different vehicles.
Yes, both types of tread were randomly assigned to each vehicle.
No, the vehicles were not put into groups of two.
No, the tires with the different types of tread were not randomly assigned to each vehicle.
This is a matched pairs design because both types of tread were randomly assigned to each vehicle.
What is matched pairs design?The term matched pairs design has to do with the situation in which participants are randomly assigned to an experiment or a control group. For each participant assigned to an experimental group, another is assigned to the control group.
Thus, this is a matched pairs design because both types of tread were randomly assigned to each vehicle.
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What multiplies to 4 and adds to 6
I need help with this math question thank you
Answer:
A
Step-by-step explanation:
please help I need this
Answer:
the best answer is B
commending, is the act of praise or approval
C
Answer:
Why because u and the person sharing room, he or she is not slave to you. he or she do 50 percent and you 50 percent to keep peace in the room. steps why if the person say they are moving out then in that case who will clean the room