Answer:
12/27
Step-by-step explanation:
Count all letters and all vowels then divide vowels by letters
The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.
What is the probability of an event in an experiment?The probability of any event suppose A, in an experiment is given as:
P(A) = n/S,
where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.
How to solve the given question?In the question, we are given an experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden".
We are asked to find the probability that the selected letter is a vowel.
Let the event of selecting a vowel from the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden" be A.
We can calculate the probability of event A by the formula:
P(A) = n/S,
where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.
The number of outcomes favorable to event A (n) = 12 (Number of vowels in the phrase)
The total number of outcomes in the experiment (S) = 27 (Number of letters in the phrase).
Now, we can find the probability of event A as:
P(A) = 12/27 = 4/9
∴ The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.
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From her purchased bags, Rory counted 110 red candies out of 550 total candies. Using a 90% confidence interval for the population proportion, what are the lower and upper limit of the interval? Answer choices are rounded to the thousandths place.
Answer:
The Confidence Interval = (0.172, 0.228)
Where:
The lower limit = 0.172
The upper limit = 0.228
Step-by-step explanation:
The formula to be applied or used to solve this question is :
Confidence Interval formula for proportion.
The formula is given as :
p ± z × √[p(1 - p)/n]
n = Total number of red candies = 550 red candles
p = proportion = Number of red candies counted/ Total number of red candies
= 110/550 = 1/5 = 0.2
z = z score for the given confidence interval.
We are given a confidence interval of 90%. Therefore, the z score = 1.6449
Confidence Interval = p ± z × √[p(1 - p)/n]
Confidence Interval = 0.2 ± 1.6449 × √[0.2(1 - 0.2)/550]
= 0.2 ± 1.6449 √0.2 × 0.8/550
= 0.2 ± 1.6449 × 0.0170560573
= 0.2 ± 0.0280555087
Hence, the Confidence Interval = 0.2 ± 0.0280555087
0.2 - 0.0280555087 = 0.1719444913
Approximately = 0.172
0.2 + 0.0280555087 = 0.2280555087
Approximately = 0.228
Therefore, the Confidence Interval = (0.172, 0.228)
Where:
The lower limit = 0.172
The upper limit = 0.228
Answer:
Lower Limit: 0.172
Upper Limit: 0.228
Step-by-step explanation:
Which is the simplified form of (StartFraction 2 a b Over a Superscript negative 5 Baseline b squared EndFraction) Superscript negative 3? Assume a not-equals 0, b not-equals 0. StartFraction b cubed Over 8 a Superscript 18 Baseline EndFraction StartFraction b squared Over 8 a Superscript 45 Baseline EndFraction StartFraction a Superscript 6 Baseline Over 4 b EndFraction StartFraction 2 a Superscript 6 Baseline Over b Superscript 5 Baseline EndFraction
Answer:
[tex]\dfrac{b^3}{8a^{18}}[/tex] matches the first choice
Step-by-step explanation:
[tex]\left(\dfrac{2 a b}{a^{-5}b^2}\right)^{-3}=(2a^{1-(-5)}b^{1-2})^{-3}=(2a^6b^{-1})^{-3}\\\\=2^{-3}a^{6(-3)}b^{-1(-3)}=8^{-1}a^{-18}b^3=\boxed{\dfrac{b^3}{8a^{18}}}[/tex]
__
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^-b = 1/a^b
Answer:
A
Step-by-step explanation:
just took the pretest! good luck!
please help me guys please find the value of 3x°
Answer:
finding the value of x first
2x + 3x + 10 = 180 (linear pair)
5x = 180 - 10
x = 170 / 5
x = 34
3x = 102
What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level
Answer:
their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
Please help. I’ll mark you as brainliest if correct! Thank you
Answer:
8 pounds of cheaper candy,
17.5 pounds of expensive candy
Step-by-step explanation:
Let's define some variables. Let's say the amount of pounds of candy that sells for $2.20/lb is x, and the $7.30 is y. Now we can write some equations!
x + y = 25.5
[tex]\frac{2.2x + 7.3y}{25.5} = 5.7[/tex]
We can start substitution. We can say that x = 25.5 - y. Plugging this into our second equation, we get:
y = 17.5
Plugging this in, we find that:
x = 8.
Theresa bought 2 pineapples for $6. She be wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part A
Using the diagram, find the constant of proportionality in terms of dollars per pineapple.
Answer:
$3 per pineapple
Step-by-step explanation:
Hey there!
If 2 pineapples are $6,
6 / 2 = 3
So 1 pineapple is $3.
Hope this helps :)
Answer:
3 dollars for 1 pineapple
Step-by-step explanation:
well 2 pinapples is 6 bucks. so 2x=6, and to get x, just divide each side by 2. 6/2=3.
Which system of linear inequalities has the point (3, –2) in its solution set?
Answer:
see below
Step-by-step explanation:
We want where both inequalities are true
y > -3
-2 >-3 this is true
y ≥ 2/3x -4
-2≥ 2/3*3 -4
-2 ≥ 2 -4
-2≥ -2
This is true
This is is the graph
Answer:
[tex]\boxed{\sf Option \ 3}[/tex]
Step-by-step explanation:
[tex]\sf The \ values \ must \ be \ true \ for \ both \ inequalities.[/tex]
[tex]x = 3\\y = -2[/tex]
[tex]y>-3\\-2>-3\\ \sf True[/tex]
[tex]y\geq \frac{2}{3}x-4 \\ -2\geq \frac{2}{3}(3)-4\\2\geq 2-4\\-2\geq-2 \\ \sf True[/tex]
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 80 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 20°. How far away from the building is the sculpture? Round your answer to the nearest hundredth.
Answer:
219.80 feet
Step-by-step explanation:
Tan 20= 80/b
Tan 20= 0.363970234266
(0.363970234266)b=80
b= 219.80 feet
The distance between the sculpture and the bottom of the building is required.
The distance between the building and sculpture is 219.80 feet.
Trigonometry[tex]\theta[/tex] = Angle of depression = Angle of elevation = [tex]20^{\circ}[/tex]
p = Height of building = 80 feet
b = Required length
From the trigonometric ratios we have
[tex]\tan\theta=\dfrac{p}{b}\\\Rightarrow b=\dfrac{p}{\tan\theta}\\\Rightarrow b=\dfrac{80}{\tan 20}\\\Rightarrow b=219.80\ \text{feet}[/tex]
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_______% of 44 = 22
Answer:
50%
Step-by-step explanation:
22 is half of 44.
So, this means 50% of 44 is 22.
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 72 58 62 38 44 66 42 49 76 52 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
72 58 62 38 44 66 42 49 76 52 ( arrange it!)
38 42 44 49 52 58 62 66 72 76 (done!)
Median: Find the number in the middle after we arranged, so the answer is (52+58)/2= 110/2 = 55
Mode : None (there is no number appear more than other number)
Mean = (38+42+44+49+52+58+62+66+72+76)/10
=559/100
=5,5
Hope it helps ^°^
HCF of x minus 2 and X square + X - 6
Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{x - 2}}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]
To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F
Let's solve
First expression = x - 2
Second expression = x + x - 6
Here, we have to find the two numbers which subtracts to 1 and multiplies to 6
= x + ( 3 - 2 ) x + 6
Distribute x through the parentheses
= x + 3x - 2x + 6
Factor out x from the expression
= x ( x + 3 ) - 2x + 6
Factor out -2 from the expression
= x ( x + 3 ) - 2 ( x + 3 )
Factor out x+3 from the expression
= ( x + 3 ) ( x - 2 )
Here, x - 2 is common in both expression.
Thus, H.C.F = x - 2
Hope I helped!
Best regards!!!
Answer:
x - 2
Step-by-step explanation:
by factorization method
1) x - 2
2) x^2 + x - 6
by splitting method
x^2 + 3x - 2x - 6
taking separate common from the first two terms and last two terms
x(x + 3) - 2(x + 3)
now writing x+3 once and the other term to get the right answer
(x + 3)(x - 2)
in both parts just see the similar term and write it as HCF
HCF= x - 2
and the second method by which you can get this answer is division method
The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in
Answer:
396 in^2
Step-by-step explanation:
The perimeter of a triangle is given by the formula:
● P = 2w+2L
L is the length and w is the width
■■■■■■■■■■■■■■■■■■■■■■■■■■
The width hereis 18 inches and the perimeter is 80 inches.
Replace w by 18 and P by 80 to find L.
● P= 2L+2w
● 80 = 2L + 2×18
● 80 = 2L + 36
Substrat 36 from both sides
● 80-36 = 2L+36-36
●44 = 2L
Divide both sides by 2
● 44/2 = 2L/2
● 22 = L
So the length is 22 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
The area of a rectangle is given by the formula:
● A= L×w
● A = 22×18
● A = 396 in^2
The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.
Answer:
7/11 = 0.6363...
Step-by-step explanation:
7 + 4 = 11
probability of winning: 7/11 = 0.6363...
The probability that the horse will in the race is [tex]\mathbf{\dfrac{7}{11}}[/tex]
Given that the odds of the horse winning the race is 7:4
Assuming the ratio is in form of a:b, the probability of winning the race can be computed as:
[tex]\mathbf{P(A) = \dfrac{a}{a+b}}[/tex]
From the given question;
The probability of the horse winning the race is:
[tex]\mathbf{P(A) = \dfrac{7}{7+4}}[/tex]
[tex]\mathbf{P(A) = \dfrac{7}{11}}[/tex]
Learn more about probability here:
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A 160-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top
Weight of man and paint = 160 + 5 = 165 total pounds.
Gravitational force is independent of the path taken so we can ignore the radius of the silo.
Work done = total weight x height
The problem says he climbs to the top so overall height is 90 feet
Work = 165 lbs x 90 ft = 14,850 ft-lbs
A box is 1 m high, 2.5 m long, and 1.5 m wide, what is its volume?
Answer:
3.75
Step-by-step explanation:
[tex]v = lbh \\ 2.5 \times 1.5 \times 1 \\ = 3.75[/tex]
The volume of the rectangular prism will be 3.75 cubic meters.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
A box is 1 m high, 2.5 m long, and 1.5 m wide.
Then the volume of the rectangular prism will be
V = L x W x H
V = 1 x 2.5 x 1.5
V = 3.75 cubic meters
Thus, the volume of the rectangular prism will be 3.75 cubic meters.
More about the volume of the rectangular prism link is given below.
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Heidi bought a machine that throws tennis balls for her dog to fetch. The height of each ball thrown by the machine, in feet, is modeled by the function f(x) = –x2 + x + 2, where x represents time in seconds. How many seconds after the machine throws the ball does it hit the ground?
Answer:
2 seconds
Step-by-step explanation:
Given the equation:
[tex]f(x) = -x^2 + x + 2[/tex]
Where f(x) represents the height of each ball thrown by machine.
and x represents the time in seconds.
To find:
The number of seconds after which the machine throws the balls hits the ground = ?
Solution:
In other words, we have to find the value of [tex]x[/tex] after which the [tex]f(x) = 0[/tex]
(Because when the ball hits the ground, the height becomes 0).
Let us put [tex]f(x) = 0[/tex] and solve for [tex]x[/tex]
[tex]f(x) = -x^2 + x + 2 =0\\\Rightarrow -x^2 + x + 2 =0\\\Rightarrow x^2 - x - 2 =0\\\Rightarrow x^2 - 2x+x - 2 =0\\\Rightarrow x(x - 2)+1(x - 2) =0\\\Rightarrow (x+1)(x - 2) =0\\\Rightarrow x =-1, 2[/tex]
[tex]x=-1[/tex] sec is not a valid answer because time can not be negative.
So, the answer is after 2 seconds, the ball hits the ground.
Given the two functions, which statement is true?
fx = 3^4, g(x) = 3^x + 5
Answer:
third option
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Given
g(x) = [tex]3^{x}[/tex] + 5 ← this represents a shift up of 5 units
Thus g(x) is the graph of f(x) translated up by 5 units
Answer:
[tex]\boxed{\sf{Option \: 3}}[/tex]
Step-by-step explanation:
g(x) is translated up 5 units compared to f(x). In a vertical translation, when the graph is moved 5 units up, 5 is added to the function. When the graph is moved 5 units down, 5 is subtracted from the function. The graphs are shifted in the direction of the y-axis.
(2²)³+(2³)²/4
Simplificar
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▹ Answer
80
▹ Step-by-Step Explanation
(2²)³ + (2³)² ÷ 4
Rewrite:
2⁶ + 2⁶ ÷ 2²
Divide:
2⁶ + 2⁴
Factor:
(2² + 1) * 2⁴
Evaluate:
(4 + 1) * 2⁴
Calculate:
5 * 16
= 80
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
A movie theater is having a special. If a group of four pays $7.25 each for tickets, each person can get popcorn and a drink for $5.75. Use the expression 4(5.75 + 7.25) to find the total cost for 4 friends.
Answer:
The price for 4 people is 52 dollars.
4 × (5.75 + 7.25) = 52
The total cost including drink and popcorn is $52 according to a given condition.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Cost of movie ticket = $7.25/person
Cost of popcorn and drink = $5.75/person
Total cost per person = 5.75 + 7.25 = $13
Now,
Number of people = 4
So,
4(5.75 + 7.25) = 4(13) = $52
Hence "The total cost including drink and popcorn is $52 according to a given condition".
For more about the equation,
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What is the probability that a randomly selected individual on this campus weighs more than 166 pounds? (express in decimal form and round final answer to 4 decimal places)
Answer:
hello attached is the missing part of your question and the answer of the question asked
answer : 0.2951
Step-by-step explanation:
Given data:
number of persons allowed in the elevator = 15
weight limit of elevator = 2500 pounds
average weight of individuals = 152 pounds
standard deviation = 26 pounds
probability that an individual selected weighs more than 166 pounds
std = 26 , number of persons(x) = 15, average weight of individuals(u) = 152 pounds
p( x > 166 ) = p( x-u / std, 166 - u/ std )
= p ( z > [tex]\frac{166-152}{26}[/tex] )
= 1 - p( z < 0.5385 )
p( x > 166 ) = 1 - 0.70488 = 0.2951
g If A and B are disjoint events, with P( A) = 0.20 and P( B) = 0.30. Then P( A and B) is: a. .00 b. .10 c. .50 d. 0.06
Answer: A) 0
P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.
We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.
Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 + 4xy − 48y2 = 2(x + By)(x − 4y)
Answer:
B = 6
Step-by-step explanation:
2x^2 + 4xy − 48y^2
Factor out 2
2(x^2 + 2xy − 24y^2)
What 2 numbers multiply to -24 and add to 2
-4 *6 = -24
-4+6 = 2
2 ( x+6y)( x-4y)
Answer:
[tex]\huge\boxed{B=6}[/tex]
Step-by-step explanation:
They are two way to solution.
METHOD 1:Factor the polynomial on the left side of the equation:
[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]
Therefore:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]
METHOD 2:Multiply everything on the right side of the equation using the distributive property and FOIL:
[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]
Compare polynomials:
[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]
From here we have two equations:
[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]
[tex]1)\\2B-8=4[/tex] add 8 to both sides
[tex]2B=12[/tex] divide both sides by 2
[tex]B=6[/tex]
[tex]2)\\-8B=-48[/tex] divide both sides by (-8)
[tex]B=6[/tex]
The results are the same. Therefore B = 6.
What is 28% of 58?
Hhhhhhh
Answer:
16.24
Step-by-step explanation:
of means multiply
28% * 58
Change to decimal form
.28 * 58
16.24
Answer:
[tex]\Large \boxed{\mathrm{16.24}}[/tex]
Step-by-step explanation:
[tex]28\% \times 58[/tex]
[tex]\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}[/tex]
[tex]\displaystyle \frac{28}{100} \times 58[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{1624}{100} =16.24[/tex]
Please help!! find the value of the expression
Answer:
7
Step-by-step explanation:
First plug in the variable amounts so the expression now looks like this:
(3 × 4 - 12) + 1/2(4 × 6 - 10)
Now, start by solving the multiplication parts first, so it now looks like this:
(12 - 12) + 1/2(24 - 10)
Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)
Next, solve the multiplication part, so it now looks like this: 0 + 7
Solve that and the answer is 7.
What is 2 cm converted to feet?
Answer:
0.065617 ft
Step-by-step explanation:
Answer:
0.0656168 feet.
Step-by-step explanation:
find the value of X from the given picture
Answer:
x = 108
Step-by-step explanation:
The sum of a circle is 360
90 + x/2 + x+x = 360
Combine like terms
90 + 2x+x/2 = 360
90 + 5/2 x = 360
Subtract 90 from each side
5/2x = 270
Multiply each side by 2/5
5/2x * 2/5 = 270*2/5
x =108
solve 27 to the power of (2/3)
Answer:
9Step-by-step explanation:
[tex]27^{\frac{2}{3}}\\\mathrm{Factor\:the\:number:\:}\:27=3^3\\=\left(3^3\right)^{\frac{2}{3}}\\\mathrm{Apply\:exponent\:rule}:\\\\\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\\\left(3^3\right)^{\frac{2}{3}}=3^{3}\times \frac{2}{3}}\\\\3\=times \frac{2}{3}=2\\\\=3^2 \\\\=9[/tex]
[tex]27^{2/3}=(3^3)^{2/3}=3^2=9[/tex]
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
Which of the following statements is TRUE about the stepwise selection procedure?
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
B. Backward stepwise procedure and forward stepwise procedure would end up with the same "best" model.
C. The "best" model determined by the stepwise selection method is the same model as what would be selected by complete search but stepwise method is usually faster.
D. Different choices of alpha limits for variable selection may end up with different final models.
Answer:
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
Step-by-step explanation:
Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.
