Answer:
[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
A combination refers to the selection of objects such that order does not matter. A permutation refers to the arrangement of objects such that order do matter.
Number of bananas = 2
Number of apples = 5
One banana and two apples are chosen.
So,
probability that one banana and two apples are chosen = [tex]\frac{C(2,1)\,C(5,2)}{C(7,3)}[/tex]
[tex]C(2,1)=\frac{2!}{1!(2-1)!}=2[/tex]
[tex]C(5,2)=\frac{5!}{2!(5-2)!}=\frac{5!}{2!31} =10[/tex]
[tex]C(7,3)=\frac{7!}{3!(7-3)!} =\frac{7!}{3!4!}=35[/tex]
So,
Probability that one banana and two apples are chosen = [tex]\frac{2(10)}{35}=\frac{4}{7}[/tex]
Answer:
Or 57.14%
Step-by-step explanation:
what is the quotient of
2 1/2 ÷ (-1 3/4)
enter your answer as a mixed number in simplified form
Answer:The exact form is -10/7 the simplified form is -1 3/7
Step-by-step explanation:
How many solutions does the equation have?
3(d+11) = 6(d +33)
O 0
O 1
O infinitely many
9514 1404 393
Answer:
1 solution
Step-by-step explanation:
The coefficients of d are different on the two sides of the equation (3d vs 6d), so the equation has one solution.
__
Dividing by 3 gives ...
d +11 = 2(d +33)
d + 11 = 2d + 66
Adding -d-66 to both sides gives ...
-55 = d . . . . . . the one solution
Answer:
The answer is B
Step-by-step explanation:
i took the test and 1 was correct so.
also this one! :( pls help again! thanks.
Answer:
9 is the answer
George is making an xylophone. So far, he has bars that are 1.75 feet, 1 and 7/12 feet, and 1 2/3 feet long. What is the length of the longest bar.
When the author visited Dublin, Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distribution), he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages can be found from the license plates. (There is no end to the fun of traveling with the author.) The ages (in years) are listed below. We might expect that taxis would be newer, so test the claim that the mean age of cars is greater than the mean age of taxis. Use α= 0.05 significance level to test the claim that in Dublin, car ages and taxi ages have the same variation.
Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8
Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4
Answer:
The Decision Rule
Fail to reject the null hypothesis
The conclusion
There is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi
Step-by-step explanation:
From the question we are told that
The data is
Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8
Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4
The level of significance [tex]\alpha = 0.05[/tex]
Generally the null hypothesis is [tex]H_o : \mu_1 - \mu_2 = 0[/tex]
the alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex]
Generally the sample mean for the age of cars is mathematically represented as
[tex]\= x_1 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x_1 = \frac{4+ 0+ 8 +11 + \cdots + 8 }{27}[/tex]
=> [tex]\= x_1 = 5.56[/tex]
Generally the standard deviation of age of cars
[tex]\sigma _1 = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }[/tex]
=> [tex]\sigma _1 = \sqrt{\frac{(4 - 5.56)^2 + (0 - 5.56)^2+ (8 - 5.56)^2 + \cdots + 8}{ 27} }[/tex]
=> [tex]\sigma _1 = 3.88 [/tex]
Generally the sample mean for the age of taxi is mathematically represented as
[tex]\= x_2 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x_2 = \frac{8 +8 +0 + \cdots + 4 }{20}[/tex]
=> [tex]\= x_2 = 5.85 [/tex]
Generally the standard deviation of age of taxi
[tex]\sigma _2 = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }[/tex]
=> [tex]\sigma _2 = \sqrt{\frac{(8 - 5.85)^2 + (8 - 5.85)^2+ (0 - 5.85)^2 + \cdots + 8}{ 20} }[/tex]
=> [tex]\sigma _2 = 2.83 [/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{(\= x_ 1 - \= x_2 ) - 0}{\sqrt{\frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2} } }[/tex]
=> [tex]t = \frac{(5.56 - 5.85 ) - 0}{\sqrt{\frac{(3.88)^2}{27} + \frac{(2.83)}{20} }}[/tex]
=> [tex]t = -0.30 [/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 -2[/tex]
[tex]df = 27 + 20 -2[/tex]
[tex]df = 45[/tex]
From the t distribution table the [tex]P(t > t )[/tex] at the obtained degree of freedom = 45 is
[tex]P(t > -0.30 ) = 0.61722067[/tex]
So the p-value is
[tex]p-value = P(t > T) = 0.61722067[/tex]
From the obtained values we see that the p-value > [tex]\alpha [/tex] hence we fail to reject the null hypothesis
Hence the there is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi
Solve the given system using the method of Example 3.25. x1 − x2 = 1 3x1 + x2 = 3 x = 1 0 Correct: Your answer is correct.
Answer:
[tex]x_1 = 1[/tex]
[tex]x_2=0[/tex]
Step-by-step explanation:
The question is incomplete as the method is not given.
However, the question can still be solved.
Given
[tex]x_1 - x_2 = 1[/tex]
[tex]3x_1 + x_2 = 3[/tex]
Make xi the subject in the first equation
[tex]x_1 = 1 + x_2[/tex]
Substitute 1 + x2 for xi in the second equation
[tex]3(1+x_2)+x_2 = 3[/tex]
Open bracket
[tex]3+3x_2+x_2=3[/tex]
[tex]3+4x_2=3[/tex]
Collect Like Terms
[tex]4x_2 = 3-3[/tex]
[tex]4x_2 =0[/tex]
Solve for x2
[tex]x_2=0/4[/tex]
[tex]x_2=0[/tex]
Recall that:
[tex]x_1 = 1 + x_2[/tex]
[tex]x_1 = 1+0[/tex]
[tex]x_1 = 1[/tex]
30=Five-sixthsY solve for Y
Given :-
A linear Question is given to us .The equⁿ is [tex]\sf 30 = \dfrac{5}{6}y[/tex]To Find :-
The value of y .Solution:-
Taking the given equⁿ :
[tex]\bf \implies30=\dfrac{5}{6}y[/tex]
[tex]\bf \implies 30\times 6=5y[/tex]
[tex]\bf\implies y=\dfrac{\cancel{30}\times6}{\cancel5}[/tex]
[tex]\underline{\boxed{\red{\bf{\longmapsto \qquad y \qquad = \qquad 36 \qquad}}}}[/tex]
[tex]\boxed{\green{\bf\pink{\dag}\: Hence\:the\:value\:of\:y\:is\:36.}}[/tex]
Some rules :-
On transposing numbers or variables,
Plus changes to minus.Minus changes to plus .Multiply changes to divide.Divide changes to multiply.What is the scale factor of AABC to ADEF?
B
72
359
66
E
-35"
A 80°
12
80*
DS
11
42
65"
A. 6
B.
1
2
1
C.
02
D. 2
so we know that the size of the triangle is decreasing witch means that the scale factor is going to be a fraction. to find this fraction you are going to divide the smaller side by the corisponding longer side.
12/72= 1/6
the correct answer is c 1/6
The scale factor of triangles ABC and DEF is 6.
Option A is the correct answer.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
From the triangles,
The ratio of the corresponding sides of the two triangles must be equal.
The value of the ratio is the scale factor.
So,
AB/DE = BC/EF = AC/DF
This can be written as,
72/12 = 66/11 = 42/7
6 = 6 = 6
Thus,
The scale factor of triangles ABC and DEF is 6.
Learn more about scale factors here:
https://brainly.com/question/20759556
#SPJ5
Is 4.95 a terminating decimal
Answer:
Definitely
since the definition of a terminating decimal is one that has an ending, and a Repeating decimal is one that never ends.
Step-by-step explanation:
How could you use a multiplication algorithm to multiply a 4-digit number by a 1-digit number?
Choose all that apply.
Multiply each place value in order. Regroup if needed. Add any regrouped values to each place value.
Add the digits in the 4-digit number and multiply by the 1-digit number.
Multiply to find the partial products and then add.
Use place value to rewrite the 4-digit number as a sum. Use the Distributive Property to find partial products. Add.
Multiply the digits in the 4-digit number and add the 1-digit number.
Answer:
is 1,2,3 the answer ? if not what is the answer cuz im doing the same question
Step-by-step explanation:
This table gives a few (x, y) pairs of a line in the coordinate plane. What is the y-intercept of the line?
Answer:
The Y-intercept is the Y value when X = 0.
Find the change in X:
-56 to -42 = 14
-42 to -28 = 14
The X value changes by 14.
For every change in X the Y change:
66-58 = 8
58-50 = 8
For X to get from -28 to 0 would be 2 more changes:
-28 +14 = -14
-14 + 14 = 0
2 more changes of Y would be:
50-8 = 42
42-8 = 34
So when X = 0, Y = 34
The Y-intercept would be (0,34)
Step-by-step explanation:
like if it helps <3
Where is the vertex of f(x) = -2x - 3| +6.4?
Grace is measured for her annual check up. She is 28 1/5 inches tall. Last year she was 25 3/5 inches tall. How much did she grow in one year?
Answer:
2 3/5 inches in a year
Step-by-step explanation:
28 1/5 - 25 3/5 = 141/5 - 128/5 = 13/5 = 10/5 + 3/5 = 2 + 3/5 = 2 3/5
You can use a calculator
Answer:
238, 000
Step-by-step explanation:
hope this helps </3
Solve the problem by entering and solving an equation.
A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 12 inches. What is the width of the frame?
Given : A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 12 inches.
To Find : The width of the frame .
Solution : Let us take the width of the frame be x . So , we know the formula to find the perimeter of rectangle as ;
[tex]\boxed{\red{\bf Perimeter_{rectangle}=2(l+b)}}[/tex]
Where , l is the length of the rectangle and b is the breadth of the rectangle .
⇒ Perimeter = 2 ( l + b ) .
⇒ 52 in. = 2 ( 12 + x ) in.
⇒ 52 in.= 24in. + 2x .
⇒ 2x =( 52 - 24 ) in
⇒ 2x = 28 in.
⇒ x = 28/2 in.
⇒ x = 14 in.
Hence the width of the rectangle is 14 inches.
5 7/12 + 4 6/12 = 9 13/12 = 1 1/12 what's the error analysis?
Answer:boo
Step-by-step explanation:booooo
Answer:
5 7/12 + 4 6/12 = 9 13/12 is correct but 9 13/12 is equal to 10 1/12 not 1 1/12 because 13/12 is 1 1/12 and you have to add 1 1/12 to 9. So the error analysis is simplifying 9 13/12 to 1 1/12.
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 8 ft, find the value of x so that the greatest possible amount of light is admitted.
Answer: x = 2
If x is the width of the window, the value for x that results in the greatest area-- presumably admitting the greatest amount of light.
Step-by-step explanation:
Initial calculations to find a starting value for w.
Determine dimensions that will have a sum of 8 as the perimeter. The length of the arc plus three sides of the rectangle.
The length of the arc is half the circumference of the circle, the width is the diameter. So, modifying the equation: C= πd, a = πw/2
Three sides of a rectangle (presumably a square for the initial calculation) 3w
Initial equation: 3w + πw/2 = 8 Substitute 3.14 for π and solve for w
2(3w) + 2(3.14w/2) = 2(8) multiply all terms by 2 to eliminate denominator
6w + 3.14w = 16 combine like terms
9.14w = 16 divide both sides by 9.14
w ≈ 1.75
Calculate the area using this value:
Area of semicircle: πr²/2 r= 1.75/2
3.14(.875)²/2 ≈ 1.203
Area of rectangle 1.75 × 1.75 = 3.0625
Total Area with width 1.75 : 4.265 ft²
Increasing the width to 2
The length of the arc becomes 3.14 This is twice the area of the semicircle.
3.14/2 = 1.57
The height of the rectangle reduces to 1.43
1.43 × 2 = 2.86
Total area with width of 2 ft 2.86 + 1.57 = 4.43 ft²
So 2 ft seems to be the optimal width.
PLEASE HELP ASAP
Prove that triangles PQR and RSQ are congruent.
Given:
PQ = RS, and
Answer:
Step-by-step explanation:
ok so lets assume that line PQ and RS and QR and PS are parallel lines cut by a transeversal. To prove this you can do it in a couple of different ways the one way i know is that if you assume these are parralel then you can uses the alternate interior anges to prove that measure of QSP and SQR then by logic you know that PQS + SQR = RSQ+QSP which symplifies to PQR = RSQ
Is the expression 6+3=9 an equation? Explain.
Answer:
No, 6+3=9 is not an equation.
Step-by-step explanation:
The reason as to why this is not an equation is because an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign. And 6+3=9 does not in fact connect two separate expressions.
Ms Liu has $40 to buy water and popcorn at the movie theater. Popcorn costs $8 per bag and water costs 3$ per bottle. write an algebraic expression that will be used to find the amount of money left when Ms. Liu 3 bags of popcorn and 4 bottles of water.
Answer:
S = 1 bag of popcorn
Y = 1 water
Step-by-step explanation:
S x 3 + Y x 4 = R
40 - R = (The Answer)
v (t) = 32,000 (0.84)
Find the initial value of the car and the value after 11 years.
Round your answers to the nearest dollar as necessary
Answer:
c
Step-by-step explanation:
c because
In the game of roulette, a wheel consists of 38 slots, numbered 0, 00, 1, 2, ..., 36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0 and 00 are green, the odd numbers are red, and the even numbers are black. To simulate outcomes from spinning the wheel, a researcher used the integer distribution to randomly generate 1000 numbers from 1 to 38, where 37 represents 0 and 38 represents 00.
Required:
a. What is the probability that the metal ball lands on green or red?
b. What is the probability that the metal ball does not land one green?
Answer:
hkkkkkkkkv
Step-by-step explanation:
khvvvvvvvvvvvvvvv
Help me out please I need it
Answer:
what do you need help with you did not provide a picture or any evidence
Step-by-step explanation:
step-by-step explanation
Uma caixa contém 40 bolinhas de jogo de tênis, sendo 10 verde, 14 azuis e 16 vermelhas. Retirando uma bola ao acaso da caixa, qual a probabilidade desta bola ser vermelha? Assinale a alternativa correta, que representa a probabilidade desta situação.
qual dessas quatro e a resposta .
14 / 40
15 / 40
16 / 40
17 / 40
Answer:
p = 15/40
Step-by-step explanation:
Since the total number of marbles is 40, that is our size of the sample. there are 16 red ones on that sample, so the probability of extracting a red marble from the box is given by the ratio of successes divided the total number of marbles:
p = 15/40
In a group of 80 people, 50 can speak Nepali, 45 can speak English and 7 of them do not
speak both languages.
a) Find the number of people who speak both languages.
b) Also illustrate the above information in Venn diagram.
Answer:
Universal set is 80
Number of people that speak Nepali is 50
Number of people that speak English is 45
Number of people that do not speak both is 7
a. Number of people that speak both languages is 22
b. As above
Step-by-step explanation:
a. Let make number of people that speak both languages x
To get x
(50-x) + (45-x) + x + 7 = 80
(50-x) + (45-x) + x = 80 - 7
(50-x) + (45-x) + x = 73
Open bracket
50-x+45-x+x= 73
50+45-2x+x = 73
95 - x = 73
-x = 73 - 95
-x = -22
x = 22
Therefore, number of people that speak both languages is 22
b. To get venn diagram
Number of people that speak Nepali is 50 - 22 = 28
Number of people that speak English is 45 - 22 = 23
Therefore, total = 28+23+22+7 = 80
What is the answer to -1x(-2)
Answer: 2x
Step-by-step explanation:
Answer:
2x
Step-by-step explanation:
Since there's two negative signs, the product should be positive. Just multiply 1x and 2 together to get the answer. :D
A number, n, is greater than -4 and less than or equal to 6.
Answer:
-3-,2,-1,0,1,2,3,4,5
Step-by-step explanation:
-4<n<6
Help me please I really need help
Answer:
it doesn't because it's not a set of ordered pairs
what is the answer to this question
Answer:
i think i am going to pick a random letter because i cant see it ts blocked so i guess c
Step-by-step explanation:
As Mexican troops drew closer to the Alamo, the Texans ________________.
a.
retreated to smaller quarters within the mission chapel
b.
sent word to Gonzales for reinforcements
c.
sent word to the United States requesting statehood
d.
suffered a rebellion from within the fort
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation: I took it on a test and got it right