Answer:
a) 7/80 = 0.0875
b) 3/16 = 0.1875
c) 1/4 = 0.2500
Step-by-step explanation:
There are a total of 16 balls. 3 are selected. There are ₁₆C₃ possible combinations.
a) If all 3 balls are the same color, they are either all yellow OR all blue OR all red.
The number of ways of choosing 3 yellow balls from 7 is ₇C₃.
The number of ways of choosing 3 blue balls from 5 is ₅C₃.
The number of ways of choosing 3 red balls from 4 is ₄C₃.
The total probability is:
P = (₇C₃ + ₅C₃ + ₄C₃) / ₁₆C₃
P = (35 + 10 + 4) / 560
P = 49 / 560
P = 7 / 80
P = 0.0875
b) The number of ways of choosing 2 yellow balls from 7 is ₇C₂.
The number of ways of choosing 1 blue ball from 5 is ₅C₁.
The probability of both is:
P = ₇C₂ ₅C₁ / ₁₆C₃
P = 21 × 5 / 560
P = 105 / 560
P = 3 / 16
P = 0.1875
c) If all 3 balls are different colors, then there is exactly 1 yellow, 1 blue, and 1 red.
The number of ways of choosing 1 yellow ball from 7 is ₇C₁.
The number of ways of choosing 1 blue ball from 5 is ₅C₁.
The number of ways of choosing 1 red ball from 4 is ₄C₁.
The probability of all events is:
P = ₇C₁ ₅C₁ ₄C₁ / ₁₆C₃
P = 7 × 5 × 4 / 560
P = 140 / 560
P = 1 / 4
P = 0.2500
Jacob and Isaac decided to run to the basketball court after school. The basketball court is 514 miles from school. The boys run at a pace of 338 miles per hour. Enter the length of time, in hours, that it will take the boys to arrive at the basketball court.
Answer:
1.5 hours
Step-by-step explanation:
Divide 514 by 338 to get 1.5207 and round it to 1.5 because we are working with time
Do these side lengths make a right triangle? 3, 4, 5 *
Answer:
This is a right triangle
Step-by-step explanation:
We can check if this is a right triangle by using the Pythagorean theorem
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2+4^2 = 5^2
9+16 = 25
25=25
This is true so it is a right triangle
The fractions 4/7 and x/21 are equivalent fractions. What is the value of x ?
Answer:
The value of x is 12
Step-by-step explanation:
4x3=12
7x3=21
Therefore 12/21
To explain further:
If you divide 12 by 3 you get 4
If you divide 21 by 3 you get 7
Therefore resulting to 4/7
(I found out that the number three goes in both numbers to begin with)
Is this clearer?
A shipping manager weighed a random sample from a shipment of 90 boxes and made the dot plot. Which interval of weights has the greatest number of boxes?
Answer:
The interval with the most amount of dots has the greatest number of boxes.
Step-by-step explanation:
Because each dot represents equal number of box(es), the interval with the most number of dots has the greatest number of boxes.
Waylon played defense in 12 soccer games. This was 60% of the total number of games he played. How many games did Waylon play?
Answer:
he played around 20 games
Answer:20
Step-by-step explanation:
N\A
drawing a 1, 2, or 3 from 9 cards numbered 1-9, replacing the card,
and drawing a 7, 8, or 9
1/3
3/8
C
1/9
d
1/12
Answer:
The required probability is option [tex]C)\ \dfrac{1}{9}[/tex]
Step-by-step explanation:
There are a total of 9 cards.
Total number of cases = 9
Let A be the event of choosing 1, 2 or 3.
Total number of favorable cases for event A = 3
Let B be the event of choosing 7, 8 or 9.
Total number of favorable cases for event B = 3
Formula for finding probability of an event E is:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Finding P(A), using the formula:
[tex]P(A) = \dfrac{3}{9}\\\Rightarrow \dfrac{1}{3}[/tex]
Now, it is given that the card is replaced, so again total number of cases are 9.
For finding P(B), using the formula:
[tex]P(B) = \dfrac{3}{9}\\\Rightarrow \dfrac{1}{3}[/tex]
To find the probability that events A and B both happen, we can simply multiply P(A) and P(B) because these are independent events.
[tex]\text{Required probability = }P(A) \times P(B)\\\Rightarrow \dfrac{1}{3} \times \dfrac{1}{3} \\\dfrac{1}{9}[/tex]
joe buys groceries for his grandfather the groceries cost $42 plus 5% tax joe wants to know the total cost of the groceries including tax how much sales tax does joe pay on the groceries
its on iready
====================================================
Work Shown:
5% = 5/100 = 0.05
5% of 42 = 0.05*42 = 2.10
tax = $2.10
total cost including tax = $42 + $2.10 = $44.10
----------
An alternative is to multiply 42 by 1.05 to get
1.05*42 = 44.10
We get the same answer. The 1.05 refers to 1 + 0.05 where the "1" is 100% and the 0.05 is 5%, so the two combine to 105%, meaning the total cost is 105% of the cost before tax is considered.
Annalise earns $4 an hour walking pets in her neighborhood. She evaluates the expression 4h, where h represents the number of hours, to find the amount she earns. Can any number be substituted for h?Expain.
Answer:
Yes any number can be substituted for h
Step-by-step explanation:
The term 'h' is an independent variable any number can be substituted for h, so long as the number represents the hours worked
So if she walks pets for 8 hours
Her pay is 4*8= $32
Which power is equivalent to the expression (g-12)-3?
StartFraction 1 Over g Superscript 36 EndFraction
StartFraction 1 Over g Superscript 9 EndFraction
g9
g36
Answer:
d. g36
Step-by-step explanation:
The solution is, g^36 power is equivalent to the expression (g-12)-3.
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
given expression is,
g^(-12)(-3)
=g^(12*3)
=g^36
Hence, The solution is, g^36 power is equivalent to the expression (g-12)-3.
To learn more on exponent number click:
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Toothy the crocodile wants to eat a delicious chicken. His mouth is open to an angle of 30 degrees.
He needs to open his mouth to an angle of 55 degrees for the chicken to fit.
What is the measure of the additional angle Toothy's mouth needs to open so he can eat the chicken?
Answer: 25°
Step-by-step explanation:
From the question, Toothy the crocodile wants to eat a delicious chicken and his mouth is open to an angle of 30 degrees but he needs to open his mouth to the angle of 55 degrees for the chicken to fit.
The additional angle that Toothy's mouth needs to be open so he can eat the chicken will be:
= 55° - 30°
= 25°
Answer:
25
Step-by-step explanation:
did it on khan academy
Find the slope
Use this form for example:y=Mx+b
Answer:
Line: y = Mx + b, passes (0, 1) => M*0 + b = 1 => b = 1
Line: y = Mx + 1, pass (2, 4) => 2M + 1 = 4 => M =3/2
=> Line: y = (3/2)x + 1
Hope this helps!
:)
Does anyone know the answer ? lmk asap
Answer:
1,253 inches cubed
Step-by-step explanation:
This is easy, just find the separate volumes of both and add.
Figure 1: 7x5x5= 175 inches cubed
Figure 2: 11x14x7= 1,078 inches cubed
Added together: 1,253 inches cubed
Therefore it's C
:))))))
Someone please help me
What is 9+9
Will give branliest if correct!!
Answer:18
Step-by-step explanation:
The probability of an event is 3:5. What is this probability expressed as a decimal ?
Answer:
.6
Step-by-step explanation:
Ratios are just another way of writing fractions. 3:5 is just 3/5 which is .6 or 60%
Each year, Alex gets a raise of 8% plus an additional $100. In 2011, Alex’s annual
salary was $47,563.84. (a) What will Alex’s salary be in 2013? (Round your answer to the nearest cent.) (b) What was Alex’s salary in 2009? (c) From the two options below, which deal will give Alex the higher salary after 4 years? • Take the salary scale from part b.
• In January 2010, get a raise of 8%, and in January of 2011, get a raise of 8.15%, and in the next two years, get raises of 8.30% and 8.45%, respectively.
Answer: .......................
Step-by-step explanation:
what is this answer plz
Answer:
THE 2 ONE
Step-by-step explanation:
Find the quotient: 8,441 ÷ 21 = ________. a. 400 r 12 b. 400 r 20 c. 401 r 12 d. 400 r 20
Answer:
Step-by-step explanation:
8441/21= 401 r 20
There are 80 coins of $5 in the purse. These coins constitute 20 % of its total
coins. How many coins are there in the purse?
Answer:
320 coins I think
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Answer:
acute acute obtuse right
Step-by-step explanation:
if it is less than 90° it will be acute. it is exactly 90° it is right. it is more than 90° it is obtuse.
good luck
The following table represents an exponential function.
x
y
a
4
1
2
2
1
3
NI-
1
4
The exponential function represented by the table can be written in the form y = ab*. Find the values
for a and b.
The values for a and b in the given exponential function are a = 4 and b = 1/2
What is an exponential function?An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.
For example, exponential functions can be used to calculate changes in population, loan interest charges, bacterial growth, radioactive decay or the spread of disease.
Given that,
The exponential function is given as, y = abˣ, we need to find the value of a and b,
When x = 0, ab⁰ = 4
a=4 (since, b⁰ = 1)
When x = 1, ab¹ = 2
4b = 2
b = 1/2
Hence, The values of a and b are a = 4 and b = 1/2
Learn more about exponential function, click;
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Simplify the square root of 7 divided by square root 27
What is the mean of the data set below? Round to the nearest tenth when necessary.19, 21, 41, 35, 43, 57
Need a bit of help with this question:
Firstly let's find hypotenuse(let it will be "n" of smaller triangle
Let use Pythagorean theorem
[tex]a^{2} + {b}^{2} = {n}^{2} \\ {20}^{2} + {10}^{2} = {n}^{2} \\ n = \sqrt{500} [/tex]
Now we need to find hypotenuse(x) of bigger triangle
[tex] {c}^{2} + {n}^{2} = {x}^{2} \\ {9}^{2} + { \sqrt{500} }^{2} = {x}^{2} \\ x = \sqrt{581} [/tex]
The value of x must be rounded to 1 DP, so
[tex] \sqrt{581} = 24.1039... \\ \sqrt{581} \simeq \: 24.1[/tex]
Answer: x=24.1
What is the surface area of the figure below?
A 12 ft?
B 36 ft?
C 54 ft?
D 90 ft2
Answer:
D
Step-by-step explanation:
6 times 3 times 4 plus 3 times 3 times 2
Answer:
D. 90 ft squared
Step-by-step explanation:
A= 2wl + 2lh + 2hw
A = 18 + 36 + 36
=90
The volume of a cylinder is approximately 72ft3. Which is the best approximation of the volume of a cone with the same base and height as the cylinder?
Answer:
24 ft^3
Step-by-step explanation:
Cylinder:
Volume = (pi)r^2h
Cone:
Volume = (1/3)(pi)r^2h
When using r and h for both a cylinder and a cone, the only difference is the factor of 1/3 for the volume of the cone.
A cone with the same radius and height as a cylinder has 1/3 the volume of the cylinder.
volume of cylinder = 72 ft^3
volume of cone = (1/3) * 72 ft^3 = 24 ft^3
Answer:
The volume of cone is 24 ft³
Step-by-step explanation:
Given that volume of cylinder = 72 ft³
Volume of cylinder = πr²h
Volume of cone = [tex]\frac{1}{3}[/tex][tex]\pi[/tex]r²h
Volume of cone = volume of cylinder/3
= 72/3
= 24 ft³
Find composite function
Answer:
1 / (99 - 40x).
Step-by-step explanation:
The whole of g(x) is input to f(x), so:
we replace the x in f(x) by g(x).
f(g(x)) = 1 / [8(12 - 5x) + 3]
= 1 /( 96 - 40x + 3)
= 1 / (99 - 40x).
What is the perimeter of this shape?
Answer:
87 feet
Step-by-step explanation:
Two of the sides here are unknown. The one on the leftmost side is equal to 9, since on the other side it also has a length of 9 feet. The section on the top right has a length of 30-9-9=12 units. Adding all of these values together now, you get a total perimeter of:
30+9+12+9+9+9+9=87 feet
Hope this helps!
Answer:
The perimeter of this shape is 87 ft.
Step-by-step explanation:
Given that all side lengths are added together in order to find perimeter. So the perimeter is :
[tex]perimeter = 9 + 9 + 9 + 12 + 9 + 30 + 9[/tex]
[tex]perimeter = 45 + 30 + 12[/tex]
[tex]perimeter = 87 \: feet[/tex]
What is the first step in solving the equation? 2(3k + 1) = 4k + 32
Answer:
The first step is to expand it to get rid of brackets .
Step-by-step explanation:
The first step, you have to eliminate brackets by expanding :
[tex]2(3k + 1) = 4k + 32[/tex]
[tex]2(3k) + 2(1) = 4k + 32[/tex]
[tex]6k + 2 = 4k + 32[/tex]
Next you have to collect like terms by making the same variable to one side and lastly, solve it :
[tex]6k - 4k = 32 - 2[/tex]
[tex]2k = 30[/tex]
[tex]k = 30 \div 2[/tex]
[tex]k = 15[/tex]
Answer:
Use the distributive Law on the left side of the equation.
Step-by-step explanation:
The first step is to distribute the 2 over the parentheses:
2(3k + 1) = 4k + 32 Distributing:
2*3k + 2*1 = 4k + 3
6k + 2 = 4k + 3
2k = 1
k = 1/2.
PLEASEEEE HURRYYYY!!!!
find the slope, y and x-intercept of
f(x)=4
i'd say it would be 4 over 1 4/1 so you go up 4 and to the right 1 if they were negative then it would be the oposite way around.