Answer:
Total number = 30Number of females = 12Number of males = 18a) Combination of 5 out of 30:
30C5 = 30!/[5!*(30 - 5)!] = 142506b) Combination of 2 males:
18C2 = 18!/[2!*(18 - 2)!] = 153Combination of 3 females:
12C3 = 12!/[3!*(12 - 3)!] = 220The number of ways with 2 males and 3 females:
153*220 = 33660c) Required probability is:
P(2 males and 3 females) = 33660 / 142506 = 0.236The law firm of Dewey, Cheetham, and Howe handled 18 personal injury cases this past year. This was 9/7 of the cases handled by the rival firm of Gypsum-Goode. How many personal injury cases were handled by Gypsum-Goode this year?
Answer:
14 cases
Step-by-step explanation:
Let x be the number of personal injury cases this year by Gypsum Goode
x* 9/7 = 18
Multiply each side by 7/9
x * 9/7 *7/9 = 18 * 7/9
x = 14
Nicholas performs an experiment in which he pulls a marble from a bag. In his experiment, he finds that he is twice as likely to pull a red marble as a blue marble. If Nicholas pulls 10 red marbles, how many blue marbles does he pull?
Answer:
5.
Step-by-step explanation:
Given that Nicholas performs an experiment in which he pulls a marble from a bag, and in his experiment, he finds that he is twice as likely to pull a red marble as a blue marble, to determine, if Nicholas pulls 10 red marbles, how many blue marbles does he pull, the following calculation must be performed:
10/2 = X
5 = X
Therefore, Nicholas pulls 5 blue marbles from the bag.
Simplify (-8-r)+(2r-4) Plato question
Answer:
−12r+32−2r 2
Step-by-step explanation:
(−8−r)(2r−4)
Apply the distributive property by multiplying each term of −8−r by each term of 2r−4.
−16r+32−2r
2
+4r
Combine −16r and 4r to get −12r.
Answer:
R-12
Step-by-step explanation:
Open the parenthesis, then solve
-8-r + 2r-4
-r+2r-8-4
r-12
Your answer will be R-12
What is 2 plus 2 minus 4 plus 2
Answer:
2
Step-by-step explanation:
2 + 2 - 4 + 2 = 2
Answer:
2
Step-by-step explanation:
2 + 2 = 4
4 - 4 = 0
0 + 2 = 2
Find the common difference of the arithmetic sequence − 19 , − 11 , − 3
Answer:
+ 8
Step-by-step explanation:
This is an arithmetic progression (AP) as there is a common difference between successive terms.
For example, looking at the first two terms,
Difference = 2nd term - 1st term
= -11 -(-19)
= -11 + 19
= +8
To check,
Looking at the second and third terms,
Difference = 3rd term - 2nd term
= -3 -(-11)
= -3 + 11
= +8
Hence, there is a common difference of +8 between consecutive terms, making it an AP.
At a sporting event, the price for 3 cheeseburgers and 2 cups of lemonade is
$19 and the price for 2 cheeseburgers and 4 cups of lemonade is $18. How much
does it cost for 1 cheeseburger and 1 cups of lemonade?
*
By solving system of linear equation we get Cost for 1 cheeseburger $5 and 1 cups of lemonade $2
What is a system of linear equations?A system of linear equations is a collection of two or more linear equations that have the same variables. A linear equation is an equation in which the highest power of the variable is 1. In other words, the equation is a straight line when graphed.
Here is an example of a system of linear equations:
3x + 2y = 19
2x + 4y = 18
This is a system of equations problem, where we can use the information provided to set up two equations and then solve for the unknown variables. Let x be the cost of one cheeseburger and y be the cost of one cup of lemonade.
From the information provided, we know that:
3x + 2y = 19 (the cost of 3 cheeseburgers and 2 cups of lemonade is $19)
2x + 4y = 18 (the cost of 2 cheeseburgers and 4 cups of lemonade is $18)
To find the cost of one cheeseburger and one cup of lemonade, we can solve this system of equations. One way to do this is by substitution.
3x + 2y = 19
we get
[tex]x=\frac{19-2y}{3}[/tex]
substituting x in equation 2x+4y=18
we get
[tex]2(\frac{19-2y}{3})+4y=18[/tex]
[tex]38 - 4y + 12y = 54\\8y = 16\\y = 2[/tex]
substituting y in equation 3x+2y=19
[tex]3x+2(2)=19\\3x=19-4\\3x=15\\x=5[/tex]
The cost of one cup of lemonade is $2
The cost of one cheeseburger is $5
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-4/3 x + (-1) =y what is the slope of this line?
Answer: y= -4 divided by 3 • x (-1)
Step-by-step explanation:
✨photo math✨
what would be themissing side length
The missing side length is 5.7.
What would be themissing side length?The missing side length AB, can be calculated using the Pythagorean Theorem.The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two sides adjacent to the right angle (A and B) is equal to the square of the length of the hypotenuse (C).In other words, AB^2 + BC^2 = AC^2.In this case, AB^2 = AC^2 - BC^2, or AB^2 = 6.7^2 - 3^2, which simplifies to AB^2 = 44.89.Taking the square root of both sides yields AB = 6.7.Therefore, the missing side length, AB, is 6.7.The missing side length of a triangle with sides of lengths a, b, and c is calculated by using the Pythagorean theorem, which states that a^2 + b^2 = c^2. In this case, we are given that side c is 3, and side a is 6.7.Using the Pythagorean theorem, we can solve for side b by rearranging the equation to read b^2 = c^2 - a^2. Plugging in our known values, we get b^2 = 9 - 44.89, or b^2 = -35.89.Since the square root of a negative number is not a real number, this implies that there is no real number solution for b, and therefore the missing side length of the triangle is not possible.
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What is the expected value of the following game?
Pay $8. Win $100 if we draw a King from a standard deck. Win nothing if we draw something else.
Answer: Expected Value = -0.31
We expect to lose about 31 cents each time we play the game.
============================================================
Explanation:
A = event of selecting a king
B = event of not selecting a king
P(A) = 4/52 since there are 4 kings out of 52 total. This fraction reduces to 1/13.
P(B) = 48/52 = 12/13
Note: P(A) + P(B) = 1.
V(A) = net value of selecting a king
V(A) = 100-8 = 92, so you net $92 if event A occurs.
V(B) = -8, meaning you lose 8 dollars if you select anything but a king
We multiply the probability values with their corresponding net values
P(A)*V(A) = (1/13)*(92) = 7.07692 approximately
P(B)*V(B) = (12/13)*(-8) = -7.38462 approximately
Add up the results:
7.07692 + (-7.38462) = -0.3077
The expected value is approximately -0.3077 which rounds to -0.31
We expect to lose on average 31 cents each time we play the game. The nonzero expected value means this is not a mathematically fair game.
Aregular decagon has a radius of 8 cm. What is the approximate area of the decagon?
Using a calculator we can approximate this to be A ≈ 568.89 cm^2.
What is regular decagon?A regular decagon is a two-dimensional geometric shape with ten sides of equal length and ten interior angles of equal measure. It is a polygon, which is a two-dimensional shape made up of line segments (straight sides).
The approximate area of a regular decagon can be calculated using the formula A = (5/2) * a^2 * tan(π/5), where a is the length of each side. Since the radius of the decagon is 8 cm, the length of each side can be calculated using the formula a = 2r * sin(π/10) where r is the radius.
Plugging these values into the formula we get A = (5/2) * (2 * 8 * sin(π/10))^2 * tan(π/5) which simplifies to A = 320 * sin^2(π/10) * tan(π/5).
Using a calculator we can approximate this to be A ≈ 568.89 cm^2.
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HELPP NO LINKS OR ELSE ILL BE SCREENSHOTTING AND REPORTING RAT
Answer:
I think it's TWO
Step-by-step explanation:
need help!!!!!!!!!!!!
can anyone help me with this. Click to see
Answer: mean = 6
median = 7
mode = 8
Step-by-step explanation:
Which of the following choices is an equivalent expression for (12r + 2t) - (4r + 10t)
Which of the following choices is an equivalent expression for (12r + 2t) - (4r + 10t)
A
8(r - t)
B
8(r + t)
C
8r + 7t
Answer: 8(r-t)
Step-by-step explanation:
[tex](12r+2t)-(4r+10t)=12r+2t-4r-10t=8r-8t=8(r-t)[/tex]
Yesterday, the price of a gallon of gas at five gas stations was $3.56, $3.71,
$3.62, $3.93, and $3.83, respectively, but today each gas station raised it:
price by $0.08. What is today's mean price of a gallon of gas at the five
stations?
O A. $3.81
O B. $3.65
O C. $3.89
O D. $3.73
Answer:
c
Step-by-step explanation:
The mean price of a gallon of gas at the five stations is $3.81. Therefore, option A is the correct answer.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
Given that, Yesterday, the price of a gallon of gas at five gas stations was $3.56, $3.71, $3.62, $3.93, and $3.83, respectively.
Today each gas station raised its price by $0.08
Now, mean =(3.56+3.71+3.62+3.93+3.83+5×0.08)/5
= (18.65+0.4)/5
= 19.05/5
= $3.81
Therefore, option A is the correct answer.
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Use circle V to find the arc measure for arc PSU.
Answer:
arcPSU = 224degrees
Step-by-step explanation:
From the given diagram;
arcPSU = arcPQ + arcQR + arcRS + arcST + arcTU
Given
arcPQ = arcTU
arcQR = arcRS = 37
arcAST = 90
Since 136 + arcPQ + 37+37+90+arcTU = 360
136+2arcPQ+ 37+37+90= 360
2arcPQ+300 = 360
2arcPQ = 360 - 300
2arcPQ = 60
arcPQ = 60/2
arcPQ = 30degrees
Substitute into the above expression
arcPSU = arcPQ + arcQR + arcRS + arcST + arcTU
arcPSU = 360 - arcPU
arcPSU = 360 - 136
arcPSU = 224degrees
A cylinder has a height of 9 inches. The radius of the cylinder is 1 3 1 3 the height of the cylinder. What is the approximate volume of the cylinder?
Answer:
254.57 in^3
Step-by-step explanation:
A cylinder has a height of 9 inches. The radius of the cylinder is 1 / 3 the height of the cylinder. What is the approximate volume of the cylinder?
volume of a cylinder = nr^2h
n = 22/7
r = radius
radius = 9 x 1/3 = 3 inches
(22/7) x (3^2) x 9 = 254.57 in^3
Can someone solve 18?
The piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function. Piecewise functions are implemented in the Wolfram Language as PiecewiseAdditional piecewise functions include the Heaviside step function, rectangle function, and triangle function.Given is the absolute value function -
f(x) = 1/2 |x|
We can write it as a piecewise function as follows. The given function is as follows :
f(x) = 1/2 |x|
The absolute value function is given as -
|x| = - x {x < 0}
|x| = x {x ≥ 0}
So, we can write the piecewise function as -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
Therefore, the piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
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4.
Calculate 30% of 500 kg
Answer:
150 kg
Step-by-step explanation:
30% of 500 kg
[tex]=0.30*500[/tex]
[tex]=150[/tex]
150 kg
PLEASE HELP!!
1. devin is making a candle by pouring melted wax into a mold in the shape of a square pyramid. each side of the base of the pyramid is 6 cm and the height of the pyramid is 9 cm. to get the wax for the candle, devin melts cubes of wax that are each 4 cm by 4 cm by 4 cm. how many of the wax cubes will devin need in order to make the candle? show your work.
Answer:
1.69
approximately 2 wax cubes
Step-by-step explanation:
number of wax cubes needed = volume of square pyramid / volume of cube
Volume of a pyramid = 1/3 x ( base area x height)
base area = length²
6² = 36
volume = 1/3 x (36 x 9) = 108
volume of a cube = length³
4³ = 64cm³
108/64 = 1.69
Write 31 5 as a mixed number.
Answer:
6 1/5
Step-by-step explanation:
Answer:
31/5 into a mixed number would be 6 1/5 .
Find the measure of line segment TU. Assume that lines which appear to be tangent to the circle are tangent.
A)
7
B)
8
0
9
D)
10
Answer:
d 10
Step-by-step explanation:
Answer:
Answer is D I’ve done it and got it right before
Step-by-step explanation:
Please help
Match the items.
a. Multiplicative Inverse
b. Additive Inverse
c. Commutative Property of Multiplication
d. Distributive Property
e. Additive Identity Property
f. Associative Property of Addition
1. 5.6=6-5
2. -8+0= -8
3. (3+5) +9=3+ (5+9)
4. 5.1=1
5. 7+(-7)=0
6. 5(x−4)=5x−20
The matching of the items as follows ,a - 4 , b - 5, c - 1 , d - 6 , e - 2 , f - 3
What is a number ?
number is used to represent the quantity of number and it is even used for calculations.
a) Multiplicative inverse
if the product the given number and reciprocal of the given number is 1.
so,
5 * 1/5 = 1
as LHS = 5 * 1/5 = 1
RHS = 1
Hence , a - 4
b ) Additive inverse
if the summation of the given number and opposite sign of given number results 0 .
7 + (-7) = 0
LHS = 7+ (-7) = 0
RHS = 0
hence , b - 5
c ) Commutative Property of Multiplication
if a.b = b.a hence it is in Commutative Property of Multiplication .
so, 5.6 = 6.5
hence , c - 1
d) Distributive property
if a ( b + c ) = a*b + a*c than it is in distributive property .
hence , d - 6
e) Additive Identity Property
if a+ 0 = a hence it is Additive Identity Property
so , b - 2
f ) Associative Property of Addition
if (a+b) + c = a + (b+c ) hence it is in Associative Property of Addition
so , f - 3.
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PLEASE HELP!!!!!!!!!!!
Answer:
the triangle is translated 2 units up, and is reflected across the x axis
Step-by-step explanation:
Miss Morgan is a science teacher she found that 30% of her 120 students are athletes and Mr. Gregory is a math teacher he found that 27 or 15% of his students are athletes
The volume of a cylinder is 542pi in?. The height of the cylinder is 16 in. What is the radius of the cylinder to the nearest hundredth?
The volume of a sphere is 5,055pi m. What is the surface area of the sphere to the nearest square meter?
Answer:
I. Radius, r = 5.82 in
II. S.A of a sphere = 19.61 meters
Step-by-step explanation:
Given the following data;
I. Volume of cylinder = 542π in³
Height = 16 in
To find the radius of the cylinder;
Volume of cylinder = πr²h
542π = πr²*16
Dividing both sides by π, we have;
542 = 16r²
r² = 542/16
r² = 33.875
Radius, r = 5.82 in
II. Volume of sphere = 5.055π m³
To find the surface area of the sphere;
First of all, we would find the radius of the sphere.
[tex] Volume \; of \; a \; sphere = \frac {4}{3} \pi r^{3} [/tex]
Substituting into the formula, we have;
[tex] 5.055 \pi = \frac {4}{3} \pi r^{3} [/tex]
Cross-multiplying, we have;
[tex] 5.055 \pi * 3 = 4 \pi r^{3} [/tex]
[tex] 15.165 \pi = 4 \pi r^{3} [/tex]
Dividing both sides by 4π, we have;
[tex] 3.79 = r^{3} [/tex]
Taking the cube root of both sides, we have;
r = 1.56 m
Next, we find the surface area (S.A) of the sphere;
S.A of a sphere = 4πr
S.A of a sphere = 4*3.142*1.56
S.A of a sphere = 19.61 meters
Use the graphs of f and g to graph h(x)=(f+g)(x). (Graph segments with closed endpoints).
The required graph of the function of h(x) is shown, where h(x) = |x| + |x + 2|.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the graph, functions f and g are absolute functions,
f = |x|
g = |x + 2|
So,
h(x) = f + g
Now substitue the functions,
h(x) = |x| + |x + 2|
Thus, the required graph of the function of h(x) is shown.
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A car dealership pays a wholesale price of $20,000 to purchase a vehicle. The car dealership wants to make a 32% profit. By how much will the mark up to the price of the vehicle?
A restaurant records the number of tables served each night, and the results have the values: minimum = 3, lower
quartile = 14, median = 23, upper quartile = 29, and maximum = 40.
Answer: A. The first one
Step-by-step explanation:
The first data can be represented in the box plot if the restaurant records the number of tables served each night, and option (A) is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have data:
Minimum = 3
Lower = quartile = 14
Median = 23
Upper quartile = 29
Maximum = 40
From the above data, we can plot the data in the box plot.
Thus, the first data can be represented in the box plot if the restaurant records the number of tables served each night, and option (A) is correct.
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the students in Mr Marcos art class use six jars of paint for their project each student uses 2/3 jars of paint how many students were in Mr Marco's class
The number of students that were in Mr Marco's class will be 9 students
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Here, the students in Mr Marcos art class use six jars of paint for their project each student uses 2/3 jars of paint
The number of students that were in Mr Marco's class will be:
= 6 ÷ 2/3
= 6 × 3/2
= 9 students
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