Answer:
134,596 diffrent ways.
Step-by-step explanation:
Combination has to do with selection. When n object is to be selected from n objects, this can be achieved using the combination formula as shown; \
nCr = n!/(n-r)!r!
If an election ballot asks voters to select six city commissioners from a group of 24 candidates, then the selection can be done in 24C6 different ways.
Applying the formula above:
24C6 = 24!/(24-6)!6!
24C6 = 24!/18!6!
24C6 = 24*23*22*21*20*19*18!/18!*6*5*4*3*2
24C6 = 24*23*22*21*20*19/24*30
24C6 = 23*22*21*20*19/30
24C6 = 134,596 different ways.
Hence, Six city commissioners can be selected from a group of 24 candidates in 134,596 different ways
The first step in solving for the variable / in the equation P= 21 + 2w is:
A. Add the 2w to both sides of the equal sign.
B. Subtract the 2w to both sides of the equal sign.
C. Divide the 2 to both sides of the equal sign.
D. None of these choices are correct.
A man is twice the age of his son,in 20 years time, the son's age will be 2/3 of that his father. what is the son's present age?
Answer:
20 years old.
Step-by-step explanation:
Let us say that the man's age is represented by x and the son's age is represented by y.
As of now, x = 2y.
In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.
(y + 20) = 2/3(x + 20)
Since x = 2y...
y + 20 = 2/3(2y + 20)
3/2y + 30 = 2y + 20
2y + 20 = 3/2y + 30
1/2y = 10
y = 20
To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.
So, the son's present age is 20 years old.
Hope this helps!
please helpppp As soon as possible
Answer: 4 pairs
Step-by-step explanation:
121-16=105. However, 121 can be made by squaring -11 or 11. 16 can be made by squaring 4 or -4. Thus, the choices are 11,4 11,-4 -11,4 -11,-4
help asapppp....thanks
Answer:
a) -8x^3 + x^2 + 6x
b)16x^2 -9
c) 24x^4 + 37x^3 +13x^2 -18x
Step-by-step explanation:
a) distribute -2x to x and 4x^2 then do the same for the other part and then add the ones w the same exponent.
b) do foil ( multiply first outside inside last) which will be 4x times 4x then 4x times 3 then -3 times 4x and 3 times -3. add like exponents
c) do the same as above
The formula to convert Fahrenheit to Celsius is C - 5 (F - 32). Convert 30°C to
Fahrenheit. Round to the nearest degree.
A. 30°F
B. -1°F
C. 112°F
D. 86°F
Answer:
D. *6F
Step-by-step explanation:
C=(F-32)*5/9
30=(F-32)*5/9
F = (30*9)/5+32
F = 86
An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf:
Answer:
a) E(X) = 16.09 ft³
E(X²) = 262.22 ft⁶
Var(X) = 3.27 ft⁶
b) E(22X) = 354 dollars
c) Var(22X) = 1,581 dollars
d) E(X - 0.01X²) = 13.470 ft³
Step-by-step explanation:
The complete Correct Question is presented in the attached image to this solution.
a) Compute E(X), E(X2), and V(X).
The expected value of a probability distribution is given as
E(X) = Σxᵢpᵢ
xᵢ = Each variable in the distribution
pᵢ = Probability of each distribution
Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)
= 2.70 + 9.381 + 4.011
= 16.092 = 16.09 ft³
E(X²) = Σxᵢ²pᵢ
Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)
= 36.45 + 149.1579 + 76.6101
= 262.218 = 262.22 ft⁶
Var(X) = Σxᵢ²pᵢ - μ²
where μ = E(X) = 16.092
Σxᵢ²pᵢ = E(X²) = 262.218
Var(X) = 262.218 - 16.092²
= 3.265536 = 3.27 ft⁶
b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.
c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars
d) E(X - 0.01X²) = E(X) - 0.01E(X²)
= 16.092 - (0.01×262.218)
= 16.0926- 2.62218
= 13.46982 = 13.470 ft³
Hope this helps!!!
Two intersecting lines l and m form an angle of 56° with each other. The reflection of a point (–4, 1) along the line l followed by a reflection along line m will cause a ________ rotation. Question 18 options: A) 56° B) 112° C) 180° D) 28°
Answer:
B) 112°
Step-by-step explanation:
After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:
2·56° = 112°
_____
In the attached, lines l and m are separated by 56°, as required by the problem statement.
When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc)
Answer:
GOOGLE :)
equation:
y=mx+b
m= slope (how steep the line is(negative is \ positive is /))
b= y intercept (where it is on the vertical line(up and down line))
step by step
1. locate y intercept and plotthe point
2.from that point use slop to find second point and plot
What is the greatest common factor of 36 and 44?
Answer:
GCF - 4
Step-by-step explanation:
36 - 1, 2, 3, 4, 6, 9, 12, 18, 36
44 - 1, 2, 4, 11, 44
Hope this helps! :)
A piece of string is 120 centimeters long. How long would the piece of string measure in meters?. Enter your answer in the box.
Answer:
1.2 metres
Step-by-step explanation:
1 metre = 100cm
so 120cm has 120 cm * 1 m/ 100cm = 1.2 m
Convert.
5 days =
lao
hours
Answer:
120 Hours
Step-by-step explanation:
24 hours in a day
5 days
24 x 5 = 120
How can you write arithmetic and geometric sequences using recursive and explicit formulas modeled in a real world context?
Answer:
The answer is below
Step-by-step explanation:
They would be written like this:
Arithmetic Progression:
Explicit formula
Tn = a + (n-1) * d
Recursive formula
Tn = Tn-1 + d
Where a is the first term, d is the common differance and n is the number of terms.
Geometric Progression:
Explicit formula
Tn = a * r ^ (n-1)
Recursive formula
Tn = Tn-1 * r
Where r is common ratio
multiply your income by 2 to get your monthly income: $900
Answer:
monthly income=$900
the monthly income was multipled by 2
so, real income was, $900/2
=$ 450
so, $450×2=$900...
The real income is $400.
MultiplicationThe term multiplication refers to the product of two or more than two numbers.
How to find real income?Let us assume that the real income is x.
We have to multiply the real income by 2 to get the monthly income of $900.
This implies that [tex]x\times 2=\$900[/tex],
Solving the above expression, we will get
[tex]x\times 2=\$900\\x=\dfrac{900}{2} \\x=400[/tex]
So, the real income is $400.
Learn more about expression here-https://brainly.com/question/14083225
#SPJ2
A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z)
Find the work done.
Answer:
Work done = 0 J
Step-by-step explanation:
work done= ∫ F. dr
= [tex]\int\limits^2_0 {x} \, dx[/tex] + [tex]\int\limits^2_2 {x} \, dx[/tex] + [tex]\int\limits^0_2 {x} \, dx[/tex] + [tex]\int\limits^0_0 {x} \, dx[/tex] + [tex]\int\limits^0_0 {y} \, dy[/tex] + [tex]\int\limits^5_0 {y} \, dy[/tex] + [tex]\int\limits^5_5 {y} \, dy[/tex] + [tex]\int\limits^0_5 {y} \, dy[/tex] + [tex]\int\limits^0_0 {z} \, dz[/tex] + [tex]\int\limits^1_0 {z} \, dz[/tex] + [tex]\int\limits^1_1 {z} \, dz[/tex] + [tex]\int\limits^0_1 {z} \, dz[/tex]
Work done= x²/2 + y²/2 + z²/2
Applying integral limits for entire pathway
Work done= 2 + 0 -2 + 0 + 0+ 25/2 - 25/2 + 0 + 1/2 + 0 - 1/2
Work done = 0 J
can someone help me with this please?!?
Answer:
The answer is 60cm^2.
hope it helps..
Nina had 17 marbles in a bag. Her mother put a handful of marbles in the bag. When Nina counts her marbles, she discovers she now has 34 of them. Which of the following equations will help Nina solve for the number of marbles, m, that her mom put in the bag? 17 + 34 = m 17 + m = 34 17m = 34 m − 17 = 34
Answer:
17+m=34
Step-by-step explanation:
Nina had 17 marbles in a bag + the x amount of marbles that her mom gives her.
so 17+x=34
(x is the variable that I chose however it could be any variable, so it would also mean the same thing as 17+m=34)
Hope this helped!
Answer:
17 + m = 34.
Step-by-step explanation:
Nina had 17 marbles;
Mother put a handful of marbles, let's say m.
Now Nina has 34 marbles.
34 marbles is [=] 17 marbles Nina had before + m from her mother.
17 + m = 34 will be the right equation.
17 + 34 = m — wrong;17 + m = 34 — right;17m = 34 — wrong;m - 17 = 34 — wrong.The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish from each of the 53 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have different mercury than the allowable amount?
Required:
State the random variable, population parameter, and hypotheses.
Answer:
Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.
The population parameter is the mean amount of mercury in the bass fish of Florida lakes.
The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.
The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
Step-by-step explanation:
The question is incomplete.
There is no data provided.
We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.
This is a hypothesis test for the population mean.
The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=53.
The sample mean is M=0.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=53-1=52[/tex]
This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]
As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
If x=3 then what is y the equation is 2x -y=5 if you have the answer lets d a t e I m f e m a l e. T a n g ie_man 18 snap without spaces.
Answer:
y = 1Step-by-step explanation:
Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;
[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]
Hence, the value of y is 1
Follow the properties of the equality given for the steps to solve the following equation:
-3(x-4)+5=-x-3
(answers and steps in photo)
Answer:
Step-by-step explanation:
-3x+12+5= -x-3 -3x+17 = -x-317 = 2x-320 =2xx=10what is the value of -x+ the absolute value of -y
Answer:
[tex]-x+| \: y\: |[/tex]
Step-by-step explanation:
[tex]-x+|-y|[/tex]
[tex]\mathrm{Apply\:absolute\:rule}: \left|-y\right|\:=| \: y\: |[/tex]
[tex]-x+| \: y\: |[/tex]
In her backyard, Mary is planting rows of tomatoes. To plant a row of tomatoes, mary needs 20/13 square feet. There are 40 square feet in Mary's backyard, so how many rows of tomatoes can mary plant??
Answer:
26 rows
Step-by-step explanation:
[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]
Can anyone please explain? Need some help :)
A regular hexagon is inscribed in a circle with a diameter of 12 units. Find the area of the hexagon. Round your answer to the nearest tenth. (there's no picture included)
Answer:
93.5 square units
Step-by-step explanation:
Diameter of the Circle = 12 Units
Therefore:
Radius of the Circle = 12/2 =6 Units
Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.
Area of the Hexagon = 6 X Area of one equilateral triangle
Area of an equilateral triangle of side length s = [tex]\dfrac{\sqrt{3} }{4}s^2[/tex]
Side Length, s=6 Units
[tex]\text{Therefore, the area of one equilateral triangle =}\dfrac{\sqrt{3} }{4}\times 6^2\\\\=9\sqrt{3} $ square units[/tex]
Area of the Hexagon
[tex]= 6 X 9\sqrt{3} \\=93.5$ square units (to the nearest tenth)[/tex]
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
25% of a class do not play basketball.
27 children do play. How many
children are in the class?
Answer: 36 children
Step-by-step explanation:
3/4 of the class plays basketball. Thus 3/4x=27. Multiply each side by 4/3 to get x = 36
Suppose that y is directly proportional to x and that y = 16 when x = 8. Find the constant of proportionality k.
Then, find y when x = 12.
Answer: 24
Step-by-step explanation:
Variation: y ∞ x
y = kx , where k is the constant of proportionality
now to find k, we substitute for y and x in the equation above
16 = 8k
therefore,
k = ¹⁶/₈
= 2.
Now, to find y , we move back to the equation above and substitute for x and k to get y
y = 12(2)
= 24
The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall? a) 95% b) 99.7% c) 34% d) 68%
Answer:
D
Step-by-step explanation:
We calculate the z-score for each
Mathematically;
z-score = (x-mean)/SD
z1 = (1.9-2.1)/0.2 = -1
z2 = (2.3-2.1)/0.2 = 1
So the proportion we want to calculate is;
P(-1<x<1)
We use the standard score table for this ;
P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%
Answer:
68
Step-by-step explanation:
How do you write 0.0026 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]2.6 \times {10}^{ - 3} [/tex]
Hope this helps you
Answer:
2.6 × 10⁻³
Step-by-step explanation:
To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.
In the decimal 0.0026, the first number that is 1 or higher is 2.
0.0026 ⇒ 2.6
When trying to figure out the exponent, here are some things to keep in mind:
- when you move the decimal to the right, the exponent is negative
- when you move the decimal to the left, the exponent is positive
You moved the decimal to the right three places. So the exponent will be -3.
The result is 2.6 × 10⁻³.
Hope this helps. :)
6th grade math , help me please :)
Answer:
A= 20x
B= 15n
C= 15x+ 9
D= a + 15
E= 9x + 3y
F= 10w + 10z
Step-by-step explanation:
Question 1 of 16,
The area of a trapezoid is 189 cm . The height is 14 cm and the length of one of the parallel sides is 8 cm. Find the length of the second parallel side.
Answer:
19cm
Step-by-step explanation:
The area of a trapezoid [tex]=\dfrac12(a+b)h[/tex] (where a and b are the parallel sides).
Given:
Area = 189 Square cm
Height, h=14cm
a=8cm
We want to find the value of the other parallel side, b.
Substitution of the given values gives:
[tex]189=\dfrac12(8+b)14\\189=7(8+b)\\$Divide both sides by 7\\8+b=27\\Subtract 8 from both sides\\b+8-8=27-8\\b=19cm[/tex]
The length of the second parallel side is 19cm.
5c + 16.5 = 13.5 + 10c
Answer:
Hello!
________________________
5c + 16.5 = 13.5 + 10c
Exact Form: c = 3/5
Decimal Form: c = 0.6
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!
Answer:
3000+3d=noods
Step-by-step explanation: