By taking the product between the combinations of possible groups fo men and women we will see that the number of different committees is:
392
In how many ways can the committee be formed?For a set of N elements, the number of different sets of K elements that can be formed is:
C(N, K) = N!/(K!*(N - K)!)
Here we have 8 men and 7 women, and we want to make a committee of 5 men and 6 women
Then the total number of different committees is given by the product between the different sets of 5 men and the different sets of 6 women, these are:
for men:
C(8, 5) = 8!/( 5!*(8 - 5)!) = (8*7*6)/(3*2*1) = 56
for women:
C(7, 6) = 7!/(6!*(7 - 6)!) = 7
Then the total number of different committees is:
C = 56*7 = 392
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The formula for simple interest is I=Prt,I=Prt, where II is the interest earned, PP is the principal, rr is the interest rate and tt is the number of years. Solve the formula for PP in terms of r,r, II and t.t.
Answer:
[tex]P=\cfrac{I}{rt}[/tex]----------------------------
GivenI = PrtSolve for P[tex]I = Prt[/tex][tex]\cfrac{I}{rt} = \cfrac{Prt}{rt}[/tex][tex]\cfrac{I}{rt} =P[/tex][tex]P=\cfrac{I}{rt}[/tex]Here is the histogram of a data distribution. All class widths are 1
Which of the following numbers is closest to the mean of this distribution?
The number that is closest to the mean of the distribution is 4 (option C)/
What is the mean?A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is the product of the frequency of the rectangle and the width of the rectangle.
Mean is the average of a set of numbers. It is determined by multiplying each bar in the histogram by its height, add the multiplication value for all the bars together and dividing it by the total frequency of the bars.
Mean = [(1 x 1) + (2 x 2) + (3 x 3) + (4 x 4) + (5 x 3) + (6 x 2) + (7 x 1)] / (1 + 2 + 3 + 4 + 3 + 2 + 1)
Mean = (1 + 4 + 9 + 16 + 15 + 12 + 7) / 16
Mean = 64 / 16
Mean = 4
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A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. Find the probability that the mean actual weight for the 100 weights is greater than 25.2
The probability that the mean actual weight for the 100 weights is greater than 25.2 is equal to 0.0136%.
How to determine the probability that the mean actual weight for the 100 weights?In order to determine the probability that the mean actual weight for the 100 weights is greater than 25.2, we would have to calculate the mean and standard deviation.
In a uniform distribution, the mean of a data set can be calculated by using this formula:
Mean, E(x) = [a + b]/2
Where:
a is the lowest boundary.b is highest boundary.Substituting the given parameters into the formula, we have;
Mean, E(x) = [24 + 26]/2
Mean, E(x) = 50/2
Mean, E(x) = 25.
For the standard deviation, we have:
Standard deviation, S(x) = √((b - a)²/12)
Standard deviation, S(x) = √((26 - 24)²/12)
Standard deviation, S(x) = √((2)²/12)
Standard deviation, S(x) = √(4/12)
Standard deviation, S(x) = 0.5774.
For the sample standard deviation, we have:
Standard deviation = S(x)/√n
Standard deviation = 0.5774/√100
Standard deviation = 0.5774/10
Standard deviation = 0.05774.
By applying the central limit theorem, we would determine the z-score as follows:
Z-score = (x - μ)/σ
Z-score = (25.2 - 25)/0.05774
Z-score = 0.2/0.05774
Z-score = 3.64
Therefore, the p-value is equal to 0.000136.
Probability (x > z) = 0.0136%.
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Represent the following expressions as a power of the number a where a ≠ 0.: (a^3)^-2
1/[tex]a^{6}[/tex] is the required number.
What is an expression?Numbers, symbols and operators (such as and times) grouped together that show the value of something.
Given an expression (a³)^-2
(a³)^-2 = [tex]a^{-6}[/tex] = 1/[tex]a^{6}[/tex]
Hence, 1/[tex]a^{6}[/tex] is the value of the expression (a³)^-2
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Which graph represents the polynomial function?
The graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.
First, let us understand the polynomial function:
A polynomial function is one that uses only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 9y + 6 is a polynomial with an exponent of 1.
We are given:
f(x) = x^3 - 2x^2 - 5x + 6
We know that, when the graph intersects the x-axis, it satisfies the equation that is f(x) = 0 at that point.
Let us check the points one by one;
Option A;
The graph intersects the x-axis at -2, 1, and 3 it should satisfy the equation f(x) = 0.
Let's put x = -2 in f(x), we will get;
f(-2) = -2^3 - 2(-2)^2 - 5(-2) + 6 = -8 - 8 + 10 + 6 = -16 + 16 = 0
f(-2) = 0.
Let's put x = 1 in f(x), we will get;
f(1) = 1^3 - 2(1)^2 - 5(1) + 6 = 1 - 2 - 5 + 6 = 7 - 7 = 0
f(1) = 0.
Let's put x = 3 in f(x), we will get;
f(3) = 3^3 - 2(3)^2 - 5(3) + 6 = 27 - 18 - 15 + 6 = 33 - 33 = 0
f(3) = 0.
So, the points -2, 1, and 3 satisfy the equation f(x).
Thus, the graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.
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PLEASE HELP ASAP!! Represent the following expressions as a power of the number a where a≠0.
(a^3)^-2
(a^-1 • a^-2)^-3
((a^2)^-2)^2
After using the property of power, the expressions as a power of the number a is [tex](a^3)^{-2} = a^{-6}[/tex] , [tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex] and [tex]((a^2)^{-2})^2=a^{-8}[/tex] .
In the given question we have to solve the given expressions as a power of the number a where a≠0.
The first given expression is [tex](a^3)^{-2}[/tex].
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
Simplifying the expression.
[tex](a^3)^{-2} = a^{3*(-2)}[/tex]
[tex](a^3)^{-2} = a^{-6}[/tex]
The second expression is [tex](a^{-1}\cdot a^{-2})^{-3}[/tex]
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(-1)\times(-3)}\cdot a^{(-2)\times(-3)}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{3}\cdot a^{6}[/tex]
Using the property of sum of power [tex]a^m\cdot a^n=a^{m+n}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(3+6)}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex]
The third expression is [tex]((a^2)^{-2})^2[/tex].
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex]((a^2)^{-2})^2=((a^2)^{(-2)\times2})[/tex]
[tex]((a^2)^{-2})^2=(a^2)^{-4}[/tex]
Again using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex]((a^2)^{-2})^2=a^{2\times(-4)}[/tex]
[tex]((a^2)^{-2})^2=a^{-8}[/tex]
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Which statement is most likely to be true for this distribution?
O A. The mean is less than the median.
• B. The mean is greater than the median.
• C. The mean is the same as the median.
The statement that is most likely correct for the negatively skewed data distribution given is B. The mean is less than the median.
What is a Negatively Skewed Data Distribution?
A negatively skewed data distribution has the tail to the left of the number line, and therefore its median is usually greater than its mean.
The dot plot shows a data distribution that is negatively skewed. Therefore, the statement that is most likely to be true is B. The mean is less than the median.
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We want 3 pizzas, each topped with 0, 1, 2, 3, 4, 5, or 6 of 6 available whole-pie toppings. How many different combinations of 3 such pizzas are possible if different pizzas need not have different toppings?
ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ. Match each angle of rotation to the
point that A' (the image of A) coincides with after that rotation.
252°
108°
135°
180°
288°
324°
A0DO
D after three rotations: 3 × 36° = 108°
F after five rotations: 5 × 36° = 180°
H after seven rotations: 7 × 36° = 252°
I after eight rotations: 8 × 36° = 288°
Given,
In the question:
ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ.
To find the each angle of rotation to the point A' coincides with after that rotation.
Now, According to the question:
let's know about Decagon:
A decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.
Every regular polygon with n sides can be divided into n congruent triangles. The angle with vertex the center of the polygon will measure
360 : n degrees. We are given a regular decagon, therefore:
n = 10
α = 360 : n = 36°
We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.
A' will coincide with D after three rotations: 3 × 36° = 108°
A' will coincide with F after five rotations: 5 × 36° = 180°
A' will coincide with H after seven rotations: 7 × 36° = 252°
A' will coincide with I after eight rotations: 8 × 36° = 288°
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The graph of the absolute value parent function, f(x) = |x), is stretched
horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
OA. g(x)= x+3|
OB. g(x) = 31x1
C. g(x) = 13x1
OD. g(x)= |||
Option A is the correct answer g(x) = |x+3| by using the relation with the parent function.
Explain absolute value function.
A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.
The definition of the absolute value parent function, f(x)=| x |, is as follows:
f(x) = [tex]\left \{ {{x ~, ~ x > 0} \atop {0 ~ , ~x = 0}} \atop {-x ~, ~x < 0} \right.[/tex]
Given parent function is f(x) = |x|
g(x) is obtained by stretching the graph of f(x) by a factor of 3.
Use the function g(x)=f(x−h) to translate the absolute value function f(x)=| x | horizontally.
The graph of f(x) is moved h units to the right to obtain g(x) for h>0
The graph of f(x) is translated h units to the left to obtain g(x) when h>0
Therefore, g(x) = |x+3|
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algebra help pleaseee
Answer:
3x^2-2x+3+1/x+2
Step-by-step explanation:
Find the distance from the point (1,2) to the line-y= 1/2x-3. Round your answer to the nearest tenth.
Answer:
the graphical explanation please
In a set of eight consecutive integers, the smallest integer is more than $\frac35$ of the largest integer. What is the smallest possible value of the sum of the eight integers?
Answer:
116.
Step-by-step explanation:
Your welcome <3.
Answer:
116
Step-by-step explanation:
Please help me thank you :))))
Answer: y= (2/3)x - 2
Step-by-step explanation:
The biggest way to remember equations like these is to know rise over run which means however many times it goes up until it intersects with both x and Y will be on the top of the fraction and however many times it goes to the right until it intersects with both x and y will be on the bottom of the fraction. So since it hits (0, -2) then intersects at (3,0) it will be 2/3x and the Y is where X equals zero so it would be -2. Hope that helps!
Answer:
y = [tex]\frac{2}{3}x - 2[/tex]
Step-by-step explanation:
Step 1:
Choose two points on the graph, (x1, y1) and (x2, y2), to find the slope.
Find the ratio between change in y-values and change in x-values.
m = (y2 - y1) / (x2 - x1)
Points I picked:
(x1, y1) = (0, -2)
(x2, y2) = (3, 0)
Then,
m = (0 - (-2)) / (3 - 0)
m = 2/3
Step 2 :
Find the y-intercept from the graph. That is the point at which the line intersects the y-axis.
The y-intercept is -2.
b = -2
Step 3 :
Use the slope (m) and y-intercept (b) to write the equation in slope-intercept form:
y = mx + b
Substitute m = 2/3 and b = -2
y = 2/3 x - 2
What is the slope of line KH if H(-4, 2) and K(2, -2)? Remember to reduce!
The slope of a line KH if H(-4, 2) and K(2, -2) is -2/3.
What is a slope?A mathematical word used to define a line's direction and steepness is its slope or gradient.
If a line is rising from left to right, it is growing. The slope is positive, or m>0
If a line decreases from left to right, it is said to be diminishing. The slope is negative, indicating that m < 0
A line has zero slopes if it is horizontal. This function is constant.
The slope of a line is y - y₁ = m(x - x₁)
Slope m = (y₂ - y₁)/(x₂ - x₁)
m = (- 2 - 2)/(2 + 4)
m = - 4/6
m = - 2/3
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WHat is 5/1 x 4/5 This is a hard one
4
Step-by-step explanation:
[tex]{ \tt{ \frac{5}{1} \times \frac{4}{5}}} [/tex]
[tex]{ \tt{ \frac{5 \times 4}{5}}} [/tex]
[tex]{ \tt{ = \frac{20}{5}}} [/tex]
[tex] = { \green{ \boxed{ \pink{ \sf{4}}}}}[/tex]
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin now has: 6 + m
Two sides are labeled 5,244 feet. The other two sides are labeled 1,495 feet. What is the perimeter to the nearest hundred?
Answer:
Step-by-step explanation:
42feet
Graph the given equation by evaluating integer values of x from −2 to 2 and plotting the resulting points
y= _2x_1
The graph of the linear equation can be seen in the image at the end.
How to graph the equation?Here we have the linear equation:
y = -2x - 1
To graph this, we need to evaluate from x = -2 to x = 2, this means replacing the value of x by the correspondent number.
if x = -2, then:
y = -2*(-2) - 1 = 4 - 1 = 3
So we have the point (-2, 3)
if x = -1
y = -2*-1 - 1 = 2 - 1 = 1
We have the point (-1, 1)
If x = 0
y = -2*0 - 1 = -1
We have the point (0, -1)
If x = 1
y = -2*1 - 1 = -3
We have the point (1, -3)
If x = 2
y = -2*2 - 1 = -5
We have the point (2, -5)
Now we just need to graph these 5 points on a coordinate axis and then connect them with a line, the graph of the linear equation can be seen below.
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PLEASE HELP!!!! I WILL GIVE YOU BRAINLIST!! PLEASE ASAP :)
Which graph shows the image of ΔABC after a rotation about the origin?
Answer:
D.
Step-by-step explanation:
just click the rotate button until it matches one of the answers
A new gaming chair costs $309.99. You have already saved $131.49 and earn $25.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
25.5w − 131.49 = 309.99; w = 17
25.5 + 131.49w = 309.99; w = 7
25.5w − 309.99 = 131.49; w = 17
25.5w + 131.49 = 309.99; w = 7
The linear equation we need to solve is:
$25.50*w = $309.99 - $131.49
And the solution is w = 7.
How to write and solve the equation?We know that the cost of the gaming chair is $309.99.
To buy this, you already have saved $131.49, and save another $25.50 per week, then the amount you have after w weeks is:
f(w) = $131.49 + $25.50*w
So the linear equation we need to solve is:
$131.49 + $25.50*w = $309.99
To solve this we need to isolate w.
$131.49 + $25.50*w = $309.99
$25.50*w = $309.99 - $131.49
w = ($309.99 - $131.49)/$25.50 = 7
So they can buy the chair after 7 weeks.
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You deposit $500 into a savings account that earns interest annually. The function g(x) = 500(1.06)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[500, ∞)
[0, 500]
[0, ∞)
Omar deposited d dollars into a savings account y years ago. ... following expressions could be used to determine the zeros of the function f (x) when f (x).
Step-by-step explanation:
How many reflection symmetry does an eight pointed star have ? How many rotational symmetry does an eight pointed star have ?
An eight pointed star have 8 rotational symmetry and 8 reflection symmetry
What is rotational symmetry?The rotational symmetry of a shape explains why an object's shape remains unchanged when rotated about its own axis.
The eight pointed star while standing on any of the edges will be symmetrical.
What is reflection symmetry?Symmetry with respect to reflections is known as reflection symmetry. Mirror or line symmetry are other names for reflection symmetry.
For a reflection symmetry to be in a figure, the figure must at least have one line dividing it into two parts, one of which is the mirror image of the other,
Each of the peak and crest in the star will make 8 reflection symmetry
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Deshaun drove 469 miles in 7 hours.
At the same rate, how long would it take him to drive 335 miles?
We're assuming Deshaun is driving at a constant speed/at the same rate,
He drove 469 miles in 7 hours -> his speed = 469 : 7 = 67 (mph)
Therefore, it would take him 335 : 67 = 5 hours to drive 335 miles.
-8 What is 9.15 x 10°° written in standard form?
The value of the number 9.15 x 10° written in standard form is equal to 9.15.
As given in the question,
Given number is equal to :
9.15 x 10°
Given number 9.15 x 10° is written in standard form.
The value of the given number 9.15 x 10° written in standard form is given by:
9.15 x 10°
Here 10° = 1
Using property of number: Any number raise to zero is always equal to 1.
9.15 x 1
Using Multiplicative identity , number multiply to 1 remain number itself.
= 9.15
Therefore, the value of the number 9.15 x 10° written in standard form is equal to 9.15.
The complete question is:
What is the value of 9.15 x 10° written in standard form?
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he residence of a city voted on whether to raise property taxes the ratio of yes votes to no votes was 4 to 7 if there was a 5918 total votes how many yes votes were there
There is a total of 2152 yes votes
How to determine the number of yes votes?From the question, the statement is given as
The ratio of yes votes to no votes was 4 to 7
Mathematically, this can be represented as
Ratio = 4 : 7
Alternatively, we have
Yes : No = 4 : 7
Express the ratio as fraction
Yes = Yes/Yes + No
So, we have
Yes = 4/4 + 7
Evaluate the sum
Yes = 4/11
From the question, we have
Total votes = 5918
So, we have
Yes = 4/11 * 5918
Evaluate
Yes = 2152
Hence, the number of yes votes is 2152
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Fabian has $700 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $387.10. He buys 3 bicycle reflectors for $4.43 each and a pair of bike gloves for $12.36. He plans to spend some or all of the money he has left to buy new biking outfits for $45.81 each. What is the greatest number of outfits Fabian can buy with the money that's left over?
Which expression can be placed on the right side of the equals sign to form an equation?
2+3³ =
1. O 5³
2. 3 +4:3
3. 10-2-9
4. 52 +4
Expression which placed on the right side of equal sign is,
[tex]2+3^3 =2 +3\times 3\times 3[/tex]
[tex]2+3^3= 2+27[/tex]
[tex]2+3^3= 29[/tex]
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
What do you mean by equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given, a expression 2 + [tex]3^3[/tex] = ?
what can be placed right side of the expression?
so, first we calculate the [tex]3^3[/tex] which means 3 x 3 x 3 = 27.
then , add 2 and 27 and the answer is 29.
but the answer is not present into the option.
Final answer will be 29 which placed right side of the equation 2 + [tex]3^3[/tex] = 29.
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Pls help I’m failing
Answer:
{-9,-8,7,8,10}
A rectangular tank with a square base, an open top, and a volume of 37044 ft^3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
The dimensions of this rectangular tank that has the minimum surface area are 42 feet and 21 feet.
How to calculate the dimensions of the tank that has the minimum surface area?First of all, we would determine the surface area of this rectangular tank with a square base by using this formula:
h = V/s²
Where:
h represents the height of a rectangular tank.s represents the side of the square base.V represents the volume of a rectangular tank.For the surface area of this rectangular tank with a square base, we have:
Surface area, A = base area + 4(lateral area)
Surface area, A = s² + 4(s × h)
Surface area, A = s² + 4(s × V/s²)
Surface area, A = s² + 4V/s
Next, we would take the first derivative of the surface area as follows:
A' = 2s - 4V/s²
Substituting the given parameters into the formula, we have;
A' = 2s - 4(37044)/s²
For the minimum surface area dimension, the first derivative of the surface area would be equated to zero:
2s - 148,176/s² = 0
148,176/s² = 2s
148,176 = 2s³
s³ = 74,088
s = ∛74,088
s = 42 feet.
For the height, we have:
Height, h = V/s²
Height, h = 37044/42²
Height, h = 37044/1764
Height, h = 21 feet.
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