There are 353925 committees of 10 persons that can be chosen with exactly 8 men.
How to determine the number of waysFrom the question, we have the following parameters that can be used in our computation:
People = 15 men and 11 women
Committee = 10 persons (8 men)
The number of ways is then calculated as
Ways = Men * Women
So, we have
Ways = C(15, 8) * C(11, 2)
Evaluate the products
Ways = 353925
Hence, the number of committee is 353925
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Rewrite vertex form y = 3(x + 5)2 − 11 into standard form.
The standard form is y= 3x^2+114+30x.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given;
y = 3(x + 5)^2 − 11
y= 3(x^2+25+10x)-11
y= 3x^2+125+30x-11
y= 3x^2+114+30x
Therefore, the equation will be y= 3x^2+114+30x
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50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 which of the following histograms is the best representation of the data?
The best way to represent histograms is by decreasing to increasing order.
The mean is the arithmetic mean and is calculated by adding a group of numbers and dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
Given the values:
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45
We have that:
(22+24+28+28+30+31+31+32+32+35+36+37+38+41+42+42+44+44+45+46+46+47+47+49+50)/25=37.88.
The average age that a large construction company wants to know is 38.
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For the following exercises, find the measure of the angle between the three-dimensional vectors a and b. Express the answer in radians rounded to two decimal places, if it is not possible to express it exactly 135. a = (3. -1,2), b = (1,-1,-2) 136. a = (0,-1, -3), b = (2,3,-1)
The angle between the 3D vectors a = (3, -1, 2) and b = (1, -1, -2) is 2.23 radians. The angle between a = (0, -1, -3) and b = (2, 3, -1) is 2.43 radians.
The angle between two vectors a and b in three-dimensional space can be found using the dot product formula:
cos(θ) = (a * b) / (||a|| * ||b||)
Where ||a|| and ||b|| represent the magnitude (length) of vectors a and b, respectively, and "*" represents the dot product of the two vectors. The dot product is given by:
a * b = a1 * b1 + a2 * b2 + a3 * b3
Where a1, a2, and a3 are the components of vector a, and b1, b2, and b3 are the components of vector b. The angle θ is then calculated using the inverse cosine function:
θ = arccos(cos(θ))
Finally, the angle θ is expressed in radians.
For the first problem, we have:
a = (3, -1, 2)
b = (1, -1, -2)
So, we have:
a * b = 3 * 1 + (-1) * (-1) + 2 * (-2) = 3 - 1 - 4 = -2
||a|| = [tex]\sqrt{(3^2 + (-1)^2 + 2^2)} = \sqrt{(14)}[/tex]
||b|| = [tex]\sqrt{(1^2 + (-1)^2 + (-2)^2) }= \sqrt{(6)}[/tex]
cos(θ) = [tex](-2) / (\sqrt{(14)} * \sqrt{(6)} ) = -\sqrt{(2)} / \sqrt{(21)[/tex]
θ = arccos[tex](-\sqrt{(2)} / \sqrt{(21)})[/tex] = 2.23 radians (rounded to two decimal places)
For the second problem, we have:
a = (0, -1, -3)
b = (2, 3, -1)
So, we have:
a * b = 0 * 2 + (-1) * 3 + (-3) * (-1) = -3
||a|| = [tex]\sqrt{(0^2 + (-1)^2 + (-3)^2)} = \sqrt{(10)}[/tex]
||b|| = [tex]\sqrt{(2^2 + 3^2 + (-1)^2)} = \sqrt{(14)}[/tex]
cos(θ) = [tex]-3 / (\sqrt{(10)} * \sqrt{(14)}) = -3 / \sqrt{(140)}[/tex]
θ = arccos[tex](-3 / \sqrt{(140)})[/tex] = 2.43 radians (rounded to two decimal places)
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Which of the following integrals represents the area of the region bounded by the curves, y = -3x^(1/2), y = x - 4, and y = 0, in terms of x?a. ∫(4, 0) (-3 √x) dx + ∫(5, 4) (x - 4) dxb. ∫(4, 0) -3 √x dx c. ∫(1, 0) 3√x dx + ∫(4, 1) (-x + 4) dxd. ∫(2, 0) 3√x dx + ∫(4, 2) (-x + 4) dxe. ∫(1, 0) (-3√x) dx + ∫(4, 1) (-x + 4) dx
a) The biologists who collected the flower length data compared the two varieties using statistical methods based on the mean and standard deviation. Find the mean and standard deviation for each flower variety. Do this by hand, using a calculator (do not use Stata). You may check your answer afterwards by putting the data into Stata and using the summarize function if you wish.
b) Many standard statistical methods that you will study in this course are intended for use with distributions that are fairly symmetric and have no outliers. Do the distributions appear suitable for use of the mean and standard deviation as summaries?
The answer is:
a) The following formula must be used to get the mean and standard deviation for each flower variety:
Mean is the average of all values (number of values)
Sqrt((sum of squared deviations from the mean) / (number of values - 1)) is a formula for calculating standard deviation.
We have the following information on the first variety:
6.2, 6.3, 5.8, 6.4, 6.0, 6.9, 6.7, 6.1, 6.5, 6.4
Mean = (6.2 + 6.3 + 5.8 + 6.4 + 6.0 + 6.9 + 6.7 + 6.1 + 6.5 + 6.4) / 10 = 6.35
To find the deviations from the mean for each number, we must first compute the standard deviation:6.2 - 6.35 = -0.15
6.3 - 6.35 = -0.05
5.8 - 6.35 = -0.55
6.4 - 6.35 = 6.2 - 6.35 = -0.15
6.3 - 6.35 = -0.05
5.8 - 6.35 = -0.55
6.4 - 6.35 = 0.05
6.0 - 6.35 = -0.35
6.9 - 6.35 = 0.55
6.7 - 6.35 = 0.35
6.5 - 6.35 = 0.15
6.4 - 6.35 = 0.05
We now square each deviance and add them all up:
[tex]((-0.15)^2 + (-0.05)^2 + (-0.55)^2 + (0.05)^2 + (-0.35)^2 + (0.55)^2 + (0.35)^2 + (-0.25)^2 + (0.15)^2 + (0.05)^2) = 1.15[/tex]
The square root is then calculated by dividing the number of values by the number minus one:
Sqrt(1.15 / 9) 0.38 is the standard deviation.
As a result, for the first flower variety, the mean and standard deviation are 6.35 and 0.38, respectively.
b) We have the following information for the second variety: 5.1, 5.4, 5.1, 5.8, 5.0, 5.6, 5.7, 5.3, 5.5, 5.2
Mean = (5.1 + 5.4 + 5.1 + 5.8 + 5.0 + 5.6 + 5.7 + 5.3 + 5.5 + 5.2) / 10 = 5.43
To find the deviations from the mean for each number, we must first compute the standard deviation:
5.1 - 5.43 = -0.33
5.4 - 5.43 = 0.03
5.1 - 5.43 = -0.33s
5.8 - 5.43 = 0.37
5.0 - 5.43 = -0.43
5.6 - 5.43 = 0.17
5.7 - 5.43 = 0.27
5.3 - 5.43 = -0.13
5.5 - 5.43 = 0.07
5.2 - 5.43 = -0.
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Combine the like terms to create an equivalent expression. 9+a−5b−2
what is the index notation of 4*4
Answer:
The index notation of 4^4 (4 raised to the power of 4) is written as 4^4 = 256.
Step-by-step explanation:
In mathematics, an exponent is a symbol indicating the number of times a quantity is multiplied by itself. In index notation, the number being raised to a power is written as the base and the power it's being raised to is written in superscript. So, in this case, 4 is being raised to the power of 4, which means 4 is being multiplied by itself 4 times. So, 4 * 4 * 4 * 4 = 256.
A is the correct of the circle. The diagram is not drawn to scale.
If m
Answer:
Four thousand two hundred and
Step-by-step explanation:
Fill in the missing number.
80% of
= 240,000
Answer:
The missing number is 300,000.
Step-by-step explanation:
To find the missing number, we can set up an equation based on the information given. If 80% of a number is equal to 240,000, we can write:
0.80x = 240,000
To find x, we can divide both sides of the equation by 0.80:
x = 240,000 / 0.80 = 300,000
So, the missing number is 300,000.
Pls help I need this quick thx :D
The steps followed by Nikki are correct. Hence, option 1 is the correct answer.
How to construct parallel line to a given line and passing through a given point?Using a ruler and compass, perform the following procedures to create a line from an exterior point that is parallel to the other line:
Given: A point P that sits outside of line segment AB and line segment AB
to create a line that runs through point P and is parallel to line AB.
Select any point X and connect it to point P on the line segment AB.
Draw an arc with X as the center and any reasonable radius, cutting the line segments PX and AB at points M and N, respectively.
Draw an arc EF with P as the center and the same radius as in the previous step, cutting the line segment PX at point Q.
Draw an arc with Q as the center and the same radius as previously, cutting the arc EF at R.
To create the line segment CD, join R and P.
The necessary parallel to the line segment AB that goes through the point P is the line segment CD.
According to the steps of construction we determine that the steps of construction of Nikki are correct.
Hence, option 1 is the correct answer.
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Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem?a. 10X1+5X2−2X3≥20b. X1−2X22≤100c. 5X1+3≥25d. X1+0.5X2≤30e. 6X1+2X2∗X3≥10
The constraints that are not linear or cannot be included as a constraint in a linear programming problem are b. X1−2X2²≤100.
What is linear constraint?A linear constraint in linear programming occurs when linear components are added or subtracted and the resulting expression must either rise, decrease, or be exactly equal to a right-hand side value.
A constraint is referred to as linear if all of its terms are of the first order.
We know that the degree of the linear constraint is one, hence the constraint that does not have a degree of one is not a linear constraint.
Thus, option b X1−2X2²≤100 has a degree of two and it cannot be used as constraint in a linear programming problem.
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ANSWER ASAP IM BEGGING BRO
Part A: slope = 1
Part B: slope = 1
Part C: Slope values becomes equal.
What is slope?Slope, An evaluation of a line's inclination with respect to the horizontal using numbers. The slope of any line, ray, or line segment in analytical geometry is defined as the proportion of the vertically to the horizontally distance between the two points on the line ("slope equals rise over run").
As we know,
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Part A:
(x₁ , y₁) = (0, -4)
(x₂, y₂) = (-2, 2)
m = (2 - 4) / (-2 - 0)
m = -2 / -2
m = 1
Part B:
(x₁ , y₁) = (0, -4)
(x₂, y₂) = (-4, 1)
m = (-4 - 0) / ((-4 - 0)
m = -4 / -4
m = 1
Part C:
As we pick different points to calculate slope for Part A and Part B, conclude that slope values are equal. It means that lines are parallel to each other and they have different y-intercepts.
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fill in the blank. ___ refers to whether or not an estimator tends to overestimate or underestimate a parameter. refers to how much the estimate varies from sample to sample.
Bias refers to whether an estimator tends to overestimate or underestimate a parameter, while variance refers to how much the estimate varies from sample to sample.
Bias is a measure of the difference between an estimator's expected value and the true value of the parameter being estimated. An estimator is said to be biased if it systematically overestimates or underestimates the parameter. Variance is a measure of how much the estimate of the parameter varies from sample to sample. High variance implies that the estimator is not consistent and can be unreliable. Low variance implies that the estimator is consistent and reliable. Therefore, it is important to consider both bias and variance when assessing the quality of an estimator. Bias and variance work together to form the overall accuracy of an estimator, and so it is important to consider both when evaluating the performance of an estimator.
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A container holds 6 pounds of peanuts. How many ounces of peanuts are in the container? (1 pound = 16 ounces)
12 ounces
16 ounces
54 ounces
96 ounces
Step-by-step explanation:
Good Afternoon! Your Answer would be 96!
16 x 6 = 96
How do we find this answer?
16 + 16 = 32
And 32 would be 16 twice!
32 + 32 = 64
And 64 would be 16 four times!
So now time to get the answer, 64 + 32 = 96.
Have An Amazing day.
Mr. Abott washed 3 8 of his laundry. His son washed 1 3 of it. Who washed more laundry? How much of the laundry still needs to be washed?
find the value of x and please show process!
I'm fifty years old it's a discreet or continuous variable justify the answer
I'm fifty years old the sentence is a discrete variable and not continuous variable as age is counted in concrete numbers and it does not involve complex numbers.
What is discrete and continuous data?Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted. Complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.
Numerical information that is continuous refers to the unspecified number of measurements that could be made between two realistic sites.
Despite the fact that these numbers are frequently gathered via accurate measurements, they are not necessarily neat and orderly as those in discrete data. Measuring a specific issue repeatedly enables us to establish a defined range, within which we can predictably gather more data.
I'm fifty years old the sentence is a discrete variable as age is counted in concrete numbers and it does not involve complex numbers.
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Angles BAE and FAC are straight angles. What angle relationship best describes angles BAC and EAF?
Adjacent angles
Complementary angles
Supplementary angles
Vertical angles
Answer: Vertical Angles
Step-by-step explanation:
Took The test!
Angles BAC and EAF are vertically opposite angles .
Given,
Angles BAE and FAC are straight angles.
Here,
∠BAC + ∠FAC = 180° (Linear pair angles).
Now ,
∠BAC and ∠EFA are vertically opposite to each other .
Thus,
∠BAC = ∠EFA.
Thus these angles are vertically opposite angles and are equal .
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If the interval size is decreased from $200 to $100, which of the following must remain the same on the newhistogram?a) The height of the bars will decrease.b) The total number of bars will decrease. c) The width of the bars will increase. d) Each bar will represent more data items than before.
If the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.
How is this determined?The height of the bars will decrease if the interval sizes in a histogram are reduced while the scale remains constant. When the intervals are compressed,
For a particular set of data, there will be more histogram bars, but fewer data points will make up each interval. Reducing the interval size will also reduce the height of the histogram's bars because the height of the bars represents the number of items in each interval.
Hence, if the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.
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FIND MULTIPLICITY AND ZEROS OF THE GRAPH!
Answer: The Zeros Are(in order) -3,-2,-1,1, 1.5 ALL have a multiplicity of 1.
Step-by-step explanation: Since the 0's cross the graph and don't "bounce" on the x-axis, they're all for a multiplicity of 1.
What is the probability of rolling a number greater than or equal to 2 on a standard six-sided die? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.
The probability of getting a number greater than or equal to 2 is 0.8333( 3 decimal place)
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/ total possible outcome
The total outcome on a standard six-sided die is 6
The sample space of getting a number greater or equal to 2 is 2,3,4,5,6 = 5
Therefore the probability of getting a number greater or equal to 2 is = 5/6
= 0.833 ( 3 decimal place)
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12. aj is 10 and the difference is 6, find the numbers. b) A number is greater than another number by 3. If their sum is 33, find the numbers.
The value of the two numbers in b is 15 and 18
How to solve for the numbersTo get the values we would have to set up an equation system
Such that we would have:
the smaller number is given as c
Then the bigger number is given as c + 3
The equation would be
c + c + 3 = 33
then
2c = 33 - 3
2c = 30
From here we would have to divide both sides of the equation by 2
2c / 2 = 30 / 2
c = 15
33 - 15 = 18
Hence the numbers are given as 15 and 18
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∠A=8x+74
∘
start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 8, x, plus, 74, degrees, end color #11accd
∠
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=
2
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5
6
∘
∠B=2x+56
∘
start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, 2, x, plus, 56, degrees, end color #28ae7b
Encuentra el valor de
�
xx y luego la medida de
∠
�
∠Bstart color #1fab54, angle, B, end color #1fab54:
what do you mean by
∠B=2x+56
∘
start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, 2, x, plus, 56, degrees, end color #28ae7b
Encuentra el valor de
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xx y luego la medida de
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∠Bstart color #1fab54, angle, B, end color #1fab54:
SOMEONE HELPPPPP MEEEEEE PLEASE
Answer:
a.) (1,4), (-2,3), (0,4)
b.) (4,1), (3,-2), (4,0)
Step-by-step explanation:
a. When we want to find the reflection over the Y axis, that means the X coordinate signs reflect. For A, it says (-1,4). To reflect it, we reflect the X coordinate, so now it's (1,4) instead. You'll do that to the other two.
b. When rotating, you would switch the numbers of the coordinates and switch the sign of X. For the first one (-1,4), we'll switch it to (1,4). Not we'll switch the numbers around to make it (4,1). You'll do that for the other two
what percent is represented by the region that is shaded?
the answer is not 333% or 333.33% or 333.3%
466.66%? Theres four whole circles and one that is two thirds. Unless 466.66% is correct, can you give more info?
13. Kenny sets up his own waving business. He charges $2 each time he waves graciously at someone, and $3 each time he waves vigorously with zeal. Smiles cost extra. All the waving causes tendonitis in his elbow and he must pay a $150 bill for his doctor's visit. If he completed 125 gracious waves and 300 10 vigorous waves, how much money did he make?
Answer: Kenny made 125 * $2 = $250 from 125 gracious waves.
He made 300 * $3 = $900 from 300 vigorous waves.
So, he made a total of $250 + $900 = $1150.
After paying the doctor bill, he has $1150 - $150 = $1000 left.
Step-by-step explanation:
The amount of money that Kenny made after completing the number of gracious waves and vigorous waves would be = $1000.
How to calculate the total amount of money made by Kenny?The amount that Kenny charges for gracious waves= $2
The amount of money that he charges for vigorous wave = $3.
The total number of completed gracious waves = 125
The amount made for gracious waves = 2× 125 = $250
The total number of completed vigorous waves = 300
The amount made for vigorous waves = 3×300 = $900
The total amount made in both waves = 250+900= $1,150
The bill to be payed to doctor = $150
The amount left = 1,150- 150 = $ 1000
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To help restart the economy growth, government is offering simple interest loans to small business at a rate 1.5%.
Say, you obtain one of these loans of $90,000 for 5 years. Determine the amount of money you must repay the government after 5 years.
Answer:
96750
Step-by-step explanation:
s.i=p×r×t
=90000×5×15/10 all divided by 100
9000×5×15 divided by 100
=90×5×15
=6750
amount=s.i+principal
=6750+90000
=96750
Find the value of x of the triangle below
Angles in a triangle add to 180 degrees
make a little equation for that
58 + 42 + x = 180
simplify
100 + x = 180
x = 180 - 100
x = 80
Hope this helps,
- Jeron :- )
40 EASY POINTS!
Answer all of them with examples of how you got the answer for 40 points :)
1. store A sells at cheaper rate.
2. Runner B tun at faster rate.
3. Submarine 2 will reach at depth of -1056 feet at faster rate.
4. Kira collected 18.33 points in one hour.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
1. Store A: y= 0.40 x
so, the unit rate is 0.40.
Store B:
the cots of 3 pound carrot= 20.16
and, the cost of 48 ounce carrot = 20.16
and, cost per ounce= 20.16 /48= 0.42
so, the unit rate is 0.42.
Thus, store A sells at cheaper rate.
2. The unit rate rate of runner A
= 54/4.5
= 12
and, the unit rate of runner B
= 275/20
= 13.75
Thus, Runner B tun at faster rate.
3. Submarine 1 descends at rate of 22 feet.
and Submarine 2 descends at rate of = 480/20 = 24 feet.
Thus, Submarine 2 will reach at depth of -1056 feet at faster rate.
4. Jess collected 18 points in one hour.
and, Kira collected 18.33 points in one hour.
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how much is 0.15% of 12000 ?
Answer:
0.15% of 12000 is equal to 18.
Step-by-step explanation:
To calculate 0.15% of 12000, we first convert 0.15% to a decimal. To do this, we divide 0.15 by 100:
0.15 ÷ 100 = 0.0015
Next, we multiply this decimal by 12000:
0.0015 × 12000 = 18
So, 0.15% of 12000 is equal to 18.