The number of different possible selections for the lottery is of:
25,872,165.
How to obtain the number of possible selections?First we decide which formula is used, as follows:
Permutation formula -> order is not important.Combination formula -> order in important.It is stated in this problem that the order of the numbers is not important, hence the combination formula is used.
The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 6 numbers are selected from a set of 54, hence the number of different combinations is of:
[tex]C_{54,6} = \frac{54!}{6!48!} = 25,872,165[/tex]
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What is the change to the graph of y=−3x−2 when the slope is changed to −1/3?
The slope of the graph will be changed. The graph is still a straight line, But it becomes steep.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
Slope of a Line :
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
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PLEASE HELP DUE IN 2 MINUTES
Please solve these radical expressions
The simplified form of given radical expression :
1) √216k⁴ = 6√6k²
2) √28x³y³ = 2xy√(7xy)
3) √192n³ = 8n√(3n)
4)∛40n² = 2∛n²n^(2/3)
5) ∛216x³ = 6x
6) ⁴√128x⁶y⁸ = 2xy8^(1/4)√(yx)
7) √252a³b^4 = 6ab²√(7a)
We need to solve given radical expressions.
1) √216k⁴
= √216 × √k⁴
= √(6 × 36) × √(k²)²
= 6√6 × k²
= 6√6k²
2) √28x³y³
= √(7 * 4) × √x³ × √y³
= 2√7 * x√x * y√y
= 2√7 * xy√(xy)
3) √192n³
= √(64 × 3) * √n³
= 8√3 * n√n
= 8n√(3n)
4)∛40n²
= ∛(8 × 5) * ∛n²
= ∛2³ * ∛5 * ∛n²
= 2∛n²n^(2/3)
5) ∛216x³
= ∛216 * ∛x³
= ∛6³ * ∛x³
= 6 * x
= 6x
6) ⁴√128x⁶y⁸
= ⁴√128 * ⁴√x⁶ * ⁴√y⁸
= ⁴√(16 × 8) * x(⁴√x²) * y(⁴√y²)
= 2 * 8^(1/4) * xy (x²y²)^(1/4)
= 2xy8^(1/4)√xy
7) √252a³b^4
= √(36 × 7) * √a³ * √b^4
= 6√7 * a√a * b²
= 6ab²√(7a)
Therefore, the simplified form of given radical expression :
1) √216k⁴ = 6√6k²
2) √28x³y³ = 2xy√(7xy)
3) √192n³ = 8n√(3n)
4)∛40n² = 2∛n²n^(2/3)
5) ∛216x³ = 6x
6) ⁴√128x⁶y⁸ = 2xy8^(1/4)√(yx)
7) √252a³b^4 = 6ab²√(7a)
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed at the end of the 6 years duration is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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What is mean absolute deviation in math example?.
The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We can determine how "spread out" the values in a data set are by looking at the mean absolute deviation.
What is mean absolute deviation?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation. Take the absolute value of each digit in the data set, then deduct the mean. Next, add up the absolute values. The mean absolute deviation is then calculated by dividing the aforementioned sum by the total number of values in the data set. Finally, tenths should be rounded.
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2.085x10^5 in standard form
Answer:
?jsp?3×4=5/6(9÷43)=2×3=45/_<7<78>(56)
48% percent of Mrs.Cano's students are in athletics. If there are 25 students in her class then how many are in athletics?
The percentage is used to denote the fraction of a quantity present.
The number of athletics students are 4. The correct answer is option A.
What is Percentage ?The percentage is defined as the portion of quantity present.
It is converted into fraction by dividing it by 100.
The percentage of students in athletics are 48%.
Total number of students in the class is 25.
The number of students in athletics is given as,
N = 48% of 25
=> N = 48 / 100 × 25
=> N = 48 / 4
=> N = 12.
Hence the number of athletics students in Mrs. Cano's class is 12.
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Lines f and g are graphed on top of each other below.Does the system of linear equation on the below graph represent infinitely many solution?
True or False
The required answer is True.
What are Graphing Systems of Linear Equations?
There exists an endless number of valid solutions for both equations if the graphs of the equations are identical.
For the given graph,
The equations are simply multiples or rearrangements of one another if graph lines meet. Every set of numbers that satisfies one of the equations also satisfies the other.
Hence, the system of the linear equation on the below graph represents infinitely many solutions and it is True.
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(2x - 5)(x-3)
Please help!!
Step-by-step explanation:
(2x - 5)(x-3)
FOIL method: multiply first, outer, inner, and last of the pairs
[tex]2x^2-6x-5x+15\\\\2x^2-11x+15[/tex]
Answer:
Step-by-step explanation:
if you have 2, 6 sided cubes and you can add any numbers to them, which numbers do you put on them so that you can display every day of the month?
Answer: its 12 and 8 10 12 14 16 either of those
Step-by-step explanation:
ITEM 14 - from the lesson Modeling with Linear Inequalities
Catherine is practicing math and science questions to prepare for her upcoming exams. It takes her 12 minutes to do a math question and 5 minutes to answer a science question.
Among the following options, which one should she choose if she wants to spend less than an hour practicing?
Hint: Set up an equation to represent the scenario. Here is how you should set your equation up.
A. 3 math questions and 5 science questions
B. 2 math questions and 7 science questions
C.5 math questions and 1 science question
D.4 math questions and 3 science questions
The option she should choose based on the given condition is Option B 2 math questions and 7 science questions.
What are linear inequalities?
When two linear expressions are compared using the inequality symbols, that is an expression of a linear inequality.
Given, Time is taken for solving single math question = 12 minutes
Time is taken for solving single science question = 5 minutes
Let 'x' be the total number of math questions and 'y' be the total number of science questions.
Then,
The total time taken for 'x' math questions = 12x minutes
The total time taken for 'y' science questions = 5y minutes
So, as defined in the question, we get
Total time she wants to spend practicing < 60 minutes
i. e. 12x + 5y < 60 .................... (i)
Now, we check this condition for each answer choice
A) x = 3 and y = 5, substituting values in equation (i)
So, 12*3 + 5*5 < 60
or, 36+25 < 60
or, 61 < 60 (Not valid)
B) x = 2 and y = 7, substituting values in equation (i)
So, 12*2 + 5*7 < 60
or, 24+35 < 60
or, 59 < 60 (Valid)
So, Option B is valid.
Hence, the required answer of choice is Option B i.e. 2 math questions and 7 science questions.
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What is the average of 17 multiple of 7?.
The average of 17 multiple of 7 is 63 average is computed by adding a set of numbers and then dividing by the total number of those numbers.
Do you mean total by average?By dividing the total number of values by the total number of numbers, the average can be computed. A mean is the mathematical average of a set of two or more data items. Common names for average include mean and mathematical mean. The term "mean" simply represents the average of the sample.
How would you define average?
The average of a list of data represents the fundamental value of a group of data mathematically. The ratio of the total number of data points to the total number of units in the list is how it is technically defined. In statistics, the term "mean" also denotes the average of a certain set of numerical data.
To calculate average=
7+14+21+28+35+42+49+56+63+70+77+84+91+98+105+112+119/17
= 1071/17
=63
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Erin recycles milk bottles, soda cans, and newspapers. If the following items are in the trash bin, what percent of the items can be recycled?
2 milk bottles, 1 banana peel, 3 newspapers, 2 soda cans, 12 apple cores
A. 35%
B. 7%
C. 100%
D. 25%
Option A. The percentage of items that can be recycled is 35%
How to solve for percentageWe are first to determine the objects that can be recycled and those that cannot be recycled.
The recyclable objects that we have here are:
milk bottles = 2
soda cans = 2
newspapers = 3
The total number of recyclables = 7
The items that can not be recycled are:
1 banana peel
12 apple cores
The total number of recyclables = 13
The total number of objects = 7 + 13 = 20
The percentage of recyclables would be 7 / 20 * 100
= 35%
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the basis for a statistical process control chart is a(the) multiple choice process capability. sampling distribution. control limit. sample range. sample mean.
The correct statement is 'the basis for a statistical process control chart is a(the) sampling distribution'
In this question, we have been given a statement.
We need to select the correct option to complete the given statement.
Given statement:
the basis for a statistical process control chart is a(the) ............
We know that statistical process control chart or graph is used to study how a process changes over time with data plotted.
A statistical process control chart is nothing but a line graph showing a measure in consecutive order, with the measure on the y-axis and time or observation number on the horizontal x-axis. The use of statistical process control chart in the monitoring and maintaining of the quality found in a sample.
Therefore, the correct statement is 'the basis for a statistical process control chart is a(the) sampling distribution'
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Patel is solving 8x2 16x 3 = 0. which steps could he use to solve the quadratic equation? select three options. 8(x2 2x 1) = â€""3 8 x = â€""1 plus or minus startroot startfraction 5 over 8 endfraction endroot x = â€""1 plus or minus startroot startfraction 4 over 8 endfraction endroot 8(x2 2x 1) = 3 1 8(x2 2x) = â€""3
Answer: 8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
Step-by-step explanation: I hope i did this right?
Answer:
A. 8(x2 + 2x + 1) = –3 + 8
B. x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
E. 8(x2 + 2x) = –3
Step-by-step explanation:
On edge 2022
Given (x – 7)2 = 36, select the values of x
Answer:
A. x = 13
B. x = 1
And the next equation answers are:
C. x = 1-5√2
D. x = 1+5√2
Step-by-step explanation:
Just took it. Edg 2020. Hope this helps :)
-5.5+10.63+(—3.7)+10.63
Answer:
12.06
Step-by-step explanation:
-5.5+10.63+(-3.7)+10.63
1) Remove parentheses.
-5.5 + 10.63 - 3.7 + 10.63
2) Simplify -5.5 + 10.63 to 5.13.
5.13 - 3.7 + 10.63
3) Simplify 5.13 - 3.7 to 1.43.
1.43 + 10.63
4) Simplify.
12.06
a political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 2% margin of error at a 90% confidence level, what size of sample is needed?
Size of sample needed to determine the percentage of people with give margin of error is equal to 1691.
As given in the question,
Margin of error = 2%
= 0.02
Sample proportion 'p' = 0.5
⇒ (1 - p) = 1 - 0.5
= 0.5
Let 'n' represents the sample size
Z- value at confidence interval 90% = 1.645
Formula used
Margin of error = z-value √ [p( 1-p)/n]
Substitute the value we get,
0.02 = 1.645 √ (0.5)(0.5)/n
Squaring on both the side
0.0004 = 2.706025 ( 0.25/n)
⇒ n = ( 2.706025 × 0.25 )/ 0.0004
⇒ n = 1691.26
⇒ n ≈ 1691
Therefore, size of sample needed with given margin of error is equal to 1691.
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(-2,-1) and (0,1) slope intercept
(stuck on it)
Slope intercept form of (-2,-1) and (0,1) is y = 3/2x +1.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
Given,
Coordinates = (-2,-1) and (0,1)
For slope:
m = y₂ - y₁/ x₂ - x₁
m = 1 + 2/0 + 2
m = 3/2
Slope intercept form:
y = mx + b
y = 3/2x +1
Slope intercept form of (-2,-1) and (0,1) is y = 3/2x +1.
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One leg of a right triangle is 8 units long, and its hypotenuse is 12 units long. What is the length of the other leg? Round to the nearest whole number.
4 units
9 units
10 units
20 units
The length of the other leg is 9 units. Therefore, option B is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, one leg of a right triangle is 8 units long, and its hypotenuse is 12 units long.
Let the length of the other leg be x.
12²=8²+x²
144=64+x²
x²=144-64
x²=80
x=√80
x=8.94
x≈9 units
Therefore, option B is the correct answer.
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Audrey and Sam divided money in the ratio of 3 to 5. Audrey obtained $36, how much money do they have altogether?
8:20 is the same as 2:5.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
= 12 + SS= (2/5)AS= (2/5)(12+S)5S = 24 + 2S3S = 24S = 24/3 = 8 = what Sam receivedA= 8+12 = 20 = what Audreyreceived8:20 is the same as 2:5divide both 8 and 20 by 4 to get the 2 to 5 ratio.hence,8:20 is the same as 2:5.
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The perimeter (adding up all the sides) of a rectangular
piece of land is 228 feet. The length of the land can be
shown by x and its width can be shown by (2x + 6).
The perimeter (adding up all the sides) of a rectangular piece of land is 228 feet. The length of the land is 74 feet and its width is 154 feet.
Define perimeter.The perimeter of a closed plane figure is referred to in geometry. You might have studied perimeter calculations in school. An equilateral triangle has a 27-foot perimeter if each of its nine sides is the same length. The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeter, meters, inches, and feet.
Given,
Perimeter = 228 feet
Length = x
Width = 2x + 6
Perimeter of rectangle = Length + Width
228 = x + 2x + 6
228 = 3x + 6
228 - 6 = 3x
222 = 3x
x = 74
The length of the land is 74 feet and its width is 154 feet.
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x+5y-3z=19
2x-3y+4z=-11
4x+y-2z=0
The solution of the system of equations is
x = -13/20 , y = 9/2 , z = 19/20
Given, a system of equations
x + 5y - 3z = 19
2x - 3y + 4z = -11
4x + y - 2z = 0
On multiplying eq (1) by 2, we get
2x + 10y - 6z = 38
On subtracting eq (1) and (2), we get
13y - 10z = 49 ... (4)
Now, On multiplying eq (2) by 2, we get
4x - 6y + 8z = -22
On subtracting eq (3) and (2), we get
7y - 10z = 22 ... (5)
Now, on subtracting eq (4) and (5), we get
6y = 27
y = 9/2
On substituting the value of y in Eq (5), we get
z = 19/20
Now, On substituting the value of y & z in Eq (1), we get
x + 5(9/2) - 3(19/20) = 19
x + 45/2 - 57/20 = 19
x + 393/20 = 19
x = -13/20
Hence, the solution of the system of equations is
x = -13/20 , y = 9/2 , z = 19/20
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make x the subject
........................................
Step-by-step explanation:
Find the attached picture
calculate the number of waffles produced if you start with 15 eggs, assuming you have enough of all other ingredients? given: 4 cups flour 6 eggs 2 tbsp oil 8 waffles
The number of waffles can be made from 15 eggs are, 20 waffles.
the waffles can be calculates as follows
4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles
we need 6 eggs to make 8 waffles
So, the waffles can we make from 15 eggs = [tex]\frac{8}{6} X 15 = 20[/tex] waffles
Hence, the number of waffles can be made from 15 eggs are 20 waffles.
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the mean of this sample is 264.4 yards. his driving distance is known to be normally distributed with a population standard deviation of 20 yards. test jean's claim that jack's driving distance is less than 275 yards at a 0.05 significance level. calculate the test statistic to 2 decimal places.
After solving, the test statistic value of z is -2.65.
In the given question,
Sample Mean x=264.4
Population standard deviation σ=20
sample size (n) = 25
significance level α=0.05
To test Jean's claim that Jack's driving distance is less than 275 yards
The null and alternative hypothesis are
H(0): μ=275
H(α): μ<275
Test Statistic Z is:
Z = (x-μ)/(σ/√n)
Z = (264.4-275)/(20/√25)
Z = -10.6/(20/5)
Z = -10.6/4
Z = -2.65
Hence, the test statistic value of z is -2.65.
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The right question is:
Jack tells Jean that his average drive of a golf ball is 275 yards. Jean is skeptical, she thinks he has overstated is driving distance and asks for substantiation. So Jack takes a random sample of 25 of his drives. The mean of this sample is 264.4 yards. His driving distance is known to be normally distributed with a population standard deviation of 20 yards. Test Jean's claim that Jack's driving distance is less than 275 yards at a 0.05 significance level. Calculate the test statistic to 2 decimal places.
A line passes through the point (5,9) and has a slope of 4. write an equation in point slope form for this line
Answer: y = 4x -11
Remeber the slope is the gradient -> m
Our equation to find the problem:
y-y1 = m(x-x1)Substitude:
y-9 = 4(x-5) because y1= 9, x1 = 5 and m = 4
y-9 = 4x - 20 multiply by 4 with the numbers in the bracets
y = 4x -11 - 9 on both sides
therfore our equation that passes through the point (5,9) and has a slope of 4 is y = 4x -11
If the area of a circle is 114 cm2, what is its circumference?
Answer: ≈ 18.91 cm
Step-by-step explanation:
r²= 114 ÷ pi/3.14 = 5700/157
r = √r²
≈ 6.025
Circumference = r × pi/3.14
≈ 18,91 cm
Please someone help me out with my math homework .
Answer:
you see that Square on the corner of B use that unit box and trace it and then go to E and Trace two unit boxes at the top
Marie will earn $15 Per hour at a new job. During training, she will earn $10 per hour.
What percent of Marie's regular hourly rate will she earn during training
The percent that Marie will earn during her training is 66.67%.
What is percentage?
Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given,
She earns working in new job = $15
She earns while training = $10
percentage she will earn during her training
= earing during training/earning during job multiplied by 100.
= 10/15(100)
=66.67%
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