Answer:
10626 different recital programs possible
Step-by-step explanation:
Since there is no repetition we can tackle this problem in the following manner.
Out of the 23 pieces, the pianist can choose the first one in 23 ways
Out of the remaining 22 pieces she can choose the second one in 22 different ways
Out of the remaining 21 pieces she can choose the third one in 21 different ways
So total number of ways in which 3 pieces can be played without repetition is 23 x 22 x 21 = 10,626 ways
There is a formula for this kind of situation
If there are a total of n items and you want to choose r items from this, the number of possible ways to do this without repetition is given by the formula
\(_{n}P_{r} = \dfrac{n!}{(n-r)!}\)
In this case, n = 23, r = 3 so we get
\(_{23}P_{3} = \dfrac{23!}{(23-3)!} = \dfrac{23!}{20!} = 23 \times 22 \times 21 = 10626\)
Same as the above
14. Given that 2a = 8b, find the ratio of a
to b in simplest form.
Answer:
1;4
Step-by-step explanation:
2a=8b/2
1a=4b
you cant simplify any more so this is the answer
A student solved the equation 7 = 3(t - 1) - 2(t - 3) as shown below. Assume there is a value for t that satisfies the equation. Provide a justification for each step of the solution process. LaTeX: 7\:=\:3\left(t-1\right)-2\left(t-3\right)7 = 3 ( t − 1 ) − 2 ( t − 3 ) LaTeX: 7\:=\:3t\:-3-2t\:+67 = 3 t − 3 − 2 t + 6 LaTeX: 7\:=\:t\:+37 = t + 3 Justification: ? like terms
PLEASE ANSWER!!
Answer:
t + 3
Step-by-step explanation:
Calculate the number of latex
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What is the exact distance from (8, 5) to (−1, 3)? (Round to the nearest tenth)
Answer:
About 9.2 units
Step-by-step explanation:
[8-(-1)^2]+[(5-3)^2]
81+4
sqrt(85)
9.2
Brainliest appreciated :)
Jasmine's average speed was 33 3/4 miles per hour.
How far did she travel if it took her 3 1/5 hours?
A. 79 1/2 miles
B. 89 1/2 miles
C. 98 miles
D. 108 miles
The distance travelled by Jasmine in 3 1/5 hours is 108 miles.
What is the distance travelled by Jasmine in the given time?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Speed = 33 3/4 miles per hourElapsed Time = 3 1/5 hoursDistance = ?Plug in given values into the above equation and solve for distance.
Speed = Distance / time
Distance = Speed × Time
Distance = 33 3/4 × 3 1/5
Convert to improper fraction
Distance = (33 × 4 + 3)/4 × ( 3 × 5 + 1)/5
Distance = 135/4 × 16/5
Distance = 2160 / 20
Distance = 108 miles
Therefore, the distance covered is 108 miles.
Option D) 108 miles is the correct answer.
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I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multiple of 6." What could the numbers be? Can you find 3 possible sets of numbers
Answer:
{4, 5, 6}, {64, 65, 66}, {124, 125, 126}
Step-by-step explanation:
x = 1st number
x + 1 = 2nd number
x + 2 = 3rd number
{4, 5, 6}, {64, 65, 66}, {124, 125, 126}
The possible set of numbers are {4,5,6}, {64,65,66} and {124,125,126}
What are consecutive number?Consecutive numbers are the numbers which follow each other in order from small to greater number.
Let three consecutive numbers are, x ,x+1 and x+2.
According to given condition,
The first number is a multiple of 4,
The second number is a multiple of 5,
And The second number is a multiple of 6.
Start from 4 and then try to find out sequence,
The numbers can be 4, 5 and 6.
Further, the number can be 64,65 and66
And The numbers can be 124,125 and 126
So, three sets of numbers are {4,5,6}, {64,65,66} and {124,125,126}
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HELP PLEASE 30 POINTS!!!!!!!!!
The dimensions of a rectangular piece of drawing paper are 15.5 inches and 20 inches. Carson folded the piece of paper along its diagonal. Which measurement is closest to the length of the diagonal in inches? 8.4 in. 12.6 in. 25.3 in. 35.5 in.
Answer:
25.3"
Step-by-step explanation:
use Pythagorean Theorem:
15.5² + 20² = c²
240.25 + 400 = c²
640.25 = c²
c = \(\sqrt{640.25}\) ≈ 25.3
help please find the measurements of angle W
the sum of all the angles = 180
13x-11 + 8x-9 + 30x-4 =180
51x-24 = 180
51x = 204
x=4
w= 8x-9= 8×4-9
= 2e°
Answer:
23°
Step-by-step explanation:
First, note that the sum of angles in a triangle is 180°.
So, m∠W + m∠B + m∠T = 180°
Substitute the measures.
(8x - 9) + (13x - 11) + (30x - 4) = 180
Simplify.
8x + 13x + 30x - 9 - 11 - 4 = 180
51x - 24 = 180
Add 24 to both sides.
51x = 204
Divide both sides by 51.
x = 4
Then, substitute x = 4 into m∠W
8x - 9 = 8 * 4 - 9 = 32 - 9 = 23°
So, m∠W = 23°
the manager of an online shop wants to determine whether the mean length of calling time of its customers is significantly more than 3 minutes. a random sample of 100 customers was taken. the average length of calling time in the sample was 3.1 minutes with a sample standard deviation of 0.5 minutes. at a 0.05 level of significance, it can be concluded that the mean of the population is:
The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level.
not significantly more than 3 minutes.
The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.
1. The null hypothesis is that the population mean is equal to 3 minutes.
2. A sample of 100 customers was taken, with an average length of calling time of 3.1 minutes and a sample standard deviation of 0.5 minutes.
3. The p-value from the sample data is 0.28, which is higher than the 0.05 significance level.
4. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.
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A company determined that the budgeted cost of producing a product is $30 per unit. On June 1, there were 84000 units on hand, the sales department budgeted sales of 350000 units in June, and the company desires to have 130000 units on hand on June 30. The budgeted cost of goods sold for June would be
Answer:
The budgeted cost of goods sold in June is $ 10,500,000
Step-by-step explanation:
In order to determine the budgeted cost of goods sold,we need to first and foremost establish goods sold in quantity terms as follows:
goods sold=opening stock+goods produced-closing stock
goods produced=sales-opening stock+closing stock
goods produced=350,000-84,000+130,000=396,000
goods sold=84,000+396,000 -130,000=350000
The cost of producing one unit is $30
costs of goods sold=goods sold*production cost per unit=$30*350000 =
$ 10,500,000.00
Alternatively:
sales units *unit cost of production=$30*350,000=$ 10,500,000.00
ali needs to solve the equation x^2 + 6x + 22 = 0 by completing the square. which pair of steps is the most efficient way to begin?
a. x^2 + 6x + 9 = -22 + 9
b. x^2 + 6x + 36 = -22 + 36
c. x^2 + 6x + 3 = -22 + 3
d. x^2 + 6x + 81 = -22 + 81
Answer:
a. x² + 6x + 9 = -22 + 9
Step-by-step explanation:
they moved the 22 to the right by subtracting it. this leaves a binomial on the left side, which if what you want to solve it.
then they completed the square by dividing b (6) by 2 = 3. then squaring 3 to get 9.
if you added 9 to the left, then you have to add 9 to the right, therefore resulting in -22 + 9.
Answer:
In TTM/Imagine Math it is top left or a.
Step-by-step explanation:
Perform the indicated operations and simplify.
(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)
Let's simplify the expression step by step: Expand the squared term:
(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²
Expand the second term:
3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)
Expand the third term:
x(3x + 4y + 3) = 3x² + 4xy + 3x
Now, let's combine all the expanded terms:
(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)
= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x
Combining like terms:
= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x
= 7x² - 5xy + 5y² + 3x
The simplified form of the expression is 7x² - 5xy + 5y² + 3x.
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What is 0.48 written as a fraction in lowest terms?
I need so much help
Answer:
12/25
Step-by-step explanation:
Convert .48 to a fraction (48/100)The GCF of 48 and 100 is 4. Divide 48 and 100 by 4. You will get 12/25.Julie takes a rectangular piece of fabric and cuts from one corner to the opposite corner. If the piece of fabric is 9 inches long and 4 inches wide, how long is the diagonal cut that Julie made?
The length of the diagonal cut that Julie made on the rectangular piece of fabric is approximately 9.85 inches.
To find the length of the diagonal cut that Julie made on the rectangular piece of fabric, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length and width of the fabric form the two sides of a right triangle, with the diagonal cut being the hypotenuse.
Given that the fabric is 9 inches long and 4 inches wide, we can label the length as the base (b) and the width as the height (h) of the right triangle.
Using the Pythagorean theorem, we have:
hypotenuse^2 = base^2 + height^2
Let's substitute the values into the equation:
hypotenuse^2 \(= 9^2 + 4^2\)
hypotenuse^2 = 81 + 16
hypotenuse^2 = 97
To find the length of the hypotenuse (diagonal cut), we need to take the square root of both sides:
hypotenuse = √97
Calculating the square root of 97 gives approximately 9.85.
Therefore, the length of the diagonal cut that Julie made on the rectangular piece of fabric is approximately 9.85 inches.
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Anona hires a decorator to redecorate her bedroom. The decorator offers her 2 different plans: the basic plan has
x wall-color options, x + 1 ceiling-color options, and x + 3 flooring options. The gold plan offers all of the basic plan
offerings, plus 3 additional options in each category.
If a layout includes a wall color, ceiling color, and flooring, which option correctly shows the comparison between the
total number of unique layouts offered by the basic and gold plans?
O 3x +4 < 3x +11
Ox3+4x2 + 3x < 6x + 42x2 + 72
Ox+4
Ox3+4x² + 3x < x + 13.x2 + 54x + 72
>
Answer:
The correct option is;
x³ + 4·x² + 3·x < x³ + 13·x² + 54·x + 72.
Step-by-step explanation:
The given parameters are;
The basic plan of the decorator = x wall-color options, x + 1 ceiling-colr options, and x + 3 floor options
The gold plan of the decorator = All of the basic plan options plus 3 additional options in each category
Therefore, the gold plan of the decorator = (x + 3) wall-color options, (x + 1 + 3) ceiling-color options, and (x + 3 + 3) floor options
The total number unique layouts offered by the basic plan = x × (x + 1) × (x + 3) = x³ + 4·x² + 3·x
Also, the total number unique layouts offered by the gold plan = (x + 3) × (x + 1 + 3) × (x + 3 + 3) = (x + 3) × (x + 4) × (x + 6) = x³ + 13·x² + 54·x + 72
Which gives;
The comparison between the total number of unique layouts offered by the basic and gold plans as x³ + 4·x² + 3·x < x³ + 13·x² + 54·x + 72.
For which pairs of functions is (f circle g) (x)?
f (x) = x squared and g (x) = StartFraction 1 Over x EndFraction
f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction
f (x) = StartFraction x minus 2 Over 3 EndFraction and g (x) = 2 minus 3 x
f (x) = one-half x minus 2 and g (x) = one-half x + 2
Answer:
2-241x
Step-by-step explanation:
Solve for x.
Answer Choices:
7
8
9
-11
Answer:
x = -11
Step-by-step explanation:
Well the two equations add up to 180 because they are a linear pair.
x + 56 + x + 146 = 180 (collect like terms)
2x + 202 = 180 (subtract 202 on both sides)
2x = -22 (divide by 2 on both sides)
x = -11
Hope this helps ya!!
x(x+7)=0
Please help
Answer:
x = 0 , x = - 7
Step-by-step explanation:
x(x + 7) = 0
equate each factor to zero and solve for x
x = 0
x + 7 = 0 ⇒ x = - 7
Sam bought a teddy bear for $3.75 and a stuffed unicorn for $7.50. He gave the cashier $20. How much change did he receive? *
Answer:
3.75+7.5 = 11.25
20 dollars in total how much change.
20 - 11.25 = 8.75
$8.75 change
i’m stuck on how to work this out , please help.
The value of x in the expression is 3 / 2.
How to find the quotient in an expression?The value of x in the expression can be found as follows:
Therefore, the quotient rule can be used to find the value of quotient x in the expression as follows:
q⁵ × q²ˣ = q¹⁰ × q⁶ / q⁸
Using the quotient rule
\(A^{x} X A^{y} = A^{x + y}\)
Therefore,
q⁵ × q²ˣ = q¹⁰ × q⁶ / q⁸
q⁵⁺²ˣ = q¹⁶ / q⁸
q⁵⁺²ˣ = q⁸
cancel the base
5 + 2x = 8
2x = 8 - 5
2x = 3
divide both sides of the equation by 2
x = 3 / 2
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Do arthetic sequence have a common ratio?
Answer:
yes
Step-by-step explanation:
its called the common ratio because it is the same to each number or common and it also is the ratio between two consecutive numbers in the sequence
Answer:
points
Step-by-step explanation:
"x = 8
When there's a root, raise both sides to the root number
(₃√x)³=2³
x = 8" How do you solve 3√x = 2?
Answer:
x = \(\frac{4}{9}\)
Step-by-step explanation:
3\(\sqrt{x}\) = 2 ( divide both sides by 3 )
\(\sqrt{x}\) = \(\frac{2}{3}\) ( square both sides )
(\(\sqrt{x}\) )² = (\(\frac{2}{3}\) )²
x = \(\frac{2^2}{3^2}\)
x = \(\frac{4}{9}\)
What is the area of the figure?
Answer: I would say it is 66cm
Step-by-step explanation:
You would do 5.5cm*12cm which would equal 66cm
Brainliest pls:)
To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.
\(\sqrt{x} 10 greater than, less than, or equal to 3\)
The square root of 10 will be greater than 3.
What is square root of a number?The square root of a number is the value which when multiplied by itself results into the number. Mathematically -
n = x²
then -
x = \(\sqrt{n}\)
Given are two numbers as -
\(\sqrt{10}\) and 3.
Now, the square root of 10 will be 3.16 (approx.)
On comparing the square root of 10 with 3, we can clearly see that the square root of 10 will be greater than 3. Mathematically -
\(\sqrt{10}\) > 3.
Therefore, we can conclude that the square root of 10 will be greater than 3.
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andy sets out to cycle from delhi to rohtak and at the same time, ben starts from rohtak to cycdle to delhi. ater passing each other they completed their journey in (13/3) hours and (52/3) hours respectively. at what rate does ben cycles, if andy cycles at 12 kmph?
The rate at which Ben cycles, if Andy cycles at 12 kmph is 48 kmph.
The formula for finding the rate at which Ben cycles, if Andy cycles at 12 kmph, is given by:
Ben's rate = Andy's rate x Time taken by Ben ÷ Time taken by Andy
Therefore, Ben's rate = 12 kmph x (52/3) hours ÷ (13/3) hours
Ben's rate = 48 kmph
To calculate Ben's rate, we first need to calculate the time taken by each of them. Andy sets out to cycle from Delhi to Rohtak, and Ben starts from Rohtak to cycle to Delhi. After passing each other, they completed their journey in (13/3) hours and (52/3) hours respectively.
We can calculate the rate at which Ben cycles as follows:
Calculate the time taken by each of them.
Time taken by Andy = 13/3 hours
Time taken by Ben = 52/3 hours
Calculate Ben's rate using the formula given above.
Ben's rate = 12 kmph x (52/3) hours ÷ (13/3) hours
Ben's rate = 48 kmph
Therefore, the rate at which Ben cycles, if Andy cycles at 12 kmph is 48 kmph.
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Suppose a political advisor is interested in the proportion of the vote an opponent will receive. If he samples voters randomly and tests hypotheses regarding p, the population proportion, what should he do to reduce his risk of making a Type II error
This will increase the probability of rejecting a false null hypothesis and accepting a true alternative hypothesis.The political advisor should ensure proper sampling, increase the alpha level, and have a larger sample size to reduce the risk of making a Type II error. A type II error is when a null hypothesis is accepted when it is false.
Suppose a political advisor is interested in the proportion of the vote an opponent will receive. If he samples voters randomly and tests hypotheses regarding p, the population proportion, he should do the following to reduce his risk of making a Type II error:To reduce the risk of making a Type II error, a political advisor interested in the proportion of the vote an opponent will receive, if he samples voters randomly and tests hypotheses regarding p, the population proportion should ensure that he has a larger sample size for testing. A larger sample size can help in making his results statistically significant and that the results are a true representation of the population.Proper sampling can also help to reduce the risk of a Type II error. Random sampling of the voters ensures that there is no bias in the selection process, which can skew the results. A random sample of voters is a fair representation of the population, and results obtained from a random sample are more likely to be accurate. This reduces the likelihood of a Type II error.The advisor should also increase the alpha level to reduce the risk of a Type II error. By increasing the alpha level, he is lowering the rejection region, which will reduce the likelihood of a Type II error. This will increase the probability of rejecting a false null hypothesis and accepting a true alternative hypothesis.The political advisor should ensure proper sampling, increase the alpha level, and have a larger sample size to reduce the risk of making a Type II error. A type II error is when a null hypothesis is accepted when it is false.
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The ratio of dogs to cats at a local animal shelter is 13/25. Which statement must be true.
for every 13 dogs, there are 25 cats. is the answer.
In parallelogram ABCD, AB is three more than twice the measure of BC. If the perimeter of the parallelogram is 18 units and all angles are right. Calculate the measure of BD.
The value of line BD in parallelogram ABCD is 2units
What is a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. The Sum of all the interior angles of a parallelogram equals 360 degrees.
The perimeter of a parallelogram is 2(l+w)
if BD is x
AB = 3+2x
P= 2(3+2x+x)
18= 2(3+3x)
divide both sides by
9= 3+3x
subtract 3 fromboth sides
6= 3x
x = 2units
therefore BD= 2units.
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Can anyone help? It’s due in the morning
21) Angle 4
Angle 5
Angle GVH
Angle GVI
Angle HVI
22) Area of parallelogram = \(bh\)
A = 9 × 4 = \(36mi^2\)
23) Area of a triangle = \(\frac{1}{2} bh\)
A = \(\frac{1}{2} (12)(7.3)\)
A = \(43.8m^2\)
24) Distance between each pair of point:
Distance between two points = \(\sqrt{(x_{B}-x_{A} )^2+(y_{B}-y_{A} )}\)
Add the values in the formula & solve:
\(=\sqrt{(-2-0)^2+(2--4)^2}\)
\(=\sqrt{(-2)^2+6^2}\)
\(=\sqrt{4+36}\)
\(=\sqrt{40}=6.3246\)
25) Midpoint \((x_{M},y_{M} )=(\frac{x_{A} -x_{B} } {2} ,\frac{y_{A}+y_{B} }{2} )\)
\(=(\frac{10+0}{2},\frac{6+7}{2} )\)
\(=(\frac{10}{2} ,\frac{13}{2} )\)
Midpoint of a line segment \((x_{M},y_{M} )=(5,6.5)\)
I hope this helps....
How many nets are there for a triangular pyramid?
The net of a triangular pyramid consist of a total of 4 triangles. it has 4 faces with the base being one of them which is also in the shape of a triangle.
A net of the triangular pyramid is the pattern formed when the surface of it is laid out flat showing each triangular face of the figure, therefore we know that the net of a triangular pyramid consist of a total of 4 triangles.
Triangular pyramid is a pyramid which has a triangular base. In geometry, vertices are essentially corners. All triangular-based pyramids, either regular or irregular, have four vertices.
It has 6 edges, 4 faces, 4 vertices.
A regular triangular pyramid has equilateral triangles all four faces
To learn more about triangular pyramids, click here:
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Help me pleaseeeeeeeeeee
Answer:
Part A: 2m/1s
Part B: 7m/6s or 5m/2s (I'm new to this as well)
Part C: 0m/1s
Part B is the fastest because the slope is the steepest and Part C is the slowest because there's no speed happening; it's at rest.
Step-by-step explanation: