Suppose we want to choose 4 objects, without replacement, from 17 distinct objects.
(a) How many ways can this be done, if the order of the choices is taken into consideration?
(b) How many ways can this be done, if the order of the choices is not taken into consideration?
Answers
a) If we select without taking the order into consideration there are 2380.
b) If we take the order into consideration, we have 57120 ways
What is selection?We talk about the selection when we are talking about how a material can be chosen in the midst of many other materials that we have. In this case we are told that we want to choose 4 objects, without replacement, from 17 distinct objects.
If the order is not important then we need to do a combination and we have;
n!/r! (n - r)!
17!/4!(17 - 4)!
17 * 16 * 15 * 14 * 13!/4! * 13!
= 57120/24
= 2380
If we are looking at the order we have;
n!/(n-r)!
17!/(17 - 4)!
17 * 16 * 15 * 14 * 13!/13!
= 17 * 16 * 15 * 14
= 57120
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Related Questions
Calculate the lateral surface area of the cylinder below. Use 3.14 for pi.
Answers
Answer:
Step-by-step explanation:
Area = 2\(\pi\)rh
=> 2 * 3.14 * 2 * 9
=> 6.28 * 18
=> 113.04Please mark as brainliest for future answers :)
3(x + 5) + 2(x – 4)
thank you if you answer this question
Answers
Answer:
5x + 7
Step-by-step explanation:
Distribute 3x + 15 + 2x - 8
Combine like-terms 5x + 7
Answer:
5x + 7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
3(x + 5) + 2(x - 4)
Step 2: Simplify
Distribute: 3x + 15 + 2x - 8Combine like terms (x): 5x + 15 - 8Combine like terms (Z): 5x + 7A person leaves home and walks 4 miles west, then 5 miles southwest.
How far from home is she?
miles
In what direction must she walk to head directly home?
degrees North of East
Answers
The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.
To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).
To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).
To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.
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An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.
to close the expansionary gap, the government would need to increase or decrease spending by $ billion.
Answers
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
To close the expansionary gap, the government would need to decrease spending by $100 billion.
The formula to calculate the change in equilibrium output due to a change in government spending is:
∆Y = (∆G / (1 - MPC))
Where:
∆Y = change in equilibrium output
∆G = change in government spending
MPC = marginal propensity to consume
Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).
Given that MPC = 3/4, we can plug in the values into the formula:
400 = (∆G / (1 - 3/4))
∆G = (1 - 3/4) * 400
∆G = (1/4) * 400
∆G = 100
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
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evaluate each expression and give the answer in both rectangular and polar form. in all cases, assume that z1=-4+j3 and z2= 1-j. (a) z1, (b) z2, (c) z1 +z2, (d) jz2, (e) z1 (-1)=1/z1, (f)z1/z2, (g) ez2, (h) z1z1, (i) z1z2
Answers
The rectangular form of z1 is -4 + j3 and the polar form is 5∠153°. The rectangular form of z2 is 1 - j and the polar form is √2∠-45°. The other expressions have similar rectangular and polar forms.
The rectangular form of complex numbers is represented by two coordinates, one real, and one imaginary. The polar form of complex numbers is represented by the magnitude and angle of the number.
In the expression (a), z1 = -4 + j3; the rectangular form is -4 + j3, and the polar form is 5∠153°. In the expression (b), z2 = 1 - j; the rectangular form is 1 - j, and the polar form is √2∠-45°.
In the expression (c), z1 + z2 = -3 + 2j; the rectangular form is -3 + 2j, and the polar form is 2.82∠29.14°. In the expression (d), jz2 = j(1 - j); the rectangular form is j(1 - j) and the polar form is 1∠-135°.
In the expression (e), z1(-1) = 1/z1; the rectangular form is 1/z1, and the polar form is 0.25∠-33.7°. In the expression (f), z1/z2 = (-4+j3)/(1-j); the rectangular form is (-4+j3)/(1-j), and the polar form is 2.24∠-118.4°.
In the expression (g), ez2 = e(1 - j); the rectangular form is e(1 - j), and the polar form is 2.72∠-44.99°. In the expression (h), z1z1 = (-4+j3)(-4+j3); the rectangular form is (-4+j3)(-4+j3), and the polar form is 25∠306°.
In the expression (i), z1z2 = (-4+j3)(1-j); the rectangular form is (-4+j3)(1-j), and the polar form is 7∠-96.6°.
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Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1
Answers
Answer:
Step-by-step explanation:
If you plot the focus and the directrix you see that the focus is above the directrix. Since a parabola always wraps itself around the focus, this parabola opens upwards and has the standard form equation:
\((x-h)^2=4p(y-k)\) where h and k are the coordinates of the vertex and p is the number of units between the vertex and the focus, or the vertex and the directrix. This number of units will be the same for both since the vertex is smack dab inbetween the focus and the directrix. The focus is also on the axis of symmetry, which means that it shares the x coordinate with the vertex (which is actually the h coordinate) of -5. Halfway between the y value of 5 and the y value of -1 is 2. So the vertex is located at (-5, 2). The number of units between the vertex and the focus is 3, so the equation is:
\((x+5)^2=4(3)(y-2)\) and simplify a bit to
\((x+5)^2=12(y-2)\)
I'm not sure how far down you need to simplify that. Taking it a few steps further gives you:
\(\frac{1}{12}(x+5)^2=y-2\) and then to
\(\frac{1}{12}(x+5)^2+2=y\)
It all depends upon the form you're being asked for.
Describe the symmetry if these functions
Answers
Answer:
see the attachment.
i hope this can help you!
10k - 60 = 180
solve for k
Answers
Answer:
K=24
Step-by-step explanation:
Add 60 on both sides
10k=240
Now divide 10 on both sides
240/10=24
10/10k=k
k=24
if i have 789.4 and my mom has 449.7 how much will we both have
Answers
Answer:
1239.1
Step-by-step explanation:
x + y = z
x = 789.4 (your money)
y = 449.7 (Your mom's money)
z = Total amount of money.
789.4 + 449.7 = z
789.4 + 449.7 = 1239.1
z = 1239.1
Which equation can be used to solve for x in the
following diagram?
(3x + 12)
Choose 1 answer:
3x + 12) + x = 180
(3x + 12) = x
3x = 180 + x
(3x + 12) + x = 90
Answers
The expression used to solve for x will be 3x + 12) + x = 180. The correct option is A.
What is the supplementary angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet. The angles having the sum of 180 degrees will be called supplementary angles.
Given that there are two angles one is 3x + 12 and the other is x separated by the inclined line on the horizontal line.
From the supplementary angle property, the sum of the two angles is equal to 180 degree.
3x + 12 + x = 180
Therefore, the expression used to solve for x will be 3x + 12) + x = 180.
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Mary lost 30 pounds. Before her diet she weighed 180 pounds. What is the percent of change?
Answers
Answer:
1.6%
Step-by-step explanation:
30/180 ?/100 30*100=300
300/180=1.6
DHL makes deliveries of a large number of products to its customers. Suppose it is known that 85% of all the orders it receives from its customers are delivered on time. Suppose a random sample of 100 orders are selected;
A. What is the mean and standard error of the sampling distributions of sample proportions in this example?
B. What is the shape of the sampling distribution of the sample proportions?
C. What is the likelihood the sample proportion of orders delivered on time will be less than 0.87?
D. The central 68.26% of the sample proportions are between which two sample proportions?
Answers
A. The mean of the sampling distribution is 0.85 (85%), and the standard error is approximately 0.085.
B. Since the sample size is 100, we can assume that the shape of the sampling distribution of the sample proportions is approximately normal.
C. The likelihood that the sample proportion of orders delivered on time will be less than 0.87 is approximately 59.07%.
D, The central 68.26% of the sample proportions are between 0.765 and 0.935.
To calculate the mean and standard error of the sampling distribution of sample proportions, we can use the following formulas:
Mean (μ) = p
= 85%
= 0.85
Standard Error (SE) = √[(p × (1 - p)) / n]
Where p is the population proportion (0.85) and n is the sample size (100).
Calculating the standard error:
SE = √[(0.85 × (1 - 0.85)) / 100]
SE = √[(0.7225) / 100]
SE = √[0.007225]
SE ≈ 0.085
The sampling distribution of sample proportions can be approximated by a normal distribution when the sample size is sufficiently large (central limit theorem).
To find the likelihood that the sample proportion of orders delivered on time will be less than 0.87, we need to calculate the z-score and refer to the standard normal distribution table.
First, we calculate the z-score:
z = (sample proportion - population proportion) / standard error
z = (0.87 - 0.85) / 0.085
z ≈ 0.02 / 0.085
z ≈ 0.235
Next, we look up the probability associated with the z-score of 0.235 in the standard normal distribution table.
The probability corresponds to the area to the left of the z-score.
Using the table, the probability is approximately 0.5907 or 59.07%.
The central 68.26% of the sample proportions are located within one standard deviation from the mean in a normal distribution.
To find the sample proportions that correspond to the central 68.26%, we can calculate the boundaries as follows:
Lower boundary: mean - standard deviation
Lower boundary = 0.85 - 0.085
Lower boundary = 0.765
Upper boundary: mean + standard deviation
Upper boundary = 0.85 + 0.085
Upper boundary = 0.935
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If f(x)=34x+56 , what is f(12)?
Answers
Answer:
f(x)= 34x +56 34(12) +56=464
Step-by-step explanation:
Find the sum of the first 274 natural numbers.
Answers
Answer:
37675
Step-by-step explanation:
ummm what is did was
274/2 = 137
and then times that by 275
because
274+1 = 275
273+2 = 275
...
137+137 = 275
so the ans is 137(275) which is equal to 37675
Find the 70th term of the arithmetic sequence 29, 17, 5
Answers
Answer:
857
Step-by-step explanation:
70th term = a + d(n-1)
d= 29-17=12
a=29
n-1 = 69
70th term = 29 + 12×69
= 29 + 828
= 857
helpppp...........................
Answers
Answer:
see explanation
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
a hexagon has 6 sides , then
sum = 180° × (6 - 2) = 180° × 4 = 720°
12
the polygon has 5 sides , so
sum = 180° × (5 - 2) = 180° × 3 = 540°
sum the interior angles and equate to 540
y + 90 + 120 + 90 + 110 = 540
y + 410 = 540 ( subtract 410 from both sides )
y = 130
13
the polygon has 7 sides , so
sum = 180° × (7 - 2) = 180° × 5 = 900°
sum the interior angles and equate to 900
p + 90 + 141 + 130 + 136 + 123 + 140 = 900
p + 760 = 900 ( subtract 760 from both sides )
p = 140
Marked angle 3 different ways
Answers
Answer:
where are question I don't understand this question
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answers
Answer:
154.2
Step-by-step explanation:
143 plus
156 plus
172 plus
133 plus
167 = 771
divide by 5 equals 154.2
What is the Measure of angle AOE in the figure below?
Answers
Answer:
The answer is D: 130
Step-by-step explanation:
(3x-28) +90+(66-x) = 180
2x + 128 = 180
2x = 52
x = 26
Therefore Angle AOE = 90 + (66-26)
= 130
Convert:
150 oz =
Lb
OZ
Answers
Answer:
9.375
Step-by-step explanation:
Answer:
9.375
Step-by-step explanation:
divide the mass value by 16.
150 / 16 = 9.375
1)
Science 5
Measurement Assignment
Name each measurement instrument below. Then, indicate which
type of measurement is performed with each one. Remember,
some instruments can be used for more than one type of
measurement!
Instrument
Name of Instrument
Measurement Type
Answers
Answer: See below
Step-by-step explanation:
The first is a beaker, it's used to measure liquid volume
The second is a ruler, it's used to measure length.
Last is a thermometer, it's used to measure temperature.
Rick invest $5,830 into a retirement saving account. The account compounds at 3.2% monthly for. How much money will Rick have in 4 years? Show work. Use comma and dollar signs in the final answer.
Answers
Answer:
$746.24
Step-by-step explanation:
3.2/100 = 0.032
5,830 X 4 = 23,320
23,320 X 0.032 = 746.24
A couple purchased a home for $225,000. At the end of each year the home increases in value by 3%.
What is the value of the home after the tenth year?
Answers
\(\\ \sf\longmapsto I=\dfrac{PRT}{100}\)
\(\\ \sf\longmapsto I=\dfrac{225000(3)(10)}{100}\)
\(\\ \sf\longmapsto I=22500(3)\)
\(\\ \sf\longmapsto I=67500\)
The value of the home after the tenth year is 67500.
To find the value of the home after the tenth year?
What is simple interest?Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Given that:
Principal=P=$225000
Rate of interest=R=3%
Time=10 year
By the use of formula:
\(I=\frac{PRT}{100}\)
\(I=\frac{225000*3*10}{100} \\\\I=22500*3\\\\I=67500\)
So, the value of the home after the tenth year is 67500.
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PLEASE HELP ASAP ILL GIVE BRAINLY!!!
(a) Write the quadratic regression equation that models the data. Let x = time in seconds
and let y = height in feet. Round all numbers to the nearest hundredth. (b) Use the equation to estimate the height of rocket after Show your work. 3 seconds
Answers
(a) A quadratic equation is in the form: y = -12.87x² + 42.22x + 1.18
(b) The height of the rocket after 3 seconds would be 12.01 feet.
What is a quadratic equation?A quadratic equation is a polynomial equation with a maximum degree of two. Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation.
Here, we have
Given: A rocket is launched upwards from the ground.
(a) A quadratic equation is in the form:
y = -12.87x² + 42.22x + 1.18
(b) When x = 3 seconds
y = -12.87(3)² + 42.22(3) + 1.18
y = 12.01 feet
Hence, the height of the rocket after 3 seconds is 12.01 feet.
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Help me please the best answer will get a crown
Answers
Answer:
is super easy Step-by-step explanation Do you?
I'LL MARK THE BRAINLIEST
The diameter of a circle is 10 3/4 inches.
What is the radius, r, of the circle?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
Answer: The radius of the circle is 5 3/8 inches.
Step-by-step explanation:
The radius of the circle is half of the diameter. We can start by converting the mixed number diameter to an improper fraction:
10 3/4 = (10 × 4 + 3)/4 = 43/4
So, the diameter of the circle is 43/4 inches. The radius is half of this, which we can find by dividing by 2:
r = (43/4) ÷ 2 = 43/8
To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 1:
r = 43/8 = 5 3/8
Therefore, the radius of the circle is 5 3/8 inches.
Answer:5 3/4
Step-by-step explanation:
10 3/4 * 1/2
1/2 * 43/4 = 43/8
8/43=5 3/4
A large brick oven takes 64 minutes to cook 16 pizzas. How long would it take to cook two pizzas?
Answers
Answer:
It would take 8 minutes to cook 2 pizzas in a brick oven.
Step-by-step explanation:
Answer:
It would take 8 minutes to cook 2 pizzas in a brick oven.
7) AC = x, BC= 2x - 18, and AB = 4. Find AC.
Answers
We get the length of AC as 14 units when we have AC = x, BC = 2 x - 18 and AB = 4 units.
We are given that the length of AB = 4.
We are also given the expressions:
AC = x and BC = 2 x - 18
We need to find the value of AC
We know that:
AB + BC = AC
Substituting he values, we get that:
4 + 2 x - 18 = x
Combining the like terms, we get that:
2 x - 14 = x
2 x - x = 14
x = 14
So, we get that,
AC = x
AC = 14 units.
Therefore, we get the length of AC as 14 units when we have AC = x, BC = 2 x - 18 and AB = 4 units.
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Please help! Brainiest will be given for correct answers only.
Answers
Answer:
see below
Step-by-step explanation:
x^2 + 10x+25 =0
This is the sum of squares
(x+5)^2 =0
x = -5 one solution
x^2 +5x = 0
x(x+5) = 0
x=0 x=-5 two solutions
x^2 -10x +25 = 0
This is the difference of squares
(x-5)^2 = 0
x=5 one solution
x^2 -25 =0
x^2 = 25
x = ±5 two solutions
\(\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}\)
\( x^2+10x+25=0\\\\(x)^2+2.x.5+(5)^2\\\\(x+5)^2 \)
one solution\(x^2+5x=0\\\\x(x+5)=0\\\\x=0,x+5=0 \)
two solution\(x^2-10x+25=0\\\\(x)^2-2.x.5+(5)^2\\\\(x-5)^2\)
one solution\(x^2-25=0\\\\x^2=25\\\\x= \binom{ + }{ - }5 \)
two solutionplease help me.. I don't understand what it is..
Answers
9514 1404 393
Answer:
22.6
Step-by-step explanation:
The diagonal of the square is they hypotenuse of an isosceles right triangle with sides of 16 inches. The Pythagorean theorem tells you its length (d) is ...
d^2 = 16^2 +16^2 = (16^2)(2)
Taking the square root, we have ...
d = 16√2 ≈ 22.6 . . . . inches