ith 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:
E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.i think is the answer
Ten different numbers are written on pieces of paper and thrown into a hat. The sum of all the numbers is 205. What is the probability of selecting four numbers that have a sum greater than 82
Answer:
The probability is 40%
Step-by-step explanation:
a) There are ten pieces of paper with ten numbers
Probability of selecting four pieces of paper = 4/10 or 40%
Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%
Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.
b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes. In other words, it is a measure of the likelihood of an event (or measure of chance).
A 1-inch rise for a 16-inch run makes it easier for the wheelchair rider to ascend a ramp. How long must a ramp be to easily accommodate a 24-inch rise to the door?
Answer: The ramp must be 32 feet long. In inches, 384.
Step-by-step explanation:
For each 16 inches of run, there is one inch of rise. To get 24 inches of rise, multiply 16 by 24 to get 384 inches. To convert to a more useful measurement, convert to feet. 12 inches per foot. 384/12 = 32
Measurement is the process of assigning numbers to physical quantities and phenomena.
If a 1-inch rise for a 16-inch run makes it easier for the wheelchair rider, this can be expressed as:
1inch rise = 16-inch run
In order to determine how long must a ramp be to easily accommodate a 24-inch rise to the door, we can write:
24in rise = x
Divide both expressions:
[tex]\dfrac{1}{24}=\dfrac{16}{x}\\[/tex]
Cross multiply:
[tex]x=16 \times 24\\x=384inches[/tex]
Hence the ramp must be 384inches long in order to easily accommodate a 24-inch rise to the door.
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I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
Step-by-step explanation:
t=V100-50/4
t=V50/4=1.76≈1.8 s
when h=0
t=V100/4=10/4=2.5 s
Answer: a) (5√2)/4 ≈ 1.77 seconds
b) 5/2 = 2.5 seconds
Step-by-step explanation:
[tex]t=\dfrac{\sqrt{100-h}}{4}\\\\\\h=50\rightarrow t=\dfrac{\sqrt{100-50}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{50}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5\sqrt2}{4}}\\\\\\\\h=0\rightarrow t=\dfrac{\sqrt{100-0}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{100}}{4}\\\\\\.\qquad \qquad =\dfrac{{10}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5}{2}}[/tex]
A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is
A. 0.100
B. 0.010
C, 0.001
D. 0.002
Answer:
D. 0.002
Step-by-step explanation:
Given;
total number of sample, N = 500 elements
50 elements are to be drawn from this sample.
The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample
The probability of the first selection = 1 / 500
The probability of the first selection = 0.002
Therefore, on the first selection, the probability of an element being selected is 0.002
The correct option is "D. 0.002"
On the first selection, the probability of an element being selected is 0.002. Option D is correct.
Given information:
A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .
We want to draw a simple random sample of 50 elements.
The probability is defined as the preferred outcomes divided by the total number of samples.
So, the probability of first selection will be calculated as,
[tex]P=\dfrac{1}{500}\\P=0.002[/tex]
Therefore, on the first selection, the probability of an element being selected is 0.002.
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Identify the range of the function shown in the graph.
Answer:
B
Step-by-step explanation:
The range is all values of y. Y goes from -1 to 1. Please mark brainliest.
Answer:
see below
Step-by-step explanation:
The domain of the function is the possible x values
The domain is all real values since x can be any number
The range of the function is the possible y value
The values of y go from -1 to 1 so
-1 ≤y≤1
Q.04: (11 points) Given the polar curve r = e θ , where 0 ≤ θ ≤ 2π. Find points on the curve in the form (r, θ) where there is a horizontal or vertical tangent line. g
I suppose the curve is [tex]r(\theta)=e^\theta[/tex].
Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.
[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]
We have
[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]
[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]
[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]
[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]
The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:
[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]
[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]
(where [tex]n[/tex] is any integer)
The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:
[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]
[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]
Please answer this correctly
Answer:
12.5%
Step-by-step explanation:
There is only one number 5 from a total of 8 parts.
1 out of 8.
1/8 = 0.125
P(5) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Spinner divided in parts = 8
Number 5 = 1
P(5) = 12.5%
What is the value of - x^2 -4 x -11 if x =.3
Answer: -32
Step-by-step explanation:
I'm just going to plug in and break down the equation to make it more understandable and easier to comprehend
-(3^2) - (4*3) -11
-(9)- (12) -11
-9 - 12 - 11
-21 -11
-32
m−4+m−5 how do i solve this?
Answer:
2m-9
Step-by-step explanation:
m-4+m-5
=m+m-4-5
=2m-9
Answer:
2m-9
Step-by-step explanation:
m-4+m-5
take the like terms
= 2m-4-5
= 2m-9
Sorry if that didn't help
What is the area of the figure below 13 in length, 11 in width, 29 in and 13 in?
Answer:
B. 533in²
Step-by-step explanation:
Step 1: Find the area of the rectangle
A = lw
A = (29)13
A = 377
Step 2: Find the leg of the triangle
13 + 11 = 24
Step 3: Find the area of the triangle
A = 1/2bh
A = 1/2(24)(13)
A = 12(13)
A = 156
Step 3: Add the areas of the 2 figures together
377 + 156 = 533
Mr.Chang needs to ship 8 boxes of cookies in a packing carton. Each box is a tight rectangular prism 8 inches long, 5 inches wide, and 3 inches high. What is the volume in cubic inches, of each box?
Answer:
120 inches cubed
Step-by-step explanation:
The formula for finding the volume of a rectangular prism is length * width * height.
In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.
So multiplying all of those together gets you 120 inches cubed.
LM=9, NR=16, SR=8. Find the perimeter of △SMP.
HURRY FIRST ANSWER I WILL MARK YOU AS BRAINLILIST PROMISE
Answer:
perimeter of △SMP = 25Step-by-step explanation:
The perimeter of the triangle △SMP is the sum of al the sides of the triangle.
Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.
Given LM=9, NR=16 and SR=8
NR = NP+PR
Since NP = PR
NR = NP+NP
NR =2NP
NP = NR/2 = 16/2
NP = 8
From △LSM, NP = PR = MS = 8
Also since LM = MN, MN = 9
From △SRP, SR = RP = PS = 9
Also SR = MP = 8
From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
perimeter of △SMP = 8+8+9
perimeter of △SMP = 25
Find the intersection point for the following linear functions. f(x) = 2x + 3 g(x) = -4x − 27
Answer:
(- 5, - 7 )
Step-by-step explanation:
Equate f(x) and g(x), that is
2x + 3 = - 4x - 27 ( add 4x to both sides )
6x + 3 = - 27 ( subtract 3 from both sides )
6x = - 30 ( divide both sides by 6 )
x = - 5
Substitute x = - 5 into either of the 2 functions for y- coordinate
Substituting into f(x)
f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7
Thus point of intersection = (- 5, - 7 )
The angles of a
quadrilateral, taken in order
are y, 5y, 4y
and
2y.
Find these angles
Answer:
30, 150, 120, and 60 degrees
Step-by-step explanation:
Since the sum of the interior angles in a quadrilateral is 360 degrees:
y+5y+4y+2y=360
12y=360
y=30
2y=60, 4y=120, 5y=150
Hope this helps!
Step-by-step explanation:
y+5y+ 4y + 2y=360°(sum of a Quadrilateral)
12y=360°
divide both sides by 12
y=30°
5y=(5×30)=150°
4y=(4×30)=120°
2y=(2×30)=60°
What is 66 tens + 24 tens
Answer:
900.
Step-by-step explanation:
66 tens are 660.
and 24 tens are 240.
so, It is 900!
–9(w + 585) = –360 w = ______
Answer:
w = 15
Step-by-step explanation:
-9(w + 585) = -360w
-9w -5265 = -360w
351w = 5265
w=15
What is the solution to the system of equations?
y=-3x – 2
5x + 2y = 15
0 (-40. 19)
(-19.55)
(19-40)
(55.-19)
Answer:
Step-by-step explanation:
y = -3x - 2
5x + 2y = 15
5x + 2(-3x -2) = 15
5x -6x - 4 = 15
-x - 4 = 15
-x = 19
x = -19
y = -3(-19) - 2
y = 57 - 2
y = 55
(-19, 55)
solution is b
Graph the line y=-1/3x+2
Answer:
Graphed below.
Step-by-step explanation:
The slope of the line is -1/3.
The y-intercept is at (0, 2).
The x-intercept is at (6, 0).
Pleaseeee hheeelppp mmmeee
Answer:
A
90 degrees
anticlockwise.
Step-by-step explanation:
It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.
1 A
The center of rotation is where the 90 degree angle has its vertex. So that would be A.
1 B
Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.
1 C
The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.
Approximate the area under the curve y = x^3 from x = 2 to x = 5 using a Right Endpoint approximation with 6 subdivisions.
Answer:
182.8125
Step-by-step explanation:
Given:
y = x^3
from [2,5] using 6 subdivisions
deltax = (5 - 2)/6 = 3/6 = 0.5
hence the subdivisions are:
[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]
hence the right endpoints are:
x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5
now the area is given by:
A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]
A = 0.5*365.625
A = 182.8125
Area using Right Endpoint approximation is 182.8125
The area of the region is an illustration of definite integrals.
The approximation of the area of the region R is 182.8125
The given parameters are:
[tex]\mathbf{f(x) = x^3}[/tex]
[tex]\mathbf{Interval = [2,5]}[/tex]
[tex]\mathbf{n = 6}[/tex] ------ sub intervals
Using 6 sub intervals, we have the partitions to be:
[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]
List out the right endpoints
[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]
Calculate f(x) at these partitions
[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]
[tex]\mathbf{f(3) = 3^3 = 27}[/tex]
[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]
[tex]\mathbf{f(4) = 4^3 = 64}[/tex]
[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]
[tex]\mathbf{f(5) = 5^3 = 125}[/tex]
So, the approximated value of the definite integral is:
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]
This becomes
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]
Hence, the approximation of the area of the region R is 182.8125
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Please answer this for me!!! 25 points to whoever answers this!!!!!!
Sean, Angelina, and Sharon went to an office supply store. Sean bought 7 pencils, 8 markers, and 7 erasers. His total was $22.00. Angelina spent $19.50 buying 4 pencils, 8 markers, and 6 erasers. Sharon bought 6 pencils, 4 markers, and 7 erasers for $17.75. What is the cost of each item?
Answer:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Step-by-step explanation:
Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:
[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]
Solving the linear system:
[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]
The price of each item is:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Find the value of x in the figure
(X+5)* 90*
Answer:
x = 85 deg
Step-by-step explanation:
We can see that there are two straight lines that intersect and that the two angles given are opposite angles.
Because they are opposite angles, the two angles have the same value, i.e
(x + 5) = 90 (subtract 5 from each side)
x = 90 - 5
x = 85 deg
Find the value of x for which a ll b
Answer:
x=35
Step-by-step explanation:
Solve by quadratic Formula:
Answer:
x = 1, x = .333
Step-by-step explanation:
Answer:
x = 1 and x = 1/3
Step-by-step explanation:
Here the coefficients of this quadratic are a = 3, b = -4 and c = 1.
The discriminant is b^2 - 4ac, or (-4)^2 - 4(3)(1) = 16 - 12 = 4.
Thus, the roots are:
-(-4) ± √4 4 ± 2
x = ---------------- = ------------- => x = 1 and x = 1/3
2(3) 6
What is the best description of the transformation shown?What is the best description of the transformation shown?
Answer:
the correct answer is a reflection over the y axis
Step-by-step explanation:
The best description of the transformation shown will be;
''Reflection over the y - axis.''
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The transformation is shown in figure.
Now,
Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.
So, The best description of the transformation shown will be;
''Reflection over the y - axis.''
Thus, The best description of the transformation shown will be;
''Reflection over the y - axis.''
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A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples of 16 people ages 30 dash 40 who do not exercise regularly and 12 people ages 30 dash 40 who do exercise regularly were selected, and the resting pulse rate (in beats per minute) of each person was measured. The summary statistics are to the right. Apply the nonpooled t-interval procedure to obtain a 95% confidence interval for the difference, mu 1 minus mu 2, between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise. Assume that the requirements for using the procedure are satisfied and round to two decimal places.
Answer:
We Reject H₀ if t calculated > t tabulated
But in this case,
0.83 is not greater than 2.056
Therefore, we failed to reject H₀
There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.
Step-by-step explanation:
Refer to the attached data.
The Null and Alternate hypothesis is given by
Null hypotheses = H₀: μ₁ = μ₂
Alternate hypotheses = H₁: μ₁ ≠ μ₂
The test statistic is given by
[tex]$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } } $[/tex]
Where [tex]\bar{x}_1[/tex] is the sample mean of people who do not exercise regularly.
Where [tex]\bar{x}_2[/tex] is the sample mean of people who do exercise regularly.
Where [tex]s_1[/tex] is the sample standard deviation of people who do not exercise regularly.
Where [tex]s_2[/tex] is the sample standard deviation of people who do exercise regularly.
Where [tex]n_1[/tex] is the sample size of people who do not exercise regularly.
Where [tex]n_2[/tex] is the sample size of people who do exercise regularly.
[tex]$ t = \frac{72.7 - 69.7}{\sqrt{\frac{10.9^2}{16} + \frac{8.2^2}{12} } } $[/tex]
[tex]t = 0.83[/tex]
The given level of significance is
1 - 0.95 = 0.05
The degree of freedom is
df = 16 + 12 - 2 = 26
From the t-table, df = 26 and significance level 0.05,
t = 2.056 (two-tailed)
Conclusion:
We Reject H₀ if t calculated > t tabulated
But in this case,
0.83 is not greater than 2.056
Therefore, We failed to reject H₀
There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.
Which statements about the circle are correct? Check all that apply Arc PQ is congruent to arc SR. The measure of arc QR is 150 The circumference of circle C is cm. Arc PS measures about 13.1 cm. QS measures about 15.7 cm.
Answer:
1st 2nd 4th 5th
Select the action you would use to solve 4x = 16. Then select the property
that justifies that action.
A. Action: Divide both sides by 4.
B. Property: Multiplication property of equality.
C. Action: Multiply both sides by 4.
D. Property: Division property of equality.
E. Property: Addition property of equality.
O F. Action: Add 4 to both sides.
Answer:
A.
Step-by-step explanation:
Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.
There are two species of plants that live along the ridge line of Old Rag, which is a mountain here in Virginia. The probability of observing the first species is 0.61, while the probability of observing the second species is 0.08. The probability of observing them growing together (i.e. right next to one another) is 0.28. When you go for a hike along this ridge line, what is the probability of observing one species or the other but not both together
Answer:
0.13
Step-by-step explanation:
First let's find the probability of finding the first species or the second species:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.61 + 0.08 - 0.28
P(A or B) = 0.41
Then, to find the probability of finding one or another but not both, we just need the symmetric difference of the events, that is: P(A or B) - P(A and B):
P(A or B) - P(A and B) = 0.41 - 0.28 = 0.13
Which function is graphed below?
Answer:
Piecewise function;
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
Step-by-step explanation:
Function graphed represents the piecewise function.
1). Equation of the line with y-intercept (-2) and slope 'm'.
Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{1}[/tex]
= 2
Therefore, equation of this segment will be in the form of y = mx + b,
⇒ y = 2x - 2 where x < 2
2). Equation of a horizontal line,
y = 4 where 2 ≤ x ≤ 5
3). Equation of the third line in the interval x > 5
Let the equation of the line is,
y = mx + b
Where m = slope of the line
b = y-intercept
Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Equation of this line will be,
y = 1(x) + b
y = x + b
Since, this line passes through (5, 6),
6 = 5 + b
b = 6 - 5 = 1
Therefore, equation of this line will be,
y = x + 1 where x > 5
Graphed piecewise function is,
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5