Answer:
P(1, B) = 1/12
Step-by-step explanation:
if given one group of 3 objects, in this case tennis balls labeled 1, 2, and 3. And another group of 4 objects, labeled a, b, c, and d. the combined probability would be 1/3 * 1/4 = 1/12. This is because there is a 1/3 chance of picking one particular object from a set of 3 total objects, and a 1/4 chance of picking one particular object from a set of 4 total objects.
The probability of drawing 1 numbered ball in the first attempt and then drawing B numbered ball in the second attempt is 1/42.
What is conditional probability ?Conditional probability is when occurrence of an event depends upon the occurrence of another event.In case of without replacement one event is dependent on another.
According to the given question
Steven has one bag that contains three table tennis balls numbered 1, 2, and 3. He also has a second bag that contains four table tennis balls lettered A, B, C, and D and Steven combined the table tennis balls into one large bag instead of two individual bags.
Here we don't need to find the probabilities individual bags.
So after he combined them into one large bag there are 7 balls in that large bag namely 1, 2, 3, A, B, C, D
P(1) = 1/7
with without replacement there is now 6 balls in the large bag
∴ p(B) = 1/6
So the probability of drawing 1 numbered ball in the first attempt and then B numbered ball in the second attempt is p(1)p(B)
∴P(1,B) is
= (1/7)×(1/6)
= 1/42.
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(2x)4 written without exponents
Answer:
(2x)(2x)(2x)(2x)
Step-by-step explanation:
I assume the 4 is an exponent.
(2x)^4 = (2x)(2x)(2x)(2x)
what is 2(4 – 16) – (–30)
FIll in the blank to make the equation true: (−8−4)÷[]=−6
Answer:
2
Step-by-step explanation:
-8-4/x= -6
multiply x to both sides of the equation.
-8-4= -6x
solve -8-4. (-12)
-12= -6x
divide both sides by -6.
2=x
5/8x3/5
help please
Answer:
3/8
Step-by-step explanation:
reduce the numbers with the greates componentes factor. 5 and then calculate the product
Consider the region bounded by the curves y=x2 and y=9. Find the volume of the solid formed when this region is rotated around the x-axis.
Answer:
V = 36Π cubic Centimetres
Step-by-step explanation:
Step(i):-
Volume of the solid
The Volume of the solid formed by revolving the region bounded by the curve y = f(x) and rotated around the x-axis defined by
[tex]V = \pi \int\limits^a_b {[f(x)]^{2} } \, d x[/tex]
Step(ii):-
Given two curves are y = x² and y = 9
The point of intersection of two curves
y = x²...(i)
and y = 9 ...(ii)
Equating both equations , we get
x² - 9 =0
⇒ x² - 3² =0
⇒ (x+3)(x-3) =0
⇒ x+3=0 and x-3=0
x = 3 ⇒ y = 9
x = -3 ⇒y = 9
The point of intersection ( -3,9) and (3,9)
Step(iii):-
[tex]V = \pi \int\limits^a_b {[(f(x)]^{2} } \, -[g(x)]^{2})d x[/tex]
The limits x- varies from -3 to 3
[tex]V =\pi (\int\limits^3_3 {x^{2} } \, dx +\int\limits^3_3{9} \, dx[/tex]
[tex]V =\pi (\frac{x^{3} }{3} -9 x)^{3} _{-3}[/tex]
[tex]V= \pi ( \frac{27}{3} - 9(3) - (\frac{-27}{3} -9(-3))[/tex]
V = π ( |-36| = 36Π cubic Centimetres
Final answer:-
The volume of the solid
V = π ( |-36| = 36Π cubic Centimetres
The following boxplot is of the birth weights (in ounces) of 160 infants born in a local hospital The following boxplot is of the birth weights (in ounces) of 160 infants born in a local hospital
About 40 of the birth weights were below?
A) 92 ounces B) 102 ounces C) 112 ounces D) 122 ounces
This question is Incomplete because it lacks the diagram of the box plot. Please find attached the diagram of the box plot
Answer:
B) 102 ounces
Step-by-step explanation:
Looking at the attached diagram, we can see the box plot it divided into different segment
The median weight of the babies = 110 ounces
The maximum weight of the babies is between = 140 and 130, approximately let's say 135 ounces
The minimum weight is 80 ounces
Then the box in the middle is divided into 3
It has the First Quartile
Median
And third Quartile
Since we have 160 infants born in the local hospital, about 40 of the birthweights we fall into
= 40/160 = 1/4
1/4 represents the first Quartile
Looking at the box plot, 40 of the birthweights were below 102 ounces.
Solve and check the solution 5/8 = 1/2(a + 2) please help me
Answer:
[tex]a=-\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]\frac{5}{8}=\frac{1}{2}\left(a+2\right)\\\\Switch\: sides\\\frac{1}{2}\left(a+2\right)=\frac{5}{8}\\\\\mathrm{Multiply\:both\:sides\:by\:}2\\2\times\frac{1}{2}\left(a+2\right)=\frac{5\times\:2}{8}\\\\Simplify\\a+2=\frac{5}{4}\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\a+2-2=\frac{5}{4}-2\\\\Simplify\\a=-\frac{3}{4}[/tex]
Check[tex]\frac{5}{8} = \frac{1}{2}\left(-\frac{3}{4}+2\right) \\\\\mathrm{Multiply\:fractions}:\\\\\quad \:a\times\frac{b}{c}=\frac{a\:\times \:b}{c}\\\\\frac{5}{8}=\frac{1\times \left(-\frac{3}{4}+2\right)}{2}\\\\\frac{5}{8}=\frac{1\times\left(-\frac{3}{4}+2\right)}{2}\\\frac{5}{8}=\frac{-\frac{3}{4}+2}{2}\\\\\mathrm{Join}\:-\frac{3}{4}+2:\quad \frac{5}{4}\\\frac{5}{8}=\frac{\frac{5}{4}}{2}\\\\\frac{5}{8}=\frac{5}{4\times\:2}\\\\\frac{5}{8}=\frac{5}{8}[/tex]please i need help!! Translate these words into symbols: The sum of fifteen and a number q equals the product of six and a number q
Answer:
15 + q = 6q
Step-by-step explanation:
Convert 1 million seconds into years (round to 3 decimal places)
Answer:
that would be 0.032 because 1 million secs is 11 days 13 hours 46 minutes and 40 secs
Answer:
0.032 years.
Step-by-step explanation:
1 year = 365 * 24 * 60 * 60 = 31,536,000 seconds.
= 1000000 / 31,536,000
= 0.03170979
Which of the following statements best describes adjacent angles
Answer:
The correct answer to this would be D, adjacent angles share a side.
Step-by-step explanation:
Adjacent angles share a common side as well as a common vertex.
I hope this helps :)
The statement that best describes adjacent angles is that adjacent angles share a side.
What is a vertex ?A vertex is where two non parallel lines meet.For example a triangle has 3 vertex.We can also say that vertex is a point where two non parallel lines meet to form an angle.
According to the given question the best description of adjacent angle is that they share a side.
We can say that adjacent angles are those angles which are placed next to each other.
Adjacent angle also share a common vertex but they do not overlap each other.
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Last year, Dana grew 1/2 of an inch and her brother grew 1/8 of an inch. How much more did Dana grow than her brother?
Answer:
3/8 inch
Step-by-step explanation:
1/2 of an inch is equal to 4/8
4/8-1/8=3/8
Hope this helps :-)
The length of Tom’s rectangular classroom floor is 8 feet longer than 2 times the
width. The perimeter of his classroom floor is 124 feet. Write and solve an
equation to find the length of his classroom.
Answer:
Length= 44 feet
Width= 18 feet
Step-by-step explanation:
Let the length= x
Let the width = y
Length is 8 feet longer than 2 times the
width.
X= 8+2y
The perimeter of his classroom floor is 124 feet
Perimeter= 2(x+y)
124= 2x+2y
But x= 8+2y
124= 2x+2y
124= 2(8+2y) +2y
124= 16 +4y +2y
124-16= 6y
108= 6y
18 = y
Width= 18 feet
X= 8+2y
X= 8 +2(18)
X= 8+36
X= 44
Length= 44 feet
What information can you obtain about the scores in a regular frequency distribution table that is not available from a grouped table.
A. The number and width of the class intervals
B. The exact frequency for each category on the scale of measurement
C. The overall frequency for each class interval
Answer: B. The exact frequency for each category on the scale of measurement
Step-by-step explanation: The main difference between a grouped table and regular frequency distribution exists in the fact that ; grouped table takes in a defined range of (X) values, that is takes more than one individual value per group and takes the frequency of all scores or values in the group, hence giving the frequency of the scores in the interval rather than the frequency of each individual score. On the other hand, the regular frequency distribution treats values or scores individually and then takes the frequency of each score. This way a regular frequency distribution enables us to know the exact number or distribution of each individual score.
The information in a regular frequency distribution table that is not available from a grouped table is (b) the exact frequency for each category on the scale of measurement
There are several similarities between a regular frequency table, and a grouped frequency table.
However, both frequency tables have a major difference.
This difference is in the frequency of the data they represent
While a regular frequency table shows the exact frequency of each data element, a grouped frequency table cannot show the exact frequency of each data element.
Hence, the true option is (b)
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Between which two integers is the positive value of the square root of 55?
I believe its between the integers of 7 and 8.
Answer:
7 and 8
Step-by-step explanation:
√55 is in between 49 and 64. Get 49 and 64 squared and you will get 7 and 8.
Suppose a change of coordinates T:R2→R2 from the uv-plane to the xy-plane is given by x=e−2ucos(5v), y=e−2usin(5v). Find the absolute value of the determinant of the Jacobian for this change of coordinates.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The solution is [tex]\frac{\delta (x,y)}{\delta (u, v)} | = 10e^{-4u}[/tex]
Step-by-step explanation:
From the question we are told that
[tex]x = e^{-2a} cos (5v)[/tex]
and [tex]y = e^{-2a} sin(5v)[/tex]
Generally the absolute value of the determinant of the Jacobian for this change of coordinates is mathematically evaluated as
[tex]| \frac{\delta (x,y)}{\delta (u, v)} | = | \ det \left[\begin{array}{ccc}{\frac{\delta x}{\delta u} }&{\frac{\delta x}{\delta v} }\\\frac{\delta y}{\delta u}&\frac{\delta y}{\delta v}\end{array}\right] |[/tex]
[tex]= |\ det\ \left[\begin{array}{ccc}{-2e^{-2u} cos(5v)}&{-5e^{-2u} sin(5v)}\\{-2e^{-2u} sin(5v)}&{-2e^{-2u} cos(5v)}\end{array}\right] |[/tex]
[tex]Let \ a = -2e^{-2u} cos(5v), \\ b=-2e^{-2u} sin(5v),\\c =-2e^{-2u} sin(5v),\\d=-2e^{-2u} cos(5v)[/tex]
So
[tex]\frac{\delta (x,y)}{\delta (u, v)} | = |det \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] |[/tex]
=> [tex]\frac{\delta (x,y)}{\delta (u, v)} | = | a * b - c* d |[/tex]
substituting for a, b, c,d
=> [tex]\frac{\delta (x,y)}{\delta (u, v)} | = | -10 (e^{-2u})^2 cos^2 (5v) - 10 e^{-4u} sin^2(5v)|[/tex]
=> [tex]\frac{\delta (x,y)}{\delta (u, v)} | = | -10 e^{-4u} (cos^2 (5v) + sin^2 (5v))|[/tex]
=> [tex]\frac{\delta (x,y)}{\delta (u, v)} | = 10e^{-4u}[/tex]
f(x) = 2x2 + 5x + 20
Find f(-9)
Answer: f(-9)=137
Step-by-step explanation:
To find f(-9), you plug in -9 into x.
f(-9)=2(-9)²+5(-9)+20 [solve parenthesis]
f(-9)=2(81)-45+20 [multiply]
f(-9)=162-45+20 [subtract]
f(-9)=117+20 [add]
f(-9)=137
BC=6x+4, AC=52, and AB=4x+8 find BC
Answer:
i'm not sure if it is the right answer or not
Step-by-step explanation:
Let's assume AC is a straight line and B is one the line, between A and C
AC-AB=BC
52-4x-8=6x+4
10x=40
x=4
--> BC=6x+4=6.4+4=28
A company says their cough syrup, called Cough-Up, is real effective and that 7 out of 10 doctors prefer it over any competitors. Using the given ratio, answer the following questions If there are 40 doctors, how many prefer Cough-Up? Your answer
Answer:
40÷10=4
7×4=28
18 doctors
The area of a triangle is 25 square Inches, base Inches. What is its helght (a) ? Use the formula A triangle = 1/2 ba
50 inches
5 inches
62.5 inches
10 inches
125 inches
Answer:
50/b in
Step-by-step explanation:
Use the area formula A = (1/2)(base)(height).
Here the area A is given and is 25 in^2; the base is not given, so use 'b.'
Then, since A = (1/2)(base)(height),
(height) = 2A/(base) = 2(25 in^2)/b = 50/b in
Find the circumference of a circle with radius of 18 in. Leave your answer in terms of pi.
A. 18 pi in.
B. 324 pi in.
C. 54 pi in.
D. 36 pi in.
Answer:
36pi. in. answer is D
Step-by-step explanation:
C = 2(18)pi= 36pi in
Please help what is the area?
Answer: 70 square units
a bucket full of milk is 80cl,how many litres are in 15 of such
Answer:
1.2 liters
Step-by-step explanation:
1 bucket has a volume of 80 cL.
15 buckets have a volume of 15 * 80 cL = 120 cL
1 L = 100 cL
120 cL * (1 L)/(100 cL) = 1.2 L
How do I factor 4x^2-12x^3?
A cafeteria worker knows that it takes 3 bottles of juice to serve a table of 18 students. How many bottles of juice are needed for 24 students? How many bottles of juice are needed for 42 students?
Answer:7
Step-by-step explanation:
quik math
What are the subsets of real numbers -7
The subsets of real numbers are known as:
rational numbers (decimals that don't repeat)irrational numbers (decimals that repeat)integers (a number that isn't a fraction)whole numbersnatural numbers (a positive number)Best of Luck!
To solve n+7=15 you should first
Answer:
Collect like terms and simplifySubtract 7 from both sidesStep-by-step explanation:
METHOD 1
[tex]n+7=15\\n =15-7\\n = 8[/tex]
METHOD 2
[tex]n+7-7=15-7\\n =8[/tex]
Answer:
Subtract 7 from both sides.
Step-by-step explanation:
Step 1:
n = 15 - 7
Answer:
n = 8
Hope This Helps :)
Which equation has no solution?
4(x + 3) + 2x = 6(x + 2)
5+2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 612 + x) = 2(3x + 8)
Answer:
[tex]4(x + 3) + 2x = 6(x + 2)[/tex][tex]5 + 2(3 + 2x) = x + 3(x + 1)[/tex]Step-by-step explanation:
[tex]5(x + 3) + x = 4(x + 3) + 3 \\ 5x + 15 + x = 4x + 12 + 3 \\ 5x + x - 4x = 12 + 3 - 15 \\ 2x = 0[/tex]
Divide both sides of the equation by 2
2x/2 = 0/2
x = 0
(4+612+x)=2(3x+8)
4+612+x=6x+16
4+612-16=6x-x
600=5x
Divide both sides of the equation by 5
600/5 = 5x
120 = x
Answer:
Its B. 5+2(3 + 2x) = x + 3(x + 1)
Step-by-step explanation:
I just took the test on edge
Tecside real estate, inc. is a research firm that tracks the cost of apartment rentals in southwest virginia. in mid-2002, the regional average apartment rental rate was $895 per month. assume that, based on the historical quarterly surveys, it is reasonable to assume that the population standard deviation is $225. in a current study of apartment rental rates, a sample of 180 apartments in the region provided the apartment rental rates.a. do the sample data enable tecside real estate, inc. to conclude that the population mean apartment rental rate now exceeds the level reported in 2002? the sample mean is $915 and the sample standard deviation is $227.50. make your decision based on α=0.10.b. what is the p-value?
Answer:
The decision is to fail to reject the null hypothesis
This means that the population mean apartment rental rate now does not exceeds the level reported in 2002
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$895[/tex]
The population standard deviation is [tex]\sigma = \$225[/tex]
The sample size is [tex]n = 180[/tex]
The sample mean is [tex]\= x = \$ 915[/tex]
The sample standard deviation is [tex]s = \$ 227.50[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu \le \$ 895[/tex]
The alternative hypothesis is [tex]H_a : \mu > \$895[/tex]
The test statistics is evaluated as
[tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 915 - 895}{ \frac{225}{ \sqrt{180} } }[/tex]
=> [tex]t =1.193[/tex]
So from z-table the p-value is obtained, the value is
[tex]p-value = P(Z > t) = P(Z > 1.193 ) = 0.11643[/tex]
So From the value obtained we see that
[tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis
Is 8.73 a rational number
Answer:
Yes
Step-by-step explanation:
8 73/ 100=8.73
3/2•3/2•3/2•3/2 rewrite product in exponential form
Answer:
1.5^4
Step-by-step explanation:
The product for this expression is 1.5 multiplied by itself 4 times. This means you raise it to the fourth power, thus giving you 3/2^4 or 1.5^4.