Answer: 0.584
Step-by-step explanation:
We have:
5 discs
6 jump ropes
3 balls
12 pieces of sidewalk.
5 + 6 + 3 + 12 = 26
If all of them have exactly the same probability of being removed, then:
in the first selection, we do not want to remove a jump rope, so we can remove one disc, one ball or one piece of sidewalk.
The total number of those objects is:
5 + 3 + 12 = 20.
Then the probability of removing one of those objects is:
P1 = 20/26 = 0.769
Now in the second selection, we have the same situation, but now we have 25 objects in total, and because in the previous selection we removed one ball, or one disc, or one piece of sidewalk, the total number of these things now is 19.
So the probability of removing another object of that set is:
P2 = 19/25 = 0.76
The joint probability is equal to the product of the individual probabilities, so we have:
P = P1*P2 = 0.769*0.76 = 0.584
Each power smoothie that Theo makes has 3 scoops of mango, 1 scoop of strawberries, and 1 scoop of spinach. If Theo makes 7 power smoothies, how many scoops will he use in all?
Answer: 35 scoops total!
Step-by-step explanation: FIrst, you would add the number of scoops in total which is 3+1+1=5 scoops.
Now you would do 7*5=35
Therefore, Theo uses 35 scoops in all. I hope this helps you!
PLEAS HELP...FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?
*a clearer picture containing the graph is shown in the attachment
Answer:
20% of the class earned a D
Step-by-step Explanation:
Step 1: Determine the total number of students represented on the graph:
9 students => D
5 students => C
14 students => B
17 students => A
Total number of students = 45
Step 2: Express each category of students who scored a particular grade as a fraction and as percentage.
9 students => D => [tex] \frac{9}{45} = \frac{1}{5} [/tex] => as percentage, we have [tex] \frac{1}{5} * 100 = 20 percent [/tex]
5 students => C => [tex] \frac{5}{45} = \frac{1}{9} [/tex] => as percentage, we have [tex] \frac{1}{9} * 100 = 11.1 percent [/tex]
14 students => B => [tex] \frac{14}{45} [/tex] => as percentage, we have [tex] \frac{14}{45} * 100 = 31.1 percent [/tex]
17 students => A => [tex] \frac{17}{45} [/tex] => as percentage, we have [tex] \frac{17}{45} * 100 = 37.8 percent [/tex]
Step 3: Check each statement to see if they are true or not based on the calculations above.
Statement 1: "⅕ of the students earned a C."
This is NOT TRUE From our calculation, ⅑ of the students earned a C.
Statement 2: "3% more students earned an A than a B." This is also NOT TRUE.
37.8% earned A, while 31.1% earned a B. Thus, about 6.7% more students earned an A than a B.
Statement 3: "20% of the class earned a D". This is TRUE.
Check calculation in step 2.
Statement 4: "¼ of the class earned a B". This is NOT TRUE.
¼ is 25% of the class. Those who earned a B account for 31.1% not 25% (¼ of the class).
The correct statement is: "20% of the class earned a D"
Draw the function
[tex]y = \tan(x) [/tex]
on the interval [-pi, pi]
Answer:
The answer is in the photo below. The interval is (-pi, pi) and the function is y = tanx.
in the factory 25 men working 26 hour can produce 1300 radios . how manny hours must the same group of men work to produce 450 radios
Answer:
9 hours
Step-by-step explanation:
Since the group of men remains the same, number of hours is proportional to number of radios.
1300/26 = 450/h
h = 26 * 450 / 1300 = 9 hours
Fine the surface area
Answer:
88 if a rectangular prism, 64 based on the net.
Step-by-step explanation:
A = 4 * 2
B = 6 * 2
C = 4 * 2
D = 6 * 2
E = 6 * 4
A/C= 8
B/D= 12
E = 24
2(8) + 2(12) + 24 = 64
Surface Area: 64
However, a rectangular prism must have 6 faces, so unless this is a box, the answer would be 88, and E = F, the last face.
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in. H = 210 + 33t How fast does the tree grow? ANSWER centimeters per year.
Answer:
The tree grows 33cm per year
Step-by-step explanation:
Here in this question, we are interested in knowing how fast the growth of the tree is.
This is easily obtainable from the equation for the height of the tree.
Mathematically, the equation is given as;
H = 210 + 33t
Interpreting this, we can have 210 as the original height of the tree when Renata moved in, while the term 33 represents the growth per year.
So we can say the tree adds a height of 33 cm each year and this translates to the yearly growth of the tree
Find the sum of the first 12 terms of the sequence 512, 256, 128, …
Answer: 1023.75 (a)
Step-by-step explanation:
The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.
a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.
Now to calculate the sum, we consider two formula here and select the one that is most appropriate,
(1) a( rⁿ - 1 )/r - 1, when r is greater than 1
(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.
In this question, formula 2 shall be appropriate because r is less than 1.
so,
S₁₂ = 512( 1 - 0.5¹² )/1 - 0.5
512( 1 - 2.44 ₓ 10⁻⁴ )/0.5
= 512( 0,9998 )/0.5
= 511.875/0.5
= 1023.75
The answer is a
A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.
Explain in context the conclusion of the test if H0 is rejected.
Answer:
For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value
Step-by-step explanation:
Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.
Mathematically, the null hypothesis is as expressed as below;
H0: μ = 1,200
The alternative hypothesis H1 would be;
H1: μ > 1,200
Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics
For us to reject the null hypothesis, one of two things, or two things must have occurred.
The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.
If this happens, then we can make a rejection of the null hypothesis
Of the three properties, reflexive, symmetric, and transitive that define the relation "is equal to," which one could also apply to "is less than" and "is greater than?" transitive reflexive symmetric
Answer: Transitive property.
Step-by-step explanation:
First, for the equality we have:
Reflexive:
For all real numbers x, x = x.
Symmetric:
For all real numbers x, y
if x= y, then y = x.
Transitive:
For reals x, y and z.
if x = y, and y = z, then x = z.
Now, let's talk about inequalities.
first, the reflexive property will say that:
x > x.
This has no sense, so this property does not work for inequalities.
Now, the reflexive.
If x > y, then y > x.
Again, this has no sense, if x is larger than y, then we can never have that y is larger than x. This property does not work for inequalities.
Not, the transitive property.
if x > y, and y > z, then x > z.
This is true.
x is bigger than y, and y is bigger than z, then x should also be bigger than z.
x > y > z.
And this also works for the inverse case:
x < y and y < z, then x < z.
So the correct option is transitive property.
PLEASE HELP- MATH
simplify the fraction
5bc/10b^2
[tex]\dfrac{5bc}{10b^2}=\dfrac{\not 5\cdot \not b\cdot c}{2\cdot \not 5\cdot \not b\cdot b}=\dfrac{c}{2b}[/tex]
Answer:
c / ( 2b)
Step-by-step explanation:
5bc/10b^2
Lets look at the numbers first
5/10 = 1/2
Then the variable b
b / b^2 = 1/b
Then the variable c
c/1 = c
Putting them back together
1/2 * 1/b * c/1
c/ 2b
What is the area of polygon EFGH?
What is 45x62 Please help.
Answer:
45
62x
______
90
2700+
_________
2790
Step-by-step explanation:
Write the phrase "the product of 19 and a number" as a mathematical expression.
A 19 + x
B) 19/x
C) 19 x
(D) 19 -x
Answer:
19x
Step-by-step explanation:
product means multiply
19*x
19x
Answer:
The answer is C.
Step-by-step explanation:
if a number and a variable are next to each other, it is assumed they will be multiplied.
Beginning 177 miles directly north of the city of Morristown, a van travels due west. If the van is travelling at a speed of 31 miles per hour, determine the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles. (Do not include units in your answer, and round to the nearest hundredth.)
Answer:
Step-by-step explanation:
From the given information;
let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c
SO, using the Pythagoras theorem
a² = c² + 177²
By taking the differentiation of both sides with respect to time t , we have
[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]
[tex]a = \sqrt{ 5041+31329}[/tex]
[tex]a = \sqrt{ 36370}[/tex]
a = 190.71
SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]
Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]
[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]
[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex] to the nearest hundredth.
perform the following division (-2/3) ÷ (4/7)
Answer:
-7/6
Step-by-step explanation:
-2/3 x 7/4 = -14/12 = -7/6
Answer: -7/6
Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).
Remember that dividing by a fraction is the same thing
as multiplying by the reciprocal of the fraction.
Before multiplying however, notice that we
can cross-cancel the 2 and 4 to 1 and 2.
So multiplying across the numerators and denominator and
remembering our negative in the first fraction, we have -7/6.
a family spent $93 at a carnival.
*they spent $18 on tickets and $30 on food. they spent the rest of the money on games.
which equation can be used to to find "g", the amount of money used on games.
Answer: 93-(18+30)=g
93-48=g
45=g
Step-by-step explanation: yup
The answer is 93-18-30-g=0 or 18+30+g=93
Your’re in charge of evening entertainment for an important client group You use the company credit card to take their four representatives out to dinner. Two people order the steak entree for 32.50 Two people order the grilled tuna for 28.90 and you order the lasagna for 24.95 When the bill comes you tip 20% what is the amount of tip you leave
Answer:
total amount paid = 32.5 + 28.9 + 24.95 = 86.35
20% of the total amount paid = 0.2 * 86.35 = 17.27
you tip 17.25$
suppose a chemical engineer randomly selects 3 catalysts for testing from a group of 10 catalysts, 6 of which have low acidity & 4 have high acidity. What is the probability that exactly2 lower acidic catalysts are selected?
Step-by-step explanation:
Total catalysts = 10
Probability of 2 lower acidic catalysts = 2/10 = 1/5
A total of n bar magnets are placed end to end in a line with random independent orientations. Adjacent like poles repel while ends with opposite polarities join to form blocks. Let X be the number of blocks of joined magnets. Find E(X) and Var(X).
Answer:
E(x) [tex]= \frac{n+1}{2}[/tex]
Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]
Step-by-step explanation:
Hint x = 1 + x1 + ......... Xn-1
[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]
attached below is the detailed solutioN
usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block
HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Option (B)
Step-by-step explanation:
The given expression is,
[tex]\sqrt{22x^6}\div\sqrt{11x^4}[/tex]
We can rewrite this expression as,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }[/tex]
Solving it further,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }=\frac{\sqrt{22(x^3)^2} }{\sqrt{11(x^2)^2} }[/tex] [Since [tex]x^3\times x^3=x^6[/tex] and [tex]x^{2}\times x^{2}=x^4[/tex]]
[tex]=\sqrt{\frac{22(x^3)^2}{11(x^2)^2} }[/tex] [Since [tex]\frac{\sqrt{a} }{\sqrt{b} }=\sqrt{\frac{a}{b} }[/tex]]
[tex]=\frac{x^3}{x^2}\sqrt{\frac{22}{11} }[/tex]
[tex]=x\sqrt{2}[/tex]
Therefore, quotient will be x√2.
Option (B) will be the correct option.
The histogram shows that nine students had grades of 80 or higher.
The histogram shows there were 22 students in the class.
The histogram shows there were 25 students in the class.
The histogram is symmetrical.
The histogram has a peak.
The histogram shows the data is evenly distributed.
The histogram shows a gap in the data
Answer:
bde
Step-by-step explanation:
Answer:
B: The histogram shows there were 22 students in the class.
D: The histogram is symmetrical.
E:The histogram has a peak.
F: The histogram shows the data is evenly distributed.
Step-by-step explanation:
edg 2020
What is the solution to this ?
Answer:
[tex]\boxed{\sf C. \ x\geq -4}[/tex]
Step-by-step explanation:
[tex]-8x+4\leq 36[/tex]
[tex]\sf Subtract \ 4 \ from \ both \ sides.[/tex]
[tex]-8x+4-4 \leq 36-4[/tex]
[tex]-8x\leq 32[/tex]
[tex]\sf Divide \ both \ sides \ by \ -8.[/tex]
[tex]\frac{-8x}{-8} \leq \frac{32}{-8}[/tex]
[tex]x\geq -4[/tex]
A car dealer recommends that transmissions be serviced at 30,000 miles. To see whether her customers are adhering to this recommendation, the dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles. By finding the P-value, determine whether the owners are having their transmissions serviced at 30,000 miles. Use α = 0.10. Are the owners having their transmissions serviced at 30,000 miles?
Answer:
No, the owners are not having their transmissions serviced at 30,000 miles.
Step-by-step explanation:
We are given that a car dealer recommends that transmissions be serviced at 30,000 miles.
The car dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles.
Let [tex]\mu[/tex] = true average mileage of the automobiles serviced.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30,000 miles {means that the owners are having their transmissions serviced at 30,000 miles}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 30,000 miles {means that the owners are having their transmissions serviced at different than 30,000 miles}
The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average mileage serviced = 30,456 miles
[tex]\sigma[/tex] = population standard deviation = 1684 miles
n = sample of customers = 40
So, the test statistics = [tex]\frac{30,456-30,000}{\frac{1684}{\sqrt{40} } }[/tex]
= 1.71
The value of z-statistics is 1.71.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 1.71) = 1 - P(Z [tex]\leq[/tex] 1.71)
= 1 - 0.9564 = 0.0436
For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0436 = 0.0872.
Since the P-value of our test statistics is less than the level of significance as 0.0872 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that the owners are having their transmissions serviced at different than 30,000 miles.
someone please help me
Answer:
3 mL
Step-by-step explanation:
The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.
A librarian needs to package up all of the children's books and move them to a different location in the library. There are 625 books, and she can fit 25 books in one box. How many boxes does she need in order to move all of the books? 5 B. 25 C. 125 D. 600 E. 650
Answer: B. 25
Step-by-step explanation:
Given: Total books = 625
Number of books can fit in one box = 25
Now, the number of boxes she need to move all of the books = (Total books) ÷ (Number of books can fit in one box )
= 625÷25
= 25
hence, she requires 25 boxes in order to move all of the books.
So, correct option is B. 25.
What is the median of these figure skating ratings?
6.0 6.0 7.0 7.0 7.0 8.0 9.0
Answer:
The median would be 7.0.
Step-by-step explanation:
The median of a set of numbers means it is the middle number. since this set has 7 numbers you would need to find the number that is in the middle of the set. This would be the 4th number since it is in the middle. 7.0 is your answer.
Evaluate the double integral ∬Ry2x2+y2dA, where R is the region that lies between the circles x2+y2=16 and x2+y2=121, by changing to polar coordinates.
Answer:
See answer and graph below
Step-by-step explanation:
∬Ry2x2+y2dA
=∫Ry.2x.2+y.2dA
=A(2y+4Ryx)+c
=∫Ry.2x.2+y.2dA
Integral of a constant ∫pdx=px
=(2x+2.2Ryx)A
=A(2y+4Ryx)
=A(2y+4Ryx)+c
The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2
The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]
The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between
the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].
Let consider x = rcosθ and y = rsinθ because x² + y² = r²;
Now, the double integral can be written in polar coordinates as:
[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]
[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]
[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]
Thus, the integral becomes:
[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]
since 2sin² = 1 - cos2θ∴
[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]
[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]
Learn more about double integral here:
https://brainly.com/question/19756166
limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)
Step-by-step explanation:
I(S) = aS / (S + c)
As S approaches infinity, S becomes much larger than c. So S + c is approximately equal to just S.
lim(S→∞) I(S)
= lim(S→∞) aS / (S + c)
= lim(S→∞) aS / S
= lim(S→∞) a
= a
As S approaches infinity, I(S) approaches a.
Given a sample of 35, what is the sample standard deviation of a pair of jeans if the 90% confidence interval is [37.14, 42.86]
Answer:
10.295Step-by-step explanation:
Using the value for calculating the confidence interval as given;
CI = xbar + Z*σ/√n
xbar is the mean = 37.14+42.86/2
xbar= 80/2
xbar = 40
Z is the z-score at the 90% confidence = 1.645
σ is the standard deviation
n is the sample size = 35
Given the confidence interval CI as [37.14, 42.86]
Using the maximum value of the confidence interval to get the value of the standard deviation, we will have;
42.86 = xbar + Z*σ/√n
42.86 = 40 + 1.645* σ/√35
42.86-40 = 1.645*σ/√35
2.86 = 1.645*σ/√35
2.86/1.645 = σ/√35
1.739 = σ/√35
1.739 = σ/5.92
σ= 1.739*5.92
σ = 10.295
Hence, the sample standard deviation of a pair of jeans is 10.295
Find the sum to infinity of the series 2+5/4+11/16+23/64+..........up to the infinity.
infinity
We have
[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]
(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)
Recall for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]
