Answer:
31/15
Step-by-step explanation:
First, find the common multiplier of 20 and 12 (the lowest number that both fractions can be increased to). This is 60 (12 x 5 = 60, 20 x 3 = 60) and adjust the numerators accordingly: multiply 17 by five to get 85, and multiply 13 by three to get 39. Add them up to get 124/60, and then simplify - the answer will be 31/15! Hope this helps! Sorry if this was tough to understand, typing off my phone, so feel free to ask any questions :)
Answer:
0.720833
Step-by-step explanation:
First find the LCM of the two fractions
Then add the numerators together
form a single fraction
Lastly cancel the numerator and denominator if possible
Find the surface area
Answer:
here
h=4 in
r=8in
total surface area =2πr(r+h)=2π×8(8+4)=192π or 603.18in²
A probability model includes p(red)=2/7 and P(blue)=3/14. Select all the probabilities that could complete the model.
Answer Key:
A: P(green)= 2/7, P(yellow)=2/7
B: P(green)=3/8, P(yellow)=1/8
C: P(green)=1/4 P(yellow)=1/4
D: P(green)= 5/21 Pyellow)= 11/21 E. P(green)= 3/7 P(yellow)=1/14
The probabilities that could complete the model and maintain a total sum of 1 are options B and E.
B: P(green) = 3/8, P(yellow) = 1/8
E: P(green) = 3/7, P(yellow) = 1/14
To determine the probabilities that could complete the model, we need to consider the sum of all probabilities. In a probability model, the sum of all probabilities should equal 1.
Given the probabilities P(red) = 2/7 and P(blue) = 3/14, let's calculate the sum:
P(red) + P(blue) = 2/7 + 3/14 = 4/14 + 3/14 = 7/14 = 1/2
Since the sum of P(red) and P(blue) is 1/2, we need to find the probabilities for P(green) and P(yellow) that, when added to 1/2, give a total sum of 1.
Looking at the answer key options:
A: P(green) = 2/7, P(yellow) = 2/7
B: P(green) = 3/8, P(yellow) = 1/8
C: P(green) = 1/4, P(yellow) = 1/4
D: P(green) = 5/21, P(yellow) = 11/21
E: P(green) = 3/7, P(yellow) = 1/14
Let's check the sums:
A: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 2/7 + 2/7 = 4/14 + 3/14 + 4/14 + 4/14 = 15/14 ≠ 1 (incorrect)
B: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 3/8 + 1/8 = 4/14 + 3/14 + 6/14 + 1/14 = 14/14 = 1 (correct)
C: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 1/4 + 1/4 = 4/14 + 3/14 + 7/14 + 7/14 = 21/14 ≠ 1 (incorrect)
D: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 5/21 + 11/21 = 6/14 + 3/14 + 10/14 + 11/14 = 30/14 ≠ 1 (incorrect)
E: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 3/7 + 1/14 = 4/14 + 3/14 + 6/14 + 1/14 = 14/14 = 1 (correct)
Based on the calculations, the probabilities that could complete the model and maintain a total sum of 1 are options B and E. So, the correct answers are:
B: P(green) = 3/8, P(yellow) = 1/8
E: P(green) = 3/7, P(yellow) = 1/14
To learn more about the probability;
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How to Evaluate 5/9 x 8
Answer:
4 4/9
Step-by-step explanation:
First, you have to set it up: 5/9 times 8/1
We made it 8/1 since it has to be a fraction in the multipying ocess and the one does not change the value.
Next, Multiply.
5/9x8/1=40/9 as an inproper fraction
As a proper fraction, it is written as 4 4/9
I NEED THIS ASAP. What is m
Answer:
The measure of ∠DFE is 67°.
Step-by-step explanation:
Angle GFE is a straight angle, meaning that its measure is 180°, per se.
180 - 113 = m of ∠DFE
180 - 113 = 67
what is 9,030×29,234?
Answer:
263,93802
Step-by-step explanation:
xd
State whether the standardized test statistic t indicates that you should reject the null hypothesis. Explain.
(a) t = 1.828
(b) t = 0
(c) t = 1.735
(d) t = -1.826
Mike works for his father sanding wooden rocking chairs. He earns $6 per chair. How many chairs does he need to sand in order to buy a portable CD player for $49.99
5. Find the probability that a randomly chosen point in the figure lies in
the shaded region.
Answer:
D
Step-by-step explanation:
area of shaded region=1/2×8×8=32 sq. units
area of larger triangle=1/2×14×16=112 sq units
reqd. probability=32/112=2/7
A group of 10 friends decides to head up to a cabin in the woods (where nothing could possibly go wrong). Unfortunately, a number of these friends have dated each other in the past, and things are still a little awkward. To get the cabin, they need to divide up into some number of cars, and no two people who dated should be in the same car.
a. What is the smallest number of cars you need if all the relationships were strictly heterosexual? Represent an example of such a situation with a graph. What kind of graph do you get?
b. Because a number of these friends dated there are also conflicts between friends of the same gender, listed below. Now what is the smallest number of conflict-free cars they could take to the cabin?
Friend A B C D E F G H I J
Conflicts with BEJ ADG HJ BF Al DJ B CI EHJ ACFI
c. What do these questions have to do with coloring?
Answer:
a) 3
b) 3
c) because of the permutations and combinations involved
Step-by-step explanation:
a) Determine the smallest number of cars needed
The number of cars are the same as conflict free cars
hence we can group the friends without conflict into the same car
1st car we will have : ACFI in it
2nd car we will have : GD in it
third care we will have : BEJH in it
∴ number of car needed = 3
b) number of conflict free cars = 3
c) Coloring is important in the question because of the permutations and combinations involved
find the least common multiple of 40a3bc and 28a2b4cd
Answer:
The least common multiple is [tex]280a^6b^4cd[/tex]
Step-by-step explanation:
We find the least common multiple of the constant, and of each term.
Least common multiple of 40 and 28:
40 - 28|2
20 - 14|2
10 - 7|2
5 - 7|5
1 - 7|7
1 - 1
2*2*2*5*7 = 280
LCM of a^3 and a².
Exponents are 3 and 2.
LCM of 3 and 2 is 6. So
[tex]a^6[/tex]
b and b^4
LCM of 1 and 4, which are the exponents, is 4. So
[tex]b^4[/tex]
c and c
LCM of 1 and 1 is 1. So c
d
In the first term, no d means that it is [tex]d^0 = 1[/tex]
In the second, [tex]d^1 = d[/tex]
LCM of 0 and 1 is 1. So
d
Least common multiple:
Multiplication of all the LCM's. So
[tex]280a^6b^4cd[/tex]
April and Cody invest $5,000 each at their local bank. April invests at a 4% simple interest rate for three years. Cody invests at a 4% compound interest rate, and earns $624.32 in interest. What is the difference in their account balances at the end of 3 years?
Answer:
106.43
Step-by-step explanation:
The difference in their account balances at the end of 3 years is $24.32
Calculations and ParametersTo solve the compound interest for Cody
First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 5,000.00(1 + 0.04/1)(1)(3)
A = 5,000.00(1 + 0.04)(3)
A = $5,624.32
To solve for the simple interest for April
P * T * R/100
5000 * 4 * 3/100
= 60,000/100
= 600.
We add the S. I of April's investment
= 5,000 + 600
= $5600.
Therefore, the difference between their account balances is $5,624.32 - $5600 = $24.32
Read more about compound interest here:
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25 points!! Pls help!! If not I will probably get a D pls I will mark brainliest but will report if answer is unrelated
Answer:
18 cm!
Step-by-step explanation:
Can you help me with this problem please?????
Answer:
The answer is the first option I hope it helps
Which does NOT represent the interior angle measures of a triangle?
A.) 50, 750, 100°
B.) 10°, 80°, 90°
C.) 20°, 60°, 100°
D.) 45°, 45°, 45°
E.) 50°, 50°,80°
Answer:
A!! it does not equal 180 while the others do
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
An interior triangle always is 180 degrees. A. is the only answer that doesn't add up to 180 degrees.
Based on the picture what is the Minimum, Maximum, Median, Q1, Q3, And the IQR?
Answer:
lol I hope I'm right ...
Step-by-step explanation:
minimum=2, maximum=10, Q1=3, median=6, Q3=8, IQR= 5
Plz help me well mark brainliest if correct!!
Answer:
(1, 1)
Step-by-step explanation:
not 100% sure though, but hope it helps
There are 25 marbles in the box. There are 10 red marbles , 8 blue marbles , and 7 yellow marbles . What percent of the marbles are NOT yellow ?
A. 28%
B. 72%
C. 32%
D. 40%
Divide. Round to the nearest tenth. .48÷9.23
[tex].48 \div 9.23[/tex]
Check out this app! It's millions of students helping each other get through their schoolwork. https://brainly.app.link/qpzV02MawO
Answer:
whow this is so great app i love it
A 20 ft ladder leans against a building and reaches a point 13 ft above the ground. Find, to the nearest degree, the angle that the ladder makes with the ground
two parallel lines are cut by a transversal what is the measure of 2
Answer:
b 80
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
A P EE X
An auto manufacturing company wants to estimate the variance of miles per gallon for its auto model AST72. A random sample of 24 cars of this model showed that the standard deviation of miles per gallon is 0.58. At the alpha = 1%, can the research department conclude that the population variance of miless per gallon for AST72 is decreased from historical value of 0.35?
A. At alpha = 1%, they reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35.
B. At alpha = 1%, they failed to reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35.
C. At alpha = 1%, they failed to reject the null hypothesis. The variance of miles per gallon for AST72 model has decreased from the historical value of 0.35.
D. At alpha = 1%, they reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35.
Answer:
Since p-value ( 0.4467 ) is greater than significance level ( 0.01 )
Fail to Reject Null hypothesis H₀ at 1%.
At 1% significance level, we can conclude that, population variance is maintained at historic value.
Thus, Option ((B) At alpha = 1%, they failed to reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35) is the correct answer.
Step-by-step explanation:
Given the data in the question;
sample size n = 24
Sample Standard deviation S = 0.58
Let δ represent the population standard deviation
so we will test;
H₀ : δ = √0.35 ≈ 0.5916
H₁ : δ < √0.35 ≈ 0.5916
Test Statistics;
we determine our test statistics as follows;
Z = [√(2(n-1))] × [ lnS - lnδ ] ~ N(0, 1 )
Now, Under H₀, [tex]Z_{obs[/tex] = [√(2(24-1))] × [ ln (0.58 / 0.5916) ]
= 6.7823 × -0.0198026
= -0.134
From z-table;
p-value = P( z < [tex]Z_{obs[/tex] ) = p( z < -0.134 ) = 0.4467
p-value = 0.4467
Since p-value ( 0.4467 ) is greater than significance level ( 0.01 )
Fail to Reject Null hypothesis H₀ at 1%.
At 1% significance level, we can conclude that, population variance is maintained at historic value.
Thus, Option ((B) At alpha = 1%, they failed to reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35) is the correct answer.
Work out the equation of the line that
is parallel to the line y= 5x - 3
passes through (-2, -4)
Answer:
y = 5x +6
Step-by-step explanation:
the slope of the given equation is 5. a slope of a line parallel has the same slope. so 5
y- -4 = 5(x - -2)
y+4 = 5x +10
y = 5x +6
A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with A random sample of 12 sample specimens has a mean compressive strength of psi. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete.
Complete Question
A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with[tex]\sigma^2=1000[/tex]. A random sample of 12 sample specimens has a mean compressive strength of [tex]\=x=3207psi[/tex]. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete.
Answer:
[tex]CI=(3189.1,3224.9)[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=12[/tex]
Standard deviation [tex]\sigma^2=1000psi^2\\\sigma=\sqrt{1000} \\\sigma=31.6[/tex]
Sample mean [tex]\=x=3207[/tex]
Confidence level =95%
[tex]\alpha=100-95\\\alpha=0.05[/tex] significance level
From table \alpha 0.05
Gives
[tex]Z_c=1.96[/tex]
Generally the equation for confidence interval is mathematically given by
[tex]CI=(\=x-\frac{z_c*\sigma}{\sqrt{n} } ),\=X+\frac{Z_C*\sigma}{\sqrt{12} })[/tex]
[tex]CI=(3207-\frac{1.96*31.6}{\sqrt{12} } ),3207+\frac{1.96*31.6}{\sqrt{12} })[/tex]
[tex]CI=(3189.1,3224.9)[/tex]
Alternate exterior angles congruent.
Which angle forms a pair of alternate
exterior angles with angle 1?
Answer:
<1 = <8
Step-by-step explanation:
Pair of alternate exterior angles are formed when two parallel lines are cut across by abl transversal line. The two angles are found on the other side of the parallel lines but located on opposite sides along the transversal line.
Thus, <1 and <8 are exterior angles of the parallel lines that are crossed by the transversal and they are on the alternate sides along the transversal.
Therefore, <1 and <8 form a pair of alternate exterior angles.
<1 = <8
Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r= 4 cm
[? ]%
Round to the nearest tenth of a percent.
please help
Answer: 31.8
Step-by-step explanation:
The probability that a randomly selected point within the circle falls
in the red shaded area is; 15.9%
What is the probability?The area of the circle is gotten from the formula;
A = πr²
A = π * 4²
A = 50.265 cm²
Area of triangle = ¹/₂ * bh
Here b = h = 4. Thus;
A = ¹/₂ * 4 * 4
A = 8 cm²
Thus;
P(randomly selected is shaded) = 8/50.265
P(randomly selected is shaded) = 0.159 = 15.9%
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A man earns $11.62 for each of the first 36 hours he works in one week and $17.43 in overtime pay for each additional hour he works in the same week.
How much money will he make if he works 48 hours in one week?
He will make s
if he works 48 hours in a week.
Answer:
21❄️....................
You want to know if an octopus (octopi are very intelligent!) can tell the difference between circles and rectangles. You provide each octopus with one circular disk and one flattened rectangle. You hide food under the rectangle. After several trials, you then count how many times the octopus picks up the circle and how many times it picks up the rectangle.
You get the following results:
Circles: 6
Rectangles: 19
Can the octopus tell the difference between circles and rectangles?
Answer:
Yes
Step-by-step explanation:
The octopus chose the rectangles 68% of the time. From this observation you can tell that the octopus has learned there is food under the rectangular shape. Its cognitive abilities are less than a human's, but they are able to discern a rectangle from a circle with success.
Good luck ^^
8b + 4 - 4b + 2 = what
8b+4-4b+2= 4b+6
collect the like terms and add
please hurry!! i have a D in math
Answer:
60, and m = 30, and 1 min 20.
Step-by-step explanation:
For A, the 60 is the starting point meaning that the temperature was intitally 60 degrees
For B, if we divided both sides by 2 we get the answer m = 30, meaning every minute, it was up 30 degrees.
For C, we know that in one minute it will be 90 degrees, so 60 seconds = 30 degrees. So lets divided both sides by 3 to get 10 degrees. We get 20 seconds. It will take 1 min and 20 for it to be 100 degrees.
Hopefully thats right.