Answer:
Pr(only one of them will pass the driving test) = 0.38
Step-by-step explanation:
The probability that Ben will pass = 0.8
Let Pr = pribability
Pr(Ben pass) = 0.8
Pr(Ben fail) = 1 - Pr(Ben pass) = 1-0.8
Pr(Ben fail) = 0.2
The probability that Tom will pass = 0.7
Pr (Tom pass) = 0.7
Pr (Tom fail) = 1 - Pr (Tom pass) = 1-0.7
Pr (Tom fail) = 0.3
Pr(only one pass) = Pr(Ben pass and Tom fail) + Pr (Tom pass and Ben fail)
Pr(only one pass) = (0.8 × 0.3) + (0.7 × 0.2)
Pr(only one pass) = 0.24 + 0.14
Pr(only one pass) = 0.38
Answer:0.38
Step-by-step explanation:
A set of middle school student heights are normally distributed with a mean of 150150150 centimeters and a standard deviation of 202020 centimeters. Darnell is a middle school student with a height of 161.4161.4161, point, 4 centimeters. What proportion of student heights are lower than Darnell's height?
Answer:
71.57% of student heights are lower than Darnell's height
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 150, \sigma = 20[/tex]
Darnell has a height of 161.4 centimeters. What proportion of student heights are lower than Darnell's height?
This is the pvalue of Z when X = 161.4.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{161.4 - 150}{20}[/tex]
[tex]Z = 0.57[/tex]
[tex]Z = 0.57[/tex] has a pvalue of 0.7157
71.57% of student heights are lower than Darnell's height
Answer:
0.7157
Step-by-step explanation:
Darnell's height is 161.4 - 150 = \goldD{11.4}161.4−150=11.4161, point, 4, minus, 150, equals, start color #e07d10, 11, point, 4, end color #e07d10 relative to the mean.
This is \dfrac{\goldD{11.4}}{20} = \blueD{0.57}
20
11.4
=0.57start fraction, start color #e07d10, 11, point, 4, end color #e07d10, divided by, 20, end fraction, equals, start color #11accd, 0, point, 57, end color #11accd standard deviations relative to the mean. This is Darnell's z-score.
Hint #22 / 4
We want to find the proportion of student heights below a z-score of \blueD{0.57}0.57start color #11accd, 0, point, 57, end color #11accd:
What does Keaton spend the most money on?
Keaton's Monthly Spending
What does Keaton spend the least money on?
Food
Keaton spends about as much money on rent as he
does on
Rent
Clothes
Hygiene Products
Entertainment
Answer:FOOD, HYGIENE, ENTERTAINMENT
Step-by-step explanation:
The answer is:
foodHygiene ProductsEntertainmentWhat is Data?Data is referred to as a collection of information gathered by observations, measurements, research, or analysis. It may comprise facts, figures, numbers, names, or even general descriptions of things. Data can be organized in the form of graphs, charts, or tables for ease in our study. Data scientists help in analyzing the collected data through data mining.
According to the given information
a)Keaton spend the most money on Food.
b) Keaton spend the least money on Hygiene Products.
c) Keaton spends about as much money on rent as he does on Entertainment.
Learn more about data here:
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Christopher drove 199.5 miles in 3.5 hours. If he drove at a constant speed, how far did he drive in one hour? *
Answer:
57 miles
Step-by-step explanation:
Answer:
57 miles
Step-by-step explanation:
divide 199.5/3.5 and you will get 57 miles
(a + 3)(a - 2) (multiplying polynomials by polynomials is the assignment, i need help lol)
Answer:
a^2 +a -6
Step-by-step explanation:
(a + 3)(a - 2)
FOIL
first: a*a = a^2
outer: -2*a = -2a
inner: 3*a =3a
Last : -2*3 = -6
Add them together
a^2 -2a+3a -6
Combine like terms
a^2 +a -6
Answer:
a² + a - 6
Step-by-step explanation:
(a + 3)(a - 2) = a² - 2a + 3a - 6 = a² + a - 6
Noah drew a triangle so that all the sides are 5 inches long. He wants to draw a new triangle, but increase the length of each side by x inches. The perimeter of the new triangle is 24 inches.
Complete question:
Noah drew a triangle so that all the sides are 5 inches long. He wants to draw a new triangle, but increase the length of each side by x inches. The perimeter of the new triangle is 24 inches. Find the value of x and length of the new side.
Answer:
x = 3 inches
The length of the new sides of the triangle is 8 inches
Step-by-step explanation:
If each of the sides of the original triangle is 5 inches, then it is an equilateral triangle.
Let the length of each of the side of the new triangle be, A, B and C.
A = 5 + x
B = 5 + x
C = 5 + x
A + B + C = 24
(5 + x) + (5 + x) + (5 + x) = 24
15 + 3x = 24
3x = 24 -15
3x = 9
x = 9/3
x = 3
A = B = C = 5 + x = 5 + 3 = 8 inches
The length of the new sides of the triangle is 8 inches
Two opposing opinions were shown to a random sample of 1,500 buyers of a particular political news app in the United States. The opinions, shown in a random order to each buyer, were as follows:
Opinion A: Improving the healthcare system is more important than improving the education system.
Opinion B: Improving the education system is more important than improving the healthcare system.
Buyers were to choose the opinion that most closely reflected their own. If they felt neutral on the topics, they were to choose a third option of "Neutral."
The outcomes were as follows:
39% chose Opinion A, 54% chose Opinion B, and 7% chose "Neutral."
Part A: Create and interpret a 98% confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B. (5 points)
Part B: The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met? (5 points)
Answer:
A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B
= (0.51, 0.57)
This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)
B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.
Critical value = 2.33
Standard error = σₓ = √[p(1-p)/n]
p = sample proportion = 0.54
n = sample size = 1500
σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287
98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.54 ± (2.33 × 0.01287)
CI = 0.54 ± 0.02998)
98% CI = (0.51, 0.57)
98% Confidence interval = (0.51, 0.57)
B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?
For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;
- The sample data must have been obtained using a random sampling technique.
- The sampling distribution must be normal or approximately normal.
- The variables of the sample data must be independent of each other.
On the second point, the condition for a binomial distribution to approximate a normal distribution is that
np ≥ 10
and n(1-p) ≥ 10
The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.
For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.
Hope this Helps!!!
Apply the distributive property to factor out the gcf 6+30=
Answer:
Step-by-step explanation:
the distributive properrty of 6 + 30
6(1 + 5)
pleaaaaaaaaaaaaaaaaaaase help meeeeee
i this correct
Answer:
15.3 miles.
Step-by-step explanation:
Area of trapezoid is given by = 1/2*( sum of parallel side) height
Given area of trapezoid = 221.85 sq. miles
Length of parallel sides = 19 miles and 10 miles.
Sum of parallel sides = 19 miles + 10 miles = 29 miles.
Plugging the above values in formula for area of trapezoid we have
Area of trapezoid is given by = 1/2*( sum of parallel sides) height
221.85 = 1/2 (29) height
=> 221.85* 2 = 29* height
=> 443.7 = 29* height
=> 443.7/29 = height
=> height = 15.3
Thus, height is 15.3 miles.
Please answer ASAP In need of help
Answer:
5/7
Step-by-step explanation:
Billy experienced a rate of catfish to toral fish of 10/14. This is 5/7. So if this rate continues, he could expect the probability of catching a catfish to be : 5/7
The length between 20 and 29
The length between is the number 9 , just add 29 to 20 which is just 9 more numbers
What symbols are used to indicated statements?
Answer: => means “implies” or “if and then”
p,q,r are statements
Step-by-step explanation:
What is the negative square root of 4,900?
Answer: -70
Step-by-step explanation: hope I helped
Students in another survey were asked whether they plan to attend summer camp. Out of the 56 students in the survey, 44% said yes. Use rounding and compatible numbers to estimate how many students plan to attend summer camp.
Answer:
Students to attend camp = 56 x 44/100 = 24.64
Students to attend camp = 25
Step-by-step explanation:
Answer:
≈25 students
Step-by-step explanation:
Find out 44% of 56:
(44*56)÷100=
2464÷100=
24.64
So about 25 students out of 56 said yes, they were going to attend summer camp.
Gabby received 6 job offers from 15 interview he did last month.Which ratio best describes the relationship between the number of jobs he was not offered and the number of jobs for which he was interviewed
Answer:
the answer is 3:5
Step-by-step explanation:
Total number of jobs for the interview = 15
number of job offers received by Gabby = 6
number of jobs not offered = 15 - 6 = 9
therefore, the relationship will be 9:15
3:5
The mean age of 5 people in a room is 37 years.
A person enters the room.
The mean age is now 38.
What is the age of the person who entered the room?
my hegarty work lol im 2 lazy 2 answer
Answer:39?
Step-by-step explanation:
Answer:
43
Step-by-step explanation:
+ Total age of 5 people: 37 x5 = 185
+ Total age of 6 people (when 1 person enters the room): 38 x 6 = 228
+ The age of the person who enter the room is: 228 - 185 = 43 age
Anthony played a dart game using the dartboard shown above. Anthony had 5 throws and then added his points. He hit the -6 twice, the 10 once, the 2 once, and the -4 once. How many points did Anthony earn?
Answer:
- 4
Step-by-step explanation:
The number of points earned by Anthony is the sum of all the individual points earned from the 5 throws. Considering that he had -6 on 2 throws, 10 from one throw, 2 and the -4 from the final set of throws, the total is equivalent to
= -6 - 6 + 10 + 2 -4
= -4
Anthony earned a total of - 4 from the 5 throws.
Jason runs 440 yards in 75 seconds.at this rate,how many minutes does it take him to run a mile
Answer:
5 minutes
Step-by-step explanation:
Do a proportion
440/75= 1760/x
cross multiply
440x=1760(75)
simplify
132000/440
ASAP WILL MARK BRAINLEST
What is the number of possible combinations of 8 objects taken 6 at a time?
The number of possible combinations of 8 objects taken 6 at a time is 28. Then the correct option is D.
What is a combination?Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
The number of possible combinations of 8 objects taken 6 at a time.
Then the number of the combination is given as
[tex]\rm ^8C_6 = \dfrac{8!}{(8-6)! 6!}\\\\\\^8C_6 = \dfrac{8 \times 7 \times 6!}{2 \times 1 6!}\\\\\\^8C_6 = 7 \times 4\\\\\\^8C_6 = 28[/tex]
More about the combination link is given below.
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The owner of a car wash combines x gallons of a 2% liquid soap and 98% water mix with y gallons of a 7% liquid soap and 93% water mix to make 500 gallons of a 5% liquid soap and 95% water mix. Write a system of linear equations that represent the situation.
A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.
This question is incomplete and it lacks the attached diagram of the square based pyramid. Find attached to this answer, the square based pyramid.
Correct Question
A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.
A. What is the slant height of the pyramid?
B. What is the surface area of the composite figure?
HINT: The surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.
C. How many cubic yards of concrete are needed to make the planter?
Answer:
A. The slant height of the pyramid = 2.24 yards.
B. The surface area of the composite figure = 12.94 square yards.
C. The cubic yards of concrete are needed to make the planter = 2.67 cubic yards.
Step-by-step explanation:
A. What is the slant height of the pyramid?
To calculate the Slant height of a pyramid we make use of the Pythagoras Theorem which is given as:
a² + b² = c²
Where a = Height of the square pyramid represent by h
b = radius of the square pyramid represented by r
c = Slant height of the square pyramid represented by s
Therefore, we have
h² + r² = s²
Looking at the attached diagram, we are given the side length = 2 yards.
The radius of the square based pyramid = side length ÷ 2
= 2÷ 2 = 1 yard.
The height of a square based pyramid = 2 yards
Since , h² + r² = s²
The slant height of the square pyramid is calculated as :
√h² + r² = s
√(2² + 1²) = s
√5 = s
s = 2.24 yards
B. What is the surface area of the composite figure?
We were given hints in the question that the the surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.
Step 1
We find the Lateral area of the faces of the insides of the inverted pyramid
We have 4 faces, Hence,
The formula is given as
a × √( a² + 4h²
a = 2 yards
h = 2 yards
So, = 2 × √( 2² + 4 ×2²
The Lateral area of the faces = 8.94 square yards.
Step 2
Area of the 5 faces of the cube
= a²
Where a = side length = 2 yards
= 2²
= 4 square yards.
Step 3
Therefore, surface area of the composite figure = 8.94 square yards + 4 square yards
= 12.94 square yards.
C. How many cubic yards of concrete are needed to make the planter?
This is calculated by find the Volume of the Square based pyramid.
The formula is given as :
V = (1/3)a²h
Where a = side length = 2 yards
h = height of the square based pyramid = 2 yards
V = 1/3 × 2² × 2
V = 2.67 cubic yards
A spinner numbered 1 through 12 is spun. Find the probability that
the number spun is an 11 given that the number spun was an odd
number. Please write your answer as a fraction.
Answer:
[tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
Let A be the event of getting an odd number.
P(A) be the probability of getting an odd number.
Total odd numbers here are 6 i.e. [tex]\{1,3,5,7,9,11\}[/tex]
Here, total numbers in the game are 12 i.e [tex]\{1,2,3,....,12\}[/tex].
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
[tex]P(A) = \dfrac{6}{12}\\\Rightarrow \dfrac{1}{2}[/tex]
Let B be the event of getting 11.
P(B) be the probability of getting 11.
Total number of possible cases is 1.
[tex]P(B) = \dfrac{1}{12}[/tex]
[tex]P(A \cap B)[/tex] is the probability that we get 11 and an odd number.
Possible number of cases = 1
[tex]P(A\cap B) = \dfrac{1}{12}[/tex]
P(B/A) is the probability that we get an 11 given that it is an odd number.
[tex]P(B/A) = \dfrac{P(A \cap B)}{P(A)}\\\Rightarrow \dfrac{\dfrac{1}{12}}{\dfrac{1}{2}}\\\Rightarrow \dfrac{1}{6}[/tex]
Hence, P(B/A) = [tex]\dfrac{1}{6}[/tex]
Answer:
The probability in fraction is [tex]\frac{1}{12}[/tex].
Step-by-step explanation:
Total number of outcomes is = 12
Now we have to find the probability that spun number is 11.
That means favorable outcome is 1.
In this case, the probability can be determined by dividing the number of favorable outcomes by the total outcome. Accordingly, the total outcomes are 12 and favorable outcome is 1.
[tex]\text{P(The spun number is 11)}= \frac{\text{Favorable outcomes}}{\text{total outcomes}} \\\text{P(The spun number is 11)}= \frac{1}{12} \ (in \ fraction)\\\text{P(The spun number is 11)} = 0.083 \ (in \ decimal)[/tex]
Shreya enlarged the size of a rectangle to a width of 5.5 in. What is the new height if it was originally 1.1 in wide and 6.8 in tall?
Answer:
I believe that it is 34
Step-by-step explanation:
Find the slope of the line passing through the points (3, 8) (7, - 7)
Answer:
[tex]-\frac{15}{4}[/tex]
Step-by-step explanation:
To find the slope or the gradient of a line you have to utilise the formula
[tex]\frac{y2-y1}{x2-x1}[/tex]
Y₂ = -7
Y₁ = 8
X₂ = 7
X₁ = 3
So,
[tex]\frac{-7-8}{7-3}[/tex]
→ Simplify
[tex]-\frac{15}{4}[/tex]
By using the given points, we will see that the slope is -15/4.
How to find the slope of a line?
If we know that a given line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
[tex]s = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here the line passes through the points (3, 8) and (7, -7).
Using the above formula, we can see that the slope is:
[tex]s = \frac{-7 - 8}{7 - 3} = \frac{-15}{4}[/tex]
If you want to learn more about linear equations, you can read:
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find the area of the smaller sector. please help last question.
Answer:
The area of smaller sector is:
S = pi x 8^2 x 80/360 = 44.68 m2
Hope this helps!
:)
The measure of an angle is seventy-one times the measure of its supplementary angle. What is the measure of each angle?
Answer:
The measures are 2.5 deg and 177.5 deg.
Step-by-step explanation:
The ratio of the measures of larger angle to the smaller angle is 71:1.
71k + k = 180
72k = 180
k = 180/72
k = 2.5
71k = 71 * 2.5 = 177.5
Answer: The measures are 2.5 deg and 177.5 deg.
your garden has a perimeter of 36 feet. what is the length of missing side.
Answer:
I think the answer is 3 for 1 length side. And in you need 12 for both length sides. So the total is 36 and one side is 12. Since it's a rectangle,you now know two side lengths since they are the same,just opposite from each other. So 12 + 12 = 24. You do 36 – 24 because you need to get the total number for length which is 12. 12 divided by 2 is 6 which is one length side. You can check by doing 6 + 6 + 12 + 12 and you get 36.
Hope this helped!
Can I get brainliest?
The circumference of a circular field is 163.28 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.
Answer:
r = 26
Step-by-step explanation:
C = 2 π r
163.28 = 2 (3.14) (r)
163.28 / 2 / 3.14
26 = r
Answer:
26 yards
Step-by-step explanation:
2πr=163.28
2×3.14×r=163.28
r=163.28÷6.28=26 yards
A culture started with 2,000 bacteria. After 2
hours, it grew to 2,200 bacteria. Predict how
many bacteria will be present after 19 hours.
Round your answer to the nearest whole
number.
und to four
P = Aekt
Enter the correct answer
DONE
O
?
Answer:
2450
Step-by-step explanation:
First you will divide;
200÷4=50
Then you multiply;
50×9=450
Last you add;
2000+450=2450
Hope this helps :D
Answer:
4949 is your answer
Step-by-step explanation:
The point P= (x,-1/7) lies on the unit circle shown below. What is the value of x in simplest form?
Answer:
[tex] x^2 + \frac{1}{49} =1 [/tex]
And solving for x we got:
[tex] x^2 = 1- \frac{1}{49}[/tex]
[tex] x^2 = \frac{48}{49}[/tex]
And taking square root we got:
[tex] x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}[/tex]
Step-by-step explanation:
For this case we have the following point given [tex] P(x , -1/7)[/tex]
And we want to find the value of x, since P lies on the unitray circle if we find the distance from P to the center of the unitary circle (0,0) we need to get 1. Using the definition of Euclidean distance that means:
[tex] d = \sqrt{(x -0)^2 +(-1/7 -0)^2}=1[/tex]
And if we square both sides of the last equation we got:
[tex] x^2 + \frac{1}{49} =1 [/tex]
And solving for x we got:
[tex] x^2 = 1- \frac{1}{49}[/tex]
[tex] x^2 = \frac{48}{49}[/tex]
And taking square root we got:
[tex] x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}[/tex]
Please help me it’s really important for me
Answer:
1. B
2. A
3. B
4. ???
5. A
6 ???
7. I can't see it
Step-by-step explanation:
