Answer:
38ft
Step-by-step explanation:
I'm assuming that you mean that the dimensions are 8ft by 11ft
If so, you need to add all the sides together, there should be two 8ft sides and two 11ft sides
8*2 = 16 (or 8+8
11*2= 22 (or 11+11
16+22 = 38
PLEASE ANSWER!URGENT! The table below shows the approximate height of a ball thrown up in the air after x seconds. Which quadratic model best represents the data?
Answer:
A) f(x) = –16x2 + 99x + 6
Step-by-step explanation:
ed2021 :)
If each edge is 5 inches, what will be the surface area of the cube? Pls help.
Answer:
C
Step-by-step explanation:
A cube has 6 square faces
Each face: 5² = 25
Surface area: 6(25) = 150 in²
In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast. If a person is selected at random, find the probability that the person preferred milk as his or her primary drink.
Answer:
Probability that the person preferred milk as his or her primary drink = 0.3
Step-by-step explanation:
Given -
In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast .
Total no of people is = 18 + 29 + 13 = 60
If a person is selected at random ,
The probability of person preferred milk = [tex]\frac{18}{60}[/tex]
The probability of person preferred coffee = [tex]\frac{29}{60}[/tex]
The probability of person preferred juice = [tex]\frac{13}{60}[/tex]
Probability that the person preferred milk as his or her primary drink =
P ( milk ) = [tex]\mathbf{\frac{No\;of\;favourable\;outcomes}{total\;no\;of\:outcomes}}[/tex]
= [tex]\frac{18}{60}[/tex] = 0.3
Hattie is making fruit baskets, which includes apples and bananas, to send to some of her real estate clients. She wants each basket to have 12 pieces of fruit, but the fruit should weigh no more than 80 ounces total. On average, each apple weighs 5 ounces, and each banana weighs 7 ounces.
Answer:
Step-by-step explanation:
The answer is 10 bananas and 2 apples
The number of apples are 2 and number of bananas is 10.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Hattie is making fruit baskets, which includes apples and bananas, to send to some of her real estate clients.
She wants each basket to have 12 pieces of fruit, but the fruit should weigh no more than 80 ounces total.
On average, each apple weighs 5 ounces, and each banana weighs 7 ounces.
Let Bananas is denoted by B and Apples are represented by A.
A+B=12...(1)
5A+7B<80...(2)
A=12-B
Substitute in equation 2.
5(12-B)+7B=80
60-5B+7B=80
60+2B=80
Subtract 60 on both sides.
2B=80-60
2B=20
Divide both sides by 2.
B=10
A+B=12
A+10=12
A=2
Hence, the number of apples are 2 and number of bananas is 10.
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Consider the following linear programming problem: The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function
Answer:
We have,
max 4x+10y
3x+4y<480
4x+2y<360
The feasible corner points are ( 48,84),(0,120),(0,0),(90,0)
Now, our problem is maximum type so put above feasible points in equation max 4x + 10y one by one and select one point at which our value from this equation is maximum,
(48,84) 4*48+10*84 1032
(0,120) 4*0+10*120 1200
(0,0) 4*0+10*0 0
(90,0) 4*90+10*0 360
Here we get maximum value at (0,120) which is 1200.
Correct option is (B)1200
Answer:
Answer is 1200.
Refer below.
Step-by-step explanation:
The maximum possible value for the objective function is 1200.
A ticketholder on the merry-go-round is riding a horse that is at a radius of 12 feet. How far does she travel after the merry-go-round rotates 3π5 radians? Give approximate answer. Round decimal to the tenth space.
The correct value of the angle of rotation is 3π/5
Answer:
Distance travelled ≈ 22.6 ft
Step-by-step explanation:
We are given;
Radius;r = 12 ft
Angle of rotation; θ = 3π/5
The formula for calculating distance travelled is;
Distance travelled = rθ
So, plugging in the relevant values;
Distance travelled = 12 x 3π/5
Distance travelled ≈ 22.6 ft
Find the value of x
Answer:
37
Step-by-step explanation:
all triangle's angle measures add up to 180
180-98-45 = x
x = 37
Answer:
x = 37 degrees.Step-by-step explanation:
All triangles = 180 degrees
^ That is known.
98 + 45 = 143
^ These 2 angles are given (98 and 45)
180 - 143 = 37
^ This was the total.
37 is the final answer.
I hope I helped you!
American Statistical Association budget is distributed normally with a mean spending of $45.67 and a standard deviation of $5.50. What is the probability that the spending is more than $42.35
Answer:
Probability that the spending is more than $42.35 is 0.7271.
Step-by-step explanation:
We are given that American Statistical Association budget is distributed normally with a mean spending of $45.67 and a standard deviation of $5.50.
Let X = American Statistical Association budget
So, X ~ N([tex]\mu=45.67,\sigma^{2} =5.5^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean spending = $45.67
[tex]\sigma[/tex] = standard deviation = $5.50
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
So, the probability that the spending is more than $42.35 is given by = P(X > $42.35)
P(X > $42.35) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{42.35-45.67}{5.5}[/tex] ) = P(Z > -0.604) = P(Z < 0.604)
= 0.7271
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.604 in the z table which will lie between x = 0.60 and x = 0.70 which has an area of 0.7271.
Hence, the probability that the spending is more than $42.35 is 0.7271.
Which equation represents a proportional relationship that has a constant of proportionality equal to 1/5
if f(x) = [tex]\frac{(3+x)}{(x-3)}[/tex], what is f(a +2)?
Answer:
[tex]f(a) = \frac{(a+5)}{(a-1)}[/tex]
Step-by-step explanation:
Given : [tex]f(x) = \frac{(3+x)}{(x-3)}[/tex]
In order to find [tex]f(a+2)[/tex] we will substitute [tex](a+2)[/tex] for [tex]x[/tex] in the given function, that is :
[tex]f(a) = \frac{(3+a+2)}{(a+2-3)}[/tex]
[tex]f(a) = \frac{(a+5)}{(a-1)}[/tex]
What is the measure of Zc?
so 90-
42
48
90
180
Angle Zc measures 90° as it is supplementary to the given 90° angle. Therefore, Zc = 90°.
To find the measure of angle Zc, we need to use the properties of angles formed by intersecting lines.
Given:
- Angle Zc is supplementary to angle 90°.
- Angle 90° is formed by the intersection of lines, let's denote them as line AB and line CD.
- Angle 90° is bisected by line EF, forming two congruent angles.
Step-by-step explanation:
1. Since angle Zc is supplementary to angle 90°, we subtract the measure of angle 90° from 180° to find the measure of angle Zc.
Measure of angle Zc = 180° - 90°
= 90°
So, angle Zc measures 90°.
6th grade math) help please
Answer:
C 66 miles
Step-by-step explanation:
88miles/4 gallons = 22 miles/gallon
22 miles/ gallon * 3 gallons = 66 miles
Answer:
66 miles per 3 gallons
Step-by-step explanation:
if you divide 88 by 4 you get 22 which means you get 22 miles to each gallon so for three gallons you would be able to drive 66 miles
Hope I helped:)
A barbershop requires appointments for perms and hair cuts. Ten percent of those making appointments cancel or simply fail to show up. Next week's appointment calendar has 64 appointments. Let x be the number of missed appointments out of the 64. The probability that more than 3 cancellations and/or no-shows will occur during the next week is:
Answer:
0.8937
Step-by-step explanation:
This is a case of binomial probability with n = 64, p = 0.10 and x = 3. This means that the probability of a cancellation is 10%. Here, we can find the probability that more than 3 cancellations or no shows will occur by finding binompdf(64,0.10, 0) + binompdf(64,0.10, 1) + binompdf(64,0.10, 2) + binompdf(64,0.10, 3) and then subtracting this sum from 1.000.
We get: 0.0012 + 0.0084 + 0.0293 + 0.0674 = sum = 0.1063
Then the desired probability is 1.0000 - 0.1063 = 0.8937
The probability that more than 3 cancellations and/or no-shows will occur during the next week is: 0.8937
This involves binomial probability distribution with the formula;
P(X = x) = ⁿCₓ × pˣ × q⁽ⁿ ⁻ ˣ⁾
We are given;
p = 10% = 0.1
n = 64
q = 1 - p = 1 - 0.1
q = 0.9
We want to find the probability that more than 3 cancellations and/or no-shows will occur during the next week is given by;
P(X > 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X =3))
From online binomial probability calculator;
P(0) = 0.0012
P(1) = 0.0084
P(2) = 0.0293
P(3) = 0.0674
Thus;
P(X > 3) = 1 - (0.0012 + 0.0084 + 0.0293 + 0.0674 )
P(X > 3) = 1 - 0.1063
P(X > 3) = 0.8937
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.
Write an equation for the line that is parallel to the given line and that passes through the given point. y=−6x+2;(−1,2)
A. y=−8x−8y=-8x-8
B. y=6x−8y=6x-8
C. y=−6x+4y=-6x+4
D. y=−6x−4y=-6x-4
7 times a number is 8 less than the square of that number. Find the negative solution.
Answer:
-1
Step-by-step explanation:
The required relation is ...
7n = n^2 -8
0 = n^2 -7n -8 . . . . put in standard form
0 = (n -8)(n +1) . . . . factor
Solutions are n=8 and n=-1.
The negative solution is -1.
Aiden learned 12new words. Wyatt learned 6 new words How many times as many new words as Wyatt did Aiden learn
Answer:
2
Step-by-step explanation:
6×2=12
That is how I got the answer.
Answer:
2
Step-by-step explanation:
identify the horizontal aysmptote of each graph. t(x)=6^x
Answer:Y=0 Y=-3
Step-by-step explanation:
Answer:
First graph y=0
Second graph y=-3
Step-by-step explanation:
Edge 2022
A rectangular prism with a volume of 8 cubic units is filled with cubes twice: once with cubes with side lengths of 1/2 unit and once with cubes with side lengths of 1/3 unit. How many more of the 1/3-unit cubes are needed to fill the prism than if we used the 1/2-unit cubes? * Your answer
Answer:
Step-by-step explanation:
Given that,
A rectangular prism with a volume of 8 cubic units, V = 8 cubic units
The rectangular prism is filled with a cube twice.
First one
A cube with ½ length unit, we should know that a cube have equal length
Then, L = ½ units
Volume of a cube is L³
V = L³
V1 = (½)³ = ⅛ cubic units
Second cube
A cube with ⅓ length unit, we should know that a cube have equal length
Then, L = ⅓ units
Volume of a cube is L³
V = L³
V1 = (⅓)³ = 1 / 27 cubic units
So, to know number of times cube one will filled the rectangular prism
V = nV1
Where V is the volume of rectangular prism
n is the number of times the cube will be able to matched up with the volume of the rectangular prism
Then, n_1 = V / V1
n_1 = 8 / ⅛
n_1 = 64 times
Also,
n_2 = V / V2
n_2 = 8 / 1 / 27
n_2 = 8 × 27 = 216 times
So, the we need more of ⅓units and we will need (216 - 64) = 152 times
We need 152 more of ⅓units
You need 152 more cubes with side lengths of 1/3 unit than cubes with side lengths of 1/2 unit to fill a rectangular prism with a volume of 8 cubic units.
To determine how many more cubes with side lengths of 1/3 unit are needed to fill the rectangular prism compared to cubes with side lengths of 1/2 unit, we first need to find the number of each type of cube that fits into the prism.
The volume of the rectangular prism is given as 8 cubic units.
First, let's calculate the volume of one small cube:
For a cube with side length 1/2 unit, the volume is (1÷2)^3 = 1/8 cubic units.For a cube with side length 1/3 unit, the volume is (1÷3)^3 = 1/27 cubic units.Next, determine how many of each type of cube are needed to fill the prism:
Number of 1/2-unit cubes: 8 / (1÷8) = 64 cubes.Number of 1/3-unit cubes: 8 / (1÷27) = 216 cubes.The difference in the number of cubes needed is:
216 (1/3-unit cubes) - 64 (1/2-unit cubes) = 152 more 1/3-unit cubes.
What is the Inverse operation needed to solve for p?
765 = p - 254
Answer:
Adding 254 to both sides.
This is an inverse operation.
On the right side of the equation, there is a -254, which you need to get rid of in order to isolate p. (You have to isolate p to find the value)
So, since it is -254, you would do +254 on BOTH sides of the equation. Hope this helps!!
The inverse operation needed to solve for p in the equation 765 = p - 254 is addition.
Explanation:To solve for p in the equation 765 = p - 254, we need to isolate p on one side of the equation. To do this, we can use the inverse operation of subtraction, which is addition. By adding 254 to both sides of the equation, we get:
765 + 254 = p - 254 + 254
Simplifying the equation gives us:
1019 = p
Therefore, the inverse operation needed to solve for p is addition.
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For a hypothesis test of the claim that the mean amount of sleep for adults is less than 9 hours, technology output shows that the hypothesis test has power of 0.4038 of supporting the claim that muless than9 hours of sleep when the actual population mean is 8.5 hours of sleep. Interpret this value of the power, then identify the value of beta and interpret that value.
Answer:
a) probability of choosing the mean amount of sleep for adult as μ < 9 hours when it is μ = 8.5 hours is 0.4038
b) There is a 0.5962 probability of failing to choose that the mean amount of sleep for adult is μ < 9 hours when it is μ = 8.5 hours
Step-by-step explanation:
a) Interpret the value of the power
The power of an hypothesis is the probability of rejecting the null hypothesis when the alternative hypothesis is valid. It is a type 1 error
Power = 0.4038
From the hypothesis test,
the null hypothesis, μ = 8.5 hours
Alternative hypothesis, μ < 9 hours
Sine the power is the probability of rejecting the null hypothesis, it means that the probability of choosing the mean amount of sleep for adult as μ < 9 hours when it is μ = 8.5 hours is 0.4038
b)
Power + β = 1
β = 1 - Power
β = 1 - 0.4038
β = 0.5962
β, type 2 error, is the probability of not rejecting the null hypothesis even when it is false.
It means that there is a 0.5962 probability of failing to choose that the mean amount of sleep for adult is μ < 9 hours when it is μ = 8.5 hours
The power of a test (0.4038 in this case) is the probability that we correctly reject the null hypothesis, given the actual population mean is 8.5 hours. Beta (1 - Power, or 0.5962 in this case) is the probability of committing a type II error, which is incorrectly accepting the null hypothesis.
Explanation:In the context of hypothesis testing in statistics, the power of a test refers to the probability that the test will correctly reject the null hypothesis when the alternative hypothesis is true. In this specific scenario, the power of the test is 0.4038. This means that there is a 40.38% chance that we would correctly conclude that the mean sleep for adults is less than 9 hours, assuming that the actual population mean is 8.5 hours.
The value of beta represents the probability of committing a type II error, which is the error of not rejecting a null hypothesis when it should be rejected; in other words, incorrectly concluding that the mean sleep for adults is not less than 9 hours when it actually is. The value of beta can be calculated as 1 minus the power of the test, so in your case it would be 1 - 0.4038 = 0.5962. This means there is a 59.62% chance of committing a type II error.
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Toilet Training You are a great friend and are taking your friend's child to the playground to play with two of his friends: Charles and Elizabeth. You overhear the dads of Charles and Elizabeth talking about a recent study regarding toilet training of children. The study found that the mean age for girls to stay dry during the day (successful completion of toilet training) is 32.5 months, and the mean age for boys is 35.0 months. These two groups had reported standard deviations for the age when a child is successfully toilet trained of 6.7 months for girls and 10.1 months for boys based on a sample of 126 girls and a second sample of 141 boys. Charles's dad and Elizabeth's dad are getting into a disagreement about how to interpret these results. Based on your knowledge from Stats 250, can you help settle their disagreement by helping to answer the following questions about the difference between the population mean age for girls to be successfully toilet trained and the population mean age for boys to be successfully toilet trained? Question 5 Subquestions 5.
a TBD points Based on our given information, should you use the unpooled (Welch's) or the pooled approach to calculate the confidence interval? Make sure to include numerical support for your answer. No answer entered. Click above to enter an answer. 5.
b TBD points The reported 95% confidence interval is (0.3927 months. 4.6073 months). Based on this confidence interval, which group was chosen to be group 1? How do you know? What is the probability that our parameter of interest, the true difference in population means of ages of successful toilet training between boys and girls, is included in the interval? No answer entered. Click above to enter an answer. 5.
C TBD points Charles's dad is upset that this result guarantees that his son will be at a disadvantage, since he will be toilet trained later than Elizabeth. Elizabeth's dad starts to correct him, stating that this only means that there is only a 95% probability that Elizabeth will be toilet trained before Charles. Are either of these statements correct? Explain why you made your choice.
Answer:
Step-by-step explanation:
Hello!
According to a study regarding the average age of female and male kids to complete toilet training is:
Females:
Average age 32.5 months
The standard deviation of 6.7 months
n= 126
Males:
Average age 35.0 months
The standard deviation of 10.1 months
n= 141
The parameter of study is the difference between the age of females are successfully toilet trained and the average age that males are successfully toilet trained. μf - μm (f= female and m= male)
a.
Assuming that both variables have a normal distribution to choose whether you'll use an unpooled or pooled-t to calculate the confidence interval you have to conduct an F-test for variance homogeneity.
If the variances are equal, then you can usee the pooled-t, but if the variances are different, you have to uses Wlche's approach:
H₀: δ²f = δ²m
H₁: δ²f ≠ δ²m
Since both items b. and c. ask for a 95% CI I'll use the complementary significance level for this test:
α: 0.05
[tex]F= \frac{S^2_f}{S^2_m} * \frac{xSigma^2_f}{Sigma^2_m} ~~~F_{(n_f-1); (n_m-1)}[/tex]
[tex]F= \frac{(6.7^2)}{(10.1)^2} *1= 0.44[/tex]
Critical values:
[tex]F_{125;140;0.025}= 0.71\\F_{125;140;0.975}= 1.41[/tex]
The calculated F value is less than the lower critical value, 0.77, so the decision is to reject the null hypothesis. In other words, there is no significant evidence to conclude the population variances of the age kids are toilet trained to be equal. You should use Welch's approach to construct the Confidence Intervals.
[tex]Df_w= \frac{(\frac{S^2_f}{n_f} + \frac{S^2_m}{n_m} )^2}{\frac{(\frac{S^2_f}{n_f} )^2}{n_f-1} +\frac{(\frac{S^2_m}{n_m} )^2}{n_m-1} }[/tex]
[tex]Df_w= \frac{(\frac{6.7^2}{126} + \frac{10.1^2_m}{141} )^2}{\frac{(\frac{126^2}{126} )^2}{126-1} +\frac{(\frac{10.1^2}{141} )^2}{141-1} } = 254.32[/tex]
b.
The given interval is:
[0.3627; 4.6073]
Using Welch's approach, the formula for the CI is:
(X[bar]f- X[bar]m) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]
or
(X[bar]m- X[bar]f) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]
As you can see either way you calculate the interval, it is centered in the difference between the two sample means, so you can clear the value of that difference by:
(Upper bond - Lower bond)/2= (4.6073-0.3627)/2= 2.1223
The average age for females is 32.5 months and for males, it is 35 months.
Since the difference between the sample means is positive, we can say that the boys were considered "group 1" and the girls were considered "group 2"
You have a95% confidence that the parameter of interest is included in the given confidence interval.
c.
None of the statements is correct, the interval gives you information about the difference between the average age the kids are toilet trained, that is between the expected ages for the entire population of male and female babies.
This represents a guideline but is not necessarily true to all individuals of the population since some male babies can be toilet trained before that is expected as some female babies can be toiled trained after the average value.
I hope it helps!
StartRoot 53 EndRoot is between 7.2 and 7.3. Estimate further to the hundredths place. Which two consecutive values does StartRoot 53 EndRoot fall between?
7.26 and 7.27
7.27 and 7.28
7.28 and 7.29
7.29 and 7.30
Answer:
7.28 7.29 c
Step-by-step explanation:
The square root of 53 can be found to lie between the values of 7.28 and 7.29.
What is the square root function?The square root function can only have non negative values. If we take thee square root of a number, we obtain a value that can be multiplied by itself to obtain the number.
The square root of 53 can be found to lie between the values of 7.28 and 7.29.
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Which statements are correct? Check all that apply.
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
If a quadratic function has two real roots, then both roots must be rational.
A quadratic function can have three zeros.
All quadratic functions touch or cross the x-axis at least once.
Answer:
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
Step-by-step explanation:
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
What is quadratic function?A quadratic function is a polynomial function with one or more in which highest exponent of variable is two.
According to the question,
A quadratic function can have two irrational roots.
example: [tex]x^{2} -2x -2 =0[/tex]
This equation have two irrational roots 1+√3 and 1 - √3.
A quadratic function can have no real number solutions
Hence, A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
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2. If 1 cm3 of iron has a mass of 7.52 g, what is the mass of an iron bar of rectangular cross section with
the dimensions shown?
120.0 cm
3.2 cm
í
1.7 cm
Answer:
248cm
Step-by-step explanation:
Graph y=4x-9 ill give brainliest for first one that is correct
Answer:
I hope this helps
Look at the cahrt below The number of satisfied customers is given below each month on the x axis select an appropriate scale for the y axis of the graph
Answer:
wydjae is męi ze tak
Step-by-step explanation:
The appropriate scale for the y-axis include:
A = 2000
B = 4000
C = 6000
D = 8000
E = 10000
F = 12000
G = 14000
In Mathematics and Euclidean Geometry, a bar chart is a type of graph that is used for the graphical representation of a data set, especially through the use of rectangular bars and vertical columns.
Since the set of axes starts from the origin (0, 0), an appropriate scale for the y-axis (number of satisfied customers) of the graph can be calculated as follows;
1 unit = 250 customers
4 units = (4 × 250) = 2,000 customers.
In this context, the appropriate scale for the y-axis should be completed as follows:
A = 2000
B = 4000
C = 6000
D = 8000
E = 10000
F = 12000
G = 14000
Complete Question;
Look at chart below.
The number of satisfied customers is given below each month on the x-axis.
Select an appropriate scale for the y-axis of the graph.
The appropriate scale for the y-axis is:
A =
B =
C =
D =
E =
F =
G =
What value of n makes the equation 2/3 times in equals 4/9 true
Answer:
the answer is 3/2
Step-by-step explanation:
because when you divide it you have to do keep change flip so you change 4/9 to 9/4 and divide it by 2/3 to get 3/2 so you put it in the equation to see if it is correct
The equation is a linear function, and the value of n that makes the 2/3 times n equals 4/9 true is 2/3
How to determine the value of n?The equation in the question implies that:
2/3 of n equals 4/9
This equation can be expressed as:
2/3 * n = 4/9
Multiply both sides by 3
3 * 2/3 * n = 3 * 4/9
Evaluate the product
2 * n = 4/3
Divide both sides by 2
n = 2/3
Hence, the value of n that makes the 2/3 times n equals 4/9 true is 2/3
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An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Find the probability of the sum of the dots indicated. A sum less than 8
Answer:
7/12
Step-by-step explanation:
Probability is a ratio defined by the number of possible outcome to the number of total outcome. The probability that an event will happen added to the probability that the event will not happen gives 1. In other words, the outcome of a probability cannot exceed 1.
The probability that an event a will happen or that another independent event b will happen is the sum of the probability that a will happen to the probability that b will happen.
For the 2 dies, the outcomes possible when rolled are as shown below
O 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
From the table, there are 36 possible outcomes but only 21 outcomes are less than 8 hence the probability required
= 21/36
= 7/12
It takes Ernesto 3 minutes to jog a lap around the school track. How many laps can Ernesto complete in 15 minutes?
Answer:
5 laps
Step-by-step explanation:
We can use ratios to solve
3 minutes 15 minutes
----------------- = ------------------------
1 lap x laps
Using cross products
3x = 15
Divide each side by 3
3x/3 = 15/3
x = 5
He can do 5 laps
manufacturing company produces digital cameras and claim that their products maybe 3% defective. A video company, when purchasing a batch of 2000 cameras, applies the following sample plan: They randomly select 20 cameras and accept the whole batch if there are more than 17 working cameras. What is the correct probability statement for the company to accept the whole batch
Answer:
P(X>17) = 0.979
Step-by-step explanation:
Probability that a camera is defective, p = 3% = 3/100 = 0.03
20 cameras were randomly selected.i.e sample size, n = 20
Probability that a camera is working, q = 1 - p = 1 - 0.03 = 0.97
Probability that more than 17 cameras are working P ( X > 17)
This is a binomial distribution P(X = r) [tex]nCr q^{r} p^{n-r}[/tex]
[tex]nCr = \frac{n!}{(n-r)!r!}[/tex]
P(X>17) = P(X=18) + P(X=19) + P(X=20)
P(X=18) = [tex]20C18 * 0.97^{18} * 0.03^{20-18}[/tex]
P(X=18) = [tex]20C18 * 0.97^{18} * 0.03^{2}[/tex]
P(X=18) = 0.0988
P(X=19) = [tex]20C19 * 0.97^{19} * 0.03^{20-19}[/tex]
P(X=19) = [tex]20C19 * 0.97^{19} * 0.03^{1}[/tex]
P(X=19) = 0.3364
P(X=20) = [tex]20C20 * 0.97^{20} * 0.03^{20-20}[/tex]
P(X=20) = [tex]20C20 * 0.97^{20} * 0.03^{0}[/tex]
P(X=20) = 0.5438
P(X>17) = 0.0988 + 0.3364 + 0.5438
P(X>17) = 0.979
The probability that there are more than 17 working cameras should be 0.979 for the company to accept the whole batch