Answer:
A,C,F
Step-by-step explanation: I took the test :)
The expression 64 is perfect cube of 3.
The expression [tex]8x^{3][/tex] is the perfect cube of [tex](2x)^{3}[/tex].
The expression [tex]12x^{9}[/tex] is perfect square of [tex](5x^{3})^{3}[/tex]
We have to determine, which to the following is perfect cube.
According to the question,
A perfect cube is an integer that is equal to some other integer raised to the third power.
To obtain the perfect cubes of the expression, it can be determined in following steps.
The given expression is 64.
To convert it into perfect square written in small factor parts.
Therefore, 64 written as,
[tex]= 64\\\\= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\\\= (2)^{3} \times (2)^{3}\\\\= (2\times 2)^{3}\\\\=( 4)^{3}[/tex]
The expression 64 is perfect cube of 3.
The given expression is 16x.
To convert it into perfect square written in small factor parts.
Then,
16x can be written as,
[tex]= 16x \\\\= 2\times 2\times 2\times 2\times x\\\\= 2x.(2)^{3}\\[/tex]
The expression 16x is not perfect cube.
The given expression is [tex]8x^{3][/tex].
To convert it into perfect square written in small factor parts.
Then,
[tex]8x^{3}[/tex] can be written as,
[tex]= 8x^{3}\\\\= 2 \times 2 \times 2 \times x^{3}\\\\= (2)^3 \times {x^{3}}\\\\= (2x)^{3}[/tex]
The expression [tex]8x^{3][/tex] is the perfect cube of [tex](2x)^{3}[/tex].
The given expression is [tex]27x^{4}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]27x^{4}[/tex] can be written as,
[tex]= 27x^{4}\\\\= 3 \times3 \times3 \times x^{4}\\\\= (3)^{3} \times x \times x^{3}\\\\= x \times (3x)^3[/tex]
The expression [tex]27x^{4}[/tex] is not a perfect cube.
The given expression is [tex]81x^{6}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]81x^6[/tex] can be written as,
[tex]= 81x^{6}\\\\= 3 \times3 \times3 \times3 \times x^{6}\\\\= 3.(3)^{3} \times x^{3} \times x^{3}\\\\= 3 \times ( 3x^{2}) ^{3}[/tex]
The expression [tex]81x^{6}[/tex] is not a perfect cube.
The given expression is [tex]81x^{6}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]125x^{9}[/tex] can be written as,
[tex]=125x^{9}\\\\= 5 \times 5 \times 5 \times x^{3} \times x^{3} \times x^{3}\\\\= (5x^{3})^{3}[/tex]
The expression [tex]12x^{9}[/tex] is perfect square of [tex](5x^{3})^{3}[/tex]
To know more about perfect square click the link given below.
https://brainly.com/question/16780291
Enter a positive common factor (other than 1) of 15 and 10
A bakery sells 11 types of sandwiches. Here are their calorie amounts 279,595, 597, 599, 601, 603, 608, 611, 617, 617, 950. Identify all values that are outliers
Answer:
279 and 950
Step-by-step explanation:
Outliers are numbers that are significantly greater or lesser than the other numbers in the data set.
The other numbers are very close together on a numerical scale, with the exception of 279 and 950.
Therefore, these two numbers are the outliers.
The outliers are 279 and 950
Outliers:Outliers are numbers that are significantly more or lesser as compared to the other numbers in the data set.The other numbers are very nearest together on a numerical scale, having the exception of 279 and 950.So, these two numbers are considered to be the outliers.Learn more about the outlier here: https://brainly.com/question/9933184?referrer=searchResults
Please help! Correct answer only, please! Consider the matrix shown below: Find the inverse of the matrix A: (i.e Find A^-1).
Answer:
Hello There Again. The correct answer is D.
Explanation: Why is D. Because 5x2=10 which everyone know that 5x2=10x3x1=30 So the best choice will be D.
Hope It Helps!
HELPPPPP
Lisa is framing a rectangular painting length more than twice the widthShe uses 30 inches of framing material. What the length of the paintingWrite equation and solve.
A.3w+3=30;21
b.3w+3=30;9
C.6w+6=30;11
D.6w + 6 = 30 = 4
Answer:
6w = 30
Step-by-step explanation:
We should know that the 30 inches of framing material were used to frame the four sides of the rectangle.
The perimeter of the rectangle is what we should be considering, whenever we are dealing with frames.
This is 2 X (length + width)
From the questions, we can get the dimensions of the rectangle using clues from the various statements made.
From the statement"a rectangular painting length more than twice the width" we can see that the
L = 2w ------------------------- equation 1
substituting this value into the formula for the perimeter of the rectangle we have
30 = 2(2w + w)
30 = 6w
w= 5
from equation 1
L =2 X (5) = 10
Hence, we can set up the equation
6w = 30
However, the closest option to what we have is option D
6w + 6 = 30 - 4
complete question:
Lisa is framing a rectangular painting. The length is three more than twice the width. She uses 30 inches of framing material. What is the length of the printing? Write an equation and solve
Answer:
D.6w + 6 = 30 = 4
Step-by-step explanation:
perimeter = 30 inches
width = w
length = 2w + 3
perimeter of a rectangle = 2l + 2w
where
w = width
l = length
Therefore,
perimeter of a rectangle = 2(2w + 3) + 2w
perimeter of the rectangle = 4w + 6 + 2w
perimeter = 6w + 6
recall
perimeter = 30 inches
6w + 6 = 30
6w = 24
divide both sides by 6
w = 24/6
w = 4
What’s the correct answer for this?
Find the probability of each one:
Taffy would be 1/6
Chips would be 1/3
Soda would be 1/3
For the probability of all three multiply them together:
1/6 x 1/3 x 1/3 = 1/54
An ice-cream shop uses the following ingredients to make one sundae.
Ingredients. Amount
Ice-cream- 2 scoops
Sprinkles- 4 spoonful's
Whipped Cream- 2 tablespoons
How many sundaes did the shop make if they used 32 spoonful's of whipped cream?
Answer:
16
Step-by-step explanation:
there are 2 tbs of whipped cream per sundae so you have to divide 32 by 2 and get 16
Answer: 8
Step-by-step explanation:
For every 1 sundae, the shop uses 4 spoonfuls of sprinkles. The ratio of sundaes to spoonfuls of sprinkles is 1:4.
The shop used 32 spoonfuls of sprinkles.
Since the number of spoonfuls of sprinkles was multiplied by 8, we also need to multiply the number of sundaes by 8.
The shop made 8 sundaes.
State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number μο and write to : μ analogous expression for Ha) Ao and the appropriate
a. The average time workers spent commuting to work in Verona five years ago was 38.2 minutes. The Verona Chamber of Commerce asserts that the average is less now
b. The mean salary for all men in a certain profession is $58,291. A special interest
c. The accepted figure for the caffeine content of an 8-ounce cup of coffee is 133 mg. A dietitian believes that the average for coffee served in a local restaurants is higher
d. The average yield per acre for all types of corn in a recent year was 161.9 bushels. An economist believes that the average yield per acre is different this year.
e. An industry association asserts that the average age of all self-described fly fishermen is 42.8 years. A sociologist suspects that it is higher.
Answer:
a) The null hypothesis is given as
H₀: μ₀ ≥ 38.2 minutes
The alternative hypothesis is given as
Hₐ: μ₀ < 38.2 minutes
b) The null hypothesis is given as
H₀: μ₀ = $58,291
The alternative hypothesis is given as
Hₐ: μ₀ ≠ $58,291
c) The null hypothesis is given as
H₀: μ₀ ≤ 133.0 mg
The alternative hypothesis is given as
Hₐ: μ₀ > 133 mg
d) The null hypothesis is given as
H₀: μ₀ = 161.9 bushels
The alternative hypothesis is given as
Hₐ: μ₀ ≠ 161.9 bushels
e) The null hypothesis is given as
H₀: μ₀ ≤ 42.8 years
The alternative hypothesis is given as
Hₐ: μ₀ > 42.8 years
Step-by-step explanation:
In hypothesis testing, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.
Taking the statements one at a time
a) The assertion is that the new average time workers spent commuting to work in Verona is now less than the old average.
The null hypothesis would be there isn't enough evidence to conclude that the new average time workers spent commuting to work in Verona is now less than the old average. That is, the new average time workers spent commuting to work in Verona is now equal to or more than the old average.
The alternative hypothesis is that the new average time workers spent commuting to work in Verona is now less than the old average.
Mathematically, if μ₀ = new average time workers spent commuting to work in Verona.
The null hypothesis is given as
H₀: μ₀ ≥ 38.2 minutes
The alternative hypothesis is given as
Hₐ: μ₀ < 38.2 minutes
b) Although the question isn't complete,
The null hypothesis is that there isn't a significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.
The alternative hypothesis is that there is significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.
Mathematically, if μ₀ = Mean of whatever is being compared in the complete question
The null hypothesis is given as
H₀: μ₀ = $58,291
The alternative hypothesis is given as
Hₐ: μ₀ ≠ $58,291
c) The claim to be proved is that the average caffeine content for coffee served in a local restaurants is higher.
The null hypothesis is that the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup. That is, the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup.
The alternative hypothesis is that average caffeine content for coffee served in a local restaurants is higher than the standard figure of 133 mg for an 8 ounce cup.
Mathematically, if μ₀ = average caffeine content for coffee served in a local restaurants.
The null hypothesis is given as
H₀: μ₀ ≤ 133.0 mg
The alternative hypothesis is given as
Hₐ: μ₀ > 133 mg
d) The economist claims that the average yield per acre this year is different from the average yield per acre in recent years.
Hence, the null hypothesis is that there is no significant difference between the average yield per acre this year and the average yield per acre in recent years.
The alternative hypothesis is that there is significant difference between the average yield per acre this year and the average yield per acre in recent years.
Mathematically, if μ₀ = the average yield per acre this year
The null hypothesis is given as
H₀: μ₀ = 161.9 bushels
The alternative hypothesis is given as
Hₐ: μ₀ ≠ 161.9 bushels
e) The sociologist suspects that the average age of all self-described fly fishermen is higher than 42.8 years.
Hence, the null hypothesis is that the average age of all self-described fly fishermen is not higher than 42.8 years. That is, the average age of all self-described fly fishermen is equal to less than 42.8 years.
The alternative hypothesis is that the average age of all self-described fly fishermen is higher than 42.8 years.
Mathematically, if μ₀ = average age of all self-described fly fishermen.
The null hypothesis is given as
H₀: μ₀ ≤ 42.8 years
The alternative hypothesis is given as
Hₐ: μ₀ > 42.8 years
Hope this Helps!!!
I need help with this question ???
Answer:
i dont know how many decimals you need but its 5.56
tell me if u want an explanation
Answer:
5.74456264654
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
Arc length : In his pizza, Arc length is the outer boundary of pizza and it can be calculated if we know the side length of the pizza and the central angle
Area of sector: since the whole pizza piece is a sector hence to calculate it's area we can use the formula of area of sector
(In degrees) = m/360 (πr²)
(In radians) = 1/2r²∅(theta)
What’s the correct answer for this question ?
Answer:
B:
Step-by-step explanation:
P(A or B) = P(A)+P(B)-P(A and B)
0.5 = 0.4 + P(B) -0.2
P(B) = 0.5-0.4+0.2
P(B) = 0.3
If prices increase at a monthly rate of 2.7 by what do they increase in a year
Answer:
37.67%
Step-by-step explanation:
Suppose initially a price of $ 100
Increasing per month at a rate of 2.7%. Which is equal to 0.027
Now applying the formula:
Vf = Vi * (1 + m) ^ n
where Vf is the final quantity, Vi is the initial value, m is the rate and n is the number of months.
We know that 1 year, is 12 months, since the rate is monthly means, n = 12, we replace:
Vf = 100 * (1 + 0.027) ^ 12
Vf = 137.67
It means price increase in 1 year = 137.67 - 100 = 37.67
Which means that n a year increases to 37.67%
Rewrite the equation by completing the square. x^2 +16x +64=0
Answer: (x+8)²
Step-by-step explanation:
When you complete the square, the factor is squared. You want to first factor the equation.
x²+16x+64=0
(x+8)(x+8)=0
Now that we have factored the equation, we can put in into squares.
(x+8)²
Answer
8 and 0 (Khan)
The rental shop charges $16 plus $9 an hour to rent a bicycle. If Luis spends $70, for how
many hours did he rent the bicycle?
Answer:
2.8 hours or 2hrs 8 min
Step-by-step explanation:
money paid per hour=16+9=$25
money paid by luis=70
time=70/25= 2.8 hrs
=2 hours and 8 minutes
hope this helps u :)
According to the general equation for conditional probability, if P(A, B) =4/7
and P(B) =7/8 - what is P(AIB)?
Answer:
[tex]P(A|B) = \frac{32}{49}[/tex]
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]
In which
P(A|B) is the probability of event A happening, given that B happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(B) is the probability of B happening.
We have that:
[tex]P(A \cap B) = \frac{4}{7}, P(B) = \frac{7}{8}[/tex]
So
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{4}{7}}{\frac{7}{8}} = \frac{4}{7}*\frac{8}{7} = \frac{32}{49}[/tex]
Then
[tex]P(A|B) = \frac{32}{49}[/tex]
In finance, one example of a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage in a certain bundle has a probability of 0.08 of default. (a) What is the probability that a randomly selected mortgage will not default? (b) What is the probability that nine randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the others? Note: A derivative might be an investment that only pays when all nine mortgages do not default. (c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of the mortgages defaults
Answer:
a) 92% probability that a randomly selected mortgage will not default
b) 47.22% probability that nine randomly selected mortgages will not default
c) 52.78% probability that the derivative from part (b) becomes worthless
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening
Suppose a randomly selected mortgage in a certain bundle has a probability of 0.08 of default.
This means that [tex]p = 0.08[/tex]
(a) What is the probability that a randomly selected mortgage will not default?
Either it defaults, or it does not default. The sum of the probabilities of these outcomes is 1. So
0.08 + p = 1
p = 0.92
92% probability that a randomly selected mortgage will not default
(b) What is the probability that nine randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the others?
This is P(X = 0) when n = 9. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{9,0}.(0.08)^{0}.(0.92)^{9} = 0.4722[/tex]
47.22% probability that nine randomly selected mortgages will not default.
(c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of the mortgages defaults
Either none defect, or at least one does. The sum of the probabilities of these events is 100%. So
p + 47.22 = 100
p = 52.78
52.78% probability that the derivative from part (b) becomes worthless
Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3times3 determinants. [Note: Finding the characteristic polynomial of a 3times3 matrix is not easy to do with just row operations, because the variable lambda is involved.]
Answer:
Step-by-step explanation:
Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3times3 determinants. [Note: Finding the characteristic polynomial of a 3times3 matrix is not easy to do with just row operations, because the variable lambda is involved.]
[tex]\texttt {let} A = \left[\begin{array}{ccc}4&-4&0\\-4&7&0\\4&6&5\end{array}\right][/tex]
The characteristics polynomial of A is [tex]|A- \lambda I|[/tex]
[tex]\to|A-\lambda I|=\left[\begin{array}{ccc}(4-\lambda)&-4&0\\-4&(7-\lambda)&0\\4&6&(5-\lambda)\end{array}\right][/tex]
[tex]=(4-\lambda)[7-\lambda)(5-\lambda)-0]+4[-4(5-\lambda)-0]+0[-4\time 6-4(7-\lambda)]\\\\=(4-\lambda)[35-7\lambda-5\lambda+\lambda^2]+4[-20+4\lambda]+0\\\\=(4-\lambda)[35-12\lambda+\lambda^2]-80+16\lambda\\\\=140-48\lambda+4\lambda^2-35\lambda+12\lambda^2-\lambda^3-80+16\lambda\\\\=-\lambda^3+16\lambda^2-67\lambda+60[/tex]
Suppose you draw a card from the set of cards, record the letter, return the card to the set, and shuffle the cards. You can repeat this experiment 22 times. Would you expect the experimental probability of drawing a vowel to be the same as the theoretical probability?
Answer:
They should not be exactly the same but they should be close.
Step-by-step explanation:
The first thing that we must take into account is the following:
Experimental probability is the result of an experiment, and theoretical probability is based on the mathematical model developed in probability theory. With the above, we can affirm that the precision of the results of the experiments depends directly on the sample size of the experiment and the precision is greater when the sample size is greater.
This means that the odds are most likely not the same, they must be very close since it has been repeated a considerable number of times and the more times it is done the closer they will be to being the same.
A population has standard deviation σ =17.5.
Required:
a. How large a sample must be drawn so that a 99.9% confidence interval for will have a margin of error equal to 4.1. Round the critical value to no less than three decimal places. Round the sample size up to the nearest integer. A sample size of_________ is needed to be drawn in order to obtain a confidence interval with a margin of error equal to 4.1 .
b. If the required confidence level were 95%, would the necessary sample size be larger or smaller?
Answer:
a) A sample size of 195 is needed.
b) Smaller
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.999}{2} = 0.0005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.0005 = 0.9995[/tex], so [tex]z = 3.27[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
a. How large a sample must be drawn so that a 99.9% confidence interval for will have a margin of error equal to 4.1.
We need a sample size of n.
n is found when [tex]M = 4.1[/tex]
We have that [tex]\sigma = 17.5[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4.1 = 3.27*\frac{17.5}{\sqrt{n}}[/tex]
[tex]4.1\sqrt{n} = 3.27*17.5[/tex]
[tex]\sqrt{n} = \frac{3.27*17.5}{4.1}[/tex]
[tex](\sqrt{n})^{2} = (\frac{3.27*17.5}{4.1})^{2}[/tex]
[tex]n = 194.8[/tex]
Rounding up
A sample size of 195 is needed.
b. If the required confidence level were 95%, would the necessary sample size be larger or smaller?
Same as above for n, the difference is that z would be 1.96 instead of 3.27. So a smaller sample size.
Find and interpret the mean absolute deviation of the data. Round your answers to the nearest tenth. If necessary 101.5 98.7 95.4 92.3 109.8 104.7
Answer:
[tex]\bar X = 100.4[/tex]
And we can calculate the deviations from each value like this:
[tex] |101.5-100.4 |=1.1[/tex]
[tex] |98.7-100.4 |=1.7[/tex]
[tex] |95.4-100.4 |=5.0[/tex]
[tex] |92.3-100.4 |=8.1[/tex]
[tex] |109.8-100.4 |=9.4[/tex]
[tex] |104.7-100.4|=4.3[/tex]
And the mean absolute deviation would be:
[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
101.5 98.7 95.4 92.3 109.8 104.7
We can calculate the mean with the following formula:
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X = 100.4[/tex]
And we can calculate the deviations from each value like this:
[tex] |101.5-100.4 |=1.1[/tex]
[tex] |98.7-100.4 |=1.7[/tex]
[tex] |95.4-100.4 |=5.0[/tex]
[tex] |92.3-100.4 |=8.1[/tex]
[tex] |109.8-100.4 |=9.4[/tex]
[tex] |104.7-100.4|=4.3[/tex]
And the mean absolute deviation would be:
[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]
Samantha and Jillian were going for a walk. Jillian left 15 seconds ahead of Samantha. Samantha walked at a speed of 7 feet per second.Jillian walked at a speed of 6 feet per second. How many seconds had Jillian been walking when the two girls had walked the same distance?
Answer:
105 seconds
Step-by-step explanation:
We can use the relation ...
distance = speed · time
to write equations for the distance each girl travels as a function of time t since Jillian started.
Jillian's distance = (6 ft/s)(t)
Samantha's distance = (7 ft/s)(t -15) . . . . Samantha starts 15 seconds after the clock starts running
These distances are the same when ...
6t = 7(t -15)
6t = 7t -105 . . . . eliminate parentheses
105 = t . . . . . . . . add 105-6t
Jillian had been walking 105 seconds when the two girls met.
Esmerelda is a home healthcare provider. When she takes a new client, she charges an initial fee of $32 and an hourly fee of $16 per hour. Her last new client paid her $144. How many hours did Esmerelda work for her new client?
What values of a, b, and c yield a true statement in the equation below?
a= ?
b=?
c=?
Answer:
(a, b, c) = (8, 3, 2)
Step-by-step explanation:
Remove cubes from under the radical. Combine terms.
[tex]\sqrt[3]{16} +2\sqrt[3]{54} =\sqrt[3]{2^3\cdot 2}+2\sqrt[3]{3^3\cdot 2}\\\\=2\sqrt[3]{2}+2\cdot 3\sqrt[3]{2}=(2+6)\sqrt[3]{2}\\\\=8\sqrt[3]{2}\equiv a\sqrt[b]{c}\ \longrightarrow\ \boxed{(a,b,c)=(8,3,2)}[/tex]
A parking lot for a new ice cream stand has an area of 5000 square yards. The length of the lot is 50 yards longer than its width. Determine algebraically the dimensions of the parking lot, in yards.
Answer:
length = 50 + 50 = 100 yards
width = 50 yards
Step-by-step explanation:
The area of parking lot for the the ice cream stand is given as 5000 yard². The length of the yard is 50 yard longer than its width.
Let
width = a
length = 50 + a
The parking lot is definitely a rectangle .
Area of a rectangle = length × width
area = (50 + a)a
5000 = (50 + a)a
5000 = 50a + a²
a² + 50a - 5000 = 0
The numbers that can be multiply together to give you -5000 is -50 and 100 and this same number can be added to give 50. Therefore,
a² - 50a + 100a - 5000 = 0
a(a - 50) + 100(a - 50) = 0
(a + 100)(a - 50) = 0
a = -100 or 50
We can't use negative value so we use 50.
length = 50 + 50 = 100 yards
width = 50 yards
Determine which statements are true in the set of real numbers3. (Select all that apply.) (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a third plane are parallel. (d) Two planes perpendicular to a third plane are parallel. (e) Two lines parallel to a plane are parallel. (f) Two lines perpendicular to a plane are parallel. (g) Two planes parallel to a line are parallel. (h) Two planes perpendicular to a line are parallel. (i) Two planes either intersect or are parallel. (j) Two lines either intersect or are parallel. (k) A plane and a line either intersect or are parallel. Incorrect: Your answer is incorrect.
Answer:
(a) True
(b) False
(c) True
(d) False
(e) False
(f) True
(g) False
(h) True
(i) True
(k) True
Step-by-step explanation:
(a) Two lines parallel to a third line are parallel
True
(b) Two lines perpendicular to a third line are parallel
Only for lines on the same plane
Therefore, false
(c) Two planes parallel to a third plane are parallel
True
(d) Two planes perpendicular to a third plane are parallel
The two planes can be at an angle to each other and so intersect
Therefore, false
(e) Two lines parallel to a plane are parallel
Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect
Therefore, false
(f) Two lines perpendicular to a plane are parallel
True
(g) Two planes parallel to a line are parallel
Where the planes are not parallel to each other, they will intersect
Therefore, false
(h) Two planes perpendicular to a line are parallel
True
(i) Two planes either intersect or are parallel
True
(k) A plane and a line either intersect or are parallel
True.
If sinA = -4/5 and cosB = 12/13, where A and B are both in Quadrant IV, what is tan(A-B)?
Answer:
4-5 12 -13
Step-by-step explanation:
Of 585 samples of seafood purchased from various kinds of food stores in different regions of a country and genetically compared to standard gene fragments that can identify the species, 19% were mislabeled. a) Construct a 99% confidence interval for the proportion of all seafood sold in the country that is mislabeled or misidentified. b) Explain what your confidence interval says about seafood sold in the country. c) A government spokesperson claimed that the sample size was too small, relative to the billions of pieces of seafood sold each year, to generalize. Is this criticism valid? a) What is the 99% confidence interval? The 99% confidence interval is from nothing% to nothing%. (Round to one decimal place as needed.)
Answer:
a) The 99% confidence interval is from 14.8% to 23.2%.
b) The confidence interval tells us that the true proportion of mislabeled is within 14.8% and 23.2%, with a 99% confidence. In other words, if we take samples of the same size, 99% of the samples will have a proportion within 0.148 and 0.232.
c) The confidence interval calculation take into account the sample size, so the width (or precision) of the interval depends on the sample size.
The only criticism that could be analyzed is to see if the sample is representative of the population.
Step-by-step explanation:
a) We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.19.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.19*0.81}{585}}\\\\\\ \sigma_p=\sqrt{0.000263}=0.016[/tex]
The critical z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.02=0.042[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.19-0.042=0.148\\\\UL=p+z \cdot \sigma_p = 0.19+0.042=0.232[/tex]
The 99% confidence interval for the population proportion is (0.148, 0.232).
Please answer this correctly. I want genius,expert and ace people to answer this correctly as soon as possible as my work is due today
Answer:
50%
Step-by-step explanation:
27 to 30 is exactly the "box" of the box plot and that, by definition, contains 50% of the results.
Answer:
50%
Step-by-step explanation:
Hope this will help
State the negation of the following statement:
It is cloudy.
saying it is cloudy is the defining that it's so gloomy outside or is probably paraphrasing to how someone feels
hope this helps
Solve the system of equations. 5x + 3y = 4 2x + y = 1
Answer:
(-1, 3)
Step-by-step explanation:
5x + 3y = 4
2x + y = 1 ⇒ y=1-2x
5x+3(1-2x)=45x+3-6x=4-x=4-3-x=1x=-1y= 1-2(-1)= 1+2=3n a basket of fruit, 5/6 of the pieces of fruit are apples. There are 20 apples in the display. The equation 5/6f= 20 can be used to find how many pieces of fruit f are the basket. Use words and numbers to explain how to solve the equation to find how many pieces of fruit are in the basket.
Step-by-step explanation:
5/6f=20apples. that means the total number of fruits is 6/6 which is whole thus
if 5/6=20
6/6=?
that is 6/6x20 divide by 5/6
=24fruits
