Answer:
0.3788
Step-by-step explanation:
12 people want to teach math at a college.
6 people have a PhD.
5 people have a master's degree.
boss wants to interview 5 people for the job.
chance that all 5 of the people interviewed have a PhD.
total number of ways to select 5 applicants out of 12 is given by the combination:
combinations formula :
nCr = n! / r! * (n – r)!
C(12, 5) = 12! / (5! * 7!) = 792
number of ways to select 3 applicants with a PhD out of the 6 available is:
C(6, 3) = 6! / (3! * 3!) = 20
remaining 2 applicants can be selected from the remaining 6 applicants with a master's degree:
C(6, 2) = 6! / (2! * 4!) = 15
total number of ways to select 5 applicants with 3 having a PhD is:
20 * 15 = 300
P(3 PhDs) = 300 / 792
P(3 PhDs) = 0.3788 (rounded to four decimal places)
So, the probability of selecting five applicants for an interview where all three applicants have a PhD is approximately 0.3788
ChatGPT
Supplementary angles
Answer: ∠EBJ
Step-by-step explanation:
Starting Angle: ∠EBH
Possible Supplement: ∠EBJ
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices – a, b, c, d, e – and only one correct answer. What is the probability that she answered both of the problems correctly? Write your answer as a fraction in simplest form
The probability that the student, who ran out of time on a multiple choice exam and randomly guessed the answers for two problems, answered both of the problems correctly is ⁹/₂₅.
What is the probability?Probability refers to the likelihood of an expected outcome occurring out of many possible outcomes.
Probability is computed as the quotient of expected outcome over total outcomes.
The number of questions left = 2
The number options of for each question = 5
Since there are 5 options for each question, 4 of which are wrong, the probability of getting both wrongs is:
⁴/₅ x ⁴/₅ = ¹⁶/₂₅ = 0.64 or 64%
Therefore, probability of getting both questions correct is 36% (1 - 64%) or ⁹/₂₅ (1 - ¹⁶/₂₅).
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Is 3.2 x 10^3 an irrational or rational
3.2 x 10^3 is considered to be a rational number.
What are rational numbers ?A rational number is a numerical value expressed as a ratio between two non-zero integers. If any given number can be appropriately displayed in the form of 'a/b,' where both 'a' and 'b' guarantee integer input, it would signify that this specified number adheres to the classification of being labeled as rational.
As we can see from the given number of 3.2 x 10^3, when we write the number after solving it, we have:
3.2 x 10 ^ 3 = 3 .2 x 1, 000
= 3, 200
This can be expressed as 3, 200 / 1 so this is a rational number.
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In a certain video game, players can create environments and populate them with a variety of characters. One player creates a magical park in which the unicorn population triples each day. The starting unicorn population is 5. What will the unicorn population be after the 4th day?
Using the laws of multiplication, we can find that after the 4th day the unicorn population of the park is 405.
Define multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors.
In the question,
Let the unicorn population be = x.
Now as per the question,
It triples every day.
The function will be = 3x.
The starting unicorn population is 5.
After the 1st day it will get tripled and become 3 × 5 = 15.
After the 2nd day the unicorn population will be 3 × 15 = 45.
After the 3rd day, 3 × 45 = 135.
Finally, after the 4th day, the unicorn population will be = 3 × 135 = 405.
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A relief worker needs to divide 2250 bottles of water and 144 cans of food into boxes that each contain the same number of items. Also, each box must contain the same type of item (bottled water or canned food). What is the largest number of relief supplies that can be put in each box?
The required, we can put 125 bottles of water or 8 cans of food in each box, and each box will contain the same number of items.
To find the largest number of relief supplies that can be put in each box, we need to find the greatest common factor (GCF) of 2250 and 144. We can do this by listing the prime factors of each number:
2250 = 2 * 3 * 3 * 5 * 5 * 5 * 2
144 = 2 * 2 * 2 * 2 * 3 * 3
To find the GCF, we need to find the highest power of each common prime factor that appears in both numbers. In this case, the common prime factors are 2 and 3, so we take the highest power of each:
2 * 3 * 3 = 18
So the largest number of relief supplies that can be put in each box is 18. We can check that this works by dividing each quantity by 18:
2250/18 = 125
144/18 = 8
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The amount of sports drink in a cooler during practice is modeled by the equation
y = -24x + 648, where y is the number of ounces in the cooler after practice and x is the number of players at practice who take drinks from the cooler.
Based on the information in the equation, which statements are true?
Group of answer choices
The cooler is meant to be used by only 24 players.
Before practice, there are 648 ounces of sports drink in the cooler.
If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink.
Based on the information in the equation, y = -24x + 648, the TRUE statement is B) Before practice, there are 648 ounces of sports drinks in the cooler.
What is an equation?An equation is an algebraic statement showing that two or more mathematical expressions are equal or equivalent.
The equality or equivalence of an equation is depicted using the equal symbol (=).
Mathematical expressions do not use the equal symbol, but they combine variables with constants, numbers, and values using mathematical operands.
Let the number of ounces in the cooler after practice = y
Let the number of players at the practice who take drinks from the cooler = x
Equation:y = -24x + 648
Thus, 648 represents the number of drinks before practice while -24x represents the number of drinks taken by players, making Option B true.
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S certain forest covers an area if 3500km^2. Supposr that each year this area decreases by 4.25%. What will the area be after 13 years? Use the calculator provided and round your answer ti the nearest square kilometer
The area of the forest after 13 years is 1990.08 [tex]km^2[/tex].
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b[tex])^x[/tex], where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
Here initial area a = 3500[tex]km^2[/tex] ,
Rate of decay = 4.25%= 4.25/100 = 0.0425
Now using exponential decay formula then,
=> [tex]y=a(1-b)^x[/tex] where x=13 years .
=> y = [tex]3500(1-0.0425)^{13}[/tex]
=> y = [tex]3500(0.9575)^{13}[/tex]
=> y = 1990.08 [tex]km^2[/tex]
Hence the area of the forest after 13 years is 1990.08 [tex]km^2[/tex].
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A psychology instructor surveys three sections of a first-year psychology course totaling 1000 students. The psychology instructor finds that SAT scores and the amount of money the students were currently carrying had a correlation of r=.07 with a p-value of 0.001. The psychology instructor claims the results were statistically significant but were not practically significant. Explain the difference between these two concepts using the results from the psychology instructor’s survey.
The concept of Statistical significance as well as practical significance are known to be two different concepts in statistics.
What is the differences in both concepts?Statistical significance refers to unlikely results not due to chance. P-values are utilized for ascertaining the statistical importance of a particular result by gauging the likelihood of procuring exceptional outcomes under the assumption that the null hypothesis holds true. A significance level of 0.05 or less for the p-value is deemed as statistically meaningful.
Since the Psychology instructor found SAT scores and amount of money carried had a correlation coefficient of r = 0.07 with a p-value of 0.001, showing a significant correlation. The chance of getting a correlation coefficient of 0.07 or greater, if no correlation exists in the population, is very low.
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3 divided by 2/5 quotient
Answer:
3 divide 2/5 is 7.5 since 2/5 is 0.4
Exercise 1.4
A. Mark the periods with commas according to the two place value systems and write the numbers in words in each system.
1. 2365358 2. 34282627 4. 90150028 5. 81552101 3. 87013569 6. 99160001
Step-by-step explanation:
2,36,53,58
Two place value system:
Twenty-three lakh, sixty-five thousand, three hundred and fifty-eight
Three place value system:
Two crore, thirty-six lakh, fifty-three thousand, three hundred and fifty-eight
3,42,82,627
Two place value system:
Thirty-four million, twenty-eight thousand, six hundred and twenty-seven
Three place value system:
Three crore, forty-two lakh, eighty-two thousand, six hundred and twenty-seven
8,70,13,569
Two place value system:
Eighty-seven million, thirteen thousand, five hundred and sixty-nine
Three place value system:
Eight crore, seventy-one lakh, thirty-five thousand, five hundred and sixty-nine
9,01,50,028
Two place value system:
Ninety million, one lakh, fifty thousand, twenty-eight
Three place value system:
Nine crore, one lakh, fifty thousand, twenty-eight
8,15,52,101
Two place value system:
Eighty-one million, five hundred and fifty-two thousand, one hundred and one
Three place value system:
Eight crore, fifteen lakh, fifty-two thousand, one hundred and one
9,91,60,001
Two place value system:
Ninety-nine million, one lakh, sixty thousand, one
Three place value system:
Nine crore, ninety-one lakh, sixty thousand, one
Suppose that you are thinking about buying a car and have narrowed down your choices to two options.
The new-car option: The new car costs $31,000 and can be financed with a three-year loan at 7.19%.
The used-car option: A three-year old model of the same car costs $16,000 and can be financed with a four-year
loan at 5.89%.
What is the difference in monthly payments between financing the new car and financing the used car? Use
PMT=
[-(19]
The difference in monthly payments between financing the new car and financing the used car is
(Round to the nearest cent as needed.)
Answer:
To calculate the monthly payments for each option, we can use the PMT function in Excel or a financial calculator.
For the new car option:
Loan amount = $31,000
Interest rate (annual) = 7.19%
Loan term = 3 years
Number of payments = 3 x 12 = 36
Using the PMT function in Excel, we get:
PMT(7.19%/12, 36, -$31,000) = $966.59
For the used car option:
Loan amount = $16,000
Interest rate (annual) = 5.89%
Loan term = 4 years
Number of payments = 4 x 12 = 48
Using the PMT function in Excel, we get:
PMT(5.89%/12, 48, -$16,000) = $385.36
The difference in monthly payments between the two options is:
$966.59 - $385.36 = $581.23
Therefore, the difference in monthly payments between financing the new car and financing the used car is $581.23.
Step-by-step explanation:
Expressions Task Card #10
What is the difference in the areas of
the polygons shown?
7/
A = x + 5
A = 4x - 6
We can see here that the difference in the areas of the polygons shown is: 3x + 1.
What is a polygon?A polygon is a two-dimensional geometric object that is made up of a finite number of sides that are connected end to end to create a closed shape.
We can find the difference in the areas of the polygons shown in the following way:
Area of Polygon 1: A = x + 5
Area of Polygon 2: A = 4x - 6
Finding their difference, we have:
(4x - 6) - (x + 5)
= 4x + 6 - x - 5
Collecting like terms, we have:
= 4x - x + 6 - 5
= 3x + 1
Thus, we see here that the difference in the areas of the polygon is =
3x + 1
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x^2+25x+136=0 use the quadratic formula
Using the quadratic equation, the solution is x = -8 and x = -17.
What is the quadratic equation?A second-order equation of the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real number coefficients and a 0.
The equation is x²+25x+136=0
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
For the given equation x² + 25x + 136 = 0, we can identify a = 1, b = 25, and c = 136.
Substituting these values in the quadratic formula, we get:
x = (-25 ± √(25² - 4(1)(136))) / 2(1)
x = (-25 ± √(625 - 544)) / 2
x = (-25 ± √(81)) / 2
imply them
x = (-25 + 9) / 2 or x = (-25 - 9) / 2
x = -8 or x = -17
Therefore, the solutions to the quadratic equation x^2 + 25x + 136 = 0 are x = -8 and x = -17.
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(Factorize) p2 + 2p - 8-q2-6q
Factor of the equation are,
⇒ p (p + 2) - q (q + 6) - 8
We have to given that;
The expression is,
⇒ p² + 2p - 8 - q² - 6q
Now, We can factor as;
⇒ p² + 2p - 8 - q² - 6q
⇒ p (p + 2) - 8 - q (q + 6)
⇒ p (p + 2) - q (q + 6) - 8
Thus, Factor of the equation are,
⇒ p (p + 2) - q (q + 6) - 8
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Mari makes bows for floral arrangements she uses 1/8 yard of ribbon for each bow .how many bows can she make from 24 yards of ribbon
First, you need to find out how much ribbon she has total. Because there are two spools, you multiply 24 x 2. The answer for that is 48. Then you have to figure out how many bows she can make. Each bow uses 1/8 of a piece of yard of ribbon, so you can divide 48 by 8. Your answer would then be 6 bows.
Here are the equations.
[tex]24\times2 = \text{X}[/tex]
[tex]\dfrac{\text{X}}{8} =\text{B}[/tex]
Where X represents the yards of ribbon available and B represents the number of bows that Mari can make.
Complete Question:
Mari makes bows for floral arrangements. She uses 1/8 of a yard ribbon for each bow. How many bows can she make from 2 spools that each has 24 yards ribbon?
what the work out 320.041 - 47.96
Working out the expression 320.041 - 47.96 gives 272.081
Work out the expression 320.041 - 47.96From the question, we have the following parameters that can be used in our computation:
320.041 - 47.96
The above expression is a difference or subtraction expression that can be done using a calculator
Using the above as a guide, we have the following:
320.041 - 47.96
Evaluate using a calculator
So, we have
320.041 - 47.96 = 272.081
Hence, teh solution of 320.041 - 47.96 is 272.081
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if I bike for 180 minutes and I cover a
total distance of 47 Mi what is my
average speed
Average Speed Calculator
The average speed of the bike is calculated as: 15.67 mph
How to find the average speed?The formula for the average speed is:
Average speed = Distance/Speed
We are given the parameters as:
Time = 180 minutes = 3 hours
Distance = 47 miles
The average speed is defined as the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.
Thus:
Average speed = 47/3
= 15.67 mph
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What should you know about your audience?
A) how much experience they have had doing research
B) their preferences for recreation
C) what are their astrological signs are
D) what they already know about your topic
Answer: B) their preferences for recreation
Step-by-step explanation:
Answer the following questions.
a) The number of weeks that she has been saving when she needs $277 is given as follows: 17 weeks.
b) The amount she will need after 5 weeks is given as follows: $505.
How to obtain the amounts?The function for this problem is defined as follows:
A(w) = 600 - 19w.
The output of the function is the amount remaining after w weeks.
Hence the number of weeks that she has been saving when she needs $277 is obtained as follows:
277 = 600 - 19w
19w = 600 - 277
w = (600 - 277)/19
w = 17 weeks.
The amount that she needs after 5 weeks is given as follows:
A(5) = 600 - 19 x 5
A(5) = $505.
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Solve for the value of x. Show your work and explain the steps you used to solve. Round your answer to the nearest
tenth.
B
D x
45
24
C
The calculated value of x from the special triangle is 17.0
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The right triangle is a special triangle that has a measure of 45 degrees
For a triangle that has a measure of 45 degrees, we have
Hypotenuse = Legs√2
In this case, we have
Leg = x
Hypotenuse = 24
So, we have
x√2 = 24
Divide by √2
x = 24/√2
Evaluate
x = 17.0
Hence, the calculated value of x is 17.0
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Solve: log2(x-1)+log2(x+5)=4
Answer: X=3
Step-by-step explanation:
Elsa repairs types of electronic devices in her repair shop. The number of each type that she repaired last week is shown in the bar graph below. Using this bar graph, answer the questions.
In 2010, the mean starting salary for college graduates who major in Statistics was $54000. An analyst for a job searching company claims that the mean starting salary has since increased. In a random sample of 40 job posting requiring knowledge of Statistics, the mean starting salary was $63500 with a standard deviation of $10540. Test the claim using a significance level of 0.05.
Our calculated t-value of [tex]4.22[/tex] is greater than the critical t-value of 1.684, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.
How can we Test the claim using a significance level of [tex]0.05[/tex]?We can use a one-sample t-test to test the claim that the mean starting salary for college graduates who major in Statistics has increased.
The null hypothesis is that the mean starting salary is still $[tex]54000[/tex], while the alternative hypothesis is that the mean starting salary is greater than $[tex]54000[/tex].
We can calculate the t-statistic as:
t = (sample mean - null hypothesis value) / (standard error of the mean)
= [tex](63500-54000)/(10540/\sqrt{40}[/tex]
= [tex]4.22[/tex]
where [tex]\sqrt{40}[/tex] is the sample size.
The degrees of freedom for the t-test is [tex](n-1) = 39[/tex], where n is the sample size.
Using a t-table or calculator with [tex]39[/tex] degrees of freedom, a one-tailed test, and a significance level of [tex]0.05[/tex], we find the critical t-value to be [tex]1.684[/tex]
Since our calculated t-value of [tex]4.22[/tex] is greater than the critical t-value of [tex]1.684[/tex], we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.
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Select the property of equality used to arrive at the conclusion. If x + 8 = 10, then x = 2. the multiplication property of equality the subtraction property of equality the division property of equality
The correct option- B. the subtraction property of equality is used to arrive at the conclusion. If x + 8 = 10, then x = 2.
Explain about the subtraction property of equality :According to the equality's feature of subtraction, equality is unaffected when the same amount is subtracted from both sides of an equation.
If the exact same number or value is removed from both sides of an equation, the difference that results on both sides is also equal. Equal deductions from both sides of such an inequality will decrease the values on each side but have no effect on the inequality's truth value. In other words, the left side of a inequality will continue to be smaller than the right in a "less than" statement.Given data:
x + 8 = 10
To find the value of x, subtract 8 from both sides:
x + 8 -8 = 10 - 8
x = 2
Thus, the subtraction property of equality is used to arrive at the conclusion. If x + 8 = 10, then x = 2.
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Correct question:
Select the property of equality used to arrive at the conclusion. If x + 8 = 10, then x = 2.
A. the multiplication property of equality
B. the subtraction property of equality
C. the division property of equality
Write an equation for an ellipse centered at the origin, which has foci at
(
0
,
±
15
)
(0,±15)left parenthesis, 0, comma, plus minus, 15, right parenthesis and co-vertices at
(
±
8
,
0
)
(±8,0)left parenthesis, plus minus, 8, comma, 0, right parenthesis.
The equation of the ellipse is:
x²/64 + y²/289 = 1
How to determine the equation of an ellipse?The standard form of the equation of an ellipse with centered at the origin and major axis parallel to the vertical is:
x²/b² + y²/a² = 1
Coordinates of covertices are ( ±b, 0) = (±8, 0)
Coordinates of foci are (0, ±c) = (0, ±15)
Also c²= a²-b²
a² = b² + c²
a² = 8² + 15²
a² =289
a = √289
a = 17
Using x²/b² + y²/a² = 1:
x²/8² + y²/17² = 1
x²/64 + y²/289 = 1
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Complete Question
Write an equation for an ellipse centered at the origin, which has foci at (0,±15) and co-vertices at (±8,0)
Find the following angles
Answer:
10. x=82 11.x=25 9. p=225
You bake 7 different pies for a bake sale. You sell 4 pies on the first day of the sale. Use the Fundamental Counting Principle to find the probability that your
friend correctly guesses which pies were sold on the first try. Write your answer as a fraction in simplest form.
Probability:
The probability of correctly guessing which pies were sold on the first day is near to 2/3.
What is Fundamental Counting Principle?The Fundamental Counting Principle states that if there are m number of ways to do an activity and n number of ways for a second activity, then there are m x n ways to do the two activities together.
In this case, there are 7 pies and 4 of them were sold on the first day. Therefore, the probability of correctly guessing which pies were sold on the first day is 4/7.
This can be written in simplest form as 2/3.
In conclusion, the probability of correctly guessing which pies were sold on the first day is 2/3.
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I need help understanding tree diagrams
The probability that she will hire a woman for the two positions is given as follows:
1/4.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
From the last node, the total number of outcomes is given as follows:
4.
The desired outcomes are Women on the first node and women on the second node, which is one outcome. (the last outcome).
Hence the probability is given as follows:
p = 1/4.
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In the state of Pennsylvania 12% of students submit box tops for education to their school. a large school district in western Pennsylvania runs a contest to see if they can increase participation. the superintendent takes a random sample of 210 students from the district and finds that 35 have submitted box tops this year.
(a) do these data provide convincing evidence that the contest has increased participation in the box tops for education program?
(b) interpret the p-value from part (a).
If in sample of 210 students from district and finds 35 have submitted "box-tops" this year, then
(a) Yes, data provide enough evidence regarding contest which has increased participation in "box-tops" for "education-program",
(b) the p-value is 0.0187.
Part(a) : To find if contest has increased the participation in "box-tops" for "education-program", we conduct a "hypothesis-test".
We use a "significance-level" of 0.05, which means we will accept a 5% chance of making a "Type I Error",
Let Null Hypothesis ⇒ The proportion of students submitting "box-tops" is = 12%,
Let Alternative Hypothesis ⇒ The proportion of students submitting "box-tops" for education is increased after contest,
To test above hypothesis, we use "one-sample" proportion-test.
We will use the sample proportion (p') = 35/210 = 0.1667, as estimate of population proportion (p).
So, "test-statistic" (z) is ⇒ z = (p' - p₀)/√(p₀ × (1-p₀)/n),
where n = sample size,
In "Null-Hypothesis", the "expected-value" of the test statistic is 0, and "standard-deviation" of the "test-statistic" is √(p₀×(1-p₀)/n),
Substituting, p₀ = 0.12 and n = 210,
We get,
⇒ z = (0.1667 - 0.12)/√(0.12 x 0.88/210) ≈ 2.08,
Now, we know that "right-tailed" critical value at 0.05 level is = 1.645,
Since, z (2.08) > 1.645, the Null-Hypothesis is Rejected.
So, above data provides enough evidence regarding contest has increased the participation in "box-tops" for "education-program".
Part(b) : We need to find the "p-value" for the test-statistic that we found in part(a),
So, p-value = P(z>2.08),
⇒ 1 - P(z ≤ 2.08),
⇒ 1 - 0.9813,
⇒ 0.0187,
Therefore, the required "p-value" is 0.0187.
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Find the value of x. Assume that segments that appear to be tangent are tangent.
x =
(50 POINTs will give BRAINIEST FOR EFFORT)