A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages.
64, 40, 45, 43, 33, 50, 47, 49, 42, 28, 55, 64, 55, 41, 65.
64, 50, 45, 51, 23, 35, 64, 43, 45, 37, 37, 47, 34, 27, 49,
62, 39, 35, 44, 23, 36, 42, 34, 32, 52.
D
The required leaves values for the given stems are calculated below.
What is Stem-and-Leaf plot?A plot where every information esteem is parted into a "leaf" (typically the last digit) and a "stem" (different digits). For instance "32" is parted into "3" (stem) and "2" (leaf). The "stem" values are recorded down, and the "leaf" values are recorded close to them.
For example , 42, 34, 48, and so on.
Here 42 and 48 qualities will be written in stem 4 as their most memorable digit is 4, while 2 and 8 will be placed in the leaf side.
Likewise, 3 will be the stem, and 4 will be the leaf for esteem 34.
4| 2, 8
3| 4
According to question:65, 40, 47, 47, 33, 55, 44, 49, 46, 22, 58, 65, 56, 41, 63, 65, 54, 42, 58, 29, 39, 66 , 49, 42, 34, 36, 42, 35, 21, 44, 61, 35, 33, 42, 27, 30, 46, 33, 35, 58.
As given in the question that the stem and Leaves are to be separated by a hyphen.
Stem-and-Leaf plot 6 - 5, 5, 3, 5, 6, 1
5 - 5, 8, 6, 4, 8, 8
4 - 0, 7, 7, 4, 9, 6, 1, 2, 9, 2, 2, 4, 2, 6
3 - 3, 9, 4, 6, 5, 5, 3, 0, 3, 5
2 - 2, 9, 1, 7
As we can see above there are 5 stems, where stem 6 has 6 leaves, stem 5 has 6 leaves, stem 4 has 14 leaves, stem 3 has 10 leaves, and stem 2 has 4 leaves.
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Select all points from the list below that lie in the solution set of the system of inequalities graphed below?
Question 3 options:
(7, 0)
(3, 0)
(0, 7)
(-3, -5)
(9, -3)
(0, -1)
The points that lie in the solution set of the system of inequalities graphed are: (7, 0), (3, 0), (9, -3)
In this question, we have been given a graph system of inequalities.
We need to select all points from the given list that lie in the solution set of the system of inequalities.
The solution set for given inequalities is the set of all points which satisfy inequalities.
The solution set is represented by the common region shaded between two inequalities.
From graph, we can see that the points (7, 0), (3, 0), (9, -3) lie in the solution set of the system of inequalities graphed.
Therefore, the points that lie in the solution set of the system of inequalities graphed are: (7, 0), (3, 0), (9, -3)
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A finance journal, which publishes research on current financial topics, states that the maturity term for a certificate of deposit is, on average, 10 years. A banker believes the average maturity term at their bank is different than the amount quoted in the finance journal. After completing a study, the banker found that the average maturity term for a certificate of deposit is 8 years, on average.
Required:
As the banker sets up a hypothesis test to determine if their belief is correct, what is the banker's claim?
Answer:
Following are the solution to the given question:
Step-by-step explanation:
In this the hypothesis is:
\(H_{0}:\mu=10\\\\H_{1}:\mu\neq10\)
The bankers assert that their bank's average maturity was distinct from that of ten years, that's why the hypothesis of the alternative.
A.solves routine and non-routine problems involving perceentage using appropriate strategies and tools.M5NS-IIIIb-40
Observe the solution to the given problem below.
christmas season is coming and ana is so excited to do her shopping in her list is a pair of shoes that she will wear for their christmas party.what made her more excited was when she saw that her dream pair of shoes is on sale.
from P 4 295, it is now sold with 20%
The sale price of the shoe is given as follows:
P3,436.
How to obtain the sale price of the shoe?The sale price of the shoe is obtained applying the proportions in the context of the problem.
The initial price is of:
P 4,295.
The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:
0.8 x 4295 = P3,436.
Missing InformationThe problem asks for the selling price of the shoe.
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Carlos has $690,000 he wants to save. If the FDIC insurance limit per
depositor, per bank, is $250,000, which of these ways of distributing his
money between three banks will guarantee that all of his money is insured?
A. $230,000 in bank A, $240,000 in bank B, $220,000 in bank C
B. $200,000 in bank A, $220,000 in bank B, $270,000 in bank C
C. $230,000 in bank A, $260,000 in bank B, $200,000 in bank C
D. $200,000 in bank A, $200,000 in bank B, $290,000 in bank C
Find the annual interest rate.
I= $562.50, P=$1500, t= 5 years
The annual interest rate is_____%
The annual interest rate is 7.5%.
What is Simple interest?
Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.
The formula for simple interest is:
I = P × r × t
where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.
In this case, we know I = $562.50, P = $1500, and t = 5 years.
we ca substitute values into the formula,
562.50 = 1500× r ×5
Simplifying, we get:
r = 562.50 / (1500 ×5)
r = 0.075
r = 7.5%
Therefore, the annual interest rate is 7.5%.
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Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
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Part of the population of 6,750 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 4 of them are infected. How many elk are likely to be infected?
Answer:
The answer is 540.
Hope this helps! :)
solve for the indicated variable 9x + y = 7: y
Answer:
y= - 9x+7
Step-by-step explanation:
For problems like these, where you solve for a variable, you want to isolate y by add/sub or mult/div to get everything else to the other side of the equation symbol.
So for example, "9x" is an addition because it is getting added to y. Because of this, you are going to subtract it from both sides of the equation symbol. You will get y=-9x+7. Since 7 is positive, it will be added.
what is the slope from the two points (7,2) and (-2,2)
Answer:
0
Step-by-step explanation:
Since we have two points, we can use the slope formula
m = (y2-y1)/(x2-x1)
= ( 2-2)/(-2-7)
=0/-9
=0
Calc question — related rates
The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.
How to determine rate?The volume of the liquid in the bowl is given by the following integral:
\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)
where r = radius of the bowl and y = height of the liquid.
The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:
r = √{(4/(8-x)) - 1}² + 1²
The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:
h = (4/(8-x)) - 1
Substituting these equations into the volume integral:
\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)
Evaluate this integral using the following steps:
Expand the parentheses in the integrand.
Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.
Integrate each part separately.
The integral of the square root term can be evaluated using the following formula:
\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)
The integral of the linear term can be evaluated using the following formula:
\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)
Substituting these formulas into the integral:
V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h
Evaluating this integral:
V = π { 16/27 (8-h)³ - 16/18 (8-h)² }
The rate of change of the volume of the liquid is given by:
dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }
The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.
Substituting these values into the equation for dV/dt:
dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π
Solving this equation for the rate of change of the depth of the liquid:
dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹
Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.
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Markers were placed at altitudes of 10 and 15 feet below sea level Enter the integer that represents the altitude closer to sea level
Answer:
43
neeed...20...charetors
The integer that represents the altitude closer to sea level is 10.
What is addition?Addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value. A numerical expression is algebraic information stated in the form of numbers and variables that are unknown.
We are informed that Markers were placed at altitudes of 10 and 15 feet below sea level
Then we need to find the integer that represents the altitude closer to sea level.
We can say that 10 is negative (below the sea level), and 10 is 10 spaces away from zero on the number line, meaning the answer could be |10|.
The sea level would be 0 and the 10 would be -10 and the 15 will be -15
Hence, the 10 is closer to the sea level.
Thus the integer that represents the altitude closer to sea level is 10,
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Please help me with this
The volume of rectangular prism is 90 unit³.
We can consider the 1 block = 1 unit.
Length of prism = 5 unit
width of prism = 6 unit
Height of prism = 3 unit
So, Volume of rectangular prism
= l w h
= 5 x 6 x 3
= 90 unit³
Thus, the volume of rectangular prism is 90 unit³.
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could anyone help me solve this?
Step-by-step explanation:
The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.
So here it is (2,7) exclusive then (7,10) exclusive.
A constant speed means a slope of 0. Here it is (3,6).
c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis
So we would get
Above is the function, don't worry bout the math part.
D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it
We must use the original graph because acceleration is a vector meaning it can be negative.
We would get
the second graph is acceleration vs time
There are two numbers whose product is 117 and quotient is 13. What are the two numbers
Answer:
Let the two numbers be x and y
Step-by-step explanation:
Given :
x × y = 117 -1
x ÷ y = 13 -2
from equation 2 ,
x = 13×y -3
putting value of x from equation 3 in equation 1
13y × y = 117
13y² = 117
y² = 117 / 13
y² = 9
y = √9
y= 3
putting value of y in equation 3
x = 13 × y
13× 3
= 39
hence the two numbers are 39 and 3
how can you use pythagora's theorem to solve problems involving right-angled triangles
Using Pythagorean theorem, the length of the ladder is 10ft
What is Pythagorean Theorem?In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:
x² = y² + z²
In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.
To calculate the length of the ladder, we can write the formula as;
x² = 8² + 6²
x² = 64 + 36
x² = 100
x = √100
x = 10
The length of the ladder is 10 feet
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what is the domain of h
h: The domain
-5 ≤ x ≤ 5
Tonya has 39 packages. Each package weighs 6 pounds. Choose the best estimate of the total weight of the packages.
Step-by-step explanation:
If were estimating, 39 is pretty close to 40 and 40x6 is 240 pounds. if we are getting exact about it, then 234 pounds
The product of two fractions is 2/1/2 if one of the fraction is 7/1/2 find the other
What is the round trip distance in miles from city 1 to city 3?
15
30
50
70
The round trip distance in miles from city 1 to city 3 is given as follows:
30 miles.
How to obtain the round trip distance?The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.
Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.
For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:
2 x 15 = 30 miles.
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Rudy correctly solved the equation 10 = 4r.
Which statement describes his solution?
A
The solution is 40 since 10 times 4 equals 40.
The solution is 2.5 since 4 times 2.5 equals 10.
С
The solution is 2.5 since 4 divided by 2.5 equals 10.
D
There is no solution because no value can be multiplied by 4 to get 10.
Answer:
its B
Step-by-step explanation:
If x/3 = 5/6, then x =
Answer:
x = 5/2
Step-by-step explanation:
We can use cross products to solve this equation
x/3 = 5/6
Multiply
x*6 = 3*5
6x = 15
Divide each side by 6
6x/6 = 15/6
Simplify
x = 5/2
hey yall i need help
$3.00 with the
same number of nickels and dimes
Answer:
15 each i think
Step-by-step explanation:
what is the correct answer?
Answer:
5
Step-by-step explanation:
Answer:4.5
[um i cant relay see it but il do my best]
An equation is shown below:
5(2x - 8) + 15 = -15
Write the steps you will use to solve the equation and explain each step. Brain list will be given if answered right
Answer:
x = 1
Step-by-step explanation:
5(2x - 8) + 15 = -15
First, let's move the 15 to the opposite side of the equation. We'll do this by subtracting 15 from BOTH sides of the equation.
5(2x - 8) + 15-15 = -15-15
5(2x-8) + 0 = -30
5(2x-8) = -30
Now let's expand that first term.
5(2x)-5(8) = -30
10x - 40 = -30
Now let's move the -40 to the opposite side of the equation. We'll do this by ADDING 40 to both sides of the equation.
10x - 40 + 40 = -30 + 40
10x -0 = 10
10x = 10
Now to solve for x, we divide BOTH sides by 10 to "isolate the variable" aka get x alone.
10x/10 = 10/10
x = 1
The answer is x = 1.
Let's check if our answer is correct!
Original equation: 5(2x - 8) + 15 = -15
Substitute 1 for x.
5(2*1-8) + 15 =
5(2-8) + 15 =
5(-6) + 15 =
-30 + 15 = -15 >>> which is exactly what we started with! So x is 1.
FIND THE PERIMETER AND THE AREA OF A TRIANGLE!!!
I WILL MARK YOU AS BRAInLiest!!!
Answer:
3,833.856
Step-by-step explanation:
Tom, Ulrika and Harriet each have some money.
Harriet has 3 times as much money as Ulrika.
Harriet has £304 more money than Tom.
5
Tom has of the amount of money that Ulrika has.
How much money does Ulrika have?
Hey there! I'm happy to help!
Let's represent Tom's money as T, Ulrika's as U, and Harriet's as H. Let's put the information we have in a system of equations and solve the problem.
H=3U (Harriet has 3x as much as Ulrika)
H=T+304 (Harriet has 304 more than Tom)
T=U (Tom has same amount as Ulrika.)
We see that 3U and T+304 are equal because they both equal H.
3U=T+304
Since T and U are interchangeable because they are equal, we can replace the U with T to solve for T, which is also the answer for U.
3T=T+304
We subtract T from both sides.
2T=304
We divide both sides by 2.
T=152
This also means that U=152.
So, Ulrika has $152.
Have a wonderful day!
Val's whole-house central air conditioner uses 2,500 watts when running. Val runs the AC 5 hours per summer day. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Quantity of electricity used in kilowatts is;
1000 watts = 1 kilowatts
2,500 watts = 2.5 kilowatts
Given that Number of hours Val runs AC per day = 5 hours
Number of days = 30 days
Cost of electricity = $0.18 kilowatts per hour
The Cost of Val’s AC to run for a summer month of 30 days can be calculated as;
= Quantity of electricity used × Number of hours Val runs AC per day × Number of days × Cost of electricity
= 2.5 × 5 × 30 × 0.18
= $67.5
The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.
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y=2/5xt 10 the rate of change and y intercept
Answer:
Below
Step-by-step explanation:
Rate of change (aka the slope) = 2/5
Y Intercept = 10