The probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.
We have the data:
Age Number of Customers
< 20 78
20 - 30 58
30 - 40 53
40 - 50 77
50 - 60 52
> 60 91
The probability that the customer is at least 30 but no older than 60 will be:
P = 182 / 409
P = 0.45
The probability that the customer is either older than 60 or younger than 40 will be:
P = 280 / 409
P = 0.68
The probability that the customer is at least 60 will be:
P = 91 / 409
P = 0.22
Therefore we get the probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.
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What is the value of x?
Enter your answer in the box.
X =
Answer: x=26 degrees
Step-by-step explanation:
90+x+64=180 ==> A right angle, x, and 64 lie on a straight line. Straight lines add up to 180 degrees and are called straight angles. Right angles are denoted with a tiny square inside them and measure 90 degrees.
90-90+x+64=180-90
x+64=180-90
x+64=90
x+64-64=90-64
x=90-64
x=26 degrees
1
2
A swimming pool has a volume of 256 yd³.
Use the table of conversion facts to find out how many gallons of water it
would take to completely fill the swimming pool.
Round your answer to two decimal places.
The water in gallons to entirely fill the swimming pool is 51705.344 gallons.
What is defined as the conversion factor?A conversion factor is an amount that is used to multiply or divide one set of units into another. When converting to an equal value, the suitable conversion factor must be used. To convert inches to feet, for example, the adequate conversion amount is 12 inches equal 1 foot.For the given question;
The volume of the pool = 256 yd³.
Convert the volume in yd³ in gallons.
1 yd³ = 201.976 gallons.
Thus, for the total volume of 256 yd³ multiply both side with 256.
1×256 yd³ = 201.976×256 gallons.
256 yd³ = 51705.344 gallons.
Therefore, the water in gallons requires to completely fill the swimming pool is 51705.344 gallons.
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Ken invested $10,000 in two bank accounts. One of the accounts pays 4% annual interest, and the
other account pays 6% annual interest. If the combined interest earned in both accounts after a
year was $514, how much money was invested in each account?
Ken invested $5,700 in the 6% account, and the other $4,300 in the 4% account.
How much money was invested in each account?Let's define the variables:
x = amount of money on the 4% account.y = amount of money on the 6% account.We know that Ken invested $10,000 in total, so:
x + y = 10,000
And the interest in one year is:
x*0.04 + y*0.06 = 514
Then we have a system of equations:
x + y = 10,000
x*0.04 + y*0.06 = 514
To solve it we start by isolating one of the variables in one of the equations, isolating x we will get:
x = 10,000 - y
Replacing that in the other equation we get:
(10,000 - y)*0.04 + y*0.06 = 514
400 - y*0.04 + y*0.06 = 514
400 + y*0.02 = 514
y = (514 - 400)/0.02 = 5,700
Then Ken invested $5,700 in the 6% account, and the other $4,300 in the 4% account.
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The first three terms of a geometric
sequence are 3, 6, 12.
The next three terms in the geometric sequence will be 24, 48 and 96.
We are given a geometric sequence:
3, 6, 12 …
We need to find the next 3 terms of the sequence.
We can see that:
a = initial term of the sequence
a = 3
r = common ratio between the consecutive terms.
r = 6 / 3 = 2
Now, nth term will be represented by:
aₙ = a rⁿ⁻¹
Substituting the values of a and r in the formula, we get that:
aₙ = 3 (2)ⁿ⁻¹
Now, the 4th term will be ( put n = 4)
a₄ = (3) (2)⁴⁻¹
a₄ = (3) (2)³
a₄ = (3) × (8)
a₄ = 24
The 5th term will be: (put n = 5)
a₅ = (3) (2)⁵⁻¹
a₅ = (3) (2)⁴
a₅ = (3) × (16)
a₅ = 48
6th term will be: (put n = 6)
a₆ = (3) (2)⁶⁻¹
a₆ = (3) (2)⁵
a₆ = (3) × (32)
a₆ = 96
Therefore, the next three terms in the geometric sequence will be 24, 48 and 96.
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Your question was incomplete. Please refer the content below:
The first three terms of a geometric sequence are 3, 6, 12. What are the next three terms?
One jar of jam weighs 516 g what is the weigh of 7 jars of jam?
if 1 jar of jam is 516 then 7 jars of jam is 3612 g
Which of the following are functions?
1. y= -3/2x
2. x= 2y - 5
3. x^2 + y^2 = 16
1. Yes. This is the equation of a lihe.
2. Yes. See 1.
3. No. This is the equation of a circle, which fails the vertical line test.
-42-3y + 4z = 1
-4y+ 2z = -2
-5z = -5
Find the unique solution to this system of equations. Give your answer as a point. (x, y, z)
The point (x,y,z) = (₋1,3,₋1) is the solution of the equations.
Given the system of equations are:
2x ₊ y ₊ 3z = ₋2 .....eq(1)
x ₋ y ₋ z = ₋3 ...... eq(2)
3x ₋ 2y ₊ 3z = ₋ 12 .... eq(3)
Solving equation 1 and 2.
2x ₊ y ₊ 3z = ₋2
x ₋ y ₋ z = ₋3
Multiply eq(1) by 1 and eq(2) by 2, we get:
2x ₊ y ₊ 3z = ₋2
2x ₋ 2y ₋ 2z = ₋6
⁻ ⁺ ⁺ ⁺
hence sign changes, then we get:
3y ₊ 5z = 4 ... eq(a)
now solving equation 2 and 3.
x ₋ y ₋ z = ₋3
3x ₋ 2y ₊ 3z = ₋ 12
Multiply eq (2) by 3 and eq (3) by 1.
₋3x ₊ 3y ₊ 3z = 9
3x ₋ 2y ₊ 3z = ₋ 12
sign changes, and we get:
y ₊ 6z = ₋3 ..... eq(b)
y = ₋3 ₋ 6z
substitute y value in eq(a)
3(₋3₋6z) ₊ 5z = 4
₋9 ₋ 18z ₊ 5z = 4
₋13z = 13
z = ₋1
substitute z value in eq(b)
y ₊ 6(₋1) = ₋3
y ₋ 6 = ₋3
y = 3
substitute y and z values in eq (2)
x ₋ (3) ₋ (₋1) = ₋3
x ₋ 3 ₊ 1 = ₋3
x ₋ 2 = ₋3
x = ₋3 ₊ 2
x = ₋1
Therefore the solution to the system of equations is: (₋1,3,₋1)
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your question is incomplete.Please find the missing content here:
2x ₊ y ₊ 3z = ₋2
x ₋ y ₋ z = ₋3
3x ₋ 2y ₊ 3z = ₋ 12
Find the unique solution to this system of equations. Give your answer as a point. (x, y, z)
A map of a small town identifies the town square as the origin (0,0). Each block along a street is represented by one unit along the x- or y- axis. The ice cream shop is at (-5,4) and the grocery store is at (3,2). The grocer wants to install an overhead delivery cable directly between the grocery store and the ice cream shop to expedite deliveries. What is the length of this cable to the nearest tenth of a blocks?
The length of this cable to the nearest tenth of a block will be 6.3 blocks.
Let one point be (x, y) and another point be (h, k). Then the distance between the points will be
D² = (x - h)² + (y - k)²
A map of a small town identifies the town square as the origin (0,0). Each block along a street is represented by one unit along the x- or y-axis. The ice cream shop is at (5. 4) and the grocery store is at (3.-2).
To speed up deliveries, the grocer plans to set up an overhead delivery wire that runs directly between the grocery store and the ice cream parlor.
The length of this cable to the nearest tenth of a block will be
[tex]D² = (5 - 3)² + (4 + 2)²D² = 2² + 6²D² = 4 + 36D² = 40[/tex][tex]D^2 = (5 - 3)^2 + (4 + 2)^2\\D^2 = 2^2 + 6^2\\D^2 = 4 + 36\\D^2 = 40[/tex]
D = 6.3 blocks
Therefore, The length of this cable to the nearest tenth of a block will be 6.3 blocks.
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The length of this cable to the nearest tenth of a block will be 6.3 blocks.
Let one point be (x, y) and another point be (h, k). Then the distance between the points will be
D² = (x - h)² + (y - k)²
A map of a small town identifies the town square as the origin (0,0). Each block along a street is represented by one unit along the x- or y-axis. The ice cream shop is at (5. 4) and the grocery store is at (3.-2).
To speed up deliveries, the grocer plans to set up an overhead delivery wire that runs directly between the grocery store and the ice cream parlor.
The length of this cable to the nearest tenth of a block will be
[tex]D^2 = (5 - 3)^2+(4+2)^2\\D^2 = 2^2 +6^2\\D^2 = 4 +36\\D^2 = 40[/tex]
D = 6.3 blocks
Therefore, The length of this cable to the nearest tenth of a block will be 6.3 blocks.
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Which of the relations shown does NOT represent y as a function of x?
The graph which does not represent y as a function of x is (B) as a line drawn can't touch the graph at two points.
The function that dose not show y as a function of x.
Y is a function of X, means that a certain variable magnitude or phenomenon Y is determined/caused by another magnitude or phenomenon X, such that the behavior of X will affect that of Y. In logic, a function symbol is a logical symbol that may be applied to an object term to produce another object term.
If a vertical line is drawn such that it touches more than one place, then it is not a function of x.
Here also if a vertical line will be drawn it will touch two places in the curve.
So, in figure B, y is not a function of x.
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As a line created can't touch the graph at two locations, graph (B) does not represent y as a function of x.
The function that hides y's relationship to x.
A variable's magnitude or phenomena Y is determined by or caused by a different variable's magnitude or phenomenon X, meaning that X's behavior will have an impact on Y's. A function symbol in logic is a logical symbol that can be used to transform one object term into another.
A vertical line is not a function of x if it is drawn so that it touches many locations.
In this instance as well, a vertical line drawn here will strike the curve twice.
Y is not a function of x in figure B, therefore.
what is 6/11 as a percentage? thank you :).
Answer: 54.55%
Step-by-step explanation:
Answer:
54.5%
Step-by-step explanation:
Fraction to percent: numerator divided by denominator times 100 and add the percent sign.
Four options are given below. Three of these options are similar to each other because they follow the
same pattern. Identify the option that is dissimilar to the other three.
1) AE6
2) FD10
3) AD6
4) DE9
The answer choice which is dissimilar to the other three as given in the task content is Choice 3; AD6.
Which of the four options as given in the task content is dissimilar to the rest of the answer choices?It follows from the task content that the answer choice which is dissimilar to the rest of the answer choices be identified.
From observation, the letters of the alphabet are assigned numbers and the sums are determined such as follows;
A = 1, E= 5, so that AE corresponds to (1+5) = AE6.F = 1, D= 5, so that FD corresponds to (6+4) = 10.A = 1, D= 4, so that AD corresponds to (1+4) = AD5. Hence, it is the dissimilar answer choice among the other answer choices.D = 1, E= 5, so that AE corresponds to (4+5) = DE9.The answer choice which is dissimilar to the other three as given in the task content is Choice 3; AD6.
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HELP ASP SHOW UR WORK YOULL GET BRAINLEST
Answer:
x = 8
Step-by-step explanation:
Subtract
44
from both sides
2
Simplify
3
Add
8x
to both sides
4
Simplify
5
Divide both sides by the same factor
6
Simplify
LAST QUESTION JUST HELP ME PLS I BEG U
describe a real-world situation where you can apply finding the unit rate
A real-world situation where you can apply the unit rate is finding the cost of a single can of soda from a pack of soda.
How can you use the unit rate?The unit rate refers to the price of a single item out of a number or group of items. It is found by dividing the total price of the group of items by the number of items in the group.
In a real-world scenario, you might see a pack of soda priced at $5.20 and you need to know the price of a single can of soda. You can find this by the formula:
= Price of soda pack / Number of soda cans
= 5.20 / 6
= $0.87
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There are two different mountains in the
state of Washington that get record snowfall.
One winter season, Mount Ranier received
1,224 inches of snow. Mount Baker received
1,140 inches of snow. What is the total
snowfall of these two mountains?
Answer:
2364 in
Step-by-step explanation:
1,224+1,140=2364
Determine f(-3) for f(x)
Answer:
9
Step-by-step explanation:
[tex]-3 \leq -3 <4 \implies f(-3)=2(-3)^2-9=9[/tex]
The following table shows the average total cost, measured as dollars expended per pupil, of operating a high school with the given enrollment. This table is based on a study of economies of scale in high school operations from the 1960s.
Enrollment: 170 250 450 650
Average total cost: 538 473 411 415
Estimate the average cost per student for a high school with an enrollment of 350 students.
The interpolated value for an enrollment of 350 students is $ ------
per student.
Answer:
$433
Step-by-step explanation:
You want the average cost per student for an enrollment of 350 students as interpolated from a table of enrollments and costs.
InterpolationThere are a number of ways the cost table might be interpolated. The one used here is to use quadratic regression to write a formula for the cost as a function of enrollment. Then the function value for 350 students is found. This is all accomplished using a graphing calculator, as shown in the attachment. The interpolated value for an enrollment of 350 students is $433 per student.
Another method of interpolation could use linear interpolation between the two nearest points. Our enrollment of interest, 350, is halfway between 250 and 450, so the cost per student could be estimated to be halfway between 473 and 411:
cost per student = (473 +411)/2 = 442 . . . dollars per student
We know this estimate is a bit high, because the cost function is concave upward. A straight line between two points on the curve will lie above the curve.
Other methods of interpolation will give other values. A cubic interpolating function gives a value of $428 per student.
1 Over 25
One-fifth
1
25
Answer:
25
Step-by-step explanation:
Divide: 5 : 1/5 = 5/1 · 5/1 = 5 · 5/1 · 1 = 25/1 = 25 Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/5 is 5/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.In other words - five divided by one fifth is twenty-five.
I hope this helps! Thanks!
Write an expression that represents the paycheck total for
any number of hours worked.
Answer: h x 5
Step-by-step explanation: it is going by 5 every hour and every hour you get paid goes up by 5$. so I would say h x 5 or pt x 5
hw pt
40 / 8.50 . 40
pt = paycheck total
hw= hours worked
A hairdresser is making 4 hair bows. She needs 13/16 yards for each bow. If she has 6 1/8 yards of ribbon, how much will be leftover after making the bows?
Answer:
2 7/8 yards
Step-by-step explanation:
Given 6 1/8 yards of ribbon, you want the leftover amount after making 4 bows that use 13/16 yards each.
Quantity usedIf each of 4 bows takes 13/16 yards, the amount required for bows is ...
4×13/16 = 13/4 . . . . yards
Quantity remainingThe amount left over is the difference between the starting amount and the amount used:
6 1/8 - 13/4 = 49/8 -26/8 = 23/8 = 2 7/8
The hairdresser has 2 7/8 yards of ribbon remaining.
__
Additional comment
Your calculator can work this problem, too.
find the value of the variable and the measure of each labeled angle!
x=
x=
simplified =
please help me im struggling
Answer:
Hello! X should equal 17 and each measured angle would be at 37 degrees.
Step-by-step explanation:
(x + 20) = (4x - 31)
Solve.
x = 17
Plug it in.
(17 + 20) = (4(17) - 31)
Solve.
37 = 37
Hope this helps! Xx
Which equation is equivalent to the statement?
Step-by-step explanation: I hope this helps. the blue, and the purple are in the same line with the green.
Answer:
What is the solution to 4(3x - 6) + 16 < -32
Answer:-2
Step-by-step explanation:add 8 to both sides 12x-8<-32=-2
HELP (20 points) using triangle ABC how does extending vertex c further away to the left of vertex b verify the relationship between sides and angles in triangles?
Answer:
a stays the same but cb cahanges
Step-by-step explanation:
Rewrite the following polynomials in standard form.
10-x- 7x ²
Answer:
- 7x ² -x +10
Step-by-step explanation:
⇒Given
10-x- 7x ²
⇒We have a polynomial of second degree that has the standard from ax²+bx+c
⇒Rearrange the terms of the polynomial to match the standard form
- 7x ² -x +10
A class has 20 boys and 25 girls, what is the ratio of boys to girls?
Answer:
4:5
Step-by-step explanation:
Boys: 20 Girls: 25
÷5 ÷5
------ ----------
4 5
For every 4 boys, there are 5 girls
I hope this helps!
Answer the questions below. Be sure to mark all answers that apply.
(a) Which numbers are divisible by 9?
(b) Which numbers are divisible by 3?
474 127 907
None of these
There is none of these numbers are divisible by 9 and the required number is 474 divisible by 3 which the correct answer would be an option (D)
What is the divisibility rule?The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.
The sum of the digits should be divisible by 9
⇒ 474 : (4+7+4=15, and again, 1+5=6)
This number is not divisible by 9
⇒ 127 : (1+2+7=10, and again, 1+0=1)
This number is also not divisible by 9
⇒ 907 : (9+0+7=16, and again, 1+6=7)
This number is also not divisible by 9
The sum of the digits should be divisible by 3
⇒ 474 : (4+7+4=15, and 15÷3 = 5)
This number is divisible by 3
⇒ 127 : (1+2+7=10, and 10÷3 = 3.333)
This number is not divisible by 3
⇒ 907 : (9+0+7=16, and 16÷3 = 5.333)
This number is not divisible by 3
There is none of these numbers are divisible by 9 and the required number is 474 divisible by 3 which the correct answer would be an option (D)
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The question seems to be incomplete the correct question would be
(a) Which numbers are divisible by 9?
(A). 474
(B). 127
(C). 907
(D). None of these
(b) Which numbers are divisible by 3?
(A). 474
(B). 127
(C). 907
(D). None of these
what is a rate and a unit rate
Answer: a unit rate is how much would you pay for one item and a rate is a fixed price for a good or service
Step-by-step explanation:
If x varies inversely as y, then find the constant of variation if y = 9 and x =
8.
The constant of variation is 72.
Constant of Variation: What is it?In a direct variation, the constant of variation is the constant (unchanged) ratio of the two variables. The formula for direct variation is. where k is the variational constant and y=kx (or y=kx).
being that
x = 8
y = 9
If x varies in opposition to y, then
x*y = fixed
which means
x*y = k (where we assume constant as k) (where we take constant as k)
Inputting the values of x and y now yields,
8*9 = k
72 = k
Consequently, 72 is the constant of variation.
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6 apples and 5 oranges are shared among 3 friends. If the apples are indistinguiable, oranges are also indistinguiable, how many ways can they share these fruits if each friend must have some fruit?
Answer:
Step-by-step explanation:
I would say that nobody gets the last one but every one else gets 2 apples and 1 orange.
Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
The point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
In this question we have been given a graph of Skateboards vs. Bikes.
We need to find the point that represents an INEFFICIENT point of production.
Inefficient production means the economy can be producing more goods without using any additional resources.
In given production possibility curve, an INEFFICIENT point of production is point A.
Therefore, the point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
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