In a survey where the ratio of students who prefer muffins to bagels is 4 to 5 and 420 prefer muffins, 525 students prefer bagels.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.
It can be expressed in different ways:
1) Use the ":" to separate the values : a : b
2) Use the word "to" : a to b
3) Write it in fraction: a / b
On the other hand, proportion is the equality of two ratios, such that
a : b = c : d
Given a proportion, the product of its means must be equal to the product of its extremes. That is:
ad = bc
If the ratio of students who prefer muffins to bagels is 4 to 5, and 420 students prefer muffins, the proportion can be written as:
4 : 5 = 420 : n
where n = number of students who prefer bagels
Solving for n,
4n = 5(420)
4n = 2100
n = 525
number of students who prefer bagels = 525
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2x-5y=5
x - y table
graphh
Answer: -3/4
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: −3/4
y-intercept: (0,0)
x y
0 0
4 -3
3 different two-digit numbers are selected and multiplied together. the probability that the product is even is where are relatively prime. what is
Probability of an even number product as requested = 7/10 = .7 = 70%
The probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Combinations of 2 digits from among 5 = 5!/(3!)(2!) = 10. Those combinations of 2 digits resulting in an even number product are even*even and even*odd. There are 2 even digits, (2,4), and 3 odd digits, (1,3,5).
Combinations of 2 even digits and 3 odd digits = 3*2 = 6. Combinations of 2 even digits = 1*1 = 1. there are thus 6+1 = 7 distinct 2 digit products that result in even numbers from among 10 possible 2 digit products.
Probability of an even number product as requested = 7/10 = .7 = 70%
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Simplify
x2 - 7x + 12
x2 -2x - 8
Answer:
5x+12
-8
Step-by-step explanation:
i think you have the problem wrong
A company is designing a new cylindrical water bottle. The volume of the bottle will be 179 cm to the power of 3. The height of the water bottle is 8.3 cm. What is the radius of the water bottle? Use 3.14 for [tex]\pi[/tex].
Answer: r=2.62 cm
Step-by-step explanation:
Cylinder Volume: V=πhr^2
179=π(8.3)r^2
179=8.3*3.14*r^2
179=26.062r^2
r^2=6.87
r=2.62 cm
What is the factored form of this expression?
Answer:
The factored form of 27t^3 - 36t^2 - 12t + 16 is:
(3t - 4) (3t+2) (3t - 2)
Find FH
FH = {Blank}
Answer:
22
Step-by-step explanation:
By the segment addition postulate, FH=8+14=22.
The equation will be,
→ FH = FG + GH
Then the value of FH will be,
→ FH = 8 + 14
→ [ FH = 22 ]
Hence, the value of FH is 22.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line shown is -2/3
Slope of a lineThe formula for calculating the slope of a line is expressed according to the formula
Slope = Rise/Run
Slope = y₂-y₁/x₂-x₁
Using the coordinate point (-9,-2) and (-6, -4)
Slope = -4+2/-6+9
Slope = -2/3
Slope = negative two third
Hence the slope of the line shown is -2/3
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in one city , the ratio of the households with pets to house holds without pets is 30 to 29. if 20,735 households do not have pets, how many house holds have pets
The number of number of house holds have pets will be 21450 when 20,735 households do not have pets.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
It is given that the ratio of the households with pets to house holds without pets is 30 to 29 and if 20,735 households do not have pets then it is find the number of number of house holds have pets. It can be find out using the ratio correlation :
That is , 29 is the ratio of house holds without pets ⇒ 20735
1 unit of house holds without pet ⇒ 20735/29 = 715 house hold
Now, the ratio of households with pets ⇒ 30 x 715 = 21450 house hold
Therefore, the number of number of house holds have pets will be 21450 when 20,735 households do not have pets.
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A company sells designer purses For $400 per purse. Usually, they sell 3000 purses per month. according to market research, they will sell 500 more purses for every 20$ reduction in price. write a function R(x) that models the company's revenue, where x is the number of price reductions. find the price that will generate the maximum revenue. find the maximum revenue.
The price that would yield maximum revenue is $260 and maximum revenue is $1,690,000
What is the revenue function?
The fact that total revenue of the company is the price per purse multiplied by the number of purses sold, means that the revenue modelled function is simply price multiplied by the quantity sold as shown below:
R(x)=P*x
R(x)=Px
R(3000)=$400*3,000
R(3000)=$1200,000
Note for every 500 more purses, the price reduces by $20
R(3500)=$380*3,500
R(3500)=$1,330,000
R(4000)=$360*4000
R(4000)=$1,440,000
R(4500)=$340*4500
R(4500)=$1,530,000
R(5000)=$320*5000
R(5000)=$1,600,000
R(5500)=$300*5500
R(5500)=$1,650,000
R(6000)=$280*6000
R(6000)=$1680,000
R(6500)=$260*6500
R(6500)=$1,690,000
R(7000)=$240*7000
R(7000)=$1,680,000
The total revenue fell at 7,000 purses, which means that the maximum revenue is $1,690,000 at 6500 purses
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which one of the following pairs of numbers contains like fractions ?
A. 6/7 and 60/79
B.4/8 and 12/16
C. 1/2 and 3/2
D. 5/4 and 4/5
Answer:
C
Step-by-step explanation:
125+s is greater than or equal to 2300 in words
125 is greater than 23.
Given the question is to explain 125 > 23.
Here we have two numbers which are 125 and 23.
Inequalities:
Whenever we check the number which is greater or lesser by taking the difference between those two numbers we conclude which is greater or lesser.
If the difference between the numbers gets a positive number then the first number is greater than the second.
If the difference between the numbers gets a negative number then the first number is lesser than the second.
If the difference between the numbers gets zero value then the two numbers are equal.
So the difference between the given two numbers are
= 125 - 23
= 102
positive
So 125 is greater than 23.
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Your question is incomplete. Please find the complete question below
.Find 125 is greater than 23. Write about it in words.
If angle 6 measures 9x+13 and angle 2 measures 11x-3 what is the measurement of angle 2
The measure of an angle 2 is 85°.
Given that, ∠6=9x+13 and ∠2=11x-3.
What are corresponding angles?Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
As we know, corresponding angles are congruent.
So, ∠6= ∠2
⇒ 9x+13=11x-3
⇒ 13+3=11x-9x
⇒ 16=2x
⇒ x=8
Now, ∠2=11x-3
=11×8-3=85°
Therefore, the measure of an angle 2 is 85°.
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Evaluate the expression when y=−2 and z=−5.
10y2z=
The value of the expression 10y²z is -750.
How to calculate the expression?We are to calculate the expression 10y²z when y=−2 and z=−5.
This will be:
10y²z
= 10 × -5² × -3
= 10 × 25 × -3
= -750
The value of the expression 10y²z is -750.
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Members of a soccer team raised $2143.50 to go to a tournament. They rented a bus for $888.50 and budgeted $62.75 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
The equation to find the number of players the team can bring to the tournament is xx = ( 2,143.50 - 888.50 )/62.75 and the number of players the team can bring to the tournament is 20.
An equation is a mathematical statement that shows that two or more mathematical expressions are equal.
Equations express the equality of mathematical expressions by using the equation mark (=).
The total amount raised for the tournament is $2,143.50
The price to rent a bus is $888.50.
The cost of budgeted meals per player is $62.75.
The number of players the team can bring to the tournament is:
xx = ( 2,143.50 - 888.50 ) / 62.75.
xx = ( 2,143.50 - 888.50 ) / 62.75
xx = 1,255 / 62.75
xx = 20
Therefore, the equation to calculate the maximum number of players the team can enter the competition is xx = ( 2,143.50 - 888.50 ) / 62.75.
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Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
Answer:
SOLUTION: .−5x + 4y = 20. 10x − 8y = −40.
Step-by-step explanation:
First, solve the first equation for y. Then, substitute for y in the second equation. This equation is an identity
How do you add this expression? -1/2 + 2/7
Answer:
You can't
Step-by-step explanation:
Write an equation of the line in point-slope form that passes through the
given points. (4, 2) and (1, 6)
The equation of line that passes through the given points in point-slope form is y - 2 = -4/3( x - 4 ).
What is the equation of line that passes through the given points?Given the data in the question;
Point A(4, 2)
x₁ = 4y₁ = 2Point B(1, 6)
x₂ = 1y₂ = 6First, we determine the slope of the line.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 6 - 2 )/( 1 - 4 )
Slope m = ( 4 )/( -3)
Slope m = -4/3
Next, plug the slope -4/3 and point (4,2) into the point slope formula y - y₁ = m( x - x₁ ) and simplify.
y - y₁ = m( x - x₁ )
y - 2 = -4/3( x - 4 )
Therefore, the equation of line that passes through the given points in point-slope form is y - 2 = -4/3( x - 4 ).
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A stationery shop orders a batch of pens from a factory. The factory could make the batch of pens in 20 days using 12 machines. Due to a fault, only 9 machines were used for the first 8 days. All 12 machines were used from day 9 onwards. Work out the total number of days taken to make the batch of pens.
The number of days taken to complete the production of a batch of pens are 22, as calculated by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.
Now, According to the question, the factories used all 12 machines in the last days, Also, for the first 8 days, only 9 machines were in use.
Thus, If the factories used all 12 machines, the batch of pens took 20 days to be manufactured.
Hence, the equation formed from the given information by basic algebra is: 20 + 12 - 9(8) / 12
28 - (72/12)
=28 - 6 = 22
Hence, The number of days taken to complete the production of a batch of pens are 22, as calculated by basic algebra.
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3/ax - 4 = 20 What is x?
x =
Answer:
[tex] \sf \large \: x=8a[/tex]
Step-by-step explanation:
Let's solve for x.
3/ax−4=20
Step 1: Multiply both sides by a.
−4a+3x=20a
Step 2: Add 4a to both sides.
−4a+3x+4a=20a+4a
3x=24a
Step 3: Divide both sides by 3.
3x/3 = 24a/3
x=8a
Determine whether function for the situation would have a discrete or continuous graph.
20. The cost of a given number of handbags
19. Amount of juice in a jug over time.
21. Area of a field based on length 22. Tires in a number of cars.
The cost of a given number of handbags - Discrete
Amount of juice in a jug over time - Continuous
Area of a field based on length - Continuous
Tires in a number of cars -Discrete
A discrete function as its name suggests has distinct or separate values against one value. That is, one at a time values are in a discrete function. So its domain and image sets will have discrete values.
A continuous function has continuous values within intervals. Its domain will be intervals having a continuous range and images will also be in a continuous range.
We need to check if the following will have a discrete or a continuous graph:
1. The cost of a given number of handbags.
This is a discrete function as the cost and number of handbags will have discrete values. So it will have a discrete graph.
2. Amount of juice in a jug over time
This is a continuous function. The variables here are the amount of juice and time in which time, clearly, is a continuous variable. So it will have continuous values in an interval. So the amount of juice can also be measured continuously. So the graph will be continuous.
3. Area of a field based on length
Here the length can take continuous values in an interval. So the area can also be measured continuously giving a continuous graph here.
4. Tires in a number of cars.
Number of tires and number of cars both will take only discrete values. So it can only give a discrete graph.
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If you roll a 6-sided die 66 times, what is the best prediction possible for the number of times you will roll an even number?
Answer:
33 times
Step-by-step explanation:
Set up an equation:
3 evens / 6 total = 1/2 probability of rolling an even
66 times x 1/2 probability= 33
Best prediction: 33 times
Hope this helps!
Jeremiah makes $15 an hour working part-time at a local fast food restaurant. He pays approximately 11% in taxes on his earnings. If h is his hours worked, model his weekly after-tax wages as a function w(h) of hours worked.
Step-by-step explanation:
11% = 0.11
the remaining part when subtracting 11% from the whole (100%) is 89%.
89% = 0.89
his after-tax wages are 89% of his total income.
w(h) = 15h × 0.89 = 13.35h
PLEASE ANSWER THIS FAST Lesson 16 Practice Problems
1. For each triangle, find the measure of the missing angle.
Figure 3
20°
Figure 1
28
729
128%
'В
K
D
Figure 4
Figure 2 122⁰ 389
7
2. Is there a triangle with two right angles? Explain your reasoning.
56°
89%
Prepare a frequency table of the following scores obtained by 40 students in a
test:
24,16,17,30,28,20,15,24,16,18,18,15,16,20,25,24,25,20,16,15,18,25,20,18,28,27
,25,24,24,18,18,25,20,16,25,20,27,28,28,16.
This contains 20 points please help me quick
Answer:
Element Frequency Cumulative Frequency
15 3 3
16 6 9
17 1 10
18 6 16
20 6 22
24 5 27
25 6 33
27 2 35
28 4 39
30 1 40
Step-by-step explanation:
Find out how many times an element(data value) appears. That will be the frequency(column 2). The cumulative frequency is the total of all frequencies prior to that element plus the current element frequency
Cumulative frequency for first element is same as its frequency
Cumulative frequency for element 16 is 3 + 6 = 9
Cumulative frequency for element 17 = 3 + 6 + 1 = 9 + 1=10. Basically it is the sum of the previous element cumulative frequency + the current frequency
The table shows the current heights and average growth rates of two different species of trees. State and solve an equation to find how long it will take for the two trees to be the same height.
Help with showing equation an answer please!!
The two different species of plants will take 5 years to reach the same height.
Given, from the table :
Tree specie A has a:
current height = 38 inches
and its annual growth = 4 inches
Therefore, total height is:
38 + 4x .. eq (1)
Tree specie B has a:
current height = 45.5 inches
and its annual growth = 2.5 inches
Therefore, total height is:
45.5 + 2.5x .. eq (2)
Equate equation 1 and equation 2.
38 + 4x = 45.5 + 2.5x
Subtract the constants.
4x = 45.5 - 38 + 2.5x
4x = 7.5 + 2.5x
now subtract the variables.
4x - 2.5x = 7.5
1.5x = 7.5
x = 7.5/1.5
x = 5
Hence the trees will take 5 years to reach the same height.
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Write the value of π correct to 5 decimal places.
Answer:
3.14159
Step-by-step explanation:
The value of π correct to 5 decimal places is 3.14159.
What are Decimal Numbers?Decimal numbers are numbers which includes a whole number part and a fractional part.
The point separating both parts is the decimal point.
Pi, which is written as the Greek symbol π, is defined as the ratio of the circumference of any circle to the diameter of that circle.
We know that,
Circumference of a circle, C = 2 π r, where r is the radius.
2r will be the diameter.
π = C / 2r
The value of pi to 5 decimal places = 3.14159
Normally we use 3.14.
Hence the value of pi is 3.14159 to 5 decimal places.
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Determine the constant rate of change
question add 1 1/3 (−5/6) using the number line. select the location on the number line to plot the sum.
Answer:
Add 11/3+(-5/6)
17/6 it present on number line between
2 and
Step-by-step explanation:
Answer:
1 1/3 (−5/6) using the number line. select the location on the number line to plot the sum
Step-by-step explanation:
i have already answered this question but got it wrong but really interested on the right answer
Answer:
You're right, It's option B.
Step-by-step explanation:
The expressions both share two common factors that are whole numbers; 9 and 6. Use those.
9: 1, 3, 9
6: 1, 2, 3, 6
3a. let’s explore the data. what are the mean lengths of yellowfish in each location? what are the variances? do they meet the assumption of equal variances?
(3a) The 95% confidence interval of σ[tex]_{1}^{2}[/tex]/σ[tex]_{2}^{2}[/tex] is: [0.1932 , 1.2032].
What is variance?Variance is the anticipated squared deviation of a random variable from its population mean or sample mean in probability theory and statistics.
F test for variances, using F distribution ([tex]df_{num}[/tex]=19,[tex]df_{denom}[/tex]=20) (two-tailed) (validation).
Hypotheses
[tex]H_{0}:sigma_{1} = sigma_{2}\\\\H_{1}:sigma_{1}\neq sigma_{2}[/tex]
1. H0 hypothesis
Since p-value > α, H0 is accepted.
The sample standard deviation (S) of LaJolla.res' population is considered to be equal to the sample standard deviation (S) of Pt.Loma.ke's population.
In other words, the difference between the sample standard deviation (S) of the LaJolla.res and Pt.Loma.ke populations is not big enough to be statistically significant.
2. P-value
The p-value equals 0.1152, ( p(x≤F) = 0.05759 ). It means that the chance of type I error, rejecting a correct [tex]H_{0}[/tex], is too high: 0.1152 (11.52%).
The larger the p-value the more it supports [tex]H_{0}[/tex].
3. The statistics
The test statistic F equals 0.4796, which is in the 95% region of acceptance: [0.3986 : 2.4821].
S1/S2=0.69, is in the 95% region of acceptance: [0.6313 : 1.5755].
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