Answer:
Part 1) [tex]\frac{5}{2}[/tex] or [tex]5:2[/tex]
Part 2) [tex]\frac{8}{1}[/tex] or [tex]8:1[/tex]
Step-by-step explanation:
Write the ratio as a fraction in simplest form
Part 1) 15 girls to 6 boys
we know that
To find out the ratio, divide the number of girls by the number of boys
so
[tex]\frac{15}{6}[/tex]
Simplify
Divide by 3 both numerator and denominator
[tex]\frac{5}{2}\ \frac{girls}{boys}[/tex]
Part 2) 24 plays for 3 teams
we know that
To find out the ratio, divide the number of plays by the number of teams
so
[tex]\frac{24}{3}[/tex]
Simplify
Divide by 3 both numerator and denominator
[tex]\frac{8}{1}\ \frac{plays}{team}[/tex]
Final answer:
To simplify the ratios 15 girls : 6 boys and 24 plays : 3 teams, find the greatest common factor and divide both parts of the ratio by it, resulting in the simplest forms rac{5}{2} and 8, respectively.
Explanation:
To write the ratios as fractions in simplest form for the given scenarios:
For the ratio of 15 girls to 6 boys, the fraction would be rac{15}{6}. To simplify, divide both the numerator and the denominator by their greatest common factor (GCF), which is 3. Thus, the simplest form is rac{15 \/ 3}{6 \/ 3} = rac{5}{2}.
For the ratio of 24 plays for 3 teams, the fraction is rac{24}{3}. Again, to simplify, divide both the numerator and the denominator by the GCF, which is 3 in this case. The simplest form is rac{24 \/ 3}{3 \/ 3} = rac{8}{1}, which can also be written simply as 8 since a denominator of 1 implies the value is a whole number.
I need this asap so if you can help that would be amazing . I can boost the points to more than 50 comment if you want more...
Multiply the number amount of cartridges by the number of books and add that tot he number of cartridges by the number of magazines.:
This needs to be either less than or equal tot he total cartridges she wants to use
40B + 30M ≤ 300
Do the same with pages:
200B + 80M ≤ 1200
The measure of <B is (3x - 4) and the measure of
<D is (2x-6)”. What are the measures of angles B
and D?
m<B=
m<D =
Step-by-step explanation:
Given information is insufficient for finding the measures of angles B and D.
Answer:
110 and 70
Step-by-step explanation:
What is 28.93 in expanded form
Answer:20+8+.9+.03
Step-by-step explanation:
Final answer:
The number 28.93 in expanded form is written as 20 + 8 + 0.9 + 0.03.
Explanation:
The number 28.93 in expanded form is written as 20 + 8 + 0.9 + 0.03. To expand a decimal number, we break it down into its place values, where each digit is represented by its value in terms of tens, ones, tenths, hundredths, and so forth. In the case of 28.93, the '2' is in the tens place and represents 20, the '8' is in the ones place and represents 8, the '9' is in the tenths place and represents 0.9, and the '3' is in the hundredths place and represents 0.03.
When a=2 b=3 and c=5 what is the value of a(b+c)
Show how you got the answer
Answer:
B =
Step-by-step explanation:B + C would be 8 because B=2 and C=5. 5 + 8 is 8
12x -3 divided by -5
Answer: 1.8x
Step-by-step explanation:
The area of a rectangular sandbox is (5x + 40) feet. Factor 5x + 40 to find possible
dimensions of the sandbox.
The possible dimensions of the sandbox are 5 and [tex](x+8)[/tex].
Important information:
The area of the rectangular sandbox is [tex]5x+40[/tex].We need to find the possible dimensions of the sandbox.
Area of a rectangle:Formula for the area of a rectangle is:
[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]
Factorize the given expression to find the possible dimensions of the sandbox.
[tex]5x+40=5x+5\times 8)[/tex]
[tex]5x+40=5(x+8)[/tex]
Thus, the possible dimensions of the sandbox are 5 and [tex](x+8)[/tex].
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A car that initially cost 42,000 depreciates in value by approximately 2,000 dollars per year write an equation to represent the value in dollars, Y, of a car X years after it was purchased
Answer:y=42000-2000x
Step-by-step explanation:
Y is price so that’s be 42000 minus 2000 every year
Answer:
[tex]y=42,000 - 2000x[/tex]
Step-by-step explanation:
The y is the total value of the car after everything that needs to be taken account of has been accounted to. You're finding the y and what the price is after x amount of years. The initial amount is 42,000 so whatever the cost of the car has depreciated would be subtracted from it. 2,000 dollars per year means what ever x is for year, let's say 5. The amount of money that the car has depreciated over the course of 5 years would be 5 multiply by 2,000. Hopes this help!
mira's kitchen holds up to 103.468 liters of water. round this amount to the nearest liter WORTH: 10 PTS
Answer:
It would round down to 103 liters.
Step-by-step explanation:
Which are true of the function f(x)=49(1/7)^x
select three options.
1) the domain is the set of all real numbers
2) the range is the set of all real numbers
3) the domain is x>0
4) the range is y>0
5) as x increased by 1, each y-value is one seventh of the previous y-value
The Option (1),(4) and (5) are correct.
Step-by-step explanation:
The function given to us is : y= f(x) =49(1/7)^x
The following statements are true regarding the above function is
As you can see that the value of y(49)is defined for all values of x , so the Domain is the set of all values of x , which is set of all real numbers.X is defined for all values of y. So the Range of all the values that y can take is also set of all real numbers greater than zero, i.e y>0.As x increased by 1, each y-value is one seventh of the previous y-valueAnswer:
The correct options are 1, 4 and 5.
Step-by-step explanation:
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is initial value and b is growth factor.
Domain of this function is all real numbers. If a>0, then range is all positive numbers.
The given function is
[tex]f(x)=49(\frac{1}{7})^x[/tex]
where, a =49 and b=1/7.
It is an exponential function. So, the domain is the set of all real numbers.
Since, a=49 which is a positive value, therefore the range is y>0.
The value of b is 1/7, it means as x increased by 1, each y-value is one seventh of the previous y-value.
Therefore, the correct options are 1, 4 and 5.
Please solve the following system of equations by
substitution.
y = 3x - 4 and 4x + 3y = 1
Answer:
(1 , -1)Step-by-step explanation:
y = 3x - 4 (1)
4x + 3y = 1 (2)
if we substitute y by 3x - 4 in the second equation we get
4x + 3(3x-4) = 1 ⇒ 4x + 9x - 12 = 1 ⇒ 13x = 13 ⇒ x = 1
now ,we substitute x by 1 in the first equation
y = 3(1) - 4 = 3 - 4 = -1
what is 489+ 9860 TELL ME SLAVES
Answer:10,349
Step-by-step explanation:
For the function defined by f(x)=12/x^2, what is the constant proportionality
A. 120
B.undefined
C. 12
D.1200
Answer:
12
Step-by-step explanation:
PLEASE ANSWER ASAP
Talk of the Town is a cell phone provider. They charge by the month. The first month of service costs $72.99. The second month of service costs $101.44. The third month of service costs $129.89. Write an equation in the form of
y=c+d(x−1)
to represent this situation. Explain how you got your equation.
Answer:
[tex]y=72.99+28.45(x-1)[/tex]
Step-by-step explanation:
Linear Modeling
Some situations in real life are bound to be modeled as mathematical functions. A model allows scientists and analysts to take decisions based on predicted values coming from those models.
To construct them we usually take or measure values of the variables of interest and find the general equation of the model. In this case, we'll find the relation between the service costs (y) of a cell phone provider and the number of months (x).
There are three points available: ( 1 , 72.99 ) , ( 2 , 101.44 ) , ( 3 , 129.89 ) and we only need two to find a function of the form
[tex]y=c+d(x-1)[/tex]
We'll use the first two points and use the third point to verify the validity of the model. Let's plug in the first point:
[tex]72.99=c+d(1-1)[/tex]
Operating
[tex]72.99=c\\c=72.99[/tex]
Now for the second point
[tex]101.44=72.99+d(2-1)[/tex]
Operating and rearranging
[tex]d=101.44-72.99=28.45[/tex]
Our model is complete:
[tex]\boxed{y=72.99+28.45(x-1)}[/tex]
Let's check the third point ( 3 , 129.89 ) by plugging x=3
[tex]y=72.99+28.45(3-1)=72.99+56.9=129.89[/tex]
The point belongs to the function.
Final answer:
The cell phone provider's escalating monthly charges can be represented by a linear equation, demonstrating the initial cost plus the consistent monthly increase. The equation is y = 72.99 + 28.45(x - 1).
Explanation:
To find the equation representing the cell phone provider Talk of the Town, we observe the costs for the first three months: $72.99 for the first month, $101.44 for the second, and $129.89 for the third. The increase in cost from one month to the next is consistent, increasing by $28.45 each time. This situation can be expressed as a linear equation in the form y=c+d(x−1), where y is the total cost, c is the starting value, d is the difference per period, and x represents the month number.
To find c (the initial cost), we look at the first month's charge: $72.99. d, the monthly increase, is $28.45. Thus the equation for the total cost of service from Talk of the Town over x months is y = 72.99 + 28.45(x - 1). This equation accounts for the initial cost in the first month and the consistent monthly increase thereafter.
What property is 3(x-y)=3x-3y
Answer:
The distributive property is used
Step-by-step explanation:
3(x - y) = 3x - 3y Distribute the 3 to the (x - y)
I have to round 312016.29 to the nearest whole number what would I do??
Answer:
312016 is your correct answer
Step-by-step explanation:
32h = 288 solve for h
Answer:
h= 9
Step-by-step explanation:
you divide both sides by 32
and 288 divided by 32 is 9
Which value is NOT equivalent to the other values? 1/25 0.04 4% 0.4
Let's convert them to decimals:
1/25 = 0.04
4% = 0.04
0.04 = 0.04
0.4 = 0.40.
So 0.4 is NOT equivalent to the other values.
The values 1/25, 0.04, and 4% are all equivalent to each other. The value that does not match with these is 0.4.
Explanation:The values given in the question are 1/25, 0.04, 4%, and 0.4. These values can be converted into the same format to compare them more easily.
Firstly, you can convert 1/25 into a decimal, which equals 0.04. Secondly, we can convert 4% into a decimal by dividing the number 4 by 100, which also equals 0.04. Lastly, when comparing these to 0.4, it becomes clear that 0.4 is not equivalent to the other numbers (0.04).
So, the value which is not equivalent to the others is 0.4.
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Match each circular flower bed on the left to its circumference and its area on the right. Some answer options on the right will not be used.
To find the circumference of a circle, use the formula C = 2πr. To find the area, use the formula A = πr^2.
Explanation:The question asks to match each circular flower bed on the left to its circumference and its area on the right. In order to find the circumference of a circle, we use the formula C = 2πr, where r is the radius of the circle.
To find the area of a circle, we use the formula A = πr^2. We can use these formulas to calculate the circumference and area of each circular flower bed and match them to the options on the right.
For example, if a circular flower bed has a radius of 3 meters, we can find its circumference by plugging the radius into the formula: C = 2π(3) = 6π meters. Similarly, we can find its area by plugging the radius into the formula: A = π(3^2) = 9π square meters.
Is 9 bigger than negative 10??
Answer:
Yes 9 is larger than -10
Step-by-step explanation:
Any positive number is larger than a negative number
Answer: yes
Step-by-step explanation: this is so because on the number line 9 comes first while -10 is far behind from -1
A bakery has 36 glazed donuts on display.This is 80% of the total number of donuts what is the total number of donuts in the bakery
Answer:
45
Step-by-step explanation:
Given:
A bakery has 36 glazed donuts on display.
This is 80% of the total number of donuts.
Question asked:
what is the total number of donuts in the bakery ?
Solution:
Let total number of donuts in the bakery = [tex]x[/tex]
80% of total number of donuts = 36 (given)
[tex]80\% of x = 36[/tex]
[tex]\frac{80x}{100} = 36[/tex]
Multiplying both side by 100
[tex]80x = 3600[/tex]
Dividing both side by 80
[tex]x = 45\\[/tex]
Thus, the number of donuts in the bakery is 45
Tina wants to run 12 3/5 miles over 7 days she wants to run the same distance each day how far must she run each day
To find out how much Tina needs to run each day, divide the total miles she wants to run by the number of days. The result is that Tina needs to run 1.8 miles each day.
Explanation:To find out how far Tina must run each day, we need to divide the total distance she plans to run by the number of days she plans to run. Tina wants to run 12 3/5 miles over 7 days. As a first step, convert her mixed number to an improper fraction. 12 3/5 is equivalent to 63/5.
Now, to find the distance she must run each day, simply divide 63/5 miles by 7 days. Carrying out this division gives us distance of 9/5 miles per day, or in decimal form, 1.8 miles per day.
So, Tina should run 1.8 miles each day to reach her goal.
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What is the solution to this system?
Y=-5x+8,y=11/7x-4/7
Answer:
Step-by-step explanation:
hello : the system is : y =-5x+8...(*)
y =11/7x-4/7 ...(**)
by (*) and (**) : 11/7x-4/7 = -5x+8
multiply by 7 : 11x-4 = -35x+56
11x+35x = 56+4
46x = 60
x = 60/46 = 30/23
continu.....put the value for x in (*) or (**)
Juan is waiting for the roller coaster at an amusement park. He has been told there is a 40% chance that he will have to wait more than 15 minutes. Find the probability both as a decimal and as a reduced fraction
Answer:
0.4, 2/5
Step-by-step explanation:
The probability that Juan has to wait more than 15 minutes is 0.4 and the probability that Juan doesn't have to wait for more than 15 minutes is 0.6
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here, there is a 40% chance that he will have to wait more than 15 minutes. Thus the probability of him waiting for more than 15 minutes is 0.4 and the probability that he has to wait less than 15 minutes is 1-0.4=0.6
Hence, P(<15)=0.6 or 3/5 and P(>15) = 0.4 or 2/5 are the probabilites for Juan
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ifyou choose one without looking, the probability you choose a green marble is StartFraction 20 Over 40 EndFraction
. How can you write this probability as a decimal? Write this probability as a decimal. Use a word or phrase to describe this probability.
How do you change the fraction to a decimal?
A.
Multiply the numerator and denominator by 3.
B.
Divide the numerator by the denominator.
C.
Divide the denominator by the numerator.
D.
Multiply the numerator by the denominator.
a) To write the probability as a decimal, we divide the numerator (20) by the denominator (40). This gives us the decimal representation of the probability.
b) To change the fraction to a decimal, we divide the numerator by the denominator.
So, the correct answer is option B: Divide the numerator by the denominator.
Explanation:
To change the fraction [tex]\( \frac{20}{40} \)[/tex] to a decimal, we perform the division [tex]\( \frac{20}{40} \)[/tex].
[tex]\[ \frac{20}{40} = 0.5 \][/tex]
Therefore, the probability of choosing a green marble as a decimal is 0.5.
The length is 3 inches more than twice the width. Which expression represents the perimeter of the frame in inches?
2w+3
Answer:
[tex](6W+6)\ in[/tex]
Step-by-step explanation:
we know that
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex] ----> equation A
where
L is the length
W is the width
we have
The length is 3 inches more than twice the width
so
[tex]L=2w+3[/tex] ----> equation B
substitute equation B in equation A
[tex]P=2(2W+3+W)[/tex]
Combine like terms
[tex]P=2(3W+3)\\P=(6W+6)\ in[/tex]
A farmer produces about $3000 eggs each day and sell them for $0.80 per dozen. On average, how much money does the farm get for its eggs each day?
Answer:
$200
Step-by-step explanation:
1. 3000 divided by 12 = 250
2. 250 x 0.80 = 200
i hope i helped
Right and solve an equation that can be used to find the width of the backyard that is 120 feet long and has a perimeter of 330 feet
The width of backyard is 45 feet.
Step-by-step explanation:
Given,
Length of backyard = 120 feet
Perimeter of backyard = 330 feet
Width of backyard = w
Perimeter = 2(Length + Width)
[tex]330=2(120+w)\\330=240+2w\\330-240=2w\\90=2w\\2w=90[/tex]
Dividing both sides by 2
[tex]\frac{2w}{2}=\frac{90}{2}\\w=45[/tex]
The width of backyard is 45 feet.
Keywords: perimeter, division
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c) Find the value of x:
5x + 2 = 4x + 8
A farmer has two pieces of land in a parallelogram shape on the same base. He grows vegetables and flowers in two triangular pieces of land as shown in diagram.
Q: Check whether the two triangular pieces of land are equal in area.
Step-by-step explanation:
In trapezoid ABCF, AB || CF.
Therefore, parallelograms ABEF & ABCD have same height and lie on the same base AB.
[tex] \therefore Ar(\parallel^{gm} ABEF) = Ar(\parallel^{gm}ABCD)\\... (1)\\\\
\because\: Ar(\parallel^{gm} ABEF) \\=Ar(\triangle AFD) + Ar(\square \: ABED)....(2) \\\\
\&\: Ar(\parallel^{gm}ABCD)\\= Ar(\triangle BCE) +Ar(\square ABED)....(3) [/tex]
From equations (1), (2) & (3), we find:
[tex] Ar(\triangle AFD) + Ar(\square \: ABED) \\ = Ar(\triangle BCE) +Ar(\square ABED)
\\ \\ \purple {\boxed {\therefore Ar(\triangle AFD) = Ar(\triangle BCE)}}
\\ [/tex]
Thus, the two triangular pieces of land are equal in area.
Hence proved.
What is the value of 4x 3+4x when x=4
Final answer:
The value of 4x when x=4 is 16, and for proportions like 1:2=4:x, you'd get x=8 by cross multiplying.
Explanation:
The value of 4x when x=4 is simply 4 multiplied by 4, which equals 16. This calculation is a basic algebraic operation, and it should not be confused with more complex problems. For example, if you're trying to solve a proportion like 1:2=4:x, you'd set up a proportion to figure out the value of x. To solve for x you can use the cross multiplication method, resulting in 1x = 8, hence x = 8.
Final answer:
The value of 4x^3 + 4x when x=4 is found by substituting 4 into the expression and simplifying step by step, resulting in a final answer of 272.
Explanation:
When answering a question such as "What is the value of 4x3 + 4x when x=4," we need to substitute the value of x into the expression and simplify.
Let's break it down step-by-step:
Substitute x with 4 into the expression: 4(4)3 + 4(4).
Calculate the exponent: (4)3 = 4 x 4 x 4 = 64.
Multiply by 4: 4 x 64 = 256.
Add the second term: 256 + 4(4).
Perform the second multiplication: 4 x 4 = 16.
Add the two results together: 256 + 16.
Get the final answer: 272.
The value of 4x3 + 4x when x=4 is 272.