Answer:
x > 2/7
Step-by-step explanation:
Step 1: Make an inequality
3/14 + x > 1/2
Step 2: Solve for x
3/14 + x - 3/14 > 1/2 - 3/14
x > 2/7
Answer: x > 2/7
Jill is 18 years old. Her sister is 3 years old. How many times older is Jill than her sister?
Answer:
6
Step-by-step explanation:
18/3=6 You have to divide 18 by 3 in order to know how many times older Jill is than her sister.
A soda can is the shape of a cylinder. It has a diameter of 8 centimeters and a volume of 653.12 cm³. What is the lateral surface area of the soda can? *
Answer:
326.56
youre welcome
Step-by-step explanation:
Frank suspects a function he created to predict the population of bacteria is flawed. His data indicates the population began with 150 cells and grew by 20 percent every hour. His prediction function is "The population of bacteria is B(h) = 150(.2)h after h hours." What is Frank's error?
Frank's error is that his function suggests a linear growth model instead of an exponential one. The correct function should be B(h) = 150 * (1.2)^h to represent an exponential growth where the population increases by 20 percent every hour.
Explanation:Frank's error in his prediction function lies in the incorrect representation of the exponential growth of bacteria. His function reads B(h) = 150(.2)h, which implies a linear growth model, adding only 20% of the original amount, rather than a certain percentage of the current population. In reality, as the context describes the bacteria population growing by 20 percent every hour, the function should represent an exponential growth model accurate to the situation. Hence, the correct function should be B(h) = 150 * (1.2)^h, where 1.2, which signifies 120 percent (the original 100% plus the additional 20%), raised to the power h, accounts for the continuous multiplication or compounding of the bacteria every hour.
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Frank's error lies in the formulation of his prediction function. It should reflect exponential growth rather than linear growth. The population is 1.20 times what it was the previous hour, not 0.20 times.
The function he created, [tex]\( B(h) = 150(0.2)^h \),[/tex] incorrectly implies that the population increases by a factor of 0.2 each hour, which would represent a decrease since 0.2 is less than 1. Additionally, the initial population is multiplied by 0.2 instead of being increased by 20% each hour.
The correct way to model the population growth, assuming it grows by 20% each hour, is to use an exponential growth formula where the population is multiplied by [tex]\( 1 + \text{growth rate} \)[/tex] each hour that passes. Since the growth rate is 20%, or 0.20 in decimal form, the correct prediction function should be: [tex]\[ B(h) = 150(1 + 0.20)^h \][/tex]
This can be simplified to: [tex]\[ B(h) = 150(1.20)^h \][/tex]
This function correctly represents a 20% increase in the population each hour, starting with an initial population of 150 cells.
Frank's error was in the growth factor used in his function. It should have been [tex]\( 1 + \text{growth rate} \)[/tex] (which is 1.20 for a 20% increase) instead of just the growth rate (0.20). The correct function reflects that each hour, the population is 1.20 times what it was the previous hour, not 0.20 times.
mike bought some t-shirts at a department store. Mike gave the cashier $100 and received $25 in change. The price of the T-shirt was $25, how many T-shirts did he buy
What is the slope of a line that is parrallel to the line y=3/4x+2 ?
Answer:
3/4
Step-by-step explanation:
Parallel lines will always have the same slope, but their y-intercepts can be any real number.
What is the unknown factor that makes each of the following statements true?
5-х = ? (х-5)
b-k= ? (k-b)
– 3х +7 = ? (3х – 7)
A. -1/2
B. 1
C. -2
D.-1
Answer:
-1 case D)
Step-by-step explanation:
5-x=-(x-5) so the unknown factor is -1
b-k=-(k-b), again, -1
Similar for third case.
John earns a base pay of $275 per week plus an 8% commission on all of his sales. Write an inequality that represents the minimum amount of sales, s, that John must earn to make more than $560 per week. *
Answer:
8% is 0.08
275 + 0.08s > 560
0.08s > 285
s > 3562.5
1. Mike and Lisa Lerner had combined wages of $91,301 last year. They also had a bank interest of $792 and
$667. They received stock dividends of $287 and $530. During the year, Lisa won a $1,000 prize. Find the
total income from wages, bank interest, dividends, and the prize.
Answer:
The total income from wages, bank interest, dividends, and the prize = $ 94577
Step-by-step explanation:
Total wages of Mike and Lisa in last year = $ 91301
Total bank interest of Mike and Lisa = $ 792 + $ 667 = $ 1459
Total income from dividends = $ 287 + $ 530 = $ 817
Prize of Lisa won = $ 1000
Thus the total income from wages, bank interest, dividends, and the prize =
$ 91301 + $ 1459 + $ 817 + $ 1000 = $ 94577
Final answer:
The total income from wages, bank interest, dividends, and the prize is $94,577.
Explanation:
To find the total income from wages, bank interest, dividends, and the prize, we need to add up all the amounts mentioned.
First, we add Mike and Lisa's wages: $91,301. Then we add their bank interests: $792 + $667 = $1,459. Next, we add their stock dividends: $287 + $530 = $817.
Finally, we add Lisa's prize: $1,000. Adding all these amounts together, the total income from wages, bank interest, dividends, and the prize is $91,301 + $1,459 + $817 + $1,000 = $94,577.
A rational number between 13/15 and 14/15
Hey there!
You can find a number halfway between two numbers by simply adding them together and then dividing by two!
13/15+14/15=1 4/5
1 4/5÷2=9/10
Your number is 9/10.
I hope this helps!
Sure, let's find the rational number between 13/15 and 14/15.
A straightforward way to get a rational number between any two given rational numbers is to calculate their average, or arithmetic mean. This is because the mean of any two numbers always falls between those two numbers.
So, let's calculate the mean of 13/15 and 14/15:
1. Begin by adding these two fractions: 13/15 + 14/15
2. In order to add fractions, we need a common denominator, which we already have in this case: 15.
Just add the numerators: 13 + 14 = 27
So, the sum of 13/15 and 14/15 is 27/15.
3. Now, calculate the mean of the two numbers by dividing their sum by 2 since mean = (a+b) / 2
So, we have: (27/15) / 2 = 27/30
Here you have it - the rational number between 13/15 and 14/15 is 27/30 or 0.9 in decimal form.
What is the coefficient of y when the expression 1/3(9y-3)-2y is simplified?
Answer:
Coefficient of y is 1 since the answer is y-1
Step-by-step explanation:
In the attached file
What is 34.02 estimated?
Answer: 34
Step-by-step explanation:
Final answer:
To estimate 34.02, we would round it to the nearest whole number which is 34.
Explanation:
When asked to estimate 34.02, we look for a number that is close in value but simpler or more convenient to use.
Estimation often involves rounding to a certain place value depending on the level of precision required.
In this case, we can round to the nearest whole number. 34.02 is very close to 34, so the estimated value is 34.
This is based on traditional rounding rules where if the digit right after the place you are rounding to is less than 5, you keep the digit the same. If it is 5 or more, you round up. Since the decimal part .02 is less than .05, we do not round up.
In the coordinate plane, what is the length of the line segment that connects points at (0,-1) and (-7, -2)?
Enter your answer to the nearest hundredth.
Answer:100cm
Step-by-step explanation:
attached is the problem, and possible answers, please solve and check
Answer:
Option B
Step-by-step explanation:
Using the law of logarithms
[tex]n log x= log x^{n}[/tex]
Therefore, since all the logs are to the same base, I will assume the base.
Also, when the bases are the same
log y+ log x= log (x+y)
[tex]\frac {1}{2}(log 4+ log 16)=log 4^{0.5}+log 16^{0.5}=log 2+log 4=log 6[/tex]
Now log 6-log 2= log (6-2)= log 4
Therefore, option B is correct
what is the answer to this
-2(4x-3)=10
Answer:
x= -1/2
Step-by-step explanation:
-2(4x-3)=10
Divide each side by -2
-2/-2 *(4x-3)=10/-2
4x-3 = -5
Add 3 to each side
4x-3+3 = -5+3
4x = -2
Divide each side by 4
4x/4 = -2/4
x = -1/2
Answer:
x=-0.5 or x=-1/2
Step-by-step explanation:
Divide both sides by the numeric factor on the left side, then solve.
To find the product of 42.12 and 10³, move the decimal point in 42.12 __ places to the right because 10³ has __ zeros.
Answer:
Both answers are 3.
Step-by-step explanation:
10^3 = 10 * 10 * 10 = 1000
When you multiply 42.12 by 10^3, you are multiplying 42.12 by 1000.
When you multiply a number by a power of 10, such as 10, 100, 1000, etc., move the decimal point of the number to the right the same number of places as the number of zeros in the power of 10.
42.12 * 1000 = 42,120
Final answer:
To find the product of 42.12 and 10³, move the decimal point in 42.12 three places to the right because 10³ has three zeros. Thus, the product is 42120.
Explanation:
To find the product of 42.12 and 10³, you need to move the decimal point in 42.12 three places to the right because 10³ has three zeros. Multiplying by powers of ten is simplified by moving the decimal point to the right for each zero in the power of ten. For instance, multiplying 2.4 by 100 involves moving the decimal two places to the right to get 240, since 100 has two zeros.
When you multiply 42.12 by 10³, which is the same as multiplying by 1000 (10 x 10 x 10), you're effectively shifting the decimal point three places to the right. If there aren't enough digits, you can use zeros as placeholders. However, in this case, there are sufficient digits to move the decimal without adding additional zeros.
Therefore, 42.12 multiplied by 10³ would be 42120. This is because you move the decimal point three places to the right to account for the three zeros in 10³, changing 42.12 into 42120.
What are the values of x in the equation 4x2 + 4x - 3 = 0?
Answer:
x= 0.5
or x= -1.5
Step-by-step explanation:
Let's solve your equation step-by-step.
4x2+4x−3=0
Step 1: Factor left side of equation.
(2x−1)(2x+3)=0
Step 2: Set factors equal to 0.
2x−1=0 or 2x+3=0
x= 1/2 or x= −3/2
Answer:
A. x = –1.5, 0.5
Please help, I need help on this one
Step-by-step explanation:
Total profit = Revenue - expenses
= $1200 - ($600 + $105 + $115 + $130)
= $1200 - $950
= $ 250
5y+1=1
Subtract 1 from both sides
Step-by-step explanation:
[tex]5y + 1 = 1 \\ subtracting \: 1 \: from \: both \: sides \\ \red{ \boxed{ \bold{ 5y + 1 - 1 = 1 - 1}}} \\ 5y = 0 \\ y = 0[/tex]
Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 60 quarts of 4% butterfat milk.
Answer:
20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk is used to make 60 quarts of 4% butterfat milk.
Step-by-step explanation:
We are given the following in the question:
Let x quarts of 6% butterfat milk be used and y quarts of 3% butterfat milk be used to make 60 quarts of 4% butterfat milk.
Thus, we can write the equation:
[tex]6\%\times x + 3\%\times y = 4\%\times 60\\6x + 3y = 240[/tex]
Total amount of 3% butterfat milk = 60
Thus, we can write the equation:
[tex]x+y = 60[/tex]
Solving the two equation, we get,
[tex]6x + 3y-(3x+3y) = 240 - 3(60)\\3x = 240-180\\3x = 60\\x = 20\\y = 60-20 = 40[/tex]
Thus, 20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk is used to make 60 quarts of 4% butterfat milk.
To get 60 quarts of 4% butterfat milk, mix 20 quarts of 6% butterfat milk with 40 quarts of 3% butterfat milk by setting up and solving a system of linear equations.
Explanation:To solve this problem, we can set up a system of equations based on the quantities and percentages of butterfat in the milk types. Let's call the amount of 6% butterfat milk x quarts and the amount of 3% butterfat milk y quarts. According to the question, we want to end up with 60 quarts of 4% butterfat milk. Therefore, we have:
First, we multiply the second equation by 100 to simplify the percentages:
6x + 3y = 4 × 60
Simplify the right side:
6x + 3y = 240
Now, divide by 3 to get:
2x + y = 80
We can subtract the first total volume equation from this new equation:
(2x + y) - (x + y) = 80 - 60
Omit the similar terms to solve for x:
x = 20
We substitute x back into the initial total volume equation:
20 + y = 60
And solve for y:
y = 60 - 20
y = 40
Therefore, to get 60 quarts of 4% butterfat milk, 20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk must be mixed together.
Which eaquation would best help solve the following problem the height of a triangle is 6 meters more than its base The area of the triangle is 56 m^2
Answer:
X²+6X=112
Step-by-step explanation:
area=1/2 base x height
56=x(x=6)/2
Multiply each side by two to eliminate the denominator
112=x(x=6)
112=x²+6x
What is 30% of 120 is what number?
Answer:
36
Step-by-step explanation:
30% as a decimal is 0.30, take that and multiply it by 120 to find 30% of 120
120 × 0.30 = 36
Divide 275 into two parts which are in the ratio 4:7?
Answer:
100 : 175
Step-by-step explanation:
Divide 275 into two parts which are in the ratio 4:7?
To divide 275 into 4 :7, we will follow the steps below
First, We will add the ratio numbers together, that is; 4 + 7 = 11
4 : 7 of 275 will be;
4/11 × 275
=4 × 275 / 11
=1100/11
=100
Then we will now proceed to the second part;
7/11 × 275
= 7 × 275 / 11
=1925/11
=175
Therefore dividing 275 into 4 : 7 yields 100 : 175
identify the numerical coefficient of the term 5xy?
Answer:
5
Step-by-step explanation:
Answer: its 5
Step-by-step explanation:
the coefficient is the leading number
How many solutions are there to the equation n^2-13n=-40
Answer:
n = 5
n = 8
Step-by-step explanation:
n^2 - 13n = -40
Equate everything to zero
n^2 - 13n + 40 = 0
Factorise
(n - 5)(n - 8) = 0
Either
n - 5 = 0
Add 5 to both sides
n - 5 + 5 = 0 + 5
n = 5
Or
n - 8 = 0
Add 8 to both sides
n - 8 + 8 = 0 + 8
n = 8
n = 5 or
n = 8
It has two real solutions
solve the following: -7x + 5 = 8x - 25
Good morning ☕️
Answer:
2Step-by-step explanation:
-7x + 5 = 8x - 25
then
25 + 5 = 8x + 7x
then
15x = 30
then
x = 2
___________________
:)
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
Given equation:
[tex]-7x + 5 = 8x - 25[/tex]
To find the value of 'x', take the terms of 'x' to one side and the constants to the other side:
Subtracting '[tex]5[/tex]' to both side:
[tex]-7x+5-5=8x-25-5\\\\-7x=8x-30[/tex]
Subtracting '[tex]8x[/tex]' both side:
[tex]-7x-8x=8x-8x-30\\\\-15x=-30[/tex]
[tex]x=\frac{-30}{-15}[/tex]
[tex]x=2[/tex]
a cone is twice as tall as a cylinder of the same radius. what is the ratio of there volumes?
The ratio of the volume of the cone to the cylinder is 2/3.
We have,
The volume of a cone is given by the formula:
= (1/3)πr²h
The volume of a cylinder is given by the formula:
= πr²h
The radius of both shapes as r, and since the cone is twice as tall as the cylinder,
h(cone) = 2 h(cylinder)
Ratio = V(cone) / V(cylinder)
= [(1/3) π r² (2h(cylinder)] / (πr²h(cylinder))
= (2/3) h(cylinder) / h(cylinder)
= 2/3
Therefore,
The ratio of the volume of the cone to the cylinder is 2/3.
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what is the expression equivalent to 64 - x^2
Answer: -(x+8)(x-8)
Step-by-step explanation:
-(x^2-64)
x^2-8^2x^2
x^2-8^2=(x+8)(x-8)
-(x+8)(x-8)
2. The length of a rectangle is 12 cm and the area is 96 cm2. What is the width?
2.
3. I need to buy a carpet for a room that measures 3 m by 2 m. How many
square meters do I need?
4. The diameter of a circle is 3 cm. What is the circumference?
5. A painting measures 40 cm by 35cm. How many squared cm does its
surface cover?
6. The circumference of a circle is 15.7 cm. What is the diameter?
7. One side of a square measures 15cm. What is its area?
8. If the area of a rectangle is 60 cm and its width is 6 cm. What is its length?
9. The area of a square is 81 cm? What is the length of one of its sides?
10. The area of a circle is 201 cm? What is the diameter?
Answer:
Step-by-step explanation:
2. To find area, you use this equation: A = l*w
Let's input the values we do know to find the width.
96 = 12 * w
Divide both sides by 12 to isolate the w.
8 = w
The width is 8 cm.
3. We need the find the area of the floor to figure out how many square meters they need. to find area, we multiply the length by the width.
3 * 2 = 6
You need 6 sq. m.
4. To find the circumference, use the equation: C = 2 * pi *r
To find the radius, divide the diameter by 2.
3/2 = 1.5
C = 2pi(1.5)
C = 3pi
The circumference is 3pi. This can also be simplified to 9.42 or 9.4
5. To find the amount of square cm. it covers, multiply the length and width.
40 * 35 = 1,400
The surface covers 1,400 sq. cm.
6. To find circumference, use this equation: C = d * pi
Input the values you do know to find the diameter
15.7 = d * pi
divide both sides by pi to isolate d
4.77 = d
The diameter is approximately 4.8 cm.
7. To find area, multiply length by width. Since we know all sides of a square are the same, you can multiply 15 by 15 to get the answer.
15 * 15 = 225
The area is 225 sq. cm.
8. To find area, use this equation: A = l * w
put the values you know into the equation to find the length.
60 = l * 6
divide both sides by 6 to isolate the l
10 = l
The length is 10 cm.
9. To find the area of a square, the equation is: A = s^2
Input the values you know to find the length of a side.
81 = s^2
Find the square root of both sides to isolate the s.
9 = s
The length of one side is 9 cm.
10. To find the area of a circle, use this equation: A = pi * r^2
Input the values you know and solve for r.
201 = pi * r^2
Find the square root of both sides and divide both sides by pi to isolate the r.
7.998 = r
The radius is approximately 8 cm. Multiply this value by 2 to find the length of the diameter.
8 * 2 = 16
The diameter is approximately 16 cm.
The formula for the area of a triangle is A=12bh .
Find the area of a triangle with a base (b) of 7 feet and a height (h) of 12 feet.
The area of the triangle is _____ square feet
Answer: 42 square feet.
Step-by-step explanation:
1/2 times 12 times 7 is 42.
Answer:
42
Step-by-step explanation:
Rectangle ABCD is drawn on a coordinated plane. A=(-6,9) and B=(5,9) What could be the locations of points C and D
Answer:
It would be C=(6, -9); D= (-5,-9)
Step-by-step explanation:
If you plot -6,9 and 5,9 on a four quadrant graph you can see the answer. (sorry I'm not good at explaining, I'm on the same question as you currently and this is the answer I got, I'm pretty sure the one above isn't correct.)
The locations of points C and D are (16, 9) and (5, 9) or (-17, 9) and (-6, 9), respectively depending on the orientation of the rectangle.
To calculate the locations of points C and D in the rectangle ABCD, consider that opposite sides of a rectangle are parallel and have equal lengths.
Given points A=(-6,9) and B=(5,9), know that points A and B lie on a horizontal line at y=9. Since opposite sides of a rectangle are parallel, points C and D should also lie on a horizontal line parallel to AB.
So, the y-coordinate of points C and D should be 9 as well.
The x-coordinate for points C and D, consider that opposite sides of a rectangle are of equal length. The length of AB represents the width of the rectangle.
The length of AB = x-coordinate of B - x-coordinate of A
AB = 5 - (-6)
AB = 11 units.
Since, opposite sides are parallel, points C and D should also have the same y-coordinate as A and B. Their x-coordinates must differ by 11 units to maintain equal side lengths.
Possible coordinates for C and D:
C = (5+11, 9) = (16, 9)
D = (-6+11, 9) = (5, 9)
Alternatively:
C = (-6-11, 9) = (-17, 9)
D = (5-11, 9) = (-6, 9)
Therefore, the possible locations for points C and D are (16, 9) and (5, 9) or (-17, 9) and (-6, 9) .
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