Answer: f(x)=3x2+30x+65
Step-by-step explanation:
F(x)=3(x+5)2-10
Using bodmas
B= bracket
O=of
D= division
M= multiplication
A= Addition
S= subtraction
So we go with the bracket
(X+5)2
=(x+5)(x+5)
Open the bracket
=x2+5x+5x+25
=x2+10x+15
Substitute for (x+5)2
F(x)=3(x2+10x+25)-10
Open the bracket
F(x)= 3x2+30x+75-10
F(x)= 3x2+30x+65
Carbon-14 is a radioactive isotope of carbon that is used to date fossils. There are about 1.5
atoms of cafbon-14 for every trillion atoms of carbon in the atmosphere, known as 1.5 ppt
(parts per trillion). Carbon in a living organism has the same concentration as carbon-14. When
an organism dies, the carbon-14 content decays at a rate of 11.4% per millennium (1000 years).
Write an equation for carbon-14 concentration (in ppt) as a function of time (in millennia) and
determine how old a fossil must be that has a measured concentration of 0.3 ppt.
Answer:
Function: A=1.5(1+0.114)^1000
Step-by-step explanation:
1.5 is the initial amount and 0.114 in the rate and the 1000 is the time
In carbon dating, the Carbon-14 concentration decays exponentially, and can be described by a formula involving its initial concentration and decay rate. To find a fossil's age with a concentration of 0.3 ppt, we use this decay formula, solve for t (time in millennia), and calculate the fossil's age.
Explanation:To determine the Carbon-14 concentration as a function of time and the age of a fossil with a concentration of 0.3 ppt, we will use the formula of exponential decay based on the half-life concept in carbon dating.
The formula for the carbon-14 concentration as a function of time (t, in millennia) is:
C(t) = C_0 × (1 - 0.114)^t
Where:
C(t) is the Carbon-14 concentration at time t,C_0 is the initial Carbon-14 concentration (1.5 ppt), and0.114 is the rate of decay per millennium (11.4%).To find the age of a fossil with a measured concentration of 0.3 ppt, we solve for t in the above equation with C(t) set to 0.3 ppt:
0.3 = 1.5 × (1 - 0.114)^t
Dividing both sides by 1.5 and taking the natural logarithm:
t = ln(0.3/1.5) / ln(1 - 0.114)
Solving this gives us the age of the fossil in millennia.
Steve went to Macy's to buy clothing, Steve got to the checkout, and he had
$96.30 worth of clothing in his arms. If he has a 30% of coupon, how much
would be his final bill?
Answer:
$67.41
Step-by-step explanation:
We want to find out how much 30% off of $96.30 is. To do that, we need to first multiply $96.30 to find out how much 30% would be. Don't forget to change 30% into its decimal form (30% - > .3).
96.30 x .3 = 28.89
This means that Steve got $28.89 dollars removed from his final bill. To find the actual final bill, subtract 28.89 from 96.30.
96.30 - 28.89 = $67.41
Mikayla designed a survey to determine the number of people expected at opening night of a community theater. The community has about 5,000 members. She selected a sample of the first 25 parents dropping off actors during theater rehearsal. Which best explains Mikayla’s sample?
Answer:
Answer is nonrandom and biased.
Refer below.
Step-by-step explanation:
Mikayla designed a survey to determine the number of people expected at opening night of a community theater. The community has about 5,000 members. She selected a sample of the first 25 parents dropping off actors during theater rehearsal. Following best explains Mikayla’s sample:
Nonrandom and biased
Answer: Answer C.
Step-by-step explanation: She only chose parents that were dropping off their kids. Therefore, the answer is nonrandom and biased.
The number of minutes Sadie spends on homework, playing outside, and practicing
piano are known. How much more time Sadie spends on homework, h, is unknown.
90 = (20 + 15) +h
Answer:
h = 55
Step-by-step explanation:
90 = (20 + 15) +h
90 = 35 + h
90 - 35 = h
h = 55
4. Consider the following polynomials: 6(x2 – 3) and 5x2 + x + 11
a. Find the sum of the polynomials.
b. Find the difference of the polynomials.
Answer:
Step-by-step explanation:
6(x² – 3) and 5x² + x + 11
a. Find the sum of the polynomials.
6(x² – 3) and 5x² + x + 11
6x²-18 + (5x² + x + 11)
6x²-18 + 5x² + x + 11
choose like terms
6x²-5x² + x + 11 -18= x²+x-7
b. Find the difference of the polynomials.
6x²-18 -(5x² + x + 11)
6x²-18 -5x² -x - 11
6x²-5x² -x - 11-18
x²-x-29
Please answer ASAP
Square ABCD has a side length of 4 inches. The square is dilated by a scale factor of 4 to
form square A'B'C'D'. What is the side length of square A'B'C'D' ?
Answer:
The side of square A'B'C'D' is 16 inches
Step-by-step explanation:
Given
Length of Square ABCD = 4 inches
Dilated with a scale factor of 4
Required
Length of square A'B'C'D'
To dilate something means to enlarge or reduce the size of that thing, depending on the scale factor.
Consider the following conditions
When the scale factor is greater than 1, then the size of new shape will be bigger than the dilated shapeWhen the scale factor is equal to 1, the new shape will maintain the same size as the dilated shapeWhen the scale factor is less than 1 but greater than 0, the size of new shape will be smaller than that of the dilated shape.Having mentioned the conditions of dilation, Here, the "thing being dilated" is a square (ABCD) on a scale factor of 4.
The scale factor is greater than 1; so, the new shape (A'B'C'D) will be bigger than the previous shape (ABCD)
Now, how is the new size calculated?
The new size is calculated by multiplying the length of the previous shape by its scale factor;
In other words,
New Length = Old Length * Scale Factor
Where
Old Length = Length of ABCD = 4 inches
Scale Factor = 4
By Substitution,
New Length = 4 inches * 4
New Length = 16 inches
Hence, the side of square A'B'C'D' is 16 inches
Find the unit rate: $3.60 for 3 pounds of apples. How much does it cost for 1 pound of apples?
Answer:
It should cost $1.2 for 1 pound of apples.
Step-by-step explanation:
To find the unit rate, divide 3.60 by 3. This gives us 1.2, which shows that for every pound you would pay $1.2.
If 3 pounds of apples cost $3.60 then costs $1.20 for 1 pound of apples.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b.
Given that,
Price for 3 pounds of apples = $3.60.
To find the cost of 1 pound of apple,
Use ratio property,
3 pounds cost = $3.60
1 pound cost = $3.60 / 3
1 pound cost = $1.20
The required cost of 1 pound of apples is $1.20.
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i need help plz ASAP
Can someone help me with the answer
Answer:
i think 4.356
Step-by-step explanation:
i just multipled them all
Answer:
1.45
Step-by-step explanation:
hope this helps :)
what is the product of 5 and w
Answer:
5w
Step-by-step explanation:
5*w=5w
Answer:
5w
Step-by-step explanation:
Product means multiply
5*w
9
Aubrey made 12 necklaces in 20
minutes. At this rate, how many
necklaces could Aubrey make in one
hour?
5
24
© 36
D 100
so the answer is 36.
Hope this will help u...
Answer:
36 necklaces
Step-by-step explanation:
Make a proportion
12/20=x/60
Cross multiply
20x=720
Divide by 20 on both sides
x=36
So, she can make 36 necklaces in an hour
Hope this helps! :)
The table below shows the total cost (TC) and marginal cost (MC) for Choco Lovers, a monopolistic firm producing different quantities
of chocolate gift boxes. Fill in the blanks in the table.
Answer:
Spreadsheet values
B3 = $15 (shown)C4 = $420 (shown)D6 = $272.5E4 = $6F2 = $16F6 = $5Other values
profit maximizing Q: 35profit maximizing P: $13maximum profit: $227.5Step-by-step explanation:
Labeling the columns of the spreadsheet A--F, and the rows 1--7, we want to find the values as follows.
a) The relationship between quantity, price, and revenue is ...
total revenue = quantity × price
price = (total revenue)/quantity
Then ...
B3 = 375/25 = 15 (as shown)C4 = 30×14 = 420 (as shown)__
b) The relationship between total cost and marginal cost is ...
mc2 = (tc2 -tc1)/(q2 -q1)
tc2 = (mc2)(q2 -q1) +tc1
Then ...
D6 = 9(40 -35) +227.5 = 272.5E4 = (192.5 -162.5)/(30 -25) = 6__
c) Marginal revenue is figured the same way as marginal cost.
mr2 = (r2 -r1)/(q2 -q1)
Then ...
F2 = (320 -0)/(20 -0) = 16F6 = (480 -455)/(40 -35) = 5__
d) The quantity maximizing profit will be the quantity such that marginal revenue is equal to marginal cost. That is, marginal profit is zero. That quantity is 35, where both marginal cost and marginal revenue are 7.
__
e) The price at a quantity of 35 is 13. This value is read from the given table.
__
f) The maximum profit is the difference between revenue and cost at the profit-maximizing quantity:
maximum profit = 455 -227.5 = 227.5
The question refers to Total Cost (TC) and Marginal Cost (MC) in economics; where TC is the sum of all production costs and MC is the cost of producing one more unit of a good. To fill the table, calculate the difference in total cost for each increase in produced units, as this difference reflects the MC.
Explanation:The question is referring to the concepts of Total Cost (TC) and Marginal Cost (MC) in economics. Total Cost is the complete expenditure made by a firm in the production process, including both fixed and variable costs. Marginal Cost, on the other hand, is the cost of producing one additional unit of a good. In the case of the Choco Lovers firm, it represents the cost of producing an extra box of chocolates.
To fill in the blanks in the table, the differences in total cost for each increase in the quantity of chocolate gift boxes produced should be calculated. This is because the MC at each level of output is the addition to total cost when one more box is produced. So, if total cost rises by $5 when output increases from 10 to 11 boxes, the MC of the 11th box is $5.
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The cylinder below has a volume of 2,512 cubic cm and a height of 8 centimeters. What is the diameter of the cylinder? Use 3.14 for pi.
Answer:
Radius=10cm
Diameter=20cm
Step-by-step explanation:
The Diameter of the cylinder is 20 centimeters.
It is given that the cylinder has a volume of 2,512 cubic cm and a height of 8 centimeters.
It is required to find the diameter of the cylinder.
What is a volume?It is defined as a three-dimensional space enclosed by an object or thing.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2h[/tex]
Where r is the radius of the cylinder and h is the height of the cylinder.
We have V = 2512 cubic centimeters and
h = 8 centimeters
[tex]\rm 2512 =3.14\times r^2\times8[/tex]
[tex]\rm \frac{2512}{3.14\times8} = r^2[/tex]
[tex]\rm r^2 =100[/tex]
r = 10 centimeters
Diameter = 2r = 2×10 ⇒ 20 centimeters.
Thus, the Diameter of the cylinder is 20 centimeters.
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Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
vorth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
A)x + y = 29, 5x + 2y = 100
B)x + y = 100, 5x + 2y = 29
C)5x + y = 29, 2y + x = 100
D)2x + y = 100, 5y + x = 29
Answer:
A IS THE CORRECT ANSWER
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Let x be 14 and y be 15 and solve A like you normally would
You had a bag of fruit snacks that you shared with 2 friends. Each of you got at most 6 fruit snacks. The inequality x divided by 3less than or equals6 models this situation. Solve the inequality to find the number of fruit snacks that were in the bag.
Final answer:
The inequality x / 3 ≤ 6 models the situation where a student shares a bag of fruit snacks equally with two friends and they each get at most 6 snacks. Solving the inequality, we find that there were at most 18 fruit snacks in the bag.
Explanation:
The inequality given for the scenario where the student shares fruit snacks with two friends is x / 3 ≤ 6. To solve this inequality, we multiply both sides of the inequality by 3 to isolate x on one side. This gives us x ≤ 18.
Therefore, the total number of fruit snacks that could have been in the bag is at most 18. This means if each person got exactly 6 fruit snacks, there would be 18 in the bag. But since the inequality allows for each person to have gotten at most 6 snacks, there could have been fewer than 18 snacks in the bag.
carl ran laps around the gym during P.E. class.He ran 8 laps in 10 minutes.If he continues running at this rate how many laps will he run in 2 hours
Answer:
96
Step-by-step explanation:
2 hours = 120 minutes
Laps : mins
8 : 10
X : 120
8/10 = X/120
X = 120 × 8/10
X = 96
Answer:
96 laps in 2 hrs
Step-by-step explanation:
2 hours divided by 10 minutes is 12
12*8=96
To check:
10/8=1.25
120/96=1.25
120=2 hours
Kim and Sonia have each drawn a line on the scatter plot shown below: The graph shows numbers from 0 to 10 on x and y axes at increments of 1. Dots are made at the ordered pairs 1, 5 and 2, 4 and 3, 3.5 and 4, 2.5 and 4.5, 2.8 and 5, 2 and 6, 1.5 and 7, 1 and 8, 0.9 and 9, 0.2 and 10, 0. A straight line labeled Line A joins the ordered pairs 0, 7.2 and 10.4, 0. A straight line labeled Line B joins the ordered pairs 0, 5 and 9.1, 0. Which line best represents the line of best fit? Line A, because it shows a negative association Line A, because it is closest to most data points Line B, because it is closest to most data points Line B, because it shows a positive association
Answer:
B because it is closest to most data points
Step-by-step explanation:
i asked my teacher
The requreid correct answer is: Line B, because it is closest to most data points.
What is a Line??A line can be defined by the shortest distance between two points is called as a line.
The line of best fit is the line that represents the trend or pattern in the data. Based on the given scatter plot, it appears that Line B is the better fit for the data since it is closest to most of the data points and shows a negative association.
Therefore, the correct answer is Line B, because it is closest to most data points.
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The basic model of a particular car (2WD) with a power sunroof costs $29,115. When equipped with four-wheel drive (4WD) and a sunroof, the vehicle's price rose to
$31,105. The cost of the basic model with 4WD was $30,205. Find the basic price, the cost of 4wd and the cost of a sunroof
Answer:
Sunflower=$900
4WD=$1090
Step-by-step explanation:
Wheareas 2WD costs $29,115 but when converted to 4WD it costs $30,205 then it means the cost of 4WD will be $30205-29115=$1090
The total cost of converting 2WD to 4WD with inclusion of sunroof is $31,105
Therefore, the total cost of 4WD and sunroof will be $31105-$29115=$1990
To get the amount for sunroof, we deduct the total cost that includes 4WD and sunroof from $1090
Cost will be $1990-$1090=$900
Which unit is not a customary unit?
A. gallon
B. ounce
C. gram
D. cup
Answer:
D.Cup
Step-by-step explanation:
We humans do not use the term Cup anymore. We now use things like Grams,Ounces,Gallons,Or Quarts.
Dimensions of a house are 300 feet by
125 feet. If 1 inch represents 50 feet,
what are the dimensions of the house
on the drawing?
Answer:
divide 300 feet by 50 which is 6, divide 125 ft by 50 which is 2.5. Therefore your dimensions are 6 in by 2.5 in
if you're in putting in the computer it may want 2.5 in fraction form which is 2 1/2 in or in improper fraction form 5/2 in
Step-by-step explanation:
What is the area of a circle with a radius of 40 cm? cm² (Use 3.14 for Pi.)
Answer:5024 cm^2
Step-by-step explanation:
Formula for area of a circle =πr^2
Where π=3.14, r=40cm
Area=3.14*40^2
=3.14*1600
=5024cm^2
One inch is approximately 252/5 millimeters. What is 25 2/5 as a decimal?
Answer:
Decimal result:
25.4
Calculation:
25+2/5
= 25.4
= 2540%
Step-by-step explanation:
Geometry is not something im good at, picture has the info :)
To find the volume of a rectangular prism, you just multiply each side.
3 x 3 x 8 = 72
Which equation describes the relationship expressed in the table?
y = x
y = 3x
y=1/6x
y=1/3x
Answer: 1/3
Step-by-step explanation:
I just did it
what is 1/2 of 3/4??
Answer:
3/8
Step-by-step explanation:
Of means multiply
1/2*3/4 = 3/8
Evaluate f(x) = 2x at x = 5.
A) 32
B) 10
C) 64
D) 25
Answer:
the answer is B)
Step-by-step explanation:
if x = 5
f(x) = 2 x 5
f(x) = 10
so the answer is 10
An arc subtends a central angle measuring
2π3\dfrac{2\pi}{3}
3
2π
start fraction, 2, pi, divided by, 3, end fraction
radians.
What fraction of the circumference is this arc?
of the circumference
Answer:
The arc is one-third of the circumference.
Step-by-step explanation:
The area of a circumference = 2πr
C = 2πr ... (1)
If an arc subtends a central angle measuring 2π/3 rad,
The length of the arc = rθ
Given θ = 2π/3
Length of the arc L = r(2π)/3
L = 2πr/3... (2)
L = 1/3(2πr)
Since C = 2πr
L = 1/3C
This shows that the arc is one-third of the circumference.
Please I need help with this question
Answer:
20
Step-by-step explanation:
Angle ABC = 40 degrees, therefore CB = 40 degrees.
An inscribed triangle is half of the angle in the center so, angle ADC = 20 degrees.
Collins middle school has 186 soxth grade students. If the sixth grade is 30 percent of the total school, how many students are in the middle school?
Answer:
620
Step-by-step explanation:
MATH
Keith wrote the expression shown to determine the cost in dollars.bor an upcoming
(127.50 - 23.50) + 3(86.50 +4)
Which expression is equivalent to the one Keith wrote?
F
107(90.50)
G 101(90.50)
H 104 + 3(90.50)
)
104 + 263.50
212
Answer:
104+3(90.5)
Step-by-step explanation:
(127.50+23.50)+3(86.50+4)
Let's take the bracket one after another
(127.50-23.50)
104.00
3(86.50+4)
3(90.50)
271.50
Back to the question
151.00+271.50
422.50
So the answer is 104+3(90.50)
Answer:
104+3(90.5)
Step-by-step explanation: becuz i said so