D. R(x) = 850x +9600
Step-by-step explanation:Selling 10 more machines increased revenue from $18100 to $26600, an increase of ...
... $26,600 -18,100 = $8,500
That is, the revenue increased by $8500/10 = $850 per machine.
Only one answer choice has this number in it:
... D. R(x) = 850x+9600
_____
Check
R(10) = 850·10 +9600 = 8500 +9600 = 18,100 . . . . OK
R(20) = 850·20 +9600 = 17000 +9600 = 26,600 . . . . OK
_____
Comment on answer selection
On multiple-choice questions, it is rarely necessary to work out the solution to the problem completely. Usually, it is sufficient to find the one number that discriminates between correct and incorrect answers.
In real life, answers are rarely multiple-choice. You are required to work the problem completely and to figure out how to tell if your answer is correct.
Here, we have worked the problem far enough to find the slope, the amount by which revenue increases when sales increases by 1 unit. The intercept can be found different ways. One of them is to see what number makes the revenue match for one of the "x" values:
... R(10) = 850·10 +b = 18100
... b = 18100 -8500 = 9600
so ...
... R(x) = 850x +9600
We can check this answer by computing R(20), as we have above.
Answer:
R(x)=850x+9600
Step-by-step explanation:
:⊃
Conrad has 6 more marbles than Rory. If r represents the numbers of marbles that Rory has, which expression represents the number of marbles that Conrad has?
Answer:
r+6
Step-by-step explanation:
r = marbles that Rory has
r+6 = marbles that Conrad has
Answer:
r+6
Step-by-step explanation:
r = marbles that Rory has
r+6 = marbles that Conrad has
you could also use c
the table shows the relationship between two variables which selection describes the relationship
Answer:
C. Decreasing; Linear.
Step-by-step explanation:
We have been given a table that shows the relationship between two variables.
Let us find slope of our given values using slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us find rate of change for points (1,5) and (2,-1)
[tex]m=\frac{-1-5}{2-1}[/tex]
[tex]m=\frac{-6}{1}=-6[/tex]
Let us find slope for points (3,-7) and (4,-13).
[tex]m=\frac{-13--7}{4-3}[/tex]
[tex]m=\frac{-13+7}{1}[/tex]
[tex]m=\frac{-6}{1}=-6[/tex]
We can see that rate of change is constant (-6), therefore, our function is a linear function. Since slope is negative (-6) and with each increase in x, our y is decreasing, therefore, our function is decreasing.
A)Simplify the expression and explain each step. 12 + 3(2y - 3) (B)Factor the expression completely. 18b - 12 (As you solve these problems do it with numbers intead of the word form like 1+1=2 instead of one plus one equals two, please and thank you. I will give brainlyist.
Answer:
A) 6y +3B) 6(3b -2)Step-by-step explanation:
A) Use the distributive property to eliminate parentheses. Then combine like terms. (The only "like terms" are the constants.)
... = 12 +3·2y +3·(-3) . . . use the distributive property to multiply each term in parentheses by the factor 3 outside those parentheses
... = 12 +6y -9 . . . . . . . . simplify
... = 6y + (12 -9) . . . . . . group like terms together
... = 6y + 3 . . . . . . . . . . simplify
___
B) Look for factors of each term that are also found in the other term.
... 18b has factors 3×6×b
... 12 has factors 2×6
The only common factor is 6, so we factor that out using the distributive property.
... 18b -12 = 6(3b -2)
_____
Comment on factoring
For factoring problems, it helps immensely if you know your times tables and some of the rules for divisibility. (Even numbers are divisible by 2, numbers ending in 0 or 5 are divisible by 5, numbers whose sum of digits is divisible by 3 are divisible by 3, for example.)
Diana invests $25,000 in a bank at the beginning of the year. She will receive 7% interest at the end of the year, but she will have to pay a 16% tax on the interest received.
A.) How much interest will Diana earn after she pays the tax?
B.) What percent of Diana's investment is the interest after paying the tax?
Answer:
A) $1470
B) 5,88%
Step-by-step explanation:
B) Diana will end up with 100% -16% = 84% of the interest she earns, so her effective interest rate is ...
... 7% × 84% = 5.88%
A) Diana's investment earns ...
... 0.0588 × $25000 = $1470
After paying a 16% tax on the interest, Diana will earn $1,470 in interest. This represents 5.88% of her original $25,000 investment.
Diana invests $25,000 in a bank at 7% interest, which she will receive at the end of the year. However, she must pay taxes at a rate of 16% on the interest earned.
First, we calculate the total interest Diana would earn without taxes:
Total Interest = Principal imes Interest Rate
Total Interest = $25,000 imes 0.07 = $1,750.
Next, we calculate the tax on the interest:
Tax on Interest = Interest Earned imes Tax Rate
Tax on Interest = $1,750 imes 0.16 = $280.
Now, we subtract the tax from the total interest to find the interest after taxes:
Interest After Taxes = Total Interest - Tax on Interest
Interest After Taxes = $1,750 - $280 = $1,470.
We find the percentage of the original investment that the interest after taxes represents:
Percent of Investment = (Interest After Taxes / Principal) imes 100
Percent of Investment = ($1,470 / $25,000) imes 100 = 5.88%.
use natural logarithmics to solve the equation round to the nearest thousandth 3e^2x +5=26
x = 0.973
Step-by-step explanation:3e^(2x) +5 = 26
3e^(2x) = 21 . . . . . subtract 5
e^(2x) = 7 . . . . . . . divide by 3
2x = ln(7) . . . . . . . .take the natural log
x = ln(7)/2 ≈ 0.973 . . . . divide by 2 and evaluate
Answer:
x= .973
Step-by-step explanation:
3e^2x +5=26
Subtract 5 from each side
3e^2x +5-5=26-5
3e^2x =21
Divide by 3 on each side
3/3e^2x =21/3
e^2x =7
Take the natural log on both sides
ln (e^2x) =ln (7)
2x = ln (7)
Divide by 2
2x/2 = ln(7)/2
x = ln(7)/2
x is approximately .972955075
Rounding to the nearest thousandth
x = .973
1.2 x 10 to the negative 3rd / 4 x 10 to the 6
Answer:
[tex]3 \cdot 10^{-10}[/tex]
Step-by-step explanation:
[tex]\dfrac{1.2\cdot 10^{-3}}{4\cdot 10^{6}}=\dfrac{12\cdot 10^{-4}}{4\cdot 10^{6}}\\\\=\dfrac{12}{4}\cdot 10^{-4-6}=3\cdot 10^{-10}[/tex]
I like to adjust the operands so the quotient needs no adjustment. Here that means rewriting the numerator to an equivalent value with a mantissa between 4 and 40.
A textbook store sold a combined total of 266 math and biology textbooks in a week. The number of math textbooks sold was 54 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Let m and b represent the numbers of math and biology books sold, respectively. The problem statement tells you ...
... m + b = 266
... m - b = 54 . . . . . . . 54 more math books were sold
Adding these two equations gives you ...
... 2m = 320
... m = 160 . . . . . divide by 2
... b = 160 -54 = 106 . . . . 54 fewer biology books were sold.
160 math textbooks and 106 biology textbooks were sold in a week.
Victor need 30 feet of rope. the rope he wants to buy is sold by the yard. he knows that there are 3 feet in 1 yard. how many yards should he But?
a. 10
b.20
c.60
d.90
Natalie chose D as the correct answer. how did she get that answer?
sherrie opened 5 bags of peanuts and counted a total of 75. At this rate, how many peanuts would be in 8 bags.
Answer:
There should be 120 peanuts
Step-by-step explanation:
We can use ratio's to solve this problem
5 bags
---------------
75 peanuts
5 bags 8 bags
--------------- = ------------------
75 peanuts x peanuts
Using cross products
5x = 75*8
5x = 600
Divide each side by 5
5x/5 = 600/5
x = 120
Answer:
if 5 bags of peanuts = 75peanuts
Then 1 bag will be 15 peanuts beacause 75 divided by 5 is 15
8 bags of peanuts will then be 15 multiply by 8 which is 120 peanuts
Step-by-step explanation:
Can someone please help me with problem 15 (picture)
$137,557.93
Step-by-step explanation:It is convenient to let a spreadsheet do the calculations. The number in the fourth column is the number in the first column divided by the number in the second column and multiplied by the number in the third column.
For example, the weighted average cost of Widgets is ...
... 135,320.00 × 866/2740 = 42,769.02
Then the total of all on-hand inventory is the sum of the inventory costs of the three items: $137,557.93.
Please answer ASAP!! which of the following is closest to 0.25 and why?
A) 9/40 B)5/16 C) 9/32 D) 0.28 E) 15/64
f(x) = -4x and g(x) = 5x-13, find f(g(x))
Answer:
-20x +52
Step-by-step explanation:
To solve this, we put the function g(x) into the function f(x) in the place of x
Put 5x-3 in for x in -4x
f(g(x)) = -4 (5x-13)
= -4*5x -4(-13)
= -20x +52
please show work with answer
∠A ≅ ∠T . . . . given
AX ≅ TX . . . . given
∠AXM ≅ ∠TXH . . . . vertical angles are congruent
ΔAXM ≅ ΔTXH . . . . ASA theorem
MX ≅ HX . . . . CPCTC
___
15.The acronyms that invoke theorems based on two or three sides being congruent are inapplicable in this case.
SSS
SAS
The heights of two cylinders are in the ratio 3:1 if the volumes of two are same find the ratio of their respective radii
Answer:
[tex]\sqrt{3}[/tex] :1
Step-by-step explanation:
Ratio of height of two cylinders are 3:1
Let C2 has the height x
then height of C1 is 3x
Let r1 is the radius of C1
and r2 is the radius of C2
As given that volume of both are equal
Also we know that formula for the volume of the cylinder is
V= π r²h
for C1
V= π (r1)²h
for C2
V=π (r2)²h
As volume of both are same so equating them
π (r1)²h1 = π (r2)²h2
as h1 =3x and h2=x
putting values
π (r1)²(3x) = π (r2)²(x)
cancelling out π and x from both side of the equation
3(r1)²= (r2)²
Taking square root of both sides give
[tex]\sqrt{3(r1)^{2} }=\sqrt{(r2)^{2} }[/tex]
r1 ( [tex]\sqrt{3}[/tex]) = r2
or
r1 : r2 = [tex]\sqrt{3}[/tex] :1
Please Help If You Know How To Do Simple Interest ;3
Worth 15 points each (I think cause I put 30 points)
Answer:
$5875
Step-by-step explanation:
The simple interest formula for the ending balance is ...
... A = P(1 +rt)
You have principal amount P=5000, interest rate r=0.05, and time t=3.5, so the amount (A) is ...
... A = $5000(1 +0.05·3.5) = $5000·1.175
... A = $5875
Which transformation confirms that rectangle ABCD and rectangle EFGH are similar?
A) Rectangle ABCD is rotated 90° clockwise about the origin and then dilated by a scale factor of 2 with the origin as the center of dilation.
B) Rectangle ABCD is rotated 90° clockwise about the origin and then dilated by a scale factor of 1 2 with the origin as the center of dilation.
C) Rectangle ABCD is rotated 90° counterclockwise about the origin and then dilated by a scale factor of 2 with the origin as the center of dilation.
D) Rectangle ABCD is rotated 90° counterclockwise about the origin and then dilated by a scale factor of 1 2 with the origin as the center of dilation.
Answer:
Option D is correct.
Step-by-step explanation:
We are given that,
'Rectangle ABCD is translated to map onto the rectangle EFGH'.
That is, 'Rectangle ABCD is similar to rectangle EFGH'.
So, we see that,
Rectangle ABCD is rotated towards the left and then decreased in size to map onto EFGH.
That is, we have,
Rectangle ABCD is rotated counter-clockwise by 90° about the origin and then dilated by a factor of [tex]\frac{1}{2}[/tex] with the origin as the center of dilation.
Hence, option D is correct.
A particular leg bone for dinosaur fossils has a mean length of 5 feet with standard deviation of 3 inches. What is the probability that a leg bone is less than 62 inches
Answer:
The probability of a leg bone measuring less than 62 inches is about 75% (74.86%).
Step-by-step explanation:
To answer this question we can calculate the z-score, then use a table to look up a corresponding percentile using z tables.
The length is a random variable with mean = 60 in and standard deviation of 3 in and we are looking at a particular sample that 62 in long. That sample has the following z value:
[tex]z = \frac{62 - \mu}{\sigma}=\frac{62-60}{3}=\frac{2}{3}\approx0.67[/tex]
The area under the normal distribution curve that corresponds to the z value of 0.67 (using a z table - available on line) is 0.7486. This is the probability that a random sample of a fossil leg length is less that our particular value 62 inches. Roughly speaking, the probability of a leg bone less than 62 in is about 75% (aka 75-th percentile).
a candle burned at a steady rate. after 32 minutes, the candle was 11.2 inches tall. Eighteen minutes later, it was 10.75 inches tall. use an equation in point-slope form to determine the height of the candle after 2 hours.
ANSWER:
The candle was 12 inches tall to begin with.
After 2 hours (120 minutes), the height of the candle is approximately 9.9625 inches.
To start, let's define our variables:
t represents time in minutes.
h represents the height of the candle in inches.
First, we find the rate at which the candle is burning. The change in height over time is [tex]\( \frac{{11.2 - 10.75}}{{32}} \)[/tex] inches per minute.
Using point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and m is the slope, we can use the point [tex]\((32, 11.2)\)[/tex] and the calculated slope to find the equation of the line.
[tex]\( h - 11.2 = \frac{{11.2 - 10.75}}{{32}}(t - 32) \)[/tex]
Simplify to: [tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(t - 32) \)[/tex]
Next, we want to find the height after 2 hours (which is 120 minutes). Substituting t = 120 into the equation:
[tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(120 - 32) \)[/tex]
[tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(88) \)[/tex]
[tex]\( h - 11.2 = -1.2375 \)[/tex]
Now, solving for h :
[tex]\( h = 11.2 - 1.2375 \)[/tex]
[tex]\( h = 9.9625 \)[/tex]
So, after 2 hours (120 minutes), the height of the candle is approximately 9.9625 inches.
HELP PLEASE ON 13- A, B, C
Can anyone tell me if the ones I did are right
Which triangle is similar to triangle SRT?
Answer:
Triangle PQR
Step-by-step explanation:
PQR I am just adding extra words so I have a higher word count so it accepts my answer :)
x^3-8/x^2+2x+4 divided by (x^2-4)
The simplified expression is [tex]\( \frac{x - 2}{x + 2} \)[/tex].
To divide the expression [tex]\(\frac{x^3 - 8}{x^2 + 2x + 4}\) by \((x^2 - 4)\)[/tex], you first factor both the numerator and denominator.
Factor the numerator:
[tex]\[ x^3 - 8 \][/tex]
[tex]\[= (x - 2)(x^2 + 2x + 4) \][/tex]
This is based on the difference of cubes: [tex]\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\), where \(a = x\) and \(b = 2\).[/tex]
Now, factor the denominator:
[tex]\[ x^2 + 2x + 4 \][/tex]
[tex]\[= (x + 2)^2 \][/tex]
The expression becomes:
[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \][/tex]
Now, divide by [tex]\((x^2 - 4)\)[/tex]:
[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \div (x^2 - 4) \][/tex]
Factor [tex]\(x^2 - 4\)[/tex] further:
[tex]\[ x^2 - 4 = (x + 2)(x - 2) \][/tex]
Now, cancel out common factors:
[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \div (x^2 - 4) = \frac{x - 2}{x + 2} \][/tex]
Therefore, the simplified expression is [tex]\( \frac{x - 2}{x + 2} \)[/tex].
Complete question:
Simplify: X^3-8/x^2+2x+4 divided by (x^2-4)
Chloe charged for admission to her play on three different nights. Each night, a different number of people were in attendance, but remarkably, Chloe collected $541 each night. If the admission charges for each child and each adult were $9 and $17, respectively, how many people in total came to the three showings?
To find the total number of people who came to the three showings, divide the total amount collected by the average admission price. Set up equations using the given information for each night and solve simultaneously to find the values of x, y, a, b, p, and q. Add those values to find the total number of people.
Explanation:To find the total number of people who came to the three showings, we need to divide the total amount collected by the average admission price. Let's calculate:
On the first night, let's assume there were x children and y adults. So, we can set up the equation.
9x + 17y = 541.
Similarly, for the second and third nights, we can set up two more equations:
9a + 17b = 541 and 9p + 17q = 541.
Solving these three equations simultaneously will give us the values of x, y, a, b, p, and q, which represent the number of children and adults present on each night. Adding those numbers together will give us the total number of people who came to the three showings.
Learn more about Total number of people at three showings here:https://brainly.com/question/29183899
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In rectangle ANHG, whose perimeter is 100, OP, PQ, and QR are congruent and mutually perpendicular and O is the midpoint of AN. If GH = 40 which is PQ?
Answer:
5
Step-by-step explanation:
The sum of adjacent sides of the rectangle is half the perimeter, 50, so ...
... AH = 50-40 = 10
Then ...
... OP +QR = 10 = 2×OP . . . . . QR ≅ OP
... OP = 5 = PQ . . . . . . . . . . . . PQ ≅ OP
the sales tax in your city is 4.4 and an item costs $3 before tax how much do u pay on the item
Answer:
$3.13
Step-by-step explanation:
We assume you mean the tax rate is 4.4%. Then the tax on $3 is ...
... tax = (tax rate) × (item cost)
... = 4.4/100 × 3.00 = 4.4 × .03 = 0.132 ≈ 0.13
The amount paid is ...
... amount paid = tax + item cost = $0.13 +3.00
... amount paid = $3.13
what are the coefficients in the following expression 8x + 5 + 6y
Answer:
8 5 and 6 are the coefficients
Step-by-step explanation:
For this case we have that by definition, a coefficient is the term that accompanies a variable. If we have the expression given by:
[tex]8x + 5 + 6y[/tex]
The number "5" is a constant.
Thus, two variables, "x" and "y", are observed.
Thus according to the definition, the coefficients are given by "8" and "6" respectively.
Answer:
8 and 6 are the coefficients
A developer buys 12 acres of land at 41,00 per acre. How much does he pay for the land
Answer:
492,000
Step-by-step explanation:
Do 41,000x12. Pls mark me brainliest if im correct!
*Functions* Fill in the blank.
The function f(x)=log x is transformed into the equation f(x)=log (1/4x).
The function f(x)=log (1/4x) is a _______ of the parent function by a factor of _______.
A. horizontal stretch
B. horizontal compression
(A and B apply to the first blank, C, D, and E apply to the second blank.)
C. 0.25
D. 1
E. 4
Answer:
A and C
Step-by-step explanation:
I hope I helped you.
Emily wants to make a rectangular model with a height of one cube
She wants to make the model in exactly 2 different ways. How many connecting cubes could emily use to make the model in only two ways.
Answer:
Three cubes
Step-by-step explanation:
The cubes have to be indistinguishable and all orientations of one cube are also have to be indistinguishable.
All ways of connecting two cubes result in the same shape. So answer is larger than two.
After connecting two cubes, there are ten faces where the third cube can be attached, and two faces which are connected, accounting for all 12 faces of two cubes.
Of the 10 exposed faces, exactly two are on opposite ends, both leading to the same straight line figure. The other 8 faces all lead to an L shape, and all L shapes can be rotated to be identical.
Hence, three cubes can only make a straight shape or an angled shape.
Four cubes can make a straight shape, a L shape, a Γ shape (but flipping it over through 3 dimensions makes L and Γ identical), a T shape, and a square shape. That is either four or five different objects depending on if they can be lifted from the table. Anyway, it is more than two.
PLEASE HELP ME ASAP: 99 points
for my career development class
you work for 40 hours a week at $8.75 an hour and pay 12% in taxes. What is your net pay?
Answer:
Net pay =$ 308
Step-by-step explanation:
Net pay is the gross pay minus taxes
Net pay = gross pay - gross pay * tax rate
Simplifying this equation by factoring out gross pay
Net pay = gross pay (1- tax rate)
Gross pay = hours worked * hourly rate
Substituting this in
Net pay = hours worked * hourly rate (1- tax rate)
We know the
hours worked = 40
Hourly rate = 8.75
tax rate = .12
Net pay = 40 * 8.75 (1- .12)
Net pay = 350(.88)
Net pay =$ 308
Which names the tiling
4, 8, 8
Step-by-step explanation:At each node, three faces meet. One is square (4 sides); the other two are octagons (8 sides). Hence the tiling can be named with three numbers: 4, 8, 8.
Answer:
4, 8, 8
At each node, three faces meet. One is square (4 sides); the other two are octagons (8 sides
Step-by-step explanation: