Answer:
9 days.
Step-by-step explanation:
If the company produced 20 more items than 40 items each day, then it must have produced 60 items each day.
Though you're probably expected to write an equation, it's easiest to solve this through educated guess and check.
If there were 120 items to be produced, the company would be required to do it in 3 days (120 items, 40 items/day) but completed it in 2 days (120 items, 60 items/day). In this case, they finished their order 1 day early. But the problem states that they finished 3 days early. So we guess 3 times 120 items, or 360 items. Checking this, they should have finished their order in 9 days (360 items, 40 items/day) but they finished in 6 days (360 items, 60 items/day). 6 is three less than 9, so our guess of 360 items was correct. We have shown that the company should have finished the order in 9 days.
If you had to use an equation:
Let the desired number of days be x. Then, the company finished its order in x - 3 days. Since number of items produced is the number of days times items per day, and it doesn't change:
number of items = 40 items/day * x days = 60 items/day * (x - 3) days
40x = 60(x - 3) = 60x - 180
180 = 20x
x = 9
9 days is the desired answer.
Answer:
9
Step-by-step explanation:
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 :)
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
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)
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
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
#SPJ12
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.
How many hours are in a decade
Answer:
87600
Step-by-step explanation:
Answer:
87600 hours
Step-by-step explanation:
1 decade = 10 years
1 year = 365 days
1 day = 24 hours
1 decade * 10 years/ 1 decade * 365 days/ 1 year * 24 hours / 1 day
87600 hours
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:
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?
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%.
Tom is 45 and pays $2042 on his mortgage each month while his total take hime pay is $5950 per month. The national average, for those aged 35-64, on housing costs is 35% of income. Compute the percent of Tom's income that he spends on housing.
Answer:
34.32%
Step-by-step explanation:
Tom is 45 years old.
Tom earning = $5950 per month
Mortgage payment = $2042
Percentage of amount paid towards mortgage in his income = (2042/5950)*100
= 34.32%
Tom pays 34.32% of his income towards mortgage.
The national average of his age group pays 35% of income towards housing.
Thank you.
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).
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:
*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.
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.
Question: Graph the line defined the equation 8x + 8y = 24
Choose: A,B,C or D!!!
Answer:
B
Step-by-step explanation:
8x + 8y = 24
-8x on both sides
8y = -8x + 24
Divide by 8 on both
y = -x + 3
Answer:
B
Step-by-step explanation:
(÷8)8x + 8y = 24(÷8)
x + y = 3
y = - x + 3
If x is negative, then the function is decreasing.
y = - x + 3
When x = 0
y = - 0 + 3
y = 3
(0,3)
When y = 0
- x + 3 = 0
- x = - 3
x = 3
(3,0)
Alternative B
I hope I helped you.
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.
Nathan just bought a car. He models the value, V, in dollars, of the car after t years as V(t)=21,000(0.861)^t. Based on this model, by what percent does the value of Nathan car decrease each year?
Answer:
Value of the car is decreasing by 13.9% each year.
Step-by-step explanation:
This equation tells us V(t) is the value of the car after a certain time in years, $21,000 is the initial value of the car. What we need to focus on is on the 0.861 part of this equation. This means that the price of the car is worth 0.861 or 86.1% of what it was worth the year prior, this means that the price of the car is decreasing over time. By how much is it decreasing? Well if we consider 1 to mean 100% (since 100 / 100 =1) then we have 100%-86.1%=13.9%. This means that the value of the car is decreasing 13.9% each year.
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
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.
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.
Jamie owns a sailboat rental company, which has a large variety of sailboats of different sizes. He observed that the speed of the sailboat (with the wind) largely depends on the length of the sailboat, and is approximately one and a half times the square root of its length. Which of the following options represents the relationship between length and speed of a sailboat?
Answer:C
Step-by-step explanation:
Formula must be S(x) = (1+1/2)√x = 1.5√x, eliminating A and D. Diagram must show that a zero length boat doesn't move, and that boat length four feet goes 1.5×2 = 3 knots. That eliminates B. Check: C says zero feet goes zero knows and 4 feet goes 3 knots.
Answer:
Graph C
Step-by-step explanation:
We know the speed is equal to one and a half times the square root of the length. This means that speed is the dependent variable (y), and length is the independent variable (x).
Since the speed, S(x), is 1.5 times the square root of the length (x), we get the function
S(x) = 1.5√x.
When x = 0, S(x) = 1.5√0 = 1.5(0) = 0. This makes it graph C.
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
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
adam spent 13.10 on supplies for school. book covers cost 1.50 and boxes of mechanical pencils were each 2.80. if he bought seven items total, then how many of each did he buy
5 book covers and 2 boxes of pencils
Step-by-step explanation:If all 7 were book covers, the cost would be 10.50. The cost is 2.60 more than that. Each box of mechanical pencils costs 1.30 more than a book cover, so there must be 2.60/1.30 = 2 boxes of mechanical pencils (and 5 book covers).
_____
If you want an equation, let p represent the number of pencil boxes. Then 7-p is the number of book covers.
... 1.50(7-p) +2.80p = 13.10
... 1.30p = 13.10 -10.50 . . . . . subtract 10.50, collect terms
... p = 2.60/1.30 = 2 . . . . pencil boxes
... 7-2 = 5 . . . . . book covers
The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table.
Which equation represents the data in the table?
A) s=4√d
B) s=0.37d+20 NOT B
C) s=13.7log20
D) s= 1/25d²
Please choose one of the answers provided.
Edit: It is not Choice B
Answer:
Hence, Option 1 is correct equation [tex]s=4\sqrt{d}[/tex]
Step-by-step explanation:
The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table.
d s
20 17.89
40 25.30
60 30.98
80 35.78
100 40.00
We will check each option for table.
[tex]s=4\sqrt{d}[/tex]
For d=20, Put d=20 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{20}\approx 17.89[/tex]
For d=40, Put d=40 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{40}\approx 25.30[/tex]
For d=60, Put d=60 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{60}\approx 30.98[/tex]
For d=80, Put d=80 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{80}\approx 35.78[/tex]
For d=100, Put d=100 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{100}\approx 40.00[/tex]
All the value of table satisfy the first equation.
Hence, Option 1 is correct equation [tex]s=4\sqrt{d}[/tex]
How do I write Domain and Range in inequality notation?
Answer:
Domain: (-infinity, infinity) Range: (-infinity, infinity)
Step-by-step explanation:
They are parabolas, therefore you can assume that they go on infinitely. To find range, you must look at your y values. Look for your lowest point. Because the line goes done forever, your beginning mark would be (-infinity.
To find the other part, you look at your positive y values. Look for the highest value. Because this goes on infinitely, the completed version of your notation would be (-infinity, infinity). Be sure to use the infinity symbol though, which looks like an 8 rotated 90 degrees.
To find domain, look at your x values. To begin, look at your left-most values, which would be the negative numbers. Because the line goes on forever to the left, your notation would be (-infinity. To find the other part of domain, look at your positive x values. Because this line goes on infinitely as well, the completed version of your notation would be (-infinity, infinity). Infinity is never bracketed, it is always in parenthesis.
HELP PLEASE ON 13- A, B, C
Can anyone tell me if the ones I did are right
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