Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet
2. 3ft 8in = 3 8/12 or reduced to 3 2/3 12ft 3in = 12 3/12 or reduced to 12 1/4 The fractional part is referring to a fraction of a foot.
3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3 P= 31 5/6 feet
4. The estimate and the actual are very close. They are 1/6 of a foot apart.
5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.
5b. Take the total and divide it by 8ft = 29 7/12 divided by 8= 3.7 You are not buying a fraction of a board so you would need 4 boards.
Question 8
Points 3
Identify the functions whose lines are parallel.
0 3x + 2y = 45 and 8x + 4y = 135
x + y = 25 and 2x + y = 15
O 2x + 2y = 50 and 4x + 2y = 90
O 2x + 2y = 4 and 4x + 4y = 16
Answer:
2x + 2y = 4 and 4x + 4y = 16
Step-by-step explanation:
For two lines to be parallel, they must have the same slope.
To determine the correct answer to the question, we shall determine the slope of each equation in the given options to see which have the same slope. This can be obtained as follow:
1st option:
3x + 2y = 45 and 8x + 4y = 135
We shall rearrange the above equations to look like y = mx + c
NOTE: m is the slope.
3x + 2y = 45
rearrange
2y = –3x + 45
Divide both side by 2
y = –3x/2 + 45/2
Slope (m) = –3/2
8x + 4y = 135
Rearrange
4y = –8x + 135
Divide both side by 4
y = –8x/4 + 135/4
Slope (m) = –8/4 = –2
The two equation has different slopes. Thus, they are not parallel.
2nd option:
x + y = 25 and 2x + y = 15
x + y = 25
Rearrange
y = –x + 25
Slope (m) = –1
2x + y = 15
Rearrange
y = –2x + 15
Slope (m) = –2
The two equations has different slopes. Thus, they are not parallel.
3rd option:
2x + 2y = 50 and 4x + 2y = 90
2x + 2y = 50
Rearrange
2y = –2x + 50
Divide both side by 2
y = –2x/2 + 50/2
Slope (m) = –2/2 = –1
4x + 2y = 90
Rearrange
2y = –4x + 90
Divide both side by 2
y = –4x/2 + 90/2
Slope (m) = –4/2 = –2
The two equations has different slopes. Thus, they are not parallel.
4th option:
2x + 2y = 4 and 4x + 4y = 16
2x + 2y = 4
Rearrange
2y = –2x + 4
Divide both side by 2
y = –2x/2 + 4/2
Slope (m) = –2/2 = –1
4x + 4y = 16
Rearrange
4y = –4x + 16
Divide both side by 4
y = –4x/4 + 16/4
Slope (m) = –4/4 = –1
The two equations have the same slopes. Thus, they are parallel.
An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 100 times the undergraduate grade point average is at least 1075. Robbin's GMAT score was 800. What must her grade point average be in order to be unconditionally accepted into the program?
Robbin's grade point average must be at least ___ in order to be unconditionally accepted into the program.
Answer:
Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program.
Step-by-step explanation:
An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 100 times the undergraduate grade point average is at least 1075
Considering the GMAT score x, and the GPA y, this situation is modeled by the following inequality:
[tex]x + 100y \geq 1075[/tex]
Robbin's GMAT score was 800.
This means that [tex]x = 800[/tex], and thus:
[tex]x + 100y \geq 1075[/tex]
[tex]800 + 100y \geq 1075[/tex]
[tex]100y \geq 275[/tex]
What must her grade point average be in order to be unconditionally accepted into the program?
Solving the above inequality for y:
[tex]100y \geq 275[/tex]
[tex]y \geq \frac{275}{100}[/tex]
[tex]y \geq 2.75[/tex]
Thus:
Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program.
The following figure appears in a math workbook. Students are asked to reflect the polygon across the line, then rotate it 90 degrees clockwise . Which figure shows the result of the two transformations?
Answer:
C
Step-by-step explanation:
tracing paper is your friend
the difference when a number doubled is subtracted from 3
Answer: Let the number be x
3-2x is the equation.
A bank gives you a loan of 1,500,000 Baht to buy a house. The interest rate of the loan is 0.01% per day (Using 1 year = 365 days) How much interest you pay after 10 years
Answer:
547 500
Step-by-step explanation:
Interest for 1 year:
0.01%×365=3.65 a year
3.65×10=36.5% for 10 years
36.5×1,500,000÷100=547 500
The interest paid after 10 years is 547 ,500 Baht.
What is Interest ?Interest is the amount paid or earned when a loan is taken or an investment is done respectively.
It is given that
Principal = 1,500,000 Baht
Rate = 0.01 % per day
Time period = 10 years
Interest = ?
Interest = P *R *T/100
Interest = 1500000 * 0.01 *365* 10 / 100
Interest = 547,500 Baht
Therefore the interest paid after 10 years is 547 ,500 Baht.
To know more about Interest
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a certain number n is 6 more than a second number and 9 less than a third number. in terms of n, which of the following expressions represents the second number
Answer:
n-6
Step-by-step explanation:
it is given that the first number is n
for the second number:
n is 6 more than a second number
more than means that we should subtract n by 6 to get the second number since n is 6 more than the second number
second number: n-6
How do I solve this. Y=f(x)+a moves the function
Answer:
up
Step-by-step explanation:
for linear functions, adding a constant will increase the y value by two and shift the line up two units on the graph.
Answer: It moves the function 'a' units up if a > 0. Or it moves the function |a| units down if a < 0.
Explanation:
Consider an example like y = f(x)+2. This shifts the f(x) curve 2 units up because we're adding 2 to each y or f(x) output. A point like (5,7) shifts up to (5,9).
As another example, y = f(x)-5 moves the curve 5 units down.
In the first example, we had a > 0 which moved the function 'a' units up (a = 2 in that case). The second example had a = -5 which means a < 0, so that's why we shifted |a| = |-5| = 5 units down.
in a class of 38 student,30 are good in mathematics and 22 are good in physics how many students are good in both mathematics and physics
Answer:
8 are bad in math and 16 in physics
Step-by-step explanation:
aulo uses an instrument called a densitometer to check that he has the correct ink colour.
For this print job the acceptable range for the reading on the densitometer is 1.8 ± 10%.
What is the acceptable range for the densitometer reading?
Answer:
The range is from 1.62 to 1.98.
Step-by-step explanation:
We have to solve for the percentage of the particular value if the range of the answer should be +/- 10% of the particular value.
The value given is 1.8, we thus want to find 10% of that: 1.8 * 10/100 = 0.18
Then, add this value to the original value of 1.8: 1.8+0.18 = 1.98
Furthermore, subtract .18 from from the original value of 1.8: 1.8-0.18 = 1.62
The range will be between these two numbers, so the range is from 1.62 to 1.98.
A telephone exchange operator assumes that 9% of the phone calls are wrong numbers. If the operator is correct, what is the probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
Answer:
0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A telephone exchange operator assumes that 9% of the phone calls are wrong numbers.
This means that [tex]p = 0.09[/tex]
Sample of 448
This means that [tex]n = 448[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{448}} = 0.0135[/tex]
What is the probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%?
More than 9% + 3% = 12 or less than 9% - 3% = 6%. Since the normal distribution is symmetric, these probabilities are the same, so we find one of them and multiply by 2.
Probability it is less than 6%
P-value of Z when X = 0.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0135}[/tex]
[tex]Z = -2.22[/tex]
[tex]Z = -2.22[/tex] has a p-value of 0.0132
2*0.0132 = 0.0264
0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
سا (a) From the definition of derivatives determine dy÷dx if y = -2÷x
Step-by-step explanation:
Given: [tex]y = -\dfrac{2}{x}[/tex]
Derivative of a power function [tex]x^n[/tex]:
[tex]\dfrac{d}{dx}(x^n) = nx^{n-1}[/tex]
Therefore,
[tex]\dfrac{dy}{dx}=-2(-1)x^{-2} = \dfrac{2}{x^2}[/tex]
Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.)
f(x) = x² + 5x – 2
relative maximum
(x, y) = DNE
relativo minimum
(x, y) =
Answer:
Relative minimum: [tex]\left(-\frac{5}{2}, -\frac{33}{4}\right)[/tex], Relative maximum: [tex]DNE[/tex]
Step-by-step explanation:
First, we obtain the First and Second Derivatives of the polynomic function:
First Derivative
[tex]f'(x) = 2\cdot x + 5[/tex] (1)
Second Derivative
[tex]f''(x) = 2[/tex] (2)
Now, we proceed with the First Derivative Test on (1):
[tex]2\cdot x + 5 = 0[/tex]
[tex]x = -\frac{5}{2}[/tex]
The critical point is [tex]-\frac{5}{2}[/tex].
As the second derivative is a constant function, we know that critical point leads to a minimum by Second Derivative Test, since [tex]f\left(-\frac{5}{2}\right) > 0[/tex].
Lastly, we find the remaining component associated with the critical point by direct evaluation of the function:
[tex]f\left(-\frac{5}{2} \right) = \left(-\frac{5}{2} \right)^{2} + 5\cdot \left(-\frac{5}{2} \right) - 2[/tex]
[tex]f\left(-\frac{5}{2} \right) = -\frac{33}{4}[/tex]
There are relative maxima.
Is the random variable described discrete or continuous? The amount of rain during the next thunderstorm.
Answer:
continuous
rain does not fall in specific units like 1 inch , 2 inches etc... but 1.23456 etc..
Step-by-step explanation:
Please help me i will give you brainlest
Answer:
x = 14/3
Step-by-step explanation:
9.
The given equation is:
(x-2)+(x-3)+(x-9)=0
After opening the brackets,
x-2+x-3+x-9=0
3x+(-2-3-9) = 0
3x-14=0
x = 14/3
So, the value of x is equal to 14/3.
Melanie has D dimes and Q quarters. She has no less than $4 worth of coins altogether. Write this situation as an inequality.
Step-by-step explanation:
D(.10) + Q(.25) = 4
I think
Answer:
D(.10) + Q(.25) = 4
Step-by-step explanation:
A recipe for chocolate chip cookies calls for 3 1/3 cups of flour. If you are making 2 1/4 recipes, how many cups of flour are needed.
Answer:
THIS IS THE ANSWER
Step-by-step explanation:
1 1/2 = 3/2
2 1/3 = 7/3
3/2 * 7/3 = 21/6 = 3 3/5 = 3 1/2 cups
PLEASE MARK ME AS A BRAINLIST!70. If set A consists of (3, 5, 7, 9) and set B consists of (1, 2, 3, 5, 8, 13), what is the average of the union of set A and set B?
A) 6
B) 3
C) 48
D) 56
⚠️will give brainliest to the best answer
Step-by-step explanation:
the answer would be 6. brrr
A) 6
{1,2,3,5,7,8,9,13}
The average is going to be 6.
Chef Amy does beginning inventory on Thursday night and finds that she has $4697 in food products in the restaurant
Throughout the week she purchases:
$668 produce
$2206 meat
$2488 dry goods
$3755 dairy
The following Thursday she does ending inventory and finds that she has $3518 in food.
She looks at her sales and finds that she made $30658 over the same 7 day period.
What is her food cost as a percentage of sales (her food cost percentage)? Please input your answer as a percentage (30%), instead of a decimal (0.3).
Answer:
Her food cost as a percentage of sales is 33.58%.
Step-by-step explanation:
Since Chef Amy does beginning inventory on Thursday night and finds that she has $ 4697 in food products in the restaurant, and throughout the week she purchases:
$ 668 produces
$ 2206 meat
$ 2488 dry goods
$ 3755 dairy
The following Thursday she does ending inventory and finds that she has $ 3518 in food.
She looks at her sales de ella and finds that she made $ 30658 over the same 7 day period.
To determine what her food cost is as a percentage of sales (her food cost percentage), the following calculation must be performed:
4,697 + 668 + 2,206 + 2,488 + 3,755 = 13,814
13,814 - 3,518 = 10,296
30,658 = 100
10,296 = X
10,296 x 100 / 30,658 = X
1,029,600 / 30,658 = X
33.58 = X
Therefore, her food cost as a percentage of sales is 33.58%.
solve the following by factolisation formula
1. x(2x+1)=0
2.4xsquere-11-3x=0
1.
X = 0
2x + 1 = 0
X = 0
X = - ½ (Because we brought the numbers from one side to the other)
2.
Not sure for number 2.
Sally bought five books.Their mean price was 3.25. The total cost for four books was 11.75.what was the cost of the fifth book
Answer:
$4.50
Step-by-step explanation:
Use the mean formula: mean = sum of elements / number of elements
Let x represent the cost of the fifth book, and solve for x:
mean = sum of elements / number of elements
3.25 = (11.75 + x) / 5
16.25 = 11.75 + x
4.5 = x
So, the cost of the fifth book was $4.50
Multiply and show work
Answer:
-15m^10 -38m8+57m^6+98m^4-30m^2
Answer:
jere is your answer i hope it will help u
A chemical company makes two brands of antifreeze the first brand contains 65% pure antifreeze and the second brand contains 80% pure antifreeze in order to obtain 60 gallons of a mixture that contains 70% pure antifreeze how many gallons of each brand of antifreeze must be used
Answer:
30 gallons of each brand
Step-by-step explanation:
1 gallon of 60% + 1 gallon of 80% = 2 gallons 70% (60/2 = 30)
Using law of sines please show process!!!
Let the <C=x
We know in a triangle
☆Sum of angles=180°
[tex]\\ \sf\longmapsto 51+26+x=180[/tex]
[tex]\\ \sf\longmapsto 77+x=180[/tex]
[tex]\\ \sf\longmapsto x=180-77[/tex]
[tex]\\ \sf\longmapsto x=103°[/tex]
What is the slope of (-1,3) and (3,1)
Work Shown:
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (1-3)/(3-(-1))
m = (1-3)/(3+1)
m = -2/4
m = -1/2 is the slope
In decimal form, this converts to -0.5, though usually slopes are in fraction form.
if a x + B Y is equal to a square minus b square and b x + A Y is equal to zero find the value of x + Y
9514 1404 393
Answer:
a-b
Step-by-step explanation:
Add the two equations together:
(ax +by) +(bx +ay) = (a² -b²) +(0)
x(a +b) +y(a +b) = (a +b)(a -b)
x + y = a - b . . . . . divide by (a+b), assuming a+b ≠ 0
What is the value of y?
Enter your answer, as an exact value, in the box.
Answer:
y=4√3 units
Step-by-step explanation:
Hi there!
We are given ΔABC, which is a right triangle (m<C=90°), m<A=60°, AB=8, and BC=y
We need to find the value of y (BC)
The side AB is the hypotenuse of the (the side opposite from the right angle).
BC is a leg, which is a side that makes up the right angle.
Now, if we have a right triangle that has one of the acute angles as 60°, the side OPPOSITE from that 60° angle (in this case, BC) is equal to [tex]\frac{a\sqrt{3}}{2}[/tex], where a is the length of the hypotenuse
Since we have the hypotenuse given as 8, the length of BC (y) is [tex]\frac{8\sqrt{3}}{2}[/tex], or 4√3
so y=4√3 units
Hope this helps!
write the volume formula beside the solid figure
Answer:
cube(v=l×l×l)
cylinder (v= πr^2h)
cone(v=1/3πr^2h)
rectangular prism (v= area of base×lenght)
pyramid (v=1/3×area of base×h)
Step-by-step explanation:
Cube:-a^3
Cuboid:-lbh
Cylinder :-pi r^2h
Cone:-1/3pi r^2h
A candy company fills a package of candy with individually wrapped pieces of candy. The number of pieces of candy per package varies because the package is sold by weight. The company wants to estimate the number of pieces per package. Inspectors randomly sample 120 packages of this candy and count the number of pieces in each package. They find that the sample mean number of pieces is 18.72. Assume the population standard deviation of .8735. What is the point estimate of number of pieces per package
Answer:
The point estimate for the number of pieces per package is of 18.72.
Step-by-step explanation:
Point estimate of a population mean:
The mean of the sample gives an estimate for the population mean.
They find that the sample mean number of pieces is 18.72.
This means that the point estimate for the number of pieces per package is of 18.72.
HELP PLEASE!!! So for this problem is got 0.48 however I just wanted to confirm that my answer is correct. Can someone please help me if the answer is wrong and how to solve it. Thank your for your time
Answer:
ur answer is correct
A =xy
A = 1.6×0.3 = 0.48
\int (x+1)\sqrt(2x-1)dx
Answer:
[tex]\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C[/tex]
Step-by-step explanation:
[tex]\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}[/tex]
[tex]\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du[/tex]
[tex]= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ][/tex]
[tex]= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\[/tex]
