Answer:
a y = 2
b.y = 14
c. y =56
Step-by-step explanation:
a .6 (1)- 4=2
y=2
b. 6 (3)- 4
=18-4
y=14
c. 6 (10) - 4
= 60 - 4 =56
It takes amy 8 minutes to mow 1/6 of her backyard. At that rate how many more minutes will it take her to finish mowing her backyard
Answer:
40 minutes
Step-by-step explanation:
If it takes her 8 minutes to mow 1/6 of it, we can find the total amount of time it will take by multiplying 8 by 6, since 1/6 times 6 is 1 (1 represents the whole lawn mowed)
8(6) = 48
The question asks for how many more minutes it will take, so subtract 48 by 8.
48 - 8 = 40
= 40 minutes
Answer:
40 minutes
Step-by-step explanation:
We can use ratios to solve
8 minutes x minutes
------------------- = ----------------
1/6 yard 1 yard
Using cross products
8 * 1 = 1/6 x
Multiply each side by 6
8*6 = 1/6 * x * 6
48 = x
48 minutes total
She has already done 8 minutes
48-8 = 40 minutes
Compute (3/4)*(8/9)*(15/16)*(24/25)*(35/36)*(48/49)*(63/64)*(80/81)*(99/100) Express your answer in the simplest way possible. (Suggestion: First, try computing 3/4*8/9 then 3/4*8/9*15/16 and so on. Look for patterns.
Answer:
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]
Step-by-step explanation:
Given
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})[/tex]
Required
Simplify
For clarity, group the expression in threes
[tex]((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the first group [Divide 8 by 4]
[tex]((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 9 by 3]
[tex]((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex]((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 15 by 3]
[tex]((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 16 by 2]
[tex]((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the second group [Divide 35 and 25 by 5]
[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 49 by 7]
[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 24 by 3]
[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Merge the first and second group
[tex]((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the last group [Divide 99 by 9]
[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))[/tex]
[Divide 63 by 9]
[tex](\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))[/tex]
[Divide 64 and 80 by 8]
[tex](\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))[/tex]
[Divide 10 and 4 by 2]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))[/tex]
[Divide 100 by 5]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))[/tex]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))[/tex]
[tex](\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})[/tex]
[tex]1*(\frac{11}{20})[/tex]
[tex]\frac{11}{20}[/tex]
Hence;
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]
An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average expense of $15,000. What is the width of the 99% confidence interval for the mean of expense? a. 364.28 b. 728.55 c. 329.00 d. 657.99
Answer:
The width is [tex]w = \$ 729.7[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma = \% 1,000[/tex]
The sample size is [tex]n = 50[/tex]
The sample mean is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 99% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 99[/tex]
=> [tex]\alpha = 1\%[/tex]
=> [tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 364.9[/tex]
The width of the 99% confidence interval is mathematically evaluated as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 364.9[/tex]
[tex]w = \$ 729.7[/tex]
An investigator claims, with 95 percent confidence, that the interval between 10 and 16 miles includes the mean commute distance for all California commuters. To have 95 percent confidence signifies that
Answer:
Hello the options to your question is missing below are the options
A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles
B.the unknown population mean is definitely between 10 and 16 miles
C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
D.the unknown population mean is between 10 and 16 miles with probability .95
Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians ( c )
Step-by-step explanation:
95% confidence
interval = 10 to 16 miles
To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,
The quotient of 8 and the difference of three and a number.
Answer: 8÷(3-x)
Answer:
Below
Step-by-step explanation:
● 8 ÷ (3-x)
Dividing by 3-x is like multiplying by 1/(3-x)
● 8 × (1/3-x)
● 8 /(3-x)
2/3a - 1/6 =1/3 please help me
Answer:
[tex]a = \frac{3}{4}[/tex]
Step-by-step explanation:
Let's convert everything to sixths to make it easier to work with.
[tex]\frac{4}{6}a - \frac{1}{6} = \frac{2}{6}[/tex]
Add 1/6 to both sides:
[tex]\frac{4}{6}a = \frac{3}{6}[/tex].
Dividing both sides by 4/6:
[tex]a = \frac{3}{6} \div \frac{4}{6}\\\\a = \frac{3}{6} \cdot \frac{6}{4}\\\\a = \frac{18}{24}\\\\a = \frac{3}{4}[/tex]
Hope this helped!
Please help. I’ll mark you as brainliest if correct!
Answer:
(DNE,DNE)
Step-by-step explanation:
-24x-12y = -16. Equation one
6x +3y = 4. Equation two
Multiplying equation two with +4 gives
4(6x +3y = 4)
24x +12y = 16...result of equation two
-24x -12y= -16...
A careful observation to the following equation will help us notice that the both equation are same thing.
Multiplying minus to equation one gives
-(-24x-12y=-16)
24x+12y = 16.
Since the both equation are same, there is no solution to it.
if given the diameter how can you find the radius
Answer:
Divide the diameter by 2.
Step-by-step explanation:
The radius of any circle is always the end to the center.
The diameter is a point of the circle to the opposite side.
This means that the diameter is twice the size of the radius, so to find the radius from the diameter, divide the diameter by 2.
Hope this helped!
Answer:
Divide the diameter by 2. d/2=r
Step-by-step explanation:
If a diameter has been given instead of a radius, you can find the radius by dividing the diameter by 2, for example.
If the diameter was 10, the radius would 10/2=5.
Twice the difference of a number and 9 is 3. Use the variable b for the unknown number.
Answer:
b = 10.5
Step-by-step explanation:
2(b-9) = 3
then:
2*b + 2*-9 = 3
2b - 18 = 3
2b = 3 + 18
2b = 21
b = 21/2
b = 10.5
check:
2(10.5 - 9) = 3
2*1.5 = 3
Karim has two investments, one in Company A, and another in Company B. Karim purchased 3,000 shares in company A at $2.65 per share. Since purchasing the shares, the price per share increased to $2.95 per share, after which point Karim decided to sell, realizing a profit. At the same time, Karim purchased 2,000 shares in Company B at $1.55 per share. Since purchasing the shares, the share price fell to $1.30 per share, after which Karim decided to sell the shares, suffering a loss. Karim is required to pay tax at a rate of 28% on the combined profit from both investments. Calculate how much tax Karim must pay.
Answer:
A:$2478
B:$728
Total:$3206
Step-by-step explanation:
2.95x3000=8850
1.30x2000=2600
8850x0.28=2478
2600x0.28=728
2478+728=3206
Two sides of a triangle are equal length. The length of the third side exceeds the length of one of the other sides by 3 centimeters. The perimeter of the triangle is 93 centimeters. Find the length of each of the shorter sides of the triangle
Answer:
30 cm
Step-by-step explanation:
let x be the lenght of the two sides of equal lenghts, so the other is x+3
and the perimeter is x+x +x +3
P=3x+3
P=3(x+1)
93=3(x+1)
31=x+1
x=30
so the shorter sides are of 30 centimeters and the longest is 33
Shyla's research shows that 8 empty cans make 1/4 pound of aluminum. Shyla wants to know how many cans does it take to make 5 pounds of aluminum. How many cans are there per pound of aluminum?
Answer:
They will need 160 cans to make 5 lbs
32 cans for 1 lbs
Step-by-step explanation:
We can use ratios to solve
8 cans x cans
--------------- = ---------------
1/4 lbs 5 lbs
Using cross products
8 * 5 = 1/4x
40 = 1/4 x
Multiply each side by 4
4 * 40 = 1/4 x * 4
160 =x
They will need 160 cans to make 5 lbs
8 cans x cans
--------------- = ---------------
1/4 lbs 1 lbs
Using cross products
8 * 1 = 1/4x
Multiply each side by 4
8*4 = x
32 cans for 1 lbs
Answer:
32 cans per pound of aluminum
160 cans per 5 pounds of aluminum
Step-by-step explanation:
will make it short and simple.
8 empty cans can make 1/4 pound of aluminum.
therefore... 8 x 4 = 32 cans per pound of aluminum.
Number of cans to make 5 pounds of aluminum = 32 x 5
= 160 cans per 5 pounds of aluminum
Use the graph showing Phillip's account balance to answer the question that follows. ^
What is the interest rate on Phillip's account?
A - 3.3%
B - 6.7%
C - 9.0%
D - 15.3%
Answer:
A - 3.3%
Step-by-step explanation:
From the graph
Where x= 0
Amount =$ 450
It shows that$450 is the capital
Then
When x= 3
Amount=$494.55
So interest generated within 3 years
= $494.55-$450
=$ 44.55
When x= 9
Amount = $583.65
So interest generated within 9 years
= $583.65-$450
=$ 133.65
PRT/10= Interest
450*x*3/100= 44.55
1350x= 4455
X= 4455/1350
X= 3.3
So the rate is =3.3%
I need help please help meee I don’t understand
Answer:
204
Step-by-step explanation:
To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.
For height of the prongs, take 4 from 6.
6 - 4 = 2
Divide by 2 as there are 2 prongs.
2 / 2 = 1
Remember L * W * H
6 * 3 * 1 = 18
Remember that there are two prongs!
3 + 4 = 7
6 * 7 * 4 = 168
168 + 2(18) = 204
PLZ HELPPPPPP. 25 POINTS.
A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?
A. y=12/x
B. y=12x
C. y=12+x
D. y=12−x
Answer:
b
Step-by-step explanation:
because its right dummy
Find (fºg)(2) and (f+g)(2) when f(x)= 1/x and g(x) = 4x +9
[tex](f\circ g)(2)=\dfrac{1}{4\cdot2+9}=\dfrac{1}{17}\\\\(f+g)(2)=\dfrac{1}{2}+4\cdot2+9=\dfrac{1}{2}+17=\dfrac{1}{2}+\dfrac{34}{2}=\dfrac{35}{2}[/tex]
Match the base to the corresponding height.
Base (b)
Height (h)
b
h
h
b
The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
What is a triangle?Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
In the given figure, three triangles is shown with base and height. Here,
The base 1 is matched with height 2, as the height shown in figure 2 is the dimension of the elevation from the opposite peak to the length of the base 1.Similarly, base 2 is matched with height 3.Base 3 is matched with height 1.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
Learn more about the base and height of the triangle here;
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88 feet/second = 60 miles/hour. How many feet per second is 1 mile/hour? (Hint: divide both sides of the equation
by the same amount.)
Round to the nearest thousandth.
One mile per hour is equivalent to
ao feet/second
A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.
Answer:
6344
Step-by-step explanation:
Find 26% of 24400
24400 * 26%
24400 * .26
6344
22 tons is equivalent to ______ kilograms.
Answer:
20000 kg
Step-by-step explanation:
Recall that 1 kg = 2.2 lb approximately. Then:
22 tons 1 kg 2000 lb
------------ * ------------ * -------------- = 20000 kg
1 2.2 lb 1 ton
How do you evaluate this?
[tex]_6C_3=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20[/tex]
Let REPEAT TM = { | M is a TM, and for all s ∈ L(M), s = uv where u = v }. Show that REPEATTM is undecidable. Do not use Rice’s Theorem.
Answer:
Step-by-step explanation:
Let REPEAT [tex]_{TM[/tex]= { | M is a TM, and for all s ∈ L(M), s = uv where u = v }
To prove that REPEAT [tex]_{TM[/tex] is undecidable.
Let REPEAT [tex]_{TM[/tex] {| M is a TM that does not accept M}
Then, we form a TM u for L by applying TM v as a subroutine.
Assume Repeat is decidable
Let M be the algorithm that TM which decides the REPEATU = on input "s" simulate the M
Accept; if M ever enters the accept state
Reject; if M ever enters the reject state
U does not decide the REPEAT as it may loop over s
so REPEAT is undecidable
A box contains 40 identical discs which are either red or white if probably picking a red disc is 1/4. Calculate the number of;
1. White disc.
2. red disc that should be added such that the probability of picking a red disc will be 1/4
Fill in the following blanks to prove that n 2^1 n < 2^n n+1 < 2^(n+1) is Box 3 Options: True | False Next, assume that Box 4 Options: 1 < 2^1 k + 1 < 2^(k+1) k < 2^k as we attempt to prove Box 5 Options: k < 2^k k + 1 < 2^(k+1) 2 < 2^1 Therefore, we can conclude that Box 6 Options: k < 2^k k + 1 < 2^(k+1) 2^1 < 2^k k + 2 < 2^(k+2)
Answer:
see below
Step-by-step explanation:
n < 2^n
First let n=1
1 < 2^1
1 <2 This is true
Next, assume that
(k) < 2^(k)
as we attempt to prove that
(k+1) < 2^(k+1)
.
.
.
Therefore we can conclude that
k+1 < 2^(k+1)
Answer:
Step-by-step explanation:
Hello, please consider the following.
First, assume that n equals [tex]\boxed{1}[/tex]. Therefore, [tex]\boxed{1<2^1}[/tex] is [tex]\boxed{\text{True}}[/tex]
Next, assume that [tex]\boxed{k<2^k}[/tex], as we attempt to prove [tex]\boxed{k+1<2^{k+1}}[/tex]
Since .... Therefore, we can conclude that [tex]\boxed{k+1<2^{k+1}}[/tex]
The choice for the last box is confusing. Based on your feedback, we can assume that we are still in the step 2 though.
And the last step which is not included in your question is the conclusion where we can say that we prove that for any integer [tex]n\geq 1[/tex], we have [tex]n<2^n[/tex].
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Lauren is a college sophomore majoring in business. This semester Lauren is taking courses in accounting, economics, management information systems, public speaking, and statistics. The sizes of these classes are, respectively, 375, 35, 45, 25, and 60.Required:Find the mean and the median of the class sizes. What is a better measure of Lauren's "typical class size"—the mean or the median?
Answer:
Mean = 108
Median = 45
The better measure of Lauren's "typical class size" is the Mean
Step-by-step explanation:
1. Calculating mean and median.
The mean is an important measure of central tendency, and it is the average of the measurement of a given set of data. It is calculated as follows:
[tex]Mean\ (\overline {X}) &= \frac{\sum X}{N}[/tex]
where X = individual data sets
N = total number of data
[tex]Mean= \frac{375\; +\ 35\ +\ 45\ +\ 25\ +\ 60}{5} \\=\frac{540}{5} \\= 108[/tex]
The Median divides the measurements into two equal parts, and in order to calculate the median, the distribution has to first be arranged in ascending or descending order. Arranging this series in descending order:
375, 60, 45, 35, 25
The formula for calculating median is given by:
[tex]M_{d} = \frac{N\ +\ 1}{2} th\ data\\\\=\frac{5\ +\ 1}{2}th\ data\\\\=\frac{6}{2} th\ data\\= 3rd\ data\\M_{d} = 45[/tex]
from the list or arranged data in descending order (375, 60, 45, 35, 25), the third data is 45.
Therefore, Median = 45
2. The better measure of typical class size is Mean because the mean depends on all the values of the data sets, whereas the median does not. When there are extreme values (outliers) the effect on the median is very small, whereas it is effectively captured by the mean.
If the normality requirement is not satisfied (that is, np(1p) is not at least 10), then a 95% confidence interval about the population proportion will include the population proportion in ________ 95% of the intervals. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
Answer:
less than
Step-by-step explanation:
If the normality requirement is not satisfied (that is, np(1 - p) is not at least 10), then a 95% confidence interval about the population proportion will include the population proportion in _less than__ 95% of the intervals.
The confidence interval consist of all reasonable values of a population mean. These are value for which the null hypothesis will not be rejected.
So, let assume that If the 95% confidence interval contains the value for the hypothesized mean, then the sample mean is reasonably close to the hypothesized mean. The effect of this is that the p- value is going to be greater than 0.05, so we fail to reject the null hypothesis.
On the other hand,
If the 95% confidence interval do not contains the value for the hypothesized mean, then the sample mean is far away from the hypothesized mean. The effect of this is that the p- value is going to be lesser than 0.05, so we reject the null hypothesis.
How do you write 30,8608
Answer:
it should be 308,608. the comma is after every three in this scenario.
Step-by-step explanation:
If f(x)=x/2-3and g(x)=4x^2+x-4, find (f+g)(x)
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
= x/2-3 + 4x²+x+4
= ..........
please help !! Solve –2.5x ≤ 25
Answer:
x ≥-10
Step-by-step explanation:
–2.5x ≤ 25
Divide each side by -2.5, remembering to flip the inequality
–2.5x/-2.5 ≥ 25 /-2.5
x ≥-10
Answer:
[tex]x\leq -10[/tex]
Step-by-step explanation:
[tex]-2.5x\leq 25[/tex]-----> Multiply by -1:
[tex]2.5x\geq -25[/tex]-----> Divide by 2.5:
[tex]x\geq -10[/tex]
Hope this helps!
1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident
Answer:
math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.
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