Answer:
The length is 35cmThe width is 5cmStep-by-step explanation:
Area of a rectangle = l × w
where
l is the length
w is the width
The length is seven times the width is written as
l = 7w
Area of the rectangle = 175 cm²
7w × w = 175
7w² = 175
Divide both sides by 7
w² = 25
Find the square root of both sides
w = √25
w = 5cm
But l = 7w
l = 7(5)
l = 35cm
The length is 35cm
The width is 5cm
Hope this helps you.
Find the indicated conditional probability
using the following two-way table:
P( Drive to school | Sophomore ) = [?]
Round to the nearest hundredth.
Answer:
0.07
Step-by-step explanation:
The number of sophmores is 2+25+3 = 30.
Of these sophmores, 2 drive to school.
So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.
Answer:
[tex]\large \boxed{0.07}[/tex]
Step-by-step explanation:
The usual question is, "What is the probability of A, given B?"
They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"
We must first complete your frequency table by calculating the totals for each row and column.
The table shows that there are 30 students, two of whom drive to school.
[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]
The heights of American men are normally distributed. If a random sample of American men is taken and the confidence interval is (65.3,73.7), what is the sample mean x¯? Give just a number for your answer. For example, if you found that the sample mean was 12, you would enter 12.
Answer:
69.5Step-by-step explanation:
Given the confidence interval of the heights of american heights given as (65.3,73.7);
Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7
Sample mean will be the average of both confidence interval . This is expressed mathematically as [tex]\overline x = \frac{L+U}{2}[/tex]
[tex]\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5[/tex]
Hence, the sample mean is 69.5
Consider circle T with radius 24 in. and θ = StartFraction 5 pi Over 6 EndFraction radians. Circle T is shown. Line segments S T and V T are radii with lengths of 24 inches. Angle S T V is theta. What is the length of minor arc SV?
Answer:
20π inStep-by-step explanation:
Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;
[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]
The length of the minor arc SV is expressed as:
[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]
Hence, The length of the arc SV is 20π in
Answer:
20 pi
Step-by-step explanation:
Convert into the following unit into 30 cm into miter
Answer:
it we'll be 0.3
Step-by-step explanation:
trust me man I like to explain but it's long
Answer:
0.3 meter or 3/10 meter
Step-by-step explanation:
As there are 100cm in 1 meter and you want to find 30cm in terms of meters.
It will be as
100cm = 1 meter (rule/lax)
100/100 cm = 1/100 meter (divide both sides of equation with 100)
1 cm = 1/100 meter
1 *30 cm = (1/100)*30 meter (multiply both sides with 30)
30 cm = 30/100 meter
30/100 more shortly can be written as 3/10 meter or in decimals 0.3 meter.
Factor completely 2x3y + 18xy - 10x2y - 90y. I need this done today in a few minutes.
Answer:
2y (x^2+9) ( x-5)
Step-by-step explanation:
2x^3y + 18xy - 10x^2y - 90y
Factor out the common factor of 2y
2y(x^3+9x-5x^2-45)
Then factor by grouping
2y(x^3+9x -5x^2-45)
Taking x from the first group and -5 from the second
2y( x (x^2+9) -5(x^2+9))
Now factor out (x^2+9)
2y (x^2+9) ( x-5)
Irvin buys a car for $21 comma 804. It depreciates 25% each year that he owns it. What is the depreciated value of the car after 1 yr? after 2 yr? The depreciated value of the car after 1 yr is $? The depreciated value of the car after 2 yr is $?
Answer:
The depreciated value of the car after 1 yr is $16,353
The depreciated value of the car after 2 yr is $12,264.75
Step-by-step explanation:
Given
purchase amount P= $21,804
rate of depreciation R= 25%
applying the formula for the car deprecation we have
[tex]A= P*(1-\frac{R}{100} )^n[/tex]
Where,
A is the value of the car after n years,
P is the purchase amount,
R is the percentage rate of depreciation per annum,
n is the number of years after the purchase.
1. The depreciated value of the car after 1 yr is
n=1
[tex]A= 21,804*(1-\frac{25}{100} )^1\\\\A= 21,804*(1-0.25 )^1\\\\A= 21,804*0.75\\\\A= 16353[/tex]
The depreciated value of the car after 1 yr is $16,353
2. The depreciated value of the car after 2 yr is
n=2
[tex]A= 21,804*(1-\frac{25}{100} )^2\\\\A= 21,804*(1-0.25 )^2\\\\A= 21,804*0.75^2\\\\A= 21,804*0.5625\\\\A= 12264.75[/tex]
The depreciated value of the car after 2 yr is $12,264.75
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables a. More than 61 pounds
Answer:
0.007
Step-by-step explanation:
We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage
Step 1
We would have to find the sample standard deviation.
We use the formula = σ/√n
σ = 12.2 pounds
n = number of house holds = 51
= 12.2/√51
Sample Standard deviation = 1.7083417025.
Step 2
We find the z score for when the sample mean is more than 61
z-score formula is z = (x-μ)/σ
where:
x = raw score = 61 pounds
μ = the population mean = 56.8 pounds
σ = the sample standard deviation = 1.7083417025
z = (x-μ)/σ
z = (61 - 56.8)/ 1.7083417025
z = 2.45852
Finding the Probability using the z score table
P(z = 2.45852) = 0.99302
P(x>61) = 1 - P(z = 2.45852) = 0.0069755
≈ 0.007
Therefore,the probability that the sample mean will be more than 61 pounds is 0.007
The graphed line shown below is y = 3 x minus 1. On a coordinate plane, a line goes through (0, negative 1) and (1, 2). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y + 1 = 3 x y = negative 3 x + 1 y = 3 x + 1 y minus 3 x = negative 3
Answer:
y + 1 = 3x
Step-by-step explanation:
In order for there to be an infinite number of solutions, the two lines need to be the same.
y+1 = 3x
y=3x-1 are both the same
Answer:
a)y + 1 = 3x
Step-by-step explanation:
find the value of k if x minus 2 is a factor of P of X that is X square + X + k
Answer:
k = -6
Step-by-step explanation:
hello
saying that (x-2) is a factor of [tex]x^2+x+k[/tex]
means that 2 is a zero of
[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]
and we can verify as
[tex](x^2+x-6)=(x-2)(x+3)[/tex]
so it is all good
hope this helps
What is the discontinuity of x2+7x+1/x2+2x-15?
The discontinuity occurs when x is either -5 or 3.
That is determined by solving denominator = 0 quadratic equation for x.
Hope this helps.
Find the area of this parallelogram.
6 cm
11 cm
Step-by-step explanation:
given,
base( b) = 6cm
height (h)= 11cm
now, area of parallelogram (a)= b×h
or, a = 6cm ×11cm
therefore the area of parallelogram (p) is 66cm^2.
hope it helps...
Diagramming Percents
Percents
Total
An item was marked down 60% from its original price.
The amount of the discount was $30. Fill in the
numbers that belong in the diagram to find the original
price
20%
20%
20%
20%
20%
A=
B=
C=
Answer:
see below
Step-by-step explanation:
Let x be the original price
x* discount rate = discount
x * 60% = 30
Change to decimal form
x * .60 = 30
Divide each side by .60
x = 30/.60
x =50
The original price was 50 dollars
Answer:
A-30 B-20 C-50
Step-by-step explanation:
A fair die is rolled repeatedly. Calculate to at least two decimal places:__________
a) the chance that the first 6 appears before the tenth roll
b) the chance that the third 6 appears on the tenth roll
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
d) the expected number of rolls until six 6's appear
e) the expected number of rolls until all six faces appear
Answer:
a. 0.34885
b. 0.04651
c. 0.02404
d. 36
e. 14.7, say 15 trials
Step-by-step explanation:
Q17070205
Note:
1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.
2. use R to find the probability values from the respective distributions.
a) the chance that the first 6 appears before the tenth roll
This means that a six appears exactly once between the first and the nineth roll.
Using binomial distribution, p=1/6, n=9, x=1
dbinom(1,9,1/6) = 0.34885
b) the chance that the third 6 appears on the tenth roll
This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.
Again, we have a binomial distribution of p=1/6, n=9, x=2
p1 = dbinom(2,9,1/6) = 0.27908
The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.
Thus the probability of both happening, by the multiplication rule, assuming independence
P(third on the tenth roll) = p1*p2 = 0.04651
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
Again, using binomial distribution, probability of 3-6's in the first 10 rolls,
p1 = dbinom(3,10,1/6) = 0.15504
Probability of 3-6's in the NEXT 10 rolls
p1 = dbinom(3,10,1/6) = 0.15504
Probability of both happening (multiplication rule, assuming both events are independent)
= p1 * p1 = 0.02404
d) the expected number of rolls until six 6's appear
Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6
= n(1-p)/p
Total number of rolls by adding n
= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36
e) the expected number of rolls until all six faces appear
P1 = 6/6 because the firs trial (roll) can be any face with probability 1
P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials
P3 = 6/4 ...
P4 = 6/3
P5 = 6/2
P6 = 6/1
So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials
Suppose the sequence StartSet a Subscript n Baseline EndSet is defined by the recurrence relation a Subscript n plus 1equalsnegative 2na Subscript n, for nequals1, 2, 3,..., where a1equals5. Write out the first five terms of the sequence.
Answer:
-10, 40, -240, 1,920 and -19, 200
Step-by-step explanation:
Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.
when n= 1;
aₙ₊₁ = -2naₙ
a₁₊₁ = -2(1)a₁
a₂ = -2(1)(5)
a₂ = -10
when n = 2;
a₂₊₁ = -2(2)a₂
a₃ = -2(2)(-10)
a₃ = 40
when n = 3;
a₃₊₁ = -2(3)a₃
a₄ = -2(3)(40)
a₄ = -240
when n= 4;
a₄₊₁ = -2(4)a₄
a₅ = -2(4)(-240)
a₅ = 1,920
when n = 5;
a₅₊₁ = -2(5)a₅
a₆ = -2(5)(1920)
a₆ = -19,200
Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200
Clara writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:
Answer:
CPCTC
Step-by-step explanation:
Statements 3 and 4 show the top and bottom triangles are congruent, and the left and right triangles are congruent. Statement 5 is making use of these facts to claim that the alternate interior angles are congruent. This claim is valid because ...
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
If 2x+9<32 then x could be
Answer:
x < 11.5
Step-by-step explanation:
2x + 9 < 32
(2x + 9) - 9 < 32 - 9
2x < 23
2x/2 < 23/2
x < 11.5
Answer:
x < 11 1/2
Step-by-step explanation:
2x+9<32
Subtract 9 from each side
2x+9-9 < 32-9
2x<23
Divide by 2
2x/2 <23/2
x < 11 1/2
X is any number less than 11 1/2
By what percent will the fraction increase if its numerator is increased by 60% and denominator is decreased by 20% ?
Answer:
100%
Step-by-step explanation:
Start with x.
x = x/1
Increase the numerator by 60% to 1.6x.
Decrease the numerator by 20% to 0.8.
The new fraction is
1.6x/0.8
Do the division.
1.6x/0.8 = 2x
The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.
The increase is 100%.
Answer:
33%
Step-by-step explanation:
let fraction be x/y
numerator increased by 60%
=x+60%ofx
=8x
denominator increased by 20%
=y+20%of y
so the increased fraction is 4x/3y
let the fraction is increased by a%
then
x/y +a%of (x/y)=4x/3y
or, a%of(x/y)=x/3y
[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]
therefore a=33
anda%=33%
Any polygon can be the base of a prism. A. True B. False
Answer:
true
Step-by-step explanation:
A prism is a solid with parallelogram sides (usually rectangles) and a polygon for the 2 bases. Any polygon can be the base.
Answer:
Hello!
__________________
Your answer would be (A) True.
Step-by-step explanation: Hope this helped you!
Any polygon can be the base of a prism so the answer is true.
Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.) P(x) = −0.004x2 + 6x − 5,000 Increasing: Decreasing:
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Step-by-step explanation:
Critical points:
The critical points of a function f(x) are the values of x for which:
[tex]f'(x) = 0[/tex]
For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.
The critical points help us find these intervals.
In this question:
[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]
So
[tex]P'(x) = -0.008x + 6[/tex]
Critical point:
[tex]P'(x) = 0[/tex]
[tex]-0.008x + 6 = 0[/tex]
[tex]0.008x = 6[/tex]
[tex]x = \frac{6}{0.008}[/tex]
[tex]x = 750[/tex]
We have two intervals:
(0, 750) and [tex](750, \infty)[/tex]
(0, 750)
Will find P'(x) when x = 1
[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]
Positive, so increasing.
Interval [tex](750, \infty)[/tex]
Will find P'(x) when x = 800
[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]
Negative, then decreasing.
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Please help! V^2 = 25/81
Answer:
C and D
Step-by-step explanation:
khan acedemy
An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the given equation v²=25/81 can be found as shown below.
v²=25/81
Taking the square root of both sides of the equation,
√(v²) = √(25/81)
v = √(25/81)
v = √(5² / 9²)
v = ± 5/9
Hence, the solutions of the given equation are A, B, and C.
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whats 1 and 1/2 + 2 and 3/10
Answer:
[tex]3\frac{4}{5}[/tex]
Step-by-step explanation:
You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.
10/10-->1
1/2--> 5/10
2--> 20/10
3/10, the denominator is already 10, so don't need to change.
10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]
Answer:
3 4/5
Step-by-step explanation:
hopefully this helped :3
heres a list of numbers 3 6 9 7 4 6 7 0 7 Find median,mean,range and mode
median=order them and find the middle=6
mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4
range= the difference between the smallest and largest number=9-3=6
mode= the one that appears the most= 7
The median, mean, range and mode will be 6, 5.4, 9 and 7.
The median is the number in the middle when arranged in an ascending order. The numbers will be:
0, 3, 4, 6, 6, 7, 7, 7, 9.
The median is 6.
The range is the difference between the highest and lowest number which is: = 9 - 0 = 9
The mode is the number that appears most which is 7.
The mean will be the average which will be:
= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.
= 49/9
= 5.4
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please please please please help i need to pass please
Answer:
D
Step-by-step explanation:
Solution:-
The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:
f ( x ) = sin ( w*x ± k ) ± b
Where,
w: The frequency of the cycle
k: The phase difference
b: The vertical shift of center line from origin
We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).
We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.
The resulting sinusoidal waveform can be expressed as:
f ( x ) = sin ( 2x ) ... Answer
my dad is designing a new garden. he has 21 feet of fencing to go around the garden. he wants the length of the garden to be 1 1/2 feet longer than the width. how wide should he make the garden?
Answer:
21=2w+2w+3 18=4w w=4.5
Perform the operation 3/a^2+2/ab^2
Answer:
Step-by-step explanation:
Least common denominator = a²b²
[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]
Factor the trinomial!! PLEASE HELP and if possible please explain how to do this!!
Answer:
d. a = 39
Step-by-step explanation:
Question:
for which value of "a" will the trinomial be factorizable.
x^2+ax-40
For the expression to have integer factors, a = sum of the pairs of factors of -40.
-40 has following pairs of factors
{(1,-40), (2,-20, (4,-10), (5,-8), (8, -5), (10,-4), (20,-2), (40,-1) }
meaning that the possible values of a are
+/- 39, +/- 18, +/- 6, +/- 3
out of which only +39 appears on answer d. a=39
What is the value of x in the equation 0.7 x - 1.4 = -3.5
Answer:
x=12.5
Step-by-step explanation:
0.7x times (-1.4)=-3.5
-0.28x=-3.5 (divide both sides)
Ans:12.5
Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals. Function Interval f(x) = 7 − 2x [1, 2]
Answer:
-2n
Step-by-step explanation:
f(x)=7-2x {1,2}
f(1)=7-2(1)=5
f(2)=7-2(2)=3
Slope (m)=3/5
{7-2(1)}-{7-2(2)}=3-5=-2
In terms of n=-2n
The upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3]
Given the function of the graph bounded by the inteval [1, 2] expressed as
f(x) = 7 - 2x
The upper limit of the function is the point where the domain of the function x is 2. Substitute x = 2 into the function, we will have:
f(2) = 7 - 2(2)
f(2) = 7 - 4
f(2) = 3
For the lower limit, the domain of the function is at x = 2:
f(1) = 7 - 2(1)
f(1) = 7 - 2
f(1) = 5
Hence the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3].
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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 58.2 σ=58.2. You would like to be 99% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation.
Answer:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
Step-by-step explanation:
Let's define some notation
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=58.2[/tex] represent the population standard deviation
n represent the sample size
[tex] ME =1[/tex] represent the margin of error desire
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
The area of a rectangular horse pasture is 268,500 square yards. The length of the pasture is 5 yards less than three times the width. What is the width of the pasture in yards? Do not include units in your answer. Please help right away! Thank you very much!
Answer: width = 300
Step-by-step explanation:
Area (A) = Length (L) x width (w)
Given: A = 268,500
L = 3w - 5
w = w
268,500 = (3w - 5) x (w)
268,500 = 3w² - 5w
0 = 3w² - 5w - 268,500
0 = (3w + 895) (w - 300)
0 = 3w + 895 0 = w - 300
-985/3 = w 300 = w
Since width cannot be negative, disregard w = -985/3
So the only valid answer is: w = 300