Answer:
The rectangle is 5 inches long by 19 inches wide.
Step-by-step explanation:
Let's start by listing what we know:
The perimeter of a rectangle is 48 inches.The width of the rectangle is 4 inches more than 3 times the length of the rectangle.Let's represent the width with "w" and length with "l", and make a system of equations based on what we know.
[tex]\left \{ {{2w + 2l = 48} \atop {w = 3l + 4}} \right.[/tex]
Now, let's solve the system of equations using substitution:
[tex]2w + 2l = 48[/tex]
[tex]2 (3l + 4) + 2l = 48[/tex]
[tex]6l + 8 + 2l = 48[/tex]
[tex]8l + 8 = 48[/tex]
[tex]8l = 40[/tex]
[tex]l = 5[/tex]
The length of the rectangle is 5 inches.
Now, let's use this to solve for the width.
[tex]w = 3l + 4[/tex]
[tex]w = 3(5) + 4[/tex]
[tex]w = 15 + 4[/tex]
[tex]w = 19[/tex]
The width of the rectangle is 19 inches.
Let's check our work:
[tex]2w + 2l = 48[/tex]
[tex]2(19) + 2(5) = 48[/tex]
[tex]38 + 10 = 48[/tex]
[tex]48 = 48[/tex]
The results match, so our answer is correct.
The rectangle is 5 inches long by 19 inches wide.
terest formula to compute the total amount accumulated and
$5000 for 3 years at 1.7% compounded monthly
The total amount accumulated after 3 years is $ 5,261.42
(Round to the nearest cent as needed.)
The amount of interest earned is $
(Round to the nearest cent as needed.)
Answer:
Interest = $261.42
Step-by-step explanation:
amount of interest earned is $
(Round to the nearest cent as needed.)
Amount = Principal + Interest
Amount - Principal = Interest
$ 5,261.42 - $5000 = Interest = $261.42
Pre-cal! Please help!
Represent the product of A and B geometrically given that point A is located at (2,45°) and B is located at (4, 45°). Give
the coordinate of AxB in polar form.
Answer:
(8,90°)
Step-by-step explanation:
To get this answer, you multiply the r values together to get 2*4 = 8. At the same time, you add the theta angles to get 45° + 45° = 90°
The general rule is that if A = (r,theta) and B = (s,phi) then
A*B = (r*s,theta+phi)
where the point (s,phi) is a polar form point.
if lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then find lim (fg)(x)
a.1
b.0
c.3
d.does not exist
Answer:
0
Step-by-step explanation:
Assuming the problem is:
"lim x-> 4 f(x)=5 lim x-> 4 g(x)=0 and lim x-> 4 h(x)=-2, then find lim x->4 (fg)(x)"
lim x->4 (fg)(x)
Since we know the limits of f and g at x=4 exist we can write the limit as:
lim x->4 f(x) lim x->4 g(x) (since fg(x) means f times g of x.)
5(0)
0
if lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then lim (fg)(x) 0
What is inequality?inequality the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Assuming the problem is:
"lim x-> 4 f(x)=5 lim x-> 4 g(x)=0 and lim x-> 4 h(x)=-2, then find lim x->4 (fg)(x)"
lim x->4 (fg)(x)
Since we know the limits of f and g at x=4 exist we can write the limit as:
lim x->4 f(x) lim x->4 g(x) (since fg(x) means f times g of x.)
=5(0)
=0
Hence the lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then lim (fg)(x) 0
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What is the 5280th digit in the decimal expansion of 7/17?
Answer:
im pretty sure its either 1 or 7
Step-by-step explanation:
Help me for a brianly
the answer is 11.3
because the circumstance formula of circle is ,
[tex]\pi \: d[/tex]
GEOMETRY
please Help
Answer:
A right circular cone
Step-by-step explanation:
What is the length of segment AB? PLEASE HELP!!!
Answer:
4
Step-by-step explanation:
we have hypotenuse and opposite so we can use sin
sin(45) =O/4√2
rearrange
sin(45)x4√2 =O
=4
Please help me with this questions
Which is the volume of the Sphere with a diameter of 6 inches?
Volume
Sphere
=
A
288 Tt in
B
48 Tt in
C 36 Tt in
D 108 Tt in
Answer:
C
Step-by-step explanation:
because 6×6 is 36 so yeahh
what its 1010 + 800 pls help
Answer:
1,810 hope this helps ;)
Answer:
1810
Step-by-step explanation:
lol, did I get trolled?
The Virginia Department of Environmental Quality (VDEQ) uses probabilistic monitoring to regulate the water quality of streams in the Commonwealth of Virginia. Of the 85 Eastern Virginia Sites (group 1), 24 do not meet minimum requirements. Of the 80 units sampled in Western Virginia Sites (group 2), 17 do not meet minimum requirements. Assume the data can be treated as independent simple random samples. To determine whether the proportions of streams that fail to meet minimum requirements in the two areas are equal or not, test the following hypotheses.
a) State the null and alternative hypotheses in order to determine whether the proportions of streams that fail to meet minimum requirements in the two areas are equal or not .
(b) Calculate the value of the test statistic z.
(c) Determine the P-value associated with this observed value of z and draw the conclusion about the hypotheses using alpha=0.05.
Step-by-step explanation:
a) Hn: p1=p2, Ha: p1≠p2
b)
Given:
p1=24/85=0.2824
p2=17/80=0.2125
p=(24+17)/(85+80)=41/165=0.2485
n1=85
n2=80
Z=(p1-p2)/[p(1-p)(1/n1+1/n2)
Z=(0.2824-0.2125)/[0.2485(1-0.2485)(1/85+1/80)
Z=1.0384
c) Since our p-value would be 0.29834, this is higher than our significance level of a=0.05, so we fail to reject the null hypothesis and conclude that there is sufficient evidence to prove that the two proportions are equal.
a) The null hypothesis is given by Hn: p1=p2, Ha: p1≠p2
What is null hypothesis?The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
Given that:
p1=24/85=0.2824
p2=17/80=0.2125
p=(24+17)/(85+80)=41/165=0.2485
n1=85
n2=80
Z=(p1-p2)/[p(1-p)(1/n1+1/n2)
Z=(0.2824-0.2125)/[0.2485(1-0.2485)(1/85+1/80)
Z=1.0384
c) Since our p-value would be 0.29834, this is higher than our significance level of a=0.05, so we fail to reject the null hypothesis and conclude that there is sufficient evidence to prove that the two proportions are equal.
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HELPPP 30PTS FOR THIS
Answer:
pucha no se
Step-by-step explanation:
Answer:0.08
Step-by-step explanation:4756454434232
Four brothers each bought two hotdogs and a bag of chips at the football concession stand.
Answer:
The total hotdogs are 8 and total bag of chips are 4 and altogether is 12
Step-by-step explanation:
1 brother gets 2 hot dogs and 1 bag of chips
. To find the total hot dogs multiply 2 by 4 and you will get 8
. To find the total chips multiply 4 from 1 and the answer is obviously 4
To find the total together add 4 and 8 you will get 12
HOPE THIS HELPS :)
A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N. A new batch of yarn was made, using new raw materials from a different vendor. In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N. Find a 90% confidence interval for the difference in mean breaking strength between the two types of yarn.
Answer:
The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes 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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal variables:
When we subtract two normal variables, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.
This means that [tex]\mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626[/tex]
In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.
This means that [tex]\mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.645*0.1314 = 0.22[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N
The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N
The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).
Please help me on this for my quiz: Which equation represents an inverse variation with a constant of 56?
A: y/x=56
B: 7/y=8/x
C: 1/4y=14x
D:xy/2=28
Answer:
D) xy/2 = 28
Step-by-step explanation:
Inverse Variation:
y = k/x
Given:
k = 56
Work:
y = k/x
y = 56/x
xy = 56
xy/2 = 28
xy = 28 * 2
xy = 56
Three students, Matthew, Thompson and Amos shared #15000 in the ratio of 5:2:x respectively. If Matthew's share is 7500, calculate the value of x.
Answer:
The value of x is 3.
Step-by-step explanation:
Matthew earned 7500 of 15000, that is, 1/2.
Rate of 5:2:x, with number 5 corresponding to Matthew, mean that his fraction of the earnings is given by:
[tex]\frac{5}{5 + 2 + x} = \frac{5}{7 + x}[/tex]
Since he earned 1/2 of the total:
We have that 5/(7+x) = 1/2. So we use this to find x.
[tex]\frac{5}{7 + x} = \frac{1}{2}[/tex]
Applying cross multiplication:
[tex]7 + x = 10[/tex]
[tex]x = 10 - 7[/tex]
[tex]x = 3[/tex]
The value of x is 3.
he first date went well. You are still dating the same person and still looking for a great person to spend your life with. You are cautiously moving forward with the relationship and know that if they are a great match, their likelihood of being kind to animals is 0.9 whereas their likelihood of being kind to animals if they are not a great match is 0.7. You see that your prospective spouse is kind to animals. What is the probability that they are a great match now?
Answer:
0.125 = 12.5% probability that they are a great match now.
Step-by-step explanation:
To solve this question, we need the probability of a person being a great match, which i will use 0.1.
This question is solved using conditional probability.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Is kind to animals.
Event B: Is a great match.
Probability of being kind to animals:
0.9 of 0.1(Is a great match).
0.7 of 1 - 0.1 = 0.9(is not a great match). So
[tex]P(A) = 0.9*0.1 + 0.7*0.9 = 0.72[/tex]
Probability of being kind to animals and a great match:
0.9 of 0.1. So
[tex]P(A \cap B) = 0.9*0.1 = 0.09[/tex]
What is the probability that they are a great match now?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09}{0.72} = 0.125[/tex]
0.125 = 12.5% probability that they are a great match now.
PLS HELLP PLS PLS
Aarons bedroom measures. feet by 14 feet by 8 feet. how many cubic feet of space does the room contain? round ur answer to the nearest hundredth
Answer:
it would be 100 rounded because 14x8=112 and 112 is rounded to 100 to the nearest hundreth. Please subscribe to Amiredagoat Yt
Step-by-step explanation:
What is the total surface area of the square pyramid?
240 square meters
280 square meters
310 square meters
380 square meters
Answer:
380 I belive! :))
Step-by-step explanation:
Correct me if I'm wrong! ((:
14. On Monday, a work group eats at Ava's café,
where a lunch special is $8 and a dessert is
$2. The total is $108. On Friday, the group
eats at Bo's café, where a lunch special Is
$6 and a dessert is $3. The total is $90. Each
time, the group orders the same number of
lunches and the same number of desserts.
How many lunches and desserts are
ordered?
what the x and y value.
Answer:
no. who eat lunch special = 12
no. who eat dessert = 6
Step-by-step explanation:
Let x = no. who eat lunch special
y = no. who eat dessert
(1) 8x + 2y = 108 (2) 6x + 3y = 90
Divide thru by 2 Divide thru by 3
4x + y = 54 2x + y = 30
-2x - y = -30
2x = 24
x = 12 2(12) + y = 30
24 + y = 30
y = 6
Which is greater, -11 or -9 ?
Answer:
-9
Step-by-step explanation:for sure
Answer:
-9
Step-by-step explanation:
Look at a number line:
<----+------+------+------+------+------+------+------+------+------+------+------+------+------+-->
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
On a number line, a number to the right is always greater than a number to its left. Just like 1 is greater than 0, -9 is greater than -11.
-9 > -11
Answer: -9
A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. Step 2 of 2 : Suppose a sample of 1067 floppy disks is drawn. Of these disks, 74 were defective. Using the data, construct the 80% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.
Answer:
The 80% confidence interval for the population proportion of disks which are defective is (0.059, 0.079).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose a sample of 1067 floppy disks is drawn. Of these disks, 74 were defective.
This means that [tex]n = 1067, \pi = \frac{74}{1067} = 0.069[/tex]
80% confidence level
So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.069 - 1.28\sqrt{\frac{0.069*0.931}{1067}} = 0.059[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.069 + 1.28\sqrt{\frac{0.069*0.931}{1067}} = 0.079[/tex]
The 80% confidence interval for the population proportion of disks which are defective is (0.059, 0.079).
Solve for the letter d
Answer:
34 I am pretty sure
Step-by-step explanation:
34+55 well is 89 so yeah d=34
Jackie wants to buy a $25,000 car, but she can afford to pay only $400 per month for 5 years. If the interest rate is 8.25% compounded monthly, how much does she need to put down?
Answer:
A down payment of $5,388.50 to get the principle to $19611.50 for a monthly payment of $400 for 60 months at 8.25%
Step-by-step explanation:
I used a payment calculator
I don't know how else to solve the problem. I thought I could find the equation, but I don't think this is it, since P didn't equal 19611.50
A = P[r(1+r)n] / [(1+r)n - 1]
if you have the correct formula follow this process
A = 400 P principle ??? r = i%/12 = 0.0825/12 = 0.006875 n= 5×12 = 60
solve for P then down payment = 25000 - P
P = A / [r(1+r)n] / [(1+r)n - 1]
= A [(1+r)n - 1] / [r(1+r)n]
= 400 [(1 +.006875)60 -1] / [0.006875( 1 +0.006875)60]
PLS HELP Find the value of x .
the answer is 6
8+10=18
12+?=18
12+6=18
Referring to the figure, find the volume of the solid shown. Round to the nearest whole number. Will mark brainliest...
Answer:
648
Step-by-step explanation:
FInd volume of bottom half (9x6x12)
find voume of pyramid 1/3Bh 1/3(11)(54)
Ixl . R.8 Trigonometric ratios : Find a side length
Help please
Find FG
Answer:
FG = 2.02
Step-by-step explanation:
tan 56° = 3/FG
1.4826 = 3/FG
1.4826FG = 3
divide both sides by 1.4826:
FG = 3/1.4826
FG = 2.02
124 oz =
Ib
I need help
Answer:
7.75
Step-by-step explanation:
Remember, 1 ounce equals 0.0625 pounds.
Multiply 124 x 0.0625 to get you answer.
Hope this helps,If you have any questions revolving around this topic,feel free to ask me,Good luck!
3. Which reason can be used to conclude that DFGH is a parallelogram?
a) There are two pairs of congruent opposite angles.
D
b) The diagonals bisect each other.
c) There are two pairs of congruent opposite sides.
d) There are two pairs of opposite parallel sides.
Answer:
D) There are two pairs of opposite parallel sides.
Step-by-step explanation:
A parallelogram is a four-sided plane rectilinear figure with opposite sides that are parallel.
brainiest exchange give me and I will give you 2+2
Answer:
4
Step-by-step explanation:
and sure
Answer:
4
Step-by-step explanation: