Answer:
difference in area = 16 ft²
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
Step-by-step explanation:
Jacks rectangular patio
width = a
length = 2a - 1
area = lw
where
l = length
w = width
area = 120 ft²
a(2a - 1)
2a² - a - 120 = 0
(a - 8) (2a + 15)
a = 8 or -15/2
Ron's rectangular patio
width = a
length = a + 5
area = lw
area = 104 ft²
a (a + 5) = 104
a² + 5a -104 = 0
(a + 8) (a - 13)
a = -8 or 13
How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,
120 - 104 = 16 ft²
The value 8 or 13 can be used for a since the width a have to be the same.
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
Please answer this correctly
Answer:
10-19 ⇒ 3
50-59 ⇒ 4
Answer:
# of ties # of racks
10-19 3
50-59 4
Step-by-step explanation:
Using the Stem and Leaf plot, our data is:
11, 12, 16
21
32, 34, 36, 37, 39
41, 45
51, 52, 53, 56
# of ties # of racks
10-19 3 (11, 12, 16)
50-59 4 (51, 52, 53, 56)
А
What is the measure of ZDAB?
&
B
Enter your answer in the box.
D
96°
C
Next
Answer:
84°
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary:
∠A = 180° -96°
∠A = 84°
i need help in homework no guess
Answer:
No
Step-by-step explanation:
Use the vertical line test. If the line intercepts more than one point, it is not a function. Since there are two points where the value of 'x' is two, the line will pass both points. The graph is not a function.
Which steps can be used to solve for the value of y?
(2013
(y +57) = 178
Answer: [tex]y = 121[/tex]
[tex](y+57) = 178[/tex]
[tex]y+57= 178[/tex]
[tex]y = 178 -57[/tex]
[tex]y = 121[/tex]
Which is required for sexual reproduction?
Answer:
2 parents are required
Step-by-step explanation:
Answer:
semen.............
Please help me with this problem
Answer:
10
-5
Step-by-step explanation:
5 - -5
Subtracting a negative is like adding
5+5 = 10
-9 - -4
-9+4
-5
Answer:
Step-by-step explanation:
5+5 = 10
-9+4 = -5
A marketing analyst randomly surveyed 150 adults from a certain city and asked which type of tooth paste they were currently using - Extra Whitening or Regular. 96 said they were currently using Extra Whitening while the rest said they were using Regular. The analyst wants to determine if this is evidence that more than half of the adults in this city are using Extra Whitening. Suppose a p-value from the correct hypothesis test was 0.0003. Which of the following is a correct interpretation of this p-value?
A. HA: p_extra White > p_Regular.
B. HA: p > 0.5, where p = the proportion of all adults in this city using Extra Whitening.
C. HA: p = 0.64, where p = the proportion of all adults in this city using Extra Whitening.
D. HA: p=0.5, where p = the proportion of all adults in this city using Extra Whitening.
A garden measuring 12 meters by 6 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 160 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).
Answer:
x=2
Step-by-step explanation:
Original width = 6
New width 6+x+x
Orignal length 12
New length 12+x+x
A = l*w
160 = ( 6+2x) ( 12+2x)
Factor
160 = 2( 3+x) 2(6+x)
Divide each side by 4
40 = (3+x) (6+x)
FOIL
40 = 18+ 6x+3x+ x^2
40 = 18 +9x+x^2
Subtract 40 from each side
0 = x^2 +9x -22
Factor
0 = (x +11) (x-2)
Using the zero product property
x +11 =0 x-2 =0
x= -11 x=2
Since we cannot have a negative sidewalk
x =2
Answer:
2
Step-by-step explanation:
Original width = 6
New width = 6 + x + x = 6 + 2x
Orignal length = 12
New length = 12 + x + x = 12 + 2x
A = l * w
160 = (6 + 2x)(12 + 2x)
160 = 2(3+x) * 2(6+x)
160 = 4 * (3 + x)(6 + x)
160/4 = (3 + x)(6 + x)
40 = 18 + 6x + 3x + x^2
40 = 18 + 9x + x^2
x^2 + 9x - 22 = 0
= x^2 + 11x - 2x - 22 = 0
= x(x + 11) - 2(x + 11) = 0
= (x + 11) (x - 2) = 0
x = - 11, 2
Since we cannot have a negative width because it's a dimension,
x = 2 is right
Share 32 beads between Joshua and kitty in the ratio 6:10 How much does Joshua gets ? Beads and kitty gets ?
Answer:one would get 12 one would get 20
Step-by-step explanation:just plug it in to the equation
Very confused, need help quick! (see attachment) Simplify and show your work.
Answer:
27/(4x^6y^8)
Step-by-step explanation:
Target the variables first. (x^a)^b is the same as x^(a x b).
In the numerator, it is x^(2 x 3) , which is x^6, and y^(4 x 3), which is y^12.
Same principle on the bottom. the denominator is x^12 and y^20.
In the numerator, the number 4 is alone so don't do anything to it. Cube 3. The coefficient of the numerator is 4 x 3^3 . The coefficient of the denominator is 2^4. Cancel like terms. when you divide same terms' exponents, you subtract the exponent on top by the exponent on the bottom. Remember that you can only simplify LIKE terms. (x with x, y with y, number with number.)
Please answer this correctly
Answer:
20 total
Shelves 3 shelves /20 total=0.15=15%
Signs 2/20=0.10=10%
Benches 6/20=0.30=30%
Tablet Holders 9/20=0.45=45%
Step-by-step explanation:
Answer:
Shelves: 15%
Signs: 10%
Benches: 30%
Tablet Holders: 45%
Step-by-step explanation:
Shelves: [tex]\frac{3}{3+2+6+9} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%
Signs: [tex]\frac{2}{3+2+6+9} =\frac{2}{20} =\frac{10}{100} =[/tex] 10%
Benches: [tex]\frac{6}{3+2+6+9} =\frac{6}{20} =\frac{30}{100}=[/tex] 30%
Tablet Holders: [tex]\frac{9}{3+2+6+9} =\frac{9}{20} =\frac{45}{100} =[/tex] 45%
PLEASE HELP
Compare the number of x intercepts of f(x)=x^2 and g(x)= (x-4)^2. Tell me the transformations involved and how g(x) moves from the parent graph.
Answer
g(x) moves 4 spaces to the left compared to f(x),
when g(4)=0 when f(0)=0
when g(3)=1 when f(-1)=1
...
and so on
What sit he shape of the cross section formed when’s. Cone intersects a plane as shown in the drawing?
Give me a reason why tok
Answer: Option D.
Step-by-step explanation:
Here we see the cross-section of a cone when it is cut by a plane that is parallel to the base of the cone.
As the plane is parallel to the base, we expect to see a figure that has the same shape as the base ( a circle) (you can think that over the plane we have a smaller cone, and the base of that cone also must be circular)
So the correct option is D.
Order the numbers from least to greatest based on their absolute values.
|23|, |−37|, |−6|, |18|, |−24|, |2|
Answer:
/-37/, /-24/, /-6/, /2/, /18/, /23/
A commuter uses a bus and a train to get to work. The train is more than 5 minutes late 1/6 of the times they use it The bus is more than 5 minutes late 3/5 of the times they use it. What is the probability that both the bus and train will be more than 5 minutes late?
Answer:
10% probability that both the bus and train will be more than 5 minutes late
Step-by-step explanation:
Independent events:
If two events, A and B, are independent, we have that:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
What is the probability that both the bus and train will be more than 5 minutes late?
The bus being more than 5 minutes late is independent of the train, and vice versa. So
Event A: Bus more than 5 minutes late
Event B: Train more than 5 minutes late
The train is more than 5 minutes late 1/6 of the times they use it
This means that [tex]P(B) = \frac{1}{6}[/tex]
The bus is more than 5 minutes late 3/5 of the times they use it.
This means that [tex]P(A) = \frac{3}{5}[/tex]
Then
[tex]P(A \cap B) = \frac{3}{5}*\frac{1}{6} = \frac{3}{30} = 0.1[/tex]
10% probability that both the bus and train will be more than 5 minutes late
The function s(t) represents the position of an object at time t moving along a line. Suppose s (1 )equals 62 and s (5 )equals 102. Find the average velocity of the object over the interval of time [1 comma 5 ].
Answer:
v = 10
the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time
Step-by-step explanation:
Given;
function s(t) represents the position of an object at time t moving along a line.
s(1) = 62 at t1 = 1
s(5) = 102 at t5 = 5
Velocity v = distance/time
Average velocity v over time t is;
v = ∆s/∆t
v = [s(5) - s(1)]/[t5 - t1]
Substituting the given values;
v = (102 - 62)/(5 - 1)
v = 10
the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.6 mm.(a)What is the probability that defect length is at most 20 mm
Answer:
14.69% probability that defect length is at most 20 mm
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 28, \sigma = 7.6[/tex]
What is the probability that defect length is at most 20 mm
This is the pvalue of Z when X = 20. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 28}{7.6}[/tex]
[tex]Z = -1.05[/tex]
[tex]Z = -1.05[/tex] has a pvalue of 0.1469
14.69% probability that defect length is at most 20 mm
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.19degreesF and a standard deviation of 0.61degreesF. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.36degreesF and 100.02degreesF? b. What is the approximate percentage of healthy adults with body temperatures between 96.97degreesF and 99.41degreesF?
Answer:
a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
b) [tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
Step-by-step explanation:
For this case we know that the distribution of the temperatures have the following parameters:
[tex] \mu = 98.19, \sigma =0.61[/tex]
Part a
From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
Part b
We can calculate the number of deviations from the mean with the z score with this formula:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And using this formula we got:
[tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
Solve: x - 1 < 3 help me plssss
Answer:
x =2
Step-by-step explanation:
becaue 2-1 is smaller than 3
Answer:
Hello!
I believe your answer is:
x=2
If this is not correct, please let me know and I will try again!
Step-by-step explanation:
Mitch opened a retirement account that has an annual yield of 4.2% compounding annually. He is planning on retiring in 13 years. How much must he deposit into that account each year so that he can have a total of $1,000,000 by the time he retires?
Answer:
P = 4878
Step-by-step explanation:
So we'll use the formula
A = p(1+r/n)^ (nt)
A = 1000000
P is the unknown
R = 4.2
N = 13
T = 13
1000000= p ( 1+ 0.42/13)^ 169
1000000 = p (1.032)^169
1000000= p 205
P = 4878
what is 2n+3n +1 +8n+4
Answer:
13n + 5
Step-by-step explanation:
2+3+8 = 13n
1+4 = 5
13n+5
Please help me please I’m stuck please
[tex]answer \\ 9 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Answer:
9
Step-by-step explanation:
The ratio of 5 to 5+3 is equivalent to the ratio of 15 to 15+x. This is because when you have a triangle inside of a triangle and both of them share two of the same sides and the third sides are parallel to each other, the side ratios of the triangles are always proportionate.
[tex]\frac{5}{5+3} =\frac{15}{15+x}[/tex] Starting equation
[tex]\frac{5}{8} =\frac{15}{15+x}[/tex] Simplify
[tex]5(15+x)=8*(15)[/tex] Cross multiply
[tex]75+5x=120[/tex] Distributive Property on left and simplify on right
[tex]5x=45[/tex] Isolate the variable
[tex]x=9[/tex] Divide both sides by 5 (Division Property of Equality)
Twice the length of the rectangle exceeds three times the width of the rectangle by one centimeter and if one-third of the difference of the length and the width is one centimeter.find the dimension.
The dimensions of the rectangle are given as 4cm and 1cm respectively.
What is a rectangle?A rectangle is a type of parallelogram having equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
Suppose the length of rectangle be x.
And, the width be y.
Then, the following equations can be written as per the information given as,
2x - 3y = 1 (1)
And, 1/3(x - y) = 1
⇒ x - y = 3 (2)
Multiply equation (2) by 2 and subtract from (1) to get,
2x - 3y - 2(x - y) = 1 - 2 × 3
⇒ -5y = -5
⇒ y = 1
Substitute y = 1 in equation (2) to get,
x - 1 = 3
⇒ x = 4
Hence, the dimensions are 4cm and 1cm respectively.
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Find the value of z Subscript alpha divided by 2 that corresponds to a confidence level of 89.48%.
Answer:
For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]
Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:
[tex] z_{\alpha/2}= \pm 1.62015[/tex]
And we can use the following excel code for example:
"=NORM.INV(0.0526,0,1)"
Step-by-step explanation:
For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]
Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:
[tex] z_{\alpha/2}= \pm 1.62015[/tex]
And we can use the following excel code for example:
"=NORM.INV(0.0526,0,1)"
Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 12 ft high? (Round your answer to two decimal places.)
Answer:
0.13 ft/min
Step-by-step explanation:
We are given that
[tex]\frac{dV}{dt}=15ft^3/min[/tex]
We have to find the increasing rate of change of height of pile when the pile is 12 ft high.
Let d be the diameter of pile
Height of pile=h
d=h
Radius of pile,r=[tex]\frac{d}{2}=\frac{h}{2}[/tex]
Volume of pile=[tex]\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3[/tex]
[tex]\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}[/tex]
h=12 ft
Substitute the values
[tex]15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}[/tex]
[tex]\frac{dh}{dt}=0.13ft/min[/tex]
1. In an arithmetic sequence, the first term is -2, the fourth term is 16, and the n-th term is 11,998
(a) Find the common difference d
(b) Find the value of n.
pls help...
Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
(a)
Given a₁ = - 2 and a₄ = 16, then
a₁ + 3d = 16 , that is
- 2 + 3d = 16 ( add 2 to both sides )
3d = 18 ( divide both sides by 3 )
d = 6
--------------
(b)
Given
[tex]a_{n}[/tex] = 11998 , then
a₁ + (n - 1)d = 11998 , that is
- 2 + 6(n - 1) = 11998 ( add 2 to both sides )
6(n - 1) = 12000 ( divide both sides by 6 )
n - 1 = 2000 ( add 1 to both sides )
n = 2001
------------------
Account A and Account B both have a principal of $2,000 and an annual interest rate of 5%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?
Answer:
Which earns more interest = Account B
How much more = $1,306.60
Step-by-step explanation:
Given;
Principal P = $2,000
Interest rate r = 5% = 0.05
Time t = 20 years
For account A;
Simple interest = P×r×t
Substituting the values;
Simple interest = 2,000 × 0.05 × 20 = $2000
Interest on account A = $2,000
For account B;
Compound interest
Final amount = P(1 + r)^t
Since it's compounded annually
Substituting the values;
Final amount = 2000(1+0.05)^20
Final amount = $5306.60
Interest = final amount - principal = $5306.60 -$2000
Interest = $3,306.60
Therefore, account B earns more interest.
Difference = account B interest - account A interest
Difference = $3,306.60 - $2,000
Difference = $1,306.60
Find the missing side. Round to
the nearest tenth.
x
9
28°
x = [?]
Answer:
19.2
Step-by-step explanation:
It's right on Acellus.
The required value of x nearest to tenth is 19.17
What is hypotenuse?The longest side of the right angled triangle is called hypotenuse
By the Pythagoras theorem in the right angled triangle
h^2 = b^2 + p^2
where h = hypotenuse, b = base, p = perpendicular
How to calculate hypotenuse?Here we have given perpendicular p = 9
and an angle = 28°
Using sin for the given angle we have
sin 28° = [tex]\frac{perpendicular}{hypotenuse}[/tex]
0.46947 = [tex]\frac{9}{x}[/tex]
x = [tex]\frac{9}{0.46947}[/tex]
x = 19.17
Hence the required length of the side hypotenuse = x = 19.17
This is the conclusion to the answer.
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What is the next number in the sequence: 3, 8, 12, 48, 29, __
Answer:
144
Step-by-step explanation:
Answer:
116
Step-by-step explanation:
3x4=12
12x4=48
8x4=32
32-3=29
29x4=116
Hope it's clear
A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.5 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?
Answer:
[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
Step-by-step explanation:
Information given
[tex]\bar X=25.5[/tex] represent the sample mean
[tex]s=1[/tex] represent the sample standard deviation
[tex]n=8[/tex] sample size
[tex]\mu_o =26[/tex] represent the value to verify
[tex]\alpha=0.06[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to est
We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 25.5[/tex]
Alternative hypothesis:[tex]\mu < 25.5[/tex]
The statistic for this case is given by;
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
