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
80 81 82 83 84 85 86 87 88 89 90
Anika's test scores are shown below.
Anika's Test Scores
80 81 82 83 84 85 86 87 88 89 90
Which statement compares the shape of the two dot plots?
There is a gap in both plots.
There is a gap in Anika's scores, but not in Lorenzo's scores.
The data is widely spread across both plots.
The data is more widely spread for Lorenzo's scores than for Anika's.
Mark this and return
Save and Exit
Answer:
D :)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Braily please
What is the final amount if 700 is increased by 4% followed by a further 3% increase
Answer:
8400
Step-by-step explanation:
Its too long and I answered it before
Once a bill leaves the Congress, how can a bill become a law? (Select all that anny
Answer:
Once both the House and Senate have approved the bill in identical form, it becomes "Enrolled" and sent to the President of the United States. The President may sign the bill into law. The President can also take no action on the bill for ten days while Congress is in session and the bill will automatically become law.
A 17-inch candle is lit and burns at a constant rate of 1.3 inches per hour. Let t represent the number of hours since the candle was lit, and suppose f is a function such that f ( t ) represents the remaining length of the candle (in inches) t hours after it was lit. Write a function formula for f . f ( t )
Answer
Since the lyla deleted it actually for a good reason let me explain. But you dont just delete random answers, you can give a comment. I can report you for doing that.
So since it burns at 1.3 per hour. Notice that since it gets removed per hour. so it would be 1.3t so it multiplies per hour. Then we need to subtract. Thats because it lowers the length of the candle. So we get the original length - 17 and get the function
f(t) = 17-1.3t
Josslyn is thinking of a number, n and she wants her sister to guess the number. Her first clue is that seven less than six times her number is between negative one and twenty-nine (inclusive). Write a compound inequality that shows the range of number that Josslyn might be thinking of.
Answer:
1<X<=6
Step-by-step explanation:
seven less than six times her number is between negative one and twenty-nine (inclusive).
The above statement can be expressed mathematically thus;
Let the number be x
6x-7= (-1 ,29]
Hence 6x-7 = -1=>6x=6=>x=1 or
6x-7= 29=>6x=36=>x=6
Hence 1<X<=6
For a long-distance person-to-person telephone call, a telephone company charges $ 0.72 for the first minute, $ 0.42 for each additional minute, and a $ 1.85 service charge. If the cost of a call is $ 8.03 comma how long did the person talk?
Answer:
13 mins
Step-by-step explanation:
8.03- 1.85= 6.18
-.72=5.46
/.42=13
Please answer this correctly
Answer:
12 2/5 hours
Step-by-step explanation:
[tex]1+1+1\frac{1}{5} +1\frac{1}{5} +1\frac{1}{5} +1\frac{3}{5} +1\frac{3}{5} +1\frac{4}{5} +1\frac{4}{5} =\\\\2+3\frac{3}{5} +3\frac{1}{5} +3\frac{3}{5} =\\\\11\frac{7}{5} =\\\\12\frac{2}{5}[/tex]
12 2/5 hours have been logged in all.
The bottom of a ladder must be placed 3 ft. from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall? Round your answer to the nearest tenth.
Use the Pythagorean theorem to solve.
Height = sqrt(12^2 -3^2)
Height = sqrt(144-9)
Height = sqrt(135)
Height = 11.6189 = 11.6 feet
A manager records the repair cost for 4 randomly selected stereos. A sample mean of $82.64 and standard deviation of $14.32 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
CI = (70.861 , 94.418)
Step-by-step explanation:
In order to determine the 90% confidence interval you use the following formula (for a population approximately normal):
[tex]CI=(\overline{x}-Z_{\alpha/2}\frac{\sigma}{\sqrt{n}},\overline{x}+Z_{\alpha/2}\frac{\sigma}{\sqrt{n}})[/tex] (1)
[tex]\overline{x}[/tex]: mean = 82.64
σ: standard deviation = 14.32
n: sample = 4
α: tail area = 1 - 0.9 = 0.1
Z_α/2 = Z_0.05: Z factor = 1.645
You replace these values and you obtain:
[tex]Z_{0.05}(\frac{14.32}{\sqrt{4}})=(1.645)(\frac{14.32}{\sqrt{4}})=11.778[/tex]
The confidence interval will be:
[tex]CI=(82.64-11.778,82.64+11.778)=(70.861,94.418)[/tex]
The 90% confidence interval is (70.861 , 94.418)
what are the answers to the following quadratic equation:
x^2-4x-12
Answer:
6 and -2
Step-by-step explanation:
x^2-4x-12
set up equal to zero
x^2-4x-12=0
lets factor:
(x-6)(x+2)=0
x-6=0
x=6
or
x+2=0
x=-2
Answer:
x=6 x=-2
Step-by-step explanation:
x^2-4x-12 = 0
Factor
What two numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6)(x+2) =0
Using the zero product property
(x-6) =0 x+2 = 0
x=6 x=-2
luvenia can row 4mph in still water. She takes as long to row 7 mi upstream as 21 mi downstream. how
Answer:
The speed of the river is 2mph.
Step-by-step explanation:
I guess that we want to find the speed of the river.
First, remember the relation: speed*time = distance
If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:
Sd = 4mph + Sr
and at this speed, in a time T, she can move 21 miles, so we have:
Sd*T = (4mph + Sr)*T = 21 mi
When moving upstream, the speed will be:
Su = (4mph - Sr)
and in the same time T as before, she moves 7 miles, so we have the equation:
Su*T = (4mph - Sr)*T = 7 mi
Then we have two equations:
(4mph + Sr)*T = 21 mi
(4mph - Sr)*T = 7 mi
Now we can take the quotient of those two equations and get:
((4mph + Sr)*T)/((4mph - Sr)*T) = 21/7
The time T vanishes, and we can solve it for Sr.
(4mph + Sr)/(4mph - Sr) = 3
4mph + Sr = 3*(4mph - Sr) = 12mph - 3*Sr
4*Sr = 12mph - 4mph = 8mph
Sr = 8mph/4 = 2mph.
George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 9 feet per second. Paula takes 50 seconds to run a lap of the track. George and Paula pass each other after 14 seconds.
After running for 4 minutes, how far east of his starting point is George?
Answer:
George is 43.20 ft East of his starting point.
Step-by-step explanation:
Let Paula's speed be x ft/s
George's speed = 9 ft/s
Note that speed = (distance)/(time)
Distance = (speed) × (time)
George takes 50 s to run a lap of the track at a speed of y ft/s
Meaning that the length of the circular track = y × 50 = 50y ft
George and Paula meet 14 seconds after the start of the run.
Distance covered by George in 14 seconds = 9 × 14 = 126 ft
Distance covered by Paula in 14 seconds = y × 14 = 14y ft
But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track
That is,
126 + 14y = 50y
50y - 14y = 126
36y = 126
y = (126/36) = 3.5 ft/s.
Hence, Paula's speed = 3.5 ft/s
Length of the circular track = 50y = 50 × 3.5 = 175 ft
So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of
9 × 240 = 2160 ft.
2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.
Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft
So, 60 ft along a circular track subtends an angle θ at the centre of the circle.
Length of an arc = (θ/360°) × 2πr
2πr = total length of the circular track = 175
r = (175/2π) = 27.85 ft
Length of an arc = (θ/360) × 2πr
60 = (θ/360°) × 175
(θ/360°) = (60/175) = 0.343
θ = 0.343 × 360° = 123.45°
The image of this incomplete lap is shown in the attached image,
The distance of George from his starting point along the centre of the circular track = (r + a)
But, a can be obtained using trigonometric relations.
Cos 56.55° = (a/r) = (a/27.85)
a = 27.85 cos 56.55° = 15.35 ft
r + a = 27.85 + 15.35 = 43.20 ft.
Hence, George is 43.20 ft East of his starting point.
Hope this Helps!!!
Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 250 companies to invest in. After 1 year, 135 of the companies were considered winners; that is, they outperformed other companies in the same investment class. To assess whether the dart-picking strategy resulted in a majority of winners, the researcher tested Upper H 0: pequals0.5 versus Upper H 1: pgreater than0.5 and obtained a P-value of 0.1030. Explain what this P-value means and write a conclusion for the researcher.
Answer:
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
The population proportion is equal to 0.5
Step-by-step explanation:
Step (i):-
Given random sample size ' n' = 250
Sample proportion 'p'
[tex]p= \frac{x}{n} = \frac{135}{250} = 0.54[/tex]
Given Population proportion P = 0.5
Q = 1-P = 1-0.5 =0.5
Null Hypothesis : H₀ : P = 0.5
Alternative Hypothesis : H₁ : P≥ 0.5
Step(ii):-
Test statistic
[tex]Z = \frac{p - P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.54-0.5}{\sqrt{\frac{0.5 X 0.5}{250} } }[/tex]
Z = 1.2903
Level of significance α = 0.05
Z₀.₀₅ = 1.96
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
Step(iii):-
P- value
The probability of test statistic
P(Z > 1.2903) = 0.5 - A ( 1.2903)
= 0.5 - 0.4015
= 0.0985≅ 0.10
i) P- value =0.10 > α = 0.05
null hypothesis is accepted
Conclusion:-
The population proportion is equal to 0.5
What is the answer to 3ab + 3ac
Answer: 3ab + 3ac
Step-by-step explanation: Although the terms in this problem look like one another, there are no like terms.
Therefore, this problem cannot be simplified.
So the answer is the same as the question.
Please help! Correct answer only, please! Find the following product if possible. Explain if it is not possible. A. B. C. D.
Answer: A
Step-by-step explanation:
To multiply matrices, multiply each term in Row 1 of the first matrix with each term in Column 1 of the second matrix and then find their sum. Repeat for Row1×Column2, Row2×Column1, and Row2×Column2.
[tex]\left[\begin{array}{ccc}1&4&-1\\3&2&2\end{array}\right] \times \left[\begin{array}{cc}2&-1\\0&3\\5&2\end{array}\right] \\\\\\=\left[\begin{array}{ccc}1(2)+4(0)-1(5)&1(-1)+4(3)-1(2)\\3(2)+2(0)+2(5)&3(-1)+2(3)+2(2)\end{array}\right] \\\\\\=\left[\begin{array}{cc}-3&9\\16&7\end{array}\right][/tex]
which set of sides make a right triangle
Answer:
A right triangle consists of two legs and a hypotenuse.
Step-by-step explanation:
The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.
A sphere and a cylinder have the same radius and height.the volume of the cylinderis 48cm3
Answer:
32 cm^3.
Step-by-step explanation:
Formulas for calculating:
sphere's volume - ;[tex]V_{sphere}=\frac{4\pi r^3}{3}[/tex]
cylinder's volume - .[tex]V_{cylinder}=\pi r^2 h[/tex]
Note that h=2r (height of the sphere consists of two radius).
Then [tex]V_{cylinder}= \pi r^2 h=\pi r^2 2r= 2\pi r^3[/tex]
Since [tex]V_{sphere}= \frac{4\pi r^3}{3}[/tex]
on calculating we get
[tex]V_{cylinder}= \frac{3V_{sphere}}{2}\\ \Rightarrow V_{sphere}=\frac{2V_{cylinder}}{3} =\frac{2\times48}{3} =32 cm^3[/tex]
What postulate would justify the following statement?
If D is between A and B, than AD+DB=AB
Answer:
A, D and B must be in a straight line.
Step-by-step explanation:
If D is between A and B, than AD+DB=AB
This would mean A, D and B would be in a straight line.
Zelie planned for a square pool to have a side length of 28 ft but found that it needs to be 14 ft long to fit in her backyard. She found the change of scale below. Which is Zelie’s error? Zelie should have divided both numbers by 14. Zelie should have written the ratio as 28/7. Zelie should have written the ratio as 14/8. Zelie should have subtracted 14 from both numbers.
Answer:
Zelie should have divided both numbers by 14 to find the scale (2)
Step-by-step explanation:
Answer:
the answers A.
Step-by-step explanation:
I TOOK THE QUIZ edg 2020
Find the exact length of the third side. (Pythagorean Theorem)
Answer:
3 sqrt(5) =c
Step-by-step explanation:
We can use the pythagorean theorem
a^2 + b^2 = c^2
3^2 + 6^2 = c^2
9+36 = c^2
45 = c^2
Take the square root of each side
sqrt(45) = sqrt(c^2)
sqrt(9)sqrt(5) = c
3 sqrt(5) =c
3.
B
С
A
D
E
How many rays intersect at point o?
what is the dot product of vectors
Answer:
The dot product of vectors is the method used to "multiply" vecotrs since vectors aren't directly multiplieable
Step-by-step explanation:
what is 12/5 as a mixed nunber
Answer:
2 2/5
Step-by-step explanation:
12/5
5 goes into 12 2 times
12 - 5*2
12-10 =2
There is 2 left over. This goes over the denominator
2 2/5
Please answer...i always answer... please
Answer:
A) -x + y = 2
B) x + 2y = 4
we add both equations
3 y = 6
y = 2
We put y = 2 into equation B)
x + 2 * 2 = 4
x = 0
***********************************************
A) -2x + y = 6
B) x + y = 0
We multiply B) by 2
B) 2 x + 2 y = 0 then we add A)
A) -2x + y = 6
3y = 6
y = 2
Therefore x = -2
Step-by-step explanation:
In the diagram below, measure of arcABC = 230º.
What is the measure of
Answer:
65°
Step-by-step explanation:
Short arc AC is the difference between 360° and long arc ABC:
arc AC = 360° -230° = 130°
The inscribed angle ABC that intercepts this short arc will have half the measure of the arc:
∠ABC = 130°/2 = 65°
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of credit card customers. Click on the datafile logo to reference the data.
a. Develop hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national.b. The file Eagle contains the sample data. Develop a point estimate of the population proportion.c. Use αα= .05 to conduct your hypothesis test. Should Eagle go national with the promotion?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. It is considering a promotion that involves mailing discount coupons to all its credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers. Out of the 100 customers, 13 customers said that they used the discount coupons to make a purchase at a Eagle Outfitters store. Use a 0.05 level of significance. (a) Develop the null and alternative hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national. (b) Compute the sample proportion. (c) Compute the test statistic. (d) Compute the critical value. (e) Based on the critical value, do we reject H0 or do we not reject H0? (f) Based on the result of the hypothesis test, should Eagle Outfitter go national with the promotion?
Solution:
a) We would set up the hypothesis test.
For the null hypothesis,
H0: p ≥ 0.1
For the alternative hypothesis,
Ha: p < 0.1
This is a left tailed test
Considering the population proportion, probability of success, p = 0.1
q = probability of failure = 1 - p
q = 1 - 0.1 = 0.9
b) Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 13
n = number of samples = 100
p = 13/100 = 0.13
c) We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.13 - 0.1)/√(0.1 × 0.9)/100 = 1
The calculated test statistic is 1 for the right tail and - 1 for the left tail.
d) Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.51/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
e) In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Since - 1 > - 1.96 and 1 < 1.96, we would fail to reject the null hypothesis.
Therefore, based on the result of the hypothesis test, the Eagle Outfitter should go national with the promotion
2. {5.0A.A.1, 5.0A.A.2} Write an expression to show....the product of eight
and two, minus the product of three and four. *
Answer:
[tex]\left ( 8\times 2 \right )-\left ( 3\times 4 \right )[/tex]
Step-by-step explanation:
Given: The statement is ' the product of eight and two, minus the product of three and four'
To find: expression for the given statement
Solution:
An algebraic expression is an expression consists of coefficients, variables, and the arithmetic operations.
Product of eight and two = [tex]\left ( 8\times 2 \right )[/tex]
Product of three and four = [tex]\left ( 3\times 4 \right )[/tex]
Therefore,
Product of eight and two, minus the product of three and four = [tex]\left ( 8\times 2 \right )-\left ( 3\times 4 \right )[/tex]
. A certain coin is a circle with diameter 18 mm. What is the exact area of either face of the coin in terms of p?
Answer:
[tex] r =\frac{D}{2}=\frac{18mm}{2}= 9mm[/tex]
The area is given by:
[tex]A= \pi r^2[/tex]
And replacing we got:
[tex] A=\pi (9mm)^2 =81\pi mm^2[/tex]
So then we can conclude that the area of the coin is [tex] 81\pi[/tex] mm^2
Step-by-step explanation:
For this case we know that we have a coin with a diamter of [tex] D =18mm[/tex], and by definition the radius is given by:
[tex] r =\frac{D}{2}=\frac{18mm}{2}= 9mm[/tex]
The area is given by:
[tex]A= \pi r^2[/tex]
And replacing we got:
[tex] A=\pi (9mm)^2 =81\pi mm^2[/tex]
So then we can conclude that the area of the coin is [tex] 81\pi[/tex] mm^2
I don’t know if it’s g(2(5)(3(5)^2-5-5
Answer:
B. 135
Step-by-step explanation:
For ...
f(x) = 3x^2 -xg(x) = 2x -5f(5) = 3·5^2 -5
= 3·25 -5 = 75 -5 = 70
Then g(f(5)) is ...
g(f(5)) = g(70) = 2·70 -5 = 140 -5
g(f(5)) = 135 . . . . . matches choice B
Which pairs of non-overlapping angles share a ray to make a right angle?
Answer:
JGH and JGF
Step-by-step explanation:
Both adjacent and make a right angle
∠KGJ and ∠FGH are the pairs of non-overlapping angles that share a ray to make a right angle.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
In the given figure, we need to find the pairs of non-overlapping angles that share a ray to make a right angle.
We can see that ∠EGF and ∠HGF make a right angle but line FG is overlapping or common in both the angles.
∠KGJ and ∠FGH make a right angle and pairs of non-overlapping angles.
So, this is the correct pair for the condition.
Learn more about a right angle;
https://brainly.com/question/7116550