Answer:
8√2
Step-by-step explanation:
4√(10) -2
= 4√8
=4√4×2
=4×2√2
=8√2
Given: Measure of arc AB = measure of arc BC,
Measure of angle x = 60°, measure of angle y = 15°
Find: Measure of arc AC
9514 1404 393
Answer:
100°
Step-by-step explanation:
The relevant relation for angle x is ...
x = (AB +DE)/2
and for angle y, it is ...
y =(AC -DE)/2
Using the second relation to write an expression for DE, we have ...
DE = AC -2y
In the first equation, this lets us write ...
x = (AB +(AC -2y))/2 = (AB +(2AB -2y))/2
2x = 3AB-2y . . . . . . . . . . . . . . multiply by 2
(2x +2y)/3 = AB = AC/2 . . . . . add 2y; divide by 3
AC = (4/3)(x +y) = (4/3)(60° +15°) . . . . multiply by 2, substitute known values
AC = 100°
(b) In a company, out of 20 candidates 14 men and 6 women apply for two vacancies. What is the probability that (1) both men are selected ? (ii) both women are selected ? (iii) one man and one woman are selected ?
i hope my answer helps you and you will give me the best answer
A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the planned implementation. Managers are considering holding informational workshops to help decrease anxiety levels among employees. To determine whether such an approach would be effective, they randomly select 16 employees to participate in a pilot workshop. These employees were given a questionnaire to measure anxiety levels about ERP before and after participating in the workshop. Do the data indicate that anxiety levels about ERP decreases as a result of the workshop
Answer:
From the data The anxiety levels decreases as a result of the workshop
given that the mean value of the differences = -1.1125
Step-by-step explanation:
Number of randomly selected employees = 16
From the data It can be noticed that the difference in anxiety levels decrease ( Tends towards values below 0 )
To determine this we have to determine the mean value of the differences
(-3) + (-3) + (-2) +(-2) +(-2) + (-2 ) + (-1) + (-1) + (-1) + (-1) + (-1 ) + 0 + 0 + 0 + 0 + 1 / 16
= -18 / 16 = - 1.1125
mean value = -1.1125.
Hi there!i am confused about this equation. Please help to solve this.
Answer:
Step-by-step explanation:
Short of taking 3 hours to type out the way that I did this, let me just tell you the process. Square both sides and multiply to distribute. You end up with radicals still, so square both sides again and multiply to distribute. What you end up with is a 6th degree polynomial that has to be factored. What I got in the end were these zeros:
x = 21.41917943
x = 1.306542114+/-7186864435i
x = -1.066667927
x = 1.28038353
x = 1.28038353
x = -.2459792634
Marie's backyard deck cost $68.29 per square meter to build. The deck is 9 meters wide and 9 meters long. How much did it cost to build the deck?
$5531.49
(9×9)×$68.29
A rectangle auditorium seats 1260 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row
Answer:
Easy, all you ha
Step-by-step explanation:
A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area
Answer:
11 meters
Step-by-step explanation:
First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).
The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is
(√3/4)((11-4x)/3)²
= (√3/4)(11/3 - 4x/3)²
= (√3/4)(121/9 - 88x/9 + 16x²/9)
= (16√3/36)x² - (88√3/36)x + (121√3/36)
The total area is then
(16√3/36)x² - (88√3/36)x + (121√3/36) + x²
= (16√3/36 + 1)x² - (88√3/36)x + (121√3/36)
Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)
When x=0, each side of the triangle is 11/3 meters long and its area is
(√3/4)a² ≈ 5.82
When x=2.75, each side of the square is 2.75 meters long and its area is
2.75² = 7.5625
Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters
The length of the square must be 4 m in order to maximize the total area.
What are the maxima and minima of a function?When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.
We have,
Length of the wire = 11 m
Let the length of the wire bent into a square = x.
The length of the wire bent into an equilateral triangle = (11 - x)
Now,
The perimeter of a square = 4 side
4 side = x
side = x/4
The perimeter of an equilateral triangle = 3 side
11 - x = 3 side
side = (11 - x)/3
Area of square = side²
Area of equilateral triangle = (√3/4) side²
Total area:
T = (x/4)² + √3/4 {(11 -x)/3}² _____(1)
Now,
To find the maximum we will differentiate (1)
dT/dx = 0
2x/4 + (√3/4) x 2(11 - x)/3 x -1 = 0
2x / 4 - (√3/4) x 2(11 - x)/3 = 0
2x/4 - (√3/6)(11 - x) = 0
2x / 4 = (√3/6)(11 - x)
√3x = 11 - x
√3x + x = 11
x (√3 + 1) = 11
x = 11 / (1.732 + 1)
x = 11/2.732
x = 4
Thus,
The length of the square must be 4 m in order to maximize the total area.
Learn more about maxima and minima here:
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If a drug has a concentration of 8.22 mg per 3.039 mL, how many mL are needed to give 7.469 gram of the drug? Round to 1 decimal.
Answer:
2.8 litres
Step-by-step explanation:
8.22 mg per 3.039 mL
2.704 mg per 1 mL
7.469 gram = 7469 milligrams
7469 milligrams per 2,761.34927mL
= 2.761 litres = 2.8 litres
The incomplete work of a student to solve an equation is shown below:
Step 1: 4x + 12 = 4
Step 2: ?
Step 3: x = −8 ÷ 4
Step 4: x = −2
What is the missing Step 2?
4x = 8
4x = 16
4x = −16
4x = −8
Hey guys please help me please and thank you
Answer:
Option B, 5/16
Step-by-step explanation:
f(4) = 5•(1/2)⁴
= 5•(1/2⁴)
= 5•(1/16)
= 5/16
An analyst has developed the following probability distribution for the rate of return for a common stock.
Scenario Probability Rate of Return
10 0.34 -19%
20 0.48 8%
30 0.18 26%
a. Calculate the expected rate of return. Round your answer to 2 decimal places.
b. Calculate the variance and the standard deviation of this probability distribution. Use the percentage values for your calculations (for example 10% not 0.10). Round intermediate calculations to 4 decimal places.
Answer:
a) 2.06
b) variance = 270.90 , std = 275.14
Step-by-step explanation:
a) Determine Expected rate of return
attached below is the calculated table for the solution provided
∴ Expected rate of return = ∑ Xp(x) = -6.46 + 3.84 + 4.68 = 2.06
b) Determine the variance and standard deviation
Variance ( Vx ) = E(x)^2 - [ Expected rate of return ]^2
= 275.14 - ( 2.06 )^2 ≈ 270.90
standard deviation = √ variance = √270.90 = 16.459
note : E(x)^2 = ∑ x^2 p(x) = 275.14
Factorise 2x3+9x2+10x+3
Answer:
Hello,
Answer is (x+1)(x+3)(2x+1)
Step-by-step explanation:
[tex]p(x)=2x^3+9x^2+10x+3\\p(-1)=2*(-1)^3+9*(-1)^2+10*(-1)+3=-2+9-10+3=0\\p(x)\ is\ divisible\ by\ (x+1)We\ arrange\ to\ put\ a\ factor\ of\ x+1\\\\2x^3+9x^2+10x+3\\\\=2x^3+2x^2+7x^2+7x+3x+3\\\\=2x^2(x+1)+7x(x+1)+3(x+1)\\\\=(x+1)(2x^2+7x+3)\\\\=(x+1)(2x^2+6x+x+3)\\\\=(x+1)(2x(x+3)+1(x+3))\\\\=(x+1)(x+3)(2x+1)\\[/tex]
enter the number that belongs in the green box (please enter both numbers for the empty boxes)
Given:
The equation is:
[tex]5x-2=4+2x[/tex]
To find:
The number that belongs in the green box and another box.
Solution:
We have,
[tex]5x-2=4+2x[/tex]
Subtracting 2x from both sides, we get
[tex]5x-2-2x=4+2x-2x[/tex]
[tex]3x-2=4[/tex]
Adding 2 on both sides, we get
[tex]3x-2+2=4+2[/tex]
[tex]3x=6[/tex]
We need to divide both sides by 3 to isolate the variable x.
On dividing both side by 3, we get
[tex]\dfrac{3x}{3}=\dfrac{6}{3}[/tex]
Therefore, the missing values are 3 and 3, and the required equation is [tex]\dfrac{3x}{3}=\dfrac{6}{3}[/tex].
Find the length of BC
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we want to find the opposite side and we know the hypotenuse. Therefore, we should use sine.
sin(51) = BC / 58
BC = 58 x sin(51)
BC = 45.1 units
Hope this helps!
Step-by-step explanation:
Hey there!
From the above given figure;
Angle CAB = 51°
AB = 58
Taking Angle CAB as reference angle we get;
Perpendicular (p) = BC= ?
Hypotenuse (h) = 58
Now;
Taking the ratio of sin we get;
[tex] \sin( \alpha ) = \frac{p}{h} [/tex]
[tex] \sin(51) = \frac{bc}{58} [/tex]
Simplify it;
0.7771459*58 = BC
Therefore, BC = 45.0744.
Hope it helps!
41. A pair of shoes was originally priced at
$90. After two successive discounts of
10% and 5%, what was the final price?
(1) $72.90
(2) $75.00
(3) $76.95
(4) $78.25
(5) $80.40
of 30 and a pe-
Answer:
Step-by-step explanation:
First discount
90/100 * 90 = 81 dollars
Second discount.
Be careful. This is usually a discount from the price in part are.
5% of 81 = 5/100 * 81 = 4.05
81 - 4.05 = 76.95
A company specializing in parachute assembly claims that its main parachute failure rate is at most 1%. You perform a hypothesis test to determine whether the company's claim is true or false. Your sample data resulted in enough evidence to go against the claim made by the company. It was later determined that the claim made by the company was actually incorrect. What kind of error, if any, was committed
Answer:
There was enough evidence to reject the null hypothesis, and in fact, the null hypothesis is false, which means that no error was committed.
Step-by-step explanation:
A company specializing in parachute assembly claims that its main parachute failure rate is at most 1%.
At the null hypothesis, we test if the proportion is of at most 1%, that is:
[tex]H_0: p \leq 0.01[/tex]
At the alternative hypothesis, we test if the proportion is of more than 1%, that is:
[tex]H_0: p > 0.01[/tex]
Type I and type II errors:
Type I: Rejection of a true null hypothesis. The null hypothesis is true, but from a sample, you get enough evidence to reject.
Type II: Non-rejection of a false null hypothesis. The null hypothesis is false, but from a sample, you do not get enough evidence to reject.
Your sample data resulted in enough evidence to go against the claim made by the company.
This means that there was enough evidence to reject the null hypothesis.
It was later determined that the claim made by the company was actually incorrect.
The null hypothesis was false.
What kind of error, if any, was committed?
There was enough evidence to reject the null hypothesis, and in fact, the null hypothesis is false, which means that no error was committed.
Use the differential to approximate the expression. Then use a calculator to approximate the quantity, and give the absolute value of the difference in the two results to four decimal places.
√
53
9514 1404 393
Answer:
0.0056
Step-by-step explanation:
f(x) = √(49 +x)
f'(x) = 1/(2√(49 +x))
A linear approximation of f(x) expanded about x=0 is ...
f(x) ≈ f(0) + f'(0)x = 7 +x/(2·7)
Then for √53, we have x=4
f(4) ≈ 7 +4/14 = 7 2/7 . . . . . approximate √53 using differentials
__
The calculator value of √53 is about 7.280110, so the difference in results is ...
approx - actual ≈ 7.285714 -7.280110 = 0.005604 ≈ 0.0056
please help me with geometry
Answer:
x = 7
Explaination:
ABC = 40°
and BD bisects the angle so ABD = 20°
so 3x-1=20
solving for x gets us
x = 7
Professor Iron always gives two exams in his communications class. He only uses the lower of the two scores that a student gets on the exams when he calculates the course grade. Put the grade on the first exam on the horizontal axis and the grade on the second exam on the vertical axis. What kind of preference a student should have for these two grades. Group of answer choices Perfect Complements Perfect Substitutes Cobb-Douglas Preference Neutral Preference
Answer:
Perfect complements
Step-by-step explanation:
Since minimum score of tests is to be considered. It is a case of perfect complements.
Correct option is
Perfect complements
Fill in the blank by performing the indicated elementary row operation(s).
6
1
5
-6R2+R
1
-5
0
Answer 7 Points
Keybo
<
Prev
In this question, we are given a matrix, and we have to perform the given operation.
The matrix is:
[tex]\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right][/tex]
The following operation is given:
[tex]R_1 \rightarrow -6R_2 + R_1[/tex]
In which [tex]R_1[/tex] is the element at the first line and [tex]R_2[/tex] is the element at the second line.
Updating the first line:
[tex]R_{1,1} = -6*1 + 6 = 0[/tex]
[tex]R_{1,2} = -6*-5 - 1 = 30 - 1 = 29[/tex]
[tex]R_{1,3} = -6*0 + 5 = 5[/tex]
Thus, the filled matrix will be given by:
[tex]\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right][/tex]
For another example where row operations are applied on a matrix, you can check https://brainly.com/question/18546657
If 4 men working 4 hours for 4 days complete 4 units of work, then how many units of work will be completed by 2 men working for 2 hours per day in 2 days.
Answer:
16 days
Step-by-step explanation:
Here,
By the question,
4 men takes 4 days working each day 4 hours to complete 4 units of work..
then..
if 1 man works 1 hour each day then i would take ( 4×4×4 ) days
= 64days
then..
if 2 men work for 2 hours per day then.
it would take
4×4×4 / 2×2 days
= 16 days
Current
How many years will it take for an initial investment of $60,000 to grow to $90,000? Assume a rate of interest of
4% compounded continuously.
>It will take about _years for the investment to grow to $90,000.
(Round to two decimal places as needed.)
Answer:
I think i don't know the answer i am so sorry!!!
maybe someone else can Answer
What is the solution set of the
equation?
(3x – 5)(2x – 10) = 0
Answer:
Step-by-step explanation:
3x - 5 = 0
3x = 5
x = 5/3
2x - 10 = 0
2x = 10
x = 10/2 = 5
With one alarm clock, we have a 0.875 probability of being awakened. What is the probability of being awakened if we are using two alarm clocks?(
The probability will be the same for both clocks.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
With one alarm clock, we have a 0.875 probability of being awakened.
The probability for the two clocks will be the same because both the clocks will ring at the same time.
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An environmentalist wants to find out the fraction of oil tankers that have spills each month.
Suppose a sample of 1036 tankers is drawn. Of these ships, 777 did not have spills. Using the data, estimate the proportion of oil tankers that had spills. Write your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The estimate of the proportion of oil tankers that had spills is 0.25.
Step-by-step explanation:
Proportion of oil tankers that had spills:
1036 tankers.
777 did not have spills.
So 1036 - 777 = 259 had spills.
The proportion is:
[tex]p = \frac{259}{1036} = 0.25[/tex]
The estimate of the proportion of oil tankers that had spills is 0.25.
Team A scored 30 points less than four times the number of points that Team B scored. Team C scored 61 points more than half of the number of points that Team B scored. If Team A and Team C shared in the victory, having earned the same number of points, how many more points did each team have than Team B?
Answer:
team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.
Step-by-step explanation:
The diameter of a regulation soccer ball is about 8 and three-fifths inches. This number was graphed on a number line.
A number line going from negative 9 to positive 9. Point A is between negative 9 and negative 8, point B is between negative 7 and negative 6, point C is between 6 and 7, point D is between 8 and 9.
Which point could be the point representing the graph of the diameter of the ball?
A
B
C
D
Answer:
D
Step-by-step explanation:
8 and 3/5 = 8.2 and 8.2 is between 8 and 9 so the answer is D.
Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol? The answer is an EXPRESSION, not an actual answer!! WILL MARK BRAINLIST!!!
Answer: [tex]\dfrac{11}{9}I[/tex]
Step-by-step explanation:
Given
There is [tex]l[/tex] liter of pure alcohol
Suppose [tex]x[/tex] liters of water is added
After addition of water, alcohol becomes 45% in concentration
[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]
Thus, [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.
HELP ME PLSSS SUMMER SCHOOL A HARD
Answer:
y=2x+8
Step-by-step explanation:
Hope this helps
The procluct of q and y digided by the sum of 8 and X
Answer: do you have any of the values?
Step-by-step explanation:
?
