Answer:
BC = 17.2.
Step-by-step explanation:
Since CAB = 90º, this is a right triangle.
The triangle format is given below:
C
A B
We have that AB = 8.6, and angle B measures 60º.
Length of BC:
BC is the hypotenyse.
Side AB is adjacent to angle B = 60º.
In a right triangle, angle [tex]\alpha[/tex], it's adjacent side with length s and the hypotenuse h are related by the cosine of the angle, that is:
[tex]\cos{\alpha} = \frac{s}{h}[/tex]
In this question, we have an angle of 60º, with has cosine 0.5. We also have that side AB = s = 8.6, and the hypotenuse h is side BC. So
[tex]\cos{\alpha} = \frac{s}{h}[/tex]
[tex]0.5 = \frac{8.6}{h}[/tex]
[tex]0.5h = 8.6[/tex]
[tex]h = \frac{8.6}{0.5}[/tex]
[tex]h = 17.2[/tex]
BC = 17.2.
Installation of a certain hardware takes a random amount of time with a standard deviation of 5 minutes. A computer technician installs this hardware on 64 different computers, with the average installation time of 42 minutes. Compute a 95% confidence interval for the mean installation time. Explain your interval in context.
Answer:
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
Step-by-step explanation:
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{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{5}{\sqrt{64}} = 1.225[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.225 = 40.775 minutes
The upper end of the interval is the sample mean added to M. So it is 42 + 1.225 = 43.225 minutes
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
The 95% confidence interval for the mean installation time is (40.775, 43.225) and this can be determined by using the formula of margin of error.
Given :
Standard deviation is 5 minutes. Sample size is 64.Mean is 42 minutes.95% confidence interval.The following steps can be used in order to determine the 95% confidence interval for the mean installation time:
Step 1 - The formula of margin of error can be used in order to determine the 95% confidence interval.
[tex]M = z \times \dfrac{\sigma}{\sqrt{n} }[/tex]
where z is the z-score, [tex]\sigma[/tex] is the standard deviation, and the sample size is n.
Step 2 - Now, substitute the values of z, [tex]\sigma[/tex], and n in the above formula.
[tex]M = 1.96 \times \dfrac{5}{\sqrt{64} }[/tex]
[tex]M = 1.225[/tex]
Step 3 - So, the 95% confidence interval is given by (M - [tex]\mu[/tex], M + [tex]\mu[/tex]) that is (40.775, 43.225).
The 95% confidence interval for the mean installation time is (40.775, 43.225).
For more information, refer to the link given below:
https://brainly.com/question/6979326
After four rounds, 74 teams are eliminated from a robotics competition. There are 18 teams remaining. Write and solve an equation to find the number of teams t that started the competition.
A club’s first meeting was attended by 72 people. Nine times as many people went to the first meeting than the second meeting. How many people attended the second meeting?
Answer:
8 people attended the second meeting.
Step-by-step explanation:
Given that:
Number of people who attended the first meeting = 72
Let,
x be the number of people who attended second meeting.
9 times people of second meeting = Number of people who attended first meeting
9x = 72
Dividing both sides by 9
[tex]\frac{9x}{9}=\frac{72}{9}\\x=8[/tex]
Hence,
8 people attended the second meeting.
Which statement has a false converse?
A If a quadrilateral is a rectangle, then the diagonals of the quadrilateral are
congruent.
B If a quadrilateral has diagonals that bisect each other, then the quadrilateral is a
parallelogram
C if a quadrilateral is a rectangle, then all angles of the quadrilateral are right angles.
D If a quadrilateral is a parallelogram, then both pairs of opposite sides of the
quadrilateral are congruent.
Answer:
B If a quadrilateral has diagonals that bisect each other, then the quadrilateral is a parallelogram
Explanation:
A rectangle just like a square has diagonals that bisect each other and they are congruent( two lines are congruent if they are equal). A parallelogram is a quadrilateral with parallel sides and when its diagonals intersect, they are congruent too. Therefore a rectangle with diagonals that bisect each other is not necessarily a parallelogram.
ACTIVITY 1
Directions: Find the unknown principal P, rate r, time t, and simple
interest Is by completing the table. Use separate sheet/s of paper for your
answer.
Principal (P)
Rate (T)
Time (t)
8%
15
2%
5
Simple Interest
(Is)
(1)
10,000
3,600
175,500
10,000
(2)
360,000
500,000
2
(3)
10.5%
Activity 2
Directions: Find the unknown principal P, maturity value, and
compound interest Ic by completing the table. Use separate sheet/s of paper
for your answer.
Maturity Value
Principal (P) Rate(r) Time(t)
Compound
Interest (Ic)
(1)
10,000
(3)
8%
2%
15
5
(2)
50,000
Answer:
500,000
2
(3)
10.5%
Activity 2
Directions: Find the unknown principal P, maturity
Which of the following can a seismograph not show scientists?
The sum of nineteen and four times a number equals 39. Suppose x represents the unknown number. Translate this problem into a mathematical statement.
Answer:
19 + 4x = 39
Step-by-step explanation:
PLEASE HELP YOU WILL GET BRAINLIEST IF YOU GET THIS RIGHT FIRST
Timothy purchased a computer for $1,000.
The value of the computer depreciates by 20% every year.
This situation represents [a.) exponential decay, b.) exponential growth]
The rate of growth or decay, r, is equal to [c.) 0.8, d.) 1.2, e.)0.2
year.
So the value of the computer each year is [f.) 20 %, g.) 80%, h.) 120%] of the value in the previous year.
It will take [i.) 3, j.) 2, k.) 4, l.) 5.] years for the value of the computer to reach $512.
Answer:
This situation represents [a.) exponential decay
The rate of growth or decay, r, is equal to c.) 0.2
So the value of the computer each year is g.) 80% of the value in the previous year.
It will take [i.) 3 years for the value of the computer to reach $512.
Step-by-step explanation:
Since the value depreciates each year, it represents exponential decay.
The rate of growth or decay, r, is equal to
Depreciates 20%, so r = 0.2.
So the value of the computer each year is ... of the value in the previous year,
Depreciates 20%, so it is 100% - 20% = 80% of the value in the previous year.
It will take x years for the value of the computer to reach $512.
The value of the computer after x years is given by:
[tex]V(x) = V(0)(1-r)^x[/tex]
In which V(0) is the initial value and r is the decay rate. So
[tex]V(x) = 1000(1-0.2)^x[/tex]
[tex]V(x) = 1000(0.8)^x[/tex]
We want to find x for which V(x) = 512. So
[tex]V(x) = 1000(0.8)^x[/tex]
[tex]512 = 1000(0.8)^x[/tex]
[tex](0.8)^x = \frac{512}{1000}[/tex]
[tex](0.8)^x = (0.512)[/tex]
Applying log to both sides:
[tex]\log{(0.8)^x} = \log{(0.512)}[/tex]
[tex]x\log{0.8} = \log{(0.512)}[/tex]
[tex]x = \frac{\log{0.512}}{\log{0.8}}[/tex]
[tex]x = 3[/tex]
So it will take 3 years.
Which type of transformation is described by (x, y)
->
+ (x + 3, y — 2)?
Answer:
(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.
Step-by-step explanation:
Given the rule of transformation:
(x, y) → (x+3, y-2)
If we move horizontally 3 units to the right, 3 is added to the x-coordinate of any given point, and then 2 units down.
In other words,
(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.
For example,
Let say if we have the point A(4, 5)
Using the translation rule:
(x, y) → (x+3, y-2)
A(4, 5) → A'(4 + 3, 5 - 2) → A'(7, 3)
Therefore, the new position of A(4, 5) after translating 3 units left and 2 units down would be: A'(7, 3)
sarah spent a total of 10 on oranges and apples at the supet marke
t. if she spent 3 dollars less for oranges than she did on apples how much did sarah spend on oranges
A laundromat charges $1.50 to wash and $1.25 to draw a load of laundry.
Choose all of the points that would lie on a graph representing the total cost, y, to wash and dry x loads of laundry:
A. (2, 2.75)
B. (2, 5.50)
C. (3, 6.75)
D. (3, 9.75)
E. (4, 10.25)
F. (4, 11.00)
Answer:
High possibility it is A, C, D. I apologize if wrong
Step-by-step explanation:
Answer:B, C, E
Step-by-step explanation:
What is the sum of
1
8
+
5
16
+
3
8
?
Answer:
41
Step-by-step explanation:
Answer:
18+516+38=18+554=572
Can someone help me please
Answer:
38 degrees
Step-by-step explanation:
just know
PLEASE HELL I NEED THIS ONE FAST PLEASE
Which statement is true about the decimal expansion of ? 3/7
O A. It is a rational number because it is a terminating decimal.
○B. It is an irrational number because it is not a terminating decimal.
○C. It is a rational number because after reaching a remainder of 3 for the second time the quotient will start repeating.
O D. It is an irrational number because after reaching a remainder of 3 for the second time the quotient will start repeating.
Answer:
A is the answer because divide 7 divided by 3 a
△ abc is an equilateral triangle, bc must be 2 cm True or False
Quadrilateral ABCD is a rhombus.
AD = 13 cm & BD = 24 cm,
find AC
Answer:
64
Step-by-step explanation:
please help meeeeeeeeeee
Answer:
area of trapezoid is [tex]\mathbf{Area=(\frac{4+8}{2})\times 6}[/tex]
Step-by-step explanation:
We have
a = 4 cm
b = 8cm
h = 6cm
We need to find area of trapezoid
The formula used is: [tex]Area=\frac{a+b}{2}\:h[/tex]
Putting values and finding expression:
We will not be solving the expression as question required just to find the expression by putting respective values.
[tex]Area=\frac{a+b}{2}\:h\\Area=(\frac{4+8}{2})\:\times 6[/tex]
So, area of trapezoid is [tex]\mathbf{Area=(\frac{4+8}{2})\times 6}[/tex]
Find the perimeter of a triangle with side lengths: (y + 5) ft, (3y + 5) ft, and (4y - 3) ft.
Answer:
8y + 7
Step-by-step explanation:
add them: y + 5 + 3y + 5 + 4y - 3 = 8y + 7
a square has an area of 1 square unit what is the length of the square
Answer:
The length is one
Step-by-step explanation:
The formula to find the area of aa square is B*H. This means to solve, you do 1*1, since the base and height are both 1, and 1*1=1
John needs to purchase a table for his room. John measured the space available as 4 ft. the actual measurement was 2.5 ft. what is John percent error.
Answer:
62.5%
Convert fraction (ratio) 2.5 / 4 Answer: 62.5%
Step-by-step explanation:
Creating a ratio to represent the amount he was specifically off by, which inherently gives you John's percent error.
3. Mandy obtains a $155,000 20/6 balloon mortgage with a rate of 4.25%. What will her monthly payments be? (2 points)
O $959.81
O $1044.46
O $1110.47
$1225.74
Answer:
$279.98
Step-by-step explanation:
A 20/6 balloon payment means loan amortization is for 20 years and constant payments is for 6 years after which balloon payment is due.
The formula to calculate her constant payments based on a 15 year amortization plan is
A= P × r × r(1+r)^n/(1+r)^n-1
Where A = constant monthly payments for the 6 year period
r= interest rate
P= mortgage value loan
n= number of months =20×12=240 payments
Substitute values in the formula:
A= $155000× 0.0425×0.0425(1+0.0425)^240/(1+0.0425)^240-1
A= $279.98
To calculate what she would pay before balloon payment is due, we simply multiply her monthly payments $279.98 by number of payments 240
mams buy 3 large sandwiches to serve at a picnic. 9 people come to the picnic. Show 3 different ways to cut the sandwich so that each person gets an equal share.
Cut each sandwich into thirds.
Hopefully, your friends aren't very hungry
< 1 2 The circumference of a circle is 47.1 feet. What is the diameter of the circle?
Step-by-step explanation:
[tex]47.1 = 2\pi \times r \\ r = \frac{47.1}{2\pi} = 7.4962996 \\ diameter = 2 \times r \\ = 14.99 = 15 \: feet[/tex]
Helpp
(Show ur work please)
This is law of cosine
Answer:
13.3
Step-by-step explanation:
[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]
[tex] a^2 = 8^2 + 18^2 - 2(8)(18) \cos 43^\circ [/tex]
[tex] a^2 = 64 + 324 - 288(0.73135) [/tex]
[tex] a^2 = 388 - 210.6299 [/tex]
[tex] a^2 = 177.370 [/tex]
[tex] a = \sqrt{177.370} [/tex]
[tex] a = 13.318 [/tex]
Answer: 13.3
A triangle has sides measuring 2 inches and 7 inches. If x represents the
length in inches of the third side, which inequality gives the range of possible
values for x?
A. 25x37
B. 5 sxs 9
C. 2
D. 5< x < 9
Answer:
its d.
Step-by-step explanation:
the other guy is wrong
Using sides of a triangle rule, the inequality gives the range of possible values for x is 5 < x < 9.
What is sides of a triangle rule?
The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
Given that two sides of triangle are 2 and 7 inches.
Let the third side be x inches.
x < 2+7 ⇒ x < 9
7 < 2 + x ⇒ x > 5
2 < 7 + x, which is true for any positive value of x.
Thus, 5 < x < 9.
Learn more about sides of a triangle rule here
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A rug shaped like a rectangle is 2.5 meters long and 1.8 meters wide what is the perimeter in meters of the rug
Answer:
P = 8.6 m
Step-by-step explanation:
Given that,
The length of a rectangle = 2.5 m
The width of a rectangle = 1.8 m
We need to find the perimeter of the rug. The perimeter of a rectangle is given by :
P=2(l+b)
= 2(2.5+1.8)
= 8.6 m
So, the perimeter of the rug is 8.6 m.
What is the constant proportionally of the graph
Help me
Answer:
The constant proportionally of the graph is:
k = 8Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
k = y/x
here 'k' is called the constant of proportionality.
From the graph, it is clear that:
at x = 0.5, the value of y = 4
so substituting x = 0.5 and y = 4 in the equation
k = y/x
k = 4/0.5
k = 8
at x = 1, the value of y = 8
so substituting x = 1 and y = 8 in the equation
k = y/x
k = 8/1
k = 8
Therefore, the constant proportionally of the graph is:
k = 8A bacterial culture is known to grow at a rate proportional to the amount present. After one hour, there are 1000 strands of bacteria and after four hours, 3000 strands. Find an expression for the number of strands present in the culture at any time t. What is the initial number of strands
Answer:
The expression is: [tex]P(t) = 693e^{0.3662t}[/tex]
The initial number of strands is 693
Step-by-step explanation:
A bacterial culture is known to grow at a rate proportional to the amount present.
This means that the bacterial model can be modeled by the following equation:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population, and r is the growth rate.
After one hour, there are 1000 strands of bacteria
This means that [tex]P(1) = 1000[/tex], So
[tex]P(0)e^{r} = 1000[/tex]
[tex]P(0) = \frac{1000}{e^{r}}[/tex]
After four hours, 3000 strands.
This means that P(4) = 3000. So
[tex]P(0)e^{4r} = 3000[/tex]
Since [tex]P(0) = \frac{1000}{e^{r}}[/tex], we have that:
[tex]\frac{1000}{e^{r}}e^{4r} = 3000[/tex]
[tex]\frac{e^{4r}}{e^{r}} = \frac{3000}{1000}[/tex]
[tex]e^{4r-r} = 3[/tex]
[tex]e^{3r} = 3[/tex]
[tex]\ln{e^{3r}} = \ln{3}[/tex]
[tex]3r = \ln{3}[/tex]
[tex]r = \frac{\ln{3}}{3}[/tex]
[tex]r = 0.3662[/tex]
The initial population is:
[tex]P(0) = \frac{1000}{e^{0.3662}} = 693[/tex]
The expression is:
[tex]P(t) = 693e^{0.3662t}[/tex]
The equation becomes [tex]y=694(1.44)^t[/tex]. The initial number of strands is 694.
An exponential growth is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the number of strands after t hours.
After one hour, there are 1000 strands of bacteria:
1000 = ab¹
ab = 1000 (1)
After four hour, there are 3000 strands of bacteria:
3000 = ab⁴
ab⁴ = 3000 (2)
Dividing equation 2 by 1:
b³ = 3
b = 1.44
ab = 1000
a = 1000/b = 1000/1.44 = 694
The equation becomes [tex]y=694(1.44)^t[/tex]
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42 % of what number is .21
Answer:
0.5
Step-by-step explanation:
0.21=42%
0.21/42=1%
0.005=1%
0.005 x 100 = 100%
0.5=100%
0.5