Answers
Answer:
D, 49.42
Step-by-step explanation:
ΔVFT=180-90-43=47
formula
a/sin A = b/sin B/ = c/sin C
So,
FV/sin90=53/sin47
FV=72.4684
FT=√(72.4684)^2-(53)^2
FT=49.4234
Ans:D
The length FT in the given right-angle triangle is 49.42.
So option D is the correct answer.
We are given a right-angle triangle and to find the length of any side we can use Pythagoras theorem or trigonometric identities.
In the triangle, we see that TV = 53 and ∠ FVT = 43°
We will find the length FT by using Pythagoras theorem or trigonometric identities.
What are trigonometric functions?
There are some commonly used trigonometric identities:
SinФ = Perpendicular / hypotenuse
Cos Ф = Base / hypotenuse
Tan Ф = Perpendicular / Base
We will use Tan Ф = Perpendicular / Base to find the length FT.
Because we need to use trigonometric identities that have TV and FT.
Tan Ф = FT / TV
Tan 43° = FT / 53
FT = Tan 43° x 53
FT = 0.932515 X 53
FT = 49.42
Thus we got FT = 49.42 using the tan function.
Learn more about trigonometric functions here:
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Related Questions
Consider the following case and determine whether there is sufficient information to solve the triangle using the low of sines. Two angles and the side included between them are known.
A. There is insufficient information because to use the law of sines, one side and the angle opposite it must be known.
B. There is sufficient information because if two angles and a side included between them are known, the third angle and the remaining two sides can be determined using the law of sines.
C. There is insufficient information because to use the law of sines, two angles and a side opposite one of them must be known.
D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
Answers
Answer:
D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
Step-by-step explanation:
A triangle is a plane shape that consists of 3 sides and 3 angles. There are different ways of solving for any unknown sides or angles of a triangle.
If any two angles and just one side of a triangle are known, then other angles and sides can also be determined using the sine rule.
For example, if a, b and c are the sides of the triangle and <A, <B and <C are the angles. The sine law is expressed as shown;
a/sinA = b/sinB = c/sinC
Any two can be equated to get any unknown sides and angles.
Also, if two of the angles are known, the third angle can be determined since the sum of angle in a triangle is 180°. If <A and <B are known for example, the third angle <C can be determined using the expression.
<C = 180°-(<A+<B)
Based on the explanation, option D is therefore the correct option i.e There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
If the function Q(t)=4e-0.00938t models the quantity (in kg) of an element in a storage unit after t years, how long will it be before the quantity is less than 1.5kg? Round to the nearest year.
Answers
Answer:
105 years
Step-by-step explanation:
Given the function :
Q(t) = 4e^(-0.00938t)
Q = Quantity in kilogram of an element in a storage unit after t years
how long will it be before the quantity is less than 1.5kg
Inputting Q = 1.5kg into the equation:
1.5 = 4e^(-0.00938t)
Divide both sides by 4
(1.5 / 4) = (4e^(-0.00938t) / 4)
0.375 = e^(-0.00938t)
Take the ln of both sides
In(0.375) = In(e^(-0.00938t))
−0.980829 = -0.00938t
Divide both sides by 0.00938
0.00938t / 0.00938 = 0.980829 /0.00938
t = 104.56599
When t = 104.56599 years , the quantity in kilogram of the element in storage will be exactly 1.5kg
Therefore, when t = 105 years, the quantity of element in storage will be less than 1.5kg
Find the vertex of this parabola:
y = x2 + 2x - 3
Answers
Answer:
(-1,-4)
Step-by-step explanation:
The equation of a parabola os written as: ax^2+bx+c
This parabola's equation is x^2+2x-3
● a= 1
● b= 2
● c = -3
The coordinates of the parabola are: ( (-b/2a) ; f(-b/2a) )
● -b/2a = -2/2 = -1
● f(-b/2a) = (-1)^2+2×(-1)-3=1-2-3= -4
So the vertex coordinates are (-1,-4)
Answer:
-1+2X
Step-by-step explanation:
Solve for x: 7 > x/4
Answers
Answer: x < 28
Step-by-step explanation:
An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses. H0: The product does not change the height of the plant. Ha: The product makes the plant grow taller. Is the following an example of a type I or type II error? The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.
Answers
Answer:
hi
Step-by-step explanation:
hji
Hi I need help with 800×200= 8 × ______ hundreds=_____ Hundreds = _______ plz help me
Answers
Answer:
800×200= 8 × 200 hundreds= 1600 Hundreds = 160000
A sequence of 1 million iid symbols(+1 and +2), Xi, are transmitted through a channel and summed to produce a new random variable W. Assume that the probability of transmitting a +1 is 0.4. Show your work
a) Determine the expected value for W
b) Determine the variance of W
Answers
Answer:
E(w) = 1600000
v(w) = 240000
Step-by-step explanation:
given data
sequence = 1 million iid (+1 and +2)
probability of transmitting a +1 = 0.4
solution
sequence will be here as
P{Xi = k } = 0.4 for k = +1
0.6 for k = +2
and define is
x1 + x2 + ................ + X1000000
so for expected value for W
E(w) = E( x1 + x2 + ................ + X1000000 ) ......................1
as per the linear probability of expectation
E(w) = 1000000 ( 0.4 × 1 + 0.6 × 2)
E(w) = 1600000
and
for variance of W
v(w) = V ( x1 + x2 + ................ + X1000000 ) ..........................2
v(w) = V x1 + V x2 + ................ + V X1000000
here also same as that xi are i.e d so cov(xi, xj ) = 0 and i ≠ j
so
v(w) = 1000000 ( v(x) )
v(w) = 1000000 ( 0.24)
v(w) = 240000
Figure out if the figure is volume or surface area.
(and the cut out cm is 4cm)
Answers
Answer:
Surface area of the box = 168 cm²
Step-by-step explanation:
Amount of cardboard needed = Surface area of the box
Since the given box is in the shape of a triangular prism,
Surface area of the prism = 2(surface area of the triangular bases) + Area of the three rectangular lateral sides
Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]
= [tex]\frac{1}{2}(6)(4)[/tex]
= 12 cm²
Surface area of the rectangular side with the dimensions of (6cm × 9cm),
= Length × width
= 6 × 9
= 54 cm²
Area of the rectangle with the dimensions (9cm × 5cm),
= 9 × 5
= 45 cm²
Area of the rectangle with the dimensions (9cm × 5cm),
= 9 × 5
= 45 cm²
Surface area of the prism = 2(12) + 54 + 45 + 45
= 24 + 54 + 90
= 168 cm²
Translate and solve: 82 less than a is at least -82
Answers
Answer:
a≥0
Step-by-step explanation:
a-82≥-82
a≥-82+82
a≥0
estimate the number 4576
Answers
Nearest 1000: 5000
Nearest 100: 4600
Nearest 10: 4580
Hope that helped!!! k
------------------------------------------------------------------------------------------
Find the surface area of the figure. ft
Answers
Answer:
486
Step-by-step explanation:
Hello!
To find the surface area of a cube we use the equation
[tex]S = 6a^{2}[/tex]
S is the surface area
a is the side length
Put what we know into the equation
[tex]S = 6*9^{2}[/tex]
Solve
S = 6 * 81
S = 486
Hope this Helps!
Answer:486[tex]ft^{2}[/tex]
Step-by-step explanation:
surface area= 6[tex]l^{2}[/tex]
l=9
sa=6 ([tex]9^{2}[/tex])= 6 x 81=486[tex]ft^{2}[/tex]
Complete the statement to describe the expression abc+def
The expression consists of ____ terms,and each term contains___ factors
Answers
Answer:
3 each
Step-by-step explanation:
The answer is already on this site
There are two pitchers of lemonade in the fridge there are 1.5 gallons of lemonade in 1 pitcher and 9 quarts of lemonade in the other pitcher how many cups of lemonade are there in the fridge
Answers
Answer:
52 cups
Step-by-step explanation:
1 gallon = 4 quarts
1.5 gallons = 6 quarts
6 + 9 = 13 quarts of lemonade in the fridge.
1 quart = 4 cups
13 quarts = 4 × 13 = 52 cups
52 cups of lemonade are in the fridge.
I would really appreciate it if you would mark me brainliest!
Have a blessed day!
Answer:
60 cups
Step-by-step explanation:
1 gal = 16 cups
1 quart = 4 cups
16 cups
1.5 gal x ------------- = 24 cups
1 gal.
4 cups
9 quarts x ----------- = 36 cups
1 quart
number of cups of lemonade in the fridge = 24 cups + 36 cups = 60 cups
nishan bought 7 marbles Rs.x per each. if he gave Rs.100 to the shop keeper. what is the balance he would receive?
Answers
Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.
Answers
Answer:
Step-by-step explanation:
Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods
1/PV (FV) = (PV(1 + r^n)1/PV divide by PV
ln(FV/PV) = ln(1 + r^n) convert to natural log function
ln(FV/PV) = n[ln(1 + r)] by simplifying
n = ln(FV/PV) / ln(1 + r) solve for n
n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually
n = 9
n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly
n = 104 months or 8.69 years
n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily
n = 3163 days or 8.67 years
Alternatively
A = P e ^(rt)
Given that r = 8%
= 8/100
= 0.08
2 = e^(0.08t)
ln(2)/0.08 = t
0.6931/0.08 = t
t= 8.664yrs
t = 8.67yrs
Which ever approach you choose to use,you will still arrive at the same answer.
A height is labeled on the triangle below.
Which line segment shows the base that corresponds to the given height of the triangle
Option A,B,C
Answers
Answer:
A
Step-by-step explanation:
The height is always perpinducular to the base. The height here is perpendicular to line segment A.
Answer:
A
Step-by-step explanation:
PLEASE HELP! (3/4) - 50 POINTS -
Answers
Answer:
C
Step-by-step explanation:
The set of data will only become more narrow when the standard deviation is decreased, so D isn't correct. The data isn't going to shift directions unless there's a translation, so A and B are both out. That leaves us with C. The opposite of answer D.
Answer:
C. It produces a wider range of probable values
Step-by-step explanation:
The set of data that we have cannot shift in directions unless there is a translation, so therefore, A and B are both out. The set of data would become smaller when the standard deviation is decreases so therefore, D isn't correct. So, that leaves us with only one answer.
C. It produces a wider range of probably values.
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose is
Answers
Answer:
8
Step-by-step explanation:
Ham with or without cheese-2 choices
Bologna with or without cheese-2 choices
Bologna with cheese with water or juice-2 choices
Bologna without cheese with juice or water-2 choices
Ham with cheese with juice or water -2 choices
Ham without cheese with juice or water -2 choices
2+2+2+2=8
Kile has 8 choices for lunch
What number represents the same amount as 8 hundreds + 10 tens + 0 ones? i was told 810 is incorrect
Answers
Answer:
900
Step-by-step explanation:
You have 10 tens not 1 ten
8 * 100 + 10 * 10 + 0*1
800 + 100 + 0
900
Answer:
[tex]900[/tex]
Step-by-step explanation:
[tex]8 \times 100 + 10 \times 10 + 0 \times 1 \\ 800 + 100 + 0 \\ = 900[/tex]
Which geometric sequence has a first term equal to 55 and a common ratio of -5? {-55, 11, -2.2, 0.44, …} {55; 275; 1,375; 6,875; …} {55, 11, 2.2, 0.44, …} {55; -275; 1,375; -6,875; …}
Answers
Answer:
The answer is 55, -275, 1375, -6875......
Step-by-step explanation:
Which expression is equivalent to x+y+x+y+3(y+5)
Answers
Answer:
2x + 5y + 15
Step-by-step explanation:
add like terms
(x+x) + (y+y)+3y+15
2x+2y+3y+15
2x + 5y + 15
i hope this helps!
One way to calculate the target heart rate of a physically fit adult during exercise is given by the formula h=0.8( 220−x ), where h is the number of heartbeats per minute and x is the age of the person in years. Which formula is equivalent and gives the age of the person in terms of the number of heartbeats per minute?
Answers
Answer:
The answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Step-by-step explanation:
Given:
[tex]h=0.8( 220-x )[/tex]
Where [tex]h[/tex] is the heartbeats per minute and
[tex]x[/tex] is the age of person
To find:
Age of person in terms of heartbeats per minute = ?
To choose form the options:
[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]
Solution:
First of all, let us have a look at the given equation:
[tex]h=0.8( 220-x )[/tex]
It is value of [tex]h[/tex] in terms of [tex]x[/tex].
We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].
Let us divide the equation by 0.8 on both sides:
[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]
Now, subtracting 220 from both sides:
[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]
Now, multiplying with -1 on both sides:
[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]
So, the answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Use the set of ordered pairs to determine whether the relation is a one-to-one function. {(−6,21),(−23,21),(−12,9),(−24,−10),(−2,22),(−22,−22)}
Answers
Answer:
the relation is not one-to-one.
Step-by-step explanation:
it can't because every number is in the 4th quadrant.
Please help with this
Answers
Answer:
B) x=80°
Step-by-step explanation:
This is a hexagon, so it has interior angles equaling 720°. (N-2)*180
So the equation would be
78+134+136+132+2x+x=720
480+3x=720
3x=720-480
3x=240
x=80°
If the length of the legs of a right triangle are 13 and 13,what is the length of the hypotenuse? Round your answer to the nearest tenth,if necessary.
Answers
Answer:
a² + b² = c²
13² + 13² = c²
169 + 169 = c²
338 = c²
c = √338 or 18.385 or 13√2
Answer:
18.4
Step-by-step explanation:
13² + 13² = x²
169 + 169 = x²
338 = x²
x = 18.38477....
How many feet are in 26 miles, 1, 155 feet? Enter only the number. Do not include units
The solution is
Answers
Answer:
137, 280 feet
Step-by-step explanation:
There are 5,280 feet in a mile.
26 * 5,280 = 137,280
There are 137, 280 feet in 26 miles.
There are 137,280 feet in 26 miles.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We know that there are 5,280 feet in a mile.
So, the solution would be;
26 x 5,280 = 137,280
Thus, There are 137,280 feet in 26 miles.
Learn more about the unitary method;
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9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d overbar and s Subscript d. In general, what does mu Subscript d represent? Temperature (degrees Upper F )at 8 AM 98.1 98.8 97.3 97.5 97.9 Temperature (degrees Upper F )at 12 AM 98.7 99.4 97.7 97.1 98.0 Let the temperature at 8 AM be the first sample, and the temperature at 12 AM be the second sample. Find the values of d overbar and s Subscript d.
Answers
Answer:
[tex]\frac{}{d}[/tex] = −0.26
[tex]s_{d}[/tex] = 0.4219
Step-by-step explanation:
Given:
Sample1: 98.1 98.8 97.3 97.5 97.9
Sample2: 98.7 99.4 97.7 97.1 98.0
Sample 1 Sample 2 Difference d
98.1 98.7 -0.6
98.8 99.4 -0.6
97.3 97.7 -0.4
97.5 97.1 0.4
97.9 98.0 -0.1
To find:
Find the values of [tex]\frac{}{d}[/tex] and [tex]s_{d}[/tex]
d overbar ( [tex]\frac{}{d}[/tex]) is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5
[tex]\frac{}{d}[/tex] = ∑d/n
= (−0.6 −0.6 −0.4 +0.4 −0.1) / 5
= −1.3 / 5
[tex]\frac{}{d}[/tex] = −0.26
s Subscript d is the sample standard deviation of the difference which is calculated as following:
[tex]s_{d}[/tex] = √∑([tex]d_{i}[/tex] - [tex]\frac{}{d}[/tex])²/ n-1
[tex]s_{d}[/tex] =
√ [tex](-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1[/tex]
= √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −
(−0.26))² + (−0.1 − (−0.26))² / 5−1
= [tex]\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }[/tex]
= [tex]\sqrt{\frac{0.712}{4} }[/tex]
= [tex]\sqrt{0.178}[/tex]
= 0.4219
[tex]s_{d}[/tex] = 0.4219
Subscript d represent
μ[tex]_{d}[/tex] represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.
A work shift for an employee at Starbucks consists of 8 hours (whole).
What FRACTION (part) of the employees work shift is represented by 2
hours? *
Answers
Answer:
1/4 of an hour
Step-by-step explanation:
2 divided by 8 = 1/4
Answer:
1/4
Step-by-step explanation:
A whole shift is 8 hours
Part over whole is the fraction
2/8
Divide top and bottom by 2
1/4
3. A medical devices company wants to know the number of MRI machines needed per day. A previous study found a standard deviation of four hours. How many MRI machines must the company study in order to have a margin of error of 0.5 hours when calculating a 90% confidence interval
Answers
Answer:
173 MRI machines
Step-by-step explanation:
Margin of error E = 0.5
Confidence interval 90% = 1-0.9 = 0.1
Standard deviation = 4 hours
Number of MRI machines needed per day n, = [(z alpha/2 * SD)/E]²
Z alpha/2 = 1.645 at alpha = 0.1
Inputting these values into n we have that
[(1.645*4)/0.5]²
= 13.16²
= 173.18 is approximately equal to 173
The company has to study 173 machines.
A rotating light is located 16 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
Answers
Answer:
a
Step-by-step explanation:
answer is a on edg
