Answer:
29 m
Step-by-step explanation:
Since Jeff's coach is at the left of the platform and the platform at an angle of elevation of 37° and Jeff's parent's are on the right of the platform with the platform at an angle of elevation of 32°. The line of sight of Jeff's coach, the distance between Jeff's coach and parents and the line of sight of Jeff's parents form a triangle.
Since the platform is 10 m high, it is a perpendicular to the base of the triangle.
This perpendicular bisects the original triangle into two right angled triangles - one on the left and one on the right - with base angle 37° and 32° respectively.
Using trigonometric ratios with the opposite side to each angle the height of the platform from the ground (10 m) and the opposite angles 37° and 32° respectively, then the length of each base is gotten from
tan37° = 10/L and tan32° = 10/L' where L and L' are the lengths of each base of the two right angled triangles respectively.
So, L = 10/tan37° = 10/0.7536 = 13.3 m and L' = 10/tan32° = 10/0.6249 = 16 m.
The length d = L + L' is the distance between Jeff's coach and Jeff's parents
So, d = L + L'
= 13.3 m + 16 m
= 29.3 m
≅ 29 m to the nearest meter.
Note that we do not need the third angle in the triangle which is 100° the angle of separation between Jeff's coach and Jeff's parents which is at the base of the platform.
An ancient Chinese candle clock tells the amount of time that has passed by the amount of wax that has been melted off the candle. Each candle is divided into 121212 sections, marked 111 inch (\text{in})(in)(, start text, i, n, end text, )apart. It takes 444 hours (\text{hrs})(hrs)(, start text, h, r, s, end text, )for each candle to completely melt, after which a new candle is lit. If two candles have completely melted and one candle has melted 4\ \text{in}4 in4, space, start text, i, n, end text, how many minutes have passed since the first candle was lit
Answer:
[tex]Time = 560\ mins[/tex]
Step-by-step explanation:
Given
[tex]Candles = 2[/tex] --- candles melted
[tex]Divisions = 12[/tex]
[tex]Time = 4\ hrs[/tex] --- time to melt
Required
The time since the first was lit
If 1 candle melts in 4 hours, 2 candles will melt in 8 hours.
i.e.
[tex]x = Candles * Time[/tex]
[tex]x = 2 * 4hrs[/tex]
[tex]x = 8hrs[/tex]
For the 3rd candle that has melted, 4 inches
First, calculate the fraction that melt
[tex]Fraction = \frac{Melt}{Division}[/tex]
[tex]Fraction = \frac{4}{12}[/tex]
[tex]Fraction = \frac{1}{3}[/tex]
The time to melt is:
[tex]y = Fraction * Time[/tex]
[tex]y= 4 * \frac{1}{3}[/tex]
[tex]y= \frac{4}{3}hrs[/tex]
So, the required time is:
[tex]Time = x + y[/tex]
[tex]Time = 8hrs + \frac{4}{3}hrs[/tex]
Convert to minutes
[tex]Time = 8*60mins + \frac{4}{3}*60mins[/tex]
[tex]Time = 480mins + 80mins[/tex]
[tex]Time = 560\ mins[/tex]
The area of a rectangle is represented by 12n2 - 19n - 21. If the width is 3n - 7, which expression represents the perimeter?
A. 7n - 4
B. 7n+4
C. 14n -8
D. 14n +8
Answer:
C 14n - 8
Step-by-step explanation:
rectangle area = length×width = 12n²-19n-21
width = 3n-7
what do we need to multiply with width to get the full area expression ?
think : what do we need to multiply with 3n to get 12n² (4n)?
and what to multiply with -7 to get -21 (3)?
=> length = 4n+3
perimeter is 2×length + 2×width
p = 2(3n-7) + 2(4n+3) = 6n-14+8n+6 = 14n-8
king monatla surprised his wife on birthday by buying her 55 inch television set.the repayment period is 36 months and the monthly installment is R570,00
write down the item number of the television
Answer:
The final price of the television set is $ 20,520.
Step-by-step explanation:
Given that King Monatla surprised his wife on birthday by buying her a 55 inch television set, and the repayment period is 36 months and the monthly installment is $ 570.00, to determine the final price of the television set the following calculation must be performed:
570 x 36 = X
20.520 = X
Therefore, the final price of the television set is $ 20,520.
Using the proper terminology, how would you explain and visually demonstrate that this is not always the case.
Answer:
you drew to much on it
Step-by-step explanation:
We put ___ beads in the ten column of an abacus for the number 7025
Answer:
2
Step-by-step explanation:
10 column=10 space in number, aka 70(2)5
Write the equation for the graph of y = | x | translated left 4 units
Answer: y = |x+4|
Explanation:
Imagine that the graph of y = |x| is carved in stone so it cannot move. What we can move though is the xy axis. If we move the xy axis 4 units to the right, then this gives the illusion the V shaped curve is moving 4 units to the left. It goes opposite whatever movement you do to the xy axis.
If we replaced x with x+4, then this moves the xy axis 4 units to the right.
Therefore, going from y = |x| to y = |x+4| will have the V shaped curve moving 4 units to the left.
A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 6 milliliters (ml) and a standard deviation of 0.4 ml. Find the dye amount that represents the 90th percentile (i.e. 90%) of the distribution.
a. 4.464 ml.
b. 4.836 ml.
c. 4.936 ml.
d. 4.964 ml.
e. 5.536 ml.
Answer:
The 90th percentile of the distribution is 6.512 ml.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 6 milliliters (ml) and a standard deviation of 0.4 ml.
This means that [tex]\mu = 6, \sigma = 0.4[/tex]
Find the dye amount that represents the 90th percentile (i.e. 90%) of the distribution.
This is X when Z has a p-value of 0.9, so X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 6}{0.4}[/tex]
[tex]X - 6 = 1.28*0.4[/tex]
[tex]X = 6.512[/tex]
The 90th percentile of the distribution is 6.512 ml.
Help ASAP. Like right now
1/5=2/10
4/6=2/3
2/8=1/4
find the value of 4th terms by using 3n-2
Answer:
Step-by-step explanation:
[tex]4^{th} term \ means \ n = 4\\\\3n - 2 = 3 \times 4 - 2 = 12 -2 = 10[/tex]
A medical equipment industry manufactures x-ray machines. The unit cost C( the cost in dollars to make each x -ray machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function C(x)=0.2x^2-100x+31,146.what is the minimum unit cost.
Answer:
18,646
Step-by-step explanation:
>you can graph the equation on a calculator and see that the minimum is at the point (250, 18646) , so the minimum unit cost is 18,646
>you can use the first derivative to find the minimum
c'(x) = (0.2x²-100x+31,146)' = .4x -100
.4x-100= 0 , so x= 250
c(x=250) = 0.2(250)² -100*250 +31,146 =18,646
Please help me!
A second-hand car is advertised for $15575 cash or $1600 deposit and 24 monthly payments
of $734.70.
a What is the difference between the cash price and the HP price?
b What annual rate of interest is paid on the HP plan?
Answer:
The difference between the cash price and the HP price is $3,657.8. The annual rate of interest paid on the HP plan is 11.74% per year.
Step-by-step explanation:
Given that a second-hand car is advertised for $ 15,575 cash or $ 1600 deposit and 24 monthly payments of $ 734.70, to determine what is the difference between the cash price and the HP price and what annual rate of interest is paid on the HP plan you must perform the following calculation:
(1600 + 734.70 x 24) - 15,575 = X
(1600 + 17,632.8) - 15,575 = X
19,232.8 - 15,575 = X
3,657.8 = X
Therefore, the difference between the cash price and the HP price is $ 3,657.8.
15,575 = 100
19,232.8 = X
19,232.8 x 100 / 15,575 = X
1,923,280 / 15,575 = X
123.48 = X
(123.48 - 100) / 2 = X
23.48 / 2 = X
11.74 = X
Therefore, the annual rate of interest paid on the HP plan is 11.74% per year.
3)
6 cm
5 cm
I
7 cm
5 cm
6 cm
Answer:
29
Step-by-step explanation:
Suppose f(x) = – 22 – 4x + 2 and g(x) =
42? +52 +5.
(f +9)(2) =
Answer:
[tex](f + g)(2) = 21[/tex]
Step-by-step explanation:
[tex]f(x) = -x^2 - 4x +2[/tex]
[tex]g(x) = 4x^2 + 5x + 5[/tex]
Required
[tex](f + g)(2)[/tex]
This is calculated as:
[tex](f + g)(2) = f(2) + g(2)[/tex]
Where:
[tex]f(2) = -2^2 - 4*2 +2 = -10[/tex]
[tex]g(2) = 4*2^2 + 5*2 + 5 = 31[/tex]
So:
[tex](f + g)(2) = f(2) + g(2)[/tex]
[tex](f + g)(2) = -10 + 31[/tex]
[tex](f + g)(2) = 21[/tex]
Factor.
x*2+11x+28
please give me the answer
Answer:
(x+4)(x+11)
Step-by-step explanation:
x^2+11x+28
What two numbers multiply to 28 and add to 11
4*7 =28
4+11
(x+4)(x+11)
Answer:
(x + 4)(x + 11)
I agree with wegner
bye
What substitution should be used to rewrite x ^ 8 - 3x ^ 4 + 2 = 0 as a quadratic equation?
Answer:
Let m= x^4
m^2 -3m +2 = 0
Step-by-step explanation:
x ^ 8 - 3x ^ 4 + 2 = 0
Let m= x^4
m^2 -3m +2 = 0
3 cm
8 cm
Find surface area of cylinder
Answer: [tex]66\pi \text{ cm}^{2[/tex]
Step-by-step explanation:
[tex]S=2\pi(8)(3)+2\pi(3)^{2}=\boxed{66\pi \text{ cm}^{2}}[/tex]
Every week a company provides fruit for its office employees. They can choose from among five kinds of fruit. What is the probability distribution for the 30 pieces of fruit, in the order listed? Fruit Apples Bananas Lemons Oranges Pears 6 9 2 8 5 Number of pleces Probability O A. 1, 1 3 1 4 1 5 10 15 15 6 ОВ. 1 I 4 2 5 10 3° 15' 15 c. bot , 1 OD. 1 1 1 4 2 • 15. 5. 15 15
Answer:
A? maybe i dont know dont quote me on that
Step-by-step explanation:
The Probability distribution is
Apples =1/5
Bananas = 3/10
Lemons = 1/15
Oranges = 4/15
Pears = 1/6
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Total Fruits = 30
Now, the probability distribution for the 30 pieces of fruit is
Apples = 6/30
= 1/5
Bananas = 9/30
= 3/10
Lemons = 2/30
= 1/15
Oranges = 8/30
= 4/15
Pears = 5/30
= 1/6
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What is 10% of 14???
Answer: 1.4
Step-by-step explanation:
Answer: 1.4
Step-by-step explanation:
14 x 0.1 = 1.4
(10% = 10/10 0= 0.1)
Find the perimeter of the figure below, in feet.
8.eft
6.6 ft
16.6A
6.6 ft
6.6 ft
eft
2 ft
6.6 ft
6.6 ft
12.4ft
12.4ft
8.2 ft
Answer:
not entirely sure but my answer is 87.6ft.
for the perimeter of the shape.
Step-by-step explanation:
I cut out the extra square-ish pieces of the sides and found
that both are 17.2 for their perimeter. so 17.2×2= 34.4
then I found the perimeter of the sides of the rectangular shape and the sides were both 18.4ft. so 2(18.4+8.2)= 53.2.
so 53.2+34.4 = 87.6ft.
Rachel is solving the system of equations below by using the elimination method. Which of the following steps could she use? 7x-21y=14. 2x+3y=11
Answer:
[tex]7x - 21y = 14 - - - (a) \\ 2x + 3y = 11 - - - (b) \\ (a) + 7 \times (b) : \\ 21x + 0y = 91 \\ x = 4.33 \\ (2 \times 4.33) + 3y = 11 \\ 3y = 2.34 \\ y = 0.78 \\ { \boxed{x = 4.33}} \\ { \boxed{y = 0.78}}[/tex]
PLEASE HELP I WILL GIVE BRAINLIEST AND 50 POINTS!!!
The following function represents the value of a truck, in dollars, after x years:
f(x) = 29,000(0.88)x
What does 0.88 represent?
The decrease in the value of the truck, which is 12%
The present value of the truck
The value of the truck after x years
The decrease in the value of the truck, which is 88%
Answer:
The decrease in the value of the truck, which is 12%
Step-by-step explanation:
f(x) = 29,000(0.88)^x
This is an exponential function of the form
y = ab^x
a is the initial value
b is the growth(decay) rate
x is the time
Since b is less than 1, we know it is decay
To find the rate
1-b = rate
1-.88 = .12
The decay rate is .12*100% = 12 %
Answer:
its A:The decrease in the value of the truck, which is 12%
Step-by-step explanation:
i got this correct
There’s 2 arcade areas and 1 swimming pool. What is the arcade area to swimming pool ratio?.
Answer:
Yeah, the person above me is right. It's 2:1
Step-by-step explanation:
There are 2 arcade areas and 1 swimming pool. the arcade area to swimming pool ratio is 2: 1.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement.
Also the ratio is a unitless(no units) quantity.
There are 2 arcade areas and 1 swimming pool.
The arcade area to swimming pool ratio is 2: 1.
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PLEASE HELP I WILL MARK BRAINLIEST
Answer:
8 x 13 = 104 yd^2
Step-by-step explanation:
To find the area of a rectangle we use the basic formula:
L x W
In this case 13 is your width and 8 is your length, multiply the two given lengths to get your area which is 104.
What is in the shape of a triangular pyramid and has a height of 10 inches the area of the base of the container is 12 in.² what is the volume of the figure actually inches
Answer:
60 cubic inches
Step-by-step explanation:
if its a triangle you have to divide it by 2 because its half of a square so its half of an answer so in this case you multiply 10 and 12 which gets you 120 divide that by 2 you get 60 and that's your answer.
A point with a positive x-coordinate and a negative y-coordinate will lie in which quadrant?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
15 POINTS (08.01) The graph shows two lines, A and B.
How many solutions are there for the pair of equations for lines A and B? Explain your answer.
what's the GCF for the pair of numbers. 27, 45
i only need the answer
Answer:
9 is the answer
Step-by-step explanation:
I WILL GIVE BRAINLIEST TO THE BEST AND CORRECT ANSWER
Choose all the statements that are true.
1. 15 pt<2 gal
2. 1 gal<5 qt
3. 12 fl oz> 2 c
4. 2 qt 1 c>10 c
5. 20 pt = 10 qt
Answer:
the answer should be 3 and 5 :)
Step-by-step explanation:
the answer speaks for itself
Help PLSSS!!!!! I will give brainlyest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 17 1/2 or decimal form = 17.5
Step-by-step explanation: Hope this helped!
Answer:
17.5 Statues im pretty sure.
Step-by-step explanation:
7/8 divided by 1/20
Determine the equation for a line that passes through the point M(-7, 3) and
perpendicular to 7x − 2y + 3 = 0. Show your complete work.
Answer:
y = 2x/7 + 5
Step-by-step explanation:
the first line is defined by
7x - 2y + 3 = 0
in the most common way to write this we need an equation like y = ...
so, we isolate the y-expression in the equation :
2y = 7x + 3
y = (7x + 3) / 2 = 7x/2 + 3/2
the factor of x is the slope of the line, which is expressed by the y/x ratio indicating how many units y will change, when x changes e.g. 1 unit.
7/2 means that y will change by 7 units for every change in x by 2 units.
the slope of a perpendicular line is inverse to the slope of the original line, which means x and y are simply trading places (original x / original y).
so, the perpendicular slope of 7/2 is 2/7 (when x changes by 7 units, then y changes by 2 units).
that means the equation for the perpendicular line is something like
y = 2x/7 + c
the c we determine by using the coordinates of the given point (x and y values).
3 = 2×(-7)/7 + c = 2×(-1) + c = -2 + c
c = 5
so, the complete equation of the perpendicular line is
y = 2x/7 + 5