The height of the skyscraper rounded to the nearest tenth of a meter is
160.0 meters.
The situation will form a right angle triangle.
The angle of elevation is 44 degrees. The horizontal distance of 164
meters from the base of the skyscraper is the adjacent side of the triangle.
Part of the height of the skyscraper is the opposite side of the triangle formed .
Using trigonometric ratio,
tan 44° = opposite / adjacent
tan 44° = h / 164
cross multiply
h = 164 × tan 44°
h = 158.372959068
Recall the angle of elevation was form from his eyes above the ground of
1.62 meters.
Therefore, the height of the skyscraper can be calculated below:
height of the skyscraper = 158.372959068 + 1.62 = 159.992959068
height of the skyscraper ≈ 160.0 meters
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500 children ages 5-11 were asked the following question:
"Do you read books for fun every day?"
Results are shown in the two-way table below.
Boy Girl Total
Yes 48 75
No 182 195
Total 500
a. In this sample, what proportion of children are boys? (Round your answer to the nearest hundredth)
b. What proportion of boys read books for fun every day? (Round your answer to the nearest hundredth)
c. What proportion of girls read books for fun every day? (Round your answer to the nearest hundredth)
d. Based on the findings, does the likelihood of reading books for fun depend on the gender of a child? Explain.
e. If a child is selected at random, find the probability that the child reads book for fun. (Round your answer to the nearest hundredth)
f. If a child is selected at random, find the probability that the child is a girl AND reads book for fun. (Round your answer to the nearest hundredth)
g. If a child is selected at random, find the probability that the child is a girl OR reads book for fun. (Round your answer to the nearest hundredth)
h. If a child is selected at random, find the probability that the child reads book for fun GIVEN that the child is a girl. (Round your answer to the nearest hundredth)
500 children ages 5-11 were asked the following question:
"Do you read books for fun every day?"
Results are shown in the two-way table below.
Boy Girl Total
Yes 48 75 123
No 182 195 377
Total 230 270 500
What are proportions?A proportion is the number of desired outcomes divided by the number of total outcomes.
a. Proportion of children that are boys.There are 500 children and 230 are boys.
230/500 = 0.46
b. Proportion of boys who read books for fun every day.There are 230 boys and 48 read books for fun every day.
48/230 = 0.21
c. Proportion of girls who read books for fun every day.There are 270 girls and 75 read books for fun every day.
75/270 = 0.28
d. Does the likelihood of reading books for fun depend on the gender of a child?Based on the results from b and c, it would seem more likely for a girl to read books for fun than for a boy.
e. For a child selected at random, what is the probability that the child reads books for fun?There are 500 children and 123 read books for fun.
P = 123/500 = 0.25
f. For a child selected at random, what is the probability that the child is a girl and reads books for fun?There are 500 children and 75 are girls who read books for fun.
P = 75/500 = 0.15
g. For a child selected at random, what is the probability that the child is a girl or reads books for fun?There are 500 children. The favorable cases are the girls (270) plus the children who read books for fun (123) minus the girls who read books for fun (75).
P = (270 + 123 - 75)/500 = 0.64
h. For a child selected at random, what is the probability that the child reads books for fun given that the child is a girl.There are 270 girls and 75 of them read books for fun.
P = 75/270 = 0.28
a. The proportion of children who are boys is 0.46.b. The proportion of boys who read books for fun every day is 0.21.c. The proportion of girls who read books for fun every day is 0.28.d. It would seem more likely for a girl to read books for fun than for a boy.e. For a child selected at random, the probability that the child reads books for fun is 0.25.f. For a child selected at random, the probability that the child is a girl and reads books for fun is 0.15.g. For a child selected at random, the probability that the child is a girl or reads books for fun is 0.64.h. For a child selected at random, the probability that the child reads books for fun given that the child is a girl is 0.28.Learn more about proportions here: https://brainly.com/question/25259185
I 13.12.21 Mather asianmen I choose the best answert the next two numbers in the pattern 1, 4, 9, 16 are. (A) 26,36 (B) 25, 36 (C) 24,35 (D) 36,48
Answer:
(B) 25, 36
Step-by-step explanation:
1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²
35 = 6²
Martin is buying inkjet cartridges that cost $22 each. He has $100 to pay for the cartridges.
Which number line shows the number of cartridges Martin can buy?
Answer: C
Step-by-step explanation:
lets think about it
you can totally buy 0 ink cartridges. you can just be like "nope ok im gone, no ink today, the prices are so high.. maybe another time. maybe ill use the school printer or smth"
so that ELIMINATES B.
and now A and D are strange because how exactly are we going to buy half of an ink cartridge? or a fraction of an ink cartridge? that simply isnt feasible
so this eliminates A and D
now C is the best because you can buy 0, 1, 2, 3, 4 ink cartridges. but not 5 because that is $110 and Martin dont got that money, am i right fellas?
Answer:
The Answer Is C
Step-by-step explanation:
Sue can ride her bike 14 km/hr faster than she can walk. It takes 17.5 min longer to walk 2.5 km
than to ride. Find Sue's walking speed.
Answer:
6 km/hr
Step-by-step explanation:
Sue can ride her bike 14 km/hr faster than she can walk. So for each step, add 14 km/hr.
Solve
[tex]-17.5r^2-245r+2100=0 \\\\r^2+14r-120=0 \\\\(r-6)(r+20)=0\\\\[/tex]
Therefore, it is 6.
A cable is 40 decimeters long. How long is the cable in meters?
Be sure to include the correct unit in your answer.
Answer:
4 Meters
Step-by-step explanation:
Formula
divide the length value by 10
let f be the function given by f(x)=sin x + e^-x +3x. which of the following statements is true for y=f(x).
Applying derivatives, it is found that the correct options are:
A. [tex]y^{\prime\prime}(x) = -\sin{x} + e^{-x}[/tex]
D. [tex]y - y^{\prime\prime\prime\prime}(x) = 3x[/tex]
The function given is:
[tex]f(x) = \sin{x} + e^{-x} + 3x[/tex]
It's first four derivatives are:
[tex]y^{\prime}(x) = \cos{x} - e^{-x} + 3[/tex]
[tex]y^{\prime\prime}(x) = -\sin{x} + e^{-x}[/tex]
Hence, option A is correct.
[tex]y^{\prime\prime\prime}(x) = -cos{x} - e^{-x}[/tex]
[tex]y^{\prime\prime\prime}(x) \neq y^{\prime}(x)[/tex], hence, option B is incorrect.
[tex]y^{\prime\prime\prime\prime}(x) = sin{x} + e^{-x}[/tex]
It is not the multiplication of the first and of the third derivative, hence option C is incorrect.
[tex]y - y^{\prime\prime\prime\prime}(x) = 3x[/tex]
[tex]\sin{x} + e^{-x} + 3x - \sin{x} - e^{-x} = 3x[/tex]
[tex]3x = 3x[/tex]
Hence, option D is correct.
A similar problem is given at https://brainly.com/question/17042788
Estimate each product 11.9×21=
Answer:
249.9
uhm.. correct me if im wrong
A raft was sent away from point A downstream. A patrol-boat left A 5 hour and 20 min later and caught up with the raft 20 km away from point A. What was the speed of the raft if the speed of the patrol-boat was 12 km/hour?
solve using a system of equations. will mark brainliest for correct answer and working
Answer:
2 6/7 km/hStep-by-step explanation:
t - time spent by boat, s - speed of the raft
time = distance / speed
Equations:
t = 20 / 12t + 5 h 20 m = 20 / sTime the patrol-boat spent:
t = 20/12 = 5/3 hTime the raft spent:
5 h 20 min + t = 5 1/3 + 5/3 =16/3 + 5/3 =21/3 =7 hoursThe speed of the raft:
7 = 20/ss = 20/7s = 2 6/7 km/h4) A teacher has an annual income of $51,750. The income tax the teacher has to pay is 7%. What is the amount of income tax in dollar and cents the teacher has to pay?
A) $3,448.25
B) $3,622.50
C) $3,891.10
D) $3,933.01
9514 1404 393
Answer:
B) $3,622.50
Step-by-step explanation:
To find the tax, multiply the income by the tax rate:
$51,750 × 0.07 = $3,622.50
Consider the following equation:
5x+4y=−3
Determine if the given ordered pair, (1,−2), satisfies the given equation
yes or no
Answer:
(1, - 2 ) is a solution
Step-by-step explanation:
Substitute the coordinates into the left side and if equal to the right side then the ordered pair is a solution.
5(1) + 4(- 2) = 5 + (- 8) = 5 - 8 = - 3 = right- side
Then (1, - 2 ) is a solution of the equation
Determine whether the ratios 8:7 and 15:14 are equivalent
Answer:
They are not
Step-by-step explanation:
We can see that 14 / 2 = 7, so we can check for the other side by dividing both sides of the ratio by 2:
15:14
\/
7.5:7 ≠ 8:7
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
The table above shows the number of each type of plant in Robert's garden. What is the ratio of the total number of plants in Robert's garden to the number of tomato plants?
Answer: C.
Step-by-step explanation:
Total number of plants in Robert's garden = 8 + 4 + 16 + 22
= 50
Number of tomato plants in Robert's garden = 8
Ratio of total number of plants to the number of tomato plants = 50 : 8
Simplify
50 : 8 = 25:4
[tex]x^{2}[/tex] = 6
Answer:
Take the root of both sides and solve.
[tex]x = \sqrt{6} , - \sqrt{6} [/tex]
Answer:
Take the root of both sides and solve:
[tex]x = \sqrt{6}, - \sqrt{6} [/tex]
Two numbers are in the ratio 7:10 If the larger number is 140,what is the smaller number
Given that nos. are in ratio 7:10
The larger no. is 140
Let the smaller no. be x
Using ratio and proportion
7 : 10 :: x : 140
⇒10 × x = 140 × 7
[tex]⇒x = \frac{140 \times 7}{10} = 98 \\ [/tex]
- BRAINLIEST ANSWERER
Answer:
[tex] \frac{7}{10 } = \frac{x}{140} [/tex]
[tex] \frac{7 \times 140}{10 \times x} [/tex]
[tex] \frac{980}{10} [/tex]
[tex]98[/tex]
ANSWER IS 98
98 IS THE SMALLEST NUMBERThe cost of producing key chains with the company logo printed on them consists
of a onetime setup fee of $265.00 plus $0.90 for each key chain produced. This
cost can be calculated using the formula C = 265.00 +0.90p, where p represents
the number of key chains produced and C is the cost. Use the formula to calculate
the cost of producing 2700 key chains.
Answer:
$2695
Step-by-step explanation:
$265 + $0.90p=C
To find out the value of C (cost), we must solve the equation by replacing P (number of keychains) with the given value, 2700.
265 + 0.90(2700) = C
Now, we use order of operations. (PEMDAS)
In this case, the parentheses stand for multiplication. Since multiplication comes first, we multiply 0.90 by 2700.
The product of 0.90(2700) is 2430.
Our new equation should look like this
265 + 2430=C
Adding those together you get 2695, to finish this off, C=$2695
(Side note: be sure to identify what the value is, for example 2695 is the cost of producing 2700 key chains, meaning it's $)
I hope this made sense and helped lol
Can someone please help me with this? I will give brainlist :(
Answer:
2nd
Step-by-step explanation:
The second one
2 1/4 x 3 1/5 i need help
Answer:
7 1/5
Step-by-step explanation:
2 1/4 * 3 1/5
Change to improper fractions
2 1/4 = (4*2+1)/4 = 9/4
3 1/5 = (5*3+1)/5 = 16/5
9/4 * 16/5
Rewriting
9/5 * 16/4
9/5 * 4/1
36/5
Change back to a mixed number
7 1/5
the book is sold for 5.4 dollars at a profit of 8% on the cost price what was the cost price
please help
Answer:
5.4*0.08=0.432 or
43 cents
Hope This Helps!!!
how do you find the y intercept on a table
Answer:
y-intercept is 10. The y-intercept is where the line crosses with the y-axis line. The y-axis line is when x = 0.
in
given points.
1. (10,4), (4, 15)
Find the slope of the line.
Answer:
[tex]m = -\frac{11}{6}[/tex]
Step-by-step explanation:
Slope is rise over run.
[tex]\frac{15-4}{4- 10}=\frac{11}{-6} = \boxed{-\frac{11}{6}}[/tex]
Hope this helps.
i need help on this math problem
Answer:
Natalie pays $9 every week.
d = 9w + 72
Step-by-step explanation:
50 Points! Please only answer if you know! Thank you.
Graph the system of linear inequalities. Your graph should demonstrate that you're following the instructions below.
Use x- and y- intercepts to graph inequality A.
Use point-slope form to graph inequality B.
A) 3x - 9y > 27
B) (y-3) ≤ -4/3 (x+7)
Show ALL work and EXPLAIN all your steps.
Thank you for helping me understand this.
Answer:
See belowStep-by-step explanation:
A) 3x - 9y > 27
x- intercept at y = 0 is:
3x = 27x = 9y-intercept at x = 0 is:
- 9y = 27y = -3Connect the two points (9, 0) and (0, -3) with dotted line (because of <) and shade below line (because y < ).
B) (y-3) ≤ -4/3 (x+7)
Use one point from the equation:
(-7, 3)Find the second point using the slope - 4/3, add 3 to x and - 4 to y:
x = -7 + 3 = - 4y = 3 - 4 = - 1Connect these two points (-7, 3) and (-4, -1) with solid line (because of ≤ ).
Shade the area below the line (because y ≤ ).
Find the slope and y-Intercept of the line in the graph. Drag and drop each number into the correct box
to complete the statement.
7
(0,5)
4 3
2
1
0
(3,-1)
-1
-2
3
TO
de
8 7
0 1 2
55
The slope is m
and they-intercept is b =
Answer:
slope = - 2, y- intercept = 5
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line
m = [tex]\frac{-1-5}{3-0}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
The y- intercept is the point on the y- axis where the line crosses
The y- intercept = 5
Please helpppp me step my step all the wayyy
Carla and Diane Bought identical suit cases at a different stores. Carla’s suitcase originally cost $75 and was discounted 15% Daniels suitcase originally cost 85$ and was on sale for 20% off the original price which suitcase was a the better deal? What do we know ? List important facts ? What do we want to find out ?? Solve ??? Show ur work? Explain starts ur Asnwer and give details ? And justify your steps ?
SOMEONE PLEASE HELPPPPPP MEEEEE
THIS IS DUEEEE RIGHT NOWWW
WITH ALL THE WORK I TRIED ALL NIGHT PLEASEEEEEEE
Answer:
carlas had the better deal
Step-by-step explanation:
if you buy an suitcase at $85 with 20% discount, you will pay 85 - 17 = 68 dollars.
if you buy an suitcase at $75 with 15% discount, you will pay 75 - 11.25 = 63.75
divide 20% by a 100 =0.2 than times 0.2 by $85 which will equal 17 subtract 17 from $85
do the same for the second one.
Pls help me with these Worksheets :(
My brain cells aren't working lol
(AGAIN IF YOU DON'T KNOW THE ANSWERS PLS JUST IGNORE THIS!)
Answer:
I'm sorry. It's messy ik.
For number 5 that I haven't done, I don't get the answer :((( so...
But basically, the speed is found by multiplying the distance and time. The distance is the same either you go upstream or downstream. Hope it help!
Answer:
Step-by-step explanation:
I'll do #5 second page
let (v) be rowing velocity in still water
let (s) be the stream velocity
d = vt
going downstream
24 = (v + s)4
24 = 4v + 4s
4s = 24 - 4v
s = 6 - v
going upstream
24 = (v - s)6
24 = 6v - 6s
24 = 6v - 6(6 - v)
24 = 6v - 36 + 6v
60 = 12v
v = 5 km/hr
s = 6 - 5 = 1 km/hr
Assuming that the data for all employees follows the same pattern, which kind of relationship is
there between years of higher education and current salary?
A- a clustered relationship
B- there is no relationship
C- a negative correlation
D- a positive correlation
Answer:
D- A POSITIVE CORRELATION
someone help me on these 2 questions asap! 50 points!!
Step-by-step explanation:
earbuds
we have a 1in : 0.2in scale of drawing to reality.
0.2 = 2/10 = 1/5
so, 1in in the drawing is actually 1/5in in reality.
how long are the 4in in the drawing ?
well, 4 times the 1in thing.
4×1/5 = 4/5 = 0.8in long
again the similar triangles
similar triangles means that each pair of corresponding lines (sides, heights, ...) in the triangles follows the same scaling factor for the length.
so, what do I need to multiply the side of the large triangle with to get the corresponding side length of the small triangle ?
27 × x = 9
x = 9/27 = 1/3
and that is the scale factor.
help !! giving brainliest.
Answer:
i guess the 2nd one
.
.........
Which relationship is represented by the graph?
Radius of a circle vs. its diameter
Circumference of a circle vs. its diameter
Area of a circle vs. its diameter
Explain your thinking.
This is because the diameter is independent towards the
unlabeled axis; just like how the circumference is depending on
the diameter.
>
What is the constant of proportionality?
The constant of proportionality is usually used in stuff regarding to coordinates. It basically is that values increase or decrease proportionally to another value, such as on a graph, say you have a linear equation that gains 4 units up for every 3 units it moves to the right. Those two values are proportional because they'll continue to move at the same predictable rate. The image below is that line. It doesn't just apply to linear equations though, it can apply to other kinds, like exponential or absolute value equations.
Sorry if this wasn't super concise, as this is a really hard topic to explain just over text. However, if it did help a lot, please give me brainliest as I'm trying to rank up. Thanks!
Constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
What is Graph?
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The relationship between diameter of circle and radius of circle is d=2r
Relationship between Area of a circle vs. its diameter
Area of circle=π(d/2)²
The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
The values increase or decrease proportionally to another value, such as on a graph, say you have a linear equation that gains 4 units up for every 3 units it moves to the right.
The x and y values are proportional because they'll continue to move at the same rate.
Hence constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
To learn more on Graph click:
https://brainly.com/question/17267403
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Need help please to this question
Answer:
c
Step-by-step explanation:
x=slope
y=intercept
The slope is put in front of the x and then you would add the y intercept.
Answer: c. y = -3x + 4