Answer:
[tex]y = \sqrt{900 - x^2[/tex]
Step-by-step explanation:
Given
From the complete question, we have:
[tex]r=30[/tex] --- radius
Required
Expression for the height of the roller coaster
We have:
[tex]x^2 + y^2 = r^2[/tex] --- equation of circle
Substitute 30 for r
[tex]x^2 + y^2 = 30^2[/tex]
[tex]x^2 + y^2 = 900[/tex]
Since the roller coaster is half of the circle, the height is defined by y.
So: make y the subject
[tex]y^2 = 900 - x^2[/tex]
Take square roots
[tex]y = \sqrt{900 - x^2[/tex]
Hence, the height is:
[tex]\sqrt{900 - x^2[/tex]
Using divisibility tests, check whether the number 240720 is divisible by
2, 3, 4, 5, 6, 8, 9, 10 and 11. (Give reason)
Answer:
Let's see each case.
a) 2
We know that a number is divisible by two if it ends in {0, 2, 4, 6, 8}
In our case, we have 240,720
We can see that it ends with a zero, so it is divisible by 2.
b) 3
A number is divisible by 3 only if the sum of its digits is a multiple of 3.
For our number, the sum of the digits gives:
2 + 4 + 0 + 7 + 2 + 0 = 2 + 4 + 7 + 2 = 6 + 9 = 15
15 is a multiple of 3, then 15 is divisible by 3.
then 240,720 is divisible by 3.
c) 4
A number is divisible by 4 if the last two digits form a number that is divisible by 4.
In this case, the last two digits are 2 and 0, so they form the number 20
and we know that 20 = 4*5 is a multiple of 4.
then 20 is divisible by 40
then 240,720 is divisible by 4
d) 5
A number is divisible by 5 if it ends in 0 or 5.
Our number ends in a 0, so it is divisible by 5.
e) 6
A number is divisible by 6 if it is divisible by 2 and 3.
We already know that our number is divisible by 2 and 3, so we can conclude that it is also divisible by 6.
f) 8
A number is divisible by 8 if, in the case where the hundreds digit is odd, the number obtained from the last two digits plus 4 must be divisible by 8.
in the case where the hundreds digit is even, the number formed by the last two digits must be divisible by 8.
In our case the hundreds digit is 7, so it is odd, so we will use the first criteria.
The last two digits form the number 20
if we add 4, we get:
20 + 4 = 24
And 24 is a multiple if 8: 8*3 = 24
Then 24 is divisible by 8, then 240,720 is divisible by 8.
g) 9
Similar for the case of the 3, a number is divisible by 9 if the sum of its digits is divisible by 3.
We know that the sum of the digits of our number is 15, which is not divisible by 9, then our number is not divisible by 9
h) 10
A number is divisible by 10 if the last digit is a zero.
In this case the last digit is a zero, so 240,720 is divisible by 10.
i) 11
A number is divisible by 11 if:
starting from the left, you need to add and subtract each subsequent digit, if this is divisible from 11, then the original number is divisible by 11.
Then for 240,720 we have:
2 - 4 + 0 - 7 + 2 - 0 = -2 - 5 = -7
-7 is not divisible by 11, so our number is not divisible by 11
simplify
[tex] \frac{2e + f}{8e - 2e {}^{2} } \times \frac{4e - e {}^{2} }{2ef + f {}^{2} } [/tex]
The answer is 1/2f
my answer is in the image above
Nutz and Boltz, Inc., employs one hundred people; eighty are lawyers and twenty are engineers. Albert, a lawyer at the company, is quiet, likes puzzles, and carries a calculator. Most people, when asked whether Albert is a lawyer or an engineer, will guess that he is an engineer. These people are using __________ to make this faulty guess. A correct guess would have been made if they had used __________.
Answer:
These people are using the representativeness heuristic to make this faulty guess. A correct guess would have been made if they had used base rate information.
Step-by-step explanation:
Representativeness heuristic occurs when the similarity of items or events causes individuals to be perplexed about the likelihood of a given result. People usually make the error of guessing that two comparable things or occurrences are more closely related than they are. Therefore, the similarity of an engineer and a calculator confuse the people to guess that Albert is an engineer.
Base rate information refers to the information provided by base rates which are a type of statistic that is used to describe the percentage of a population that exhibits a certain feature. Base rates suggest the likelihood of something based on the lack of other facts. Using the information in the question as an example, if 20% of the employees were engineers and 80% were lawyers, the base rate of lawyers is simply 80%. This implies that Albert is a lawyer, but we won't know for sure until we look at the total number of workers that the base rate information reveals that he is a lawyer.
Therefore, these people are using the representativeness heuristic to make this faulty guess. A correct guess would have been made if they had used base rate information.
Which expression is equivalent to log Subscript 5 Baseline (StartFraction x Over 4 EndFraction) squared?
Answer:
[tex]\log_5(\frac{x}{4})^2 = 2\log_5(x) - 2\log_5(4)[/tex]
Step-by-step explanation:
Given
[tex]\log_5(\frac{x}{4})^2[/tex]
Required
The equivalent expression
To do this, we apply the following law of indices:
[tex]\log_a(b)^c = c\log_a(b)[/tex]
So, we have:
[tex]\log_5(\frac{x}{4})^2 = 2\log_5(\frac{x}{4})[/tex]
To further simplify:
[tex]\log(\frac{a}{b}) = \log(a) - \log(b)[/tex]
So, we have:
[tex]\log_5(\frac{x}{4})^2 = 2(\log_5(x) - \log_5(4))[/tex]
Open brackets
[tex]\log_5(\frac{x}{4})^2 = 2\log_5(x) - 2\log_5(4)[/tex]
Answer:
C.
Explanation:
Edge 2021
simplify 5x-26y+7x+32y
My pigg y bank has only pennies and nicklels in it , and 2/7 of the coins are nickel If i remove 84 pennies then 1/3 of the remening are pennies 1} suppose there are initially p pennies and n nickels in the pigy bank write an equation using the fact that 2/7 of the coins initially in the
Answer:
There are 105 pennies in the piggy bank.
There are 42 nickels in the piggy bank.
Step-by-step explanation:
there are:
p pennies in the piggy bank
n nickels in the piggy bank
Then we can define T, the total number of coins, as:
T = p + n
We know that 2/7 of the total number of coins are nickels.
This can be written as:
n = (2/7)*T = (2/7)*(n + p)
And if we remove 84 pennies, 1/3 of the remaining coins are pennies.
This can be written as:
p - 84 = (1/3)*(n + p - 84)
Then we have a system of two equations:
n = (2/7)*(n + p)
p - 84 = (1/3)*(n + p - 84)
Let's solve the system, to do it, we first need to isolate one of the variables in one of the equations.
We can isolate n in the first one, to get:
n = (2/7)*(n + p) = (2/7)*n + (2/7)*p
n - (2/7)*n = (2/7)*p
n*(5/7) = (2/7)*p
n = (7/5)*(2/7)*p = (2/5)*p
n = (2/5)*p
Now we can replace this in the other equation:
p - 84 = (1/3)*(n + p - 84)
p - 84 = (1/3)*( (2/5)*p + p - 84)
Let's solve this for p
p - 84 = (1/3)*( (7/5)*p - 84)
3*(p - 84) = (7/5)*p - 84
3p - 252 = (7/5)*p - 84
3*p - (7/5)*p = 252 - 84
(15/5)*p - (7/5)*p = 168
(8/5)*p = 168
p = (5/8)*168 = 105
There are 105 pennies in the piggy bank.
And we know that:
n = (2/5)*p = (2/5)*105 = 42
There are 42 nickels in the piggy bank.
An object is experiencing an acceleration of 30 m/s2 while traveling in a
circle at a velocity of 3.7 m/s. What is the RADIUS of its motion?
Answer:
[tex]{ \tt{formular :}} \\ { \boxed{ \bf{centripental \: acceleration = \frac{ {v}^{2} }{r} }}} \\ \\ { \tt{30= \frac{ {3.7}^{2} }{r} }} \\ \\ { \tt{r = \frac{ {3.7}^{2} }{30} }} \\ \\ { \tt{radius = 0.456 \: meters}}[/tex]
I need the volume of e and f
Answer:
e-154
f-648
Step-by-step explanation:
rttyyuuguguvuhuhihihuhuhuhihihih7
Answer:
for e
[tex] v = \frac{1}{ 2} \times 8 \times 7 \times 5.5 = 154[/tex]
for f
v=6×9×12=648
Fragrant Fields Greenhouse sells rose bushes for $19.90 each. Last weekend, they made $477.60 on rose bushes. How many rose bushes did they sell?
Answer:
Fragrant Fields Greenhouse sold 24 rose bushes.
Step-by-step explanation:
We know that:
1 rose bush = $19.90
And last weekend, the company ended up making $477.60 on rose bushes.
An equation that can represent this situation is:
19.90x = 477.60
To find x, divide:
477.60 ÷ 19.90 = 24
CHECK IT:
19.90(24) = 477.6
That is also $477.60, in terms of money
THEREFORE, the company sold 24 rose bushes.
Hope this helps!
Does this graph show a function? Explain how you know.
A. Yes; there are no y-values that have more than one x-value.
B. No; there are yvalues that have more than one x-value.
• C. Yes; the graph passes the vertical line test.
• D. No; the graph fails the vertical line test.
Answer:
yes
Yes; the graph passes the vertical line test.
Step-by-step explanation:
if it were a graph of a circle it would not pass
the vertical line test because the vertical line would touch at least 2 points
graph is probably a cubic function
something like
y = x^3-4x+6
If you answer I will mark you brainliast
Exercise 6
Use the x button on a calculator. You will need basic trigonometry (page 209).
1. The chord AB subtends an angle of 130° at the centre O.
The radius of the circle is 8 cm. Find:
a) the length of AB
b) the area of sector OAB
c) the area of triangle OAB
d) the area of the minor segment (shown shaded).
2. Find the shaded area when:
a) = 6 cm, 0 - 70°
b) r=14 cm, 0 = 104°
c) r=5 cm, 0 = 80
8 cm
1.
3. Find and hence the shaded area when:
a) AB = 10 cm, r= 10 cm
b) AB=8 cm, r = 5 cm
4. How far is a chord of length 8 cm from the centre of a circle of radius 5 cm?
5. How far is a chord of length 9 cm from the centre of a circle of radius 6 cm?
Step-by-step explanation:
Refer Fig 1 as attached
1a. angle a = angle b = 25°
AM = 8 x cos 35° = 6.553
so AB = AM x 2 = 13.1
1b. Area of sector OAB / Area of the circle
= 130 / 360
Area of sector OAB = 8x8xpi x 130/360
= 23pi
1c. Area OAB = 2 X ( AM x OM) /2 = AM x OM
OM = AM x tan (angle a) = 13.1 x tan 25°
= 6.109
so Area OAB = 6.553 x 6.109 = 40.03
1d. Area of the minor segment
= Area of sector OAB - Area of triangle OAB
= 23pi - 40.03
= 32.23
2, 3 Please refering the approach as above to find the answers
4. Refer Fig 2 as attached
a = 3
the cord is 3 cm from the centre
5. Repeat the approach of 4 above please.
The length of a rectangle is 18 cm and the width is 6 cm. A similar rectangle has a width of 2 cm.What is the length of the second rectangle? pls help im solving hw ._.
Answer:
Length = 6cm
Step-by-step explanation:
You would get 6cm as the length, because 6 ÷ 3 = 2, that is your width. So in the same way, you would divide 18 by 3 and get 6, thus the length of the second rectangle is 6 centimeters
Hope it helps :D
6 cm po tama to mag quandary pi akyu
Expected value is: Group of answer choices the average probability of all possible outcomes of a future event occurring, weighted by each possible outcome individually the sum of all probabilities of all possible outcomes of a future event occurring the sum of all possible outcomes of a future event, weighted by its probability of occurring
Answer:
the average probability of all possible outcomes of a future event occurring, weighted by each possible outcome individually
Step-by-step explanation:
An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).
This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.
In Statistics, an expected value can be defined as the average probability of all possible outcomes of a future event occurring in an experiment, weighted by each possible outcome individually. Thus, an expected value in theory refers to the outcome an individual expect to obtain from an experiment in the long-run.
Mathematically, an expected value can be calculated by summing the products of each distinct outcome and their probability respectively.
A grocer noticed that customers buy both pet and baby supplies with a probability of 0.12. Considered separately, the probability that
customer buys pet supplies is P(A) = 0.64, and the probability that a customer buys baby supplies is P(B) = 0.25.
Move expressions and numbers into the blanks to create an equation that represents the probability that a customer buys either pet
supplies or baby supplies.
Answer:
0.77
Step-by-step explanation:
Given that:
P(A) = 0.64
P(B) = 0.25
P(AnB) = 0.12
Probability that customer buys either pet or baby supplies ; P(AuB)
P(AuB) = P(A) + p(B) - p(Ann)
P(AuB) = 0.64 + 0.25 - 0.12
P(AuB) = 0.77
what frcation is equal to 4
(FIRST CORRECT FOR BRAINIEST) Given that triangle GHJ = triangle XYZ, what is m
Answer:
∠ J = 71°
Step-by-step explanation:
Given that the triangles are congruent then corresponding angles are congruent, so
∠ H = ∠ Y = 38°
Since GH = JH then Δ GHJ is isosceles and the 2 base angles are congruent
∠ J = [tex]\frac{180-38}{2}[/tex]= [tex]\frac{142}{2}[/tex] = 71°
Four test scores are given. The first three test scores are 20% of the final grade and the last test score is 40% of the final grade. Find the weighted mean of the test scores. Round to the nearest tenth.90 88 95; 92
What is an equation of the line that passes through the point (-6,5) and is parallel
to the line 2 - 3y = 21?
Answer:
y=1/3x+7
Step-by-step explanation:
Hi there!
We're given the equation x-3y=21 and we want to find the equation of the line parallel to x-3y=21 that passes through (-6,5)
Parallel lines have the same slopes, but different y intercepts
So we need to find the slope of x-3y=21
To do that, we can convert x-3y=21 from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept).
We'll need to isolate y onto one side
subtract x from both sides
-3y=-x+21
divide both sides by -3
y=1/3x-7
1/3 is in the place where m is, so 1/3 is the slope of the line
it's also the slope of the line parallel to x-3y=21
here's the equation of the line parallel to x-3y=21 so far:
y=1/3x+b
we need to find b
as the line passes through (-6,5), we can use it to solve for b
substitute -6 as x and 5 as y
5=1/3(-6)+b
multiply
5=-2+b
add 2 to both sides
7=b
Substitute 7 as b into the equation
y=1/3x+7
Hope this helps!
PLEASE HELP! Which is not a mathematical sentence?
A. 8 + 7 = 15
B. k+ 2<6
C. n+ 19
D. 222
Answer:
D
Step-by-step explanation:
its just rabdom numbers
Answer:
D thats just a number no sequence or any thing
Step-by-step explanation:
Divide. (7t^5 + 14t^4 − 28t^3 + 35t^2) ÷ (7t^2) step by step pls
a. t^3 + 2t^2 − 4t + 5
b. t^3 − 2t^2 − 4t + 5
c. t^7 + 2t^2 − 4t + 5
d. t^3 + 2t^2 − 4t − 5
Answer:
choice: A
Step-by-step explanation:
the ratio of fiction books to non-fiction
books in Roxanne's library is 7 to 9.
If Roxanne owns 182 fictions books
how many non-fiction books does she
Answer:
234
Step-by-step explanation:
182/7= 26 9x26=234
why is there a minimum number of characters needed
An equation having p = -3 as its solution, then the equation is .................
Answer:
2p + 9 = 3
2p = 3 - 9
2p = -6
p = -6/2
p = -3
If 2 tan x/ 1- tan^2 x=1, then x can equal:
Answer: x=pi/8+npi and x=5pi/8+npi
Step-by-step explanation:
Mr Yadav buys a radio for Rs 640 and sells it for Rs 672 Find it's profit percent In process
Answer:
(672-640)/640 x 100 = 5%
Can i get some help pls!
Answer:
Graph the system on linear equations.
Step-by-step explanation:
(-4, 4) & (-4, -6)
Find the slope of a line through the points (0,0) and (2, 9). Round your
answer to 1 decimal place.
SLope = y2-y1 / x2-x1
Answer:
Slope = 4.5
Step-by-step explanation:
We need to find the slope of a line through the points (0,0) and (2, 9).
We know that, the slope of a line is given by :
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have, x₁ = 0, x₂ = 2, y₁ = 0 and y₂ = 9
Put all the values,
[tex]m=\dfrac{9-0}{2-0}\\\\m=4.5[/tex]
So, the slope of the line is 4.5.
In ΔGHI, HI = 13, IG = 8, and GH = 16. Which list has the angles of ΔGHI in order from largest to smallest?
Answer:
m<I, m<G, m<H
Step-by-step explanation:
The angle that sees the longest side length has the biggest measurement
so
if we were to list the angles from largest to smallest
m<I, m<G, m<H
Help me, please :)
I need to find the value of x
A jam recipe requires 3 quarts of raspberries. Raspberries are available in 1.5 pint containers at a grocery store. How many containers are required for the recipe?
There are two pints per quart
3 q * 2 p/qt = 6 pints needed
6 pint /1.5 pint/container = 4 containers
What is the simplified value of the exponential expression 273?
不
1
Ο Ο Ο
9
Answer:
The answer is 3
For the steps, Im leaving it blank for you to figure it out first.
If you really need help, ask anytime and I'll reply as soon as i can :)