Answer:
7/8
Step-by-step explanation:
63 ÷ 9/72 ÷ 9
= 7/8
Answer:
7/8
Step-by-step explanation:
63/9 = 7
72/9 = 8
then:
63/72 = 7/8
20 PTS PLEASE HELP!!!!
Select the correct answer from each drop-down menu.
The function below describes the number of students who enrolled at a university, where f(t) represents the number of students and t represents the time in years.
Initially, (1.03, 3, 19,055, 18,500) students enroll at the university. Every,(1years, t years, 2years, 3years) the number of students who enroll at the university increases by a factor of (1.03, 3, 19,055, 18,500).
Answer:
Initially 18,500 students
Every 1 year
increase by a factor 1.03
Step-by-step explanation:
The missing information is selected from the given options from the drop down menu. The correct answers are : Initially 18,500 students enroll at the university. Every 1 years the number of students who enroll at the university increases by a factor 1.03.
F(t) = 18,500 * (1.03)^t
The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.
Answer:
83 adult tickets and 217 student tickets.
Step-by-step explanation:
Let number of adult tickets sold = [tex]x[/tex]
Given that total number of tickets = 300
So, number of student tickets = 300 - [tex]x[/tex]
Cost of adult ticket = $15
Cost of student ticket = $11
Total collection from adult tickets = $[tex]15x[/tex]
Total collection from student tickets = [tex](300-x)\times 11 = 3300-11x[/tex]
Given that overall collection = $3630
[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]
So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.
Now , collection = $3632
A timeline. 27 B C E to 180 C E PAX ROMANA. 44 B C E The Roman Empire was founded. 80 C E The Colosseum was built. 121 C E Hadrian's Wall was built in England to keep out enemies. 306 C E Constantine became emperor.
How many years passed between the building of the Colosseum and the building of Hadrian’s Wall?
201
121
41
36
Answer:
the answer is 41
Step-by-step explanation:
C. 41
Step-by-step explanation:
A toy box in the shape of a rectangular prism has a volume of 6,912 cubic inches. The base area of the toy box is 288 square inches. What is the height of the toy box?
Answer:
h= 24 inches
Step-by-step explanation:
(Volume)= (Base Area) * (Height)
6,912= 288h
h=
Solve using quadratic formula.
1.)5x^2+13x=6
2.)3x^2+1=-5x
PLEASE HELP!!! WILL MARK BRAINLIEST!!!
Answer:
1. 2/5,-3 2. [tex]x=\frac{-5+-\sqrt{13} }{6}[/tex]
Step-by-step explanation:
i used the quadratic formula to find x also please note that 2 has 2 answers bc of the +- beofre the sqrt of 13
Step-by-step explanation:
1).5x² + 13x - 6 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a = 5 , b = 13 c = - 6
We have
[tex]x = \frac{ - 13± \sqrt{ {13}^{2} - 4(5)( - 6) } }{2(5)} [/tex]
[tex]x = \frac{ - 13± \sqrt{169 + 120} }{10} [/tex]
[tex]x = \frac{ - 13± \sqrt{289} }{10} [/tex]
[tex]x = \frac{ - 13±17}{10} [/tex]
[tex]x = \frac{ - 13 + 17}{10} \: \: \: \: \: or \: \: \: \: x = \frac{ - 13 - 17}{10} [/tex]
x = 2/5 or x = - 32).3x² + 5x + 1 = 0
a = 3 , b = 5 , c = 1
[tex]x = \frac{ -5 ± \sqrt{ {5}^{2} - 4(3)(1)} }{2(3)} [/tex]
[tex]x = \frac{ - 5± \sqrt{25 - 12} }{6} [/tex]
[tex]x = \frac{ - 5± \sqrt{13} }{6} [/tex]
[tex]x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} [/tex]
Hope this helps you
Al’s Produce Stand sells 6 ears of corn for $1.50. Barbara’s Produce Stand sells 13 ears of corn for $3.12. Write two equations, one for each produce stand, that model the relationship between the number of ears of corn sold and the cost.
Answer:
6n = 1.50
and
13n = 3.12
Step-by-step explanation:
Here in this question, we are interested in writing equations that relate the number of ears of corn sold and the cost.
For Al’s produce stand, let the price per corn sold be n
Thus;
6 * n = 1.50
6n = $1.50 •••••••(i)
For the second;
let the price per corn sold be n;
13 * n = $3.12
-> 13n = 3.12 •••••••••(ii)
Need help ASAP!!!! THX
Answer:
C
Step-by-step explanation:
f(x) = x - 2
f(2) = (2) - 2
f(2) = 0
A + B are wrong cuz..
f(-2) = -2 - 2
f(-2) = -4
PLEASE HELP!!!
Which expression shows a way to find the area of the following rectangle?
Answer:
B
Step-by-step explanation:
This rectangle appears to have 7 boxes on the bottom, and 3 box for the side.
Since area is base×height
It would be 7×3
Multiply. (2x - 3)(x + 4) a 2x² + 11x - 12 b 2x² + 5x - 12 c 2x² + 11x - 7 d 2x² + 3x - 7
Answer:
2x^2 +5x-12
Step-by-step explanation:
(2x - 3)(x + 4)
FOIL
first 2x*x = 2x^2
outer 2x*4 = 8x
inner -3x
last -3*4 = -12
Add these together
2x^2 +8x-3x-12
Combine like terms
2x^2 +5x-12
How to do this question plz.
plz work out for me in your notebook or sheet if you can plz the question so I can understand more plzz
Answer:
[tex]3\pi[/tex]
Step-by-step explanation:
The circumference of a circle is [tex]2\pi r[/tex].
If we want to find the circumference of this semi-circle, we can find the circumference if it was a whole circle then divide by 2.
[tex]2 \cdot \pi \cdot r\\2 \cdot \pi \cdot 3\\6 \cdot \pi\\ 6\pi[/tex]
Now we know the circumference of the whole circle.
To find the circumference of half the circle we divide by 2.
[tex]6\pi \div 2 = 3\pi[/tex]
Hope this helped!
jim buys a calculator that is marked 30% off. If he paid $35, what was the original price?
Answer:
x = 50
Step-by-step explanation:
Let x be the original price.
He got 30% off
The discount is .30x
Subtract this from the original price to get the price he paid
x - .30x = price he paid
.70x = price he paid
.70x = 35
Divide each side by .7
.70x/.7 = 35/.7
x=50
if your ans is correct i will choose you as a brainlist when the number of student of a school was increased by 30% it became 455. Find the previous number student.
Step-by-step explanation:
find 30% of 455
which is = 136.5
then subtract 136.5 from the original number(455)
455 - 136.5
=318.5 student
Answer it answer it answer it.
Answer:
Option C. P = 3/q
Step-by-step explanation:
To know the the correct answer to the question, do the following:
Let us assume a certain number for P say 2 and 3, and then, find the corresponding value for q in each case to see which will give a decreased value for q.
Option A
When P = 2, q =.?
P = 3q
2 = 3q
Divide both side by 3
q = 2/3
When P = 3, q =.?
P = 3q
3 = 3q
Divide both side 3
q = 3/3
q = 1
From the above illustration, we can see that as P increase, q also increase.
Option B
When P = 2, q =.?
P – 3 = q
2 – 3 = q
q = – 1
When P = 3, q =.?
P – 3 = q
3 – 3 = q
q = 0
From the above illustration, we can see that as P increase, q also increase.
Option C
When P = 2, q =.?
P = 3/q
2 = 3/q
Cross multiply
2 × q = 3
Divide both side by 2
q = 3/2
q = 1.5
When P = 3, q =.?
P = 3/q
3 = 3/q
Cross multiply
3 × q = 3
Divide both side by 3
q = 3/3
q = 1
From the above illustration, we can see that as P increase, q decreases.
Option D.
When P = 2, q =.?
1/p = 3/q
1/2 = 3/q
Cross multiply
1 × q = 2 × 3
q = 6
When P = 3, q =.?
1/p = 3/q
1/3 = 3/q
Cross multiply
1 × q = 3 × 3
q = 9
From the above illustration, we can see that as P increase, q also increase.
Now, haven done the above, only option C gives a decreased value for q as the value of P increases.
c
this before
Step-by-step explanation:
Find the coefficient of third term of (2x−1)^6.
240
using pascals trianle
for the power 6 it is
1, 6,15,20, 15,6, 1
and for the third term (2x)^4 and (-1)^2
[tex]15 \times {(2x)}^{4} \times {( - 1)}^{2} [/tex]
[tex]240 {x}^{4} [/tex]
Since only the coefficient is needed
the answer is 240.
The required coefficient of third term is 480.
Coefficient of the third term of (2x−1)^6 to be determine.
Coefficient is defined as the integer present adjacent to the variable.
Here, (2x−1)^6
Using binomial expansion,
Third term = P(6,2)(2x)^6-2(-1)^2
= 6*5*16x^4
= 480x^4
Thus, the required coefficient of third term is 480.
Learn more about coefficient here:
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A cyclist travels at $20$ kilometers per hour when cycling uphill, $24$ kilometers per hour when cycling on flat ground, and $30$ kilometers per hour when cycling downhill. On a sunny day, they cycle the hilly road from Aopslandia to Beast Island before turning around and cycling back to Aopslandia. What was their average speed during the entire round trip?
Answer:
Average speed during the trip = 24 km/h
Step-by-step explanation:
Given:
Speed of cyclist uphill, [tex]v_1[/tex] = 20 km/hr
Speed of cyclist on flat ground = 24 km/h
Speed of cyclist downhill, [tex]v_2[/tex] = 30 km/h
Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.
That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h
To find:
Average speed during the entire trip = ?
Solution:
Let the distance between Beast Island and Aopslandia = D km
Let the time taken to reach Beast Island from Aopslandia = [tex]T_1\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_1 = 20 = \dfrac{D}{T_1}[/tex]
[tex]\Rightarrow T_1 = \dfrac{D}{20} ..... (1)[/tex]
Let the time taken to reach Aopslandia back from Beast Island = [tex]T_2\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_2 = 30 = \dfrac{D}{T_2}[/tex]
[tex]\Rightarrow T_2 = \dfrac{D}{30} ..... (2)[/tex]
Formula for average speed is given as:
[tex]\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}[/tex]
Here total distance = D + D = 2D km
Total Time is [tex]T_1+T_2[/tex] hours.
Putting the values in the formula and using equations (1) and (2):
[tex]\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}[/tex]
So, Average speed during the trip = 24 km/h
Hi how to solve this pythagoras theorem
Answer:
The perimeter of the triangle is 40.
Step-by-step explanation:
Pythagorean Theorem: If x and y are the leg lengths of a right triangle, then r = √(x^2 + y^2) is the length of the hypotenuse. Alternatively, x^2 + y^2 = r^2.
The side lengths 2x, 4x - 1 and 4x + 1 are already arranged in ascending order. Thus, (2x^)2 + (4x - 1)^2 = (4x + 1).
Performing the indicated operations, we get:
4x^2 + 16x^2 - 8x + 1 = 16x^2 + 8x + 1. Simplify this first by combining like terms:
20x^2 - 16x = 16x^2, or
4x^2 - 16x = 0, or
4x(x - 4) = 0. Thus, x = 0 (which makes no sense here) or x = 4.
The perimeter of the rectangle is the sum of the three sides 2x, 4x - 1 and 4x + 1. Substituting 4 for x, we get
P = 8 + 16 - 1 + 16 + 1, or 40.
The perimeter of the triangle is 40.
If we did not write the equation 5x=21, instead we wrote it 21=5x,
we would get a different solution.
O True
O False
Answer:
Step-by-step explanation:
5x = 21 and 21 = 5x are identical relationships, and so the solution would be the same in both cases. (Commutative Property: order of addition/subtraction is immaterial)
Find an equation of the line: Through the point (2, −4) with a y-intercept of −2 Through the points (4,2) and (3,1) Through the point (3,2) with a slope of −2
Answer and Step-by-step explanation: Equations of line through points and slope can be determined by:
[tex]y-y_{0}=m(x-x_{0})[/tex]
m is slope
Point (2,-4) and y-intercept = -2Y-intercept is point (0,-2)
m = [tex]\frac{y_{a}-y_{b}}{x_{a}-x_{b}}[/tex]
m = [tex]\frac{-4-(-2)}{2-0}[/tex]
m = - 1
Equation:
[tex]y+2=-1(x-0)[/tex]
[tex]y=-x-2[/tex]
Points (4,2) and (3,1)m = [tex]\frac{2-1}{4-3}[/tex]
m = 1
Equation:
[tex]y-2=(x-4)[/tex]
[tex]y=x-2[/tex]
Point (3,2) and slope = -2m = -2
Equation:
[tex]y-2=-2(x-3)[/tex]
[tex]y=-2x+6+2[/tex]
[tex]y=-2x+8[/tex]
Can someone plz help me ASAP!!!!!!!!
Answer:
A) The number halfway between -2 and 6 is 2.
B) -10 is halfway between -18 and 8
Angles L and M are supplementary. What is the sum of
their measures?
The sum of the measures of angles L and M is
180 degree
Step-by-step explanation:
supplementary means anhke havinv sum of 180 degree
so sum to two supplemrntary angles is 180 drgree
Supplementary angles always add to 180.
One way I think of it is "supplementary angles form a straight angle", and both the words "supplementary" and "straight" start with the letter "S".
In contrast, complementary angles form a corner. Both "complementary" and "corner" start with "co". By "corner", I mean a 90 degree corner.
-3 = 7 - BLANK pls tell me what blank is
Answer:
10
Step-by-step explanation:
-3 = 7 - x
Add x to both sides
x -3 = 7 - x +x
x - 3 = 7
Now, add 3 to both sides
x - 3 + 3 = 7 + 3
x = 10
Answer:
[tex]\boxed{10}[/tex]
Step-by-step explanation:
[tex]-3=7- \sf BLANK[/tex]
[tex]\sf Subtract \ 7 \ from \ sides.[/tex]
[tex]-3-7=-7+7- \sf BLANK[/tex]
[tex]-10=- \sf BLANK[/tex]
[tex]\sf Multiply \ both \ sides \ by \ -1.[/tex]
[tex]-10(-1)=(-1)- \sf BLANK[/tex]
[tex]10= \sf BLANK[/tex]
April typed a 5 page report in 50 mintues. Each page had 500 words at what rate is April typing
Answer:
Amy types at a rate of 50 words per minute
Step-by-step explanation:
In this question, we are interested in calculating the rate at which April is typing.
From the question, we can deduce that she typed a 5 page report, with each page having a total of 500 words.
Now, if each page has 500 words, the total number of words in all of the pages will be 5 * 500 = 2,500 words
Now, from here, we can see that 2,500 words were typed in 50 minutes.
The number of words per minute will be ;
Total number of words/Time taken = 2500 words/50 minutes
That will give a value of 50 words per minute
Find the total surface area.
Answer:
143.4 mi²
Step-by-step explanation:
Top: 8x6=48
Bottom: 3x8=24
Sides: 3x8=24 and 24
Trapezoids sides: (6+3)/2*2.6=4.5*2.6=11.7 and 11.7
TOTAL: 48+24+24+24+11.7+11.7= 143.4 mi²
Loreto quería decorar un viejo tambor metálico para usarlo de paragüero. Para ello, contaba con un grueso cordón que pretendía pegar en el contorno del borde superior del tambor. Sabiendo que el diámetro de este era 58,5 cm, cortó el cordón, dejando el trozo más largo de 175,5 cm de longitud de modo que le alcanzara justo, pero le faltaron 7 cm. ¿Cuál fue el error de Loreto?
Answer:
u should put the question in English to so English people can also help
Find the length of the base and the height and calculate the area
Answer:
44
Step-by-step explanation:
base = 3- -5 = 8
height = 8 - -3 = 11
1/2 bh
1/2(8)(11) = 44
In politics, marketing, etc. We often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Describe the conclusion about p using an absolute value inequality.
Answer: |p-72% |≤ 4%
Step-by-step explanation:
Let p be the population proportion.
The absolute inequality about p using an absolute value inequality.:
[tex]|p-\hat{p}| \leq E[/tex] , where E = margin of error, [tex]\hat{p}[/tex] = sample proportion
Given: A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .
|p-72% |≤ 4%
⇒ 72% - 4% ≤ p ≤ 72% +4%
⇒ 68% ≤ p ≤ 76%.
i.e. p is most likely to be between 68% and 76% (.
The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
What is absolute value inequality?An expression using absolute functions and inequality signs is known as an absolute value inequality.
We know that the absolute value inequality about p using an absolute value inequality is written as,
[tex]|p-\hat p| \leq E[/tex]
where E is the margin of error and [tex]\hat p[/tex] is the sample proportion.
Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,
[tex]|p-0.72|\leq 0.04\\\\(0.72-0.04)\leq p \leq (0.72+0.04)\\\\0.68 \leq p\leq 0.76[/tex]
Thus, the p is most likely to be between the range of 68% to 76%.
Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,
[tex]|p-\hat p|\leq E\\\\|p-0.32|\leq 0.022\\\\(0.32-0.022)\leq p \leq (0.32+0.022)\\\\0.298\leq p\leq 0.342[/tex]
Thus, the p is most likely to be between the range of 29.8% to 34.2%.
Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
Learn more about Absolute Value Inequality:
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6 points are place on the line a, 4 points are placed on the line b. How many triangles is it possible to form such that their verticies will be the given points, if a ∥b?
Answer: 96
Step-by-step explanation:
Ok, lines a and b are parallel.
We can separate this problem in two cases:
Case 1: 2 vertex in line a, and one vertex in line b.
Here we use the relation:
"In a group of N elements, the total combinations of sets of K elements is given by"
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.
Then if we have two vertices in line a, we have:
N = 6, K = 2
[tex]C = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15[/tex]
And the other vertex can be on any of the four points on the line b, so the total number of triangles is:
C = 15*4 = 60.
But we still have the case 2, where we have 2 vertices on line b, and one on line a.
First, the combination for the two vertices in line b is:
We use N = 4 and K = 2.
[tex]C = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6[/tex]
And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:
C = 6*6 = 36
Then, putting together the two cases, we have a total of:
60 + 36 = 96 different triangles
A shell of mass 8.0-kg leaves the muzzle of a cannon with a horizontal velocity of 600 m/s. Find the recoil velocity of the cannon, if its mass is 500kg.
Answer:
velocity of recoil velocity of cannon is -9.6 m/sec
Step-by-step explanation:
according to law of conservation of momentum
total momentum of isolated system of body remains constant.
momentum = mass of body* velocity of body.
__________________________________
in the problem the system is
shell + cannon
momentum of shell = 8*600 = 4800 Kg-m/sec
let the velocity of cannon be x m/sec
momentum of cannon = 500*x = 500x Kg-m/sec
initially the system of body is in rest (before the shell is fired) hence, total momentum of the system i is 0
applying conservation of momentum
total momentum before shell fired = total momentum after the shell is fired
0 = momentum of shell + momentum of cannon
4800 + 500x = 0
x = -4800/500 = -9.6
Thus, velocity of recoil velocity of cannon is -9.6 m/sec
here negative sign implies that direction of velocity of cannon is opposite to that of velocity of shell.
G(x)= -\dfrac{x^2}{4} + 7g(x)=− 4 x 2 +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, squared, divided by, 4, end fraction, plus, 7 What is the average rate of change of ggg over the interval [-2,4][−2,4]open bracket, minus, 2, comma, 4, close bracket?
Answer:
-1/2Step-by-step explanation:
Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;
Rate of change of the function is expressed as g(b)-g(a)/b-a
where a - -2 and b = 4
[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]
[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]
average rate of change of g(x) over the interval [-2,4] will be;
[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]
Manuel made at least one error as he found the value of this expression. Identify the step in which Manuel made his first error. After identifying the step with the first error, explain the corrected steps and find the final answer.
Answer:
Manuel made his first mistake in step 2 leading to the continuous mistakes
Final answer=185
Step-by-step explanation:
Manuel made at least one error as she found the value of this expression. 2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50) Step 1: 2(-20) + 3(-25) + 5(20) + 4(50) Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50) Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405 Identify the step in which Chris made her first error. After identifying the step with the first error, write the corrected steps and find the final answer.
2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50)
Step 1: 2(-20) + 3(-25) + 5(20) + 4(50)
Step 2: -40 - 75 + 100 +
200
Step 3: -115 + 300
Step 4: 185
Manuel made his first error in step 2 by combining two different terms into one as he has done
(3 + 2)(-20 + -25) and also (5 + 4)(20 + 50)
Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50)
Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405
He should have evaluated the terms separately as I have done above, giving us 185 as the final answer in contrast to his 405 final answer.
