Answer:
Average rate of fall = [tex]\frac{h(3)-h(0)}{3}[/tex]
Step-by-step explanation:
Since they give you an expression for the position of the object as a function of time, one can derive the average velocity of the object during the first 3 seconds of the fall by estimating the position of the object at time 0, the position of the object at time 3 seconds, finding the displacement of the object (distance covered) in that interval of time (via a subtraction of these two quantities), and finally dividing this change by the elapsed time (3 seconds) thus using the concept that velocity is the quotient between distance covered over the elapsed time:
Average rate of fall = (h(3) - h(0))/ 3
Average rate of fall = [tex]\frac{h(3)-h(0)}{3}[/tex]
Answer:
D
Step-by-step explanation:
Solve for x 5 x − 1 = 6 x − 9
Answer:
The value of x in this equation is 8.
Step-by-step explanation:
5x - 1 = 6x - 9
Subtract 6x on both sides.
-x - 1 = -9
Add 1 to both sides.
-x = -8
Divide by -1 on both sides.
x = 8
A company makes 100 bags. 32 of the bags have buttons but no zips. 32 of the bags have zips but no buttons. 35 of the bags have neither zips nor buttons. A bag is selected at random. What is the probability that the bag has buttons?
Answer:
32%, 8/25
Step-by-step explanation:
Since we are looking under the category of buttons, only 1 of the 3 options fit the description. 32 have buttons but no zips. All the others are either just zip or neither of them.
This means out of 100, only 32 have buttons
32/100 or 32%
We can simply 32/100 to 8/25
Answer:
8 / 75
Step-by-step explanation:
the probability of choosing a bag with buttons is ⅓ since there are three types of bags(with buttons, with zips and with neither)
there are 32 bags with buttons out of the 100, probability of choosing a bag with buttons is 32 / 100
multiply the two values
⅓ × 32 / 100
= 8 / 75
the annual rate of inflation is given by the formula I = (p2/p1)^1/n - 1, where p1 is the initial price of an item and p2 is the final price of an item over a period of n years. In 1980, the average price of an ounce of gold was $850. By 2011, the average price was $1,800. In this situation, what is n?
Answer:
The value of [tex]n[/tex] is 31 years.Step-by-step explanation:
The given equation is formed by different variables, where [tex]n[/tex] indicates the period of time in years where the rate of inflation is calculated.
In this case, we have a period from 1980 to 2011. The difference between these years would be the period of time used to find the inflation rate.
[tex]2011-1980=31[/tex]
Therefore, the value of [tex]n[/tex] is 31 years.
write an equation of the line that passes through (4,-6) and is parallel to the line y=-3x-9
Answer:
y - 7 = 3(x - 3)
y - 7 = 3x - 9
y = 3x - 2
Step-by-step explanation:
Hope this helped you!
The minimum weekly commission earned to be a STAR sales person is $9000. If Sandra receives a 12% commission on the sale of all cars, write and solve an inequality to represent the minimum number of cars she must sell in order to be a sales person
Answer:
[tex]numbers\ of\ cars \geq \frac{75000}{price\ of\ the\ car}[/tex]
Step-by-step explanation:
Hello, I can help you with this
Step 1
define
The minimum weekly commission earned to be a STAR sales person is $9000, let's name this value as M
if Sandra receives a 12% commisions of the sale of all cars, then that 12% must be equal or higher than 9000 in order to become a STAR sales person
Step 2
using a rule of three find the 100%
if
12% ⇔ $9000
then
100% ⇔x
the ratio is
[tex]\frac{12}{9000}=\frac{100}{x}\\[/tex]
Now, solve for x
[tex]\frac{12}{9000}=\frac{100}{x}\\\\\frac{12*x}{9000}=\frac{100}\\\\{12x}=9000*100\\\\12x=900000\\x=\frac{900000}{12}\\ x=75000\\[/tex]
so, Sandra must sell a minimun of $75000
Now, to give a response, we need to asume a only price for every car(p).
now, in matemathical terms.
the minimun number of cars she must to sell is
minum number of cars sandra has to sell to become a STAR sales person
is [tex]\frac{75000}{price\ of\ the\ car} \\[/tex]
[tex]\frac{75000}{price\ of\ the\ car} \\[/tex]
now, price of the car* number of the car = 75000
where
[tex]numbers\ of\ cars \geq \frac{75000}{price\ of\ the\ car}[/tex]
Have a nice day
Find the value of x.
Answer:
x=6.09cm
Step-by-step explanation:
Working out AB:
7.5²+4.9²
= √80.26
AB= 8.96cm
To work out x:
AB is the opposite, where BC is the adjacent. This means that we have to use TOA.
x=8.96/Tan(55.8)
x= 6.09cm
Answer:
6.1 cm
Step-by-step explanation:
Use the Pythagorean theorem for triangle ABD to find the hypotenuse.
7.5^2+4.9^2=c^2. After solving you get that the missing length is about 9 cm. The hypotenuse of ABD is also a leg for ABC so you can use a trigonometric function, tangent, to find x. Set up the equation for opposite and adjacent sides to angle measure 55.8. The equation is tan(55.8)=9/x. In order to isolate the variable you multiply both sides by x to get (x)tan(55.8)=9, then divide both sides by tan(55.8), this leaves you with x=9/tan(55.8). You can then plug this into the calculator to get x is approximately 6.1 cm.
Write these numbers in standard form.
a)
seventeen thousand
b) twenty six million
c)
seven hundred and forty thousand
Answer:
A) 17,000 = 1.7x10^4
B) 26,000,000 = 2.6x10^7
C) 740,000 = 7.4x10^5
Step-by-step explanation:
Answer:
1.7x10
Step-by-step explanation:
Suppose that each country currently has 90 workers and each decides to transfer some amount of labor toward its area of comparative advantage. The United States transfers 10 workers away from socks toward producing cell phones. Thailand transfers 18 workers away from cell phones toward producing socks. What will be the new total output of cell phones for both countries combined?
Answer:
I got 41000 cell phones.
Step-by-step explanation:
Step 1: I figured out the amount of each workers from 90
US Sock Production: 18 workers
Thailand Sock Production: 15 workers
US Cell Production: 27 workers
Thailand Cell Production: 30 workers
Step 2: I adjusted the workers amounts to the question's changes
US Sock Production: 18 - 10 = 8 workers
Thailand Sock Productions: 18 + 15 = 33 workers
US Cell Production: 27 + 10 = 37 workers
Thailand Cell Production: 30 - 18 = 12 workers
Step 3: Find the total amount of cell phones produced
4(1000) + 37(1000) = 41000 cell phones
*12/3 = 4 because 3 workers are needed to make 1000 cell phones
(blank) ÷ by 7 > 800 send help...
Answer:
(blank) > 5600
Step-by-step explanation:
Triangle ABC has vertices at A(8,3), B(8,5), and C(4,3).
What is the area of Triangle ABC?
Answer: 4 units squared
Step-by-step explanation:
A = (l * w) / 2
5 - 3 = 2
8 - 4 = 4
4 * 2 = 8
8 / 2 = 4
Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can get at least 25% of the student population to sign a petition. So far, 82 students have signed the petition. Jose used the following steps to write an inequality that can be used to determine the number of student signatures still needed: Step 1. Declare the variable: Let x = the number of student signatures still needed. Step 2. Create a ratio equivalent to StartFraction total number of signatures needed over total number of students in the school EndFraction : StartFraction x + 82 over 426 EndFraction. Step 3. Convert 25% to a decimal: 25% = 0.25. Step 4. Write the inequality: StartFraction x + 82 over 426 EndFraction less-than-or-equal-to 0.25. What is Jose’s error? In Step 1, x should be equal to the total number of students in the school. In Step 2, the ratio should be StartFraction x over 426 EndFraction. In Step 3, the decimal should be 0.025. In Step 4, the inequality should
Answer: Step 4
Step-by-step explanation:
1. Define variable x as student signatures still needed (Correct)
[tex]2)\ \dfrac{x+82}{426}[/tex] (Correct)
3. 25% = 0.25 (Correct)
[tex]4)\ \dfrac{x+82}{426}\leq 0.25[/tex] (Error)!
The inequality symbol should be GREATER THAN or equal to (≥) because Jose needs 25% or more (not less).
Answer:
In Step 4, the inequality should be StartFraction x + 82 over 426 EndFraction greater-than-or-equal-to 0.25.
¯\_ _/¯
( ﾉ ﾟｰﾟ)ﾉ ＼(ﾟｰﾟ＼)
An object accelerates from rest at 10m/s2 for 20s. Calculate the velocity reached.
Answer:
400 m/s
Step-by-step explanation:
u=0 m/s
t=20 s
a=20 m/s²
v=u+at
=0+20×20
=400 m/s
Find the solution of this system of equations -2x+3y=-3 and -2x-5y=-75
Answer:
X=15y=9please see the attached picture for full solution..
Hope it helps...
Good luck on your assignment...
A square has a side length x and a circle has a radius (x-1). At what value of x will the two figures have the same area?
a. 1.66
b. 2.29
c. 0.5
d. 1.25
Answer:
B
Step-by-step explanation:
The area of the square can be calculated using S^2 = x^2
The area of the circle is pi * r^2
= 22/7 * (x-1)^2
= 22(x-1)^2/7
So we need the value of x, that will make;
x^2 = 22(x-1)^2/7
In this kind of scenario, since we have options, it is best to test values instead of going through long calculations
Let’s try 2.29
So;
2.29^2 = 22/7(2.29-1)^2
5.2441 = 5.23
So close , but let’s see if any other value will
give us a closer value
Let’s work with 1.66
1.66^2 = 22/7(1.66-1)^2
2.7556 = 1.369
This is far from what we need
Let’s try 0.5
0.5^2 = 22/7(0.5-1)^2
Thus gives a negative answer on the right hand side, so no need trying
And lastly 1.25
1.25^2 = 22/7(1.25-1)^2
1.5625 = 0.1946
So the first test still gives the most probable answer to a decimal place accuracy
Answer:
b. 2.29
Step-by-step explanation:
the answer above is correct please give them the brainiest
in a survey of 9000 people, 4000 likes tea,4500 like coffee. among them 2500 dont like tea and coffee. find number of people who like tea and coffee both
Step-by-step explanation:
No of people likes tea = 4000
No of people like coffee = 4500
Total = 8500
No of people don't like tea and coffee = 2500
No of people like tea and coffee = 8500 - 2500 = 6000
Answer:
500
Step-by-step explanation:
n(t)=4000
n(c)=4500
n(tea only )= 4000-x
n(coffee only )= 4500-x
n(coffee and tea )= x
note...using Venn diagram ..all together must add up to 9000
(4000-x)+(4500-x) +x = 9000
..............
...........collect like terms
9500-9000 = x
x = 500
Describe the follow scenario involves a permutation or combination. Then find the number of possibilities. Cody and Aaliyah are planning trips to two countries this year there in 15 countries they would be interested in visiting one trip will be one week long another two weeks
Answer:
This is a permutation problem because the order of their choice is important.
There are 210 ways in which this choice can be made.
Step-by-step explanation:
Complete Correct Question
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities. Cody and Aaliyah are planning trips to two countries this year. There are 15 countries they would be interested in visiting. One trip will be one week long and the other two weeks.
Solution
Permutation is used to calculate the number of possibilities or number of ways k choices can be made from n options given that the order of picking the choices is important. If there are choices A, B and C, picking ABC is different from CAB if order of picking is important like permutation preaches.
Combination on the other hand, is used to calculate the number of possibilities or number of ways k choices can be made from n options given that the order of picking the choices is unimportant. If there are choices A, B and C, picking ABC is the same as picking CAB if order of picking is unimportant like combination preaches.
So, in this question, Cody and Aaliyah want to pick 2 countries to visit, out of 15. They plan to spend 2 weeks in one country and 1 week in the other country.
This last sentence makes the order in which they pick the countries to visit important. If they chose to spend two weeks in country A and one week in country B, it is now a different possibility from spending two weeks in country B and one week in country A.
Hence, this is a permutation problem
The number of possibilities of picking 2 countries out of 15 countries to spend 2 weeks in first country and spend 1 week in the other country is ¹⁵P₂ = 15! ÷ (15 - 2)!
= 210 ways in which this choice can be made.
Hope this Helps!!!
Please sb help and write it down on paper then send a pic❤️
Answer:
Step-by-step explanation:
1) We would determine the cube root of 27 and find its square.
Cube root of 27 = 3
3² = 9
Solution = 9
2) 36³ = 46656
√36³ = √46656 = 216
3) we would find the 5th roof of - 243 and find its cube
5th root of - 243 = - 3
- 3³ = - 27
Solution = - 27
4) Looking at the expression, 40⅔, we can see that
a = 2
b = 3
c = 40
Answer: 1) We would determine the cube root of 27 and find its square.Cube root of 27 = 33² = 9Solution = 92) 36³ = 46656√36³ = √46656 = 2163) we would find the 5th roof of - 243 and find its cube5th root of - 243 = - 3- 3³ = - 27Solution = - 274) Looking at the expression, 40⅔, we can see that a = 2b = 3c = 40
Step-by-step explanation:
perpendicular to 2x-3y+12=0
Answer:
3x +2y = 0
Step-by-step explanation:
Swapping the x- and y-coefficients and negating one of them will get you a perpendicular line. Since you have not specified a point, we can make it go through the origin:
3x +2y = 0
бу2 + 13y – 8 how to factorize this?
Answer:
We have 6y² + 13y - 8. We can rewrite this as 6x² + 16x - 3x - 8. Grouping terms we get 2x(3x + 8) - (3x + 8) and since both terms have the common factor of (3x + 8) the answer is (3x + 8)(2x - 1).
1) For question 1, use the figure below. a) Are the following polygons similar? Explain. (2 pts) Yes or No b) Assume the polygons are similar. Write a similarity statement for the polygons. (1 pt) c) A new figure is created, Polygon JKLM, such that Polygon ABCD is similar to Polygon JKLM, and side JM is 36. Given this information, what is the scale factor between Polygon JKLM and Polygon ABCD. Show the calculations that lead to your results. (2 pts)
Answer: a) Yes b) Polygon ABCD ~ Polygon EFGH c) JKLM is 3x bigger than polygon ABCD
Step-by-step explanation:
(for part c)
JM= 36
AD= 12
36/12= 3
JKLM is 3x bigger than polygon ABCD
A projectile is fired straight up from ground level with an initial velocity of 112 ft/s. Its height, h, above the ground after t seconds is given by h = –16t2 + 112t. What is the interval of time during which the projectile's height exceeds 192 feet?
A. 3
B. t<4
C. t>4
D. 3>t>4
Answer: 3 < t < 4
Step-by-step explanation:
Given the following information :
Initial Velocity of projectile = 112 ft/s
Height (h) above the ground after t seconds :
h = –16t2 + 112t
To calculate the time when h exceeds 192 Feets (h >192)
That is ;
-16t^2 + 112t = > 192
-16t^2 + 112t - 192 = 0
Divide through by - 16
t^2 - 7t + 12 = 0
Factorizing
t^2 - 3t - 4t + 12 =0
t(t - 3) - 4(t - 3) = 0
(t-3) = 0 or (t-4) =0
t = 3 or t=4
Therefore, t exist between 3 and 4 for height in excess of 192ft
–16(3)^2 + 112(3) = 192 feets
–16(4)^2 + 112(4) = 192 feets
3 < t < 4
For any nonegative real number b,
Answer:
b
Step-by-step explanation:
The square root is the opposite of squaring
( sqrt(b))^2 =
sqrt(b) * sqrt(b)
b
HELP!! Given rhe polynomual function below find f(3)
Answer:
34
Step-by-step explanation:
You substitute 3 in for x, so your equation is now 2(3)^3 - 7(3) + 1.
You solve using P.E.M.D.A.S.
Start with 3^3 (3*3*3) = 27 Now the equation is 2(27) - 7(3) + 1.
-7(3)= -21 and 2(27)= 54.
Now it's 54 - 21 + 1.
54 - 21 is 33, add 1.
34.
Hope this helps!
What is the value of x?
Answer:
The answer is option C.
Step-by-step explanation:
Angles in a triangle add up to 180°
To find x add up all the angles in the triangle and subtract it from 180°
Thus
x + 95 + 57 = 180
x = 180 - 152
x = 28°
Hope this helps
Write an equation in point-slope form for each line (If possible please show work)
Hey there! :)
Answer:
x = 1/2(y -3)
Step-by-step explanation:
Begin by finding the slope using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates:
[tex]m = \frac{4-3}{2-0}[/tex]
Simplify:
[tex]m = \frac{1}{2}[/tex]
Recall that point-slope form is:
[tex](x-x_{1}) = m(y-y_{1})[/tex]
Plug in the slope and coordinates into the equation:
(x - 0) = 1/2(y - 3)
x = 1/2(y -3)
PLEASE HELP!!!! |6n+7|=8 |3x–1|=4
Answer:
|6n+7|=8= n=1/6,-5/2
|3x–1|=4 x=5/3,-1
Step-by-step explanation:
Erika calculated that she would spend $115 on school supplies this year. She actually spent $82.50 on school supplies. What is Erika's percent of error?
Answer:
Percentage error is 39.39%
Step-by-step explanation:
It is given that,
The calculated value that Erika spend on school supplies this year is $115.
Actual value that she spent is $82.50.
We need to find Erika's percent of error. Percentage error is given by the formula as follows :
[tex]\%=\dfrac{\text{calculated value}-\text{actual value}}{\text{actual value}}\times 100\\\\\%=\dfrac{115-82.5}{82.5}\times 100\\\\\%=39.39\%[/tex]
So, Erika's percent of error is 39.39%.
There are 300 students in the seventh grade at Lincoln Middle School. When the students voted on new school colors, 65% of the seventh graders voted for the combination of blue and silver. How many seventh graders voted for the blue and silver color combination?
Answer:
195 students voted for the blue and silver color combination.
Step-by-step explanation:
First, you have to convert 65% to a decimal ( You should get 0.65 ).
Next, you multiply 300 by the decimal ( 0.65 )
You should get 195, so that's how many people voted for the blue and silver color combination.
Answer:
195
Step-by-step explanation:
The ratio of the amount of vitamin A in cow milk to the amount of vitamin A in goat milk is 333 to 444. If a liter of cow milk has 156015601560 international units (\text{IU})(IU)left parenthesis, start text, I, U, end text, right parenthesis of vitamin A, how many \text{IU}IUstart text, I, U, end text of vitamin A are in a liter of goat milk?
Answer:
[tex]Goat = 2080IU[/tex]
Step-by-step explanation:
Given
Ratio = 3 : 4
Litre of cow = 1560IU
Required
IU of a litre of goat
The ratio represents ratio of cow milk to goat milk
In other words;
[tex]Cow:Goat = 3 : 4[/tex]
To calculate the number of IU in a litre of goat milk; we substitute Cow with 1650 in the above expression
[tex]Cow:Goat = 3 : 4[/tex]
[tex]1560:Goat = 3 : 4[/tex]
Convert to fraction
[tex]\frac{1560}{Goat} = \frac{3}{4}[/tex]
Multiply both sides by 4
[tex]4 * \frac{1560}{Goat} = \frac{3}{4} * 4[/tex]
[tex]\frac{4 * 1560}{Goat} = \frac{ 4 * 3}{4}[/tex]
[tex]\frac{6240}{Goat} = 3[/tex]
Multiply both sides by Goat
[tex]Goat * \frac{6240}{Goat} = 3 * Goat[/tex]
[tex]6240 = 3 * Goat[/tex]
Divide both sides by 3
[tex]\frac{6240}{3} = \frac{3 * Goat}{3}[/tex]
[tex]\frac{6240}{3} = \frac{3 * Goat}{3}[/tex]
[tex]2080 = Goat[/tex]
[tex]Goat = 2080[/tex]
HELP ASAP ! Identify the volume and surface area of a sphere in terms of pi with a great circle area of 144pi ft^2.
Answer:
Area of sphere = 576 pi ft^2
Volume of sphere = 2,304 pi ft^3
Step-by-step explanation:
Radius of great circles are the same as radius of the sphere
So let’s calculate the radius of the sphere from the area given;
Mathematically;
pi * r^2 = 144pi
r^2 = 144
r = square root of 144
r = 12 ft
Volume of sphere = 4/3 * pi * r^3
= 4/3 * pi * 12^3 = 2,304 pi ft^3
Area of sphere = 4 * pi * r^2 = 4 * pi * 12^2 = 4 * 144 * pi = 576 pi ft^2
