Answer:
[tex]\displaystyle \int {84} \, dx = 84x + C[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsDefinite/Indefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {84} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {84} \, dx = 84\int {} \, dx[/tex][Integral] Reverse Power Rule: [tex]\displaystyle \int {84} \, dx = 84x + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integrations
in the box of Stones ,the ratio of red marbles is 2:5. the ratio of green stones to the total stones is 3:10 .if the stones that are neither red nor green are blue ,how many blue are in the box.if there are 40 marbles in the box?.
According to the Federal Election Commission, 53.6% of all registered voters in 2012 voted in the US presidential elections in 2012. A political study conducted in January 2016 surveyed 1,251 eligible voters and found that 86% said they planned to vote in the 2016 presidential election. Based on this information, match each term to its value.
1. 1,251
2. 53.6%
3. 86%
a. statistic
b. sample size
c. parameter
Answer:
SEE BELOW
Step-by-step explanation:
1. sample size - 1,251
2 .statistic - 53.6%
3. parameter - 86%
hope this helps :)
The mother was fed 21 fish, how many fish was the cub fed?
Please help me to find this answer
Answer:
Look in Step by Step Explanation
Step-by-step explanation:
3)SOHCAHTOA
tan=opposite/adjacent
tan(20)=x/83
83tan(20)=x
x=30.209
2) SOHCAHTOA
Tangent=opposite/adjacent
Tan(62)=x/8
8tan(62)=x
x=15.04
3)SOHCAHTOA
Sin=opposite/hypotonouse
sin(25)=30/x
x=30/sin(25)
x=70.986
Hi.
• Easy question.
• No Copy paste
1) 40 + 5 × 5 =
Note : actually i come from another country •-•
Answer:
65
Step-by-step explanation:
40 + 5 × 5
40 + 25
65
Good Luck!Note: I also come from another country •-•
[tex]{ \boxed {\huge{ \sf{ \color{blue}{answer : }}}}}[/tex]
65
Step-by-step explanation:
= 40 + 5 × 5
= 40 + 25
= 65
-
#Good_LuckIf a^2+b^2= 4 and ab = 5, what is the value of
(a+b)^2?
A. 10
B. 12
C. 14
D. 16
Answer:
14
Step-by-step explanation:
(a+b)^2
(a+b)(a+b)
FOIL
a^2 + ab+ab + b^2
Combine like terms
a^2 +2ab + b^2
Rearranging
a^2+b^2 +2ab
We know a^2+b^2 = 4 and ab= 5
4 + 2(5)
4+10
14
Answer:
C. 14.
Step-by-step explanation:
We use the identity:-
a^2 + b^2 = (a + b)^2 - 2ab
So 4 = (a + b)^2 - 2(5)
(a + b)^2 = 4 + 2(5)
= 14.
Karen is having a party. She'll have 4 tables for every 12 guests. Complete the table below showing the number of tables and the number of guests.
Find the measure of the missing angles.
Answer:
Step-by-step explanation:
e = 61°, f = 119°, and d = 90°
We know that vertically opposite angles are equal.
So, e = 61° [Vertically opposite angles]
We know that linear pair of angles are supplementary (180°).
So, f + 61° = 180° [Linear pair of angles]
=> f = 180° - 61°
=> f = 119°
and d + 90° = 180° [Linear pair of angles]
=> d = 180° - 90°
=> d = 90°
A textbook store sold a combined total of 473 chemistry and sociology textbooks in a week. The number of sociology textbooks sold was 59 less than the number of chemistry textbooks sold. How many textbooks of each type were sold?
Answer:
I. C = 266 textbooks.
II. S = 207 textbooks.
Step-by-step explanation:
Let the chemistry textbook be C.
Let the sociology textbook be S.
Translating the word problem into an algebraic expression, we have;
C + S = 473 ..... equation 1
S = C - 59 ..... equation 2
Substituting eqn 2 into eqn 1, we have;
C + C - 59 = 473
2C - 59 = 473
2C = 473 + 59
2C = 532
C = 532/2
C = 266 textbooks.
Next, we would determine the value of S;
S = C - 59
S = 266 - 59
S = 207 textbooks.
Check:
C + S = 473
266 + 207 = 473
473 = 473
Find h(-5) when: h(x) = x2 + 2x + 2
Answer:
17
Step-by-step explanation:
h(x) = x^2 + 2x + 2
Let x = -5
h(-5) = (-5)^2 + 2(-5) + 2
= 25 -10 +2
= 17
Martina got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 19 cents per yard. If after that purchase there was $15.63 left on the card, how many yards of ribbon did Martina buy?
Phone card = $20
You need to minus 17.92 from 20 = $2.08
$2.08 / 0.13 = how many minutes
= 16
A distribution of values is normal with a mean of 1986.1 and a standard deviation of 27.2.
Find the probability that a randomly selected value is greater than 1914.8.
P(X> 1914.8) =
Enter your answer as a number accurate to 4 decimal places. *Note: all z-scores must be rounded to
the nearest hundredth.
Answer:
I used the function normCdf(lower bound, upper bound, mean, standard deviation) on the graphing calculator to solve this.
Lower bound = 1914.8Upper bound = 999999Mean = 1986.1Standard deviation = 27.2Input in these values and it will result in:
normCdf(1914.8,9999999,1986.1,27.2) = 0.995621
So the probability that the value is greater than 1914.8 is about 99.5621%
I'm not sure if this is correct 0_o
Suppose that a category of world-class runners are known to run a marathon in an average of 147 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons. (Round your answer to two decimal places.)
Answer:
0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Average of 147 minutes with a standard deviation of 12 minutes.
This means that [tex]\mu = 147, \sigma = 12[/tex]
Consider 49 of the races.
This means that [tex]n = 49, s = \frac{12}{\sqrt{49}} = \frac{12}{7} = 1.7143[/tex]
Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons.
This is the p-value of Z when X = 150 subtracted by the p-value of Z when X = 146. So
X = 150
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{150 - 147}{1.7143}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a p-value of 0.9599
X = 146
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{146 - 147}{1.7143}[/tex]
[tex]Z = -0.583[/tex]
[tex]Z = -0.583[/tex] has a p-value of 0.3075.
0.9599 - 0.3075 = 0.6524.
0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.
Becky Anderson must pay a lump sum of $6000 in 5 yr. If only $5000 is available to deposit right now, what annual interest rate is necessary for the money to increase to $6000 in 5 yr?
Hello!
Out equation is: [tex]A=P(1+\frac{r}{n} )^t^n[/tex]
A= 6000
P=5000
N=1
T=5
R= What we are trying to find
This means we will have [tex]6000=5000(1+r)^5[/tex]
Divide both sides by 5000:
[tex]\frac{6000}{5000} = (1+r)^5[/tex]
Move the power to the other side by rooting both sides:
[tex]\frac{6000}{5000} ^1^/^5 = 1+r[/tex]
Subtract 1 from both sides:
[tex]\frac{6000}{5000} ^1^/^5 -1 = r[/tex]
Now we just need to calculate: R = 0.03713728...
I don't know how many decimal places you can have, but I will round to 2. This will give you an Interest Rate of 3.71%.
I hope this helps! :)
plz help I will give Brianly
A pair of linear equations is shown below: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points) Select one: a. On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. b. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. c. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. d. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Answer:
the answer is 89
Step-by-step explanation:
this is a hard one to salve but basically if you know and lern hout to do it it is not that hard
How many mL of a 10% magnesium sulfate solution will contain 14 grams of magnesium sulfate?
Answer:
Upto 40 g or 160 mmols
Step-by-step explanation:
Can you plz mark me as brainliest?
Answer:
140 mL
Step-by-step explanation:
10% of 140 is 14
The ratio of total interior angles to total exterior angles of a quadrilateral is
Select one:
a. 3:1
b. 1:2
c. 1:1
d. 2:1
9514 1404 393
Answer:
c. 1 : 1
Step-by-step explanation:
The total of exterior angles of any convex polygon is 360°. The total of interior angles of a quadrilateral is 360°. So, the ratio of interest is ...
interior : exterior = 360° : 360° = 1 : 1
Solve using the addition principle. 3y - 11 ≤ 2y - 2
Answer:
y ≤ 9
Step-by-step explanation:
3y - 11 ≤ 2y - 2
Subtract 2y from each side
3y-2y - 11 ≤ 2y-2y - 2
y - 11 ≤ - 2
Add 11 to each side
y - 11+11 ≤ - 2+11
y ≤ 9
Answer:
[tex]y \leqslant 9[/tex]
Step-by-step explanation:
[tex]3y - 11 \leqslant 2y - 2 \\ 3y - 2y \leqslant 11 - 2 \\ y \leqslant 9[/tex]
URGENT 100 POINTS AND BRAINIEST!!!!!!
Question 4 (Essay Worth 10 points)
(02.05 HC)
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
A graph with two linear functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Using the points stated in the original problem, I have determined the lines for the graph.
f(x)=3x-1
g(x)= 3x+17
Using the basic descriptions of transformations, we can determine the movement of the lines as being either horizontal or vertical shifts. (to put a visual to this problem, I the diagram in Desmos and then marked the stated points on the graph.)
Horizontal shifts move the line either to the left or to the right. Vertical shifts move the line either up or down.
If you look at the graphs as being the same x-value for the functions, the change in the y- value is +18, which is a vertical shift.
If you look at the graphs as being the same y-values, the change in x is -6 which is a horizontal shift.
So, the value of k is the amount of change each equation has to have to match the points given. (from f(x) to g(x))
The vertical shift is g(x)=f(x) +18
The horizontal shift is g(x)=f(x-6)
Answer:
The vertical shift is g(x)=f(x) +18
The horizontal shift is g(x)=f(x-6)
Step-by-step explanation:
Please Help! I will give you the brainiest and a lot of points!
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
please answer quick i need to go to my friends to get my joy con fixed
The area is just the base times the height. In this case, the base is (x+4) and the height is (x+6), and then you just distribute to get x^2 +4x+6x+24 which is x^2+10x+24.
Choose the expression that represents “divide 0.04 by n.”
Answer:
.04/n=4/100n or 4÷100n
Please help explanation if possible
Answer:
10% gain
Step-by-step explanation:
[P2-P1]/P1
(33-30)/30=3/30=.1 or 10% gain.
Answer:
10%
Step-by-step explanation:
→ Minus the new share from the old one
33 - 30 = 3
→ Divide the answer by the original price
3 ÷ 30 = 0.1
→ Multiply the answer by 100
0.1 × 100 = 10%
a. 1.5
b. 2.3
c. 2.4
d. 1.9
Answer:
2.3
Step-by-step explanation:
.5 - .3 = .2
.8 - .5 = .3
1.2 - .8 = .4
1.7 - 1.2 = .5
We should add .6 next
1.7+.6 = 2.3
A panel of 10 interviewers was to interview two candidates A and B to decide who was suitable for a job. 7 said A was suitable, 5 said B was suitable while 2 said neither A nor B was suitable. (i) How many said both A and B were suitable. (ii) How many said A alone was suitable.
Answer:
(i) 4 interviewers
(ii) 3 interviewers
A)15.8 inches
B) 17.8 inches
C)16.2 inches
D)14.8 inches
Answer:
B
Step-by-step explanation:
Use pythagorean theorem
4^2+5^2=AC^2, AC= 6.4
7^2+9^2=CB^2, CB=11.4
What is the measure of b, in degrees
Answer:
B) 32
Step-by-step explanation:
(sin 74) / 10 = (sin c) / 10
c = 74
180 - 74 -74
= 32
plot the following points on a xy-plane.
(5,2) , (-2, 1) , (-1,-3)
Answer: See below
Step-by-step explanation:
Answer:
Answer below
Step-by-step explanation:
Solve each equation for the specified variable
Answer: Solve for the specified variables
Step-by-step explanation:
1. w= A/l
2. d=C/pi
3. s=v-gt
4. y= 5/2x-11/2
5. P^2= P^1V^1 / P^2 Put ^ as lowercase as shown, can't find symbol on my keboard T.T
6. W= Ke2g / V^2
7. h= V / 2/3 pi r^2
8. n=2S/a+k
9. S=A/pi r - r (not 100% sure on that one)
10. r= E/I-R
11. h= E-1/2mv^2/mg
12. a=K+5b/b+3
13. c=ab/b+a
Wooh, finally finished all that. Hope I didn't make any mistakes. Have a great day!
Please help I’m really stuck!!
Step 1: Solve for one variable
---I will be using the first equation and solving for a.
a + c = 405
a = 405 - c
Step 2: Substitute into the other equation
---Now that we have a value for a, we can substitute that value into the second equation. Then, we can solve for c.
12a + 5c = 3950
12(405 - c) + 5c = 3950
4860 - 12c + 5c = 3950
-12c + 5c = -910
-7c = -910
c = 130
Step 3: Plug back into the first equation
---We now know one variable, which means we can plug back into our first equation and solve for the other.
a = 405 - c
a = 405 - 130
a = 275
Answer: 275 adults, 130 children
Hope this helps!
