Answer:
[tex]\displaystyle \frac{dy}{dx} = -40x \sin (5x^2) \cos^3 (5x^2)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \cos^4 (5x^2)[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 4 \cos^3 (5x^2)[\cos (5x^2)]'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 4 \cos^3 (5x^2) \sin (5x^2) (5x^2)'[/tex]Basic Power Rule [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = -40x \sin (5x^2) \cos^3 (5x^2)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Find the vertex of the following. f(x) = x2 - 12x + 35
Write the LCD (Least Common Denominator I think) for each pair of fractions.
1/3, 1/5 | 2/7, 1/4 | 3/4, 3/5 | 2/9, 5/12 | 1/3, 3/7 | 1/6, 4/9
Please help. ASAP
Answer:
answer: 15, 28, 20, 36, 21, 18
Find the present value that will grow to $1000 if the annual interest rate is 5.5% compounded quarterly for 10 years
Answer:
1708.14 rounded
Step-by-step explanation:
Y= a•b^x
5.5% = 0.055
1+0.055=1.055
Y= 1000•1.055^10
Y= 1708.14
if there is no number in front of a letter, it is really number 1
Answer: Yes, if there is no number in front of a variable(or letter, as you said), it is actually 1.
a = 1a
x^2 = 1x^2
2m + n = 0 means 2m + 1n = 0
Step-by-step explanation:
Use the dot plot to find the MEAN.
Answer:
Step-by-step explanation: To find the mean of the dot plot, you will need to add all of the dots together.
For example: Above 2, there are 3 dots , so you would need to multiply 2 by three to get 6 dots above the number 2.
Do that for all of the numbers on the dot graph from 1 - 6, and you will have this equation:
1 + 6 + 18 + 20 + 15 + 12
Next, you will need to add all those numbers together and you will get 72.
Lastly, divide by how many numbers there are, and there are 6 numbers.
So, that will be 72/6 which is 12.
Your answer will be 12.
The perimeter of the shape is 25.71 cm
Calculate the value of the radius
Take π to be 3.142
Answer:
The radius of the circle is: 4.09 cm
Step-by-step explanation:
Assuming the shape to be a circle.
The perimeter of a circle is called circumference and is given by the formula.
[tex]C = 2\pi r[/tex]
For the time being, we know
[tex]\pi = 3.142\\C = 25.71cm[/tex]
Putting the values in the formula we get: as x is the radius
[tex]25.71 = 2 * 3.142 * x\\25.71 = 6.284x\\x = \frac{25.71}{6.284}\\x = 4.09\ cm[/tex]
Hence,
The radius of the circle is: 4.09 cm
Brand A is $5 per 60 pound bag and Brand B is $12 per 150 pound bag. What Is the unit rate that brand A is selling for
Answer:
YEEYEE
Step-by-step explanation:
235 people are at a summer camp. There are 35 more boys than girls, and 70 fewer adults than girls. How many people of each group are at the camp?
Answer:
125 boys, 90 girls and 20 adults
Step-by-step explanation:
Let the number of boys be x
Let the number of girls be y
Let the number of adults be z
If there are 235 people at the summer camp, then;
x + y+ z = 235 ..... 1
If there are 35 more boys than girls, then;
x = y + 35 .... 2
If there are 70 fewer adults than girls then;
y = z - 70
z = y - 70....3
Substitute 2 and 3 into 1;
x + y+ z = 235 ..
(y+35)+y+(y-70) =235
3y -35 = 235
3y = 270
3y/3 = 270/3
y = 90
Since x = y + 35
x = 90 + 35
x = 125
Also z = y - 70
z = 90+70
z = 20
There are 125 boys, 90 girls and 20 adults
Answer:
There are 90 girls, 125 boys, and 20 adults.
Step-by-step explanation:
Let x be the number of girls. How many boys were there?
x + 35
How many adults were there?
x - 70
We know that 235 people are at RSM summer camp. Use this to make an equation.
x + (x + 35) + (x - 70) = 235
x + x + 35 + x - 70 = 235
3x - 35 = 235
3x - 35 + 35 = 235 + 35
3x = 270
3x ÷ 3 = 270 ÷ 3
x = 90
x, x + 35, x - 70
90, 125, 20
which best describes how to solve a question below?
64x=37
Answer:
X=37/64
Step-by-step explanation:
64x=37
x=37/64
Which decimal makes the comparison true? 7.68 > ______ a. 8.81 b. 8.68 c. 7.86 d. 7.56
Answer:
D. 7.56
Step-by-step explanation:
First we can see it has a less than symbol meaning whatever we put has to be less than the first number.
So the only number less than 7.68 is 7.65!
Answer:
D
Step-by-step explanation:
The number we're dealing with is 7.68.
the symbol means that whatever number comes after it is less than 7.68. So, we look at the other numbers to see if they're bigger than 7.68.
8.81 is bigger than 7.68.
8.68 is bigger than 7.68.
7.86 is bigger than 7.68.
7.56 is smaller than 7.68.
what is the remainder of 58,511 divided by 21, the quotient is 2,786 R
Answer:
the remainder is 5. 2,786 R 5
If line b is perpendicular to line a, and line c is perpendicular to line a, what is the slope of line c?
mc =
Answer:
the slope would be the same as line b
Step-by-step explanation:
the slope would be the same as line b because they are both perpendicular to line a, meaning they both have the same slope.
Answer:
mc= 1
Step-by-step explanation:
correct on edge 2020
Suppose the local Barons team wins every game they play with a probability of 0.75. What is the probability that the Barons would win a best-of-seven-game series (i.e., they play games until one team has won four game)?
Answer:
The probability is 0.173
Step-by-step explanation:
The probability is of winning is 0.75 = 75/100 = 3/4
This means that the probability of losing is 0.25 = 25/100 = 1/4
So if they are two win 4 games, they will lose three
We can get this probability using the Bernoulli approximation of the binomial theorem
So here, we have
P(X = 4) = 7 C 4 * 0.75^4 * 0.25^3
= 0.173034667969
which is approximately 0.1730
Help me please. Thanks
Answer:
ç sir kasi multiplication gamitinnnyan
Answer:
A
Step-by-step explanation:
Find the area of the square
Area = s^2
s = 8
Area = 64 square feet.
Find the area of 1 circle.
r = d / 2
r = 4 / 2
r = 2
Area of 1 circle = pi r^2
Area of 1 circle = 3.14 * 2^2
Area of 1 circle = 12.56
Area of 4 circles
Area of 4 circles = 4 * 12.56
Area of 4 circles = 50.24
Area of unshaded area
Area of unshaded area = area square - area 4 circles.
Area of unshaded area = 64 - 50.24
Area of unshaded area = 13.76
Which operation should you perform after (9 + 6) in the expression 12^2 + 10 × 2 − (9 + 6) ÷ 5?
Answer:
12²
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition SubtractionStep-by-step explanation:
Step 1: Define expression
12² + 10 × 2 - (9 + 6) ÷ 5
Step 2: Steps
We do parenthesis first, so (9 + 6) is the first thing we do.
The next thing we do is exponents (according to BPEMDAS), so we do 12².
Answer:
Following PEMDAS
Next step : Exponents
Next step : Multiplication
Next step : Division
Next step : Addition
Next step : Subtraction
Step-by-step explanation:
12²+10×2-(9+6)÷5
Open parentheses
12²+10×2-15÷5
Exponents : 12²= 144
144+10×2-15÷5
Multiplication : 10×2=20
144+20-15÷5
Division : -15÷5= -3
144+20-3
Add :144+20=164
164-3
Subtract
= 161
Write an equation that passes through the point (1, 3) and is perpendicular to x – 2y = -8.
Answer:
y = -2x + 5
Step-by-step explanation:
Given:
Passes through point (1, 3)
Perpendicular to x – 2y = -8
Solve:
x – 2y = -8
y = 1/2x + 4
The slope is m = 1/2
The slope of the perpendicular line is the inverse of the slope of the original equation.
The slope of the inverse equation is m = -2.
Making an inverse equation of y = -2x + a
Find a:
Use point, (1, 3) where (x, y):
3 = (-2)*(1) + a
a = 5
y = -2x + 5
Answer:
y=½x+5
Step-by-step explanation:
Passes through, (1,3)
Perpendicular to x-2y=-8.
Step 1
write the equation in form of y=mx+c
x-2y=8
-2y=-x+8
Dividing both sides of the equation by -2 we get;
y=-x/2+8
y=-½x+8
Thus the gradient is -½. Call it M1
Recall, The product of the gradients(slopes) of perpendicular lines is -1 i.e
M1 × M2= -1
Solve for M2
-½×M2=-1.
Dividing both sides by -½ we get
M2=-1×-2
M2=2Now, use this slope(M2) with the points (1,3) to find the new equation that is perpendicular to x-2y=-8
Note: Given two points (x1,y1) and (x2,y2) the the slope would be ∆x/∆y i.e (x1-x2)/(y1-y2).
Therefore, identify new point (x,y). Use this new point with point (1,3) and the slope M2 to get the new equation.
Slope=∆x/∆y
M2=(x-1)/(y-3)
but M2 is 2
2=(x-1)/(y-3)
2/1=(x-1)/(y-3) Note: 2= 2/1
Cross multiplying we get:
2(y-3)=1(x-1)
Open the brackets
2y-6=x-1
Solve for y so as to write the equation in form of y=mx+c
2y=x-1 +6
2y=x+5
Divide both sides of the equation by 2
y=x/2+5
y=½x+5evaluate 103 × 97 without directly multiplying
Answer:
9991
Step-by-step explanation:
103 × 97
(100 +3) (50+47)
get two number which you can add to get the value in the question
n then expand
100(50+47) +3(50+47)
5000+4700+150+141
9991
16 correct answer out of 20 question. How many % got right?
Answer: You got 80% right
Step-by-step explanation: 100÷20=5 5×16=80
PLEASE MARK ME BRAINLIEST
80% got the right answers out of 20 questions.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The number of questions are twenty 20.
Out of this 20 questions 16 questions are correct.
We need to find the percentage of the right answers.
20x=16
Divide both sides by 20
x=16/20
x=0.8
Now to find the percentage multiply x value with 100 as it is a hundredth part.
0.8×100=80%
Hence, 80% got the right answers out of 20 questions.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ2
Brainliest...don’t need an explanation
Answer:
8
Step-by-step explanation:
Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in customers’ cars in less than 30 minutes on average. Further suppose that several complaints have been filed from customers stating that their oil change took longer than 30 minutes. Upper-level management at Speedy Oil Change headquarters has requested that you investigate the complaints. To begin your investigation, you randomly audit 36 oil changes performed by Speedy Oil Change and record the time each customer waited for the oil change. The number of minutes to complete each of the 36 oil changes is reported below.
Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in customers’ cars in less than 30 minutes on average. Further suppose that several complaints have been filed from customers stating that their oil change took longer than 30 minutes. Upper-level management at Speedy Oil Change headquarters has requested that you investigate the complaints. To begin your investigation, you randomly audit 36 oil changes performed by Speedy Oil Change and record the time each customer waited for the oil change. The number of minutes to complete each of the 36 oil changes is reported below.
42
29
19
11
10
27
41
27
22
26
28
32
17
15
25
35
31
22
13
31
17
37
33
25
18
24
28
21
40
19
33
30
14
23
22
10
1. Write the null and alternative hypothesis. Label each accordingly.
2. Calculate the Test Statistic and the P-value. Label each accordingly, and report the P-value to 4 decimal places.
3. Using the P-value calculated in #2, explain why you would or would not reject the null hypothesis? Answer using a complete sentence, proper grammar and correct spelling. Do NOT write a conclusion.
4. Based on your answer to #3, write a final conclusion for the test of hypotheses, and explain if the company is fulfilling its promise to “change the oil in customers’ cars in less than 30 minutes on average?” Answer using a complete sentence, proper grammar and correct spelling.
Answer:
Explained below.
Step-by-step explanation:
(1)
The hypothesis can be defined as follows:
H₀: The Speedy Oil Change will change the oil in customers’ cars in more than 30 minutes on average, i.e. μ > 30.
Hₐ: The Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average, i.e. μ ≤ 30.
(2)
Use Excel to compute the sample mean and standard deviation as follows:
[tex]\bar x=\text{AVERAGE(array)}=24.917\\\\s=\text{STDEV.S(array)}=8.683[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{24.917-30}{8.683/\sqrt{36}}=-3.51[/tex]
The degrees of freedom is:
df = n - 1
= 36 - 1
= 35
Compute the p-value as follows:
[tex]p-value=P(t_{35}<3.51)=0.0006[/tex]
(3)
The p-value = 0.0006 is very small.
The null hypothesis will be rejected at any of the commonly used significance level.
(4)
There is sufficient evidence to support the claim that the Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average.
Using the t-distribution, we have that:
1.
The null hypothesis is [tex]H_0: \mu \geq 30[/tex]
The alternative hypothesis is [tex]H_1: \mu < 30[/tex]
2. The test statistic is t = 3.51.
3. The p-value is of 0.0063.
4. Since the p-value is of less than the standard significance level of 0.05, we reject the null hypothesis, and can conclude that the company is fulfilling its promise.
Item 1:
At the null hypothesis, we test if the mean is of at least 30 minutes, that is:
[tex]H_0: \mu \geq 30[/tex]
At the alternative hypothesis, we test if the mean is of less than 30, that is:
[tex]H_1: \mu < 30[/tex]
Item 2:
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem:
[tex]\mu = 30, n = 36[/tex]Using a calculator, [tex]\overline{x} = 24.92, s = 8.68[/tex]The test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{24.92 - 30}{\frac{8.68}{\sqrt{36}}}[/tex]
[tx]t = 3.51[/tex]
The test statistic is t = 3.51.
Item 3:
The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with t = 3.51 and 36 - 1 = 35 df.
Using a calculator, this p-value is of 0.0063.
Item 4:
Since the p-value is of less than the standard significance level of 0.05, we reject the null hypothesis, and can conclude that the company is fulfilling its promise.
A similar problem is given at https://brainly.com/question/16194574
1/2 + 5/2 =
I need help with this
Answer:
3
Step-by-step explanation:
1/2+5/2= 6/2= 3/1= 3
I hope this helps you and good luck!
solve cos(2x + 30) = 0.5 for -180≤x≤180
Answer:
x = 15°
x = 135°
x = -45°
x = -180°
Step-by-step explanation:
Trigonometric Equations
Solve
cos(2x + 30°) = 0.5 for -180° ≤ x ≤ 180°
Applying the inverse cosine function:
2x + 30° = arccos(0.5)
There are several angles whose cosine is 0.5. They are 60°, 300°, -60° and -300°, thus we have these candidate solutions:
2x + 30° = 60°
2x + 30° = 300°
2x + 30° = -60°
2x + 30° = -300°
Subtracting 30° to all the equations:
2x = 60° - 30° = 30°
2x = 300° - 30° = 270°
2x = -60° - 30° = -90°
2x = -60° - 300° = -360°
Dividing by 2 we have the complete set of solutions:
x = 15°
x = 135°
x = -45°
x = -180°
The diagram compares the ratio of girls in the chorus to boys in the chorus . What is the ratio of girls to boys ? If there are 40 students in the chorus, how many are girls and how many are boys.
Answer:
The diagram can't be seen
Step-by-step explanation:
.... Sry.. I can't solve this one... I can't see the diagram
How can this be correct? 6>6 X+3+4=9
Answer:
its not
Step-by-step explanation:
because the x equals 4 so it will be 4+3+4=9 because 3+4 equals 5 so you add 4 and get 9
A recipe for punch requires 8 quarts of orange juice concentrate, 2 quarts of cranberry juice, and enough water to make a total of 14 quarts of punch. How much water is needed for this recipe?
A new LED light bulb uses 10 watts of power. Since energy = power × time , then the energy used for this light bulb can be found my multiplying the power times the time the bulb is lit. If the bulb is lit for one hour, the energy used will be 10 watt*hours or 10 Wh. If three 10 watt bulbs in one room are kept on for 5 hours, how many watt*hours of energy are used?
9514 1404 393
Answer:
150 Wh
Step-by-step explanation:
We know the energy per bulb is 10 Wh per hour, so the total energy used by 3 bulbs in 5 hours is ...
(10 Wh/(bulb·hour))×(3 bulbs)×(5 hours) = 10·3·5 Wh = 150 Wh
Can somebody help me with solve this question
Answer:
f⁻¹(y) = y^(-7/17)
Step-by-step explanation:
f(x) = x^(-17/7)
To find the inverse, switch x and y, and solve for y.
x = y^(-17/7)
x^(-7/17) = y
Therefore, f⁻¹(y) = y^(-7/17).
4+4
[tex]4 + 4[/tex]
Answer:
4+4 = 8.
Step-by-step explanation:
Or 44, depends on whether you're trolling. XD
Hope this helped...
[tex] \huge \: Your \: answer \: is \: 8[/tex]
For the following pair of lines, identify the system by type.
equivalent
consistent
inconsistent
Answer:
The answer is C inconsistent
Step-by-step explanation:
A stop sign in the shape of a regular octagon is
resting on a brick wall, as shown in the
accompanying diagram.
STOP
X
What is the measure of angle x?
Answer:
45°
Step-by-step explanation:
First, find the measure of each interior angle of the octagon.
Measure of each interior angle of the octagon = [tex] \frac{(n - 2)180}{n} [/tex]
Where, n = 8.
Plug in the value of n into the formula
[tex] = \frac{(8 - 2)180}{8} [/tex]
[tex] = \frac{(6)180}{8} [/tex]
[tex] = \frac{1,080}{8} = 135 [/tex]
x = 180 - 135 (straight line theorem.)
x = 45°