Answers
Step-by-step explanation:
Question 7.[tex] \frac{{(3 + u)}^{2} }{8} [/tex]
[When u = 5]
[tex] = \frac{{(3 + 5)}^{2} }{8} [/tex]
[tex] = \frac{ {(8)}^{2} }{8} [/tex]
[tex] = \frac{8 \times 8}{8} [/tex]
= 8 (Ans)
Question 8.-2(a - 7)
(Using Distributive property)
= - 2 × a -2 × (-7)
= -2a + 14 (Ans)
Answer:
7. 8
8. -2a+14
Step-by-step explanation:
(Excuse this form of the expression)
7.
u = 5
(3 + u)²
---------
8
Plug in
(3 + 5)²
---------
8
(8)²
---------
8
64
---- = 8
8
8.
-2(a - 7)
Multiply -2 with each number in the parenthesis
-2a + 14
Related Questions
find the differential equation of this function and indicate the order y = e^3x (acos3x +bsin3x)
Answers
Answer:
y"-6y'+18y=0
Second order
Step-by-step explanation:
Since there are 2 constants, the order of the differential equation will be 2. This means we will need to differentiate twice.
y = e^(3x) (acos3x +bsin3x)
y'=3e^(3x) (acos3x+bsin3x)
+e^(3x) (-3asin3x+3bcos3x)
Simplifying a bit by reordering and regrouping:
y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)
y"=
3e^(3x) cos3x (3a+3b)+-3e^(3x) sin(3x) (3a+3b)
+3e^(3x) sin3x (3b-3a)+3e^(3x) cos(3x) (3b-3a)
Simplifying a bit by reordering and regrouping:
y"=
e^(3x) cos3x (9a+9b+9b-9a)
+e^(3x) sin3x (-9a-9b+9b-9a)
Combining like terms:
y"=
e^(3x) cos3x (18b)
+e^(3x) sin3x (-18a)
Let's reorder y like we did y' and y".
y = e^(3x) (acos3x +bsin3x)
y=e^(3x) cos3x (a) + e^(3x) sin3x (b)
Objective is to find a way to combine or combine constant multiples of y, y', and y" so that a and b are not appearing.
Let's start with the highest order derivative and work down
y"=
e^(3x) cos3x (18b)
+e^(3x) sin3x (-18a)
We need to get rid of the 18b and 18a.
This is what we had for y':
y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)
Multiplying this by -6 would get rid of the 18b and 18a in y" if we add them.
So we have y"-6y'=
e^(3x) cos3x (-18a)+e^(3x) sin3x (-18b)
Now multiplying
y=e^(3x) cos3x (a) + e^(3x) sin3x (b)
by 18 and then adding that result to the y"-6y' will eliminate the -18a and -18b
y"-6y'+18y=0
Also the characteristic equation is:
r^2-6r+18=0
This can be solved with completing square or quadratic formula.
I will do completing the square:
r^2-6r+18=0
Subtract 9 on both sides:
r^2-6r+9=-9
Factor left side:
(r-3)^2=-9
Take square root of both sides:
r-3=-3i or r-3=3i
Add 3 on both sides for each:
r=3-3i or r=3+3i
This confirms our solution.
Another way to think about the problem:
Any differential equation whose solution winds up in the form y=e^(px) (acos(qx)+bsin(qx)) will be second order and you can go to trying to figure out the quadratic to solve that leads to solution r=p +/- qi
Note: +/- means plus or minus
So we would be looking for a quadratic equation whose solution was r=3 ×/- 3i
Subtracting 3 on both sides gives:
r-3= +/- 3i
Squaring both sides gives:
(r-3)^2=-9
Applying the exponent on the binomial gives:
r^2-6r+9=-9
Adding 9 on both sides gives:
r^2-6r+18=0
An experiment to investigate the survival time in hours of an electronic component consists of placing the parts in a test cell and running them under elevated temperature conditions. Six samples were tested with the following resulting failure times (in hours): 34, 40, 46, 49, 61, 64. (a)Calculate the sample mean and sample standard deviation of the failure time. (b)Determine the range of the true mean at 90% confidence level. (c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time
Answers
Answer:
a) The sample mean is of 49 and the sample standard deviation is of 11.7.
b) The range of the true mean at 90% confidence level is of 9.62 hours.
c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
Step-by-step explanation:
Question a:
Sample mean:
[tex]\overline{x} = \frac{34+40+46+49+61+64}{6} = 49[/tex]
Sample standard deviation:
[tex]s = sqrt{\frac{(34-49)^2+(40-49)^2+(46-49)^2+(49-49)^2+(61-49)^2+(64-49)^2}{5}} = 11.7[/tex]
The sample mean is of 49 and the sample standard deviation is of 11.7.
b)Determine the range of the true mean at 90% confidence level.
We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0.150
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample. So
[tex]M = 2.0150\frac{11.7}{\sqrt{6}} = 9.62[/tex]
The range of the true mean at 90% confidence level is of 9.62 hours.
(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.
This is the confidence interval, so:
The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.
The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.
The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
for every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If each of 35 people bought a $9.75 ticket, how many people bought the more expensive ticket?
Answers
9514 1404 393
Answer:
21
Step-by-step explanation:
The number who bought expensive tickets is 3/5 of the number who bought cheap tickets.
(3/5)(35) = 21
21 people bought the more expensive ticket.
Answer:
21 people
Step-by-step explanation:
$9.75 $14.50
5 people to 3 people
35 people to ? people
consider the proportions: 5/3 = 35/?
we need the equivalent fraction of 5/3 that has 35 on the denominator
so 5/3 = (5/3)(7/7) because 7/7 =1, and 5*3 =35
5/3 = 5*7/3*7 = 35/21
how do we write a set in set- builder method?
Answers
Answer:
(×:x is a natural number up to 10) just an example
Match each equation to its graph.
1. y= x-2
2. y= -2x
3. x= -2
4. y= -2
Answers
If the equation is...
y=c, where c is a constant, the line is horizontal across that c value, on y axis. x=c the line would be vertical across that c, on x axis.
The equation of the graph is : x = -2
What is a graph?A graph is a pictorial representation of the locus of a certain point.
How to draw a graph?A graph can be drawn by picking some fixed points from the locus of the point.
Here, the straight line passes through the points are : (-2,1); (-2,2); (-2,-5);(-2,-5).
Hence, the straight line is to be parallel to the x-axis and the equation of the graph is x= -2.
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39.948859° What is the measurement in degrees, minutes, and seconds?
Answers
Answer:
try to calculate
here some examples
Step-by-step explanation:
Decimal Degrees to Degrees, Minutes, Seconds Calculator
Enter decimal degrees to convert to minutes and seconds. See the formulas below to see how it’s done.
Angle:
Decimal:
47.31
°
degrees, minutes, seconds to decimal
Degrees, Minutes, & Seconds:
47° 18′ 36″
I hope it helps
the first four terms of a sequence are shown below:
7,4,1,-2
which of the following functions best defines this sequence?
A) f(1)=7, f(n+1)= f(n)+3; for n>= 1
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
C) f(1)=7, f(n+1)= f(n)-4; for n >= 1
D) f(1)=7, f(n+1)= f(n)+4; for n >= 1
Answers
9514 1404 393
Answer:
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
Step-by-step explanation:
The first term of the sequence is 7 and the next (4) is found by adding -3 to that: 4 = 7-3. This is described in answer choice B.
please help, it’s urgent !!!
Answers
Answer:
1. purple graph
2. orange graph
3. green graph
4. blue graph
Change these percentages to decimals.
30%
45%
60%
5%
1%
55%
80%
10%
Answers
.45
.60
.05
.01
.55
.80
.10
Percentages are just a number out of 100, so to find the percentage you but the number over 100. An example is 30%, to find the decimal you first put it over 100. 30/100, now we divide and make it a decimal. 30/100’s decimal is .30.
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
This table shows the ratio of number of people to liters of Find the missing values in the ratio table
ginger ale needed.
A=
People
Ginger Ale
Answers
Answer:
A= 2 B= 6
Step-by-step explanation:
What is the circumference of the circle in terms of [tex]\pi[/tex]?
a. 900[tex]\pi[/tex] in.
b. 90[tex]\pi[/tex] in.
c. 60[tex]\pi[/tex] in.
d. 30[tex]\pi[/tex] in.
Answers
Answer:
[tex]c. \: 60\pi \: in.[/tex]Step-by-step explanation:
Given,
Radius = 30 in
So,
Circumference
[tex] = 2\pi r[/tex]
[tex] = 2 \times \pi \times 30in.[/tex]
[tex] = 60\pi \: in.(ans)[/tex]
[tex] \sf \: r \: = 30 \: in. \\ \sf \: C \: = 2\pi r \\ \\ \sf \: C \: = 2\pi(30) \\ \sf \: C = 2 \times 30\pi \\ \sf \: C = \boxed{\underline{ \bf c. \: 60\pi \: in.}}[/tex]
Of the delegates at a convention, 60% attended the breakfast forum, 70% attended the dinner speech and 40% attended both events. If a randomly selected delegate is known to have attended the dinner speech, the probability that he also attended the breakfast forum is
Answers
Answer:
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Attended the dinner speech.
Event B: Attended the breakfast forum.
70% attended the dinner speech
This means that [tex]P(A) = 0.7[/tex]
40% attended both events.
This means that [tex]P(A \cap B) = 0.4[/tex]
The probability that he also attended the breakfast forum is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714[/tex]
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
Karl wants to raise money for charity. He designs a game for people to play.
Karl uses a ten sided dice for the game. The dice is numbered 1 to 10.
Each person will roll the dice once. A person wins the game if the dice lands on a multiple of 4.
Ali plays the game once,
a) Work out the probability that Ali will win the game.
(2 m
Answers
Answer:
0.2 = 20% probability that Ali will win the game.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total outcomes:
The 10 sides that the dice can land, which means that [tex]T = 10[/tex]
Desired outcomes:
Sides that are multiple of 4, that is, side 4 and side 8, so [tex]D = 2[/tex]
Work out the probability that Ali will win the game.
[tex]p = \frac{D}{T} = \frac{2}{10} = 0.2[/tex]
0.2 = 20% probability that Ali will win the game.
Classify the following triangle 120 degrees
options
a. acute
b.Scalene
c.isosceles
d.obtuse
e.right
f. equilateral
Answers
Answer:
I think it is Obtuse.
Step-by-step explanation:
120 Degrees - Obtuse
Solve this application problem using a system of equations: A grocery store recently sold a
bag of peanuts for $0.76 and a bag of pistachios for $3.68. At the end of that day, 50 bags of
peanuts and pistachios were sold for a total of $128.52. How many bags of each were sold?
Answers
Answer:
19 bags of peanuts and 31 bags of pistachios were sold.
Step-by-step explanation:
This question is solved by a system of equations.
I am going to say that:
x is the number of bags of peanuts sold.
y is the number of bags of pistachios sold.
50 bags of peanuts and pistachios were sold
This means that [tex]x + y = 50[/tex], that is: [tex]x = 50 - y[/tex]
A grocery store recently sold a bag of peanuts for $0.76 and a bag of pistachios for $3.68. Were sold for a total of $128.52.
This means that:
[tex]0.76x + 3.68y = 128.52[/tex]
Since [tex]x = 50 - y[/tex]
[tex]0.76(50 - y) + 3.68y = 128.52[/tex]
[tex]2.92y = 90.5[/tex]
[tex]y = \frac{90.5}{2.92}[/tex]
[tex]y = 31[/tex]
[tex]x = 50 - y = 50 - 31 = 19[/tex]
19 bags of peanuts and 31 bags of pistachios were sold.
WHAT IS THE ANSWER TO 9-3:3= ?
I NEEDD HELP I ONLY GOT 2 MIN I WILL GIVE BRAINLY
Answers
Answer: 8
Hope this help :)
3.3.C-1
If one tablet of calcium pantothenate contains 0.5 gram, how much is contained in
n 2 1/4 tablets? How many tablets are needed to make up 2.3 grams?
Answers
Simply divide the top by the bottom of the fraction. If the division has no remainder, the decimal number is called a terminating decimal.
Now start the division process as below
Therefore,
A fraction calcium pantothenate contains 0.5 gram of a tablet 5 tablets to make up 2.3 grams.
To calculate the amount of calcium pantothenate contained in a given number of tablets, use the given information that one tablet contains 0.5 grams.
Amount in n 2 1/4 tablets:
To calculate the amount of calcium pantothenate in n 2 1/4 tablets, we need to calculate the total amount for each part (whole tablets and the fraction of a tablet) and then sum them up.
Amount in n whole tablets: n tablets × 0.5 grams/tablet
Amount in 1/4 tablet: (1/4)× 0.5 grams
So, the total amount in n 2 1/4 tablets would be:
Total amount = n ×0.5 + (1/4) ×0.5 grams
Tablets needed to make up 2.3 grams:
To calculate the number of tablets needed to make up 2.3 grams of calcium pantothenate, set up a proportion using the given tablet amount (0.5 grams/tablet).
Let x be the number of tablets needed.
0.5 grams/tablet = 2.3 grams / x tablets
Cross-multiply:
0.5 × x = 2.3
x = 2.3 / 0.5
x = 4.6
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Hi can someone answer this question please thank you
Answers
Answer:
25
Step-by-step explanation:
5:20
We want to get the second number to 100
100/20 = 5
Multiply each term by 5
5*5 : 20*5
25 : 100
x is 25
Given that,
→ 5 : 20 :: x : 100
Then we have to,
find the second number to 100.
→ 100/20
→ 5
Now multiply each term by 5 in 5:20,
→ 5 × 5 : 20 × 5
→ 25 : 100
→ x = 25
Now these ratio will be,
→ 5 : 20 :: 25 : 100
Hence, the value of x is 25.
the cost of 2 pairs of trousers and 3 shirts is $825 it shirt cost $50 less than the trouser. find the cost of each shirt and trouser
Answers
Answer:
a pair of trousers cost = x = 195 $
one shirt costs = x - 50 = 145 $
Step-by-step explanation:
let the cost of trouser be x.cost of shirt = (x - 50)2 pairs of trousers cost = 2x 3 shirts cost = 3(x - 50)= 3x- 150
2 trousers and 3 shirts cost = 825
=> 2x + 3x - 150 = 825
=> 5x = 975
x = 195
a pair of trousers cost = x = 195 $
a pair of trousers cost = x = 195 $ one shirt costs = x - 50 = 145 $
4. Write the number 3.8 in the form using integers, to show that it is a rational number. 8 11 38 10 10 38 100
Answers
Answer:
38 divided by 10 equals 3.8
What's the equivalent expression.
(2-7. 5)² =?
Answers
Answer:
The Answer of the above question is 30.25
Step-by-step explanation:
Hope it helps you.
Step 1: Rewrite equation
To start off, I find it helpful to rewrite the equation. This will give you a better understanding of the problem. Let’s do this now.
(2-7.5)²
Step 2: Understand PEMDAS
Now that we have written down the equation, let’s solve using PEMDAS. In case you are unfamiliar, I will write down what each letter stands for. Keep in mind that the letters go in the order you need to solve.
P- Parentheses
E- Exponent
M- Multiplication
D- Division
A- Addition
S- Subtraction
Step 3: Solve
Finally, we can solve the equation. Using the knowledge from step 2, we will be able to solve in the correct order. Let’s start with parentheses, and find the answer for 2-7.5.
(2-7.5)²
-5.5²
Now let’s move on to the next letter and solve using the exponent. We will multiply -5.5 by itself. This will be the final step; although there are other letters in PEMDAS, the equation will end after this step since we will already have the answer.
-5.5²
30.25
Hope this helps! Comment below for more questions.
Uuannsnnsnndn d. DND. D
Answers
Answer:
im so confused
Step-by-step explanation:
Answer:
what is this goat saying
how many itegers from 15 to 85, inclusive are multibles of 8
Answers
Answer:
9 multiples
Step-by-step explanation:
16,24,32,40,48,56,64,72,80
9
The total number of vertices adjacent to the vertex is called?
Answers
Answer:
The degree of vertex is the total number of vertices adjacent to the vertex .
The total number of vertices adjacent to the vertex is called degree of the vertex.
What is vertex?" Vertex is defined as when two adjacent side meet at one point."
According to the question,
The degree of a vertex is always as the total number of adjacent side to the vertex.
If adjacent sides far away from each other degree is more.
If adjacent sides near to each other degree is less.
Hence, the total number of vertices adjacent to the vertex is called degree of the vertex.
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Use calculus to find the absolute maximum and minimum values of the function. f(x) = 5x − 10 cos(x), −2 ≤ x ≤ 0 (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
Answers
Answer:
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Answer:
The absolute maximum is about -5.84 at x = -2.
And the absolute minimum is about -11.28 at x = -π/6.
Step-by-step explanation:
We want to find the absolute maximum and minimum values of the function:
[tex]\displaystyle f(x) = 5x-10\cos x\text{ for } -2\leq x\leq 0[/tex]
First, we should evaluate the endpoints of the interval:
[tex]\displaystyle f(-2) = 5(-2) - 10\cos (-2) \approx -5.8385[/tex]
And:
[tex]f(0) = 5(0) -10\cos (0) = -10[/tex]
Recall that extrema of a function occurs at its critical points. The critical points of a function are whenever its derivative is zero or undefined.
So, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ 5x - 10\cos x\right][/tex]
Differentiate:
[tex]\displaystyle f'(x) = 5 + 10\sin x[/tex]
Set the function equal to zero:
[tex]\displaystyle 0 = 5+10\sin x[/tex]
And solve for x:
[tex]\displaystyle \sin x = -\frac{1}{2}[/tex]
Using the unit circle, our solutions are:
[tex]\displaystyle x = \frac{7\pi}{6} + 2n\pi\text{ or } \frac{11\pi}{6} + 2n\pi \text{ where } n\in \mathbb{Z}[/tex]
There is only one solution in the interval [-2, 0]:
[tex]\displaystyle x = \frac{11\pi}{6} - 2\pi = -\frac{\pi}{6}\approx -0.5236[/tex]
Thus, we only have one critical point on the interval.
Substituting this back into the function yields:
[tex]\displaystyle\begin{aligned} f\left(-\frac{\pi}{6}\right) &= 5\left(-\frac{\pi}{6}\right) - 10\cos \left(-\frac{\pi}{6}\right) \\ \\ &=-\frac{5\pi}{6} - 5\sqrt{3}\\ \\ &\approx -11.2782 \end{aligned}[/tex]
In conclusion, the absolute maximum value of f on the interval [-2, 0] is about -5.8385 at x = -2 and the absolute minimum value of f is about -11.2782 at x = -π/6.
We can see this from the graph below as well.
What is the percent discount if a 12,500 car is now on special for 10,250?
Answers
Answer:
Step-by-step explanation:
the answer is 2250 percent is = 22.5
Answer:
18% discount
Step-by-step explanation:
Percent discount is found by the following formula:
[tex]\frac{original-discount}{original}[/tex]
In this scenario, the original is 12500 and the discount, or special is 10250.
We can plug this into the formula to get
[tex]\frac{12500-10250}{12500}[/tex]
We can simplify the numerator by subtracting, and we get that answer as 2250.
We get the remainder of the answer as 2250 divided by 12500. We divide that, and get the answer as 0.18, which can be rewritten as 18%.
Rewrite the following expanded notation in standard form. 600,000 + 80,000 + 1,000 + 400 + 70 + 5
Answers
Answer:
this is the answer
681,474
√12 + √10 − √2) is
(a) A positive rational number
(b) Equal to zero
(c) An irrational number
(d) A negative integer
Answers
Hello!
[tex] \bf \sqrt{12} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} \times 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} } \sqrt{ 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \boxed{ 2 \sqrt{3} + \sqrt{10} - \sqrt{2}} [/tex]
Answer: (c) An irrational number
Good luck! :)
the vertex of this parabola is at (2,-4). when the y-value us -3, the x-value is -3. what is the coefficient of the squared term in the parabolas equation?
Answers
Answer:
The coefficient of the squared term is 1/25.
Step-by-step explanation:
We are given that the vertex of a parabola is at (2, -4). We also know that y = -3 when x = -3.
And we want to determine the coefficient of the squared term of the equation.
Since we are given the vertex, we can use the vertex form of the quadratic:
[tex]\displaystyle y = a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient. The leading coefficient is also the coefficient of the squared term, so we simply need to find the value of a.
Since the vertex is at (2, -4), h = 2 and k = -4. Substitute:
[tex]\displaystyle y = a(x-2)^2-4[/tex]
y = -3 when x = -3. Solve for a:
[tex]\displaystyle (-3) = a((-3)-2)^2-4[/tex]
Simplify:
[tex]\displaystyle 1 = a(-5)^2\Rightarrow a = \frac{1}{25}[/tex]
Therefore, our function in vertex form is:
[tex]\displaystyle f(x) = \frac{1}{25}\left(x-2)^2-4[/tex]
Hence, the coefficient of the squared term is 1/25.
Answer:
-5
Step-by-step explanation:
from a p e x
PLZ HELP URGENT
Find all two - digit numbers with the following property: the difference of the nuber and the number with the same digits in reverse order is 54.
Answers
Answer:36
Step-by-step explanation:
