Answer:
[tex]\mathbf{I =2{\sqrt{x+36}} + 6 \ In \begin {vmatrix} \dfrac{{\sqrt{x+36}}-6}{{\sqrt{x+36}}+6}\end {vmatrix}+ C}[/tex]
Step-by-step explanation:
Given that :
[tex]I = \int \dfrac{\sqrt{x+36}}{x} \dx = \int \dfrac{2u^2}{u^2-36} \ du[/tex]
x = u² - 36
Let u = [tex]\sqrt{x+36}[/tex]
Then:
[tex]du =\dfrac{1}{2 \sqrt{x+36}}dx[/tex]
[tex]2 \sqrt{x+36} \ \ du =dx[/tex]
[tex]2 u^2 \ \ du =dx[/tex]
[tex]\dfrac{2u^2}{u^2-36} \\ \\ 2u^2 \\ \\ 2u^2 - 72[/tex]
∴
[tex]I = \int 2 du + \int \dfrac{72}{u^2-36}\ du[/tex]
[tex]I = \int 2 du + 72 \int \dfrac{du}{u^2-6^2}[/tex]
[tex]I =2u+ 72 \times\dfrac{1}{2\times 6} \ In \begin {vmatrix} \dfrac{u-6}{u+6}\end {vmatrix}+ C[/tex]
[tex]I =2u + 6 \ In \begin {vmatrix} \dfrac{u-6}{u+6}\end {vmatrix}+ C[/tex]
substituting the value of u, we have:
[tex]\mathbf{I =2{\sqrt{x+36}} + 6 \ In \begin {vmatrix} \dfrac{{\sqrt{x+36}}-6}{{\sqrt{x+36}}+6}\end {vmatrix}+ C}[/tex]
A 1000 L tank now contains 240 L of water. How long will it take to fill the tank using a pump that pumps 25 L per minute
Answer:
30.4 minutes
Step-by-step explanation:
The tank already has 240L in it, so we need to fill 1000 - 240 = 760L of water.
Since the pump pumps 25L per minute, we can find how many minutes it takes to pump 760L.
760 / 25 = 30.4 minutes.
It will take 30.4 minutes to fill the tank completely.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, The 1000 L tank contains 240 L of water, therefore, the free space in the tank is :
1000-240
= 760 L
The pump fills the tank at a rate of 25 L per minute.
Therefore, it can be represented as:
25 L = 1 minute
1 L = (1/25) minutes
760 L = (1/25)×760 minutes
760 L = 30.4 minutes.
Hence, it will take 30.4 minutes to fill the tank completely.
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6 ten thousand 5 hundred x10
Answer:
60,500
Step-by-step explanation:
Neal is a coffee drinker. At the local coffee shop, the price
of a cup of coffee is $3. Neal's total benefits from
drinking coffee are indicated in the accompanying table.
Use this information to calculate Neal's marginal benefit
of consuming each cup of coffee.
Quantity of
coffee
(cups per day)
Total
benefits
2
3
$8
$14
SI8
$20
$21
4
5
a. The marginal benefit of the first cup is 5
b. The marginal benefit of the second cup is $
10
c. The marginal benefit of the third cup is $15
d. The marginal benefit of the fourth cup is 25
e. The marginal benefit of the fifth cup is s
f. Neil should consume
cups of coffee per day.
Answer and Step-by-step explanation: Marginal Benefit is the maximum a person is willing to pay for an additional good or service. It can be calculated as:
[tex]marginal=\frac{Change total benefit}{Change quantity}[/tex]
For each cup of coffee:
For the first cup, benefit is $8;
For the second:
[tex]marginal=\frac{14-8}{2-1}[/tex]
marginal = 6
For the third:
[tex]marginal=\frac{18-14}{3-2}[/tex]
marginal = 4
For the fourth:
[tex]marginal=\frac{20-18}{4-3}[/tex]
marginal = 2
For the fifth:
[tex]marginal=\frac{21-20}{5-4}[/tex]
marginal = 1
The cost of the coffe is $3, so comparing benefit and cost, Neal should consume 4 cups of cofee per day.
Point q is the image of Q(5, -3) after a translation down 2 units and right 4 units. What are the coordinates of Q?
Answer:
(9,-5)
Step-by-step explanation:
When you go down, the number will decrease. The vertical position is the Y axis. -3-2=5.
When you go right, the number will increase. The horizontal position is the X axis. 5+4=9
(9,-5)
Hope this helps :-)
Jacob is the most popular name amongthe 2,086,814 males born in 2000. The Jacobs make up 1.6516% of all males born that year. How many Jacobs were born in 2000?
Answer:
34,466 children
Step-by-step explanation:
Given the following :
Total number of males born in year 2000= 2,086,814
Percentage number of Jacob's born in year 2000 = 1.6516%
The Jacobs make up 1.6516% of all males born that year?.
The number of Jacob's born in year 2000 will be :
1.6516% of the total number of children born in the year 2000
(1.6516 / 100) × 2,086,814
0.016516 × 2,086,814
= 34465.820024
= about 34,466 children
Which statement identifies how to show that j(x) = 11.6ex and k(x) = In (StartFraction x Over 11.6 EndFraction) are inverse functions? All that needs to be shown is that j(k(x)) equals x. All that needs to be shown is that j(k(x)) equals 1. It must be shown that both j(k(x)) and k(j(x)) equal x. It must be shown that both j(k(x)) and k(j(x)) equal 1.
Answer:
It must be shown that both j(k(x)) and k(j(x)) equal xStep-by-step explanation:
Given the function j(x) = 11.6[tex]e^x[/tex] and k(x) = [tex]ln \dfrac{x}{11.6}[/tex], to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,
For j(k(x));
j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)
j[(ln x/11.6)] = 11.6 * x/11.6
j[(ln x/11.6)] = x
Hence j[k(x)] = x
Similarly for k[j(x)];
k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
Hence k[j(x)] = x
From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6[tex]e^x[/tex] and k(x) = [tex]ln \dfrac{x}{11.6}[/tex] are inverse functions.
Answer:
the answer is C
Step-by-step explanation:
I did the test and got it right
8 The health department of the city wants to evaluate the increase in respiratory illnesses among citizens over the past 15 years. Which meas would be displayed in a graph most appropriately representing this information? OA. the percent of Increase of all illnesses per year OB. the total increase of all illnesses per year the percent of increase in the number of hospitals per year D. the percent of increase of respiratory illnesses per year Reset Next Reserved
Answer:
Option D : "he percent of increase of respiratory illnesses per year"
Step-by-step explanation:
Since you want to show how the respiratory illnesses increase over the last 15 years, then plot a graph that shows such increase year by year.
The four cases in which we can solve a triangle are ASA SSA SAS SSS.
1) In which of these cases can we use the Law of Sines to solve the triangle?
A) ASA.
B) SSA.
C) SAS
D) SSS
2) Which of the cases listed can lead to more than one solution (the ambiguous case)?
A) ASA
B) SSA
C) SAS
D) SSS
Answer:
1) ASA
2) SSA
Step-by-step explanation:
The sine rule is used when we have; ASA, AAS or SSA cases. However, SSA is an ambiguous case which occurs when there are two sides and a given angle opposite one of these given sides. The triangles resulting from a situation like this requires a much closer look in comparison to SSS, ASA, and AAS cases. SSA may result in one triangle, two triangles, or even no triangle at all.
On Saturday morning, Owen earned $26. By the end of the afternoon he had earned a total of $57. Enter an equation, using x as your variable, to determine whether Owen earned $31 or $34 on Saturday afternoon.
Answer:
$26 + X = $57
$26 + $31 = $57
X = $31
My first time ever answering a question hope it helped =) (And sry it took long)
Step-by-step explanation:
You are contacted by the top cookie-selling Girl Scout troop in the city. As part of their sales plan for next year’s cookie selling season, they need to know (with 99% confidence, or α = 0.01) if the types of cookies purchased by their customers depends on where the scouts sell them. Here is their confidential sales data from last year:
Answer:
The types of cookies purchased by the customers depends on where the scouts sell them.
Step-by-step explanation:
The data provided is:
Sales Type of Cookie Sold
Method
Thin Mints Tagalongs Do-si-dos Trefoils Samoas
At
parents’ 472 641 350 223 401
workplace
Door
-to- 840 1092 673 511 542
Door
Community 683 742 491 420 374
Events
A Chi-square test for goodness of fit will be used to determine whether the types of cookies purchased by the customers depends on where the scouts sell them.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
The formula to compute the expected frequency is:
[tex]E_{i}=\frac{i^{th}\ \text{Row Total}\times i^{th}\ \text{Column Total}}{N}[/tex]
Consider the Excel output for the expected frequency values.
The Chi-square test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=56.788[/tex]
The degrees of freedom is:
df = (r - 1)(c - 1)
= (3 - 1)(5 - 1)
= 2 × 4
= 8
The p-value is:
[tex]P(\chi^{2}_{8}>56.788)<0.00001[/tex]
*Use a Chi-square table.
The p-value of the test is very small.
The null hypothesis will be rejected at 1% level of significance.
Conclusion:
There is enough evidence to support the claim that the types of cookies purchased by the customers depends on where the scouts sell them.
What is the measure of the complement?
Answer:
64 degrees
Step-by-step explanation:
complementary-angle adds up to 90 degrees.
90-26 is 64 degrees.
find the value of x2 values that separate the middle 90% from the rest of the distribution for 8 degrees of freedom
Answer:
With alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
Step-by-step explanation:
The significance level ∝ = 1- 0.9 = 0.1
But we need the area of the middle so we divide this significance level with 2
so that we get exactly the middle area .
Dividing 0.1/2= 0.05
So we will have two values for chi square
One with 0.9 + 0.05 = 0.95 alpha and one with 0.05 alpha . This is because the chi square is right tailed.
So with alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
This can be shown with a graph.
If AABC = ADEC,
ZB = 5x and ZE = 45°
А
D
с
B
E
x = [?]
Answer:
x=9
Step-by-step explanation:
If the triangles are congruent, then the angles B and E are also congruent (because they lie in the same place). Set an equation where B is equal to E:
∠[tex]B=[/tex]∠[tex]E[/tex]
Substitute values:
[tex]5x=45[/tex]
Solve for x. Divide both sides by 5:
[tex]\frac{5x}{5}=\frac{45}{5}\\\\ x=9[/tex]
So, when ΔABC≅ΔDEC, and ∠B=5x and ∠E=45°, the value of x is 9.
:Done
Answer:
I agree with the first answer
Step-by-step explanation:
What is the value of x in the equation 4x − 17 = 65?
Answer: x=20.5
Step-by-step explanation:
Given
4x-17=65
Add 17 on both sides (addition property of equality)
4x-17+17=65+17
4x=82
Divide 4 on both sides (division property of equality)
4/4x=82/4
x=20.5
Hope this helps!! :)
Please let me know if you have any question
Answer:
x = 20.5
Step-by-step explanation:
4x - 17 = 65
4x = 65 + 17
x = 82 ÷ 4
x = 20.5
Hope it helps.
Score: 0 of 1 pt
4 of 8 (2 complete)
2.2.15
A large western state consists of 4423 million acres of land. Approximately 19% of this land is federally owned. Find the number of acres that are not federally owned.
Answer:
3583 million acres
Step-by-step explanation:
If 19% is federally owned, then 81% is not.
0.81 × 4423 million acres = 3583 million acres
that are not federally owned.
_____
This is a typo or refers to some country other than the US. The largest US state (Alaska) is about 425 million acres.
Determine the quantity needed to replace the question mark to make the scale balance The weight times the distance on both sides of the fulcrum (the triangle) must be the same to make the scale balance
6 kg
3m
-
600 cm
The quantity needed to replace the question mark to make the scale balance is ? grams
work please, I wanna understand how to do it. thank you:)
Answer:
3kg = 3000 gm
Step-by-step explanation:
we use this formula
m1x (distance of m1 )= m2 x( distance of m2)
* the distance far from the triangle*
m1 =6 kg
d1 = 3m
m2 = ê (kg )
d2 = 600 cm = 6 m
m1 d1 = m2 d2
6 x 3 = ê 6
ê = 3 kg
mass = 3kg = 3000 gram
#
To make the scale balance, the weight must be added is 3000g.
What is a balancing equation?"A balanced equation is an equation where both sides are equal to the same amount. The answer to the expression on the left side of the equals sign (=) should be equal to the value on the right side of the equals sign".
For the given situation,
From the diagram shown, the distance on both sides of the fulcrum (the triangle) must be the same to make the scale balance.
We know that
1 kg = 1000 g
1 m = 100 cm
Let the unknown quantity be 'x'
To write a balanced equation, units should be the same on both sides.
6 kg = 6000 g
3 m = 300 cm.
The equation is represented as
[tex]6000[/tex] × [tex]300 = x[/tex] × [tex]600[/tex]
⇒ [tex]x = \frac{(6000)(300)}{600}[/tex]
⇒ [tex]x=3000[/tex]
Hence we can conclude that to make the scale balance, the weight must be added is 3000g.
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It takes a hose 4 minutes to fill a rectangular aquarium 11 inches long, 12 inches wide and 13 inches tall. How long will
it take the same hose to fill an aquarium measuring 21 inches by 24 inches by 32 inches? Round your answer to the
nearest minute.
Answer:
38 minutes
Step-by-step explanation:
Volume of the first aquarium:
V = lwh = 11*12*13 = 1716 in³Volume of the second aquarium
V = 21*24*32 = 16128 in³The second aquarium is:
16128/1716 = 9.4 times bigger by volumeIt will take
4*9.4 ≈ 38 minutesto fill this aquarium
a grocery store charges 1.25$ for every 3/4 pound of chocolate purchased. How much will the store charge a customer who purchases 9 pounds of chocolate?
Given :
A grocery store charges 1.25 $ for every 3/4 pound of chocolate purchased.
To Find :
How much will the store charge a customer who purchases 9 pounds of chocolate .
Solution :
3/4 pound store charges 1.25 $ .
Let , cost of 1 pound is x .
So ,
[tex]\dfrac{3x}{4}=1.25\\\\x=\dfrac{1.25\times 4}{3}\\\\x=1.67\ \$[/tex]
Now , cost of 9 pounds chocolate is :
[tex]C=9\times 1.67\ \$\\\\C=15.03\ \$[/tex]
Therefore , cost of 9 pounds chocolate is 15.03 $ .
Hence , this is the required solution .
please help I don't know how to do this
Answer:
792/7 is the correct answer
Step-by-step explanation:
V=4/3pi r^3
=4/3×22/7×3x×3x×3x
=88×9x÷7=792/7
What is the answer please help
8-10=-2+k
Answer:
k =0Step-by-step explanation:
[tex]8-10=-2+k[/tex]
Switch sides
[tex]-2+k=8-10[/tex]
Subtract the numbers : 8-10=-2
[tex]-2+k=-2[/tex]
Add 2 to both sides
[tex]-2+k+2=-2+2[/tex]
Simplify
[tex]k = 0[/tex]
Answer:
k=0
Step-by-step explanation:
Simplify 8-108−10 to -2−2.
−2=−2+k
regroup those terms
−2=k−2
cancel -2 on both sides
0=5
switch sides k=0
i recommend using cymath free and very easy
How much cash did the person who filled out this deposit slip receive? a. $381.23 b. $451.02 c. $88.79 d. $436.02
Answer:
c
Step-by-step explanation:
its c
The cash received by the person who filled out this deposit is $88.79.
Option C is the correct answer.
Given,
Description Amount ($)
Cash, including coins. 15.00
Check 1 62.44
Check 2 27.83
Check 3 45.75
Subtotal ??.??
Less cash received ??.??
Total 62.23
We need to find the less cash received.
What is a deposit slip?A deposit slip is a bank form where the customer fills in the required date such as the date, the depositor's name, the depositor's account number, and the deposit amounts.
Find the subtotal.
= Cash included coins + check 1 + check 2 + check 3
= 15.00 + 62.44 + 27.83 + 45.75
= 151.02
Find the less cash received.
We have,
Total = 62.23
Total = Subtotal - less cash received
62.23 = 151.02 - less cash received
less cash received:
= 151.02 - 62.23
= 88.79
Thus, the cash the person who filled this deposit slip received is $88.79.
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The complete question:
Consider the following incomplete deposit slip:
Description - Amount ($)
Cash, including coins - 15.00
Check 1 - 62.44
Check 2 - 27.83
Check 3 - 45.75
Subtotal - ?? ??
Less cash received - ?? ??
Total - 62.23
How much cash did the person who filled out this deposit slip receive?
a. $381.23
b. $451.02
c. $88.79
d. $436.02
Charlie had a -$38.65 balance in his checking account. He deposited $126.00 into the account. What is his new balance?
Answer: $87.35
Step-by-step explanation:
Answer:
$164.65
Step-by-step explanation:
$38+$126.65=$164.65
For the following study identify the sources of sampling bias and describe how it might affect the study and conclusion and how you might alter the sampling method to avoid the bias.A nutritionist is interested in the eating habits of college students and observes what each student who enters a dining hall between 8:00 A.M. and 8:30 A.M. chooses for breakfast on a Monday morning.
Answer:
1. 1. Because convenient sampling is adopted here data is only gotten from students that eat in the hall in a given period of time so this is a source of bias
Also one study center that is the Hall of only one school is used this is also biased and may affect the result of the study
To avoid this bias a simple random sampling where each student have an equal chance of being selected in the study should be adopted
What is the area of a rectangle
5 inches long and 6 inches wide?
A
29 square inches
B
32 square inches
с
30 square inches
11 square inches
Answer:
(C) 30 inches
Step-by-step explanation:
The area of a rectangle is always it’s length times its width. Since we are given the length and width, we can multiply these two numbers to get our total area.
[tex]6\cdot5=30[/tex]
Hope this helped!
Answer:
[tex]\large\boxed{Area = 30 inches}[/tex]
[tex]\huge\underline\bold\blue{Given}[/tex]
Length = 5 inches
Breadth= 6 inches
we know that the area of rectangle = length×breadth
Area of rectangle = length × breadth
[tex]\rightarrow[/tex] Area = 5 × 6
[tex]\rightarrow[/tex]Area = 30inches
Hope it helps
How many ink cartridges can you buy with 168 if one cost 14 dollars ?
168 ÷ 14 =12
ink
...
.
...
Answer:
Let the cost the number of cartridges be x.
We have given that cost of one cartridge is 14 $/cartridge.
And we have 168 $ with us.
So, according to question we have an equation-
14x=168
x=168/14
x=12
Hence, we can buy 12 cartridges if we 168 $ and the cost of one cartridge is 14 $.
A cake recipe calls for 2 3/4 cups of sugar. A caterer has 14 1/2 cups of sugar on hand. How many cakes can he make?(answer needs to be rounded down to a whole number)
Answer:
5 Cakes
Step-by-step explanation:
14.5/2.75=5.27
A cake recipe calls for 2 3/4 cups of sugar. A caterer has 14 1/2 cups of sugar on hand. He can make 5 cakes.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given; A cake recipe calls for 2 3/4 cups of sugar. A caterer has 14 1/2 cups of sugar on hand.
WE have to do 4 x the amount you know you can such as 10.
Then we have to multiply the 1/2 by that same number
Then we divide
14.5/2.75=5.27
Therefore, They can make 5 cakes.
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Joan has $375.24 in a savings
account. She deposits $37.50 each
week and makes no withdrawals.
Which expression represents the
amount of money in the account
in w weeks?
Answer:
C. 375.24 + 37.50w
Step-by-step explanation:
He already has 375.24
He adds 37.5 every week.
W = the number of weeks.
Example:
=> If he deposits for 10 weeks, then it will be
=> 375.24 + 37.5(10)
=> 375.24 + 375
=> 750.24
The correct expression to represent this problem is Option C.
what is the distance between between 120 and -50 on the number line
is the decimal for 4/3 a repeating decimal? explian
Answer:
Step-by-step explanation:
Yes, it's a repeating decimal: 1.3333333....
Beatrice has 0.26 in her pocket. What percent of a dollar does Beatrice have?
28%
Answer:
26%
Step-by-step explanation:
If 1 dollar is 100%
Then 0.26 dollar is:
0.26*100= 26%