Answer:
Length = 52 ft
Width = 40 ft
Step-by-step explanation:
Given information:
length = 19.5 inwidth = 15 inscale = 3 in : 8 ftScale
[tex]\implies \sf 3 \: in : 8 \: ft[/tex]
[tex]\implies \sf 1 \: in : \dfrac{8}{3} \: ft[/tex]
To find the length and width of the studio in feet, multiply the length and width in inches by 8/3:
[tex]\sf Length = 19.5 \times \dfrac{8}{3}=52\:ft[/tex]
[tex]\sf Width = 15 \times \dfrac{8}{3}=40\:ft[/tex]
Therefore, the length of the actual studio is 52 ft and the width of the actual studio is 40 ft.
Scale is 3in:8ft
So
1in=8/3ftLength
19.5(8/3)ft52ftWidth
15(8/3)40ft-7πh = 98π
solve for h
Answer:
h = -14
Step-by-step explanation:
-7πh = 98π
⇔ -7h = 98 (Just Divide both sides by π)
⇔ h = 98 ÷ (-7) = -14
Hi :)
We should find h. All it takes is some algebra skills ^•^
————————First off, you can see than we have π on both sides. So, why not divide both sides by π and get it out of the way?
We end up with
[tex]\boldsymbol{-7h=98}[/tex]
Super! Now all we have to do is divide both sides by -7
We end up with
[tex]\boldsymbol{h=-14}[/tex]
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
(1,-2) and (2,-4) exponential formula f(x)=ab^x
We conclude that the exponential function is:
f(x) = -1*(2)ˣ
How to find the exponential function?Here we know that we have an exponential function of the form:
f(x) = a*b^x
And we know two points on the function, that are:
f(1) = -2 = a*b^1 = a*b
f(2) = -4 = a*b^2
Then we have a system of equations to solve, which is:
-2 = a*b
-4 = a*b^2
From the first equation we can solve:
-2/a = b
Replacing that in the other equation we can get:
-4 = a*(-2/a)^2 = 4/a
a = 4/-4 = -1
Now that we know the value of a, we can get the value of b:
-2/a = b
-2/-1 = 2 = b
In this way, we conclude that the exponential function is:
[tex]f(x) = -1*(2)^x[/tex]
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Two regular 6-sided dice are tossed. Compute the probability that the sum of the pops on the upward faces of the 2 dice is the following. 1
Answer: 0
Step-by-step explanation:
3. Complete the table (showing work) and draw a graph of the logarithmic function f(x) = log 1/5 x
Answer:
Step-by-step explanation:
Find the product of the complex numbers. Express your answer in trigonometry form. Z1= 7cos(15) + isin(15)) z2= 2(cos(110)+ isin(110))
Answer:
14(cos(125°) +i·sin(125°))
Step-by-step explanation:
The product of two complex numbers is the product of their magnitudes at an angle equal to the sum of their angles.
ApplicationFor A = a·cis(α) and B = b·cis(β), the product AB is ...
AB = (a·cis(α))·(b·cis(β)) = ab·cis(α+β)
where "cis(x)" stands for the sum (cos(x) +i·sin(x)).
The product of interest is ...
Z1·Z2 = (7cis(15°))·(2cis(110°)) = (7·2)cis(15°+110°)
Z1·Z2 = 14cis(125°) = 14(cos(125°) +i·sin(125°))
Supervisor: "Last week, you spoke with 800 customers in 40 hours."
Employee: "That is an average of ____ customers every 30 minutes."
Answer: 10
Step-by-step explanation: 800/80 = 10
One serving of chicken has 148 grams of protein, which is 80% of the recommended daily amount.
Answer:
x = 185 grams
Step-by-step explanation:
let 100% of the recommended daily amount = x
148 = 80%x
148 = 0.8x
divide by 0.8 both sides
x = 185
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
WILL GIVE BRAINLIEST FOR ACCURATE ANWSER
The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.
Given that BD is diameter of the circle and angle BAC is 100°.
We are required to find the central angle, major arc, minor arc, m BEC, BC.
Angle is basically finding out the intensity of inclination of something on the surface.
In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.
Major arc of a circle is that arc whose length is larger than all other arcs in the circle.
In our circle the major arc is arc BED.
Minor arc of a circle is that arc whose length is smaller.
In our circle the minor arc is arc ADC.
We know that arc's length is 2πr(Θ/360)
In this way BC=2π*(BD/2)*100/360
=(5π*BD)/18
We cannot find angle BEC.
Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.
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Write all possible values of y if y is a multiple of 9: 248
The possible values of y are 9n where n is an integer greater than 0 equal to 0
How to determine the possible values of y?The statement is given as;
y is a multiple of 9
The above means that
The number y can be divided by 9 without remainder
The numbers in this category are:
Numbers = 9, 18, 27, 36, 45......
This can be rewritten as:
Numbers = 9n where n is an integer greater than 0 equal to 0
Hence, the possible values of y are 9n where n is an integer greater than 0 equal to 0
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A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The outcomes are listed in the table below. Note that each outcome has the same probability.
The probability of occurrence for the events A, B and C is; 1/4.
What is the probability of occurrence of.the described events?For the first event A in which case, there's no odd number on the first two rolls, the possible events are; EEE and EEO. Consequently, the required probability is;
Event A = 2/8 = 1/4.
For the event B in which case, there's an even number on both the first and last rolls; the possible events are; EEE and EOE. Consequently, the required probability is;
Event B = 2/8 = 1/4.
For the event C in which case, there's an odd number on each of the first two rolls; the possible events are; OOO and OOE. Consequently, the required probability is;
Event C = 2/8 = 1/4.
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22. Kim earns x dollars per hour for the first 40 hour she works in a week
and 1-
1¹/1/12 times as much for each hour over 40. If she worked 52 hours
last week, how much, in dollars, did she earn?
(A) 52X
0+1=1/x
(C) 52x+1-¹-x
(B) 40+1
(D) 52x-1-x
(E) 58x
40+1 in dollars per hour
sin theta =-(1)/(\sqrt(17))and (3\pi )/(2)<=\theta <=2\pi then tan\theta =
Using a trigonometric identity, and considering that the angle is in the fourth quadrant, the tangent of the angle is given as follows:
tan(theta) = -1/4
Which trigonometric identity relates the sine and the cosine of an angle?The following identity is used to relate the measures, considering an angle [tex]\theta[/tex]:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
For this problem, the sine is given as follows:
[tex]\sin{\theta} = -\frac{1}{\sqrt{17}}[/tex]
Then the cosine, which we need to find the tangent, is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\left(-\frac{1}{\sqrt{17}}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\frac{1}{17} + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = \frac{16}{17}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{16}{17}}[/tex]
Since the angle is in the fourth quadrant, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{4}{\sqrt{17}}[/tex]
What is the tangent of an angle?It is the sine of the angle divided by the cosine of the angle, hence:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{-\frac{1}{\sqrt{17}}}{\frac{4}{\sqrt{17}}} = -\frac{1}{4}[/tex]
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A garrison has provision for 10 days. At the end of 2 days 1/2 of the men left the garrison. how long the food will now last?
Please answer with explanation?
After half of the men go away, the provisions will last for another 16 days.
how long the food will now last?
First, we know that the garrison has provisions for 10 days.
2 days after that, the garrison has provisions for another 8 days. Here we know that the number of men on the garrison is reduced to its half. Then, the time that the provisions in the garrison will last is multiplied by 2.
So we just need to solve the product:
2*8 days = 16 days.
After half of the men go away, the provisions will last for another 16 days.
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[tex]h(x) = x -1 + \frac{1+ ln {}^{2} (x) }{x}[/tex]
[tex]\displaystyle \lim_{x\to0} h(x)= \: ? \\ \displaystyle \lim_{x\to \infty } h(x)= \: ?[/tex]
Apply L'Hôpital's Rule if possible
Answer:
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]
[tex]\lim_{x\rightarrow 0 } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]
Step-by-step explanation:
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]
[tex]= [\lim_{x\rightarrow +\infty } (x-1)]+[ \lim_{x\rightarrow +\infty } (\frac{1+ln^{2}x}{x})][/tex]
= +∞ + 0
= +∞
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]
[tex]= [\lim_{x\rightarrow 0 } (x-1)]+[ \lim_{x\rightarrow 0 } (\frac{1+ln^{2}x}{x})][/tex]
= -1 + +∞
= +∞
Select the common ratio and the 4th term of the geometric series: 9, -6,4...
The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.
A geometric sequence is a special series where every term is the product of the previous term and a common ratio.
The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.
In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........
The first term of the sequence, a = 9.
The second term of the sequence, a₂ = -6.
By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:
a₂ = a.r²⁻¹.
Substituting the values, we get:
-6 = 9(r²⁻¹),
or, r²⁻¹ = -6/9,
or, r = -2/3.
Thus, the common ratio of the given geometric sequence is -2/3.
The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:
a₄ = a.r⁴⁻¹ = a.r³.
Substituting the values, we get:
a₄ = 9(-2/3)³,
or, a₄ = 9.(-8/27),
or, a₄ = -8/3.
Thus, the 4th term of the given geometric sequence is -8/3.
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For what value of x is the rational expression below undefined?
3x+15/6-x
Let the function be (3x+15)/(6-x) then the value of x exists at -5.
What is the value of x?Given: Rational Expression (3x+15)/(6-x)
To find the value of x when given a rational expression equivalent to 0.
To estimate the value of x, convey the variable to the left side and convey all the remaining values to the right side. Simplify the values to estimate the result.
Consider, (3x+15)/(6-x) = 0
3x + 15 = 0(6-x)
3x + 15 = 0
Subtract 15 from both sides of the equation, e get
3x + 15 - 15 = 0 - 15
simplifying the above equation, we get
3x = 0 - 15
3x = -15
Divide both sides by 3, then we get
x/3 = -15/3
x = -5
Therefore, the value of x exists at -5.
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Three books are what percent of four books?
If four books are 100%, then 3 books are how much percent of total books?
[tex]\frac{3}{4}[/tex] × 100 = 3 × 25 = 75%
Hope it helps!
The answer is 75%.
To find the percentage, divide the number of given books by total books and multiply by 100%.
(3 ÷ 4) × 100%0.75 × 100%75%A recipe for a single batch of cookies calls for 3 eggs.
Step 1. Write an equation that represents the total number of eggs we need (n) for some batches (b) of this recipe.
Step 2. How many eggs do we need to make 6 batches of this recipe?
The total number of eggs needed for b batches is n = 3b
The total number of eggs needed for 6 batches is 18.
How many eggs are needed?
Multiplication is one of the basic mathematical operation that is used to determine the product of two or more numbers. The sign used to denote multiplication is x. Other mathematical operations include addition, subtraction and division.
In order to determine the total number of eggs needed, multiply the number of eggs needed for one batch by the total number of batches.
Total eggs needed = eggs needed for one batch x total number of batches
n = 3 x b
n = 3b
6 x 3 = 18
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A large party balloon is being filled with helium at a constant rate. After 8 seconds, there is 2.5L of helium in the balloon.
b) The balloon will burst if there is more than 10 L of helium in it. How long will it take to fill the balloon with that much helium?
Answer:
32 seconds
Step-by-step explanation:
first 8 secknds gives us the value of set 2.5l
2.5L to make 10 =
10÷2.5=4
That said 2.5L fills 1pL by 4 giving us;
4×2.5= 10L
Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5
Answer: -6
Step-by-step explanation:
[tex]x+3y=-5\\\\3y=-x-5\\\\y=-\frac{1}{3}x-\frac{5}{3}[/tex]
So, since parallel lines have the same slope, the slope of the line we need to find is -1/3.
Substituting into point-slope form, the equation is
[tex]y-2=-\frac{1}{3}(x+7)\\[/tex]
Converting to the required form,
[tex]y-2=-\frac{1}[3}x-\frac{7}{3}\\\\\frac{1}{3}x+y=-\frac{1}{3}\\\\-3x-9y=3[/tex]
So, B-A is equal to -6.
A man can take a same time to row 13km downstream and 7km upstream.His speed in still water is 5km/hr.The speed of stream is
Answer:
0.6 km/hr
Step-by-step explanation:
Speed downstream: 13/5= 2.6 km/hr
Speed upstream: 7/5= 1.4 km/hr
Therefore, Velocity of current is: 1/2 (2.6-1.4) km/hr = 1/2(1.2) km/hr
a. Use the adjusted trial balance to prepare the December 31 year-end income statement. b. Use the adjusted trial balance to prepare the December 31 year-end statement of owner's equity. The E. Happ, Capital account balance was $69,623 on December 31 of the prior year, and there were no owner investments in the current year. c. Use the adjusted trial balance to prepare the December 31 year-end balance sheet.
It should be noted that a trial balance is a report which lists the balances of the ledger accounts of a company.
How to illustrate the information?It should be noted that the information is incomplete. Therefore, an overview will be given. It should be noted that the accounts that are reflected on a trial balance are related to the accounting items.
The adjusted trial balance simply lists the general ledger account balances after the adjustments have been made. In such a case, these adjustments typically include prepaid and accrued expenses, and non-cash expenses such as depreciation.
Furthermore, a trial balance is a list of the closing balances of ledger account while adjusted balance is a list of general account. An adjusted trial balance is typically prepared by creating a series of journal entries which are designed to account for any transactions that haven't been completed.
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Find center,foci and vertices of ellipse for 4x2+y2+2x-10y=6
Answer:
center:
(-0.25, 5)
foci :
(-0.25, 0.158771) | (-0.25, 9.84123)
vertices :
(-0.25, -0.59017) | (-0.25, 10.5902)
wolframramalpha
First dispensed is 1/3 of a quart, later 1/4and then you dispensed 3 1/2 quarts. What’s the total volume that is dispensed
Answer:4 1/12.
Step-by-step explanation: First, you add 3 and a half with a quarter. A half equals two quarters so it equals 3 and 3/4. Then, you add 3 3/4 with 1/3. A common denominator here is 12. 3/4 times 3/3 = 9/12. 1/3 times 4/4 = 4/12. 9+4 = 13. The answer is more than one so we carry and get 4 and 1/12.
Which of the LCM (40,120,150)?
Answer:
2400
Step-by-step explanation:
40 = 2^3 * 5
120 = 2^5 * 5
150 = 2 * 3 * 5^2
LCM = 2^5 * 3 * 5^2
Please hurry quick I need an answer
Answer:
slope is 4
Step-by-step explanation:
Slope is rise/run
for every 4 units it rises it runs 1 unit
4/1=4
What is (43/7÷ x+32/9) ÷25/6=4/3
The value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14
How to solve for x in the equation?The equation is given as:
(43/7 ÷ x + 32/9) ÷ 25/6 = 4/3
Rewrite as a product
(43/7 ÷ x + 32/9) x 6/25 = 4/3
Multiply both sides of the equation by 25/6
(43/7 ÷ x + 32/9)= 4/3 x 25/6
Evaluate the product
(43/7 ÷ x + 32/9)= 50/9
Rewrite the equation as:
43/7x + 32/9= 50/9
Subtract 32/9 from both sides
43/7x = 2
Multiply both sides by 7x
14x = 43
Divide by 14
x =43/14
Hence, the value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14
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IF THE ODDS AGAINST A PARTICULAR CANDIDATE WINNING AN ELECTION ARE 9
TO 5, WHAT IS THE PROBABILITY THAT THE CANDIDATE WILL WIN?
The probability that the candidate will win is P = 0.357
How to find the probability?
We know that the odds against the particular candidate are 9 to 5.
The the odds for the candidate are 5 to 9, this means that in 5 cases the candidate will win, and in 9 cases the candidate will lose.
Then the candidate wins in 5 out of 14 cases, then the probability that the particular candidate wins the elections is given by the quotient:
P = 5/14 = 0.357
The probability that the candidate will win is P = 0.357
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9e-6(-2e+7)= please help me solve this problem
[tex]\bold{Answer:} \small\boxed{21e-42}[/tex]
Step-by-step explanation:
[tex]To\ solve\ : \ 9e-6(-2e+7)[/tex]
we first must use the distributive property. You can think about solving this like this:
[tex]=9e-(6)(-2e+7)[/tex]
Notice how we are not distributing -6, but only 6. Now we can solve normally:
[tex]=9e-(-12e+42)[/tex]
Now we distribute the '-' sign to the terms in parenthesis.
[tex]=9e+12e-42[/tex]
[tex]\longrightarrow \large\boxed{21e-42}[/tex]
The decimal form is 15.08 rounded.
Use synthetic division to determine which of the following is a factor of [tex]2x^3-3x^2-5x+6\\[/tex]
Option A. x + 6
Option B. x - 2
Option C. x - 3
Option D. x + 2
The factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2
How to determine the factor using the synthetic division?The polynomial is given as:
2x^3 - 3x^2 - 5x + 6
Next, we test the factors
Option A. x + 6
Set the factor to 0
x + 6 = 0
Solve for x
x = -6
So, we set up the division as follows:
-6 l 2 - 3 -5 6
Bring down the leading coefficient
-6 l 2 - 3 -5 6
2
Multiply 2 and -6
-6 l 2 - 3 -5 6
-12
2
Add -3 and -12
-6 l 2 - 3 -5 6
-12
2 -15
Repeat this process
-6 l 2 - 3 -5 6
-12 72 -402
2 -15 67 -396
-396 is the remainder of the above division.
This means that x + 6 is not a factor of the polynomial
Option B. x - 2
Set the factor to 0
x - 2 = 0
Solve for x
x = 2
So, we set up the division as follows:
2 l 2 - 3 -5 6
Bring down the leading coefficient
2 l 2 - 3 -5 6
2
Multiply 2 and 2
2 l 2 - 3 -5 6
4
2
Add -3 and -12
2 l 2 - 3 -5 6
4
2 1
Repeat this process
2 l 2 - 3 -5 6
4 2 -6
2 1 -3 0
0 is the remainder of the above division.
This means that x - 2 is a factor of the polynomial
There is no need to check for the remaining options
Hence, the factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2
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