Answer:
33 units²
Step-by-step explanation:
From the net, we can see that the surface area consists of four triangles and one square:
Surface area = 4(area of triangle) + (area of square)
The base of the triangles (b) = 3, and their perpendicular height (h) = 4.
Area of triangle = (1/2)bh
Area of triangle = (1/2)(3)(4)
Area of triangle = 6
The square has side length (L) 3.
Area of square = L²
Area of square = 3²
Area of square = 9
Surface area = 4(area of triangle) + (area of square)
Surface area = 4(6) + (9)
Surface area = 24 + 9
Surface area = 33
What is the area of a rectangle with a length of 1/3 yards and width of 3/4 yard?
Answer:
1/4 yards squared
Step-by-step explanation:
Area of a rectangle equals length times width.
1/3 x 3/4 = 3/12, or 1/4
Answer:
It would be 1/4 and if not try 3/12
Step-by-step explanation:
I hope this helped
Suppose there is a simple index of two stocks, stock A and stock B. Stock A opens on Monday with 5000 shares at $2.75 per share. Stock B opens on Monday with 3000 shares at $4.30 per share. Stock A opens on Tuesday at $3.10 per share, and stock B opens on Tuesday at $4.85 per share. Both stocks have the same number of shares that they opened with on Monday. What is the rate of change of this simple index over 1 day?
The rate of change of the simple index over one day is approximately 12.78%.
To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.
On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:
Total value of Stock A on Monday = 5000 * $2.75 = $13,750
Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:
Total value of Stock B on Monday = 3000 * $4.30 = $12,900
The total value of the index on Monday is the sum of the values of Stock A and Stock B:
Total value of the index on Monday = $13,750 + $12,900 = $26,650
On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.
The total value of Stock A on Tuesday is:
Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500
The total value of Stock B on Tuesday is:
Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550
The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:
Total value of the index on Tuesday = $15,500 + $14,550 = $30,050
To calculate the percent change in the index, we use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%
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What is 0.007 divided by 0.498 to nearest tenth
Answer:
0.0
Step-by-step explanation:
To find 0.007 divided by 0.498, we can perform the following calculation:
0.007 / 0.498 ≈ 0.0141
Rounding this to the nearest tenth gives:
0.0141 ≈ 0.0
Therefore, the result, rounded to the nearest tenth, is 0.0.
Constant of Variation
Find the y-intercepts of the graph y = 10/x² ?
a. There are no y-intercepts
b. y-intercept is (0,1)
c. y-intercept is (0,2)
d. y-intercept is (0,3)
Please select the best answer from the choices provided
Answer:
A. There are no y-intercepts
Step-by-step explanation:
I calculated it logically
helpppppppppppppppppppppp i will give star thanks bralienst
Answer:
90/x=70/100 that's my answer
\(90 \x = 70 \100\)
Answer:
90/x = 70/100
Step-by-step explanation:
Is means equals and of means multiply
90 = 70% *x
Changing to decimal form
90 = .70x
Changing to fraction form
90 = 70/100 *x
Divide each side by x
90/x = 70/100
H
Which side has a length of 10 units?
G
8
O HG
O GJ
4
O HI
OJ
-8
-4
4
8
1
-4
-8
Done
Intro
Answer:
HI sorry for the late answer:>
Step-by-step explanation:
Answer:
it is indeed HI
Step-by-step explanation:
Write the sum of the circumferences of all three circles in factored form.
Answer:
2π(x+y+z)
is the factorization
it takes 9 people 40 minutes to clean a hotel lobby. How many minutes would it take 4 people
Answer:
90 minutes
Step-by-step explanation:
9 people = 40 minutes
4 people = 40/4=10
10 * 9= 90
therefore 4 people will finish the work in 90 minutes
Algebra
9.5.3 Test (CST): Polynomials
Question 24 of 25
Add.
(2x - 7) + (3x - 1)
O A. 5x + 8
O B. 5x + 6
O C. 5x - 6
O D. 5x – 8
PREVIOUS
Previous
Can I get some help??
The simplified expression is 5x - 8.
So the correct answer is (D) 5x - 8.
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
To simplify the expression, we need to combine like terms.
(2x - 7) + (3x - 1)
= 2x + 3x - 7 - 1 (grouping like terms)
= 5x - 8 (combining like terms)
Therefore,
The simplified expression is 5x - 8.
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484 in standard form
In order to express the number 484 in standard form, consider that such a form is given by m x 10ⁿ, where m is a number between 1 and 10 and n is an integer number.
Consider that 484 can be written as 4.84 x 100 = 484, moreover, take into account 100 can be written as 10².
Then, you can write:
484 = 4.84 x 100 = 4.84 x 100²
Then, you have m = 4.84 and n = 2.
Hence, the given number in standard form is 4.84 x 10²
Compute for the mean expenses of the XYZ Corporation given the following: Name Total Sales Total Expenses Quezon City 14,950.00 4,933.50 Caloocan City 18,290.00 6,035.70 Marikina City 37,200.00 12,276.00 Cebu City 18,900.00 6,237.00 Davao City 45,000.00 14,850.00 Mandaluyong City 23,000.00 7,590.00 Cavite 22,000.00 7,260.00 Laguna 21,000.00 6,930.00 Manila 66,000.00 21,780.00 Iloilo 34,000.00 11,220.00
The computed mean expenses of the XYZ Corporation based on the given information are 9,911.22.
What is the mean?The mean refers to the average value.
The mean is computed as the quotient that results from dividing the total value of the data set by the number of items in the set.
Name Total Sales Total Expenses
Quezon City 14,950.00 4,933.50
Caloocan City 18,290.00 6,035.70
Marikina City 37,200.00 12,276.00
Cebu City 18,900.00 6,237.00
Davao City 45,000.00 14,850.00
Mandaluyong City 23,000.00 7,590.00
Cavite 22,000.00 7,260.00
Laguna 21,000.00 6,930.00
Manila 66,000.00 21,780.00
Iloilo 34,000.00 11,220.00
Total 99,112.20
Mean Expenses = 9,911.22 (99,112.20 ÷ 10)
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0.06 + 2 =
0.03 + 0.4 =
0.5 + 0.02 =
0.06 + 5 =
0.01 + 0.5 =
0.2 + 4 =
0.02 + 2 =
0.6 + 0.1 =
0.5 + 0.1 =
0.05 + 3 =
00.3 + 1 =
0.0 + 0.2 =
0.4 + 00.1 =
0.1 + 0.3 =
0.02 + 0.00 =
0.02 + 0.05 =
0.01 + 6 =
0.2 + 3 =
0.03 + 0.5 =
0.2 + 1 =
Answer:
1.) 2.06
2.) 0.43
3.) 0.52
4.) 5.06
5.) 0.51
6.) 4.2
7.) 2.02
8.) 0.7
9.) 0.6
10.) 3.05
11.) 1.3
12.) 0.2
13.) 0.5
14.) 0.4
15.) 0.02
16.) 0.07
17.) 6.01
18.) 3.2
19.) 0.53
20.) 1.2
Step-by-step explanation:
Simple addition with decimals. If you have a whole number like 5, with a decimal like 0.07, 5+0.07 would be 5.07. 5 would take the spot of 0 in the ones place and .07 would remain. If you have 0.10+0.8, it would be 0.9 as your answer since we make 0.8 to 0.80 or 0.10 to 0.1 and add the two together. Hope this helped!
If (2x, x + 17, x + 21, ....) is an arithmetic sequence find the value of x ?
Answer:
Since (2x, x + 17, x + 21, ...) is an arithmetic sequence, we know that the common difference between consecutive terms is constant.
The common difference can be found by subtracting any two consecutive terms in the sequence. Let's subtract the second term (x + 17) from the first term (2x):
2x - (x + 17) = x - 17
Now let's subtract the third term (x + 21) from the second term (x + 17):
(x + 17) - (x + 21) = -4
Since the common difference is constant, we can set the two expressions for the common difference equal to each other:
x - 17 = -4
Solving for x, we get:
x = 13
Therefore, the value of x that makes the sequence (2x, x + 17, x + 21, ...) an arithmetic sequence is x = 13.
which equation is equivalent to -7x+11=32
(16x-8)
4. Expanded form
Answer:
The expanded form of (16x-8) is 16x - 8.
Step-by-step explanation:
In mathematics, the expanded form of a mathematical expression is a way of writing out the terms of the expression using their full definitions.
For example, the expression (16x - 8) can be written in expanded form as 16x - 8. This is because the expression consists of two terms: 16x and -8. The term 16x represents the product of 16 and x, while the term -8 represents the negative of 8.
In general, the expanded form of a mathematical expression is obtained by writing out each term in the expression using its full definition, rather than using abbreviations or symbols. This can be helpful for understanding the structure of an expression and how it is derived.
The mean and standard deviation of the maximum loads supported by 60 cables are 11.09 tons and 0.73 tons, respectively. Find (a) 95%, (b) 99% confidence limits for the mean of the maximum loads ofall cables produced by the compan
Answer:
The 95% confidence interval is \( 10.91 < \mu <11.28 \)
The 99% confidence interval is \( 10.85 < \mu <11.33 \)
Step-by-step explanation:
From the question we are told that
The sample mean is \(\= x = 11.09 \ tons\)
The standard deviation is \(\sigma = 0.73 \ tons\)
The sample size is n =60
From the question we are told the confidence level is 95% , hence the level of significance is
\(\alpha = (100 - 95 ) \%\)
=> \(\alpha = 0.05\)
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 1.96\)
Generally the margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }\)
=> \(E = 1.96 * \frac{ 0.73 }{\sqrt{n60 }\)
=> \(E = 0.1847 \)
Generally 95% confidence interval is mathematically represented as
\(\= x -E < \mu < \=x +E\)
=> \( 11.09 - 0.1847 < \mu <11.09 + 0.1847 \)
=> \( 10.91 < \mu <11.28 \)
From the question we are told the confidence level is 99% , hence the level of significance is
\(\alpha = (100 - 99 ) \%\)
=> \(\alpha = 0.01/tex]
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 2.58 \)
Generally the margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }\)
=> \(E = 2.58 * \frac{ 0.73 }{\sqrt{n60 }\)
=> \(E = 0.2431 \)
Generally 95% confidence interval is mathematically represented as
\(\= x -E < \mu < \=x +E\)
=> \( 11.09 - 0.2431< \mu <11.09 + 0.2431 \)
=> \( 10.85 < \mu <11.33 \)
The confidence limits for the mean of the maximum loads of all cables produced by the company are: for 95%, it is [10.935,11.245]. For 99%, it is [10.87 ,11.309].
What is the margin of error for large samples?Suppose that we have:
Sample size n > 30Sample standard deviation = sPopulation standard deviation = \(\sigma\)Level of significance = \(\alpha\)Then the margin of error(MOE) is obtained as
Case 1: Population standard deviation is knownMargin of Error = \(MOE = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\)
Case 2: Population standard deviation is unknown\(MOE = Z_{\alpha/2}\dfrac{s}{\sqrt{n}}\)
where \(Z_{\alpha/2}\) is critical value of the test statistic at level of significance
The confidence interval for specific level of significance \(\alpha\) is:
\([\overline{x} - |MOE|, \overline{x} + |MOE|]\)
where \(\overline{x}\) is the sample mean.
For this case, we are given that:
Sample size = n = 60Sample mean = \(\overline{x}\) = 11.09 tonsSample standard deviation = s = 0.73 tonsCalculating the confidence limits of given confidence level:
Case 1: Confidence interval of 95%The level of significance = \(\alpha = 100 - 95\% = 5\% = 0.05\)
The critical value of Z at this level of significance is \(Z_{\alpha/2} = Z_{0.05/2} = \pm 1.645\)
Thus, the confidence interval is:
\([\overline{x} - |MOE|, \overline{x} + |MOE|] = [11.09 - 1.645 \times \dfrac{0.73}{\sqrt{60}}, 11.09 + 1.645 \times \dfrac{0.73}{\sqrt{60}}]\\\\\approx [11.09 - 0.155, 11.09 + 0.155] = [10.935,11.245]\)
Thus, the confidence interval at 95% is [10.935,11.245]
Case 2: Confidence interval of 99%The level of significance = \(\alpha = 100 - 99\% = 1\% = 0.01\)
The critical value of Z at this level of significance is \(Z_{\alpha/2} = Z_{0.05/2} \approx \pm 2.33\)
Thus, the confidence interval is:
\([\overline{x} - |MOE|, \overline{x} + |MOE|] = [11.09 - 2.33 \times \dfrac{0.73}{\sqrt{60}}, 11.09 + 2.33 \times \dfrac{0.73}{\sqrt{60}}]\\\\\approx [11.09 - 0.1847, 11.09 + 0.1847] = [10.87 ,11.31]\)
Thus, the confidence interval at 99% is [10.87 ,11.309]
Thus, the confidence limits for the mean of the maximum loads of all cables produced by the company are: for 95%, it is [10.935,11.245]. For 99%, it is [10.87 ,11.309].
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7 (x+y) - 7 x with all the steps plz
Answer:
7y
Step-by-step explanation:
7x+7y-7x=0+7y=7y
Answer:
7y
Step-by-step explanation:
7(x+y)-7x - Distribute 7 through the peretheses
7x+7y-7x - since two opposites add up to 0, remove them from the expression
= 7y
HELP ASAP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT What number is the opposite of 6.4?
Answer:
D -6.4
Step-by-step explanation:
Opposite numbers are the same numbers but with opposite signs.
the answer should be -6.4
20. There is a number x sum that x2 is irrational but x is rational. Then x can be
(a) √5102.0 (£)
(b) √2
(c) 3/2
(d) 4/5
The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)
To explain further, we need to understand the properties of rational and irrational numbers.
A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.
In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.
Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.
Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.
Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.
In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)
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if 14 inches on a map represent a distance of 74 miles,what distance does 8 inches represents?
Answer:
42 M
Step-by-step explanation:
14 =74
8/14 = ?/74
8/14= 0.57
So,
0.57*74 = 42
Answer:
x=42
Step-by-step explanation:
Please see the picture attached. I hope this helps!
solve for 8v = 3v + 25
Answer:
v = 5
Step-by-step explanation:
Collect like-terms:
\(8v = 3v + 25\)
\(8v - 3v = 25\)
\(5v = 25\)
Divide both sides by 5 to make v the subject:
\(v = 5\)
11. In a swimming race, Yvonne swam 0.18 mile.
David swam 4 times as far as Yvonne. How far
did David swim?
(A) 2.2 miles
B
0.22 mile
C.7.2 miles
D
0.72 mile
Answer: D= 0.72
Step-by-step explanation: Because 0.18 times 4 is 0.72 miles.
Answer:
D. 0.72 miles
Step-by-step explanation:
Since David swam 4 times as far is Yvonne, he swam 4 times more than 0.18. 0.18 times 4 is 0.72. If you want/need to do it in your head, just imagine 0.18 as 18, and that multiplied by 4 is 72. then move the decimal point back over before the 7, to get your answer.
Two of the other choices are clearly wrong because the actual answer is way less than the other choices (except for B). One way to quickly figure out which two (or sometimes three) are wrong is by rounding 0.18 up to 0.2. You can try this quickly because 0.2 is barely bigger than 0.18, and 0.2 is easy to multiply by 4. The answer you would get from multiplying 0.2 is not exactly correct, but gives you a general idea.
A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
\(f(x) = \lambda e^{-\lambda x}\)
And the cumulative distribution function (CDF) is,
\(CDF = 1 - e^{-\lambda x}\)
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank is approximately 12,628 pounds.
To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.
Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.
In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.
By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.
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WRITE THE FIRST 4 TERMS OF THE SEQUENCE DEFINED BY THE GIVEN RULE ( PLEASE ANSWER FAST PLEASE QUICKLY WILL GIVE BRAINLIEST AND THANKS!!!! PLEASE HURRY!!!!)
Step-by-step explanation:
5.) f(1) = 7, f(n) = -4※f(n-1) + 15
\(f(2) = - 4 \times 7 + 15 = - 13 \\ f(3) = - 4 \times ( - 13) + 15 = 67 \\ f(4) = - 4 \times 67 + 15 = - 253\)
The first four terms are 7, -13, 67, -253.
7.) f(1) = 3, f(n) = [f(n-1)]²
\(f(2) = (3)^{2} = 9 \\ f(3) = ( {9)}^{2} = 81 \\ f(4) = ( {81)}^{2} = 6561\)
The first four terms are 3, 9, 81, 6561.
James has a job moving lawns during the summer. Suppose the formula for calculating the number of hours he will have to work each week is five times the difference of thirty-eight and three times the difference of fifteen and four hours. How many hours will James have to work each week?
Please help me with the formula
The number of hours that James have to work each week will be 25 hours.
How to calculate the number of hours?The word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge.
In this case, James has a job moving lawns during the summer. Suppose the formula for calculating the number of hours he will have to work each week is five times the difference of thirty-eight and three times the difference of fifteen and four hours.
The number of hours that James have to work each week will be:
= 5(38) - 3(15 - 4)
= 5(38) - 3(11)
= 5(38 - 33)
= 5 × 5
= 25 hours
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Drawing a number divisible by 3 then drawing a 1
Answer:
Step-by-step explanation:
The probability of drawing a number that is divisible by 3 is 1/3, since there are 3 numbers (3, 6, and 9) out of the 9 possible numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) that are divisible by 3.
The probability of drawing a 1 after drawing a number that is divisible by 3 is 1/10, since there is only one 1 among the 10 possible digits (0-9) that could be drawn after the first number.
To find the probability of both events happening together (drawing a number divisible by 3 and then drawing a 1), we need to multiply the probability of the first event by the probability of the second event. Therefore, the probability of drawing a number divisible by 3 and then drawing a 1 is:
(1/3) x (1/10) = 1/30
So the probability of drawing a number divisible by 3 and then drawing a 1 is 1/30, or approximately 0.0333, or about 3.33%
Answer:
If I understand this correctly you can draw a 9 and then draw the one if I'm wrong just delete this
Step-by-step explanation:
A softball team bought 24 jerseys and 15 hats for a total cost of $1713. Later, they bought 5 more jerseys and 12 more hats for a total cost of $490. If the cost per item was the same for each order, what was the cost of each jersey and each hat ?
Answer:
x represents jerseys, y represents hats
x= $62 y=$15
Step-by-step explanation:
Now I used a matrix (linear algebra), but I think elimination is better for you
So the idea of elimantion is so that both side have one variable that is the same
so we know that the equations are
4(24 x + 15y = 1713)
-5(5x + 12x = 490)
Multiply first equation by 4 and second equation by -5
If two of the varblies have opposite signs it means you are adding, but its subtracting if they have the same signs!
96x+60y=6852
+ −25x−60y=−2450
71x + 0y =4402
71x/71 = 4402/71
x= 4402/71
x=62
Now that we know this, we can plug into any other the orignial equation of x to get y.
I'll use the first one
24x+15y=1713
substitute 62 for x
(24)(62)+15y=1713
15y+1488=1713(Simplify both sides of the equation)
bring 1488 to the other side (swaps signs)
15y= 1713−1488
15y=225
15y/15 = 225/15
y= 15
Therefore, x= 62 and y= 15 or cost of the jerseys is $62 each and cost of hats is $15 each.
ora started watching a movie at 2:45 p.m. She watched the movie for hours before stopping the movie for hours to eat dinner. After dinner, Nora finished watching the remaining hours of the movie. At what time did the movie end?
Answer: Movies Average around 1 hour to 2 hours long. 1:30 to 2:30 so id say somewhere around 4-5 pm. Which leaves time for dinner after
Step-by-step explanation:
Suppose that the functions fand g are defined as follows.
f(x)=(4+x)(6+x)
g(x) = 1+x
Find (f/g)(-5)
Find all values that are NOT in the domain of f/g
(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.
To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).
Given:
f(x) = (4+x)(6+x)
g(x) = 1+x
Substituting -5 into the functions:
f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1
g(-5) = 1+(-5) = -4
Now, we can calculate (f/g)(-5):
(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4
Therefore, (f/g)(-5) equals 1/4.
Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.
To find the values that make the denominator zero, we solve the equation:
1 + x = 0
Subtracting 1 from both sides, we get:
x = -1
So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.
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