The correct answer is (5x + 1) / (x+7).
What error did the student make?
The student made an error in adding the rational expressions. They attempted to add the numerators directly without finding a common denominator.
To add rational expressions, we must first find a common denominator, which is the Least Common Multiple (LCM) of the two denominators. Then, we can add the numerators.
Here is the correct solution:
Problem:
(5x) / (x+7) + 1 / (x+7)
First, note that both rational expressions have the same denominator (x+7). In this case, the LCM is simply (x+7). We can now add the numerators:
Work:
(5x) / (x+7) + 1 / (x+7) = (5x + 1) / (x+7)
Solution:
(5x + 1) / (x+7)
The correct answer is (5x + 1) / (x+7).
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Based on the family the graph below belongs to, which equation could represent the graph?
On a coordinate plane, a curve starts at (0, 2) and curves up and to the right in quadrant 1.
y = 2 Superscript x Baseline 3
y = log (2 x) + 3
y = 2 x squared + 2
y = StartFraction 1 Over 2 x EndFraction + 2
Answer:
Second option [tex]y=\text{log}(2\text{x})+3[/tex]
Solution:
Based on the family of graphs shown in the attached file, the equation could represent the graph is [tex]y=\text{log}(2\text{x})+3[/tex]
This graph is the graph of the function [tex]y=\text{log}(\text{x})[/tex] stretched horizontally by a factor of 2 and translated 3 units upward.
Answer:
B
Step-by-step explanation:
Edge 2023
How to get the unadjusted cost of sales in cost and management accounting
Answer:
Step-by-step explanation:
To calculate unadjusted cost of goods sold, sum the beginning inventory value and the cost of goods manufactured, then subtract the ending inventory value.
3 Cassie wants to determine the length of the shadow that a 60-foot tall telephone pole casts without measuring it. If Cassie's mailbox, which is 42 inches in height, casts a shadow that is 31.5 inches in length, how long is the shadow that the telephone pole casts? A. 43 feet B. 45 feet C. 52 feet D. 55 feet
The answer is (B) 45 feet
Step-by-step explanation:
We can use proportions to solve this problem.
Let x be the length of the shadow cast by the telephone pole. Then we have:
(42 / 31.5) = (60 / x)
We can cross-multiply to get:
42x = 31.5 * 60
Simplifying this equation, we get:
x = (31.5 * 60) / 42
x = 45 feet
Therefore, the length of the shadow that the telephone pole casts is 45 feet.
a restaurant menu offers tomato, broccoli, and potato soups. customers order potato soup 50% of the time, broccoli 30% of the time, and tomato 20% of the time the chef designs a simulation to estimate how many of her next 10 customers will order broccoli soup. she labels five index cards p, three cards b, and two cards t. she shuffles the cards and randomly chooses a card from the pile. she records the letter, returns the card, and draws another. she repeats this process for a total of 10 draws. she completes this simulation five times. based on the simulations, how accurate is the chef's estimation regarding broccoli soup orders?
The simulation suggests that the chef's estimation of 30% broccoli soup orders is reasonable, but actual orders will vary from one set of customers to the next.
The chef's estimation of 30% broccoli soup orders seems reasonable based on the probabilities given, but the actual number of broccoli soup orders will likely vary from one set of 10 customers to the next. To estimate the accuracy of the chef's estimation, she conducts a simulation by shuffling cards representing the soup choices and randomly selecting one for each of the 10 customers. She repeats this process five times.
Based on the simulation results, we can see that the actual number of broccoli soup orders varies quite a bit from the expected value of 1.5. However, this is to be expected due to the random nature of the simulation.
To further estimate the accuracy of the chef's estimation, we could calculate the mean and standard deviation of the results to get a better sense of the distribution of possible outcomes.
Overall, the simulation suggests that the chef's estimation of 30% broccoli soup orders is a reasonable estimate, but the actual number of broccoli soup orders will likely vary from one set of 10 customers to the next.
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PLS COMPLETE ALL OF IT!! 50 POINTS!
A. The length of the cord needed to reach corner C is 17.6 m
B. The distance between the electrical outlet and corner N is 14.3 m
A. How do i determine the length of cord needed?The length of the cord needed can be obtained as follow:
Length BC = Opposite = 8 mAngle (θ) = 27°Length of cord =?Sine θ = opposite / hypotenuse
Sine 27 = 8 / Length of cord
Cross multiply
Length of cord × sine 27 = 8
Divide both sides by sine 27
Length of cord = 8 / sine 27
Length of cord = 17.6 m
B. How do i determine the distance between electrical outlet and corner NFirst, we shall determine the length OB. Details below:
Angle (θ) = 27°Length BC = Opposite = 8 mLength OB =?Tan θ = Opposite / Adjacent
Tan 27 = 8 / Length OB
Cross multiply
Length OB × tan 27 = 8
Divide both sides by tan 27
Length OB = 8 / tan 27
Length OB = 15.7 m
Finally, we shall determine the distance between the electrical outlet and corner N. Details below:
Length OB = 15.7 mLength BN = 30 mLength ON = Distance =?Length BN = Length OB + Length ON
30 = 15.7 + Distance
Collect like terms
Distance = 30 - 15.7
Distance = 14.3 m
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Pupils in a class were asked how they travel to school. The results were recorded in the table below
Car 13 bus 6 train 5 walk 8
If s pupil in the class was picked at random what is the probability that one of them walked to school as a percentage
Answer:
1/3
Step-by-step explanation:
5.7. Suppose n = 2911 and e = 11. Encrypt the following messages as in
Example (5.3).
a) "OK"
b) "HELP" (Break this up into two blocks.)
Note that,
the encrypted message for "OK" is the pair of numbers (616, 2385).
and the final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).
To encrypt a message using RSA, we need to first represent the message as numbers using a suitable encoding scheme. For simplicity, we can use the ASCII code for each character, which is a standard encoding scheme for text.
a) To encrypt "OK", we first convert each letter to its corresponding ASCII code:
"O" = 79
"K" = 75
Next, we use the RSA encryption formula:
C ≡ [tex]M^{e}[/tex] (mod n)
For "O", we have C ≡ 79¹¹ (mod 2911) ≡ 616 (mod 2911)
For "K", we have C ≡ 75¹¹ (mod 2911) ≡ 2385 (mod 2911)
Therefore, the encrypted message for "OK" is the pair of numbers (616, 2385).
b) To encrypt "HELP", we break it up into two blocks:
Block 1: "HE"
Block 2: "LP"
For block 1, we have:
"H" = 72
"E" = 69
Using the RSA encryption formula, we get:
C1 ≡ 72¹¹ (mod 2911) ≡ 738 (mod 2911)
C2 ≡ 69¹¹ (mod 2911) ≡ 1277 (mod 2911)
Therefore, the encrypted message for "HE" is the pair of numbers (738, 1277).
For block 2, we have:
"L" = 76
"P" = 80
Using the RSA encryption formula, we get:
C3 ≡ 76¹¹ (mod 2911) ≡ 1479 (mod 2911)
C4 ≡ 80¹¹ (mod 2911) ≡ 2252 (mod 2911)
Therefore, the encrypted message for "LP" is the pair of numbers (1479, 2252).
The final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).
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Suppose you have income of $24, the price of x is $2, the price of y is $4. Your utility is given by the function U=3x^2/3y^1/3. Solve for utiltiy maximizing bundle. Suppose the government intewrvenes in this market and limits purchases of x to no more than 4 units . Are you better off? You need to demonstrate graphically or with calculations
Answer:
Step-by-step explanation:
To find the utility-maximizing bundle of goods, we need to solve for the values of x and y that maximize U while still satisfying the budget constraint. The budget constraint can be written as:
2x + 4y = 24
or
x + 2y = 12
We can use the method of Lagrange multipliers to solve for the utility-maximizing values of x and y subject to this constraint. The Lagrangian function is:
L = 3x^(2/3)y^(-1/3) + λ(x + 2y - 12)
Taking partial derivatives with respect to x, y, and λ, we get:
dL/dx = 2x^(-1/3)y^(-1/3) + λ = 0
dL/dy = -x^(2/3)y^(-4/3) + 2λ = 0
dL/dλ = x + 2y - 12 = 0
Solving these equations simultaneously, we get:
x = 6
y = 3
So the utility-maximizing bundle is 6 units of x and 3 units of y.
To see if the individual is better off with the government intervention, we can plot the budget line and the indifference curve for the utility-maximizing bundle with and without the limit on x.
Without the limit, the budget line is the same as before (x + 2y = 12), and the indifference curve for the utility-maximizing bundle passes through the point (6, 3) on the graph.
With the limit, the budget line becomes x = 4, since the individual is prohibited from purchasing more than 4 units of x. The corresponding budget line has a slope of -1/2 and intercepts the y-axis at 6.
If we draw the indifference curve for the utility-maximizing bundle of (4,4), which lies on the budget line, we can see that the individual is not better off with the government intervention. This is because the slope of the budget line under the intervention is steeper, so the individual would have to give up more y than x to afford the same amount of utility. Thus, the individual would have to move to a lower indifference curve with lower utility.
Therefore, the individual is not better off with the government intervention.
Which data set has the largest range?
O A. 14, 19, 18, 35, 32, 38, 40
O B. 102, 105, 103, 110
O C. 5, 6, 75
O D. 1, 9, 2, 5, 4, 19, 2, 4, 3
The data set that has the largest range is C. 5, 6, 75, which is calculated as 75 - 5 = 70.
What is the Range of a Data Set?To find the largest range, we need to calculate the difference between the highest and lowest value in each data set and compare them.
A. For 14, 19, 18, 35, 32, 38, 40, we have:
Range = 40 - 14 = 26
B. For 102, 105, 103, 110, we have:
Range = 110 - 102 = 8
C. For 5, 6, 75, we have:
Range = 75 - 5 = 70
D. For 1, 9, 2, 5, 4, 19, 2, 4, 3, we have:
Range = 19 - 1 = 18
Therefore, data set C has the largest range of 70.
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Which fraction is larger 3/4 or 1/4
Answer:
3/4
Step-by-step explanation:
3/4 is larger because since they have the same denominator (the bottom value), you compare the numerators (the top value). Whichever numerator is bigger gives you the larger fraction.
Answer: 3/4 is larger, this is simply because 3/4 is = 75%
whereas 1/4 = 25%
3) Given that f(x) = 3x – 5 g(x) = 2x – 6 and h(x) = x + 4
4 2x
Find:- i) f(-3) = ii) g[f(0)] = iii) f[h(2)] =
iv) hᴏf(x) v) h-1(1) =
The Answer for the given functions are:
i) f(-3) = -14.
ii) g[f(0)] = -16.
iii) f[h(2)] = 13.
iv) hᴏf(x) = 3x - 1.
v) h-1(1) = -3.
What is the functiοn nοtatiοn?Functiοn nοtatiοn is a way οf representing a functiοn using algebraic symbοls. It is a shοrthand way οf expressing a relatiοnship between twο quantities οr variables, where οne variable depends οn the οther.
i) Tο find f(-3), we substitute x = -3 in the expressiοn fοr f(x) and simplify:
f(-3) = 3(-3) - 5 = -9 - 5 = -14
Therefοre, f(-3) = -14.
ii) Tο find g[f(0)], we first evaluate f(0) and then substitute that value intο g(x):
f(0) = 3(0) - 5 = -5
g[f(0)] = g(-5) = 2(-5) - 6 = -10 - 6 = -16
Therefοre, g[f(0)] = -16.
iii) Tο find f[h(2)], we first evaluate h(2) and then substitute that value intο f(x):
h(2) = 2 + 4 = 6
f[h(2)] = f(6) = 3(6) - 5 = 18 - 5 = 13
Therefοre, f[h(2)] = 13.
iv) Tο find hᴏf(x), we substitute f(x) intο the expressiοn fοr h(x) and simplify:
hᴏf(x) = h[f(x)] = f(x) + 4 = (3x - 5) + 4 = 3x - 1
Therefοre, hᴏf(x) = 3x - 1.
v) Tο find h-1(1), we need tο sοlve fοr x in the equatiοn h(x) = 1:
h(x) = x + 4 = 1
Subtracting 4 frοm bοth sides, we get:
x = 1 - 4 = -3
Therefοre, h-1(1) = -3.
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1.1.3 Quiz: Exponents
Question 2 of 10
Simplify (6^7)³.
Answer:6^21
Step-by-step explanation:
Leslie is making these two recipes. Which takes
longer to make, the strawberry bread or the
spaghetti sauce? How many minutes longer
Based on the information in the image, we can infer that the recipe that takes the longest is the one for spaghetti sauce.
How to identify the recipe that takes the longest?To find the recipe that takes the longest we must take into account the information of each of the recipes. In this case, we have preparation time and cooking time. To know the total time we must add these two values.
Additionally, we must establish a magnitude to be able to relate all the values, in this case the most appropriate would be the number of minutes.
So, the preparation of the spaghetti sauce takes 10 minutes and its cooking takes an hour and a half, that is, 90 minutes. On the other hand, strawberry bread takes 20 minutes to prepare and 55 to cook:
10 + 90 = 100 minutes20 + 55 = 75 minutesAccording to the above, the spaghetti sauce takes longer because it takes 25 minutes longer than the strawberry bread.
Note: This question is incomplete. Here is the complete information:
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Find the probability of winning second prize in a 5/45 lottery. That is, picking 4 of the 5 winning numbers
Answer:
The probability of winning second prize in a 5/45 lottery is 1 in 8,145. This is calculated by taking the total number of possible combinations (8,145) and dividing it by the total number of possible outcomes (1).
What will be the result of substituting 2 for x in both expressions below?
Substituting for x in an expression means replacing the variable x with a specific value or expression. This is often done to evaluate the expression for that particular value or to simplify the expression.
What is the substituting for x in expressions?Substituting 2 for x in the first expression, we get:
[tex]1/2(2) + 4(2) + 6 - 1/2(2) - 2 = 1 + 8 + 6 - 1 - 2 = 12[/tex]
Substituting 2 for x in the second expression, we get:
[tex]2(2) + 2 - 1 = 5[/tex]
One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
Therefore, the first expression evaluated with x = 2 is 12, and the second expression evaluated with x = 2 is 5. Since they do not have the same value, the correct option is:
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The given question is incomplete. The complete question is given below:
What will be the result of substituting 2 for x in both expressions below? One-half x + 4 x + 6 minus one-half x minus 2 Both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Both expressions equal 6 when substituting 2 for x because the expressions are equivalent. One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent. One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
What is the GCF in simplify form
So the Greatest Common Factor of The given expressions is -63x²y, 9x³y³, and 90x³y is 9x²y.
What is expression?In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a value or a quantity. Expressions can be simple or complex, and they can involve arithmetic operations, functions, and algebraic operations. Expressions can be evaluated, simplified, or manipulated using mathematical rules and techniques. They are used in many areas of mathematics, including algebra, calculus, and geometry, as well as in other fields such as physics, engineering, and economics.
Here,
To find the greatest common factor (GCF) of the given terms, we need to factor out any common factors of the coefficients and variables.
-63x²y = (-1) × 3² × 7 × x² × y
9x³y³ = 3² × x³ × y³
90x³y = 2 × 3² × 5 × x² × y
The common factors among these terms are 3², x², and y. Therefore, the GCF of the given terms is:
GCF = 3² × x² × y
= 9x²y
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i need help with my geometry work please . giving 45 points !!!
Write an expression describing all the angles that are coterminal with 8°. (Please use the variable k in your answer. Give your answer in degrees, but do not include a degree symbol in your answer.)
the expression describing all the angles that are coterminal with 8° is: θ = 8° + 360°k, where k is an integer.
How to solve and what is angle?
An angle of 8° has an initial side on the positive x-axis and rotates counterclockwise by 8°.
Any angle coterminal with 8° can be expressed as:
θ = 8° + 360°k
where k is an integer.
Therefore, the expression describing all the angles that are coterminal with 8° is:
θ = 8° + 360°k, where k is an integer.
An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians and are used to measure the amount of rotation or turn between two intersecting lines or planes.
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what is a prime number
Answer: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that is only divisible by 1 and itself.
Step-by-step explanation:
For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and so on, are prime numbers because they can only be divided by 1 and themselves without any remainder.
However, 4 is not a prime number because it can be divided by 1, 2, and 4, and 6 is not a prime number because it can be divided by 1, 2, 3, and 6.
Answer:
A prime number is a number that can be multiplied by one and itself~
eg- 2,3,5,7,11
Let me know if this helps
Patrick had earned 125 points so far this year in math class. After the most recent assignment, Patrick now has 328 points. What was the percentage increase in points? Round your answer to the nearest
Answer: 162%.
Step-by-step explanation:
To find the percentage increase in points, we need to calculate the difference between the two values, divide it by the original value, and then multiply by 100 to get the percentage.
The difference between Patrick's old score and his new score is:
328 - 125 = 203
The percentage increase is:
203/125 x 100% = 162.4%
Rounded to the nearest whole number, the percentage increase is 162%.
Help ASAP DUE IN 30 MINUTES
Answer:
53 in2 is the answer for this question
Answer:
53
Step-by-step explanation:
If you divide the figure into two parts by extending the 4 in side, you get a right triangle and a rectangle.
Area of rectangle:
6*8 = 48 in²
Area of triangle:
1/2*(13 - 8)*(6 - 4) = 1/2 times 5 times 2 = 5 in²
Total area is:
48 + 5 = 53 in²
hope this helps x
Please help need to get a good score
Tom recorded the outdoor temperature for 8 consecutive days. Seven of those temperatures were 71, 80, 69, 80, 73, 77, and 70. The average for all 8 days was 75. What was the temperature on the eighth day?
Answer:
The temperature on the eighth day is 80.
Step-by-step explanation:
Let t = temperature on the eighth day.
[tex] \frac{71 + 80 + 69 + 80 + 73 +77+ 70 + t}{8} = 75[/tex]
[tex] \frac{520 + t}{8} = 75[/tex]
[tex]520 + t = 600[/tex]
[tex]t = 80[/tex]
Evan is going to invest in an account paying an interest rate of 5.4% compounded annually. How much would Evan need to invest, to the nearest dollar, for the value of the account to reach $1,360 in 5 years
On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.
What is interest ?Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. The interest rate on the loan is known as this percentage.
here,
we have
P = 1360;
R = 5.4 ;
T = 12
so, we get,
SI = 1360 X 5.4 X 12 /100
SI =88128/100
= 881.28
Hence, On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.
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eight different names were put into a hat. A name is chosen 124 times and the name fred is chosen 17 times. What is the experimental probability of the name fred being chosen? What is the theoretical probability of the namedred being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
The answer of given Theoretical Probability Question is 0.1379 , 0.125
Experimental probability of the name Fred being chosen = number of times Fred is chosen / total number of trials
= 17/124
= 0.1379 (rounded to four decimal places)
Theoretical probability of the name Fred being chosen = number of outcomes in which Fred is chosen / total number of possible outcomes
Since there are eight different names in the hat, the total number of possible outcomes is 8. The number of outcomes in which Fred is chosen is 1 (since there is only one Fred in the hat).
Therefore, the theoretical probability of Fred being chosen is:
1/8 = 0.125 (rounded to three decimal places)
If the number of names in the hat were different, both the experimental and theoretical probabilities would change.
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Find the sum. -
3/4 + 1/2 =
Answer:
Is the problem -3/4 + 1/2 or 3/4 + 1/2?
I'll just do both then.
-3/4 + 1/2 = -1/4
3/4 + 1/2 = 5/4 or 1 1/4
Step-by-step explanation:
You're welcome.
Answer:
[tex] \frac{3}{4 } + \frac{1}{2} [/tex]
take lcm of denominators i.e. 4and 2
so, the lcm of 4 and 2 is 4.
[tex] \frac{3}{4} + \frac{2}{4} [/tex]
[tex] \frac{3 + 2}{4} [/tex]
[tex] \frac{5}{4} [/tex]
Step-by-step explanation:
hope this will be helpful:)
Find the value of X. Round to the nearest tenth
Answer:i don't know the answer
Step-by-step explanation: i don't konw
Given f(x)=5-3x, if f(x)=-19, find x.
A container contains 145.2 ounces of lemonade. If the lemonade is poured equally into 15 cups, how many ounces will be poured into each cup?
A. 8.78
B. 9.12
C. 9.64
D. 9.68
Show answer.
Answer: D. 9.68
Step-by-step explanation:
145.2 oz/ 15 cups = 9.68 oz per cup
Find a1 in the geometric series Sn=3045, r=2/5, and an=120 Please help this is due at 11:59 pm TONIGHT! Remember to show work!
Answer:
a1 = 1875
Step-by-step explanation:
You want a1 for the geometric series that has r = 2/5, an = 120, and Sn = 3045.
Series relationsThe n-th term of the geometric series with first term a1 and common ratio r is ...
an = a1·r^(n-1)
The sum of the first n terms of the geometric series is ...
Sn = a1·(r^n -1)/(r -1)
ApplicationWe can use the expression for an to substitute for r^n in the sum equation:
[tex]a_n=a_1(r^n)(r^{-1})\\\\r^n=\dfrac{a_n}{a_1r^{-1}}=\dfrac{a_nr}{a_1}\\\\S_n=a_1\dfrac{r_n-1}{r-1}=a1\dfrac{\dfrac{a_nr}{a_1}-1}{r-1}\\\\S_n=\dfrac{a_nr-a_1}{r-1}\\\\a_1=a_nr-S_n(r-1)=a_nr+(1-r)S_n\\\\a_1=(120)\dfrac{2}{5}+(1-\dfrac{2}{5})(3045)=\dfrac{2\cdot120+3\cdot3045}{5}\\\\\boxed{a_1=1875}[/tex]
__
Additional comment
The sum is of the first four terms:
1875 +750 +300 +120 = 3045
We can also find this by working backward. The previous term is 5/2 times the current term. We need to find the terms that have a sum of 3045.
120 +300 +750 +1875 +4687.5 +...
Clearly, 5 terms is too many. The sum of the first 4 terms of the backward series is 3045, so we know n=4 and the first term is 1875—the last term of our 4-term backward series.