A student added the rational expressions as follows:
Problem:
Work:
5x
+
x+7
5x
+
x+7
Solution:
7
x
7(7)
x+7
5x+49
x+7
Describe and correct the error the student made. Solve the problem correctly.

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%.

Answer:

  a1 = 1875

Step-by-step explanation:

You want a1 for the geometric series that has r = 2/5, an = 120, and Sn = 3045.

The 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)

We 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.

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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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

Answer:i don't know the answer

Step-by-step explanation: i don't konw

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.

Based on the information in the image, we can infer that the recipe that takes the longest is the one for spaghetti sauce.

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:

According 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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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.

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%

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]

On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.

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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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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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:)

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

The data set that has the largest range is C. 5, 6, 75, which is calculated as 75 - 5 = 70.

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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Answer: D. 9.68

Step-by-step explanation:

145.2 oz/ 15 cups = 9.68 oz per cup

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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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.

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.

Answer:6^21

Step-by-step explanation:

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.

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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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

The length of the cord needed can be obtained as follow:

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

First, we shall determine the length OB. Details below:

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 BN = Length OB + Length ON

30 = 15.7 + Distance

Collect like terms

Distance = 30 - 15.7

Distance = 14.3 m

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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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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.

So the Greatest Common Factor of The given expressions is -63x²y, 9x³y³, and 90x³y is 9x²y.

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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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).

Answer:

1/3

Step-by-step explanation:

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