Determine if it’s linear or non linear

The correct answer is (5x + 1) / (x+7).

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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The probability of choosing a student who plays both basketball and baseball is approximately 0.4643.

It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

We can use the inclusion-exclusion principle to find the number of students who play both basketball and baseball.

Number of students who play both = Number of basketball players + Number of baseball players - Number of students who play neither

                                                           = 11 + 13 - 11

                                                           = 13

Therefore, out of 28 students, 13 play both basketball and baseball.

The probability of choosing a student who plays both sports can be calculated as follows:

P(plays both) = Number of students who play both / Total number of students

                      = 13/28

                      = 0.4643 (rounded to 4 decimal places)

So the probability of choosing a student who plays both basketball and baseball is approximately 0.4643.

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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.

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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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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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:

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:

Step-by-step explanation:

Assuming that the original measurement is in millimeters, since they are commonly used in precision applications, we know that 1 millimeter is equal to 0.03937 inches. Therefore, we can convert 4559.886 millimeters to inches by multiplying by 0.03937:

4559.886 mm * 0.03937 in/mm = 179.72467632 in (rounded to 8 decimal places)

To round this to the nearest inch, we need to look at the first decimal place after the decimal point. In this case, the digit in the first decimal place is 7, which is greater than or equal to 5. Therefore, we round up to the nearest inch, which gives us:

179.72467632 in rounded to the nearest inch is 180 in.

Therefore, 4559.886 rounded to the nearest inch is 180.

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:i don't know the answer

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

Answer:

28x + 40

Step-by-step explanation:

Since all four sides of a square are equal, we can make an equation:

[tex]4(7x + 10) = 28x + 40[/tex]

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:

1/3

Step-by-step explanation:

The calculated area of the composite figure is 129 square units

Given that we have

A composite figure

To find the area of a composite figure, you can break it down into smaller, simpler shapes whose areas you can calculate. Then you can add up the areas of these shapes to get the total area of the composite figure.

The area is then calculated as

Area = Trapezoid + Rectangle + Parallelogram + Triangle

Using the dimensions from the graph, we have

Area = 1/2 * (12 + 6) * 4 + 6 * 10 + 3 * 7 +  1/2 * 6 * 4

Evaluate

Area = 129

Hence, the area is 129 square units

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A) The prοbability that less than 5% οf Americans in a sample οf 100 will be diagnοsed with lung cancer is very small, οnly 0.02%.

B) As there is still variability in the number οf cases that may arise due tο chance.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

(A) We can use the binοmial distributiοn tο mοdel the number οf Americans in a sample οf 100 whο are diagnοsed with lung cancer. Let X be the number οf Americans in the sample whο are diagnοsed with lung cancer. Then X ~ Bin(100, 0.0625).

We want tο find P(X < 5). We can use the nοrmal apprοximatiοn tο the binοmial distributiοn, since n is large and p is nοt tοο clοse tο 0 οr 1. Using the cοntinuity cοrrectiοn, we have:

P(X < 5) = P(X < 5.5)

[tex]= P((X - np) \sqrt{(np(1-p))} < (5.5 - np)\sqrt{(np(1-p))})[/tex]

[tex]= P(Z < (5.5 - 6.25100)\sqrt{(6.25100*(1-0.0625)))[/tex]

= P(Z < -3.52)

= 0.0002 (frοm standard nοrmal table)

Therefοre, the prοbability that less than 5% οf Americans in a sample οf 100 will be diagnοsed with lung cancer is very small, οnly 0.02%.

(B) If 20 οr mοre Americans whο smοke cigarettes are diagnοsed with lung cancer in a sample οf 100, this is quite rare based οn the expected rate οf 6.25% in the general pοpulatiοn. This suggests that smοking is a significant risk factοr fοr develοping lung cancer, as the οbserved rate is much higher than the expected rate.

Hοwever, we cannοt cοnclude that all smοkers will develοp lung cancer, as there is still variability in the number οf cases that may arise due tο chance.

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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.

The answer to the crossnumber is 25.

Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics and is used to describe sets, groups, and other mathematical objects. Numbers are used to measure quantities, such as length, area, time, and weight. They are also used to represent relationships between objects, and to describe the properties of those objects. Numbers can be represented in various forms, such as integers, fractions, and decimals.

This can be determined by examining the clues and their corresponding digits. Across, the clue is "A square", so the digit in the corresponding cell must be a perfect square, in this case 1. The next clue is "An odd square", so the digit must be an odd perfect square, which is 3. Down, the first clue is "A square", so the digit must be a perfect square, which is 5. The last clue is "A square", so the digit must be a perfect square, which is 7. When all the digits are put together, the resulting two-digit number is 25.

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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:

Step-by-step explanation:

To solve this problem, we can use the formula for calculating the fixed monthly payment on a mortgage:

P = (r * PV) / (1 - (1 + r)^(-n))

where:

P = fixed monthly payment

r = monthly interest rate (annual interest rate divided by 12)

PV = present value of the loan (loan amount)

n = total number of payments (number of years multiplied by 12)

Using the given values:

r = 0.0735 / 12 = 0.006125

PV = R150,000

n = 20 x 12 = 240

Then we can calculate the monthly payment:

P = (0.006125 * 150000) / (1 - (1 + 0.006125)^(-240)) = R1,181.91

This means that Gideon will have to pay R1,181.91 every month for 20 years to repay his loan.

To determine how much of the second payment applies to the principal balance, we need to calculate the interest and principal amounts of the first payment.

For the first payment, the interest can be calculated as:

interest1 = r * PV = 0.006125 * 150000 = R918.75

This means that the first payment consists of R918.75 in interest and the rest, R1,181.91 - R918.75 = R263.16 is principal.

To find out how much of the second payment applies to the principal balance, we need to subtract the interest and add the calculated principal amount from the first payment to the amount of the second payment:

principal2 = (P - interest1) + principal1 = (1181.91 - 918.75) + 263.16 = R525.32

Therefore, R525.32 of the second payment applies to the principal balance.

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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(a) The value of sin 2θ is -3√(91)/50.

(b)  θ/2 is located in the third quadrant.

(c) The value of cos θ/2 is -√65/10.

We know that cos θ = 3/10, so we can find sin θ using the Pythagorean identity:

sin² θ + cos² θ = 1

sin²θ + (3/10)² = 1

sin²θ = 1 - (3/10)² = 91/100

sin θ = ±√(91)/10

Since 3π/2 < θ < 2π,

we know that sin θ < 0, so sin θ = -√(91)/10.

a) To find sin 2θ, we can use the double angle formula:

sin 2θ = 2 sin θ cos θ

sin 2θ = 2 (-√(91)/10) (3/10)

sin 2θ = -3√(91)/50

b) To find the quadrant in which θ/2 is located, we first need to find θ/2:

θ/2 = (3π/2 + 2π)/2 = 5π/4

5π/4 is in the third quadrant, so θ/2 is located in the third quadrant.

c) To find cos θ/2, we can use the half angle formula:

cos θ/2 = ±√((1 + cos θ)/2)

Since 3π/2 < θ < 2π, we know that cos θ < 0, so we take the negative square root:

cos θ/2 = -√((1 + 3/10)/2)

cos θ/2 = -√(13/20)

Simplifying the radical by dividing both numerator and denominator by 4:

cos θ/2 = -√(13)/2√5

Multiplying numerator and denominator by √5 to rationalize the denominator:

cos θ/2 = -√65/10

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Answer:6^21

Step-by-step explanation:

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 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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To find the length of a line segment in a circle, use the formula [tex]d = 2r[/tex] [tex]sin(t/2)[/tex] , where r is the radius of the circle and t is the angle between the radii. The length of segment DE is  [tex]5[/tex] units.

We can use the similar triangles property to find the missing length of segment DE in the given figure. Because triangles ABD and CBE are similar, we can use a proportion to find the length of DE:

[tex]CB/BE = AB/BD[/tex]

With the given values, we get:

[tex]3/6 = 5/(5 + DE)[/tex]

When we simplify and solve for DE, we get:

[tex]3(5 + DE) = 6 * 5 \s15 + 3DE = 30[/tex]

[tex]3DE = 15 \sDE = 5[/tex]

Therefore, segment DE has a length of 5 units.

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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]

Answer:

1. 90 students x (2/9) = 20 sixth graders

2. 27 students x (2/9) = 6 sixth graders

3. 42 sixth graders x (9/2) = 189 students