Which expression is equivalent to 1/4(8 - 6x + 12)?

Answer: To have infinitely many solutions, the equation must be true for all values of x. In other words, the left side and right side of the equation must be equivalent, meaning that the coefficients of x on both sides of the equation must be equal, and the constant terms on both sides must be equal.

We can simplify the given equation as follows:

5(x + 3) = a(x + 4) + 3x + b

5x + 15 = ax + 4a + 3x + b

Simplifying further, we get:

8x + 4a + b = 5x + 15

Rearranging terms, we get:

3x + 4a + b - 15 = 0

For this equation to have infinitely many solutions, the coefficients of x on both sides must be equal to zero, meaning that:

3 = 0

This is not possible, so the equation cannot have infinitely many solutions for any values of a and b.

Therefore, there are no values of a and b for which the given equation will have infinitely many solutions.

(a) Miguel had the greatest spread in training times.

(b) The middle 50% of Adam's training times had the least spread.

(a) To find the greatest spread in training times, we need to calculate the range of each person's training times. Range is the difference between the maximum and minimum values. Comparing the ranges, we can say that Miguel had the greatest spread in training times since his range is the largest.

(b) The middle 50% of the training times refers to the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).

To find the least spread in the middle 50% of the training times, we need to compare the IQRs of each person. Adam's IQR is the smallest, which means the middle 50% of his training times had the least spread.

(c) The answers to parts (a) and (b) indicate that Miguel had a wider range of training times compared to Adam. However, Adam's middle 50% of training times had the least spread. This suggests that while Miguel's overall training times varied more, Adam's training times were more consistent within the middle range.

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The original house has 70 square feet of flooring.

If the ratio of the miniature house to the original structure is 2:35, then we can say that the miniature house is 2/35th the size of the original house in terms of floor area. Let's assume that the original house has x square feet of flooring. Then, we can set up a proportion based on the ratios:

2/35 = 4/x

Solving for x, we get:

x = 70

Therefore if the ratio of ambers miniature house to the original structure is 2:35 and the miniature requires 4 square feet of the flooring then original house has 70 square feet of flooring.

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A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.

To find out how many ounces of fruit juice are in a 20-ounce smoothie from Blender Splendor, given that 40% of the smoothie is fruit juice, follow these steps:

1. Convert the percentage to a decimal: 40% = 0.40
2. Multiply the total ounces of the smoothie by the decimal: 20 ounces * 0.40 = 8 ounces

Your answer: A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.

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Rounded to the thousandth place, your friend's z-score for the 10 years is approximately -0.404.

To calculate your friend's z-score for the 10 years she stayed in Ithaca, NY, you can use the following formula:

z = (X - μ) / σ

where:
- z is the z-score
- X is the sample mean (in this case, 34 inches)
- μ is the population mean (in this case, 36.1 inches)
- σ is the standard deviation of the population (in this case, 5.2 inches, rounded to 5.200 for thousandth place)

Plugging in the values:

z = (34 - 36.1) / 5.200
z = -2.1 / 5.200
z = -0.404

Therefore, your friend's z-score for the 10 years is approximately -0.404, rounded to the thousandth place.

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Answer:

[tex]\overline{\sf QR}=28\sqrt{2}[/tex]

Step-by-step explanation:

If ΔPQR is a right triangle, where angles P and R both measure 45°, then the triangle is a special 45-45-90 triangle.

The measure of the sides of a 45-45-90 triangle are in the ratio 1 : 1 : √2.

This means that the length of each leg is equal, and the length of the hypotenuse is equal to the length of a leg multiplied by √2.

The legs of ΔPQR are segments PQ and QR.

The hypotenuse of ΔPQR is segment PR.

Therefore, to find the length of the leg QR, divide the length of the hypotenuse PR by √2.

[tex]\begin{aligned}\implies \overline{\sf QR}&=\dfrac{\overline{\sf PR}}{\sqrt{2}}\\\\&= \dfrac{56}{\sqrt{2}} \\\\&=\dfrac{56}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}\\\\&=\dfrac{56\sqrt{2}}{2}\\\\&=28\sqrt{2}\end{aligned}[/tex]

Therefore, the length of segment QR is 28√2.

The survey results show that the estimates for the number of students in the school who prefer rap music range from 110 to 154. The center of the estimates is around 121, with a variation of about 66.

To estimate the number of students who prefer rap music, multiply the proportion who prefer rap in each sample by the total number of students in the school (440)

Sample 1: 0.25 x 440 = 110

Sample 2: 0.20 x 440 = 88

Sample 3: 0.30 x 440 = 132

Sample 4: 0.35 x 440 = 154

The center of the estimates is the average of the four estimates: (110 + 88 + 132 + 154) / 4 = 121. Variability can be described using the range (154 - 88 = 66) or the standard deviation of the estimates, which requires additional calculations.

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Herberto travelled through Amusement Park (AP), City Park (P), Landmark (L), High School (HS), City Hall (CH).

Herberto can take the following path to travel from the amusement park (AP) to the city hall (CH):

Amusement Park (AP) -> City Park (P) -> Landmark (L) -> High School (HS) -> City Hall (CH)

This path takes him through the city park, then to the landmark, followed by the high school, and finally to the city hall.

Please note that without a specific map or layout of Knappville, there could be multiple valid paths from the amusement park to the city hall. The path provided above is just one example.

When Herberto travels from the amusement park to the city hall, he can choose various paths depending on the specific layout of Knappville. The path mentioned earlier is just one example, but the actual paths could differ based on the town's infrastructure and the locations of the landmarks.

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Gordon sprinkles 2 cups of powdered sugar onto the plate of cookies after he sprinkles 1/2 of the sugar, or 2 cups, onto the plate of lemon bars.

Gordon has 4 cups of powdered sugar. He sprinkles 1/2 of the sugar onto a plate of lemon bars and the rest onto a plate of cookies. We want to find out how much sugar he sprinkles on the cookies.

If Gordon sprinkles 1/2 of the sugar onto the plate of lemon bars, he uses 1/2 x 4 = 2 cups of powdered sugar for the lemon bars.

This leaves him with 4 - 2 = 2 cups of powdered sugar remaining for the plate of cookies.

Therefore, Gordon sprinkles 2 cups of powdered sugar onto the plate of cookies.

We can also verify this answer by using subtraction. If Gordon uses 2 cups of powdered sugar for the lemon bars, he has 4 - 2 = 2 cups of powdered sugar remaining. This means that he must have used the remaining 2 cups of powdered sugar for the plate of cookies.

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Answer:

6:45pm

Step-by-step explanation:

Given: The time is currently 9:45am

To find: The time in 9 hours

To do this, we have to add 9 hours to 9:45am.

9:45am+9 hours=

6:45pm

Hope this helps! :)

The equation of demand of candle sticks can be modeled by

y = 14 - 0.02x while the revenue function will be xy = 14x - 0.02x².

Here we are given the information that

200 candles are sold for $10 and,

250 candles are sold for $9

Let the Price be y while the Quantity sold be x

Hence, by one unit decrease in price P, the quantity sold is increased by 50 units.

Here the slope of the function will be

(10 - 9)/(200 - 250)

= - 1/50

= - 0,02

Now we will use the formula of the equation of a straight line

(y - y₁) = m(x - x₁)

where, m is the slope and x₁ , y₁ are some point on line

Hence we get

(y - 10) = -0.02(x - 200)

or, y - 10 = -0.02x + 4

or, y = 14 - 0.02x

The revenue function will be xy = 14x - 0.02x²

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Correct Question

A candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week. he finds that when he reduces the price by $1, he then sells 50 more candle sets each week. a function can be used to model the relationship between the candlemaker's weekly revenue, r(x), after one-dollar decrease in price. this situation can be modeled by the equation y =

Answer:

Step-by-step explanation:

To plot the given rational function f(x) = (5x+20)/(x^2 - 20), we need to find the vertical asymptote, horizontal asymptote, x-intercepts, y-intercepts, and holes.

Vertical asymptote:

The denominator of the rational function cannot be zero. Therefore, we need to find the value of x when the denominator equals zero.

x^2 - 20 = 0

x^2 = 20

x = ±√20

The vertical asymptotes are x = √20 and x = -√20.

Horizontal asymptote:

To find the horizontal asymptote, we need to compare the degree of the numerator and denominator. The degree of the numerator is 1, and the degree of the denominator is 2. Therefore, the horizontal asymptote is

y = 0.

X-intercepts and y-intercept:

To find the x-intercepts, we need to set the numerator equal to zero.

5x + 20 = 0

x = -4

Therefore, the x-intercept is (-4,0).

To find the y-intercept, we need to set x equal to zero.

f(0) = (5(0) + 20) / (0^2 - 20)

f(0) = -1

Therefore, the y-intercept is (0,-1).

Hole:

We can factor the numerator and denominator of the rational function to find if there is a hole. Factoring 5x + 20, we get 5(x+4). Therefore, there is a hole at x = -4.

To summarize, the features of the rational function f(x) = (5x+20)/(x^2 - 20) are:

Vertical asymptotes at x = √20 and x = -√20

Horizontal asymptote at y = 0

X-intercept at (-4,0)

Y-intercept at (0,-1)

Hole at x = -4

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The function f(x) = 8x + 3x^(-1) has a local maximum at x = 2 with a value of f(2) = 19, and a local minimum at x = -2 with a value of f(-2) = -19.Explanation:

To find the local extrema of a function, we need to find the critical points of the function, which are the points where the derivative is either zero or undefined. In this case, the derivative of f(x) is f'(x) = 8 - 3x^(-2), which is undefined at x = 0.Setting the derivative equal to zero, we get:8 - 3x^(-2) = 0Solving for x, we get:x = ±2

These are the critical points of the function. To determine whether each critical point is a local maximum or a local minimum, we need to examine the second derivative of the function.

The second derivative of f(x) is f''(x) = 6x^(-3), which is negative for x > 0 and positive for x < 0.Therefore, x = 2 is a local maximum of the function with a value of f(2) = 19, and x = -2 is a local minimum of the function with a value of f(-2) = -19. These are the only local extrema of the function, since the function is increasing for x < -2 and decreasing for -2 < x < 0, and then increasing again for x > 0.

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The required answer is P(at least 2) = P(at least 1) * (1/2) = (1 - e^(-λ * a)) * (1/2)

a. To find the long-term average number of people in line, we will use the following formula:

Average number of people in line = λ * a

Here, λ is the arrival rate of customers following a Poisson process, and a is the average time taken by the chef to process an order.

b. To find the long-term probability that there are at least two people in line, we first need to calculate the probability that there is at least one person in line. Then, we will subtract this probability from 1 to find the probability of having at least two people in line.

Probability of at least one person in line = 1 - Probability of no one in line

Since the arrival of customers follows a Poisson process, the probability of having no one in line is given by:

P(0) = e^(-λ * a)

Thus, the probability of at least one person in line is:

P(at least 1) = 1 - e^(-λ * a)

Now, we can calculate the probability of having at least two people in line by considering that the second person joins the line with probability 1/(1 + 1) = 1/2. So, the probability of at least two people in line is:

P(at least 2) = P(at least 1) * (1/2) = (1 - e^(-λ * a)) * (1/2)

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The approximate APR for Morgan's sofa purchase is 1.7%.

To calculate the approximate APR (Annual Percentage Rate) for Morgan's sofa purchase, we can use the formula:

APR ≈ (finance charge / # of months) x 12 / amount financed

Here, the finance charge is $25, the number of months is 15, and the amount financed is the total cost of the sofa minus the finance charge, which is:

financed= $216.00 - $25.00 = $191.00

on substitution:

APR ≈ (25 / 15) x 12 / 191

APR ≈ 0.2778 x 0.06283

APR ≈ 0.01743

Rounding the answer to the nearest tenth, we get:

APR ≈ 1.7%

Therefore, the approximate APR for Morgan's sofa purchase is 1.7%.

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The company’s earnings per share reported in its financial statements for the year ended December 31, 2020 is $1.45. The correct option is c.

To calculate earnings per share, we need to take the company's net income and divide it by the weighted average number of shares outstanding during the year.

First, let's adjust for the stock dividend on July 31. Since the dividend was 100%, we can double the number of shares outstanding to 416,000:

Jan. 1: 200,000 shares
Feb. 1: 8,000 new shares
July 31: 200,000 shares doubled to 400,000 shares
Dec. 31: 416,000 shares

Next, we need to calculate the weighted average number of shares outstanding during the year. We can do this by taking the number of shares outstanding for each period and multiplying it by the number of months those shares were outstanding:

Jan. 1 to Jan. 31: 200,000 shares x 1 month = 200,000
Feb. 1 to July 31: (200,000 + 8,000) shares x 6 months = 1,248,000
Aug. 1 to Dec. 31: 416,000 shares x 5 months = 2,080,000

Total weighted average shares outstanding: 3,528,000

Finally, we can divide the net income of $560,000 by the weighted average shares outstanding of 3,528,000 to get earnings per share of $0.1585. Multiplying this by 9 (since there are 9 months of the year remaining after February 1) gives us earnings per share of $1.4265. Rounded to the nearest penny, the answer is $1.45.

Thus, The correct option is c.

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The volume of the air in the container is: 3,585.125 in³

The volume of a box or cuboid is given by the formula:

V = L * W * H

Where:

L is length

W is width

H is height

We are given the external dimensions as:

Length = 22 inches

Width = 15 inches

Height = 12 inches

Since the glass is 1/2 inch thick, then the interior dimensions are:

New length = 22 - 1/2 = 21.5 inches

New Width = 15 - 1/2 = 14.5 inches

New height = 12 - 1/2 = 11.5 inches

Thus:

Volume of air in container = 21.5 * 14.5 * 11.5

= 3,585.125 in³

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Plan C has the lower expected cost, so, this is best to minimize costs for safety glass coverage.

In order to compare expected cost of Plan C and D, we must calculate expected payout for each plan and add to the premium.

For Plan C, expected payout is:

= 0.5*(0) + 0.3*(50) + 0.2*(300)

= 15 + 60

= 75

The total expected cost of Plan C is:

= 75 + 50 + 20

= 145

For Plan D, expected payout is:

= 0.5*(0) + 0.3*(50) + 0.2*(300)

= 15 + 60

= 75

The total expected cost of Plan D is:

= 75 + 100 + 0

= 175

Therefore, the Plan C has the lower expected cost.

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We will be sure to take your time and carefully consider the given information in order to find the missing angle and arc measures accurately.

To find the missing angle and arc measures, follow these steps:

1. Look at the given diagram to identify the angles and arcs involved.

2. Use the angle sum property of a circle to find the measure of the missing angle. This property states that the sum of the angles in a circle is equal to 360 degrees. So, if you know the measures of the other angles in the circle, you can subtract their sum from 360 to find the missing angle.

3. Use the arc angle formula to find the measure of the missing arc. This formula states that the measure of an arc is equal to the measure of its corresponding central angle. So, if you know the measure of the missing angle, you can use it to find the measure of the missing arc.

4. Check your answer by making sure that the sum of all the arc measures in the circle is equal to the circumference of the circle.

Overall, be sure to take your time and carefully consider the given information in order to find the missing angle and arc measures accurately.

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Answer:

It's 14⁹.

Add the powers in the process of multiplying.

Which is -3 + 12 answer is 9.

Hope this helped!

Answer:

The price of the meal after the discount was (A)$48.11 and the final price of the meal was (B)$57.73.

Step-by-step explanation:

Let us consider the amount of money $56.60 as the cost of the meal.

So the amount of money is 56 dollars and 60 cents.

A: The family has a 15% off coupon.

Discount = 15% of 56.60=0.15x56.60=8.49

Now we subtract the discount amount from the original amount.

Cost of the meal = 56.60-8.49=48.11

So the final price of the meal for the family is $48.11 or 48 dollars and 11 cents.

B: The family gave a tip of 20%.

Amount of money tipped= 20% of 48.11=0.20 x 48.11=9.622

To get the final amount we add the tip to the discounted price.

The final cost of the meal= 48.11+9.622=57.732=57.73

Therefore the family paid a total of 57 dollars and 73 cents for the final cost of the meal after the discount and tip.

Hope this helps :)

The inverse of the function f(x) = √(x+1) is [tex]f^-1[/tex](x) = x² - 1.

Given a function f(x), its inverse function, denoted as [tex]f^-1[/tex](x), is a function that takes the output of f(x) and returns the original input. In other words, if y = f(x), then x = [tex]f^-1[/tex](y).

To find the inverse of the function f(x), we follow these steps:

Step 1: Replace f(x) with y:

   y = √(x+1)

Step 2: Interchange x and y:

   x = √(y+1)

Step 3: Solve for y:

   x² = y+1

   y = x² - 1

Step 4: Replace y with f^-1(x):

   f^-1(x) = x² - 1

Therefore, the inverse of the function f(x) = √(x+1) is [tex]f^-1[/tex](x) = x² - 1.

To verify this, we can check that ([tex]f^-1[/tex] o f)(x) = x and (f o [tex]f^-1[/tex])(x) = x for all x in the domain of the functions:

([tex]f^-1[/tex] o f)(x) = [tex]f^-1[/tex](f(x)) = (√(x+1))² - 1 = x

(f o [tex]f^-1[/tex])(x) = f([tex]f^-1[/tex](x)) = √((x² - 1) + 1) = √(x²) = |x| + 1

Since the range of f(x) is [0, infinity), we restrict the domain of [tex]f^-1[/tex](x) to [1, infinity) to ensure that the inverse is a function.

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The manager will need to pay $244.95 to purchase the silverware, including sales tax.

What is decimal?

Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point.

According to the given information:

If the silverware costs $230 and the sales tax is 6.5%, we need to calculate the amount of tax that will be added to the cost of the silverware:

Tax = 6.5% of $230 = 0.065 x $230 = $14.95

So the total cost of the silverware including tax is:

$230 + $14.95 = $244.95

Therefore, the manager will need to pay $244.95 to purchase the silverware, including sales tax.

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The angle of depression from the man to the building below is approximately 39.81°.

To find the angle of depression from the man to the building below, we'll use the tangent function and the given information.

Given:
- The man is 40,000 feet away from the building horizontally.
- The man's altitude is 33,000 feet.

Step 1: Identify the opposite and adjacent sides in relation to the angle of depression.
- The opposite side is the altitude (33,000 feet).
- The adjacent side is the horizontal distance (40,000 feet).

Step 2: Use the tangent function to find the angle of depression.
tan(angle) = opposite/adjacent
tan(angle) = 33,000/40,000

Step 3: Find the inverse tangent of the ratio to get the angle.
angle = arctan(33,000/40,000)

Step 4: Calculate the angle.
angle ≈ 39.81°

The angle of depression from the man to the building below is approximately 39.81°.

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Answer:

-√3/2

Step-by-step explanation:

sin(x) is equal to 1/2 when x=7π/6 or 11π/6

cos(7π/6) = -√3/2

cos(11π/6) = √3/2

In the question, it says that cos(x) is <0, which means that it has to be negative

So, the answer is -√3/2

Answer:  C

Step-by-step explanation:

Think of a unit circle

sin x = -1/2 happens at 7[tex]\pi[/tex]/6 and 11[tex]\pi[/tex]/6, 3rd and 4th quadrant

Out of those 2 quadrants cos x is negative in the 3rd quadrant

So cos x= -√3/2

Rational expressions and equations can be used to describe relationships and solve problems that involve proportions or rates of change.

They involve expressions that are fractions of polynomials, where the numerator and denominator can be thought of as values that change according to some variable.

For example, rational expressions can be used to represent rates of change in physics or finance, such as the speed of an object or the interest rate on a loan. By setting up equations with rational expressions, we can solve for unknown values or relationships between variables.

Rational equations can also be used to describe relationships between quantities that are proportional, such as the volume of a container and the amount of liquid it can hold. By solving for an unknown variable in a rational equation, we can determine the relationship between the two quantities and use it to make predictions or solve practical problems.

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To find the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we need to find the probability of getting NNNNN as the first five patients. Since the success rate is 0.3 and the failure rate is 0.7, the probability of getting NNNNN is:

0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807

Therefore, the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is 0.16807.

To find the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients, we need to count the number of ways we can select three patients out of four and multiply it by the probability of getting EEE and NEEE for the selected patients and non-selected patients, respectively. The number of ways to select three patients out of four is:

4C3 = 4

The probability of getting EEE and NEEE for the selected patients and non-selected patients, respectively, is:

(0.7)^3 x (0.3) x (0.7) = 0.1029

Therefore, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is 4 x 0.1029 = 0.4116 (rounded to 4 decimal places).

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Answer:

3.9

Step-by-step explanation:

pythagorean theorem states:

[tex]a^{2} +b^{2} =c^{2}[/tex]

We know that a is the height of the triangle, 2.

We also know that b is the base of the triangle, 3.

So, solve for c:

2²+3²=c²

simplify

4+9=c²

15=c²

take the square root of both sides

c=3.9

So, the spider and the fly are 3.9 ft apart from each other

Hope this helps :)

Answer:

3.6 feet

Step-by-step explanation:

The Pythagorean theorem states that a^2+b^2=c^2, where c is the hypotenuse, or longest side of the triangle opposite to the right angle, and a and b are the two legs of the triangle (the other two sides.)

In the question, sides a and b are given as 2ft and 3ft long. Plugging 2 and 3 into the equation, we will get that 2^2+3^2=c^2. 2 x 2 = 4 and 3 x 3 = 9, so 4 + 9 = c^2, or, c^2 = 13.

However, this is still c^2, not c, so we must take the square root of both sides. This is because the equation is now essentially saying that c x c = 13, so if we find a number that when multiplied by itself equals 13, that number will be c. to do this, we must take the square root of 13. This will give us an irrational number- approximately 3.605551275. The question asks to round it to the nearest tenth though, so this will simply become 3.6.

In the context of this question, it means that the spider and the fly are 3.6ft apart.

The inequalities in the given table are "t > 0" and "3 < a."

To identify the inequalities from the provided options, we need to understand the meaning of the symbols and check if they represent a comparison between two values.

-3 = y: This is not an inequality symbol but rather an equality symbol. It represents that -3 is equal to y, not greater or less than.

t > 0: This is an inequality symbol. The symbol ">" represents "greater than." Therefore, t is greater than 0.

-4. 3 < a: This is another inequality symbol. The symbol "<" represents "less than." Hence, 3 is less than a.

g = 5 and one-half: This is an equality symbol. The symbol "=" denotes equality, indicating that g is equal to 5 and one-half, not greater or less than.

k less-than Negative Start Fraction 5 Over 7 End Fraction: This is also an inequality symbol. The phrase "less than" indicates a comparison. The fraction "Negative Start Fraction 5 Over 7 End Fraction" represents -5/7. Therefore, k is less than -5/7.

x = 1: This is an equality symbol. The symbol "=" indicates that x is equal to 1, not greater or less than.

In summary, the inequalities in the table are "t > 0" and "3 < a."

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Answer:

Step-by-step explanation:

3x4