which value of x makes this inequality true? x+9<4x

The value of angle x is 149°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Since MN and OP are parallel lines, we can introduce a transverse that will cut through Q and extend the parallel lines of MN and OP

Therefore;

The adjascent angle of N will be

180-138 = 42°

This means that angle Q is divided into 42° and 31° i.e 42+31 = 73°

This means the adjascent angle of P is 31°( alternate angles)

Therefore x = 180-31

x = 149°

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After calculating a percentile using the z score, you should c. Always check that your answer makes sense.

After calculating a percentile using the z-score, it is important to check that your answer makes sense. This step helps ensure the accuracy and validity of your calculations. Let's go through the process step by step:

Calculate the z-score: The z-score is a measure of how many standard deviations an observation or data point is from the mean. It is calculated using the formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Use the z-score to find the percentile: Once you have the z-score, you can refer to a standard normal distribution table or use statistical software to find the percentile associated with that z-score. The percentile represents the percentage of data points that fall below the given value.

Check the percentile: After obtaining the percentile, it is crucial to examine whether it makes sense in the context of the problem. Percentiles range from 0 to 100, representing the percentage of values below the given data point. Therefore, the percentile should always be between 0 and 100.

a. If the calculated percentile is greater than 100 or less than 0, it suggests an error in the calculation. Review the calculations and ensure accuracy.

b. If the percentile falls within the expected range of 0 to 100, it is a valid result. However, it is still recommended to assess whether the calculated percentile aligns with the problem's context and expectations.

Finalize your answer: Once you have verified that the calculated percentile is within the appropriate range and makes sense in the given context, you can confidently use it as your answer.

Hence, the correct step to take after calculating a percentile using the z-score is c. Always check that your answer makes sense.

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Option D is the most appropriate choice, stating that the graph is a function but not a one-to-one function.

Based on the limited information provided, it is not possible to determine the exact nature of the graph.

However, by analyzing the given options, we can make an inference.

Option A states that the graph is a one-to-one function.

A one-to-one function is a function where each input has a unique output.

From the given information, it is not clear whether the graph satisfies this condition.

Option B states that the graph is not a function.

A function is a relation where each input has exactly one output.

Without additional context or information, it cannot be concluded definitively whether the graph represents a function or not.

Option C states that the graph is a many-to-one function. A many-to-one function is a function where multiple inputs can have the same output. Again, without more information, we cannot determine if this is the case for the given graph.

Option D states that the graph is a function, but it is not one-to-one. This option seems to be the most reasonable choice based on the available options.

It suggests that the graph represents a function, but there may be multiple inputs that correspond to the same output.

In summary, without a more detailed description or additional information, option D is the most appropriate choice, stating that the graph is a function but not a one-to-one function.

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The probability that either four students out of the 10   students are females or four students outof the 10 students would like to take Math for Business next semester is approximately 0.206 or 20.6%.

The probability of Event A (Four students are females) can be calculated as follows  -

P(A) = (0.2)⁴ * (0.8)⁶ * (10 C 4)

    = 0.0016 * 0.4096 * 210

    ≈ 0.135

The probability of Event B (Four students would like to take Math for Business) can be calculated as follows:

P(B) = (0.6)⁴ * (0.4)⁶ * (10 C 4)

    = 0.1296 * 0.0256 * 210

    ≈ 0.071

To calculate   the probability of either Event A OR Event B occurring,we sum the probabilities:

P(A or B) = P(A) + P(B)

         ≈ 0.135 + 0.071

         ≈ 0.206

Hence,  the probability that either four students out of the 10 students are females or 4students out of the 10 students would like to take Math for Business next semester is approximately 0.206 or 20.6%.

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The correct answer is: The median stays 6.5.

The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median.

To determine how the median changes when a shoe size of 4 is added to the data, we need to arrange the shoe sizes in ascending order:

4, 5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8.5

The median is the middle value in a sorted list. In this case, since there are 10 values, the median is the average of the two middle values: 6.5 and 6.5. So, the median is 6.5.

Adding a shoe size of 4 to the data does not affect the median because the new value is lower than all the other values in the list. Therefore, the median stays the same at 6.5.

So, the correct answer is: The median stays 6.5.

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Answer:

Step-by-step explanation:

Bob made a little mistake there. 5 multiplied by 800 is actually equal to 4,000.

The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2

From the question, we have the following parameters that can be used in our computation:

-3/4 + 2/5x = 7/20x -1/2

The first step is to collect the like terms

So, we have

2/5x - 7/20x = 3/4 - 1/2

This represents an equation of the possible way to begin solving for x

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Based on the information provided, the total area of the shape given is 25 square centimeters.

The shape given is made up of two different shapes or two different rectangles. Due to this, to calculate the area, let's calculate the area of each of the rectangles, and then let's add the areas obtained.

First rectangle:

area = side x side

area = 2 cm x 3 cm

area = 6 square centimeters

Second rectangle:

area = side x side

area = 4 cm x 2 cm

area = 8 square centimeters

Total area: 6 square centimeters +  8 square centimeters

Total area = 14 square centimeters

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Answer:

B = 76, C = 38

Step-by-step explanation:

A + B + C = 196

substitute A = 82 and B = 2C into the equation

82 + 2C + C = 196

82 + 3C = 196 ( subtract 82 from both sides )

3C = 114 ( divide both sides by 3 )

C = 38

B = 2C = 2 × 38 = 76

Alright, let's take this for a spin! We're gonna be using the binomial probability formula, which is kind of like a recipe to calculate the likelihood of something happening a specific number of times. The formula looks like this:

P(x; n, p) = C(n, x) * (p^x) * ((1 - p)^(n-x))

Where:

- P(x; n, p) is the probability of getting x successes in n trials,

- C(n, x) is the combination of n items taken x at a time (how many different ways we can get x successes),

- p is the probability of success on an individual trial (in this case, the chance a random student plans to go to college),

- x is the number of successes we want,

- n is the total number of trials (students),

- and (1 - p) is the probability of failure (a student not planning to go to college).

For all these problems, n = 19 (our number of students), and p = 0.72 (the percentage of students planning to go to college).

a.) To find the probability that all 19 students plan to attend college, we'd set x = 19. We plug in these values:

P(19; 19, 0.72) = C(19, 19) * (0.72^19) * ((1 - 0.72)^(19-19))

= 1 * (0.72^19) * (0.28^0)

= 0.72^19

= 0.0001 (rounded to four decimal places)

b.) Now, for the probability that exactly eleven of them plan to attend college, we set x = 11:

P(11; 19, 0.72) = C(19, 11) * (0.72^11) * ((1 - 0.72)^(19-11))

= 75582 * (0.72^11) * (0.28^8)

= 0.1013 (rounded to four decimal places)

c.) For the probability that at most fourteen of them plan to attend college, we need to add up the probabilities for x = 0 through 14:

P(x ≤ 14; 19, 0.72) = ∑ P(i; 19, 0.72) for i = 0 to 14

Calculating this might take a while by hand, so I'd recommend using a binomial distribution calculator. Doing so gives us approximately 0.5745.

d.) Finally, for the probability that at least seventeen of them plan to attend college, we add up the probabilities for x = 17, 18, and 19:

P(x ≥ 17; 19, 0.72) = P(17; 19, 0.72) + P(18; 19, 0.72) + P(19; 19, 0.72)

Again, I'd suggest a binomial distribution calculator for this. The result should be around 0.0258.

So, yeah, that's the way the cookie crumbles! Hope this helps you out, fam!

The length of the wire used to make the cuboid is 36 meters.

To find the length of the wire used to make the cuboid, we need to calculate the perimeter of all the edges of the cuboid.

The cuboid has dimensions:

Length = 4m

Width = 2.5m

Height = 2.5m

Let's calculate the perimeter of each face of the cuboid and then sum them up to find the total length of the wire.

Face 1: Length x Width

Perimeter of face 1 = 2(Length + Width) = 2(4m + 2.5m) = 2(6.5m) = 13m

Face 2: Length x Height

Perimeter of face 2 = 2(Length + Height) = 2(4m + 2.5m) = 2(6.5m) = 13m

Face 3: Width x Height

Perimeter of face 3 = 2(Width + Height) = 2(2.5m + 2.5m) = 2(5m) = 10m

Now, let's sum up the perimeters of all three faces to find the total length of the wire:

Total wire length = Perimeter of face 1 + Perimeter of face 2 + Perimeter of face 3

                 = 13m + 13m + 10m

                 = 36m

Therefore, the length of the wire used to make the cuboid is 36 meters.

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To pay off the balance of $7000 on a credit card with an APR of 16.99% in 2 years, the monthly payment to be made is $349.11. So, the correct option is (a) $349.11.

What is APR?

APR stands for Annual Percentage Rate, which is the rate at which credit is issued and expressed as a yearly rate. Interest and fees are included in the APR, which makes it the most precise way to determine the actual expense of borrowing.

What is monthly payment?

A monthly payment is an amount of money that is paid to a creditor or lender every month as part of a loan or debt repayment plan. The monthly payment must be sufficient to pay off the interest accrued during the month and a portion of the principal balance to make a dent in the outstanding debt owed.

What is the formula for calculating monthly payments?

The formula for calculating monthly payments is: Monthly Payment = [APR/12 × (Present balance)] / [1 - (1 + APR/12)-n], Where APR is the Annual Percentage Rate, Present balance is the amount owed, n is the number of payments to be made. To pay off the balance of $7000 on a credit card with an APR of 16.99% in 2 years, the monthly payment to be made is $349.11. Therefore, the correct option is (a) $349.11.

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The length of fencing that must be purchased to enclose the entire field is 459.7 feet.

To find the length of fencing required to enclose the entire field, we need to calculate the perimeter of the parallelogram.

Length of one side of the parallelogram = 208.8 feet

Length of another side of the parallelogram = 21.05 feet

Altitude to the longer side = 14.66 feet

The perimeter of a parallelogram can be calculated by adding the lengths of all four sides.

In this case, we have two pairs of congruent sides.

First, let's calculate the length of the longer side using the altitude:

Area of the parallelogram = base [tex]\times[/tex] altitude

Area = 208.8 feet [tex]\times[/tex] 14.66 feet

Area = 3057.408 square feet

Since the length of one side is 208.8 feet, the length of the other congruent side is also 208.8 feet.

Next, let's calculate the length of the shorter side:

Area = base [tex]\times[/tex] altitude

3057.408 square feet = 21.05 feet [tex]\times[/tex] altitude.

altitude = 145.38 feet

Now we have all the side lengths:

Side 1: 208.8 feet

Side 2: 21.05 feet

Side 3: 208.8 feet

Side 4: 21.05 feet.

To find the perimeter, we add all four sides:

Perimeter = 208.8 feet + 21.05 feet + 208.8 feet + 21.05 feet

Perimeter = 459.7 feet

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Answer:

Exact Form:

35/6

Decimal Form:

5.83

Mixed Number Form:

5 5/6

Answer:8/3

Step-by-step explanation:

4-4/3

=12-4/3

=8/3

Chronological order of transactions:

Accommodation at a rate of $100.00 CAD per night for May 12 & 13.

$15.00 movie rental charge for the afternoon of the 13th.

$40.00 room service charge for dinner on the evening of the 13th.

Mr. Ritz settling his account with his Visa card.

Hotel Guest Folio

Guest Name: Mr. Caesar Ritz

Room Number: 1010

Check-Out Date: May 14, 2023

Telephone: 905-575-1212

Fax: 905-575-2319

Guest Room Rate: $100.00 CAD per night

Chronological Order of Transactions:

May 12-13, 2023:

Accommodation at a rate of $100.00 CAD per night for May 12 & 13.

Debit: $200.00 CAD

May 13, 2023:

Afternoon movie rental charge of $15.00.

Debit: $15.00 CAD

May 13, 2023:

Room service charge for dinner of $40.00.

Debit: $40.00 CAD

May 14, 2023:

Settlement of the account with a Visa card.

Credit: $-255.00 CAD (Total charges: $200.00 + $15.00 + $40.00 = $255.00)

Balance Outstanding: $0.00 CAD

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Ray uses 1/4 of a gallon of gasoline to drive a distance of 5 1/2 miles. At this rate, Ray can drive 22 miles on 1 gallon of gas.

Let's analyze the given information:

Ray uses 1/4 of a gallon of gasoline to drive a distance of 5 1/2 miles.

We need to determine how many miles Ray can drive on 1 gallon of gas. To do this, we'll calculate the rate of gas consumption in terms of miles per gallon.

Rate of gas consumption = Distance traveled / Gas used

Gas used = 1/4 gallon

Distance traveled = 5 1/2 miles = 5 + 1/2 = 11/2 miles

Now, let's substitute the values into the formula:

Rate of gas consumption = (11/2) miles / (1/4) gallon

To divide by a fraction, we can multiply by its reciprocal:

Rate of gas consumption = (11/2) miles * (4/1) gallon

Simplifying:

Rate of gas consumption = (11 * 4) miles / (2 * 1) gallon

Rate of gas consumption = 44 miles / 2 gallon

Rate of gas consumption = 22 miles per gallon

Therefore, based on the given information, Ray can drive 22 miles on 1 gallon of gas.

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Question

Ray uses 1/4 of a gallon of gasoline to drive a distance of 5 1/2 miles. At this rate, how many miles can he drive on 1 gallon of gas?

Ray can drive ???? miles on 1 gallon of gas.

The Length of Zorn's patio is (8x + 9) feet.

To find the length of Zorn's patio, we need to use the information given about the perimeter of the patio and the width labeled as (seven x plus four) feet.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (Length + Width)

In this case, the width is (seven x plus four) feet. So, we can write the equation for the perimeter as:

30x + 26 = 2 * (Length + (seven x + four))

Simplifying the equation, we have:

30x + 26 = 2 * (Length + 7x + 4)

30x + 26 = 2 * (Length + 7x) + 2 * 4

30x + 26 = 2 * Length + 14x + 8

Next, we can simplify further:

30x + 26 = 14x + 2 * Length + 8

To islate the Length term, we subtract 14x from both sides and subtract 8 from both sides:

30x - 14x + 26 - 8 = 2 * Length

16x + 18 = 2 * Length

Dividing both sides by 2, we get:

8x + 9 = Length

Therefore, the length of Zorn's patio is (8x + 9) feet.

From the given options, the correct choice is option D. (8x + 9) feet.

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The formula to find the 10th term of the sequence is -512(x-1).

The given sequence is generated by starting with the term x-1 and then multiplying each term by -2 to get the next term.

Therefore, the nth term of the sequence can be expressed as:

[tex](-2)^(n-1) * (x-1)[/tex]

To find the 10th term of the sequence, we substitute n = 10 into the formula

[tex](-2)^(10-1) * (x-1) = (-2)^9 * (x-1)[/tex]

= -512(x-1)

So the formula to find the 10th term of the sequence is -512(x-1).

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Answer:

2.most employees scored 800 or above

3 The graph assessment results range from 200 to 1899

4.40 employees scored between 1400 and 1599

5. Twice as many employees scored 1099.5compared to those that scored 1499.5

These statements are correct

Graph C:This graph intersects the x-axis at only one point, so the equation it represents has only one solution. Therefore, the answer is Graph C.

In order to identify which graph has only one solution, we need to understand what it means for an equation to have only one solution. In algebra,

a solution is a value of the variable that makes the equation true. So, if an equation has only one solution, it means that there is only one value of the variable that makes the equation true.

There are several ways to determine the number of solutions an equation has, but one common method is to graph the equation and look at the intersection of the graph with the x-axis. If the graph intersects the x-axis at only one point,

then the equation has only one solution. If the graph intersects the x-axis at two or more points, then the equation has two or more solutions. If the graph does not intersect the x-axis at all, then the equation has no solutions.

With this in mind, let's examine each of the given graphs to determine which one has only one solution.

Graph A:This graph intersects the x-axis at two points, so the equation it represents has two solutions.

Graph B:This graph does not intersect the x-axis at all, so the equation it represents has no solutions.

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Answer:

  31.2 g

Step-by-step explanation:

You want to know the average weight of the remaining eggs if two from a dozen with average weight 32 g are broken, and their weights are 35 and 37 g.

The two broken eggs differ from average by ...

  (35 -32) +(37 -32) = 3 +5 = 8 . . . . . grams

The remaining eggs must differ from that average by the opposite amount, a total of -8 g.

Distributed over 10 eggs, this difference is -0.8 g, so the average weight of the remaining eggs is 32 -0.8 = 31.2 g.

The average weight of the remaining 10 is 31.2 g.

The average weight is the sum of all weights divided by the number of eggs:

  avg = W/N

  W = N·avg = 12·32 g = 384 g

The new sum of weight will be this amount less the weights of the broken eggs:

  W' = 384 g -35 g -37 g = 312 g

The new number of eggs is 2 fewer: N' = 12 -2 = 10.

So, the new average weight is ...

  avg' = W'/N' = 312 g/10 = 31.2 g

__

Additional comment

By working with the differences from average, we don't have to figure the old and new sums. We're only concerned with the way that sum changes, and the average amount of that change. Often, this means we can solve the problem using only mental arithmetic.

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Answer:

No

Step-by-step explanation:

3 x 5 is 15 because is multiplying 3 x 5

3^5 is 3 x 3 x 3 x 3 x 3 and gives a bigger result.

(a) The average cost in 2011 is  

(b) A graph of the function g for the period 2006 to 2015 is shown below.

(c) Assuming that the graph remains accurate, its shape suggest that the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.6Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2011 - 2006) + 6

x = 5 + 6

x = 11 years.

Next, we would substitute 11 for x in the function:

g(11) = -1736.7 + 1661.6In(11)

g(11) = $2247.64

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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Complete Question:

The average annual cost (in dollars) for health insurance in a country can be approximated by the function g(x) = -1736.7 + 1661.6Inx, where x = 6 corresponds to the year 2006.

(a) Estimate the average cost in 2011.

(b) Graph the function g for the period 2006 to 2015

(c) Assuming that the graph remains accurate, what does the shape of the graph suggest regarding the average cost of health insurance?

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

In order to enhance strong number sense in children, there are various methods that can be used.

In the given scenario, Mme Potatana asked the children to count as a whole class from 1 to 20 while Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count.

Both methods have their own benefits, but the method of counting seeds by touching each can be more effective in enhancing strong number sense in children.

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children because it allows them to experience each number physically.

This helps them in developing a strong sense of numbers. By touching each seed as they count, children can feel and see each number, which helps them in understanding numbers better. Additionally, it helps in developing the concept of one-to-one correspondence and counting by rote.

Here are some appropriate examples for enhancing strong number sense using the method of counting seeds by touching each:

1. Use counters: Provide children with counters such as small objects, blocks, or toys. Ask them to count the number of counters by touching each as they count.

2. Counting on fingers: Encourage children to count on their fingers. This helps them in developing a strong sense of numbers and helps them in understanding the concept of one-to-one correspondence.

3. Counting objects in a pile: Ask children to count objects in a pile by touching each as they count. This helps in developing the concept of counting by rote and helps in enhancing strong number sense.

Overall, the method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

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By using the graph the estimates for the solutions of each equation are as follows;

i) (-1, 5) and (2, 5).

ii) (-0.554, 2.446) and (1.804, 4.804).

In Mathematics and Geometry, a point of intersection is the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair with a point that corresponds to the x-coordinate and y-coordinate on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations 4x² - 4x -3 = 5 and 4x² - 4x - 1 = x + 3, the solution is denoted by the point of intersection of both the x-coordinate and y-coordinate as shown in the image attached below.

4x² - 4x -3 = 5 are (-1, 5) and (2, 5).

4x² - 4x - 1 = x + 3 are (-0.554, 2.446) and (1.804, 4.804).

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The average rate of change of the function over the interval is 4x + 2h

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x² + 9

The interval is given as

From x = x to x = x + h

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(x) = 2x² + 9

f(x + h) = 2(x + h)² + 9

Next, we have

Rate = (2(x + h)² + 9 - 2x² - 9)/(x + h - x)

Evaluate

Rate = 4x + 2h

Hence, the rate is 4x + 2h

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Answer:

Solution:  (-1, -1)

Step-by-step explanation:

Thus, the solution to the system is (-1, -1) as this is the point where the two lines intersect.

Answer:

67.5

Step-by-step explanation:

1.5 + 3 + 4.5 + ... + 13.5

In the first three terms, the common difference is 1.5, so this series is:

1.5 + 3 + 4.5 + 6 + 7.5 + 9 + 10.5 + 12 + 13.5

There are 9 terms.

       1.5 + 3  +   4.5 + 6 + 7.5

  +13.5  + 12 + 10.5 + 9

-----------------------------------------------

     15   + 15   + 15   + 15 + 7.5

1.5 + 3 + 4.5 + 6 + 7.5 + 9 + 10.5 + 12 + 13.5 = 4.5 × 15 = 67.5

You can also use the formula:

For an arithmetic series with n terms,

S_n = (n/2)(a_1 + a_n)

S_9 = (9/2)(1.5 + 13.5)

S_9 = 4.5(15)

S_9 = 67.5

The equivalent expression after combining like terms is 15.4z - 12.

To combine like terms and simplify the given expression, let's distribute the -5 to the terms inside the parentheses and then combine the like terms:

Expression: 7.4z - 5(-1.6z + 2.4)

Distributing -5 to the terms inside the parentheses:

7.4z - 5(-1.6z) - 5(2.4)

Simplifying the distributed terms:

7.4z + 8z - 12

Combining the like terms:

(7.4z + 8z) - 12

(7.4 + 8)z - 12

15.4z - 12

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