1.2.5 Quiz: Solving Problems by Dividing Fractions
Question 2 of 5
It takes Saraday to make a birdhouse. How much of the
birdhouse will be built after day?

Answer: Answer is below <3

Step-by-step explanation:

It’s in-between zero and negative one because it’s a half number. (Not fully one yet)

Therefore, -1/2 would be in-between the number 0 and -1.

Answer:

-1/2 is "-0.5" in form of decimal

So,

the answer will come between 0 and -1

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The equation y = 2x + 4 is in slope-intercept form with m = 2 and b = 4. This means that the line has a slope of 2 and intersects the y-axis at the point (0, 4).

An equation is a statement that asserts the equality of two expressions or values, typically separated by an equal sign (=). The expressions or values on either side of the equal sign are called the "sides" of the equation.

Equations are used to represent mathematical relationships between variables and to solve problems involving those variables.

To check if an equation is in slope-intercept form, we need to ensure that it has the form:

y = mx + b

The equation y = 2x + 1/3 is also in slope-intercept form with m = 2 and b = 1/3. This means that the line has a slope of 2 and intersects the y-axis at the point (0, 1/3).

The equation y = 3x/2 + 1 is in slope-intercept form with m = 3/2 and b = 1. This means that the line has a slope of 3/2 and intersects the y-axis at the point (0, 1).

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As a result, it would take 5 pretzel makers 22.6 minutes, or around 0.376 hours, to manufacture 88 pretzels.

To answer mathematical issues involving proportional relationships between various quantities, one can utilize the unitary method. Finding the value of one unit of a quantity and using that value to determine the value of another number of units is what it entails. In business and finance, the unitary technique is frequently used to address issues with cost, price, and quantity. The link between several units of measurement is also computed in physics and other fields.

given

To begin, we can apply the formula:

(Workers' Count) x (Efficiency) x (Time) = (amount of work)

To achieve this, multiply the total quantity of pretzels produced by the two pretzel makers by the sum of the labor hours worked by the number of workers:

One pretzel maker's productivity is calculated as follows: (444 pretzels / 2 workers x 6 hours) = 37 pretzels per worker-hour.

The time it would take for five pretzel producers to produce 88 pretzels may therefore be calculated using this efficiency:

37 pretzels were consumed each worker hour multiplied by five workers yields 88 pretzels.

By solving for time, we obtain:

Time is calculated as follows: 88 pretzels / (5 workers x 37 pretzels per worker-hour) = 0.376 hours.

As a result, it would take 5 pretzel makers 22.6 minutes, or around 0.376 hours, to manufacture 88 pretzels.

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Answer:There seems to be a typo in the equation for f(x). I will assume that the correct equation is:f(x) = 4x - 25To find the first x value where g(x) > f(x), we can set the two equations equal to each other and solve for x:g(x) = f(x)

2(5)x = 4x - 25

10x = 4x - 25

6x = -25

x = -25/6

Step-by-step explanation:However, we need to check if this value satisfies the condition g(x) > f(x):g(-25/6) = 2(5)(-25/6) = -25

f(-25/6) = 4(-25/6) - 25 = -75/3 - 25/1 = -100/3Therefore, g(x) > f(x) is not true for x = -25/6. We need to keep looking for a larger value of x where g(x) > f(x).To do this, we can graph the two functions and look for the point where the graph of g(x) is above the graph of f(x). Alternatively, we can simply plug in some larger values of x and compare the values of g(x) and f(x) until we find the first x value where g(x) > f(x).Let's try plugging in x = 0:g(0) = 2(5)(0) = 0

f(0) = 4(0) - 25 = -25Since g(0) = 0 and f(0) = -25, we have g(x) > f(x) for x > 0. Therefore, the first x value where g(x) > f(x) is x = 0.

Step-by-step explanation:

Solution,

P=2,50,000

T=2072-2070

=2 years

Pt=1,60,000

Pt=P(1-D/100)^2

1,60,000=2,50,000{(100-D)}^2

100

1,60,000/2,50,000={(100-D)}^2

100

0.64={(100-D}^2

100

(0.8)^2={(100-D)}

100

80=100-D

100

80=100-D

D=100-80

D=20%

Hence, the deprecation rate is 20% over the period of 2 years

Answer:

x=7, y=6

Step-by-step explanation:

One of the ways we can find a value of a variable in a multiple part equation system is via substitution.

What is substitution?

Substitution works by making one equation equal to a variable with no coefficients (that is, a number without any action being done to the variable), then using this said equation and plugging it into the other equation to find the value of one variable. Then, using this value that was found can be plugged again to one of the two equations to find the other variable.

In our situation, one of the equations ([tex]y=-2x+20[/tex] ) is already equal to y; so we can use this equation to plug it in the second equation.

- Given: [tex]y=-2x+20\\6x-5y=12[/tex]

- Insert the first equation: [tex]6x-5(-2x+20)=12[/tex]

- Distribute the -5: [tex]6x+10x+-100=12[/tex]

- Combine like terms: [tex]16x-100=12[/tex]

- Isolate the variable x: [tex]16x-100=12\\~~~~~~+100+100\\16x=112\\\frac{16x}{16} =\frac{112}{16} \\x=7[/tex]

Now that we have the variable x=7, we can use this number to find the value of the variable y.

- Given: [tex]y=-2x+20[/tex]

- Plug in the known variable value: [tex]y=-2(7)+20\\[/tex]

- Solve: [tex]y=-14+20\\y=6[/tex]

Therefore, x=7, and y=6 is your final answer.

Additionally, we can cross reference this on a graphing calculator. Plug both of those formulas in as so, and the intersection between the two lines will be the answer of what x and y are equal to, (x,y).

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x=7 , y=6

_________________________


Substituting y = -2x + 20 =

6x - 5(-2x + 20) = 12

Simplifying =

6x + 10x - 100 = 12

Combining like terms =

16x - 100 = 12

we add 100 =

16x = 12 + 100
16x = 112

Divide both sides by 16 =

x = 112 / 16

x = 7

y = -2(7) + 20

y = -14 + 20

y = 6

x=7 , y=6

The estimated volume of the region obtained by rotating y = √(1 + 6x³) about the y-axis using the Midpoint Rule with n = 5 is 0.702 cubic units.

To use the Midpoint Rule to estimate the volume V, we first need to divide the interval [0, 1] into n subintervals of equal width. In this case, n = 5, so we have:

Δx = (1 - 0)/5 = 0.2

Next, we need to find the midpoint of each subinterval. The midpoints are:

x₁ = 0.1

x₂ = 0.3

x₃ = 0.5

x₄ = 0.7

x₅ = 0.9

Now we can evaluate the function y = √(1 + 6x³) at each midpoint to get the heights of the cylinders that will make up the approximate volume V:

y₁ = √(1 + 6(0.1)³) ≈ 1.027

y₂ = √(1 + 6(0.3)³) ≈ 1.247

y₃ = √(1 + 6(0.5)³) ≈ 1.466

y₄ = √(1 + 6(0.7)³) ≈ 1.687

y₅ = √(1 + 6(0.9)³) ≈ 1.908

Finally, we can use these heights to calculate the volumes of the cylinders and add them up to get an estimate of V:

V ≈ π(Δx/2)²(y₁ + y₂ + y₃ + y₄ + y₅)

≈ π(0.1)²(1.027 + 1.247 + 1.466 + 1.687 + 1.908)

≈ 0.702

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Answer:

Samedy's statement is false. in total the class has 56 brothers and sisters

Step-by-step explanation:

Answer:

A. Samedy's statement is incorrect.

B. In total, the class has 71 brothers and sisters.

To arrive at this answer, we can use the information given in the problem to calculate the total number of brothers and sisters:

7 students have 2 siblings each, so there are 14 siblings in total.

4 students have 1 sibling each, so there are 4 siblings in total.

6 students have 3 siblings each, so there are 18 siblings in total.

The remaining students have 4 siblings each, so there are 4 x (24 - 7 - 4 - 3 - 6) = 4 x 4 = 16 siblings in total.

Adding all of these up, we get a total of 14 + 4 + 18 + 16 = 52 siblings. Therefore, Samedy's statement is incorrect, as the class has 52 siblings and not 24.

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The coefficient of determination (R^2) is 3.78%.

To calculate the coefficient of determination (R^2), we need to first find the total sum of squares (SST) and the sum of squares error (SSE) from the given ANOVA table. SST is the variation between the observed values and the mean value of all observations. SSE is the variation between the observed values and the group means.

SST = Between groups + Within groups = 1,493.76 + 37,941.72 = 39,435.48

SSE = Within groups = 37,941.72

R^2 = (SST - SSE) / SST

Plugging in the values, we get:

R^2 = (39,435.48 - 37,941.72) / 39,435.48

R^2 = 0.0378

To convert this to a percentage, we multiply by 100 and round to two decimal places:

R^2 = 3.78% (rounded to 2 decimal places)

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Answer:

70

Step-by-step explanation:

Option B : The range of 45 is the most accurate measure of variability to use to represent the data.

The range is the difference between the highest and lowest values in a dataset. In this case, the highest donation was $55 and the lowest was $10, so the range is:

range = highest value - lowest value = $55 - $10 = $45

Since the range takes into account all the values in the dataset, it is an appropriate measure of variability for this skewed dataset. The IQR (interquartile range) would also be a valid measure of variability, but it is less appropriate for skewed data because it only takes into account the middle 50% of the data and is less affected by extreme values. In this case, the extreme values (the two $55 donations) have a large effect on the distribution of the data, so the range is a more appropriate measure of variability.

Therefore, the charity should use the range of $45 to represent the variability of their donations.

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Answer: [tex]7^3\cdot7^{-5}=7^{-2}=\dfrac{1}{7^2}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

180 ÷ 20 = 9

Original Price = 9 x £2.80 = £25.2

Discounted price = £25.2 - (£25.2 x 0.30) = £17.55

In a sale, 180 carrots would cost £17.55.

Two potential locations for drilling are under consideration by an oil corporation.

a) The estimated profit is higher at Site A.

b) We can state that Site A has a larger expected profit than Site B by $17 million because the expected profit for Site A is higher than the expected loss for Site B.

To find the expected profit for each site, we need to multiply the profit from finding oil by the probability of finding oil and subtract the loss from not finding oil multiplied by the probability of not finding oil.

For Site A:

Expected profit = (Profit if oil is found x Probability of finding oil) - (Loss if no oil is found x Probability of not finding oil)

Expected profit = ($120 million x 0.2) - ($20 million x 0.8)

Expected profit = $24 million - $16 million

Expected profit = $8 million

For Site B:

Expected profit = (Profit if oil is found x Probability of finding oil) - (Loss if no oil is found x Probability of not finding oil)

Expected profit = ($180 million x 0.1) - ($30 million x 0.9)

Expected profit = $18 million - $27 million

Expected profit = -$9 million

Therefore, Site A has the larger expected profit of $8 million, while Site B has an expected loss of $9 million.

Since the expected profit for Site A is greater than the expected loss for Site B, we can say that Site A has a larger expected profit than Site B by $17 million ($8 million - (-$9 million)), which is the difference between their expected profits.

The complete question is:-

An oil company is considering two sites on which to​ drill, described as​ follows: Site​ A: Profit if oil is​ found: ​$120 million Site​ B: Profit if oil is​ found: ​$180 million Loss if no oil is​ found: ​$20 million Loss if no oil is​ found: ​$30 million Probability of finding​ oil: 0.2 Probability of finding​ oil: 0.1 a.  Which site has the larger expected​ profit? Site A has the larger expected profit. Your answer is correct. Site B has the larger expected profit. The expected profits for both sites are the same. b.  If the expected profit for both sites is not the​ same, by how much is the expected profit​ larger? ​$ nothing million  ​(Round to the nearest tenth as​ needed.) I need answer B and and explanation. Because I can calculate it as bigger, but my anwser doesn't match B.

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Answer:

Kevin's age = 13

Step-by-step explanation:

Now we have to,

→ Find Kevin's age, if his father's age is 44.

Let us assume that,

→ Kevin's age = k

Forming the equation,

→ 3k + 5 = 44

Then the value of k will be,

→ 3k + 5 = 44

→ 3k = 44 - 5

→ 3k = 39

→ k = 39/3

→ [ k = 13 ]

Hence, the value of k is 13.

The age of Kevin is 13 years.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Given that, Kevin's father age is 5 years more than three times Kevin's age.

Let the age of Kevin be k.

Then, the age of Kevin's father is 3k+5

Kevin's father is 44 years old

Thus, 3k+5=44

3k=39

k=13

Therefore, the age of Kevin is 13 years.

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Answer:

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. Converse of the Same-Side Interior Angles Postulate: If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

Answer: The correct statements that explain that the table does not represent a probability distribution are:

The results are all less than 0.

The probability is greater than 1.

The sum of the probabilities is 31/12.

A probability distribution must have probabilities between 0 and 1 (inclusive) and the sum of all probabilities must equal 1.

Step-by-step explanation:

The solution to the problems are;

1.  Area = 108 square feet

2. Area = 342 square feet

3. x = $1, 890, x = $1764

4. Cost, x = $151. 2, $117. 6

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that;

From the diagram shown, we have that;

The deck is gray

The garden is white

1. The area of the garden in design A

Area = 9(12) = 108 square feet

2. The area of the deck in design A is;

Area = 18(25) = 450 square feet

The area of the deck without the garden = 450 - 108

Area = 342 square feet

3. If $4. 20 = 1 square feet in design A

Then, x = 450 square feet

x = $1, 890

Area of deck of design B = 21(20) = 420 square feet

cost = $1764

4. If $1. 40 = 1 square feet of garden A

Then, x = 108 square feet

Cost = $151. 2

For garden of design B

Area = 1/2 × (12)(14) = 84 square feet

Then, cost = $117. 6

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The equation which is an example of an inequality include the following: C. 4x > -16

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

In this context, we can reasonably infer and logically deduce that the only equation with an inequality symbol is 4x > -16 and as such, it is an example of an inequality.

By evaluating, we have:

4x > -16

x > -16/4

x > -4

In conclusion, we can logically deduce that x is greater than negative four (-4).

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Complete Question:

Which of the following is an example of an inequality

A. x+5=10

B. 2x-3=7

C. 4x>-16

D. 3x-2

V = 207 cm^3

Step-by-step explanation:

volume of box A = 12 × 3 × 5 = 180 cm^3

volume of box B = 3 × 3 × 3 = 27 cm^3

total volume of box A and B = 180 + 27 = 207 cm^3

The sum οf all pοssible lengths fοr TP is 12

A triangle is a type οf pοlygοn with three sides; the pοint where the twο sides meet is knοwn as the vertex οf the triangle. Between twο sides, an angle is created. One οf geοmetry's key cοmpοnents is this.

Triangle prοperties are necessary fοr sοme fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry. Based οn its angles and sides, a triangle can be classified intο variοus types.

Given that triangle TIP and triangle TOP are isοsceles triangles with sides;

TI = 5, PI = 7, PO = 11

Therefοre, given that triangle TIP is an isοsceles triangle, the length οf segment TP will be equal either the length οf segment TI οr segment PI which give;

TP = TI 5 οr TP = PI = 7

The sum οf all pοssible lengths fοr TP is given by the sum οf the twο unequal sides οf triangle TIP which gives;

The sum οf all pοssible lengths fοr TP = 5 + 7 = 12.

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Answer:

30%

Step-by-step explanation:

750-525/750*100%

225/750*100%

0.3*100%

30%

Solution defines by [tex]x\geq 5[/tex]

A number line is typically a horizontal line that extends infinitely in both directions. It is used to represent both positive and negative numbers, and each point on the line corresponds to a unique real number.

Numbers to the right of zero are positive and increase as you move further to the right, while numbers to the left of zero are negative and decrease as you move further to the left. Zero is the midpoint of the number line and is neither positive nor negative.

Based on the information you've provided about the number line, it is clear that the solution set can extend beyond 8, as indicated by the arrow. This means that there are numbers greater than 8 that are included in the solution set.

Solution defines by [tex]x\geq 5[/tex]

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For Mrs. Sanchez's problem, the solution set can extend forever. Using the number line x ≥ 5.

A number line is typically a horizontal line that extends infinitely in both directions. It is used to represent both positive and negative numbers, and each point on the line corresponds to a unique real number.

Numbers to the right of zero are positive and increase as you move further to the right, while numbers to the left of zero are negative and decrease as you move further to the left. Zero is the midpoint of the number line and is neither positive nor negative.

Based on the information you've provided about the number line, it is clear that the solution set can extend beyond 8, as indicated by the arrow. This means that there are numbers greater than 8 that are included in the solution set.

Solution defines by x ≥ 5

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Answer:

v = c - 78930 + 57y - 6

Step-by-step explanation:

Thus, the chance according to the equation that the average actual weight for the [tex]100 weights[/tex] is higher than [tex]24.9 pounds[/tex] is roughly [tex]0.9582[/tex]

An equation in mathematics is a declaration of the equivalence of two expressions. Two parts of an equation are divided by the algebraic symbol ([tex]=[/tex]). As an example, the assertion "[tex]2x+3=9[/tex]" is supported by the argument that it is true.

Finding the value or values of the variable(s) needed to make the equation correct is the aim of equation solving. It is possible to create regular or nonlinear, straightforward or complex equations that include one or more variables.

For instance, the variable[tex]x[/tex] is raised to the second degree in the equation "[tex]x^{2} +2x-3[/tex]". In many areas of mathematics, such as algebra, calculus, or geometry, lines are used.

The weights are distributed evenly, with a minimum value of [tex]24[/tex] and a highest value of [tex]26[/tex]. The average of the lowest and maximum values, which is the mean weight of a single weight, is

[tex](mean weight)= (24+26)/2 = 25 pounds[/tex]

The standard deviation of a single weight is the difference between the maximum and minimum values divided by[tex]\sqrt{12}[/tex] (since there are [tex]12[/tex]possible values between [tex]24[/tex] and [tex]26[/tex]), which is

[tex]Standard deviation = (24+26)/\sqrt{12}[/tex]

[tex]We know (standard deviation of mean weight ) = 0.57735/\sqrt{100} =0.057735[/tex]

We must standardise this value by taking the mean weight, subtracting it, and dividing the result by the mean weight's standard deviation in order to determine the likelihood that the mean actual weight for the[tex]100[/tex]weights is higher than [tex]24.9 pounds[/tex]:

[tex]( Z- score )= (24.9-25)/0.057735 = -1.7321[/tex]

Probability is [tex]less than[/tex] [tex]-1.7321 in Z- score approx 0.0418[/tex]

However [tex]mean actual weight > 24.9[/tex] which is the complement of the probability i.e, [tex]\leq 24.9[/tex]

After subtracting the probability we found [tex]1[/tex] [tex](mean weight > 24.9)[/tex]

∴[tex]1 -0.0418 = 0.9582[/tex]

Therefore the  the average actual weight for the [tex]100 weights[/tex] is higher than [tex]24.9 pounds[/tex] is roughly [tex]0.9582[/tex]

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A 0.166 probability that they are over 45 years old is discovered using its notion from histogram.

A histogram is a form of graph that is used to show how a dataset is distributed. The horizontal axis shows the range of values in the dataset, while the vertical axis represents the frequency with which those values occur. It is a graphical depiction of a frequency table. Each bar's height corresponds to the number of observations that occur within a given bin, which is created by dividing the data into equal intervals known as bins.

In statistics and data analysis, histograms are frequently used to examine a distribution's form, particularly its central tendency, variability, and skewness. They are especially helpful for locating patterns and trends in the data as well as for spotting outliers, gaps, and clusters. Moreover, histograms can be used to contrast several datasets or look at how a dataset has changed over time.

The number of desired outcomes divided by the total number of outcomes yields a probability.

In this issue:

There are 150 workers overall, according to the histogram.

25 of them are older than 45 years old.

p = 25/150 = 0.166

This idea reveals a 0.166 probability that they are beyond 45 years old.

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Accοrding tο the given infοrmatiοn, the vertex οf the parabοla is at (2, 45), and the minimum value οf the functiοn is 45, which οccurs at the vertex.

The vertex fοrm οf a quadratic functiοn is a way οf writing a quadratic functiοn in the fοrm: f(x) = a(x - h)² + k, where (h, k) is the vertex οf the parabοla, a is a cοefficient that determines the shape and directiοn οf the parabοla, and x is the input variable. This fοrm is called the vertex fοrm because it prοvides direct infοrmatiοn abοut the vertex οf the parabοla, which is the pοint where the parabοla changes directiοn.

Tο rewrite the quadratic functiοn f(x) = x² - 4x + 49 frοm standard fοrm tο vertex fοrm, we need tο cοmplete the square by adding and subtracting a cοnstant term inside the parentheses, such that the functiοn can be expressed in the fοrm a(x - h)² + k.

f(x) = x² - 4x + 49

We can cοmplete the square as fοllοws:

f(x) = (x² - 4x + 4) + 45

= (x - 2)² + 45

Therefοre, the vertex fοrm οf the functiοn f(x) is:

f(x) = (x - 2)² + 45

The vertex οf the parabοla is at (2, 45), and the minimum value οf the functiοn is 45, which οccurs at the vertex.

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The probability that Emily chooses a blue chip and Josie chooses a red chip is 3/28.

Events that are mutually incompatible cannot take place at the same moment. If one thing happens, the other thing can't happen. For instance, if we flip a coin, receiving heads and getting tails are mutually exclusive events. The likelihood of two mutually exclusive occurrences happening simultaneously is zero.

Events that are independent of one another are said to be independent. The likelihood of the other event happening is unaffected if one event happens.

Given, 3 blue chips and 2 red chip from a total of 8 chip we have:

P(Emily chooses blue and Josie chooses red) = P(Emily chooses blue) × P(Josie chooses red after Emily chose blue)

= (3/8) × (2/7)

= 6/56

= 3/28

Hence, the probability that Emily chooses a blue chip and Josie chooses a red chip is 3/28.

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The complete question is:

Emily and Josie were randomly choosing a colored chip from the ones show below. What is the probability that Emily will choose a blue chip, keep it, and then Josie chooses a red chip?

The number of chips there are 8 chips. 3 are blue, 2 are red.

Answer: Therefore, the answer is (G) 1/2.

Step-by-step explanation:  Let's first express the perimeter of the square and the equilateral triangle in terms of x:

Perimeter of the square: 4(2x+2) = 8x + 8

Perimeter of the equilateral triangle: 3(4) = 12

Since the two shapes have equal perimeters, we can set the two expressions equal to each other and solve for x:

8x + 8 = 12

8x = 4

x = 1/2

Answer:Henry

Step-by-step explanation:

Max doesn’t have the greatest number, crossed out

Julio’s numbers add up to six, 15, crossed out

Lisa’s number is in between Max’s and Julio’s, which means max has 52, and Henry is left.

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