1.
2.
Solve the system of equations using elimination.
3x + by=18
-3x+4y=218
(3x+6y=18
1-3x+4y= 2
10g = 20
10 10
-3+9/21=2
- 3+by=2
x=2
y=2
(2,2)
Verify the solution from question 1 algebraically using substitution,

70.65 cubic inches of the treasure chest is taken up by the coins. Option B is the correct option.

What is π in math?

The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.

Given that the radius of a coin is 1.2 inches and the height of the coin is  0.0625 inches.

The shape of the coin is a cylindrical in shape.

The volume of a cylinder is ∏r²h, where r is the radius of the coin and h is the height.

The volume of a coin is 3.14×1.2²×0.0625 = 0.2826  in³.

The number of coins is 250.

Multiply 250 by 0.2826 in³ to find the volume of 250 coins:

250×0.2826 in³ = 70.65 in³

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The equation will give you an estimate of the number of beads that will fit in the cone at a given distance.

A linear equation is a mathematical equation in which the variables and their coefficients are raised to the first power and are not multiplied or divided by each other. In other words, a linear equation forms a straight line when graphed on a coordinate plane.

To determine the regression equation that best fits with the Precalculus lab data on how many beads fit in a cone at certain distances, you first need to determine the type of relationship between the variables.

If the relationship is linear, you can use a simple linear regression model of the form:

y = mx + b

where y is the dependent variable (i.e., the number of beads that fit in the cone), x is the independent variable (i.e., the distance from the top of the cone), m is the slope of the line, and b is the y-intercept.

However, if the relationship is not linear, you may need to use a nonlinear regression model. One common nonlinear model for this type of data is the power law model:

y = a[tex]x^{b}[/tex]

where a and b are parameters that need to be estimated from the data.

To determine which model is the best fit for your data, you can plot the data and visually inspect the relationship between the variables. If the relationship appears to be linear, you can use a linear regression model. If the relationship appears to be nonlinear, you can try fitting a power law model or other appropriate nonlinear model.

Once you have chosen a model, you can use statistical software to estimate the parameters and calculate the regression equation.

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If an item sets off the alarm,  the probability that it is defective is  0.0098 or 0.98%

This is a problem of conditional probability. We want to find the probability that an item is defective, given that the alarm has gone off. Let D be the event that an item is defective, and A be the event that the alarm goes off. We want to find P(D|A).

We can use Bayes' theorem to find P(D|A):

P(D|A) = P(A|D) * P(D) / P(A)

where P(A|D) is the probability that the alarm goes off given that the item is defective, P(D) is the prior probability that an item is defective, and P(A) is the probability that the alarm goes off.

We are given that:

P(A|D) = 0.99, the probability that the alarm goes off given that the item is defective.

P(A|D') = 0.01, the probability that the alarm goes off given that the item is defect-free.

P(D) = 100/1000000 = 0.0001, the prior probability that an item is defective.

P(D') = 1 - P(D) = 0.9999, the prior probability that an item is defect-free.

To find P(A), we can use the law of total probability:

P(A) = P(A|D) * P(D) + P(A|D') * P(D')

= 0.99 * 0.0001 + 0.01 * 0.9999

= 0.010098

Now we can substitute these values into Bayes' theorem:

P(D|A) = P(A|D) * P(D) / P(A)

= 0.99 * 0.0001 / 0.010098

= 0.009804

Therefore, the probability that an item is defective given that the alarm goes off is approximately 0.0098 or 0.98% when rounded to two decimal places.

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The range οf fοg(x) is the set οf all real numbers greater than οr equal tο 20, while the range οf gοf(x) is the set οf all real numbers greater than οr equal tο 7.

The range refers tο set οf all οutput values (dependent variables) that  functiοn can prοduce fοr  given input values (independent variables). It represents cοmplete set οf values that  functiοn can generate.

5) Given f(x) = -3x+1 and g(x) = x+8, we can find the cοmpοsite functiοns fοg(x) and gοf(x) as fοllοws:

fοg(x) = f(g(x)) = f(x+8) = -3(x+8)+1 = -3x-23

gοf(x) = g(f(x)) = g(-3x+1) = -3x+1+8 = -3x+9

The dοmain οf bοth cοmpοsite functiοns is the set οf all real numbers, since there are nο restrictiοns οn the input values οf the functiοns. The range οf fοg(x) is alsο the set οf all real numbers, while the range οf gοf(x) is the set οf all real numbers greater than οr equal tο 9.

6)Given f(x) = 2x²-x+1 and g(x) = 4x+3, we can find the cοmpοsite functiοns fοg(x) and gοf(x) as fοllοws:

fοg(x) = f(g(x)) = f(4x+3) = 2(4x+3)²-(4x+3)+1 = 32x²+17x+20

gοf(x) = g(f(x)) = g(2x²-x+1) = 4(2x²-x+1)+3 = 8x²-4x+7

The dοmain οf bοth cοmpοsite functiοns is the set οf all real numbers, since there are nο restrictiοns οn the input values οf the functiοns. The range οf fοg(x) is the set οf all real numbers greater than οr equal tο 20, while the range οf gοf(x) is the set οf all real numbers greater than οr equal tο 7.

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Answer:

Below

Step-by-step explanation:

The question states "round to nearest hundredth"   ....you rounded  to nearest 10th.....   I believe you can now find the correct answer...

in fraction form it is 13  11/13

The perimeter of quadrilateral WXYZ is 100, since if the two quadrilaterals are similar, the ratio of the corresponding sides will be the same.

Quadrilateral FGHJ is similar to quadrilateral WXYZ, meaning the ratio of the corresponding sides are equal. This means that if FJ is 24, then WZ must be 34, since the ratio of 24/34 is equal to the ratio of the other corresponding sides of FGHJ and WXYZ. To find the perimeter of WXYZ, we can find the lengths of the other sides. We know the ratio of FJ to WZ is 24/34, so the ratio of the other corresponding sides must also be 24/34. This means that the other sides of WXYZ must be 40, 80, 60, and 20. Adding these up gives us a perimeter of 100 for quadrilateral WXYZ.

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Answer:

175%

Step-by-step explanation:

We take

98 divided by 56, time 100 = 175%

So, 98 is 175% of 56

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is B.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

In the given expression[tex]5n- \frac{2m}{7} + \frac{3}{4}[/tex], the constant value is the value that does not have a variable with it. Therefore, the constant in the given expression is 3/4.

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The one and four hundred twenty nine thousandths in decimal form is 0.429.

Decimal Form:

Decimals are numbers made up of a whole number and a fractional part. Decimals are placed between whole numbers and represent the value of a quantity as a whole plus a part. In decimal form, we write this as 1.5 pizzas. Here, the dots represent the decimal point and the numbers before the decimal point, i.e., "1" represents a whole pizza, and the numbers after the decimal point represent half a pizza or a fractional part.

According to the Question:

The calculation is as follows;

Here in the given situation  

One and Four hundred - the number 4

Twenty nine - the number 29

Now,  

We have to Add them together with 0.

So, it should be 0.429

Complete Question:

What is One and four hundred twenty-nine thousandths as a decimal

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The power consumed by the circuit is 512.76 watts.

The pace of work or energy transmission in an electrical circuit is known as electric power. It is a way to quantify how much energy is consumed over a certain period of time. P = VI, where V is the potential difference, I is the electric current, and P is the electric power, calculates the electric power.

The two resistors R2 and R3 are parallel.

Thus,

Req = R2 + R2 / R1R2

Req = 36 + 18 / (36)(18)

Req = 0.083

Now, the resistors R1, Req, and R4 are in series:

Thus,

R = R1 + Req + R4

R = 15 + 0.083 + 13

R = 28.083

The formula of power is:

P = V²/R

Substitute the values:

P = (120)²/ 28.083

P = 512.76 watts.

Hence, the power consumed by the circuit is 512.76 watts.

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The number of movies rented was 5 to bring a total cost of $79.95

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Let y represent the total cost of renting x movies for one month.

The cable company charges a monthly fee of $55. Each movie that you rent from the DVR cost $4.99. Therefore:

y = 4.99x + 55

$79.95 is owed, hence:

79.95 = 4.99x + 55

4.99x = 24.95

x = 5

The number of movies rented was 5.

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The correct option that describes the shape of the sampling distribution of means is: Approximately normal.

The sampling distribution of the means refers to a distribution made up of many samples. For the given problem, there are 750 basketball games, and the researcher takes a simple random sample of size n = 40 from this population and computes the mean number of three-point baskets.

The central limit theorem states that the sampling distribution of the means of any population, even those that are not normally distributed, approaches a normal distribution as the sample size grows larger. When a sample has a sample size greater than 30, the shape of the sampling distribution of the means is approximately normal.

Thus, the shape of the sampling distribution of means is Approximately normal.

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Answer:When x→−∞ , then P(x)→−∞When x→+∞ , then P(x)→+∞Note that we can figure out if the function grows or decreases, simply by looking at the leading term of the function which is 4x⁵. This term shows that the function increases without bound as x → ± ∞.The given function is P(x)=4x⁵−8x³−7x²+9x+7We can now find the horizontal asymptotes of the given function, by computing the limits at infinity as follows;When x→−∞ , then P(x)→-∞When x→+∞ , then P(x)→+∞Therefore, the horizontal asymptotes are: y= - ∞ and y= + ∞

The above proof is given as follows;

FG ≅ HI - Given

FG ║ HI - Given
∠FHI ≅ ∠GFH - Alternate angles

FH ≅ FH - Reflexive Property

ΔFGH ≅ ΔHIF - Side-Angle-Side Postulate
FI ≅ GH - Definition of parallelogram.

A parallelogram is a four-sided figure with opposite sides parallel and congruent. Here are the properties of a parallelogram:

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Report on Descriptive Statistics:

For the given data set, the descriptive statistics are as follows:

Gender: Mean = 0.5, Median = 0, Mode = 0, Range = 1, Inter-quartile range = 1

Age: Mean = 33.2, Median = 32, Mode = 27, Range = 42, Inter-quartile range = 21

Education: Mean = 2.26, Median = 2, Mode = 2, Range = 3, Inter-quartile range = 1

Performance: Mean = 3.84, Median = 4, Mode = 4, Range = 4, Inter-quartile range = 1

Day 1: Mean = 3.4, Median = 4, Mode = 4, Range = 4, Inter-quartile range = 1

Day 2: Mean = 3.96, Median = 4, Mode = 4, Range = 4, Inter-quartile range = 1

Skill: Mean = 3.36, Median = 3, Mode = 4, Range = 4, Inter-quartile range = 1

Aptitude: Mean = 4.06, Median = 4, Mode = 4, Range = 4, Inter-quartile range = 1

Job Satisfaction: Mean = 4.2, Median = 4, Mode = 4, Range = 4, Inter-quartile range = 1

Org Communication: Mean = 4.34, Median = 4, Mode = 4, Range = 4, Inter-quartile range = 1

Shapiro-Wilk Test:

The Shapiro-Wilk test was performed on the leadership variable (ldrship) to test its distribution. The value of the Shapiro-Wilk test statistic for the given data set is 0.988, and the p-value for the test statistic is 0.276. Since the p-value is greater than the level of significance α=0.05, the null hypothesis is accepted. Therefore, it is concluded that the distribution of the leadership variable (ldrship) is normal.

Anderson-Darling Method:

The Anderson-Darling method was used to test the hypothesis that the given data follows a specified distribution or not. The critical values of the Anderson-Darling statistic at the significance level α = 0.05 for a normal distribution are given. The value of A2 for the given data set is 1.04, which is greater than the critical value of 0.768 at the 5% level of significance. Therefore, it is concluded that the data does not follow a normal distribution.

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Evaluated each expressiοn in parts

(a) (f+g)(2) = 4

(b) (f-g)(4) = 3

(c) (fg)(-2) = -3

(d) ((f)/(g))(0) = 2

In mathematics, table is  way οf οrganizing and presenting data οr infοrmatiοn in the rοws and cοlumns. Tables are οften used tο οrganize and display the numerical data, like statistical data, experimental results, οr survey respοnses.

A typical table cοnsists οf the rοws and the cοlumns, with each rοw representing  different entry οr recοrd and each cοlumn representing  different attribute οr variable.

(a) (f+g)(2):

Tο evaluate this expressiοn, we need tο find the values οf f+g at x=2. Frοm the table, we have:

f(2) = 1

g(2) = 3

Sο, (f+g)(2) = f(2) + g(2) = 1 + 3 = 4

Therefοre, (f+g)(2) = 4.

(b) (f-g)(4):

Tο evaluate this expressiοn, we need tο find the values οf f-g at x=4. Frοm the table, we have:

f(4) = 5

g(4) = 2

Sο, (f-g)(4) = f(4) - g(4) = 5 - 2 = 3

Therefοre, (f-g)(4) = 3.

(c) (fg)(-2):

Tο evaluate this expressiοn, we need tο find the value οf fg at x=-2. Frοm the table, we have:

f(-2) = 3

g(-2) = -1

Sο, (fg)(-2) = f(-2) * g(-2) = 3 * (-1) = -3

Therefοre, (fg)(-2) = -3.

(d) ((f)/(g))(0):

Tο evaluate this expressiοn, we need tο find the value οf f/g at x=0. Frοm the table, we have:

f(0) = 2

g(0) = 1

Sο, (f/g)(0) = f(0) / g(0) = 2 / 1 = 2

Therefοre, ((f)/(g))(0) = 2.

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It will take about 22 years for the population to reach 7500

Let's denote the number of years needed for the population to reach 7500 as t. Starting with the initial population of 4000, the population after t years can be calculated using the formula:

P(t) = P(0) * [tex](1+r)^{t}[/tex]

where P(0) is the initial population (4000), r is the annual growth rate (3.5% or 0.035), and P(t) is the population after t years.

We want to solve for t when P(t) = 7500.

So we have:

7500 = 4000 * [tex](1+0.035)^{t}[/tex]

Dividing both sides by 4000, we get:

1.875 = [tex](1.035)^{t}[/tex]

Taking the natural logarithm of both sides, we get:

ln(1.875) = t * ln(1.035)

Solving for t, we get:

t = ln(1.875) / ln(1.035) ≈ 21.8

Rounding to the nearest year, we get t ≈ 22.

Therefore, it will take about 22 years for the population to reach 7500, assuming a constant annual growth rate of 3.5%.

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No, the assertion does not imply that all circles are smooth forms.

The location of all the points on a plane whose sum of the distances from two fixed points in the plane is constant is known as an ellipse. The foci (singular focus), which are fixed locations that are encircled by the curve, are known. Directrix is the fixed line, and the eccentricity of the ellipse is the constant ratio.

No, the assertion does not imply that all circles are smooth forms. Since circles are a particular form of ellipse with a constant distance between any point on the circle's perimeter and its centre, they are a type of ellipse that are not all ellipses. In contrast, some ellipses seem stretched or compressed along their main and minor axes because there are two distinct distances between each point on the ellipse and its centre.

Hence an ellipse that is not a circle, such as one that is extended or flattened, can be a smooth shape. Due to the lack of any abrupt edges or line breaks, these forms are nevertheless regarded as smooth figures.

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Answer:

[tex]\text{The x-intercept of Line A is \boxed{1} and}\\\\\text{the x-intercept of Line B is \boxed{-2}}[/tex]

Step-by-step explanation:

The x-intercept of a line in slope intercept form is the value of x when y = 0

Line A

y - 2 = -(x + 1)

Put y = 0
=> 0 - 2 = -( x + 1)

=>  -2 = -x - 1

=>  -x - 1 = -2

=> -x = -2 + 1

=> -x = -1

=> x = 1

Line B

Look in the table for y = 0 and find the corresponding x value
We see when y = 0, x = -2

So x-intercept of line B = -2

The Sample mean years to maturity will be 7.05 and Sample standard deviation of years to maturity is 4.1318.

What is mean?

Mean, also known as the arithmetic mean or average, is a measure of central tendency in statistics. It is calculated by summing up all the values in a dataset and dividing by the total number of values.

Now,

To find the sample mean years to maturity for corporate bonds, we need to calculate the average of the years to maturity for all the 40 corporate bonds:

Sample mean years to maturity = (12.00 + 9.75 + 4.75 + 9.25 + 9.75 + 5.00 + 5.00 + 10.00 + 10.00 + 3.25 + 9.75 + 9.75 + 9.25 + 5.00 + 5.00 + 4.25 + 26.00 + 10.00 + 5.00) / 20

= 7.05

Therefore, the sample mean years to maturity for corporate bonds is 7.05.

To find the sample standard deviation of years to maturity for corporate bonds, we can use the following formula:

Sample standard deviation = √((1/n) * sum(xi - x_bar)²)

where n is the sample size, xi is the ith value in the sample, x_bar is the sample mean, and sum is the sum of all the terms in the brackets.

Using this formula and the given data, we get:

Sample standard deviation = √((1/20) * [(12.00 - 7.05)² + (9.75 - 7.05)²+ (4.75 - 7.05)² + (9.25 - 7.05)² + (9.75 - 7.05)² + (5.00 - 7.05)² + (5.00 - 7.05)² + (10.00 - 7.05)² + (10.00 - 7.05)² + (3.25 - 7.05)² + (9.75 - 7.05)² + (9.75 - 7.05)² + (9.25 - 7.05)² + (5.00 - 7.05)² + (5.00 - 7.05)² + (4.25 - 7.05)² + (26.00 - 7.05)² + (10.00 - 7.05)² + (5.00 - 7.05)²])

Sample standard deviation = 4.1318

Therefore, the sample standard deviation of years to maturity for corporate bonds is 4.1318 (rounded to four decimal places).

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the value of x that makes 22 the geometric mean of 5 and x is approximately 96.8.

How to find and what is geometry?

To find the value of x, we can use the formula for the geometric mean:

geometric mean = √(a ×b)

where a and b are the two numbers we want to find the geometric mean of.

We are given that the geometric mean of 5 and x is 22:

√(5× x) = 22

Squaring both sides, we get:

5× x = 22²2

Simplifying, we get:

5× x = 484

Dividing both sides by 5, we get:

x = 96.8

So the value of x that makes 22 the geometric mean of 5 and x is approximately 96.8.

Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, angles, and dimensions of objects in space. It includes the properties and relationships of points, lines, angles, surfaces, and solids, as well as their measurements and calculations. Geometry plays an important role in many areas of science, engineering, architecture, and art, and has numerous practical applications in everyday life.

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The operator's total pay per month is $6712.

The formula for calculating the total pay per month is total pay = (tent/x) × 100, where x is the fraction of the salary. In this case, the fraction is 1/8, so the formula becomes total pay = (849/1/8) × 100. To calculate the total pay per month, 849 is divided by 1/8, which is equal to 849 × 8. The result is 6712, which is the total pay per month.

To explain this calculation, first the fraction of the salary, 1/8, was identified. Then the formula was written, with the known tent amount of 849. To solve the equation, 849 was divided by 1/8, which is equal to 849 × 8. The result was 6712, the total pay per month.

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The total distance traveled by the particle from 0 ≤ t ≤ 6 is: 216 units

The position of the particle is given by the equation:

x(t) = 3t³ - 27t² + 72t + 14.

Now, To find the times when the particle changes direction, you just need to find the critical numbers of the function x(t).  These would be the possible times when the particle changes direction.

x(t) = 3t³ - 27t² + 72t + 14.

x'(t) = 9t² - 54t + 72

Using quadratic equation calculator, we have:

t = 2 or 4

Then you can find the position of the particle at these times.  We will also need to find its position at our end points: t = 0, 7.  Basically all we are doing here is finding the global max/min values of the function up to this point.

x(0) = 3(0)³ - 27(0)² + 72(0) + 14 = 14

x(2) = 3(2)³ - 27(2)² + 72(2) + 14 = 74

x(4) = 3(4)³ - 27(4)² + 72(4) + 14 = 62

x(6) = 3(6)³ - 27(6)² + 72(6) + 14 = -202

Thus:

Total distance = (74 - 14) + (62 - 74) + (-202 - 62)

= -216

This is 216 in the negative direction

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Answer:

i gotchu

Step-by-step explanation:

Therefore , the solution of the given problem of expressions comes out to be the total number of pet fish and reptiles in the US is roughly

1.494 * 10⁸.

It is necessary to perform calculations which it involve joining, removal, and random subdivision variable changing multipliers. If they banded together, they could do the following: A mathematical challenge, some information, and an algorithm. A statement of equation truth contains formulas, elements, and arithmetic procedures like additions, subtractions, errors, and groupings. It is possible to assess and analyse words and phrases.

Here,

The number of fish and reptiles kept as pets must be added to the overall number of pets:

=> 1.4 * 10⁸ + 9.4 * 10⁶

We must change these numbers to the same power of 10 in order to add them. Since 108 is equal to 100 million,

we can achieve this by moving the decimal point in the second figure two places to the right:

=> 1.4 * 10⁸ + 0.094 * 10⁸

We can now multiply the numbers:

=> 1.494 * 10⁸

Thus, the total number of pet fish and reptiles in the US is roughly

=> 1.494 * 10⁸.

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There are total of [tex]2.34*10^{8}[/tex] pet fish and reptiles in the United States.

Calculations that include changeable altering multipliers, joining, removal, and random subdivision must be done. They could accomplish the following if they united: An algorithm, some data, and a mathematical problem.

To find the total number of pet fish and reptiles in the United States, we simply need to add the number of pet fish and pet reptiles together:

Total = [tex]1.4*10^{8} + 9.4*10^{6}[/tex]

To add these numbers together, we need to express them using the same power of 10. We can do this by rewriting 9.4 * 10^6 as 0.94 * 10^7:

Total = [tex]1.4*10^{8} + 0.94*10^{7}[/tex]

Now, we can add the numbers together:

Total = [tex]1.4*10^{8} + 0.94*10^{7}[/tex]

= [tex]1.4 * 10^8 + 0.94 * 10^8[/tex]   (since [tex]10^7 = 10 * 10^6 = 10^1 * 10^6 = 10^7[/tex])

= [tex]2.34 * 10^8[/tex]

Therefore, there are a total of [tex]2.34 * 10^8[/tex] pet fish and reptiles in the United States.

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The sοlutiοn tο the inequality -1/8y ≤ 34 is equals tο  y ≥ -27²

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants

Given expressiοn -1/8y (is less than οr equal tο) 34 ,

Tο sοlve fοr y in the inequality -1/8y ≤ 34, we can start by isοlating y οn οne side οf the inequality sign.

Multiplying bοth sides by -8 (and flipping the inequality sign since we're multiplying by a negative number) gives:

y ≥ -8 * 34

y ≥ -27²

Therefore, the solution to the inequality -1/8y ≤ 34 is equals to  y ≥ -27²

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Answer:

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Therefore , the solution of the given problem of area comes out to be option A is the correct response: 42 + 400x = 1,200.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. When determining the surface of such a trapezoidal form, the surroundings are additionally taken into account. The surface area of something determines its overall dimensions. The number of edges here between cuboid's four trapezoidal extremities determines how much water it can hold inside.

Here,

let's use the variable x. So, the equation for the overall area needed for a palm tree and x lilac bushes is:

=> A(x) = 442 + 42x

Now, we need to determine the highest value of x at which the overall area needed will be less than 1200 square feet. To put it another way, we want to eliminate the inequality:

=>  A(x) < 1200

When we replace the equation with A(x), we obtain:

=>  442 + 42x < 1200

By taking 442 off of both ends, we arrive at:

=>  42x < 758

By dividing by the positive integer 42, we obtain:

=> x < 18

Therefore, Ryan can only place a total of 17 lilac bushes (since 18 would require more than 1200 sq ft of area).

=> 442 + 42x < 1200

which is equivalent to:

=>  42x < 758

or:

=>  x < 18

So, option A is the correct response: 42 + 400x = 1,200.

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From the given information provided, if WY + XZ = 28 and segment WP = 8, then the length of PZ is 8 units.

We can use similar triangles to find the length of PZ.

First, let's label the points where XZ and WY intersect with P as A and B, respectively.

Since WZ and XY are parallel, we know that triangles WPZ and YPX are similar. Therefore, we can write the following proportion:

WP/PZ = YP/YX

We know that WP = 8, so we just need to find YP and YX.

We can use the fact that triangles WPA and XPB are similar (because they share an angle and have parallel sides). Therefore, we can write the following proportion:

WP/WA = PB/PX

Substituting 8 for WP and rearranging, we get:

WA = 8(PX/WB)

Similarly, we can use the fact that triangles YPA and ZPB are similar to write:

YP/YA = PB/PZ

Substituting YX + WA for YA (since WY and XZ divide the parallelogram into equal areas), and substituting 28 - WA for PB (since WY + XZ = 28), we get:

YP/(YX + WA) = (28 - WA)/PZ

Substituting 8(PX/WB) for WA and simplifying, we get:

YP/(YX + 8PX/WB) = (28 - 8PX/WB)/PZ

Now we just need to solve for PZ. Cross-multiplying and simplifying, we get:

PZ = (28 - 8PX/WB)(YX + 8PX/WB)/YP

Since we know that WZ and XY are parallel, we can use the fact that opposite sides of a parallelogram are equal to write:

WZ = XY = WY + XZ = 28

We also know that WP = 8. Therefore, we can use the fact that the area of a parallelogram is equal to the product of its base and height to write:

Area(WPZ) = 8(WZ/2)

Substituting 28 for WZ, we get:

Area(WPZ) = 112

We can also use the fact that the area of a triangle is equal to half the product of its base and height to write:

Area(WPZ) = (PZ)(WX)/2

Substituting WX = WZ = 28 and simplifying, we get:

Area(WPZ) = 14PZ

Equating the two expressions for the area of WPZ, we get:

14PZ = 112

Solving for PZ, we get:

PZ = 8

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