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Writing and Solving System of Equations for Word Problems

Write a system of two equations to represent the situations. Define your variables (like let x = and y =) and solve the equations. You may use substitution or elimination methods. SHOW ALL WORK

Answer:

3/7

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

Let’s assume that we have 7 units of paint in total. Then, we have 3 units of green paint and 4 units of red paint. When we mix them together, we get 7 units of brown paint.

Because 3 out of the 7 units of paint are green, the fraction of the brown paint that is green paint is [tex]\frac{3}{7}[/tex].

Therefore, [tex]\frac{3}{7}[/tex] of the brown paint is green.

April has six pieces of paper, each measuring 8 inches in length which can be calculated using fractions.

April starts with a sheet of paper that is 4 feet long, which is equivalent to 48 inches since there are 12 inches in a foot. She then cuts the length of paper into halves, which gives her two pieces, each of them 24 inches long.

Next, she cuts the length of each of these 24-inch pieces into thirds, which gives her six pieces in total. Each of these pieces is 8 inches long, since 24 divided by 3 equals 8. Therefore, April has six pieces of paper, and each piece is 8 inches long.

It's worth noting that April's process of cutting the paper into halves and then into thirds is an example of how fractions can be used to divide a whole into equal parts. In this case, cutting the paper into halves means dividing it into two equal parts, and cutting each of these halves into thirds means dividing each half into three equal parts.

Overall, April has six pieces of paper, each measuring 8 inches in length. These pieces could be useful for various purposes, such as for creating small origami figures, for making decorations, or for use in a crafting project.

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The coordinates of the vertices of the enlarged shape A are (3, -3), (7, -3), (1, -6), and (0, -6).

In mathematics and geometry, a scale factor is a numerical factor that describes how much a figure or object has been enlarged or reduced in size. It is the ratio of any two corresponding lengths in the original figure and the scaled figure.

In geometry, a vertex (plural vertices) is a point where two or more line segments, lines, or rays meet to form an angle. In other words, a vertex is a point where two or more edges of a polygon, polyhedron, or any other geometrical shape meet.

In the given question,

To enlarge the shape A by a scale factor of 2 with a centre of enlargement of (-3, -5), we need to:

Translate the centre of enlargement to the origin (0, 0) by adding 3 to the x-coordinates and 5 to the y-coordinates of all points.

Apply the enlargement by multiplying the coordinates of each point by 2.

Translate the centre of enlargement back to its original position by subtracting 3 from the x-coordinates and 5 from the y-coordinates of all points.

So, the coordinates of the vertices of the enlarged shape A are:

Vertex 1:

Original coordinates: (0, -4)

Translate to origin: (3, 1)

Enlarge: (6, 2)

Translate back: (3, -3)

Final coordinates: (3, -3)

Vertex 2:

Original coordinates: (2, -4)

Translate to origin: (5, 1)

Enlarge: (10, 2)

Translate back: (7, -3)

Final coordinates: (7, -3)

Vertex 3:

Original coordinates: (1, -6)

Translate to origin: (4, -1)

Enlarge: (8, -2)

Translate back: (1, -6)

Final coordinates: (1, -6)

Vertex 4:

Original coordinates: (0, -6)

Translate to origin: (3, -1)

Enlarge: (6, -2)

Translate back: (0, -6)

Final coordinates: (0, -6)

Therefore, the coordinates of the vertices of the enlarged shape A are (3, -3), (7, -3), (1, -6), and (0, -6).

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Conducting a hypothesis test at the 5% significance level we can conclude that the girls' mean is higher than the boys' mean.

To conduct a hypothesis test to determine if the girls' mean is higher than the boys' mean, you will need to use a two-tailed hypothesis test with a significance level of 5%. The null hypothesis is that the girls' mean is not higher than the boys' mean, and the alternative hypothesis is that the girls' mean is higher than the boys' mean. The test statistic is calculated using the formula:

Test statistic = (Girls' mean - Boys' mean) / (Standard deviation of the difference / √(sample size))

The test statistic for this study is calculated as: (3.3 - 1.6) / (1.6/√40) = 4.375.

Using a 5% significance level and two-tailed hypothesis test, the critical value for this test is 1.96. Since the test statistic (4.375) is greater than the critical value (1.96), the null hypothesis can be rejected.

Therefore, we can conclude that the girls' mean is higher than the boys' mean.

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The length of the segment SR for the given pentagons is 9 units.

A polygon having 5 sides and 5 angles is called a pentagon. The words "pentagon" (which implies five angles) are formed up of two other terms, namely Penta and Gonia. End to end, the sides of a pentagon come together to form a shape. Hence, there are 5 sides in a pentagon.

The pentagon is a polygon with five sides and five angles, just like other polygons including triangles, quadrilaterals, squares, and rectangles. There are several sorts of pentagon forms, including regular and irregular pentagons as well as convex and concave pentagons, depending on the sides, angles, and vertices.

We know that, for similar figures the length of the ratios of their corresponding segments are equal.

Thus,

NM/TS = ML/SR

4/7.2 = 5/x

Using cross multiplication we have:

4x = 5(7.2)

4x = 36

x = 9

Hence, the value of the segment SR for the given pentagons is 9 units.

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Answer:

i believe its D

im sorry if i am incorrect

Answer:

D is the answer

Step-by-step explanation:

Answer:

7.81 units

Step-by-step explanation:

To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the coordinates given in the problem, we can plug in the values into the formula:

d = √((4 - (-2))^2 + (1 - (-4))^2)

Simplifying this expression, we get:

d = √((6)^2 + (5)^2)

d = √(36 + 25)

d = √61

Therefore, the distance between the two points (-2,-4) and (4,1) is √61 (square root of 61), which is approximately 7.81 units.

Answer: the answer is x < 2.80

Step-by-step explanation: can i get brainliest pls

The value of x is 8

The theorems of triangle are the rules that governs solving mathematical problems. Part of this theorem is a theorem that states that: The line joining the midpoint of the two sides of a triangle is parallel to the base.

Therefore ;

If we represent a side by y, using similar triangle,

y/2y = x+8/(3x+8)

1/2 = x+8/(3x+8)

3x +8 = 2(x+8)

3x +8 = 2x +16

collect like terms

3x-2x = 16-8

x = 8

therefore the value of x is 8

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The average mother stays in the maternity ward when local maternity ward delivers 1,500 babies per year is equal to 1.22 days.

Total number of babies delivered by maternity ward per year = 1,500

⇒ Total number of patients = 1,500

On average number of beds filled in the maternity ward at any given time = 5

Total patient days per year is,

⇒ Total patient days = Average number of beds filled x Number of days in a year

Since there are 365 days in a year,

⇒Total patient days = 5 x 365

                                 = 1,825

Use the formula,

Average length of stay = Total patient days / Total number of patients

⇒Average length of stay = 1,825 / 1,500

⇒Average length of stay = 1.22 days

Therefore, the average mother stays in the maternity ward for 1.22 days.

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Answer:

  (B) one

Step-by-step explanation:

You want to know how many points on the interval [0, 5] the function f(x) = e^(2x) have a slope equal to the average slope.

The instantaneous rate of change of function f(x) is its derivative:

  f'(x) = 2e^(2x)

This is a continuously increasing function (as is f(x)), so in any given interval there will be only one point that has any given slope.

The Mean Value Theorem says there is at least one point in the interval with the same slope as the average slope. The nature of the derivative tells you there is exactly one point with the same slope as the average slope.

The average rate of change on [0, 5] is ...

  AROC = (e^(2·5) -e^(2·0))/(5 -0) = (e^10 -1)/5

The instantaneous rate of change will have that value where ...

  f'(x) = 2e^(2x) = (e^10 -1)/5

  2x = ln((e^10 -1)/10)

  x = ln((e^10 -1)/10)/2 ≈ 3.84868475302

For this value of x, f'(x) = AROC

Answer:

Greater than

Step-by-step explanation:

With negative numbers the smaller it is, the more its worth. (If that makes sense) -2 is MUCH bigger than -500

:)

Standard deviation of the following data is 0.655.

The standard deviation is equal to the variance's positive square root. It is a fundamental statistical analysis method. The amount by which data values deviate from the mean is referred to as "standard deviation," or "SD."

Whereas a big standard deviation implies that the values are much outside the mean, a low standard deviation shows that the values are frequently only a few standard deviations from the mean.

Here in the question,

Total kids = 20.

Mean = 9+9.5+9.5+10+10+10+10+10.5+10.5+10.5+10.5+11+11+11+11+11+11+11.5+11.5+11.5/20

= 10.52

Now square of distance between mean and ages.

(9-10.52) ² = 2.31

(9.5-10.52) ² = 1.04

(10-10.52) ² = 0.27

(10.5-10.52) ² = 0.0004

(11-10.52) ² = 0.23

(11.5-10.52) ² = 0.96

Now sum of all the differences = 2.31 + 1.04 + 1.04 + 4×0.27 + 4× 0.0004 + 6× 0.23+ 3×0.96

= 8.73

Now standard deviation = √8.73/20

= √0.43

= 0.655

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Answer: 96 in squared.

First find the area of the whole triangle:

= 1/2(24+6)(8)

= 1/2(30)(8)

= 120

Then, find the area of the triangle formed by dotted lines:

= 1/2(6)(8)

= 24

Subtract the two areas:

= 120 - 24

= 96

In order for ΔCAM≅ΔCOM to be proved, all three sides and all three angles must be equal. So the correct answer is E. ΔCAM≅ΔCOM.

Corresponding sides are two sides in a polygon that are directly across from each other. This can be seen when two sides are connected by a line that is perpendicular to the other two sides.

ΔCAM≅ΔCOM can be proved when the two triangles have three corresponding sides and three corresponding angles that are equal.

However, option E does not provide proof of this as it only states that two angles are equal.

The other four options provide such proof.

Option A states that two angles are equal, Option B states two lines are equal and two angles are equal, Option C states two lines are equal and two angles are equal, and Option D states two lines are equal and two lines are equal. All of these provide the proof that ΔCAM≅ΔCOM.

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In order for ΔCAM≅ΔCOM to be proved, all three sides and all three angles must be equal. Option E does not provide proof of this as it only states that two angles are equal. So the correct answer is E. ΔCAM≅ΔCOM.

Corresponding sides are two sides in a polygon that are directly across from each other. This can be seen when two sides are connected by a line that is perpendicular to the other two sides.

ΔCAM≅ΔCOM can be proved when the two triangles have three corresponding sides and three corresponding angles that are equal.

However, option E does not provide proof of this as it only states that two angles are equal.

The other four options provide such proof.

Option A states that two angles are equal,

Option B states two lines are equal and two angles are equal,

Option C states two lines are equal and two angles are equal, and Option D states two lines are equal and two lines are equal.

All of these provide the proof that ΔCAM≅ΔCOM.

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The surface area of the composite figure is; SA = 224 in.²

From the composite figure attached, we can find the surface area of each of the rectangular/square external face seen as:

[tex]SA= 2(10 \times 2) + 2(4 \times 7) + 2(4 \times 4) + 2(4 \times 2) + (4 \times 7) + (10 \times 4) + (3 \times 4)[/tex]

[tex]SA = 40 + 56 + 32 + 16 + 28 + 40 + 12[/tex]

[tex]SA = 224 \ \text{in}.^2[/tex]

Thus, we can conclude that the surface area of the composite figure is:

[tex]SA = 224 \ \text{in}.^2[/tex]

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Answer:26

Step-by-step explanation:

If at least 3 of 4 balls must be blue then the number of possible selections = 462

Let us assume that m represents the number of red balls in a bowl.

So, m = 7

And n  represents the number of blue balls in a bowl.

So, n = 8

A woman selects 4 balls at random from the bowl.

We need to find the number of possible selections if at least 3 balls must be blue.

The first combination would be 4 blue balls + 0 red balls

And the second combination would be 3 blue balls + 1 red ball

so, using combination formula the number of possible selecctions:

(⁸C₄ × ⁷C₀) + (⁸C₃ ×  ⁷C₁)

= (70 × 1) +(56 × 7)

= 462

Therefore, the number of possible selections: 462

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The population in 2026 according to the exponential growth function will be approximately 54,515.

Given,

The population in 2001 = 26,100

Annual growth rate = 4%

Population growth function can be written as,

[tex]P(t) = P0e^rt[/tex]

Where,P(t) = Population after t years

P0 = Population at time t = 0

r = Annual growth rate (in decimal form)

t = Time (in years)

According to the given question,In the year 2026, the number of years from 2001 is,2026 – 2001 = 25 years

Therefore,t = 25 years

r = 4% = 0.04

Using these values in the population growth function,

[tex]P(t) = P0e^rt[/tex]

Population in 2026 = P(25)

[tex]P(25) = 26,100e^(0.04 x 25)[/tex]

P(25) = 26,100e

P(25) ≈ 54,515

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Using functions, we can find that the population of Smalltown reached its minimum in year 1995.

Functions are the central idea of calculus in mathematics. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics.

A mapping or transformation in mathematics represents a function.

The minimum point of this function corresponds to the vertex of the upward-opening parabola it creates.

You must consider the sign of the coefficient of the quadratic term, "a," in order to calculate the direction of the parabola without graphing it.

The parabola widens if the value of "a" is positive.

The parabola begins at the bottom if "a" is negative.

Now, you must use the following formula to find the x-coordinate of the vertex of a quadratic function represented in standard form:

x = -b/2a

a = 0.34

b = -4.08

x = -(-4.08)/2 × 0.34

= 4.08/0.68

= 6

Now, f (6) = 0.34 × 6² - 4.08 × 6 + 16.2

= 12.24 - 24.48 + 16.2

= 3.96

≈ 4

So, coordinates of the vertices are: (6,4)

If x = 0 is year 1989

Then, x = 6 is year 1989 + 6 = 1995.

This means that the population of Smalltown reached its minimum in year 1995.

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According to the information, each of the cases of equations has a different solution depending on the value that is given to the unknown or x.

Let p = √(x - 3), then the equation becomes p^2 - 2p - 3 = 0. This is a quadratic equation that can be factored as (p - 3)(p + 1) = 0. Therefore, p = 3 or p = -1. Since p = √(x - 3) and we want real solutions, we have two cases:

Case 1: p = √(x - 3) = 3. Squaring both sides, we get x - 3 = 9, so x = 12.

Case 2: p = √(x - 3) = -1. This case gives no real solution, since the square root of a real number cannot be negative. Therefore, the only real solution is x = 12.

Let p = √(x - 5), then the equation becomes p^2 - 4p - 12 = 0. This is a quadratic equation that can be factored as (p - 6)(p + 2) = 0. Therefore, p = 6 or p = -2. Since p = √(x - 5) and we want a real solution, we have only one case:

Case 1: p = √(x - 5) = 6. Squaring both sides, we get x - 5 = 36, so x = 41. However, we need to check that this solution is valid. Since p = √(x - 5) = 6 > 0, we have x - 5 > 0, so x > 5. Therefore, the only real solution is x = 41.

Let p = 3^x, then the equation becomes p^2 + 11p - 12 = 0. This is a quadratic equation that can be factored as (p + 12)(p - 1) = 0. Therefore, p = -12 or p = 1. Since p = 3^x and we want a real solution, we have only one case:

Case 1: p = 3^x = 1. This gives x = 0. However, we need to check that this solution is valid. Since 3^x > 0 for all x, we have x > -∞. Therefore, the only real solution is x = 0.

There is only one real solution because the function 9^x + (11x3^x) - 12 is continuous and strictly increasing for all x, which means that it can cross the x-axis at most once. Since we have found one real solution, there cannot be any others.

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Therefore , the solution of the given problem of unitary method comes out to be the temperature will continue to drop at a rate of 3°C per hour, meaning that it will be 3°C colder .

The task may be completed using this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, you may have another opportunity to interact with the item. Otherwise, all significant factors that affect how algorithmic factor proof behaves will be gone.

Here,

=> T = -3t + 0

We need only change the value of t in the equation and simplify to determine the temperature at a particular moment.

For instance:

T equals 1 after one hour:

=> T = -3(1) + 0 T = -3

So, the weather is -3°C after an hour.

T equals 2 after two hours:

=> T = -3(2) + 0 T = -6

Thus, the temperature is -6°C after two hours.

T equals 3 after three hours:

=> T = -3(3) + 0 T = -9

So, the weather is -9°C after three hours.

so forth,

As a result, the temperature will continue to drop at a rate of 3°C per hour, meaning that it will be 3°C colder after each hour than it was the hour before.

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Answer: 3 pens

Step-by-step explanation: The ratio of pencils to pens Monique has is 2:1, this means that for every 2 pencils Monique has she will have 1 pen. To plot this on a graph you can put one point at (2,1) and another point at (4,2)

The letter O has the experimental probability that is closest to its theoretical probability.

Probability is an area of statistics that deals with the study of random events and their likelihood of occurrence.

The theoretical probability of drawing a particular letter is the number of balls of that letter divided by the total number of balls in the game. For each letter, the theoretical probability is:

B: 15/75 = 0.2

I: 15/75 = 0.2

N: 15/75 = 0.2

G: 15/75 = 0.2

O: 15/75 = 0.2

The experimental probability of drawing a particular letter is the number of times that letter was actually drawn divided by the total number of draws. For each letter, the experimental probability is:

B: 247/1250 = 0.1976

I: 272/1250 = 0.2176

N: 238/1250 = 0.1904

G: 241/1250 = 0.1928

O: 252/1250 = 0.2016

Compare the differences between the theoretical and experimental probabilities for each letter. The letter with the smallest difference is the one whose experimental probability is closest to its theoretical probability.

Here, the differences between the theoretical and experimental probabilities for each letter are:

B: 0.2 - 0.1976 = 0.0024

I: 0.2 - 0.2176 = 0.0176

N: 0.2 - 0.1904 = 0.0096

G: 0.2 - 0.1928 = 0.0072

O: 0.2 - 0.2016 = 0.0016

Based on these calculations, we can see that the letter O has the smallest difference between its theoretical and experimental probabilities, with a difference of only 0.0016.

Therefore, the letter O has the experimental probability that is closest to its theoretical probability.

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Answer:

64.86

Step-by-step explanation:

Given: (-77.92) + (-8.39) + 59.4 - (-91.77)

The + and - will become -, and the - and - will become +:

-77.92 - 8.39 + 59.4 + 91.77

Finally, calculate:

-86.31 + 151.17

= 64.86

The shaded portion of the rectangle is approximately 21.8% of the rectangle, rounded to the nearest 10th.

In geometry, a rectangle is a four-sided polygon with four right angles (90-degree angles) and opposite sides that are parallel and congruent to each other. It is a special case of a parallelogram in which all angles are right angles.

The properties of a rectangle include:

Opposite sides are parallel and congruent.

All angles are right angles.

Diagonals are congruent and bisect each other.

The area of a rectangle is given by the formula A = lw, where l is the length and w is the width.

The perimeter of a rectangle is given by the formula P = 2l + 2w.

To solve this problem, we first need to find the areas of the shaded regions and the rectangle:

Area of rectangle = l × w = 26 × 16 = 416

Area of circle = (π × (d/2)²)/4 = (π × 4²)/4 = π

Area of pentagon = (5/2) × r² × sin(72°) = (5/2) × 5.5² × sin(72°) = 51.3

Area of right-angled triangle = (1/2) × h × d = (1/2) × 8 × 8 = 32

Total area of shaded region = Area of circle + Area of pentagon + Area of right-angled triangle = π + 51.3 + 32 ≈ 90.8

To find the percentage of the rectangle that is shaded, we divide the area of the shaded region by the area of the rectangle and multiply by 100:

Percentage of shaded region = (90.8/416) × 100 ≈ 21.8%

Therefore, the shaded portion of the rectangle is approximately 21.8% of the rectangle, rounded to the nearest 10th.

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Answer:

144

Step-by-step explanation:

The angles on the line next to the big c must add up to 180, and 180-58=122, so the space next to the 58 must be 122

The interior angles of a polygon can be calculated with 180(n-2) where n is the sides, so a pentagon has 540 degrees of interior angles

540 - 96 - 88 - 90 - 122 = 144

Answer:

Step-by-step explanation:

90+96+88+180-58=540-k

k=540-396

k = 144