Solve the simultaneous equations below using substitution.

y=10x+6
2y+5x=17

Give your answers as integers or decimals.​

An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.

Inequality is an algebraic statement that two or more mathematical expressions are unequal.

Inequalities can be represented as:

The total amount received by the island = $32,000

The daily receipt of donations = $4,500

Let the number of days = x

Let the funds raised for aid = y

y ≤ 32,000 + 4,500x

Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.

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Regina needs to travel an additional 5,600 meters to get home.

The total distance Regina travels from school to the grocery store and then to her house is

4.2 km + 1.4 km = 5.6 km

To find out how much farther Regina needs to get home, we need to subtract the distance from the grocery store to her house (which we don't know yet) from the total distance she travels.

Let's say the distance from the grocery store to Regina's house is x kilometers. Then we can set up an equation

5.6 km - x km = the distance Regina needs to get home

To solve for x, we can isolate it on one side of the equation by subtracting the distance Regina needs to get home from both sides

5.6 km - (the distance Regina needs to get home) = x km

We know that Regina needs to get home, so we can substitute that into the equation

5.6 km - 0 km = x km

Simplifying, we get

x = 5.6 km

Now we know that the distance from the grocery store to Regina's house is 5.6 km. We need to convert this to meters to find out how much farther Regina needs to get home

5.6 km = 5,600 meters

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The mean of the sampling distribution will be 3.54. Thus, the correct option is C.

The population means is equal to the mean of the sampling distribution for all feasible samples of size 4. In this instance, 3.54 pounds is shown as the population means.

This suggests that the mean weight of the population of banana bunches will be 3.54 pounds if we pick several random samples of size four, compute the mean weight for each sample, and then average those sample means.

The Central Limit Theorem, which asserts that the sampling distribution of the sample means approaches a normal distribution centered on the population mean as the sample size grows, is a fundamental idea in statistics.

Thus, the correct option is C.

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1. cost of 3 1/10 mile for the taxi service charges: $0.40.

2. Relation is explained as direct proportional.

The top number of an improper fraction is greater than (or equal to) that bottom number.

Using the example:

The steps below can be used to change a mixed fraction into an improper fraction:

Fixed taxi charge = $1.00 for the first 1/10 mile

Additional charge = $0.10 mile

1. cost of 3 1/10 mile

covert mixed into improper = (30 +1)/10 = 31/10

The cost of 31/10 miles.

= $1.00 * 1/10 + (31/10 - 1/10)*$0.10

= $0.100 + 30/10*$0.10

= $0.100 + $0.30

= $0.40

2. As the distance increases the price also increases.

Relation is explained as direct proportional.

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The statement that is true about the rotated figure in the question is  (x,y) → (y,−x) .

A rotation of 270 degrees clockwise about the origin means that each point in the figure is moved around the origin in a circular path, traveling 270 degrees in the clockwise direction (which is equivalent to 90 degrees in the counterclockwise direction).

Now, let's consider the transformation (x, y) → (y, -x).

This transformation corresponds to a rotation of 90 degrees counterclockwise about the origin.

Therefore, the correct answer is A: x, y → (y, -x).

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Let's assume that the length of the rectangle is x cm.

According to the problem, the width is 1/2 of the length. Therefore, the width is 1/2 x cm, or (1/2)*x cm.

The area of the rectangle is given as 388 square centimeters.

We know that the formula for the area of a rectangle is:

Area = Length x Width

So, we can plug in the values we have:

388 = x * (1/2)*x

Simplifying this equation:

776 = x^2

Taking the square root of both sides:

x = √776 ≈ 27.87 cm

Therefore, the length of the rectangle is approximately 27.87 cm, and the width is (1/2)*x, or approximately 13.94 cm.

So the dimensions of the rectangle are approximately 27.87 cm by 13.94 cm.

Answer:

x = 4

Step-by-step explanation:

Alternative interior angles means these angles are equal in magnitude and sign

[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]

Answer:

The second figure.

Step-by-step explanation:

The first figure's perimeter is:

70 in + 42 in + 56 in = 168 inches.

And the second figure's perimeter is:

42 in + 33 in + 33 in + 64 in = 172 inches.

Therefore, Figure 1 < Figure 2.

a. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{17}}$.

b. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{51}}$.

c. You would need to know that the population distribution of X, teacher salaries, is normal in order to answer the questions regarding any sample size.

d. Assuming a sample size of 51, the probability that the sampling error is within $1000 is approximately 0.84 or 84%.

e. Assuming a sample size of 51, the 90th percentile for the average teacher's salary is approximately $54488.

f. Assuming that teacher's salaries are normally distributed, the 90th percentile for an individual teacher's salary is approximately $56396.

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The number of bicycles they need to sell to make equal money is 5. The amount they would make is $500.

In contrast to variable costs, which change depending on the volume of production or sales, fixed costs are expenses that remain constant. Rent, insurance, and salary are examples of fixed costs that are constant regardless of the volume of output or sales. Materials, labour, and shipping expenses are examples of variable costs that change according to the volume of output or sales.

Let us suppose the number of bicycle sold = x.

Then the equation for Jimmy is:

$250 + 50x

The equation for Tom is:

$400 + 20x

To make the same amount we equate the two equations as follows:

250 + 50x = 400 + 20x

30x = 150

x = 5

Substituting the value of x in equation 1 we have:

J = 250 + 50(5)

J = 250 + 250

J = 500

Hence, the number of bicycles they need to sell to make equal money is 5. The amount they would make is $500.

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As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .

A vector is a mathematical concept that possesses both magnitude (or length) and direction. In physics, engineering, and other sciences, physical quantities with both a size and a direction, such as velocity, force, and acceleration, are frequently represented by vectors. In geometry, vectors can be represented as arrows, with the direction of the arrow indicating the vector's magnitude and the length of the arrow indicating its magnitude. In addition to being able to represent points in space and describe curves and surfaces, vectors may also be added, subtracted, and multiplied by scalars to create new vectors.

given

Based on the provided table and the growth function graph, I would argue that the report on the growth of the mosquito population is better supported by the graph.

On the other hand, there is no visual representation of the growth of the mosquito population in the table; it merely displays the data in a tabular format.

Although the table contains the same data as the graph, it is more difficult to understand and evaluate.

As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .

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Answer:

4.25 x + 7 = 24

Second choice

Step-by-step explanation:

Plug in x = 4 into each equation and see which one is consistent

The correct answer is 4.25x + 7 = 24

Left side = 4.25(4)  + 7

= 17 + 7

=24

which matches the right side 24

The z-score when x=108 is 3.1034. The z-score tells you that x=108 is 3.1034 standard deviations to the left of the mean.

Z-score is used in statistics to compare a score to a normal distribution. The z-score is a measure of how far away from the mean a value is in standard deviation units.

To find the z-score when x = 108, we use the formula:

z = (x - μ) / σ

where x = 108, μ = 153, and σ = 14.5.

Substituting these values, we get:

z = (108 - 153) / 14.5 = -3.1034

So the z-score when x = 108 is -3.1034.

The z-score tells us how many standard deviations away from the mean a particular value is. In this case, since the z-score is negative, we know that x = 108 is to the left of the mean.

The absolute value of the z-score tells us how many standard deviations away from the mean the value is. In this case, the absolute value of the z-score is approximately 3.1034, which means that x = 108 is approximately 3.1034 standard deviations to the left of the mean.

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Value of angle x is 41 degree.

A straight line is a one-dimensional geometric object that extends infinitely in both directions. It can be defined as the shortest path between two points in a plane, and it has a constant slope (i.e., rate of change) between any two points on the line.

The standard equation for a straight line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis). Another commonly used form is the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Given, total angle=236°

236°=76°+119°+x

x=236°-76°-119°

x=41°

Hence, Value of angle x is 41 degree.

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Answer:

668.376

Step-by-step explanation:

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To simplify 650 – 0.394 + 18.77, we can first add 650 and 18.77 since they're both whole numbers:

650 + 18.77 = 668.77

Then, we can subtract 0.394 from 668.77:668.77 - 0.394 = 668.376

Therefore, 650 – 0.394 + 18.77 simplifies to 668.376.

The dimensions of the box to minimize the cost of materials are 3.16 cm x 3.16 cm x 3.16 cm.

To minimize the cost of materials for the jewelry box with a square base, you will need to find the dimensions of the box. The volume of the box is 40 cm3. The sides of the box will be silver plated and cost $12 per cm2, while the top and bottom will be nickel plated and cost $1 per cm2.

Since the box has a square base, each of the sides has the same area and the total area of the box is four times the area of one side. To minimize cost, the sides of the box need to be as small as possible. The equation for the area of a square is A = l2.

We can use this equation to find the length of one side of the box. 40 cm3 = l2 x 4, so l2 = 10 cm2. The length of one side of the box is the square root of 10, which is approximately 3.16 cm.

Therefore, the dimensions of the box to minimize the cost of materials are 3.16 cm x 3.16 cm x 3.16 cm.

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You poured approximately 0.267 liters of cooking oil from the entire large bottle into the smaller bottle.

To find out how much of the entire large bottle of cooking oil was poured into the smaller bottle, we need to multiply the fraction of the large bottle that was poured into the smaller bottle by the total amount of cooking oil in the large bottle.

Given that you have [tex]\frac{4}{9}[/tex] of the large bottle of cooking oil, the fraction of the large bottle that you poured into the smaller bottle is [tex]\frac{3}{5}[/tex] of [tex]\frac{4}{9}[/tex]. We can find this fraction by multiplying [tex]\frac{3}{5}[/tex] by [tex]\frac{4}{9}[/tex]:

[tex]\frac{3}{5} * \frac{4}{9} = \frac{12}{45}[/tex]

Simplifying this fraction by dividing both numerator and denominator by 3, we get:

[tex]\frac{12}{45}= \frac{4}{15}[/tex]

Therefore, you poured [tex]\frac{4}{15}[/tex] of the entire large bottle of cooking oil into the smaller bottle. To find the actual amount, you can multiply this fraction by the total amount of cooking oil in the large bottle. For example, if the large bottle contains 1 liter of cooking oil, then you poured:

[tex]\frac{4}{15} * 1 = 0.267[/tex] liters.

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Answer:

Below.

Step-by-step explanation:

Yes.

-9 = 3/4x - 3     -6 = 3/4 x     x = -8

-6 = 3/4x - 3    -3 = 3/4 x     x = -4  (there's a pattern!)

0 = 3/4x - 3    3 = 3/4 x     x = 4

3 = 3/4x - 3    6 = 3/4 x     x = 8

Hope this helps!

The approximate area under the curve f(t) = 1/t when found between 1 and 3 is equivalent to option D: 1.1.

Calculating an integral is called integration. Mathematicians utilize integrals to determine a variety of useful quantities, including areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. One of the two primary calculus topics in mathematics, along with differentiation, is integration.

We can find the approximate area using the concept of integration as follows:

[tex]\int\limits^3_1 {1/t} \, dt[/tex]

We generally know that:

[tex]\int\limits^a_b {x} \, dx[/tex]= ㏑(x)

Therefore,

[tex]\int\limits^3_1 {1/t} \, dt[/tex]

= ㏑ (3) - ㏑ (1)

= 1.1, more specifically it would be 1.09.

From the table of logarithm, you can verify is equivalent to 1.1.

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Correct question is:

In Exploration 3.1.1 you found the area under the curve f(t)=1/t

between 1 and 3. What was the approximate area that you came

up with?

A. 1.3

B. .9

C. .7

D. 1.1

If the rectangle is 40 cm long, 30 cm wide, and 20 cm high, then its volume will be given as 24000 cubic centimeter.

Volume is defined as the space enclosed by the three dimensional figure in itself. No two dimensional object can have volume as volume can be determined only when the length, breadth and height of the figure is known and the value of height is missing in two dimensional figures.

The formula for volume of a cuboid which has rectangular faces is given as follows:

Volume of cuboid = Length × Breadth × height

Volume of cuboid = 40 × 30 × 20

Volume = 24000 cubic centimeter

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Refer to complete question below:

Find the volume of a rectangular cuboid whose dimensions are given as 40 cm long, 30 cm wide, and 20 cm high.

The total area under the curve for x ≥ 6 is 449/4500.

The area under the curve y = 2x-3 from x = 6 to x = t and its evaluation at t = 10 and t = 100The area under the curve y = 2x-3 from x = 6 to x = t can be calculated as follows:

We know that the area of the region under the curve f(x) between x = a and x = b is given by [tex]A = ∫abf(x)dx[/tex]

Since the given function is y = 2x-3, we can write it as y = 2x^(-3) by applying the power rule.

Hence,A = [tex]∫62x^(-3)dx = [-2x^(-2)]6t = -2/t^2 + 2/36[/tex]We need to evaluate this area for t = 10 and t = 100, so we get[tex]A = -2/10^2 + 2/36 = -1/25 + 1/18 = 7/450andA = -2/100^2 + 2/36 = -1/5000 + 1/18 = 449/4500[/tex]Total area under this curve for x ≥ 6

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A, C, and D. The angles that have a measure of 180-x are angles that have a measure of 180 minus the value of x. In this case, x is equal to mz1, so the angles that have a measure of 180-x are √3, √5, and √10.

Angle is a mathematical concept that is used to measure the amount of rotation of a line or a plane around a point. An angle is typically measured in degrees, which is the unit of angular measurement. Angles are used in many different fields of mathematics, such as geometry, trigonometry, and calculus. In geometry, angles are used to measure the size of a triangle, the size of a circle, or the angle between two lines. In trigonometry, angles are used to solve problems involving the length of sides and the measure of an arc. In calculus, angles are used to measure the rate of change of a function.

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AE is classified as a chord.

A chord can be thought of as a piece of the circle that connects two points on the circle. The length of a chord depends on the distance between the two points it connects, as well as the size of the circle itself. The longest possible chord in a circle is the diameter, which is a chord that passes through the center of the circle and divides it into two equal halves.

A tangent line to a circle is a straight line that intersects the circle at exactly one point. This point of intersection is called the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency, and it lies in the same plane as the circle.

In the given question,

AE is passing through two points of the circumference of the circle and is also the diameter.

Hence, AE is the longest forming chord of the circle.

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Answer:

Step-by-step explanation:

5+3x/4 = 7/12

[(5*4)+3x]/4 = 7/12

(20+3x)/4 = 7/12

20+3x = 7/12*4

20+3x = 7/3

3x = 7/3 - 20

3x = [7-(20*3)]/3

3x = (7-60)/3

3x = -53/3

x = -53/3/3/1 ( reciprocal )

x = -53/3*1/3

x= -53/9

The dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 19 in. by 11 in. by cutting congruent squares from the corners and folding up the sides are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is 113.78 in³.

The dimensions of the box can be found with the following steps:

First, determine the side length of the square that is to be removed from each corner of the cardboard box. Since this will be done uniformly on all four corners, let the side length be x. The dimensions of the cardboard box can then be written as:

Length = 19 in. - 2x

Breadth = 11 in. - 2x

Height = x

After folding the cardboard along the creases, the base of the rectangular box will be (19 - 2x) in. by (11 - 2x) in. with the height of the box being x in. The volume of the box can then be found by multiplying the base and height of the box, i.e.,

Volume = (19 - 2x) (11 - 2x) x

Let V(x) be the volume of the rectangular box in terms of x. Then:

V(x) = (19 - 2x) (11 - 2x) x

Simplifying,

V(x) = 4x³ - 60x² + 209x

The maximum value of V(x) can be found by differentiating V(x) with respect to x and equating the result to zero. Therefore,

V'(x) = 12x² - 120x + 209 = 0

Solving, V(x) has a maximum value when x = 19/3 - 2(2/3)√14 or x = 19/3 + 2(2/3)√14. The value x = 19/3 - 2(2/3)√14 is the maximum value because x must be less than 5.5, which is the minimum of 11/2 and 19/2 divided by 3, the upper bound for x. Therefore, the dimensions of the box are

Length = 19 - 2(19/3 - 2(2/3)√14) = 6.33 in.

Breadth = 11 - 2(19/3 - 2(2/3)√14) = 3.33 in.

Height = 19/3 - 2(2/3)√14 = 5.33 in.

Thus, the dimensions of the box are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is:

V = 6.33 x 3.33 x 5.33 = 113.78 in³.

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Answer:  Try $44.81

Step-by-step explanation:

equation

30(1+.059)^t

t=7

Don't forget to account for the value you already have that is represented at 1 in the equation so then you don't have to add 30 afterwards.

Answer: "x" is 4.5

Step-by-step explanation:

first lets find the leg of the first right triangle using the given leg of 6 and the hypoteneuse of 9 using Pythagorean theorem a^2 + b^2 = c^2.

6^2 + b^2 = 9^2

36 + b^2 = 81

subtract 36 from both sides to isolate b

36 - 36 + b^2 = 81 - 36

simplify

b^2 = 45

take square root of both sides

[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{45}[/tex]

b = 6.7

Now we can find x of the 2nd right triangle using the know hypoteneuse of 6.7 and the known leg of 5

a^2 + b^2 = c^2

5^2 = b^2 = 6.7^2

25 + b^2 = 44.9

subtract 25 from both sides to isolate b

25 - 25 + b^2 = 44.9 - 25

b^2 = 19.9

take square root of both sides

[tex]\sqrt{b^2}[/tex] = [tex]\sqrt{19.9}[/tex]

b= 4.5

so your answer to what is "x" is 4.5

Total seats in plane: 186

108+64+14

5/7 of 14 is: 10

14÷7= 2

2x5= 10

5/16 of 64 is: 20

64÷16=4

5×4= 20

5/9 of 108 is: 60

108÷9= 12

12x5= 60

60+20+10=90

90/186 of seats are being used

simplified: 15/31

No

From the given data of hunters and do we find out there are 9 hunters and 15 dogs.

Let's assume that there were "h" hunters and "d" dogs.

Each hunter has two legs, and each dog has four legs, so the total number of legs can be expressed as:

2h + 4d = 78

We can simplify this equation by dividing both sides by 2:

h + 2d = 39

We also know that there were 24 heads in total, which includes the hunters and the dogs:

h + d = 24

We can now solve these two equations simultaneously to find the values of h and d.

First, we can solve for h in terms of d from the second equation:

h = 24 - d

We can substitute this expression for h in the first equation:

(24 - d) + 2d = 39

Simplifying and solving for d:

d = 15

Now that we know there were 15 dogs, we can substitute this value back into one of the equations to find the number of hunters:

h + d = 24

h + 15 = 24

h = 9

Therefore, there were 9 hunters and 15 dogs.

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The length of a side of the square is 8 cm.

What do you mean by perimeter of a rectangle and square?

When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.

The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.

Calculating the length of a side of the square:

The length of the rectangle is 11 cm and the width is 5 cm.

Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.

Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.

Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:

[tex]32 = 4s[/tex]

[tex]s = 32/4[/tex]

[tex]s = 8[/tex]

Therefore, the length of a side of the square is 8 cm.

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