2 Al gives food pellets to the animals on the farm.
• Rabbits: 0.3 kilogram
• Chickens: 1,300 grams
• Ducks: 0.7 kilogram
How many more grams of pellets does Al give
the chickens than he gives the rabbits and
ducks combined?
A 1,000 g
B 2,300 g
C 3,000 g
D 300 g

To determine whether the relation represented in the given table is a function, we need to check whether each input (x-value) in the table is associated with a unique output (y-value).

We can see that the input value "12" has two different output values, "16" and "19". This means that the relation is not a function since the same input is associated with multiple outputs.

Therefore, the relation represented in the given table is not a function.

Joseph must invest approximately $110840.16 today to reach his retirement goal of $2 million, assuming a consistent rate of inflation of 7.5%.

To calculate the amount Joseph needs to invest today to reach his retirement goal of $2 million, we can use the future value formula for a lump sum investment:

[tex]$FV = PV x (1 + r)^n[/tex]

where FV is the future value, PV is the present value, r is the rate of return (in this case, the inflation rate of 7.5%), and n is the number of years.

In this case, we want to solve for PV, which represents the amount Joseph needs to invest today. We know that:

Joseph has 40 years until he retires (65 - 25 = 40)

His retirement goal is $2 million

The inflation rate is 7.5%

Plugging these values into the formula, we get:

[tex]$2,000,000 = PV \times (1 + 0.075)^{40}[/tex]

Simplifying, we have:

[tex]$PV = \frac{2,000,000}{(1 + 0.075)^{40}}[/tex]

PV = $2,000,000 / 18.044

Therefore, Joseph must invest approximately $110840.16 today to reach his retirement goal of $2 million, assuming a consistent rate of inflation of 7.5%.

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After answering the provided question, we can conclude that The quadratic equation completed perfect square trinomial is (2c - 11)².

A quadratic equation is x[tex]ax2+bx+c=0[/tex], which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Fundamental Theorem of Algebra ensures that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. The formula "[tex]ax2 + bx + c = 0[/tex]" is a common solution for quadratic equations. where a, b, and c are numerical coefficients or constants. where the variable "X" is unidentified.

To make the trinomial [tex]4c² - 22c[/tex] + ... a perfect square, we need to add a constant term that will make it a perfect square trinomial.

Here are the steps to follow:

Therefore, the missing monomial is 121.

The completed perfect square trinomial is (2c - 11)².

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Answer: 41 degrees

Step-by-step explanation: To determine the angle at which the pizza was cut, we need to use the formula for the area of a sector of a circle:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a constant (approximately equal to 3.14), and r is the radius of the circle.

In this case, we know that the area of the sector that corresponds to the slice of pizza that was eaten is 17 square inches. We also know that the pizza has a diameter of 14 inches, which means that the radius is 7 inches.

Substituting these values into the formula, we get:

17 = (θ/360)π(7²)

17 = (θ/360)49π

θ/360 = 17/(49π)

θ = (17/49π) * 360

θ ≈ 41 degrees (rounded to the nearest whole number)

Therefore, the pizza was cut at an angle of approximately 41 degrees.

No, we cannot prove that war is near based on these propositions only.

In logic and mathematics, a proposition is a statement or assertion that is either true or false. It is also referred to as a declarative sentence. Propositions are often used as the building blocks for logical reasoning and mathematical proofs.

Here,

The given propositions are a chain of conditional statements, also known as if-then statements. To prove that war is near, we would need a statement or evidence that directly supports this claim. None of the given propositions directly state or imply that war is near. Even if we assume that all the given propositions are true, the only thing we can conclude is that Notre Dame de Paris cathedral started burning. We cannot make any conclusions about whether war is near or not.

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Step-by-step explanation:

I think this is the way it has to be done (I added a photo)

Answer:

8

Step-by-step explanation:

7+1

Answer:

x = 100 , y = 6

Step-by-step explanation:

[tex]\frac{x}{5}[/tex] = 20 ( multiply both sides by 5 to clear the fraction )

x = 5 × 20 = 100

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

8y - 6 = 9y - 12 ( subtract 9y from both sides )

- y - 6 = - 12 ( add 6 to both sides )

- y = - 6 ( multiply both sides by - 1 )

y = 6

It transform rectangle in  8 units left and then 7 units down then  x-axis and subsequently the y-axis were reflected and after this translated 7 units down

A set of translations, rotations, reflections, and dilations on a figure constitute a series of transformations in geometry. A composition of transformations is what results when two or more transformations are joined to create a new transformation. In a composition, one transformation creates a picture that serves as the foundation for the subsequent other transformation.

The possible transformations that rectangle ABCD could have undergone to become rectangle A′′B′′C′′D′′ are as follows: -

It was translated 8 units left, then 7 units down, for rectangle ABCD.

- First, the x-axis and subsequently the y-axis were reflected by the rectangle ABCD.

- Rectangle ABCD was translated 7 units down after being rotated 180 degrees around its origin.

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The value of x is 1.0 for the given triangle.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are:

The given triangle is a right triangle because it presents one of your angles equal to 90º. The figure shows:

Therefore, you have the opposite side of the angle u, the angle u and the variable x. Thus, you can apply the equation for sin (u) for finding x.

[tex]sin (x) = \frac{opposite\ side}{hypotenuse} \\ \\ sin (37) = \frac{0.6}{x}[/tex], knowing that sin37°=0.602

[tex]0.602=\frac{0.6}{x} \\ \\[/tex]

x=0.997, round to the nearest tenth

x=1.0

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The perimeter of the given quadrilateral EGFH is 33 inches as shown in below figure.

A quadrilateral is a geometric shape with four angles and four straight sides. Quadrilaterals come in a wide variety of shapes, including squares, rectangles, trapezoids, and kites. Each kind of quadrilateral has its own set of characteristics and properties, but they all have four sides and four angles in common.

Draw two tangents from an outside point to the circle always in equal lengths;

So, the perimeter of quadrilateral EGFH = length of each tangents

the perimeter of quadrilateral EGFH = EG + GF + FH + HE

the perimeter of quadrilateral EGFH = 12 + (5+4) + (4+0.5) + (0.5+7)

the perimeter of quadrilateral EGFH = 12+ 21

Therefore, the perimeter of quadrilateral EGFH = 33 inches

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Complete question in figure-

Answer:o calculate the compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, P = £8500, r = 5.7% = 0.057, n = 1 (since the interest is compounded annually), and t = 6.

So, plugging in the values:

A = £8500(1 + 0.057/1)^(1*6)

A = £8500(1.057)^6

A = £11260.23

Therefore, Brian will have £11260.23 in his bank account after 6 years with compound interest. Rounded to the nearest penny, the answer is £11,260.23.

Step-by-step explanation:

Answer:

x=√715

Step-by-step explanation:

Using Pythagorean Theorem,,

(34) ^2= (21)^2+x^2

⇒x^2= 1156-441

⇒x^2= 715

⇒x= √715

The slope of the line is 7/5 its y-intercept is (0,5) and x-intercept is (-25/7,0) when the equation of the line is 7x‐5y=‐25.

To write the equation of the line 7x-5y=-25 in slope-intercept form, we need to solve for y:

7x - 5y = -25

-5y = -7x - 25

y = (7/5)x + 5

Therefore, the equation of the line in slope-intercept form is y = (7/5)x + 5.

To find the slope, we can see that the coefficient of x is 7/5, so the slope is 7/5.

To find the y-intercept, we can see that the y-intercept is the value of y when x = 0. Plugging in x=0 into the equation, we get:

y = (7/5)(0) + 5 = 5

Therefore, the y-intercept is (0,5).

To find the x-intercept, we can set y=0 and solve for x:

0 = (7/5)x + 5

-5 = (7/5)x

x = -25/7

Therefore, the x-intercept is (-25/7,0).

To draw an accurate graph, we can plot the x- and y-intercepts and then use the slope to draw the line through those points. The slope of 7/5 means that for every 5 units to the right, the line goes up 7 units. We can use this to plot additional points and draw the line. The line should pass through the points (-25/7,0) and (0,5), and continue in both directions.

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Answer:

a dilatation centred at the origin with scale factor 3

Step-by-step explanation:

under a dilation centred at the origin with scale factor k

a point (x, y ) → (kx, ky )

here

A (2, 4 ) → A' (3(2), 3(4) ) → A' (6, 12 )

B (1, 6 ) → B' (3(1), 3(6) ) → B' (3, 18 )

C (5, 3 ) → C' (3(5), 3(3) ) →C' (15, 9 )

thus the transformation for Δ ABC → Δ A'B'C'

is a dilatation centred at the origin with scale factor 3

Answer:

As the height of the rider increases by 1 inch, the bike frame increases by 0.29 inches

Step-by-step explanation:

Lets label what we know here:

b = size of the bike frame in inches

h = height of the rider in inches

We are also given the equation [tex]b=0.29h+1.35[/tex], which is in slope intercept form. This means that the y intercept is 1.35 and the slope is 0.29.

This means that, as the height of the rider increases by 1 inch, the bike frame will also increase. Lets put this to the test:

[tex]b=0.29(1) + 1.35[/tex]

[tex]b=1.64[/tex]

We will get a different size of the bike frame depending on what we set h equal too.

In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

To find the annual rate of change between 1992 and 2006, we can use the formula:

r = [tex](V_2/V_1)^{1/n}-1[/tex]

where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.

=>r = -0.0839

Therefore, the rate of change between 1992 and 2006 is -0.0839.

To express the rate of change in percentage form, we can multiply the result from part A by 100:

=>r = -0.0839 x 100

=> r = -8.39%

Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.

To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.

From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:

where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.

=>V = 11792.51

Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).

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Side A and Side B are both equal to 32/3, which is 10 2/3 centimeters and the total number of hours the girls spent cleaning is 15 hours.

The perimeter of a shape can be found by adding up the lengths of all its sides.

The perimeter of a triangle is the sum of the lengths of its three sides, so in this case the equation to solve for the length of each of the two sides is:

Perimeter = 2 x Side A + Side B

32 = 2x + x

3x = 32

x = 32/3

Therefore, Side A and Side B are both equal to 32/3, which is 10 2/3 centimeters.

Kelsey and her 4 sisters spent an equal amount of time cleaning their home. To find the total number of hours the girls spent cleaning, we can write and solve a division equation. Let c be the total number of hours the girls spent cleaning.

c / 5 = 3

c = 15

Therefore, the total number of hours the girls spent cleaning is 15 hours.

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The intercepts of h(x) are (-1, 0), (4, 0), and (0, 4), and the asymptotes are x = 2 and y = 3. To find these intercepts and asymptotes using the graph, we need to look for the points where the graph intersects the x-axis and the y-axis, and where the function approaches infinity or a constant value as x approaches certain values.

From the graph, we can see that the function h(x) has a vertical asymptotes at x = 2, which means that as x approaches 2 from either side, the function approaches positive or negative infinity. We can also see that the function has a horizontal asymptote at y = 3, which means that as x approaches positive or negative infinity, the function approaches 3. To find the intercepts of h(x), we need to look for the points where the graph intersects the x-axis and the y-axis. From the graph, we can see that the function intersects the x-axis at x = -1 and x = 4, which means that these are the x-intercepts. The function intersects the y-axis at y = 4, which means that this is the y-intercept.

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So the probability of it not snowing today is 0.7 or 70%.

what is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability theory is a branch of mathematics that deals with the study of random events and their properties.

In the given question,

The complement of an event is the probability that the event does not occur. In this case, the complement of "it snows today" would be "it does not snow today".

To calculate the complement of an event, you can subtract the probability of the event from 1. So if the probability of it snowing today is 0.3 (or 30%), then the probability of it not snowing today would be:

1 - 0.3 = 0.7

So the probability of it not snowing today is 0.7 or 70%.

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Answer: Since the parabola opens down and has a focus at (0, -12), its directrix is a horizontal line located 12 units above the vertex. Let the vertex of the parabola be (h, k).

Since the focal diameter is 20, the distance between the focus and the directrix is also 20. Therefore, the directrix is the horizontal line y = k + 12, and the distance from the vertex to the focus is equal to the distance from the vertex to the directrix, which is 10.

Using the definition of a parabola, we can write:

sqrt((x - h)^2 + (y - k)^2) = 10 + (y - k - 12)

Squaring both sides, we get:

(x - h)^2 + (y - k)^2 = (10 + y - k - 12)^2

Expanding the right-hand side and simplifying, we get:

(x - h)^2 + (y - k)^2 = (y - 2)^2

Simplifying further, we get:

x^2 - 2hx + h^2 + y^2 - 2ky + k^2 = y^2 - 4y + 4

Rearranging the terms, we get:

x^2 - 2hx + h^2 + 2ky - 4y + k^2 - 4 = 0

Since the parabola opens down, the coefficient of x^2 must be negative. Therefore, we can write:

-(x^2 - 2hx + h^2 + 2ky - 4y + k^2 - 4) = 0

Multiplying out the negative sign, we get:

-h^2 + 2hx - 2ky + 4y - k^2 + 4 = 0

Therefore, the equation of the parabola that opens down, has focus (0, -12), and a focal diameter of 20 is:

-h^2 + 2hx - 2ky + 4y - k^2 + 4 = 0

Step-by-step explanation:

To find the annual interest rate, we can use the formula:

simple interest = (principal x rate x time) / 100

where principal is the initial amount, rate is the annual interest rate, and time is the time period in years.

We know that the principal is $100, the simple interest is $3, and the time period is 6 months, which is half a year.

So, we can plug in these values and solve for the annual interest rate:

$3 = ($100 x rate x 0.5) / 100

$3 = $0.5 x rate

rate = $3 / $0.5

rate = 6

Therefore, the annual interest rate is 6%.

Answer:

To calculate the annual interest rate, we can use the simple interest formula:

I = P * r * t

Where:

- I is the interest earned

- P is the principal amount

- r is the annual interest rate

- t is the time period in years

In this case, we know that the principal amount is $100, the interest earned is $3, and the time period is 6 months, or 0.5 years. We can plug these values into the formula and solve for r:

3 = 100 * r * 0.5

r = 3 / (100 * 0.5)

r = 0.06, or 6%

Therefore, the annual interest rate is 6%.

I hope this helps!

a. Using a standard normal distribution table,  p(z > 2.10) = 0.0188.

b.  p(z > -1.50) = 0.9332.

c. p(z < -0.55) = 0.2912.

The study of random occurrences or phenomena falls under the umbrella of the mathematic discipline known as probability. It is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To find the probabilities for a normal distribution, we need to use a standard normal distribution table or a calculator with a normal distribution function.

a. p(z > 2.10)

Using a standard normal distribution table, we can find that the area to the right of z = 2.10 is 0.0188. Therefore, p(z > 2.10) = 0.0188.

b. p(z > -1.50)

The area to the right of z = -1.50 is the same as the area to the left of z = 1.50. Using a standard normal distribution table, we can find that the area to the left of z = 1.50 is 0.9332. Therefore, p(z > -1.50) = 0.9332.

c. p(z < -0.55)

Using a standard normal distribution table, we can find that the area to the left of z = -0.55 is 0.2912. Therefore, p(z < -0.55) = 0.2912.

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Step-by-step explanation:

Area of ENTIRE circle = pi r^2 = pi (18)^2 = 1017.876 cm^2

the shaded area is   221 out of 360    ( 360 is the ENTIRE circle area)

221 / 360   * area =   221/ 360 * 1017.876  = 624.8 = ~ 625 cm^2

Answer:

2, 3, 3, 7, 10

Which values are the same?

Mean- 5

Mode- 3

Median- 3

Thus the mode and the median are the same

Step-by-step explanation:

You're welcome.

Answer: Mode and Median...

Step-by-step explanation: Mode and Median: Mode(Number that you see most) 3, Median(Middle number in least to greatest order) 3

Mode and Mean: Mode( Number you see most) 3, Mean(   Add up all the values in the set, then divide the sum by how many values there are. ) 2+3+3+7+10=25 25 divided by 5=5  (3 and 5)

Range and Mean: Range( Largest value minus the Smallest value) 10-2=8 Mean(Add up all the values in the set, then divide the sum by how many values there are.) 2+3+3+7+10=25 25 divided by 5=5 (8 and 5)

Answer:

The given statement is False. When the interest is compounded half yearly the number of conversion periods will be two because a year comprises 12 months and has two periods of six months each.

Step-by-step explanation:

if it helped you please mark me a brainliest :))

Answer:

(6,0 ) is located in 1st quardrant o is x axis and 6 is y axix upuards

The inequality or system of inequalities matched with the respective graphs are:


26) = Graph A
27) = Graph B
28) = Graph D

For y ≤ 3x² -
For any given value of x, the corresponding value of y can be found by squaring x and multiplying it by 3. Since the coefficient of x² is positive, the parabola represented by this inequality opens upward.

The graph of this inequality is a shaded region below or on the curve of the parabola. This means that any point (x, y) that lies on or below the curve satisfies the inequality, while any point above the curve does not.

For y ≥ - x²; y < x² + 3 -

The system of inequalities includes two quadratic functions in two variables, x and y. The first inequality y ≥ -x² represents a parabola that opens downward, while the second inequality y < x² + 3 represents a parabola that opens upward. The solution set for the system includes all points that satisfy both inequalities simultaneously. This solution set lies in the region above the first parabola and below the second parabola, and is bounded by the x-axis.

For y ≥ x²-5; y ≤ -2 x² + 3x + 3 -

The system of inequalities includes two quadratic functions in two variables, x and y. The first inequality y ≥ x² - 5 represents a parabola that opens upward, while the second inequality y ≤ -2x² + 3x + 3 represents a parabola that opens downward. The solution set for the system includes all points that satisfy both inequalities simultaneously. This solution set lies in the region between the two parabolas, and is bounded by the x-axis.


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10. Showing that ΔWVU ∼ ΔQRS, x = B. 5

11. Showing that ΔKML ∼ ΔEMD, x = A. 8.

A triangle is a geometric shape that is formed by connecting three straight lines to form a closed shape. It is a three-sided polygon and is one of the most basic shapes in geometry. The three lines that form a triangle are called sides, and the points where the sides meet are called vertices.

10. Showing that ΔWVU ∼ ΔQRS, we have:

WV/QR = VU/RS

⇒ (13x + 7)/45 = 88/55

Cross-multiplying, we have:

(13x + 7)55 = 45 x 88

= 715x + 385 = 3 960

= 715x = 3 960 - 385 = 3 575

∴ x = 3 575/715 = 5.

Thus, x = 5.

11. Showing that ΔKML ∼ ΔEMD, we have:

KM/EM = ML/MD = (3x - 2)/14 = 27/18

(3x - 2)18 = 14 x 27

= 54x - 54 = 378

= 54x = 378 + 54 = 432

⇒ x = 432/54 = 8.

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Answer:

The answer is: m = B(3x + 1) degrees.

Step-by-step explanation:

In the given equation m/B= (3x + 1)°, we need to find the measure of m.

To find m, we need to isolate it on one side of the equation.

We can do this by multiplying both sides of the equation by B, which gives us m = B(3x + 1)°.

This means that m is equal to the product of B and (3x + 1)°.

We can simplify further by multiplying 3x + 1 by the degree symbol, which gives us m = B(3x + 1) degrees.

The formula used in this problem is m/B = angle measure, where m is the unknown side, B is the length of the known side, and the angle measure is given in degrees.

When solving problems like this, it is important to watch for units and make sure they are consistent throughout the equation.

For example, if B is measured in meters, then the units of m should also be in meters.

A real-world example of using this formula could be calculating the height of a building based on the length of its shadow and the angle of the sun's rays.

Answer: m = B(3x + 1) degrees.

Math: m = B(3x + 1)°

Formula: m/B = angle measure

Name of formula: Trigonometric ratio

Real-world example: Finding the height of a building based on the length of its shadow and the angle of the sun's rays.

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