Examine this system of equations. What integer should the first equation be multiplied by so that when the two equations are added together, the x term is eliminated?

StartFraction 1 Over 18 EndFraction + four-fifths y = 10

Negative five-sixths x minus three-fourths y = 3

If the height of a model of the Cape Hatteras Lighthouse given that the scale used is 8 inches to 30 feet. This means that for every 8 inches on the model, the actual lighthouse is 30 feet tall. Therefore, the height of the model is 4.67 feet.

The actual lighthouse is 210 feet tall. To find the height of the model, we need to use a proportion. We can set up the proportion as:

8 inches / 30 feet = x inches / 210 feet

We can cross-multiply to get:

8 inches * 210 feet = 30 feet * x inches

Simplifying, we get:

x inches = (8 inches * 210 feet) / 30 feet = 56 inches

However, the question asks for the height of the model in feet, so we need to convert 56 inches to feet by dividing by 12:

56 inches / 12 inches per foot = 4.67 feet

Therefore, the height of the model is 4.67 feet.

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Answer:

5.6 miles

Step-by-step explanation:

the patteren in 0.3    0.6     0.3       0.6

To find the volume and surface area of the composite figure, we need to find the volume and surface area of the right cylinder and the hemisphere separately, and then add them together.

First, let's find the volume of the right cylinder.

The formula for the volume of a right cylinder is V = πr^2h, where r is the radius and h is the height. In this case, the radius is half of the diameter, which is 4/2 = 2 inches. So, the volume of the right cylinder is:

V1 = π(2)^2(12) = 96π cubic inches

Next, let's find the volume of the hemisphere. The formula for the volume of a hemisphere is V = (2/3)πr^3, where r is the radius. In this case, the radius is also 2 inches. So, the volume of the hemisphere is:

V2 = (2/3)π(2)^3 = 16/3π cubic inches

To find the total volume of the composite figure, we just need to add V1 and V2:

Vtotal = V1 + V2 = 96π + 16/3π = 320/3π cubic inches

Now, let's find the surface area of the composite figure.

To do this, we need to find the surface area of the curved surface of the cylinder, the top of the cylinder, and the curved surface of the hemisphere separately, and then add them together.

The formula for the surface area of the curved surface of a cylinder is A = 2πrh, where r is the radius and h is the height. In this case, the radius is still 2 inches, and the height is 12 inches. So, the surface area of the curved surface of the cylinder is:

A1 = 2π(2)(12) = 48π square inches

The formula for the surface area of the top of a cylinder is A = πr^2, where r is the radius. In this case, the radius is still 2 inches. So, the surface area of the top of the cylinder is:

A2 = π(2)^2 = 4π square inches

Finally, the formula for the surface area of the curved surface of a hemisphere is A = 2πr^2, where r is the radius. In this case, the radius is still 2 inches. So, the surface area of the curved surface of the hemisphere is:

A3 = 2π(2)^2 = 8π square inches

To find the total surface area of the composite figure, we just need to add A1, A2, and A3:

Atotal = A1 + A2 + A3 = 48π + 4π + 8π = 60π square inches

So, the volume of the composite figure is 320/3π cubic inches, and the surface area of the composite figure is 60π

square inches.

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Let's say we add 'x' red candies and 'y' blue candies to the bag to create the desired ratio of 3 to 2:

Then, the total number of red candies in the bag will be 5 + x, and the total number of blue candies will be 1 + y.

According to the problem, the ratio of red candies to blue candies should be 3 to 2:

(5 + x) / (1 + y) = 3/2

Cross-multiplying this equation, we get:

2(5 + x) = 3(1 + y)

Simplifying this equation, we get:

10 + 2x = 3 + 3y

2x - 3y = -7

We want to find the least number of red and blue candies that can be added to the bag to satisfy this equation.

One way to do this is to try different values of x and y that satisfy the equation until we find the smallest possible values that work.

For example, we can start by setting x = 1 and y = 2:

2(5 + 1) = 3(1 + 2)

12 = 9

This doesn't work, so let's try another set of values, x = 4 and y = 5:

2(5 + 4) = 3(1 + 5)

18 = 18

This set of values works, so we have found the least number of red and blue candies that can be added to the bag to create a ratio of 3 to 2 for the number of red candies to the number of blue candies:

We need to add 4 red candies and 5 blue candies to the bag to create a ratio of 3 to 2 for the number of red candies to the number of blue candies.

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The length of NM and OL in the parallelogram LMNO are both 36 units.

Since LMNO is a parallelogram, we know that opposite sides are equal in length. Therefore, we can set NM and OL equal to each other:

NM = OL

We also know that NM = x + 27 and OL = 3x + 9, so we can substitute these expressions into the equation:

x + 27 = 3x + 9

Solving for x:

2x = 18

x = 9

Now that we know x, we can substitute it back into the expressions for NM and OL:

NM = x + 27 = 9 + 27 = 36

OL = 3x + 9 = 3(9) + 9 = 36

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The size  of square tablecloth needed to cover the entire square tabletop is 25 ft^2 (Option B).

To determine the size of the tablecloth needed to cover a square tabletop with a perimeter of 20 feet, we will first find the side length of the square and then calculate the area.

Step 1: Determine the side length of the square.
Since the perimeter of a square is equal to 4 times its side length (P = 4s), we can find the side length by dividing the perimeter by 4.
Side length (s) = Perimeter (P) / 4 = 20 ft / 4 = 5 ft

Step 2: Calculate the area of the square.
The area of a square is equal to the side length squared (A = s^2).
Area (A) = Side length (s) ^ 2 = 5 ft ^ 2 = 25 ft^2

So, the size of the tablecloth needed to cover the entire square tabletop is 25 ft^2 (Option B).

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The number of times more that Gina can play the playlist of children's songs in an hour would be 94. 7 times.

The playlist that Gina made of children's songs. In an hour, the number of seconds we have is :

= 60 secs x 60 mins

= 3, 600 seconds

The number of times that "Row, Row, Row Your Boat" can be played is:

= 3, 600 / 8

= 450 times

The number of times that Gina can play "Twinkle, Twinkle, Little Star" is :

= 3, 600 / 20

= 180 times

The number of times more :

= 450 - 180

= 270 times

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Answer:

Step-by-step explanation:

The bumblebee flutters its wings more times in 1 minute, as it flutters its wings 7,800 times in one minute, whereas the hummingbird flaps its wings 80 times in one second, which translates to 4,800 times in one minute.

To understand this calculation in more detail, we can use unit conversions and multiplication. Since the hummingbird's wing flaps are given in seconds and the bumblebee's wing flutters are given in minutes,

we convert the hummingbird's wing flaps from seconds to minutes by multiplying by 60. We then compare the total number of wing flaps for each animal and find that the bumblebee flutters its wings more times in one minute than the hummingbird flaps its wings.

This is due to the bumblebee's higher frequency of wing movement, which enables it to achieve more wing flutters in a given amount of time.

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According to the given information in the question to find the length of side v in triangle VWX, we can use the Law of Sines. the length of side v is approximately [tex]281.8[/tex] cm.

image for "define centimeters in high-level mathematics." A centimeter is a metric unit used to quantify small distances and the object's length. Cm is used to represent it in writing.

It can also be described as the measure of length in the current metric system, referred to as the International System of Units (SI). It is equal to one-hundredth of a meter.

which states that:

[tex]a/sin(A) = b/sin(B) = c/sin(C)[/tex]

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the opposite angles.

In this case, we know the length of side w (600 cm), and the measures of angles V and W.

To find the length of side v, we can use the Law of Sines with sides v and w and angle V:

[tex]v/sin(V) = w/sin(W)[/tex]

[tex]v/sin(26^\circ) = 600/sin(80^\circ)[/tex]

[tex]v = (600 \times sin(26^\circ))/sin(80^\circ)[/tex]

[tex]v \approx 281.8 cm[/tex] (rounded to the nearest 10th of a centimeter)

Therefore, the length of side v is approximately [tex]281.8 cm[/tex].

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There are approximately 500 times more high school football players than professional football players in the United States.

To determine how many times more high school football players there are than professional football players in the United States, we need to divide the number of high school players by the number of professional players:

1 x 10⁶ / 2 x 10³ = 500

Therefore, there are approximately 500 times more high school football players than professional football players in the United States.

We can determine this by dividing the two numbers and finding the ratio of high school players to professional players. The result tells us how many times greater the number of high school players is than the number of professional players. In this case, the ratio is 500:1, which means that for every professional football player, there are 500 high school football players.

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The measure of angle PQR is 90 degrees.

Since PR is the diameter of the circle, it follows that angle POR is a right angle, i.e., it measures 90 degrees.

By the inscribed angle theorem, the measure of angle PQR is half the measure of angle POR. Thus,

angle PQR = 1/2 * angle POR

= 1/2 * 90

= 45 degrees.

However, this is not the final answer since angle PQR is not a stand-alone angle, but rather a part of a right-angled triangle PQR.

Since the three angles in a triangle add up to 180 degrees, and we already know that angle PQR is 45 degrees, it follows that:

angle PRQ + angle PQR + angle QPR = 180 degrees

Since angle PQR = 45 degrees, we have:

angle PRQ + 45 + angle QPR = 180 degrees

Rearranging, we get:

angle PRQ + angle QPR = 135 degrees

Since angles PRQ and QPR are complementary angles (together they form a right angle), their sum is 90 degrees. Therefore,

angle PRQ + angle QPR = 90 degrees

Substituting this into the previous equation, we get:

90 degrees = 135 degrees

This is a contradiction, and hence our assumption that angle PQR measures 45 degrees is false.

Therefore, we conclude that angle PQR must measure 90 degrees, since it is the only angle that can satisfy the given conditions.

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The measure of the central angle that intercepts the arc of the circle is approximately 286.48 degrees.

A circle's circumference is comprised of arcs. In other words, if you draw any two locations on a circle's circumference, the curved line that joins them around the border of the circle is referred to as an arc.

The formula for the relationship between arc length and central angle is:

arc length = radius x central angle

We are given the arc length and radius, so we can solve for the central angle:

10 = 2 x central angle

Dividing both sides by 2, we get:

central angle = 10/2

= 5 radians

To convert from radians to degrees, we multiply by 180/π:

central angle = 5 x 180/π

≈ 286.48 degrees.

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A population of 600 organisms is expected to increase by 50.

We can use the equation I = k * n to determine whether the anticipated growth (I) of an organism population is directly related to the size of the current population (n).

Where k is a proportionality constant that connects the anticipated growth to the current population.

We can use the details provided in the problem to determine the value of k. We can write: 20 = k * 240 to represent an increase of 20 in a sample of 240 organisms.

We can calculate k as follows: k = 20 / 240 = 1 / 12.

Now that we know the value of k, we can use it to calculate the predicted growth for a population of 600:

I = (1 / 12) * 600 = 50

Therefore, a population of 600 organisms is expected to increase by 50.

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a. If t represents time in hours and d represents distance in miles, and Caden walks at a steady rate of 3.6 miles per hour, the equation that models the relationship between these variables is:

d = 3.6t

b. To calculate the distance Caden will walk in 3/4 of an hour, plug 3/4 into the equation for t:

d = 3.6(3/4) = 2.7 miles

Caden will walk 2.7 miles in 3/4 of an hour.

c. To calculate how long it will take for Caden to walk 4.32 miles, plug 4.32 into the equation for d and solve for t:

4.32 = 3.6t
t = 4.32/3.6 ≈ 1.2 hours

It will take Caden approximately 1.2 hours to walk 4.32 miles.

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The correct answers are:True, True, False.

The first statement is true. The initial investment is represented in the formula as the coefficient of the growth factor[tex](1+0.05)^t[/tex].

The second statement is true. The growth factor in the formula is (1+0.05), which represents a 5% increase or a multiplier of 1.05.

The third statement is false. The annual interest rate is not 50%. The growth factor (1+0.05) represents a 5% increase, but the actual annual interest rate is 5%, not 50%.

Therefore, the correct answers are:

True

True

False

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The sample space for choosing one marble from the given marbles which are red, green, blue, yellow, and orange is s = {red, green, blue, yellow, orange}

Given color of the marbles which are present in the paper bag are,

The five color marbles are present in the paper bag so, the sample space also contains all five marbles without repeating any color again.

Sample space: sample space is nothing but listing all the outcomes of the event. In the above event, we have to list the all outcomes when choosing one marble from the paper bag which containing five different marbles.

So, the sample space S = {red, green, blue, yellow, orange}

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When rounded to the nearest hundredth, the result of the expression tan 33° × cos 42° × sin 70° is approximately 0.4511 .

To evaluate the given expression using the terms tan 33°, cos 42°, and sin 70°, you can use a scientific calculator or an online tool like the ALEKS calculator.

After evaluating each term, you would multiply the values together and round the result to the nearest hundredth. Here's the breakdown:

tan 33° ≈ 0.6494
cos 42° ≈ 0.7431
sin 70° ≈ 0.9397

Now multiply the values:

0.6494 × 0.7431 × 0.9397 ≈ 0.4511

So, the result of the expression tan 33° × cos 42° × sin 70° is approximately 0.4511 when rounded to the nearest hundredth.

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Answer:

Step-by-step explanation:

cat

The number of times she should expect to pull a yellow marble is 13

From the question, we have the following parameters that can be used in our computation:

Color of Marble Frequency

Yellow 26

Green 34

Purple 18

Red 22

This means that

Times she should expect to pull a yellow marble is

Yellow = P(Yellow) * 50

So, we have

Yellow = 26/(26 + 34 + 18 + 22) * 50

Evaluate

Yellow = 13

Hence, the number of times she should expect to pull a yellow marble is 13

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To find the length of border needed to put around a rectangular room, you can follow these steps:

Measure the length and width of the room using a tape measure or ruler. Let's say the length is L and the width is W.

Determine the type and width of the border you want to put around the room. Let's say you want to use a wallpaper border that is 6 inches wide.

Calculate the length of the border needed for the top and bottom of the room.

This can be done by adding the width of the room to twice the width of the border. So the length of the top and bottom borders would be:

Length of top/bottom borders = 2(W + 6 inches)

Calculate the length of the border needed for the left and right sides of the room. This can be done by adding the length of the room to twice the width of the border. So the length of the left and right borders would be:

Length of left/right borders = 2(L + 6 inches)

Add up the length of all four borders to get the total length of border needed to put around the room:

Total length of border = 2(W + 6 inches) + 2(L + 6 inches)

Simplifying the above equation, we get:

Total length of border = 2L + 2W + 24 inches

So the total length of border needed to put around the room is 2L + 2W + 24 inches.

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Numerator: e^(1 + ln ∞) * (1/∞) = e^(1 + ∞) * 0 = 0, Denominator: 1 + e^∞ = ∞. So, the limit of the expression is: lim (x→∞) [e^(1 + ln x) / ln (1 + e^x)] = 0/∞ = 0

To find the limit of the given function, let's first rewrite the terms using the provided limit notation:

lim (x→∞) [e^(1 + ln x) / ln (1 + e^x)]

To solve this limit, we will apply L'Hôpital's rule, which states that if the limit has the form 0/0 or ∞/∞, we can find the limit by taking the derivative of the numerator and denominator with respect to x:

Numerator: d(e^(1 + ln x))/dx = e^(1 + ln x) * d(1 + ln x)/dx = e^(1 + ln x) * (1/x)
Denominator: d(ln(1 + e^x))/dx = (1/(1 + e^x)) * d(e^x)/dx = (1/(1 + e^x)) * e^x

Now, we will find the limit of the new expression:

lim (x→∞) [(e^(1 + ln x) * (1/x)) / ((1/(1 + e^x)) * e^x)]

Simplify the expression by canceling out the e^x terms:

lim (x→∞) [(e^(1 + ln x) * (1/x)) / (1 + e^x)]

Now, let's substitute x→∞:

Numerator: e^(1 + ln ∞) * (1/∞) = e^(1 + ∞) * 0 = 0
Denominator: 1 + e^∞ = ∞

So, the limit of the expression is:

lim (x→∞) [e^(1 + ln x) / ln (1 + e^x)] = 0/∞ = 0

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The volume of the cylinder after the rotation of rectangle is V = 12π units³ = 37.68 units³

Given data ,

Let the width of the rectangle be w = 2 units

Let the length of the rectangle be l = 3 units

Now , on rotating a rectangle , we get a cylinder

And , the radius of the cylinder = 2 units

And , the height of the cylinder = 3 units

Now , Volume of Cylinder = πr²h

On simplifying , we get

V = π ( 2 )² ( 3 )

V = 12π units³

V = 37.68 units³

Hence , the volume of cylinder is V = 37.68 units³

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To find the equation of the plane, we first need to find two vectors that lie on the plane. We can do this by taking the differences between the three given points:

$\vec{v_1} = \begin{pmatrix}6 \\ 0 \\ 3\end{pmatrix} - \begin{pmatrix}0 \\ 0 \\ 0\end{pmatrix} = \begin{pmatrix}6 \\ 0 \\ 3\end{pmatrix}$

$\vec{v_2} = \begin{pmatrix}-3 \\ -1 \\ 5\end{pmatrix} - \begin{pmatrix}0 \\ 0 \\ 0\end{pmatrix} = \begin{pmatrix}-3 \\ -1 \\ 5\end{pmatrix}$

Now we can find the normal vector to the plane by taking the cross product of these two vectors:

$\vec{n} = \vec{v_1} \times \vec{v_2} = \begin{pmatrix}6 \\ 0 \\ 3\end{pmatrix} \times \begin{pmatrix}-3 \\ -1 \\ 5\end{pmatrix} = \begin{pmatrix}3 \\ -27 \\ 6\end{pmatrix}$

Next, we can use the point-normal form of the equation of a plane:

$(\vec{r} - \vec{a}) \cdot \vec{n} = 0$

where $\vec{a}$ is a point on the plane and $\vec{n}$ is the normal vector.

We can choose any of the three given points as $\vec{a}$. Let's use $(0, 0, 0)$:

$(\begin{pmatrix}x \\ y \\ z\end{pmatrix} - \begin{pmatrix}0 \\ 0 \\ 0\end{pmatrix}) \cdot \begin{pmatrix}3 \\ -27 \\ 6\end{pmatrix} = 0$

Simplifying, we get:

$3x - 27y + 6z = 0$

This is the equation of the plane.
To find the equation of the plane passing through points (0, 0, 0), (6, 0, 3), and (-3, -1, 5), first find two vectors in the plane and then compute their cross product to obtain the normal vector of the plane. Finally, use the normal vector and a point on the plane to find the equation of the plane.

Vectors in the plane:
V1 = (6, 0, 3) - (0, 0, 0) = (6, 0, 3)
V2 = (-3, -1, 5) - (0, 0, 0) = (-3, -1, 5)

Cross product (normal vector N):
N = V1 x V2 = (0*(-5) - 3*(-1), 3*(-5) - 6*5, 6*(-1) - 0*(-3))
N = (3, -15, -6)

Equation of the plane using the normal vector and a point on the plane (0, 0, 0):
3x - 15y - 6z = 0

So, the equation of the plane is 3x - 15y - 6z = 0.

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Answer:

Recall 5%=.05 as a decimal. Then multiply 140(.05)=7 to get how many centimeters he grew. Add 140+7=147 to get his current height.

The volume of the oblique cylinder whose base and height is given would be = 9,646.08 m³. That is option B.

To calculate the volume of a cylinder, the formula that should be used is given as follows:

Volume of a cylinder = πr²h

π = 3.14

R = diameter/2 = 16/2 = 8m

Height = 8²+48² (using the Pythagorean formula)

= 64+2304

=√ 2368

= 48.66cm³

The volume of the cylinder = 3.14 × 8×8×48.66

= 9,646.08 m³

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Answer:

x^9√x

Step-by-step explanation:

About 10,676 gallons of paint were used to paint the 157 newly built homes in the subdivision, assuming each house required exactly 68 gallons of paint and 13 paint brushes.

The statement problem states that there are 157 newly built homes in a subdivision, and that 68 gallons of paint and 13 paint brushes were used for each house. This means that each house required 68 gallons of paint and 13 paint brushes.

To find the total amount of paint used for all 157 houses, we need to multiply the amount of paint used per house (68 gallons) by the number of houses (157):

Total amount of paint = 68 gallons/house x 157 houses

Total amount of paint = 10,676 gallons

Therefore, approximately 10,676 gallons of paint were used for the 157 newly built homes in the subdivision.

It's worth noting that this calculation assumes that each house required exactly 68 gallons of paint and 13 paint brushes. In reality, there may be some variation in the amount of paint and brushes used for each house, so the actual total may be slightly different.

However, this calculation provides a reasonable estimate of the total amount of paint used

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The analogy that best represents the bold letters for each question is related to relationships and cross-sections.

Some analogies are given below:

Explanation: The relationship between happy and sad is that they are opposite emotions.

Similarly, up and down are opposite directions, so the analogy holds.

Explanation: The relationship between a cat and a kitten is that a kitten is a young cat.

Similarly, a puppy is a young dog, so the analogy holds.

Explanation: The relationship between circle and sphere is that a circle is a two-dimensional shape, while a sphere is a three-dimensional shape that has a circular cross-section.

Similarly, a square is a two-dimensional shape, while a cube is a three-dimensional shape that has a square cross-section, so the analogy holds.

Explanation: The relationship between the oven and baking is that an oven is a tool used to bake food.

Similarly, a grill is a tool used to grill food, so the analogy holds.

Explanation: The relationship between mother and father is that they are the parents of a child.

Similarly, a daughter and a son are the children of their parents, so the analogy holds.

Explanation: The relationship between a book and a chapter is that a book is divided into chapters.

Similarly, a play is divided into acts, so the analogy holds.

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If x² + bx - 9 is factorable, then the possible values for b are -6 and 6.

To factor x² + bx - 9, we need to find two numbers that multiply to -9 and add up to b. We can write this as (x + a)(x + b) = x² + bx - 9. Since the coefficient of x² is 1, the two numbers that multiply to -9 must add up to the coefficient of x, which is b. We can find the factor pairs of -9 to see which ones add up to b:

-1 and 9 add up to 8

-3 and 3 add up to 0

-9 and 1 add up to -8

3 and -3 add up to 0

1 and -9 add up to -8

9 and -1 add up to 8

Only -6 and 6 add up to b, so the possible values for b are -6 and 6. Therefore, x² - 6x - 9 and x² + 6x - 9 are both factorable.

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