. A retailer sold 10 packs of pens in 3 days. There were 48 pens in each pack. He sold twice as many pens on Sunday than on Monday. He sold 55 pens fewer on Tuesday than on Sunday. How many pens did the retailer sell on Monday?

The equation of an ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0) is \($\frac{x^2}{16}+\frac{y^2}{81}=1$$\).

As per the given data the ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

If the ellipse has its x-intercepts at points (4, 0) and (-4, 0) and y-intercepts at points (0, 9) and (0, -9), then it's symmetric across the y- axis and the x-axis.

The equation of an ellipse where the major axis 2a is greater than the minor 2b.

When 2b > 2a , then the equation becomes \($\frac{(y-h)^{2} }{b^{2} } + \frac{ (x-k)^{2} }{a^{2} } =1\)

Moreover h = 0 and k = 0 because the center is on the origin, so the equation becomes:

\($\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Moreover,

a = 4

b = 9

The equation of the such ellipse is

\($\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Hence, the equation of the ellipse is

\($\frac{x^2}{4^2}+\frac{y^2}{9^2}=1\)

\($\frac{x^2}{16}+\frac{y^2}{81}=1$$\)

Therefore the equation of an ellipse is  \($\frac{x^2}{16}+\frac{y^2}{81}=1$$\).

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Find the equation of the ellipse with the following properties. The ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

Answer:

Solution Given:

let pitcher which is small be S medium be M and large be L and barrel be B.

By question

6S+3M+1L= 1B...... eq. 1

2S+1M+3L=1B.......eq. 2

The difference in 2L from the first to the second is 4S and 2M

Therefore, each L=2S+M

In equation 2

2S+1M+3L=1B

replacing 2S +1M by L,we get

L+3L=1B

4L=1B

Therefore, 4 large pitcher is required

Answer:

4 large pitchers

Step-by-step explanation:

Define the variables:

Create two equations with the given information and the defined variables.

Equation 1

If the barrel can be filled with 6 small pitchers, 3 medium pitchers and 1 large pitchers:

⇒ 6x + 3y + z = b

Equation 2

If the barrel can be filled with 2 small pitchers, 1 medium pitcher and 3 large pitchers:

⇒ 2x + y + 3z = b

Substitute Equation 2 into Equation 1

⇒ 6x + 3y + z = 2x + y + 3z

Subtract 6x from both sides:

⇒ 3y + z = -4x + y + 3z

Subtract y from both sides:

⇒ 2y + z = -4x + 3z

Subtract z from both sides:

⇒ 2y = -4x + 2z

Divide both sides by 2:

⇒ y = -2x + z

Substitute the found expression for y into Equation 1:

⇒ 6x + 3(-2x + z) + z = b

⇒ 6x - 6x + 3z + z = b

⇒ 4z = b

Therefore, 4 large pitchers are needed to fill the barrel.

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Based on the given information, the researcher should not reject the null hypothesis if using an alpha level of 0.05.

In hypothesis testing, the null hypothesis is typically assumed to be true until there is sufficient evidence to reject it. To determine whether to reject the null hypothesis, researchers often compare the calculated F-value from an ANOVA test with the critical F-value. The critical F-value is based on the significance level (alpha) chosen for the test. In this case, the given F-value is 3.47 with degrees of freedom (3, 32), indicating that there are three groups and a total of 32 observations. To make a decision, the researcher needs to compare the calculated F-value to the critical F-value. If the calculated F-value is greater than the critical F-value, the null hypothesis is rejected. However, if the calculated F-value is less than or equal to the critical F-value, the null hypothesis is not rejected. Since the critical F-value corresponding to alpha = 0.05 is not provided in the question, we cannot determine whether the null hypothesis should be rejected.

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Answer:

no

Step-by-step explanation:

If the relationship is not one-to-one, it can still be regarded as a function if it is a many-one relationship, which means that the function has the same y value for a variety of x values.

This cannot be a function if we flip it around and make it a one-to-many relationship since the same input cannot produce various results.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

If the relation is not one-to-one it can still be considered as a function if it is a many-one function meaning for some different values of x the function has the same y value.

If we reverse this and make it a one to many it will not function as

same input can not lead to different outputs.

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Answer: 3x+6y > 21

Step-by-step explanation:

total distance kylie runs is the combined amount of loops from both paths. 3x represents however many loops she runs times the length of the short path. 6y represents however many loops she runs times the long path. Both of them have to add up and be greater than 21.

The true statements regarding the plot of normal distributions A and B are B has the larger mean, and B has the larger standard deviation; options 2 and 3.

A plot of a normal distribution is a bell-shaped curve that represents the probability distribution of a continuous random variable that follows a normal distribution.

The plot shows the frequency of occurrence of values of the variable, with the most common values near the mean and the less common values near the tails of the distribution.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the center of the distribution, while the standard deviation determines the spread or width of the distribution.

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PDF using the method of transformation for the given functions are:fY(y)=-1/2 e*-Y/2, for Y=-2in(X)and fY(y)=1/|y|×1/√(2π)× e-(lny)²/2, for Y=exand fY(y)=1/2√(2πy)× e-y/2, for Y=x².

Probability density function (PDF) is a function that describes the relative likelihood of a continuous random variable X taking on a particular value x. In order to derive the PDF using the method of transformation, the formula given below is used:

fY(y)=fX(x)|d/dyG-1(y)|

where X and Y are two random variables, and G is a function used for transforming X to Y.

Here, d/dyG-1(y) denotes the derivative of the inverse function of G with respect to y.

Now, we have to find the PDF of Y=-2in(X). Given, X is Uniform(0,1).We know that, X~Uniform(0,1).

Using the transformation formula, fY(y)=fX(x)|d/dyG-1(y)|

where G(x)= -2in(x) and G-1(y)= e*-y/2, we get

Y=G(X)= -2in(X).So, G-1(Y)= e*-Y/2.

To calculate the PDF of Y=-2in(X), we will first find the PDF of X.

PDF of X:fX(x)=1, for 0≤x≤1; otherwise 0.

From the transformation formula,

fY(y)=fX(x)|d/dyG-1(y)

By differentiating G-1(Y)= e*-Y/2

d/dyG-1(Y)=-1/2 e*-Y/2

Using the above formula,

fY(y)=fX(x)|d/dyG-1(y)|=-1/2 e*-Y/2×1=-1/2 e*-Y/2

The PDF of Y=-2in(X) is given by,

fY(y)=-1/2 e*-Y/2, where y>0.

Now, we have to find the PDF of Y=ex.

Given, X~N(0,1).

We know that, X~N(0,1).

Using the transformation formula,

fY(y)=fX(x)|d/dyG-1(y)

where G(x)=ex and G-1(y)= ln(y),

we get

Y=G(X)= ex.So, G-1(Y)= ln(Y).

To calculate the PDF of Y=ex, we will first find the PDF of X. PDF of X:fX(x)=1/√(2π)× e-x²/2

From the transformation formula,

fY(y)=fX(x)|d/dyG-1(y)|

By differentiating G-1(Y)= ln(Y), we get

d/dyG-1(Y)= 1/Y

Using the above formula,

fY(y)=fX(x)|d/dyG-1(y)|

=1/Y×1/√(2π)× e-(ln(y))²/2

=1/Y×1/√(2π)× e-(lny)²/2

=1/|y|×1/√(2π)× e-(lny)²/2

The PDF of Y=ex is given by,

fY(y)=1/|y|×1/√(2π)× e-(lny)²/2, where y≠0.

Now, we have to find the PDF of Y=x².

Given, X(x)= (x+1)/2.

We know that, X(x) is a function of X.

Let Y=x².

So, we need to find the PDF of Y. PDF of

Y:fY(y)=fX(x)|d/dyG-1(y)|where G(x)=x²

G-1(y)=√y.

Since, X(x)= (x+1)/2.

We can write X as

x=2X-1.

Now, G(X)=X², so

G(X(x))=[2X(x)-1]² = 4X²(x)-4X(x)+1

To calculate the PDF of Y=x², we will first find the PDF of X.

PDF of X:

fX(x)=1/√(2π)× e-x²/2

From the transformation formula

fY(y)=fX(x)|d/dyG-1(y)|

By differentiating G-1(Y)= √Y, we get

d/dyG-1(Y)= 1/2√y

Using the above formula,

fY(y)=fX(x)|d/dyG-1(y)|

=1/2√y×1/√(2π)× e-(√y)²/2

=1/2√(2πy)× e-y/2

The PDF of Y=x² is given by,

fY(y)=1/2√(2πy)× e-y/2, where y≥0.

Therefore, the PDF using the method of transformation for the given functions are:

fY(y)=-1/2 e*-Y/2,

for Y=-2in(X)and

fY(y)=1/|y|×1/√(2π)× e-(lny)²/2, for

Y=exand

fY(y)=1/2√(2πy)× e-y/2, for Y=x².

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Answer:

30

Step-by-step explanation:

Answer: B and D

Step-by-step explanation:

This is all!!!

Since A and C and E don't work.

1/5x*5 don't equal to 25

5-5 don't equal to 10 and 7*5 don't equal to 28

Answer:

D) 448.69

Step-by-step explanation:

i just looked the answer up ....

Answer:

line 1, the slope is positive. line 2,the slope is undefined. line 3, the slope is negative. line 4, the slope is zeeo

Answer:

1. Negative

2. Zero

3. Positive

4. Undefined

Step-by-step explanation:

1. The slope is going down, therefore negative

2. A slope that is horizontal is zero

3. The slope is going up, therefore positive

4. The slope is vertical, therefore undefined

I hope this helps!

Answer:

y=2x+5

y=-1.5x+9

3y=-2x+10

Step-by-step explanation:

2x+y=5

y=2x+5

9-y=1.5x

-y=1.5-9

y=-1.5x-9

2x=-3y+10

3y=-2x+10

The parametric equations for the motion of the particle in the xy plane that traces the counterclockwise ellipse are x = 6cos(t) and y = 4sin(t), where t is the parameter. The parameter interval for the motion is 0 ≤ t ≤ 2π.

To find the parametric equations for the counterclockwise motion of the particle along the given ellipse, we can start by parameterizing the ellipse equation  \(16x^2 + 9y^2 =\) 144. We divide both sides of the equation by 144 to normalize it, giving us  \((x^2/9) + (y^2/16\)) = 1. By comparing this equation with the standard form of an ellipse, we can see that a = 3 and b = 4.

We can then use the trigonometric parametrization of an ellipse to obtain the parametric equations. Letting x = acos(t) and y = bsin(t), where t is the parameter, we substitute the values for a and b, resulting in x = 6cos(t) and y = 4sin(t). These equations represent the motion of the particle along the ellipse.

Since we want the particle to trace the ellipse counterclockwise, we need to cover the full circumference of the ellipse. This corresponds to a parameter interval of 0 ≤ t ≤ 2π, which completes one full revolution around the unit circle. Therefore, the parametric equations for the motion of the particle are x = 6cos(t) and y = 4sin(t), with a parameter interval of 0 ≤ t ≤ 2π.

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Answer:29

Step-by-step explanation:$25-$46=-21

-21+50=29

\(\longrightarrow{\blue{ c. \: y.x = z }}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\( \frac{z}{y} = x\)

\(➺ \: z = y.x\)

\(➺ \: y.x = z\)

\(\bold{ \green{ \star{ \orange{Mystique35}}}}⋆\)

Option C : y . x = z is the correct answer.

We have the following expression -

\($\frac{z}{y} = x\)

We have to identify the true statements from the one's mentioned.

We have -

⇒ \($\theta = \theta_{o}\)(1 + R)

⇒ R =  \(\frac{\theta}{\theta_{o} } - 1\)

According to the question, we have -

\($\frac{z}{y} = x\)

We can rewrite it as -

x . y = z

Hence, Option C is the correct answer.

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To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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Answer:

236 for children and 288 for adults

Step-by-step explanation:

→ Set up 2 simultaneous equations

a + c = 524

2.25a + 1.25c = 891

→ Multiply 1st equation by 1.25

1.25a + 1.25c = 655

2.25a + 1.25c = 891

→ Minus from each other

-a = -236 ⇔ a = 236

→ Substitute into first equation

236 + c = 524 ⇔ c = 288

Answer:

You just add the 2 equations together and fill in the 3 into the x where the f(x) equation is located and 7 into the x where the g(x) equation is located. I hope this helps. Have a great rest if your day!

The turning point of a parabola, also called the vertex, is the point on the parabola where the graph changes from increasing to decreasing, or from decreasing to increasing.

What is parabola?

A parabola may be a formed plane curve wherever any point is at an equal distance from a fixed point (known because the focus) and from a fixed line that is known because the directrix.

Main BODY:

When a graph is rising from left to right, we say that it is increasing. When a graph is falling from left to right, we say that it is decreasing. The points at which this trend changes in a graph are called the turning points of the graph. Since a parabola has the shape of a U or an upside down U, it has exactly one turning point, which we can identify using the following facts:

Hence ,The turning point of a parabola is called the vertex.

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Answer:

B

Step-by-step explanation:

1/5 is larger than 1/10

hope this helps ^^

if it did pls mark brainliest if possible

The correct option is False. The standard formulas for the derivatives of sine and cosine are true when the angle is in radians. These formulas are derived based on the properties of the trigonometric functions in the context of radians. The derivatives of sine and cosine with respect to an angle measured in radians are as follows:

\(\[\frac{d}{dx}(\sin(x)) = \cos(x)\]\)

\(\[\frac{d}{dx}(\cos(x)) = -\sin(x)\]\)

If the angle is measured in degrees, these formulas would not hold true. To differentiate trigonometric functions when the angle is measured in degrees, conversion factors and additional adjustments would be necessary.

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Answer:

10.3 ft

Step-by-step explanation:

Perimeter of window

= perimeter of semicircle + length of diamdter

\( = \frac{1}{2} \pi \: d + d \\ \\ = \frac{1}{2} \times 3.14 \times 4 + 4 \\ \\ = 3.14 \times 2 + 4 \\ \\ = 6.28 + 4 \\ \\ = 10.28 \: ft

\)

= 10.3 ft

Answer:

=> 10.3

Step-by-step explanation:

Perimeter of window

= perimeter of semicircle + length of diameter

= 10.3 ft

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Answer:

16=x

Step-by-step explanation:

the two sides are equal, soo i set them equal to each other and add 18 to 16 then divide each side by two and get 16 = x

Answer:

b

Step-by-step explanation:

Answer:

the answer is 7.25

Step-by-step explanation:

Hope this helps :)

Answer: 5 to the power of 2

Step-by-step explanation:

Answer:

\(5^{2}\)

Step-by-step explanation:

\(\frac{5^4 x 5^3}{5^5} = \frac{5^7}{5^5} = 5^2\)

The total force on the bottom of the swimming pool is 3.35 × 10⁶ N.

The total force on the bottom of a swimming pool can be calculated by using the formula: F = pA, where F is the force, p is the pressure, and A is the area of the bottom of the pool.

First, we need to calculate the area of the bottom of the pool:
A = 28.5 m × 7.5 m = 213.75 m²

Next, we need to calculate the pressure on the bottom of the pool. The pressure is equal to the weight of the water above the bottom of the pool, which can be calculated by multiplying the density of water (ρ), the acceleration due to gravity (g), and the height of the water (h):
p = ρgh = (1000 kg/m³)(9.8 m/s²)(1.6 m) = 15680 N/m²

Finally, we can calculate the total force on the bottom of the pool by multiplying the pressure and the area:
F = pA = (15680 N/m²)(213.75 m²) = 3.35 × 10⁶ N

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Answer:60

Step-by-step explanation:

Answer:

45 hope this helps! If its wrong let me know!

I believe its 2

The Slope Is: m=2. The y -intercept Is: b=9 or (0,9)

We know that the slope intercept form equation is:

Now, let's compare both these equations.

We can clearly see that m = 2.

Hence, the slope is 2.

Hoped this helped.

\(BrainiacUser1357\)

The number of cruise passengers must there have been in 2017 is  26.7 million.

The term "percentage" comes from the Latin phrase "per centum," meaning "by the hundred." Percentages represent fractions with a denominator of 100. In other terms, it is the relationship between portion and whole in which the value of the whole is always assumed to be 100.

Now according to the question;

Let x represent the total number for cruise passengers during 2017.

In 2018, a 6.7% rise in x results in 28.5 million cruise passengers.

So, 106.7 % of x = 28.5

\(\begin{aligned}&\frac{106.7}{100} * x=28.5 \\&\frac{106.7 x}{100}=28.5\end{aligned}\)

Multiplying both sides by 100;

\(\begin{aligned}&\frac{106.7 x}{100} * 100=28.5 * 100 \\&106.7 x=2850\end{aligned}\)

Dividing both sides by 106.7;

\(\frac{106.7 x}{106.7}=\frac{2850}{106.7}\)

x = 26.7

Therefore, the number of cruise passengers in 2017 must have ranged from 26.7 million.

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