. Henri and Talia are mixing paint for an art project. They mixed pliters of red paint, 0.6 liters of blue paint, and p– 0.4 liters of white paint. They then divided the mixture evenly into 2 jars. If each jar contains 2.4 liters of paint, how much red paint did they use?

The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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Answer:

X=-18

Step-by-step explanation:

2x-6x+9x+25=150+10x-35

combine like terms

5x+25=115+10x

move Xs to one side

25=115+5x

sebstract 115 from 25

-90=5x

divide -90 by 5

x=-18

Answer:

50 is the answer to this question

Answer:

50

Step-by-step explanation:

Well, you're having trouble with how it's supposed to be 50 right? So I suggest breaking it down a little bit.

As you see:

1100 ÷ 22

1100 and 22 are both divisible by 2 so if we divide both numbers by 2 you get:

550 ÷ 11

now try solving from there!!

If you still don't get it here:

firstly 11 goes into 5 zero times so put nothing

next does 11 go into 55? Yes! it does so how many times does it go into 55?

well let's see: 11 + 11 + 11 + 11 + 11 = 55

now if we count how many 11s there are there is 5! so then you put:

5_

now lets see the next number is 0 and does 11 go into 0? Nope! so we just put:

50 and that is your answer!!

The center of the circle represented by the equation r = sin(θ) is at (0, 0) and the radius is 1.

The equation r = sin(θ) represents a circle in polar coordinates. In this form, r represents the distance from the origin to a point on the circle and θ represents the angle between the positive x-axis and the line connecting the origin to the point on the circle.

To find the center of the circle, we look for the point where r = 0, which is the origin (0, 0).

To find the radius of the circle, we look for the maximum value of r, which occurs when sin(θ) = 1. This happens when θ = π/2 or θ = 3π/2. At these values of θ, r = sin(π/2) = sin(3π/2) = 1, so the radius of the circle is 1.

Therefore, the center of the circle is at (0, 0) and the radius is 1.

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On solving the provided question, we can say that  - he need 56  answers he need to get correct if he want a grade of 80 percent on a test with 70 questions

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56

Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.

\(70-56=14\)

So, the maximum number of questions you may omit is 14.

As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.

20% of 70 \(= .20)(70) = 14\)

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Given that

The equation is -x²(x − 3)(x + 2)(x - 1) = 0 and we have to find the correct option for its domain and range.

Explanation -

For the domain,

All the real numbers are the domain for the polynomial.

For the range,

First, we will find the minimum value of the function and then the maximum.

But here the degree of the polynomial is odd.

Degree = Highest power of x = 5

And for the polynomial having an odd degree the range is all the real numbers.

So the range will also be real numbers.

Two sides of triangle are equal triangle ABC acute scalene triangle. Option B right choice.

The type of triangle ABC can use the Pythagorean to check if it is a right triangle and the distance formula to check if it is an isosceles or scalene triangle.

Using the distance formula can find the lengths of the three sides of triangle ABC:

AB = √((6-0)² + (0-0)²) = 6

BC = √((3-6)² + (7-0)²) = √(58)

AC = √((3-0)² + (7-0)²) = √(58)

BC=AC ≠AB , and the triangle is a acute scalene triangle.

The triangle is a right triangle can use the Pythagorean:

If the triangle is a right triangle, then one of the sides must be the hypotenuse and the other two sides must be the legs.

Let's assume that AC is the hypotenuse and AB and BC are the legs. Then, we have:

(AC)² = (AB)² + (BC)²

Substituting the values we found earlier, we have:

(√58)² = 6² + (BC)²

58 = 36 + (BC)²

(BC)² = 22

22 is not a perfect square so (BC)² cannot be equal to the difference between two perfect squares.

Triangle ABC is not a right triangle.

Option B right choice.

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To find the volume between the planes 4x + 3y + z = 8 and 5x + 5y + z = 8, and above the region defined by x + y ≤ 2, x ≥ 0, and y ≥ 0, we can set up a triple integral over the specified region.

The volume can be calculated as follows:  ∭V dV

Where V represents the volume and dV represents the differential volume element. To define the limits of integration, we need to determine the boundaries of the region in the xy-plane and the range of z values.

In the xy-plane, the boundaries are determined by the inequalities x + y ≤ 2, x ≥ 0, and y ≥ 0. These inequalities define a triangle in the first quadrant with vertices at (0, 0), (2, 0), and (0, 2). Therefore, the limits of integration for x and y are:

0 ≤ x ≤ 2

0 ≤ y ≤ 2 - x

For the z values, we need to consider the intersection of the two planes 4x + 3y + z = 8 and 5x + 5y + z = 8. By solving these equations simultaneously, we find that z = 0. Therefore, the limits of integration for z are:

0 ≤ z ≤ 8 - 4x - 3y

Putting it all together, the triple integral for the volume is:

\(\int\ \int\ \int V dV = \int\limits^2_0 \int\limits^{2-x}_0 \int\limits^{8-4x-3y}_0dz dy dx\)

This represents the volume between the planes 4x + 3y + z = 8 and 5x + 5y + z = 8, and above the region defined by x + y ≤ 2, x ≥ 0, and y ≥ 0

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Answer:

C) g(x) = f(x) + 4

Step-by-step explanation:

A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A

-anumber would slide the function DOWN instead.

As for the other answers:

A) the 3multiplied in front is a vertical STRETCH.

D) the 1/2 multiplied in front is a vertical shrink (smash)

B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.

Answer:

f(-2) = 6

Step-by-step explanation:

f(-2) means find the value of the function when x = -2.

The function f(x)  is  4-x  when x= -2.

f(-2) = 4 - (-2)

        4+2

          6

f(-2) = 6

The mean and median of the given data values are 15.8333 (approx) and 16.5 (approx) respectively.

Given data values = 21 , 20, 17 , 9 , 16 , 12 and

We are to compute the mean and median of the given data values.

For calculating mean of the given data values we need to use the formula given below:

Mean = (Sum of all data values) / (Total number of data values)

Or, Mean = ∑ xi / n,

where xi = ith data value,

n = total number of data values

Now, Sum of all data values = 21 + 20 + 17 + 9 + 16 + 12

= 95

Therefore, Mean = 95 / 6

= 15.8333 (approx)

Hence, the mean of the given data values is 15.8333 (approx).

Next, we need to calculate the median of the given data values.

The median is defined as the middlemost value of a data set or the average of the middle two values for a data set with an even number of values.

To find the median:

We need to first arrange the data values in ascending or descending order.

So, arranging the given data values in ascending order, we get: 9, 12, 16, 17, 20, 21

Next, to find the median we need to see if the number of data values is odd or even.

Since the total number of data values is even, we need to find the mean of the middle two data values.

Hence, the median of the given data values is (16 + 17) / 2 = 16.5 (approx).

Conclusion:

Therefore, the mean and median of the given data values are 15.8333 (approx) and 16.5 (approx) respectively.

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Miguel will need approximately 636.76 cubic inches more air to completely fill the ball.

To help you with your question, we'll first determine the total volume of the ball using the given radius and then calculate the additional air needed to fill it completely. The ball has a radius of 7 inches.

To find its total volume, we use the formula for the volume of a sphere: V = (4/3) * π * r³.

Plugging in the radius, we get V = (4/3) * π * (7³) ≈ 1436.76 cubic inches.

Miguel has already put 800 cubic inches of air into the ball

To find out how much more air is needed, subtract the air already inside from the total volume:

1436.76 - 800 = 636.76 cubic inches.

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Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

A slope field, which displays the slope of a differential equation along specific vertical and horizontal axes of the x-y plane, can be used to estimate the tangent slope at a particular point on a curve, where the curve is one possible solution to the differential equation.

Here,

For figure 1 slope field=

\(\frac{dy}{dx}=\frac{-17x-2y}{y}\)

For figure 2 slope field=

\(\frac{dy}{dx} = xy-3\\\)

For figure 1 a solution passing through the point (0,-1)

therefore,

slope=

\(\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(0)-2(-1)}{-1}=-2\)

so slope comes out to be negative

For figure 1 a solution passing through the point (-2,2)

\(\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(-2)-2(2)}{-1}=-30\)

so slope comes out to be negative

For the slope field in figure 2. a solution passing through the point (1.-3)

\(\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(1*-3)-3=-6\)

so slope comes out to be negative

\(\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(0*4)-3=-3\)

so slope comes out to be negative.

Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

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Answer:

\(n \leq \frac{21k - W}{3}\)

Step-by-step explanation:

W ≤ 21k-3n

⇒ W + 3n ≤ 21k

⇒ 3n ≤ 21k - W

⇒ \(n \leq \frac{21k - W}{3}\)

The distance from tire race to the rope climb is; 80 yards

The formula for the distance between two coordinates is;

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

We are given the coordinates of tire race and rope climb as;

Tire race = (-40, -30)

Rope climb = (40, -30)

Thus distance between tire race and the rope climb is;

D = √[(-30 - (-30))² + (40 - (-40))²]

D = √(80²)

D = 80 yards

Thus, we conclude that is the distance from tire race to the rope climb.

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Answer:

I think its like a cartoon or something like that

https://hbomax-images.warnermediacdn.com/images/GXyniGAhmEcJZOgEAAABz/tileburnedin?size=1280x720&format=jpeg&partner=hbomaxcom&productCode=hbomax&host=artist.api.cdn.hbo.com&w=1200

there image I think

Step-by-step explanation:

(a)

\( \frac{b + x}{3} = \frac{b - x}{4} \\ 4b + 4x = 3b - 3x \\ b = - 7x\)

(b)

\(p = \frac{y}{1 + y \\ } \\ p + py = y \\ y - py = p \\ y = \frac{p}{1 - p} \)

(c)

\( \frac{1}{a} = \frac{1}{b} - \frac{1}{c} \\ \frac{1}{c } = \frac{1}{b} - \frac{1}{a} \\ \frac{1}{c} = \frac{a - b}{ab} \\ c = \frac{ab}{a - b} \)

Answer:

Dividing or Subtracting

Step-by-step explanation:

Answer:

multiply

Step-by-step explanation:

When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide.

We have 792 ways to pick five students for the student council from a group of twelve candidates.

We will use the combination formula, which is nCr = n! / r!(n - r)! is find  number of ways to pick five students.

In this case, we want to choose 5 students from 12 candidates:

12C5 = 12! / 5!(12 - 5)!

12C5 = (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1)

12C5 = 95040 / 120

12C5 = 792

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Answer:

$27,840 is the correct answer

Step-by-step explanation:

hope this helps!

Answer:

after a 4% decrease, you would have $27,260 left

Step-by-step explanation:

The vector-valued function at each given value of t  is :

a) i

b)  1/√2i+9/√2j

c)−cos(θ)i+9sin(θ)j

d)  −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

The given problem is related to trigonometric Ratios of Angle, where there are six trigonometric ratios sine, cosine, tangent, cotangent, cosecant, and secant. Since it is given that a  vector valued function:

r(t)= cos(t)i + 9 sin(t)j

r(t)=cos(t)i+9sin(t)j

so ,  r(0)=  cos(0)i+9sin(0)j = i ( sine cos0 =1 and sin0 =0)

r(π/4) =  cos(0)i+4sin(0)j = cos(π/4)i+9sin(π/4)j

           = 1/√2i+9/√2j

r(θ−π)= cos(θ−π)i+9sin(θ−π)j= −cos(θ)i+9sin(θ)j

(π/6+△t)−r(π/6)= cos(π/6+△t)i+9sin(π/6+△t)j−cos(π/6)i−9sin(π/6)j

=  cos(π/6+△t)i−cos(π/6)i+9sin(π/6+△t)j−9sin(π/6)j

= −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

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Evaluate (If possible) the vector-valued function at each given value of t. (If an answer does not exist, enter DNE.)

r(t)=cos(t)i+9sin(t)jr(t)

a)r(0)=?

b)r(π/4)=?

c)r(θ−π)=?

d)r(π/6+△t)−r(π/6)=?

The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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Answer:

a:

Felipe: y = 80x + 510

Melissa: y = 60x + 590

b:

80x + 510 = 60x + 590

(simplifies to x = 4)

Answer:

16

Step-by-step explanation:

=3+25−9÷3(4)

=28−9÷3(4)

=28−(3)(4)

=28−12

=16

I hope this helps. Have a good day!!

Answer:

180-45=135

2x-5=135

2x=140

x=70

Step-by-step explanation:

The eigenvalue of the state-space coefficient matrix [-1] is λ = -1.

To calculate the eigenvalue of the state-space coefficient matrix [-₁, we need to use the methods demonstrated in the lecture notes. Let's proceed with the calculation.

To find the eigenvalues, we need to solve the characteristic equation |A - λI| = 0, where A is the coefficient matrix, λ is the eigenvalue, and I is the identity matrix.

The coefficient matrix is:

[-1]

Subtracting λ from the diagonal elements, the characteristic equation becomes:

|[-₁ - λ]| = 0

Expanding the determinant, we have:

(-₁ - λ)(- λ) - ( - ₁)(0) = 0

Simplifying further:

(λ + ₁)(λ) = 0

The eigenvalues are the values of λ that satisfy this equation. From the equation, we can see that there are two eigenvalues: λ = -₁ and λ = 0.

Now, we need to determine the value of ₁ based on the given conditions. Since the eigenvalues are real and different, we take the smaller absolute value, which is 0. Therefore, ₁ = 0.

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To find the probability distribution for X, the number of dollars won, we need to determine the probabilities of winning different amounts of money.

Let's consider the sides of the die. We have numbers 1, 2, 3, 4, 5, and 6. The probability of each side showing is proportional to the number on that side.

To calculate the proportionality constant, we need to find the sum of the numbers on the die: 1 + 2 + 3 + 4 + 5 + 6 = 21.

Now, let's calculate the probability of winning $1. Since the die is loaded, the probability of rolling a 1 is 1/21. Therefore, the probability of winning $1 is 1/21.

Similarly, the probability of winning $2 is 2/21 (rolling a 2), $3 is 3/21 (rolling a 3), $4 is 4/21 (rolling a 4), $5 is 5/21 (rolling a 5), and $6 is 6/21 (rolling a 6).

In conclusion, the probability distribution for X, the number of dollars won, is as follows:
- Probability of winning $1: 1/21
- Probability of winning $2: 2/21
- Probability of winning $3: 3/21
- Probability of winning $4: 4/21
- Probability of winning $5: 5/21
- Probability of winning $6: 6/21

This distribution represents the probabilities of winning different amounts of money when rolling the loaded die.

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The expression that can be used to convert 80 US dollars (USD) to Australian dollars (AUD) is:

80 USD × 1.0343 AUD / 1 USD

Since 80 USD is the amount of USD we want to convert and (1.0343 AUD / 1 USD) is the exchange rate between USD and AUD.

To convert 80 USD to AUD, we can use the following expression:

80 USD × 1.0343 AUD / 1 USD

Thus, 82.74 AUD is the amount of AUD you will receive after the conversion.

Therefore, the expression that can be used to convert 80 US dollars (USD) to Australian dollars (AUD) is 80 USD × 1.0343 AUD / 1 USD

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Answer:

y = x - 6

y = x - 2

Step-by-step explanation:

In order to find the equation for each line, we have to first find the slope.

\(m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

m = \(\frac{7-6}{1-0}\)

m = \(\frac{1}{1}\) = 1

Now, we have to find the y-intersect, b. In order to do that, plug y and x into the equation and solve for b.

y = m(x - b)

6 = 1(0 - b)

6 = -b

b = -6

After finding b, plug everything into the equation.

y = m(x - b)

y = x - 6

m = \(\frac{0-(-6)}{2-(-4)}\)

m = \(\frac{6}{6}\) = 1

Now, we have to find the y-intersect, b. In order to do that, plug y and x into the equation and solve for b.

y = m(x - b)

0 = 1(2 - b)

0 = 2 - b

-2 = -b

b = 2

After finding b, plug everything into the equation.

y = m(x - b)

y = x - 2

hope it helps :)

mark brainliest!!! (put in a lot of effort and time!)