An art teacher has 8 gallons of paint. Her class uses 3/4 of the paint. The teacher divided the rest of the paint into 4 bottles. How much paint is in each bottle?

Answer:

A - x= -13

Step-by-step explanation:

x + 3 = -10

Step 1) Subtract 3 on both sides

Step 2) x = -13

The mean advertising spent for the automotive sector is $72,450 and for the department store sector is $67,650.

The standard deviation for the automotive sector is $10,808.16 and for the department store sector is $8,265.49.

The range of advertising spent for the automotive sector is $41,000 and for the department store sector is $30,800.

The interquartile range for the automotive sector is $14,250 and for the department store sector is $10,200.

Based on this sample and the answers to the previous questions, it can be seen that the automotive sector spends more on advertising on average than the department store sector. The automotive sector also has a larger standard deviation, indicating that there is more variation in the amount of advertising spent by companies in this sector.

The range of advertising spent for the automotive sector is also larger than that of the department store sector, indicating that there is a larger difference between the highest and lowest amounts spent on advertising in this sector.

The interquartile range for the automotive sector is also larger than that of the department store sector, indicating that there is a larger difference between the 25th and 75th percentiles of advertising spent in this sector.

Overall, these results suggest that there is more variation in the amount of advertising spent by companies in the automotive sector compared to the department store sector.

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Answer:

To find 3.5% of 21, we can convert 3.5% to a decimal by dividing by 100:

3.5% = 3.5/100 = 0.035

Then, we can multiply 0.035 by 21 to find the answer:

0.035 * 21 = 0.735

Therefore, 3.5% of 21 is 0.735.

0.735

because o.31 percent of 21 is 0.735

[tex]y = \frac{1}{2} x - 2[/tex]

the line of stars is parallel to the blue line, so the slope doesn't change.

if you take the star at x = 4, the y coordinate is zero. at this same point of x = 4, the y coordinate of the blue line is 6. So to get from 6 to 0, subtract 6. This means the whole line goes down 6 points, and so does the y intercept. 4-6 = -2, so the new y intercept is -2.

(1) The polynomial x^2 − 2 can be factored into (x + 5)(x − 5) in Z7[x].
(2) The polynomials x^3 − k, where k = 0, 1, 2, 3, 4, 5, 6, are all irreducible in Z7[x].

(3) The polynomial x^4 − 1 can be factored into (x − 1)(x + 1)(x^2 + 1) in Z7[x].

This is because 5 and −5 are both roots of the polynomial, since 5^2 ≡ 2 (mod 7) and (−5)^2 ≡ 2 (mod 7).

This is because none of them have any roots in Z7, which means they cannot be factored into lower degree polynomials.

For example, x^3 − 0 has no roots in Z7, since there is no integer x such that x^3 ≡ 0 (mod 7). Similarly, x^3 − 1 has no roots in Z7, since there is no integer x such that x^3 ≡ 1 (mod 7), and so on for the other values of k.

This is because 1, −1, and ±i are all roots of the polynomial, since 1^4 ≡ 1 (mod 7), (−1)^4 ≡ 1 (mod 7), and (±i)^4 ≡ 1 (mod 7). Therefore, x^4 − 1 = (x − 1)(x + 1)(x^2 + 1) in Z7[x].

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Answer:

False

Step-by-step explanation:

...............

A basis for the subspace  of R4 defined by the equation−2x1​−7x2​+2x3​−4x4​=0 is the set of vectors {(-7/2, 1, 0, 0), (1, 0, 1, 0), (-2, 0, 0, 1)}.

A basis for the subspace of −2x1​−7x2​+2x3​−4x4​=0 can be found by solving for one of the variables in terms of the others and then finding the general solution.

First, solve for x1 in terms of the other variables:
-2x1 = 7x2 - 2x3 + 4x4
x1 = (-7/2)x2 + x3 - 2x4

Now, the general solution can be written as:
(x1, x2, x3, x4) = (-7/2)x2 + x3 - 2x4, x2, x3, x4

This can be rewritten in terms of the free variables x2, x3, and x4:
(x1, x2, x3, x4) = x2(-7/2, 1, 0, 0) + x3(1, 0, 1, 0) + x4(-2, 0, 0, 1)

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The mass of the sample decays by a factor of 3/5 every 4.27 months.

In science, decay refers to the natural process of deterioration or breakdown of a substance over time. Decay can occur in many different contexts, such as the decay of radioactive materials, the decay of organic matter, and the decay of physical structures.

In radioactive decay, unstable atoms release energy and subatomic particles as they decay into more stable forms. This process occurs at a predictable rate, which can be used to determine the age of rocks and other materials.

In organic decay, biological matter breaks down into simpler compounds through the action of bacteria and other decomposers. This process is an essential part of the natural cycle of life and death, and it helps to recycle nutrients and other vital substances in ecosystems.

To find the time it takes for the mass to decay by a factor of 3/5, we can set up the following equation:

M(t) = (3/5)M(0)

[tex]120(\frac{625}{81} )^{t} = \frac{3}{5} \\\frac{625}{81}= \frac{3}{5}^{\frac{1}{t} } \\ln(\frac{625}{81})=ln(\frac{3}{5}^{\frac{1}{t} })\\[/tex]

[tex]t=\frac{ln(\frac{625}{81})}{ln(\frac{3}{5})} = 4.27months[/tex]

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Answer: No

Step-by-step explanation: because in order to find out if a triangle is a right triangle you use the Pythagorean Theron which is A squared+ B squared= C squared and since 8 times 8 is 64 and 12 times 12 is 144 if you add then it is 208 which is not equal to 225 to it isn’t a right triangle

Answer: No

Step-by-step explanation:

To test if this is a right triangle, let's test these side lengths with the Pythagorean Theorem.

a^2 + b^2 = c^2

c is the hypotenuse, the longest side of a right triangle.

a and b are the legs of the right triangle.

8²+12²=15²

64+144=225

208 ≠ 225

The IikeIihood that the hawk wiII first take a songbird and subsequentIy a rabbit is therefore (2/9) x (8/11) = 16/99, or roughIy 0.1616.

In mathematics, a percentage is a number or ratio that may be stated as a fraction of 100. Divide a number by the whole and multiply the result by 100 to calculate its percentage. As a result, the percentage represents a part per hundred. 100% is meant by the phrase %. The symbol "%" is used to indicate it.

The probability that a hawk will eat a songbird before a rabbit is calculated as the product of those probabilities.

Given that there are four songbirds with eight rabbits, the IikeIihood that a songbird wiII be consumed by a hawk is 4/(4+6+8) = 4/18 = 2/9.

Three songbirds & eight rabbits remain after the hawk consumes a songbird, hence the IikeIihood that the hawk wiII eat a rabbit next is 8/(3+8) = 8/11.

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x = 1 is 68

The polynomial function that satisfies the given conditions is f(x) = (x-3)(x-3i)(x-4)(x-4i) = x4 - 11x3 + 34x2 + 104x - 324. Graphically, this function has 4 real zeros at x = 3, 3i, 4, and 4i, and the function value at x = 1 is 68.

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The solution of the heat equation subject to the boundary and the initial conditions is u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt).

The heat equation with the given boundary conditions is:

∂u/∂t = k ∂^2u/∂x^2

where k is a constant. We can use separation of variables to solve this equation. Let:

u(x, t) = X(x)T(t)

Substituting this into the heat equation, we get:

X(x)T'(t) = k X''(x)T(t) / X(x)T(t)

Dividing both sides by X(x)T(t) and rearranging, we get:

X''(x)/X(x) = T'(t)/(kT(t))

The left-hand side depends only on x, while the right-hand side depends only on t. Since they are equal, they must be equal to a constant:

X''(x)/X(x) = -λ

T'(t)/(kT(t)) = λ

where λ is a constant. The boundary conditions u(0,t) = u(1,t) = 0 imply that X(0) = X(1) = 0. The general solution for X(x) is then:

X(x) = A sin(nπx)

where A is a constant and n is a positive integer. The eigenvalues λ are:

λ = -(nπ)^2

The general solution for T(t) is:

T(t) = B exp(-kλt)

where B is a constant. The solution for u(x, t) is then:

u(x, t) = Σ[ A_n sin(nπx) exp(-(nπ)^2 kt) ]

where the sum is taken over all positive integers n.

We can now use the initial condition u(x,0) = 4sin3πx+8sin6πx to determine the constants A_n. Since the solution only contains sine terms, we can use the Fourier sine series to expand the initial condition:

4sin3πx+8sin6πx = Σ[ A_n sin(nπx) ]

where the sum is taken over all positive odd integers for n = 3 and all positive even integers for n = 6. The coefficients A_n are:

A_3 = 4π/3

A_6 = 16π/6

Substituting these values into the solution for u(x, t), we get:

u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt)

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Answer:

8 small and 14 large is the answer

Step-by-step explanation:

Difference in the medians as a multiple of the IQR = 5.

The Interquartile Range (IQR) formula computes the median of a set of data. One of the smallest statistical measurements of dispersion is the interquartile range. The interquartile range refers to the spread between the upper and lower quartiles.

The interquartile range is defined as Upper Quartile - Lower Quartile.

According to the question,

Data set of Mount Vernon= 55, 60, 65, 70, 75, 80, 85, 90

Data set of Lakewood= 65, 70, 75, 80, 85

Data sets are already in ascending order.

Median for Mount Vernon = 70+75/2 = 77.5

Median for lower half of set= 55+60+65+70/4 = 62.5

Median for upper half of set= 75+80+85+90/4 = 82.5

IRQ for Mount Vernon = 82.5-62.5 = 20

Now similarly in case of Lakewood,

Median= 75.

Median for lower half of set = 65+70/2 = 67.5

Median for upper half of set = 80+85/2 = 82.5

IRQ = 82.5 - 67.5 = 15.

Hence, difference in IRQ = 20-15 = 5.

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The fund manager should invest $7.5 million in bonds and $27.5 million in mutual funds to maximize annual interest, and the maximum annual interest is given as  $2.595 million.

To solve this, we

Let x = amount invested in bonds and

y = amount invested in mutual funds.

We then can deduce the following constraints:

x + y ≤ 35 (total investment is at most $35 million)

x ≥ 5 (at least $5 million is invested in bonds)

y ≥ 20 (at least $20 million is invested in mutual funds)

100x + 200y ≤ 6000 (the total fees paid which cant exceed $6000)

Maximizing  the annual interest, which is given by:

0.06x + 0.09y

We will  use the method of Lagrange multipliers, to solve the optimization problems.

Let L(x, y, z) be the Lagrangian:

and we have that L(x, y, z) = 0.06x + 0.09y + z(x + y - 35) + μ(x - 5) + ν(y - 20) + ρ(100x + 200y - 6000)

We will have to take partial derivatives of L with respect to x, y, and z, and set them to be equals zero.

0.06 + z + μ + 100ρ = 0

0.09 + z + ν + 200ρ = 0

x + y - 35 = 0

Simplifying these equations, we have:

x = 7.5, y = 27.5, λ = -0.06, μ = 0, ν = 0, ρ = -0.02

0.06(7.5) + 0.09(27.5) = $2.595 million is the annual interest.

So then, It has been found that the fund manager should invest $7.5 million in bonds and $27.5 million in mutual funds to maximize annual interest, which is  $2.595 million.

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I - The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages: C. Problems in financial markets.

II - Consumers are very worried about the economy: B. Negative demand shift.

1 - The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages falls into the category of "Problems in financial markets" (C). This event can lead to a recession because it can cause a decrease in the wealth of households, leading to a decrease in consumer spending and a decrease in aggregate demand.

II - Consumers being very worried about the economy falls into the category of "Negative demand shift" (B). This event can lead to a recession because when consumers are worried about the economy, they tend to save more and spend less, leading to a decrease in aggregate demand. This decrease in demand can cause businesses to decrease production and lay off workers, leading to a decrease in income and further decrease in demand.

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Answer:

Step-by-step explanation:

The number of the students chose action movies, is 4

A survey is a list of questions aimed for extracting specific data from a particular group of people. Surveys may be conducted by phone, mail, via the internet, and also at street corners or in malls

Given that, a survey asked 1,200 students which movie genre was their favorite.

We need to find that how many students chose action movies,

There are 45 % of the students watched the same genre,

Therefore, the number of the students chose action movies, =

45 / 1200 x 100

= 3.75

≈ 4

Hence, the number of the students chose action movies, is 4

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To get the total area of the figure: 6 x 705 = 1725.9 ft².

What is area?

Area is a measure of the size of a two-dimensional surface, such as a region of land or a space in a building. It is typically measured in square units, such as square feet or square meters. Area can also be calculated for three-dimensional objects, such as a cube or other solid shape. Area is an important concept in mathematics and is used to measure the size of many different shapes.

The correct answer is A) 1725.9 ft². To find the area of the regular figure, calculate the area of one of the triangles, and then multiply this by 6 (the number of triangles in the figure). The area of a triangle is A = ½bh, where b is the base and h is the height. The base of the triangle is 19 ft and the height is 12.5 ft. Therefore, A = ½(19) (12.5) = 117.5 ft². Multiply this by 6 to get 6 x 117.5 = 705 ft. Finally, multiply this by the number of triangles in the figure, which is 6, to get the total area of the figure: 6 x 705 = 1725.9 ft².

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So the expression that shows how many glitter pens Lindsey puts in each goody bag is 24 divided by the number of goody bags, represented by "b".

How likely something is to happen can be determined using probability. For instance, while flipping a coin, there is a one in two chance of receiving heads because there is only one way to get a head and a total of two outcomes. the tail or the head. We set P(heads) = 12 in this case.

Let's represent the number of glitter pens Lindsey puts in each goody bag by the variable "p".

To find the value of "p", we can divide the total number of glitter pens by the number of goody bags:

p = 24 / b

So the expression that shows how many glitter pens Lindsey puts in each goody bag is 24 divided by the number of goody bags, represented by "b".

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Answer: (-35, 30)

Step-by-step explanation:

Since the scale factor is four, it denotes that it’s a positive dilation. The question is asking for 5 times the point. In other words, where would the point be if it was stretched out 5 times.

If you draw a line from the given to the QED, (-7, 6) to (-35, 30), then you’ll realize that the image is 5 times the original point.

K= (-7*5, 6*5)

Any number less than one means the point or shape is being compressed or made smaller.

Answer:

2.4.1. To calculate how many litres of fuel are needed to travel 400km, we need to use the given fuel consumption rate of 8L/100km:

Fuel consumed for 400km = (8/100) x 400 = 32 litres

Therefore, 32 litres of fuel are needed to travel 400km.

2.4.2. To calculate how far you can travel with 50L of fuel, we can rearrange the formula from part 2.4.1 to solve for distance:

distance = (fuel consumed / fuel consumption rate) x 100

Plugging in the values we have:

distance = (50 / 8) x 100 = 625 km

Therefore, with 50 litres of fuel, you can travel 625 km.

What fraction of the trip has Andre completed.

A fraction is a way of representing a part of a whole or a quantity that is not a whole number. It is a mathematical expression that represents a ratio of two numbers, where the number above the line (numerator) represents the part being considered, and the number below the line (denominator) represents the whole or the total number of parts. Fractions are usually written in the form a/b, where a is the numerator and b is the denominator.

Given that the entire road to be covered is  1 5/8 kilometers and so far Andre has walked 1/3 kilometer, the expression represents the fraction that has been covered.

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Missing parts;

Heathercain

01/24/2020

Mathematics

Middle School

answered • expert verified

3. Andre is walking from home to a festival that is 1 5\8 kilometers away. He takes a quick rest after walking 1\3 kilometers. In this situation, which question can be represented by the equation: ?× 1 5\8 = 1\3?

a. What fraction of the trip has Andre completed?

b. How many more kilometer does he have to walk to get to the festival?

c. What fraction of the trio is left.

d. How many kilometers is it from home to the festival and back home?

The baker will use 2.5 cups of flour.

Multiplication is a mathematical operation that involves combining two or more numbers to find their product or the total number of objects in equal groups. It is represented using the multiplication symbol (*) or a dot (·). For example, 2 * 3 = 6, which means that two groups of three objects will give you a total of six objects.

To solve this problem, we need to find the amount of flour required for each cupcake and cookie, and then multiply by the total number of cupcakes and cookies.

For the cupcakes:

1.5 cups of flour make 18 cupcakes

1 cup of flour will make 12 cupcakes (divide both sides by 1.5)

To make 30 cupcakes, we need 2.5 cups of flour (multiply both sides by 2.5)

For the cookies:

3 cups of flour make 36 cookies

1 cup of flour will make 12 cookies (divide both sides by 3)

To make 60 cookies, we need 5 cups of flour (multiply both sides by 5)

Therefore, to make 30 cupcakes and 60 cookies, the baker will need:

2.5 cups of flour for the cupcakes

5 cups of flour for the cookies

Total: 2.5 + 5 = 7 cups of flour

Therefore,  the baker will use 2.5 cups of flour.

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The mean is 389.875, the median is 333.5, and there is no mode for this set of numbers.

To find the mean, median, and mode for the set of numbers 244, 276, 114, 628, 572, 313, 354, 618, we will use the following steps:

1. Mean: The mean is the average of the numbers. To find the mean, we add up all the numbers and divide by the number of numbers in the set.

Mean = (244 + 276 + 114 + 628 + 572 + 313 + 354 + 618) / 8 = 3119 / 8 = 389.875

2. Median: The median is the middle number in the set when the numbers are arranged in ascending order. If there is an even number of numbers, the median is the average of the two middle numbers.

First, we arrange the numbers in ascending order: 114, 244, 276, 313, 354, 572, 618, 628
Since there are 8 numbers, the median is the average of the 4th and 5th numbers: (313 + 354) / 2 = 333.5

3. Mode: The mode is the number that appears most frequently in the set. If there are multiple numbers that appear the same number of times, they are all considered the mode.

In this set, there are no numbers that appear more than once, so there is no mode.

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Step-by-step explanation:

this represents a trigonometric triangle (right-angled) inside an imaginary circle.

imagine the triangle is turned 90° counterclockwise, so that A is the bottom left vertex, B is the bottom right vertex.

then x is the angle (40°) defining radius of the circumscribing circle.

remember, sine is the up/down leg, cosine is the left/right leg. and in a larger circle they are all multiplied by the radius.

so,

4 = cos(40) × x

x = 4 / cos(40) = 5.221629157... ≈ 5.22

Answer:

Sin A = [tex]\frac{12}{13}[/tex] ; Cos A = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

The sine of a given angle is  [tex]\frac{opposite}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length opposite to angle A is 24, and the hypotenuse is 26. This gives  [tex]\frac{24}{26} = 12/13[/tex].

The cosine of a given angle is   [tex]\frac{adjacent}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length adjacent to angle A is 10, and the hypotenuse is 26. This gives  [tex]\frac{10}{26} = 5/13[/tex].

Answer:

8cfct on cypur574 6th 9

Step-by-step explanation:

f5g uh yo h tu g fn l dl uge ser k

The Noah’s mean is 87, median is 85.5, and mode is 85.

The Gabriel’s mean is 87.17, median is 86, and mode is 86.

The solution has been obtained by using measures of central tendency.

A central tendency measure seeks to define the core value of a data collection in order to characterise it. The metrics of central tendency are mean, median, and mode.

Noah’s scores: 84, 85, 85, 86, 90, 92

Mean = (84 + 85 + 85 + 86 + 90 + 92) / 6

Mean = 522 / 6

Mean = 87

Median = (85 + 86) / 2

Median = 85.5

Mode = 85

Gabriel’s scores: 82, 85, 86, 86, 90, 94

Mean = (82 + 85 + 86 + 86 + 90 + 94) / 6

Mean = 523 / 6

Mean = 87.17

Median = (86 + 86) / 2

Median = 86

Mode = 86

Hence, the mean, median and mode have been obtained.

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Recall definitions:

Use the triangle to define each ratio.

Use Pythagorean theorem:

Proved

Proved

Answer:

245

Step-by-step explanation: