Simplify the expression.

(3.65u − 11) − (−5 + 8.7u)

12.35u + (−6)
−5.05u + (−16)
−5.05u + (−6)
12.35u + (−16)

Answer:

7 weeks

Step-by-step explanation:

Jasmine=$10

Nat=$11

10+11=$22 each week

135/22=6.14

at least 7 weeks

Leo is approximately 13.928 km away from the starting point.

Given that Leo walked 7 km south and then 12 km east, we need to determine the distance from the starting point,

To determine the distance from the starting point, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the distance Leo walked south forms one side of a right triangle, and the distance he walked east forms the other side. The distance from the starting point will be the length of the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance from the starting point as follows:

Distance² = (7 km)² + (12 km)²

Distance² = 49 km² + 144 km²

Distance² = 193 km²

Taking the square root of both sides gives us:

Distance = √(193)

Distance ≈ 13.928 km

Therefore, Leo is approximately 13.928 km away from the starting point.

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Complete question =

Leo walk 7km south then 12km east. How far is he from the starting point?

Answer:

13×n =234

n=234÷13

n=18

18 is ans

Answer: I believe -2 is the answer

Step-by-step explanation: To solve for the function over an interval, you need to know the equation of the function. If you have the equation, you can plug in the values of the interval into the equation to find the corresponding y-values. For example, if the function is y = 2x + 1 and the interval is [0,3], you can plug in x = 0 and x = 3 to find the corresponding y-values and get the ordered pairs (0,1) and (3,7).

Step-by-step explanation:

Let the coordinates of the left endpoint of the line segment be (x1, y1) and the coordinates of the right endpoint be (x2, y2). Let the point dividing the line segment be (x, y). Then the distance between the left endpoint and (x, y) is mx/(m+n) and the distance between (x, y) and the right endpoint is nx/(m+n).

Using the distance formula, we have:

\(distance \: between \: (x1, y1) \: and \: (x, y) = \sqrt{((x - x1)^2 + (y - y1)^2)} = \frac{mx}{(m+n)} \)

\(distance \: between \: (x, y) \: and \: (x2, y2) = \sqrt{((x2 - x)^2 + (y2 - y)^2)} = \frac{nx}{(m+n)} \)

Squaring both equations, we get:

\((x - x1)^2 + (y - y1)^2 = \frac{mx}{(m+n)^2}\)

\((x2 - x)^2 + (y2 - y)^2 = \frac{nx}{(m+n)^2}\)

Expanding the squares, we get:

\(x^2 - 2x1x + x1^2 + y^2 - 2y1y + y1^2 = \frac{mx}{(m+n)^2} \)

\(x^2 - 2x2x + x2^2 + y^2 - 2y2y + y2^2 = \frac{nx}{(m+n)^2}\)

Rearranging and simplifying, we get:

\(x = \frac{(mx2 + nx1)}{(m+n)} \: and \: y = \frac{(my2 + ny1)}{(m+n)}\)

Therefore, the point that divides the line segment into two parts so that the ratio of the lengths is m: n and the point is closer to the left endpoint is:

\((x, y) = \frac{(mx2 + nx1)}{(m+n)}, \frac{(my2 + ny1)}{(m+n)}\)

1. The general solution of the differential equation is:

y(x) = c₁x^(-3) + c₂x^(-2).

2.The general solution of the differential equation is:

y(x) = c₀x^(-1)ln(x) + c₁x^(-1),

To solve the given differential equations using the Frobenius method, we assume a power series solution of the form:

y(x) = ∑(n=0)^(∞) aₙx^(r+n),

where aₙ is the nth coefficient of the series, r is a constant, and x is the independent variable.

1. For the equation 2xy'' + 5y' + xy = 0:

Substituting the power series solution into the equation and simplifying, we obtain:

x²∑(n=0)^(∞) aₙ(r+n)(r+n-1)x^(r+n-2) + 5∑(n=0)^(∞) aₙ(r+n)x^(r+n-1) + x∑(n=0)^(∞) aₙx^(r+n) = 0.

Now, equating the coefficient of each power of x to zero, we get:

∑(n=0)^(∞) (aₙ(r+n)(r+n-1)x^(r+n-2) + 5aₙ(r+n)x^(r+n-1) + aₙx^(r+n)) = 0.

This gives us a recurrence relation:

aₙ(r+n)(r+n-1) + 5aₙ(r+n) + aₙ = 0.

Simplifying, we find:

aₙ[(r+n)² + 5(r+n) + 1] = 0.

Setting the coefficient to zero, we have:

(r+n)² + 5(r+n) + 1 = 0.

Solving this quadratic equation, we obtain the values of r:

r₁ = -3, r₂ = -2.

Therefore, the general solution of the differential equation is:

y(x) = c₁x^(-3) + c₂x^(-2),

where c₁ and c₂ are constants.

2. For the equation 4xy'' + (1/2)y' + y = 0:

Following the same steps as above, we obtain the recurrence relation:

aₙ[(r+n)(r+n-1) + (1/2)(r+n) + 1] = 0.

Simplifying, we find:

aₙ[(r+n)² + (3/2)(r+n) + 1] = 0.

Setting the coefficient to zero, we have:

(r+n)² + (3/2)(r+n) + 1 = 0.

Solving this quadratic equation, we find the value of r:

r = -1.

Therefore, the general solution of the differential equation is:

y(x) = c₀x^(-1)ln(x) + c₁x^(-1),

where c₀ and c₁ are constants.

These are the solutions obtained using the Frobenius method for the given differential equations.

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The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.

We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.

If angles QRP and PSQ are supplementary, their sum is 180°:

(2x + 20)° + 30° = 180°

Now, we can solve for x:

2x + 50 = 180

Subtract 50 from both sides:

2x = 130

Divide by 2:

x = 65

The graph could be the graph of f(x) which is the correct answer would be option (B).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

We are given the degree of the polynomial function f(x) to be 3; and

the roots of the equation f(x) to be 0 are -1, 0, and 4.

So we will put these values in the polynomial function of degree 3 to get:

f(x) = (x  -(-1))(x-0)(x-4)

f(x) = (x  + 1)x(x-4) = x³ - 3x² - 4x

According to this, the x-intercepts of this function on the graph will be:

(0, 0)

(-1, 0)

(4, 0)

So we will look for a graph that intercepts the x-axis at these points.

Therefore, the graph of the option (B) at the bottom right satisfies the conditions and is the graph of f(x).

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Answer:

90,747

Step-by-step explanation:

Clair delivery=79 per day

Total delivery per year=79×365 days

=28,835

Reagan delivery=2490 per month

Total delivery per year=2490×12 months

=29,880

Anthony delivery= 616 per week

Total delivery per year =616×52 weeks

=32,032

Total delivery altogether in a year=28,835+29,880+32,032

=90,747

Answer:

Step-by-step explanation:

Clair delivers 79 papers a day.

Assuming that there are 365 days in a year, it means that the number of newspapers that Clair delivers in a year is

79 × 365 = 28835

Reagan delivers 2490 papers a month. There are 12 months in a year. it means that the number of newspapers that Reagan delivers in a year is

12 × 2490 =29880

Anthony delivers 616 papers a week. Assuming that there are 52 weeks in a year, it means that the number of newspapers that Anthony delivers in a year is

52 × 616 = 32032

Therefore, the number of newspapers that they deliver altogether in a year is

28835 + 29880 + 32032 = 90747

The value of x + 3x - 4.2 when x = 5 is 15.8 and the first step is to substitute the value of x into the expression.

The first step when evaluating x + 3x - 4.2 when x = 5 is to substitute the value of x into the expression.

So, we substitute x = 5 into the expression:

5 + 3(5) - 4.2

Now, we can simplify the expression by performing the operations in order:

5 + 15 - 4.2

The first step is to perform the multiplication:

5 + 15 = 20

Now, we can subtract 4.2 from 20:

20 - 4.2 = 15.8

Therefore, the value of x + 3x - 4.2 when x = 5 is 15.8.

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If (x, y) represents the location of any point on the original square, the ordered pair which represents the coordinates of the corresponding point on the resulting square is: (0.4x, 0.4y).

In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either enlarge or reduce their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (0.4x, 0.4y)

Where:

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Complete Question:

A square with the perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.

If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?

answer choices

(0.4x, 0.4y)

(x + 20, y + 20)

(x + 0.4, y + 0.4)

(20x, 20y)

To find missing values in a triangle with angles between 0° and 90° (or 0 and π/2 radians), an appropriate triangle can be constructed based on the given information. Trigonometric relationships can then be applied to determine the missing values.

In a triangle with angles between 0° and 90° (or 0 and π/2 radians), we can construct an appropriate triangle by considering the information provided. The specific construction depends on the given values or missing values that need to be determined.

For example, if we are given the lengths of two sides of a right triangle, we can construct the triangle by drawing a base representing one side and constructing a perpendicular line segment representing the other side. The angle between these sides would be 90°, forming a right triangle.

Once the triangle is constructed, we can use trigonometric relationships such as sine, cosine, or tangent to find missing values. For instance, if we know the length of one side and the measure of one angle, we can use the sine or cosine function to find the lengths of other sides or angles.

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The height is changing by 0.5 each minute

The question implies that we calculate the slope of the table

From the table of values, we have the following points

(0, 150) and (1, 150.5)

The slope is then calculated as:

m = (y2 - y1)/(x2 -x1)

This gives

m = (150.5 - 150)/(1 - 0)

Evaluate

m = 0.5

Hence, the height is changing by 0.5 each minute

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Answer:

670.21 inches^3

Step-by-step explanation:

To find the volume of the spheres, all you need to know is the formula for the volume of a sphere, which you've included in your problem. From the problem, you also know that r = 2. From here, you calculate the volume of 1 of the spheres, which turns out to be:

V = 33.51032

Since there are 20 spheres in this box, you multiple the volume of a single sphere by 20 to get the total volume occupied by the spheres.

V = 20 * 33.51032

V = 670.2064

If you round to 2 decimal places, this becomes 670.21.

The values of f ◦ g is equal to (x + 2)^2 + 1 and g ◦ f is equal to x^2 + 3.

f ◦ g is the composition of functions f and g, which means that for any x in the domain of g, we substitute g(x) into f(x) to get f(g(x)) = (x + 2)^2 + 1.

g ◦ f is the composition of functions g and f, which means that for any x in the domain of f, we substitute f(x) into g(x) to get g(f(x)) = x^2 + 1 + 2

So f ◦ g = (x + 2)^2 + 1 and g ◦ f = x^2 + 3

It's important to notice that the order of the functions matters when composing them, f ◦ g is not the same as g ◦ f. The composition of functions is a fundamental concept in mathematics and it's used to chain multiple functions together to create a new function.

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The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.

The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.

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Answer:

I believe they are equal but I'm not for sure

The wildflowers in this population, the white allele is present in about 30% of the individuals, while the red allele is present in about 70% of the individuals.

The frequency of the white allele (CW) in the population can be determined by subtracting the frequency of the red allele (CR) from 1, since the frequencies of all alleles in a population must add up to 1.

So, the frequency of the white allele (CW) can be calculated as follows:

CW = 1 - CR

Given that the frequency of the red allele (CR) is p = 0.7, we can substitute this value into the equation:

CW = 1 - 0.7

  = 0.3

Therefore, the frequency of the white allele (CW) in this population is 0.3.

In genetic terms, alleles are alternative forms of a gene, and the frequencies of different alleles within a population can be used to study genetic variations. In this case, we are considering a population of wildflowers and examining the frequencies of the red allele (CR) and white allele (CW).

The total frequency of alleles in a population is always 1 since each individual carries two alleles (one from each parent). Therefore, the frequency of the white allele can be obtained by subtracting the frequency of the red allele (0.7 or 70%) from 1. This is because the sum of the frequencies of all alleles must equal 1.

By performing the calculation, we find that the frequency of the white allele in this population is 0.3 or 30%.

This means that among the wildflowers in this population, the white allele is present in about 30% of the individuals, while the red allele is present in about 70% of the individuals.

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Complete Question

Consider a population of wildflowers in which the frequency of the red allele CR is p = 0.7.

What is the frequency of the white allele (CW ) in this population?

Mr. Jackson will roll a 4 between 3 and 7 times, inclusive, out of his 30 rolls of a number cube is 0.332,

P(X=k) = \(C(n,k)\)\(* p^k * (1-p)^{n-k}\)

Where:

P(X=k) is the probability of getting k successes

n is the total number of trials

k is the number of successful trials

p is the probability of success in one trial

(1-p) is the probability of failure in one trial

here, in the question given that

n = 30 (total number of rolls)

k = 3, 4, 5, 6, or 7 (number of times rolling a 4)

p = 1/6 (probability of rolling a 4 on one roll)

Now we can calculate the probability of rolling a 4 between 3 and 7 times:

P(3<=X<=7) = P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)

now for  each value of k, we get:

\(P(X=3) = C(30,3) * (1/6)^3 * (5/6)^{27} = 0.182\)

\(P(X=4) = C(30,4) * (1/6)^4 * x)5/6)^{26} = 0.106\\P(X=5) = C(30,5) * (1/6)^5 * (5/6)^{25} = 0.035\\P(X=6) = C(30,6) * (1/6)^6 * (5/6)^{24} = 0.008\\P(X=7) = C(30,7) * (1/6)^7 * (5/6)^{23} = 0.001\)

Adding these probabilities , we get:

P(3<=X<=7) = 0.182 + 0.106 + 0.035 + 0.008 + 0.001 = 0.332

Therefore, the probability that Mr. Jackson will roll a 4 between 3 and 7 times, inclusive, out of his 30 rolls of a number cube is 0.332,

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Answer:

-8

Step-by-step explanation:

Hey there!

(1/2)(10) - (-12) - 25

= 1/2(10) - (-12) - 25

= 5 - (-12) - 25

= 5 + 12 - 25

= 17 - 25

= -8

Therefore, your answer is: -8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The amount of calling that will make the two plans cost the same is 400minutes of call and the cost is $70

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent the amount by y and the number of minutes by x

14 +0.14x = y equation 1

22 + 0.12 x = y equation 2

subtract equation 2 from 1

-8 + 0.02x = 0

0.02x = 8

x = 8/0.02

x= 400minutes

substitute 400 for x in equation 1

14+ 0.14(400) = y

y = 56+14

y = $70

therefore the subscribers will have to call for 400 minutes and the cost will be $70

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Answer:

Step-by-step explanation:

E is just that Vertex/Angle.

\(sin\) is a measure of an angle.

You should learn SOHCAHTOA

\(sin = opposite/hypotenuse\\cos(ine) = adjacent/hypotenuse\\tan(gent)=opposite/adjacent\)

The opposite side is relative to the angle.

In this case, the opposite of E is 20

The hypotenuse is 29

so,

\(sin(E)= \frac{20}{29}\)

The additional variable used to determine the values of the original variables in the ordered pair of a system of equations whose solution is an infinite number of solution is called a parameter.

A parameter is an unknown variable that is not included in the original equations of a system of equations.

In algebra, a system of equations is a collection of two or more equations involving the same set of variables. The solution to a system of equations is the point or points at which the equations are true. A system of equations can have a unique solution, no solution, or an infinite number of solutions.

When a system of equations has an infinite number of solutions, it means that the equations are dependent on each other. This means that one of the equations can be expressed in terms of the other equation. The solution to the system of equations is then written in terms of the parameter, which is the variable that is not included in the original equations.

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The pair of figures having same volume are:

a. The cylinder has a radius of 3 units and a height of 8 units ; The cone has a radius of 6 units and a height of 6 units.

b. The cone has a radius of 8 units and a height of 9 units ; The cylinder has a radius of 4 units and a height of 12 units.

c. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units ; The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

What is volume of a figure?

Volume is a unit of measurement for three-dimensional space. It is usually stated quantitatively in terms of a number of imperial or US-standard units as well as SI-derived units.

i. The cone has a radius of 4 units and a height of 12 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(4^{2} \frac{12}{3}\)

⇒ Volume = 64 π

⇒ Volume = 201 cubic units

ii. The rectangular prism has a length of 18 units, a width of 6 units, a height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 18 * 6 * 6

⇒ Volume = 648 cubic units

iii. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 16 * 6 * 6

⇒ Volume = 576 cubic units

iv. The cylinder has a radius of 3 units and a height of 8 units.

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π\(3^{2}\) * 8

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

v. The cone has a radius of 8 units and a height of 9 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(8^{2} \frac{9}{3}\)

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

vi. The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

⇒ Volume = length * width * height

⇒ Volume = 8 * 8 * 9

⇒ Volume = 576 cubic units

vii. The cylinder has a radius of 4 units and a height of 12 units.

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π\(4^{2}\) * 12

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

viii. The cone has a radius of 6 units and a height of 6 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(6^{2} \frac{6}{3}\)

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

Hence, three pairs have the same volume.

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The missing figures have been attached below.

Answer:

Step-by-step explanation:

for 1. The addition property of equality esssentially means that if you were to add/subtract the same value to both sides of the equation, the equation would remain equal. this would be associated with 3. since adding 12 to both sides would give x on one side and 16 on the other which is equal to x=16

for 2. "given" just means the problem, so it is the 1st option. it just means "given the problem..."

for 3. collectiing like terms is the addition of -5x +6x. since they are on the same side eof the equation, and are in the same measurements (of x) they can be combined to eqaul positive x, this is represented by option 2

For an exponential function  \(f(x) = 3^{-x}2\) as x goes to infinity, f(x) goes to zero.

We have been given an exponential function \(f(x) = 3^{-x}2\)

We need to check the end behavior of f(x) as x goes to infinity.

Consider,

\(\lim_{x \to \infty} f(x)\\\\= \lim_{x \to \infty} 3^{-x}2\\\\=2\times \lim_{x \to \infty} 3^{-x}\\\\=2\times 3^{-\infty}\\\\=2\times 0\\\\=0\)

This means, x \(\rightarrow\) infinity, f(x) goes to 0

As x goes to infinity, f(x) goes to zero.

Therefore, for an exponential function  \(f(x) = 3^{-x}2\) as x goes to infinity, f(x) goes to zero.

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The cost per pound of the cinnamon tea and of the spice tea would be = cinnamon $31.76 dollars per pound

spice $58.24 dollars per pound.

The volume of the cinnamon tea = 8 Ib

The volume of the spice tea = 6 Ib

The total volume of mixture = 14 Ib

The volume of the cinnamon tea = 4 Ib

The volume of the spice tea = 16 Ib

The total volume of mixture = 14 Ib

Add the both constitutes of the mixture;

Total volume of cinnamon tea in both mixture = 8+4 = 12 Ib.

Total volume of spice tea in both mixture = 6+16 = 22 Ib

Total weight of the both mixture = 12+22 = 34 Ib

Total price for both mixture = 38+52 = $90

The cost of cinnamon alone;

= 12/34 × 90/1

= 1080/34

= $31.76

The cost of spice tea = 90- 31.76 = $58.24.

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