PLEASE HELP ME!!

Marcus got a job through an employment agency that charges a fee equal to 35% of the first four weeks' pay. The job pays $545 per week. How much does Marcus have to pay the employment agency?

A)$190.75
B)$763
C)$2,180
D)$1,144.50

The particular solution to the differential equation dy/da = (a+1)(y+1) with the initial condition y(4) = 3 is:

[tex]y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

What is differential equation?

Differential equations are used to model a wide range of phenomena in science, engineering, and mathematics, including physics, chemistry, biology, economics, and engineering.

Integration is a mathematical concept and technique used to find the integral of a function. The integral of a function is a measure of the area under the curve of the function, between two specified points on the x-axis.

To find the particular solution to the differential equation

[tex]\frac{dy}{da} = (a+1)(y+1)[/tex]

with the initial condition y(4) = 3, we can use separation of variables:

[tex]\frac{dy}{y+1} = (a+1) da[/tex]

Integrating both sides:

[tex]\int \frac{dy}{y+1} = \int (a+1) da\ln |y+1| = \frac{1}{2}a^2 + a + C_1, \text{ where } C_1 \text{ is an arbitrary constant of integration}[/tex]

Solving for y, we get:

[tex]y+1 = Ce^{\frac{1}{2}a^2 + a}[/tex]

where C is another arbitrary constant of integration. We can solve for C using the initial condition y(4) = 3:

[tex]3+1 = Ce^{\frac{1}{2}(4^2) + 4}C = 4e^{10}[/tex]

Substituting back, we get:

[tex]y+1 = 4e^{\frac{1}{2}a^2 + a + 10}y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

Therefore, the particular solution to the differential equation dy/da = (a+1)(y+1) with the initial condition y(4) = 3 is:

[tex]y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

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To make the larger sculpture with each linear dimension 75% greater, the artist needs to use 265.625% or 3.65625 times more clay than the original sculpture.

Let's assume that the original sculpture is a cube with side length x cm. Therefore, its volume would be x³ cm³.

To make the larger sculpture, each linear dimension needs to be increased by 75%, which means that each side length will become 1.75x cm. Thus, the new volume of the sculpture will be (1.75x)³ = 5.378125 x³ cm³.

To find the amount of clay required to make the larger sculpture, we need to find the ratio of the new volume to the original volume (5.378125 x³ cm³) / (x³ cm³) = 5.378125

This means that the artist needs to use 5.378125 times more clay than the original amount used to make the larger sculpture.

Therefore, to find the actual amount of clay needed, we multiply the original amount of clay by 5.378125: n cm³ x 5.378125 = 5.378125n cm³

So, the artist needs to use 3.65625 or 265.625% times more clay than the original sculpture to make the larger sculpture with each linear dimension 75% greater.

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Vertical angles are a pair of opposite angles formed by two intersecting lines. Vertical angles are congruent, meaning they have the same measure.

For example, if two lines intersect and form four angles, the two angles that are opposite each other  are vertical angles.

Adjacent angles are two angles that have a common vertex and a common side but do not overlap.

In other words, they share a ray or line segment, but they don't share any interior points.

Adjacent angles may or may not be congruent, depending on their measurement.

For example, if two angles are next to each other and share a vertex and a side, they are adjacent angles.

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Answer: 1280 in³

Step-by-step explanation:

Volume of 8 Soup Cans = Volume of box

V = l x b x h

V = 10 x 16 x 8

V = 1280

option (c) -No, 20 is NOT a reasonable solution because at x=-20,

an equation in which highest power of variable is always 1.

by solving the equation -6+2log(-5x)=-2 :

-6 + 2log(-5x) = -2

2log(-5x) = 4

log(-5x) = 2

-5x = 10^2

-5x = 100

x = -20

So, we found that x = -20 satisfies the equation. However, we need to check whether it is a reasonable solution or not.

Option C is correct: -20 is NOT a reasonable solution because at x = -20, the logarithm is not defined. The logarithm function is defined only for positive real numbers.

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Regenerate response

Answer:

3 one

Step-by-step explanation:

As a result, 2x + 10 is the expression that describes how long Malik will cook the sirloin for if the asparagus grills for x minutes.

So, 1+1 is a straightforward illustration of a statement. This expression has one action, two constant elements, and (addition). Another illustration is x3.

Let's start by using the given information to create expressions for each item:

Let's call the time it takes to grill the fish "f". Then, according to the problem, Malik grills the steak for "f + 10" minutes.

Grilling time for the seafood is double that of the vegetables. Thus, if it requires "x" minutes to grill asparagus, "2X" minutes are needed to grill salmon.

For "x + 1" minutes, and this is one minute more than he roasts the asparagus, Malik cooks the tomatoes that have been cut in half.

Using these expressions, we can create an equation for the time it takes to grill the steak:

Time to grill steak = Time to grill fish + 10

(f + 10) = 2x + 10

Therefore, if the asparagus cooks for x minutes, the phrase that denotes how long Malik will grill the sirloin is:

2x + 10

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If there are 30 students in the class, then the number of students who play soccer but do not play basket-ball are 13 students.

The total-students in the class is = 30 students,

The Number of students who play basketball is = (2/5) × 30 = 12,

The Number of students who play soccer is = (7/10) × 30 = 21,

⇒ Number of basketball players who also play soccer = (2/3) × 12 = 8,

So, out of the 21 students who play soccer, 8 also play basketball.

To find the number of students who play soccer but not basketball, we can subtract the number of students who play both from the total number of soccer players:

⇒ 21 - 8 = 13 students play soccer but not basketball.

Therefore, the required number of students are 13 students.

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Answer:

44

Step-by-step explanation:

come on now.

the perimeter is

2×length + 2×width = 110

width = 4×length

so, we use the second equation in the first :

2×length + 2×(4×length) = 110

2×length + 8×length = 110

10×length = 110

length = 110/10 = 11

width = 4×length = 4×11 = 44

The area of the triangles are:

Triangle 1: 144√3 unit²

Triangle 2: 64√3 unit²

The area of a triangle is given by the formula:

A = 1/2 * b * h

where b is the base and h is height of the triangle

1st triangle:

The vertical line divides the base into two right triangles.

Considering the right triangle to the right. Let L represent the length of the base. Thus, we can say:

tan 60° = (12√3)/L

√3 = (12√3)/L

(√3)L = 12√3

L = 12

Since b = 2* L

b = 24 units

A = 1/2 * 24 * 12√3

A = 144√3 unit²

2nd triangle:

cos 60° = L/16

0.5 = L/16

L = 0.5 * 16

L = 8 units

b = 2 * 8 = 16 units

h = √(16² - 8²)    (Pythagoras)

h = 8√3 units

A = 1/2 * 16 * 8√3

A = 64√3 unit²

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The probability that Betty is first in line or Mary is last in line is (n^2 - n - 1)/n(n-1), as a function of n.

We can approach this problem by considering the probability of the complementary event, i.e., the probability that neither Betty is first in line nor Mary is last in line, and then subtracting this probability from 1 to get the probability we want.

The total number of ways the n kids can line up is n!, since there are n choices for the first person in line, n-1 choices for the second person, and so on down to 1 choice for the last person.

The number of ways in which neither Betty is first in line nor Mary is last in line is (n-2)!, since there are (n-2) choices for the first person in line (excluding Betty and Mary), (n-3) choices for the second person, and so on down to 1 choice for the second-to-last person.

Therefore, the probability that neither Betty is first in line nor Mary is last in line is

[(n-2)! / n!] = 1/n(n-1)

The probability we want is

1 - 1/n(n-1) = (n^2 - n - 1)/n(n-1)

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The given question is incomplete, the complete question is:

A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. There are two kids in the class named Betty and Mary. The use of the word “or” in the description of the events, should be interpreted as the inclusive or. That is “A or B” means that A is true, B is true, or both A and B are true.

What is the probability that Betty is first in line or Mary is last in line as a function of n? Simplify your final expression as much as possible and include an explanation of how you calculated this probability.

The general solution of the given higher-order differential equation is y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2)).

To find the general solution of the given higher-order differential equation, first, let's rewrite the equation in a more standard form:
16y'''' + 16y'' + 4y = 0
Now, we'll solve this fourth-order linear homogeneous differential equation using the characteristic equation method.
1. Write the characteristic equation:
16r^4 + 16r^2 + 4 = 0
2. Divide the equation by 4 to simplify:
4r^4 + 4r^2 + 1 = 0
3. Apply a substitution: let t = r^2, then the equation becomes:
4t^2 + 4t + 1 = 0
4. Solve the quadratic equation for t using the quadratic formula:
t = (-B ± √(B^2 - 4AC)) / 2A
t = (-4 ± √(4^2 - 4(4)(1))) / (2 * 4)
t = (-4 ± √(16 - 16)) / 8
t = -4/8 = -1/2
5. Substitute back r^2 for t:
r^2 = -1/2
6. Solve for r:
r = ±√(-1/2)
r = ±(1/√2)i
7. Since the roots are complex conjugates, the general solution can be written as:
y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2))
where A and B are arbitrary constants determined by the initial conditions of the problem.

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Thus, the theoretical probability that Kelvin will select a red marble is 5/12.

Probability that is established using logic is known as theoretical probability.

Experimental probability is calculated based on the outcomes of numerous iterations of an experiment.

A probability is a number that falls between (and includes) 0 and 1.

If the likelihood of a situation E is represented by P(E), then:

Given:

Total marbles in  bag = 12

theoretical probability P(E) = favourable outcome / total outcome

P(red marble) = 5/12

Thus, the theoretical probability that Kelvin will select a red marble is 5/12.

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Answer:

20

Step-by-step explanation:

c²=a²+b²

c²=16²+12²

c²=400

c=20

Then answer and explanation is in the doc below.

The calculated value of n in the cube with the given properties is 5

If we cut the original cube into smaller cubes of side length 1 unit, then the total number of smaller cubes is given by the formula:

Total number of smaller cubes = (number of cubes along each edge of the original cube)^3 = n^3

So, we have

n^3 = 125

Take the cube root of both sides

n = 5

Hence, the value of n is 5

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The equation of the line parallel to the line shown in the graph passing through the point (-2, 3) is y = (2/3)x + (13/3) and the equation of the line perpendicular to the line shown in the graph passing through the point (-2, 3) is y = (-3/2)x.

What is slope?

The slope of a line passing through two points [tex](x_1, y_1) \: and \: (x_2, y_2)[/tex] is given by slope = [tex]\frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Given line passes through (0,-6) and (9,0)

To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope.

The slope of the line passing through (0,-6) and (9,0) can be found using the slope formula

slope = (change in y) / (change in x)

= (0 - (-6)) / (9 - 0)

= 6 / 9

= 2/3

Therefore, any line parallel to this line will also have a slope of 2/3.

We can now use the point-slope form of a line to find the equation of the line passing through (-2,3) with a slope of 2/3:

y - y1 = m(x - x1) (point-slope form)

where m is the slope, and (x1,y1) is a point on the line.

Substituting the values, we get:

y - 3 = (2/3)(x - (-2))

y - 3 = (2/3)(x + 2)

y - 3 = (2/3)x + (4/3)

y = (2/3)x + (4/3) + 3

y = (2/3)x + (13/3)

Therefore, the equation of the line parallel to the line passing through (0,-6) and (9,0) shown in the graph passing through the point (-2, 3) is y = (2/3)x + (13/3).

Using the points (0,-6) and (9,0), we can find the slope of the original line:

slope = (0 - (-6)) / (9 - 0) = 6/9 = 2/3

The slope of any line perpendicular to this line will be the negative reciprocal of this slope. So, the slope of the perpendicular line will be:

perpendicular slope = -1 / (2/3) = -3/2

Now we have the slope of the perpendicular line, and we also have a point it passes through: (-2, 3). We can use the point-slope form of a line to write the equation of the perpendicular line: y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is the point it passes through. Plugging in the values we have, we get:

y - 3 = (-3/2)(x - (-2))

Simplifying:

y - 3 = (-3/2)x - 3

y = (-3/2)x + 0

So the equation of the line perpendicular to the line passing through (0,-6) and (9,0), and passing through (-2, 3), is y = (-3/2)x.

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Step-by-step explanation:

a) from n = 1 to 4 this equals

      -4       -4 (2/3)      -4 (2/3)^2    - 4 (2/3)^3

=      -4       - 8/3          - 16/9          - 32/27

b) converges  ===  since  common ratio, r= (2/3) is less than 1

c ) sum =  -4 / ( 1-r) =   -4 / (1- 2/3 ) =  -12    

Answer:

[D] No, it is not a polynomial

Step-by-step explanation:

Polynomial- (Have)

Polynomial -(Can't/Don't)

There are 3 different types of polynomials:

As we can see based on the given;

5x²y⁴ + x√3 isn't a polynomial.

As a result, the answer is [D] No, it is not a polynomial

RevyBreeze

No , because 7 t shirts will cost 56 $ in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have $50 to buy T-shirts.

You can buy 3 T-shirts for $24.

                 You can buy 1 T-shirts for = 24/3 = 8

then 3 + 3 = 6 = 24 + 24 = 48 + 8 =  $56

so, you don't buy 7 t - shirts because you have only $56 .

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Answer:

  7. shifted right 8 units

  8. shifted left 4 and up 12 units

  9. shifted up 8 units

Step-by-step explanation:

You want to compare the given functions with p(x) = a(x -h)² +k and tell the value and effect of a, h, and k on the vertex.

In the equation for p(x) above, the value 'a' represents a vertical scale factor. It expands the graph vertically by the factor 'a'. If a < 0, the graph is reflected across the x-axis.

The values 'h' and 'k' in the equation for p(x) represent a right shift of the graph by 'h' units and a shift up by 'k' units. That is, the graph is translated by (h, k).

We have h = 8. The graph is shifted right 8 units.

We have (h, k) = (-4, 12). The graph is shifted left 4 units and up 12 units.

The values of the transformation parameters are a = -1/2 and k = 8. The vertical compression and reflection do not affect the vertex. The vertex is shifted up 8 units.

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

We can solve mathematical equations thanks to algebra's inherent characteristics. Take note that both addition and multiplication adhere to these characteristics.

This Order of Operations is a set of rules that enables mathematicians to solve issues uniformly. In this order:

using the algebraic formula:

(a² - b²) = (a + b)(a - b)

Given expression:

= 1 - 4sin²a

This can be written as:

= 1² - (2sina)²

Now, using identity:

= (1 + 2sina)(1 - 2sina)

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

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Complete question-

Express the given as the product of both values.

1 - 4sin²a

Answer: 216

Step-by-step explanation:

Brainliest pls:)

Answer:

20

Step-by-step explanation:

7 computers every 5 printers

7/5 = 28/x

Cross multiply

7x = 5*28

7x = 140

x = 20

Or in words,

7 times 4 is 28

5 times 4 is 20, which is your answer

Step-by-step explanation:

Remember that in order to find the volume you need to multiply 6.3 x 2.4 x 8.   I don't know for sure but if that is true the answer should be 120.96.  If they ask you to round I think you know how to do that.  

Hope this helps.

We know that the sum of the angles of a triangle is 180 degrees. So, we can find the value of angle LNM as follows:

m/L + m/M + m/N = 180 degrees

Substituting the given values, we get:

40 + 41 + m/N = 180

m/N = 99

Now, we can see that angle LNM is greater than both angles L and M. So, we can conclude that:

OMN > NL > LM

The experimental probability of choosing the name Maya is [tex]23/118[/tex].

and theoretical probability is of choosing name maya is [tex]1/5[/tex]

Probability is a measure of how likely an event is to occur. Many events are impossible to forecast with absolute accuracy. We can only anticipate the possibility of an event occurring, i.e. how probable they are to occur, using it. Probability can range from 0 to 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of all events in a sample space equals one.

According to the given information:

The experimental probability = [tex]\frac{Number of times an event occur}{ Total number of trials}[/tex]

Here total trials = 118,

The number of times the name maya has been chosen =23 times.

Therefore, experimental probability = [tex]\frac{23}{118}[/tex].

Theoretical probability = [tex]\frac{Number of favourable outcome}{Number of possible otucome}[/tex]

favourable outcome = 1 (Maya)

Possibleble outcome = 5 (Total no of Names in a hat)

And the theoretical possibility of the name maya has been chosen is [tex]1/5[/tex]

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Answer:

A

Step-by-step explanation:

Given:

r (radius) = 2 in

h (height) = 8 in

Find:

A (surface area) - ?

.

First, we have to find the lateral area of the cylinder:

[tex]a(lateral) = 2\pi \times r \times h = 2 \times π\times 2 \times 8 = 32\pi \: {in}^{2} [/tex]

Now, let's find the area of both bases (since a cylinder has 2 identical bases, we have to multiply the area of one base by 2):

[tex]a(2 \: bases) = 2 \times \pi {r}^{2} = 2 \times π\times {2}^{2} = 8\pi \: {in}^{2} [/tex]

In order to find the surface area, we have to add both lateral and bases' areas together:

[tex]a(surface) =32\pi + 8\pi = 40\pi \: {in}^{2} [/tex]