Can someone please help me answer these 2 questions with a full explanation of how you got the answer so I can do the rest myself?

Mr. Frank can fertilize 53 plants with 1.01 kilograms of fertilizer, assuming each plant gets 94 mg of fertilizer two times a year.

To determine the number of plants Mr. Frank can fertilize with 1.01 kilograms of fertilizer, we need to convert the given amount of fertilizer from kilograms to milligrams. Since there are 1,000 milligrams in one gram and 1,000 grams in one kilogram, we can calculate that 1.01 kilograms is equal to 1,010,000 milligrams of fertilizer.

Next, we need to determine how much fertilizer each plant will need. Since each plant needs 94 mg of fertilizer two times a year, the total amount of fertilizer needed per plant per year is 188 mg (94 mg x 2).

Therefore, to calculate the total number of plants Mr. Frank can fertilize with 1.01 kilograms of fertilizer, we need to divide the total amount of fertilizer by the amount needed per plant per year:

1,010,000 mg ÷ 188 mg/year = 5,372.34 plants

However, since we can't have a fraction of a plant, we need to round down to the nearest whole number to get the final answer:

Number of plants = 5,372 (rounded down from 5,372.34)

Therefore, Mr. Frank can fertilize 5,372 plants with 1.01 kilograms of fertilizer.

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Answer:

1) 27/2 2) 8pi 3) 48 4) 16+2pi

Step-by-step explanation:

1) The length of the triangle is 9 (found by finding the distance between (-5,-3) and (4,-3)) and the height is 3 (found by finding the distance between (1,0) and (1,-3)). The area of a triangle is 1/2 (length times height) which in this case is 27/2.

2) The shape is a semicircle, so the area is 1/2 pi*r^2.

1/2 * pi * r^2=8pi

3) B*H=8*6=48

4) The figure is a semicircle and a square.

The area of the semicircle is 1/2 * pi * r^2=2pi

The area of the square is b*h=4*4=16

The area is 16+2pi.

Answer:

You want to leave a 15% tip on a meal that cost $20. 0.15 x $20.00=$3.00. So, the amount of tip you are going to leave is $3.00.

Step-by-step explanation:

Answer $3.00

Step-by-step explanation:

Answer:

-40

Step-by-step explanation:

Let me know if you have any more questions

\(\huge\text{Hey there!}\)

\(\mathsf{8 = 2x + 88}\\\mathsf{2x + 88 = 8}\\\large\text{Subtract 88 to both sides}\\\mathsf{2x + 88 - 88 = 8 - 88}\\\large\text{Simplify it:}\\\mathsf{2x = 8 - 88}\\\mathsf{2x = -80}\\\large\text{Divide 2 to both sides:}\\\mathsf{\dfrac{2x}{2} = \dfrac{-80}{2}}\\\large\text{Simplify it:}\\\mathsf{x = \dfrac{-80}{2}}\\\\\mathsf{x = -40}\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{x = -40}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

I think it's not right.

Step-by-step explanation:

The right one is PTA, because you have to go to the right order.

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

The required general solution of the differential equation y" - 2y – 3y = e^(-t) + 1 is given by the expression,

y = A e^(3t) + B e^(-t) + C t e^(-t) + Ate^(-t) + B

We are required to find the general solution of the differential equation y" - 2y – 3y = e^(-t) + 1 using the Annihilator Method.

The given differential equation is, y" - 2y – 3y = e^(-t) + 1

The characteristic equation of the given differential equation is, r² - 2r - 3 = 0(r - 3)(r + 1) = 0r₁ = 3 and r₂ = -1

Now, we will consider the following cases:

Case I: When the right-hand side has a term of the form f(t) = e^(rt), then we take the annihilator as (D - r).

∴ The annihilator for e^(-t) is (D + 1).

Case II: When the right-hand side has a constant term, then we take the annihilator as D.

∴ The annihilator for 1 is D⁰.

Now, we will write the annihilators for the given differential equation. The annihilator for y" is (D - 3)(D + 1)

The annihilator for 2y is 2D⁰

The annihilator for 3y is 3D⁰

The annihilator for e^(-t) is (D + 1)

The annihilator for 1 is D⁰

Using the Annihilator Method, we have, (D - 3)(D + 1)(D + 1) [y"] + 2 [D⁰] y - 3 [D⁰] y = 0(D - 3)(D + 1) [D + 1] y" + 2 y = 3 y - e^(-t)

Now, we will solve the homogeneous equation, (D - 3)(D + 1) [D + 1] y" + 2 y = 3 y(D - 3)(D + 1) (r - 3) (r + 1) (r + 1) yh = A e^(3t) + B e^(-t) + C t e^(-t)

Now, we will find the particular integral, yₚ, for e^(-t) + 1. The particular integral for e^(-t) is, yp₁ = Ate^(-t)

And, the particular integral for 1 is, yp₂ = B

Therefore, the particular integral yₚ = yp₁ + yp₂ = Ate^(-t) + B

The general solution of the given differential equation is, y = yh + yₚ = A e^(3t) + B e^(-t) + C t e^(-t) + Ate^(-t) + B

Therefore, the required general solution of the differential equation y" - 2y – 3y = e^(-t) + 1 is given by the expression, y = A e^(3t) + B e^(-t) + C t e^(-t) + Ate^(-t) + B

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Answer:

0.0389

Step-by-step explanation:

(0.35) / (9) = 0.389

or,

35/100 x 1/9 = 35/900 = 0.0389

Therefore , the solution of the given problem of triangle comes out to be curve C has a measure of 70 degrees.

If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

Sum of Triangle Angles According to a theorem, a triangle's internal angles always add up to 180 degrees.

We are aware that angle B in the trapezoid is 50 degrees and angle A is 60 degrees. As a result, we can apply the Triangle Angle Sum Theorem to determine the size of angle C:

Angle A +Angles B + C = 180 degrees.

With the known numbers substituted, we obtain:

Angle C:  60° + 50°+60° = 180°

By condensing the left half, we obtain:

Angle C = 180-110 degrees

By taking away 110 degrees from each side, we arrive at:

C = 70-degree slope.

As a result, curve C has a measure of 70 degrees.

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Using a system of equations, the quantity of Type A coffee that Trey's Coffee Shop blended with Type B coffee was 78 pounds.

A system of equations or simultaneous equations is two or more equations solved concurrently, simultaneously, or at the same time.

Unit Cost Per Pound:

Type A coffee = $5.80

Type B coffee = $4.25

The total quantity of pounds of the blend = 142 pounds

The total cost of 142 pounds = $724.40

Let the number of Type A coffee = x

Let the number of Type B coffee = y

x + y = 142 ... Equation 1

5.8x + 4.25y = 724.40 ... Equation 2

Multiply Equation 1 by 4.25:

4.25x + 4.25y = 603.5 ... Equation 3

Subtract Equation 3 from Equation 2:

5.8x + 4.25y = 724.40

-

4.25x + 4.25y = 603.5

1.55x = 120.9

x = 78

Substitute x = 78 in either equation:

x + y = 142

78 + y = 142

y = 64

Thus, 78 pounds of Type A coffee was used for the mixture.

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The dot plot has 43 dots.

The dot plot has 10 dots to the left of the center and 1 dot to the right of the center.

The center of the data set is 6.

This can be solved using the concept of dot plot.

For relatively small data sets with values falling into a handful of discrete bins, a dot plot, also known as a dot chart, is a sort of straightforward histogram-like display used in statistics. To create a dot plot, count the data points that fall into each bin and then draw a stack of dots that is that many dots high for each bin. The form and distribution of sample data may be seen using dot plots, which are particularly helpful when comparing frequency distributions. The frequency distribution of a dataset shows how frequently certain values occur. Dot plots display the same kinds of data as histograms.

From the given figure it is clear that 1 has 6 dots, 2 has 5 dots, 3 has 4 dots, 4 has 2 dots, 5 has 3 dots, and 6 has 2 dots. It means the data set is:

1,6,2,5,3,4,4,2,5,3,6,2

Total number of observations = 43

The dot plot has 43 dots.

Median:

43 is an odd number, so the median of the data is:

Median = {(n+1)/2} / 2

Median = 11

The 11th term of the data is 6, therefore the median of the data is 6.

The dot plot has 10 dots to the left of the center and 1 dot to the right of the center.

The center of the data set is 6.

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Answer:

\( \sqrt{11} \)

Step-by-step explanation:

c2=a2+b2

that's how

Answer: 135 degrees

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

sum of triangle angles = 180

then JLK =. 180 -(70+65) = 180 - 135 = 45

then JLK = 45

since JLM = 180

then KLM = 180 - 45 = 135

The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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Answer:

Inequality Form:

h > 6

Interval Notation:

( 6 , ∞ )

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The equation of the tangent line to the curve at the point (x, y) = (-1.77, 3.13) is y - 3.13 = -cot(2) (x + 1.77).

To find the equation of the line tangent to the curve at the point defined by the given value of t, we need to calculate the first derivative dy/dx and evaluate it at t = 2.

First, let's find dy/dx by differentiating y = 4sin(t) with respect to x:

dx/dt = -4sin(t) (differentiating x = 4cos(t) with respect to t)

dy/dt = 4cos(t) (differentiating y = 4sin(t) with respect to t)

Now, we can calculate dy/dx using the chain rule:

dy/dx = (dy/dt) / (dx/dt) = (4cos(t)) / (-4sin(t)) = -cot(t)

To evaluate dy/dx at t = 2, substitute t = 2 into the expression:

dy/dx = -cot(2)

Now, we have the slope of the tangent line at the point (x, y) = (4cos(t), 4sin(t)) when t = 2.

To find the equation of the tangent line, we need a point on the line. Since the point is defined by t = 2, we can substitute t = 2 into the parametric equations:

x = 4cos(2) = -1.77

y = 4sin(2) = 3.13

Now, we have a point on the tangent line, which is (-1.77, 3.13), and the slope of the tangent line is -cot(2).

Using the point-slope form of a line, the equation of the tangent line is:

y - 3.13 = -cot(2) (x + 1.77)

Simplifying the equation gives the final result.

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Given:

The equation of a line is

\(y=\dfrac{3}{4}x-11\)

Line v passes through point (6,6) and it is perpendicular to the given line.

Line w passes through point (-6,10) and it is parallel to the line v.

To find:

The equation in slope intercept form of line w.

Solution:

Slope intercept form of a line is

\(y=mx+b\)         ...(i)

where, m is slope and b is y-intercept.

We have,

\(y=\dfrac{3}{4}x-11\)      ...(ii)

On comparing (i) and (ii), we get

\(m=\dfrac{3}{4}\)

So, slope of given line is \(\dfrac{3}{4}\).

Product of slopes of two perpendicular lines is -1.

\(m_1\times m_2=-1\)

\(\dfrac{3}{4}\times m_2=-1\)

\(m_2=-\dfrac{4}{3}\)

Line w is perpendicular to the given line. So, the slope of line w is \(-\dfrac{4}{3}\).

Slopes of parallel line are equal.

Line v is parallel to line w. So, slope of line v is also \(-\dfrac{4}{3}\).

Slope of line v is \(-\dfrac{4}{3}\) and it passes thorugh (-6,10). So, the equation of line v is

\(y-y_1=m(x-x_1)\)

where, m is slope.

\(y-10=-\dfrac{4}{3}(x-(-6))\)

\(y-10=-\dfrac{4}{3}(x+6)\)

\(y-10=-\dfrac{4}{3}x-\dfrac{4}{3}(6)\)

\(y-10=-\dfrac{4}{3}x-8\)

Adding 10 on both sides, we get

\(y=-\dfrac{4}{3}x-8+10\)

\(y=-\dfrac{4}{3}x+2\)

Therefore the equation of line v is \(y=-\dfrac{4}{3}x+2\).

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The number of the seat in the 18th row will be 113.

Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as

\(\rm a_n = a_1 + (n - 1)d\)

Denise is designing the seating arrangement for a concert, an outdoor theater.

To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats.

Then Denise plans the rest of the seating by solving for how many seats are in row 18.

Then the number of the seat in the 18th row will be given as

a₁ = 11

d = 6

n = 18

Then we have

a₁₈ = 11 + (18 – 1) x 6

a₁₈ = 11 + 17 × 6

a₁₈ = 11 + 102

a₁₈ = 113

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y = (At + B) e^(rt)

where A = -r/2 and B = 3r/2, as expected.

When the two roots of the characteristic equation are both equal to r, we say that the roots are equal or repeated. In this case, the general solution to the corresponding second order linear homogeneous ODE with constant coefficients is of the form:

y = (At + B) e^(rt)

where A and B are constants to be determined by the initial or boundary conditions.

However, the form given in the question, (at+b)âe^rt, is not correct. The â symbol is not standard notation for mathematical expressions and its meaning is unclear. It is possible that it was intended to represent a coefficient or parameter, but without more information, we cannot determine its value or significance.

To see why the correct form of the solution is y = (At + B) e^(rt), we can use the method of undetermined coefficients. Suppose that y = e^(rt) is a solution to the homogeneous ODE with repeated roots. Then, we can try the solution y = (At + B) e^(rt) and see if it satisfies the ODE.

Taking the first and second derivatives of y, we get:

y' = A e^(rt) + r(At + B) e^(rt) = (Ar + r(At + B)) e^(rt)

y'' = A r e^(rt) + r^2(At + B) e^(rt) = (Ar^2 + 2rAt + r^2B) e^(rt)

Substituting y, y', and y'' into the homogeneous ODE with repeated roots, we get:

(Ar^2 + 2rAt + r^2B) e^(rt) = 0

Since e^(rt) is never zero, we can divide both sides by e^(rt) to get:

Ar^2 + 2rAt + r^2B = 0

This is a linear equation in A and B, and we can solve for them by using the initial or boundary conditions. For example, if we are given that y(0) = 1 and y'(0) = 0, we have:

y(0) = A e^(0) + B e^(0) = A + B = 1

y'(0) = (Ar + rB) e^(0) + A e^(0) = Ar + A = 0

Solving this system of equations, we get:

A = -r/2, B = 3r/2

Therefore, the general solution to the homogeneous ODE with repeated roots is:

y = (-rt/2 + 3r/2) e^(rt)

which can be rewritten as:

y = (At + B) e^(rt)

where A = -r/2 and B = 3r/2, as expected.

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The probability that a 25-year-old person from this group prefers biking is: 68/229.

The total number of people in the survey between the ages of 23 and 27 is 229. The number of people who prefer biking in this group is 68.

Therefore, the probability that a 25-year-old person from this group prefers biking is: 68/229

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor (GCF), which is 1:

68/229 = 68/229

So the probability that a 25-year-old person from this group prefers biking is 68/229.

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Answer:

Step-by-step explanation:

First calculate the amount of notebooks and textbook

Cost of 2 notebooks = 2 *8.75

                                  = $ 17.5

Cost of 1 textbook = $ 74.95

Total cost = 17.5 + 74.95

                 = $ 92.45

Tax = 7% of total cost

      = 0.07 * 92.45

      = $ 6.47

Total cost = 92.45 +6.47

                 = $ 98.92

Jaleesa bought 2 notebooks for dollar 8. 75 and 1 textbook for dollar 74.95 . If the sales tax was 7\({\%}\),

what was the total cost of Jaleesa's purchases?

In this question we are provided with the cost of each textbook and notebook and it is given that Jaleesa bought 2 notebook and 1 textbook and the sale tax was.7% and we are asked to calculate the total cost of Jaleesa's purchases

First we will calculate the cost of two notebooks

Rate of 1 notebook = $8.75

Cost of 2 notebook = $(8.75 × 2) = $17.5

Now, we will calculate the total cost

Total cost of 2 notebook and 1 textbook = $(17.5 + 74.95) = $92.45

Sales tax was 7%

7% of $92.45

→ \(\dfrac{7}{100}\) × 93.45

→ $6.47

Total cost = $(92.45 + 6.47) = $98.92.

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

The fractions of students that attended the dance is 11/19

From the question, we have the following parameters that can be used in our computation:

Number of students = 380

Number of students in attendance = 220

The fraction is then represented as

Fraction = Number of students in attendance/Number of students

Substitute the known values in the above equation, so, we have the following representation

Fraction = 220/380

Simplify

Fraction = 11/19

Hence, the fraction is 11/19

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The probability that when the die is rolled twice, the sum is 7 is 0.233.

The probability of rolling each number on the die can be expressed as follows:

P(1) = 1/6, P(2) = 2/6, P(3) = 3/6, P(4) = 4/6, P(5) = 5/6, P(6) = 6/6

To find the probability of rolling a sum of 7 when the die is rolled twice, we can use the concept of the convolution of probability distributions.

We can calculate the probability of obtaining each possible sum by multiplying the probabilities of the individual outcomes that add up to that sum, and then summing these products over all possible combinations of the outcomes. The possible sums that can be obtained when rolling the die twice are 2, 3, 4, ..., 11, 12.

For example, the probability of obtaining a sum of 7 is:

P(1 and 6) + P(2 and 5) + P(3 and 4) + P(4 and 3) + P(5 and 2) + P(6 and 1)

= (1/6)×(6/6) + (2/6)×(5/6) + (3/6)×(4/6) + (4/6)×(3/6) + (5/6)×(2/6) + (6/6)×(1/6)

= 0.233. Therefore, the probability of rolling a sum of 7 when the die is rolled twice is 0.233.

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