Write and find the general solution of the differential equation that models the verbal statement.

The rate of change of P is proportional to P. When t=0,P=6,000 and when t=1,P=3,900. What is the value of P when t=4 ?

Write the differential equation. (Use k for the constant of proportionality.)

dP/dt= _____
Solve the differential equation.
P = _____
Evaluate the solution at the specified value of the independent variable. (Round your answer to three decimal places.)
_________

The statement that is correct on Quadrilateral EFGH is B. Quadrilateral EFGH is a rectangle.

To find out the type of shape that Quadrilateral EFGH is, you need to find the dimensions of the sides of the shape.

This can be found by the formula :

d=√(( x2 – x1 ) ² + ( y2 – y1 ) ² )

Using the formula, Side EF is 6 units

Side FG = 4 units

Side GH = 6 units

Side EH = 4 units

Two sides are therefore the same which means that this is a rectangle.

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Options for this question include:

A. Quadrilateral EFGH is a square.

B. Quadnlateral EFGH is a rectangle.

C. Quadrilateral EFGH is a rhombus

D. Quadriateral EFGH is a trapezium.

The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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The size of the crowd that fit 5 feet deep and 1 mile long on one side of the street is 8448.

Given:

in 5ft by 5ft = 25ft^2, there can be 1 person

A normal street is 30ft wide

Then, if we want the width such that is 5 ft deep (from both sides)

Then we should subtract two times 5 ft:

30ft - 5ft - 5ft = 20ft.

Now the length is 1 mile.

and 1 mile = 5280 ft

Then the area is:

There are 5280 feet in a mile. So, that's exactly 1056 lengths of 5 feet each.  To estimate, 5250 is 5×1050 lengths

In each 5 ft by 5 ft square, 8 people fit comfortably.  So, estimating, 8×1050 is 8400

To check (or verify),   8(5280/5) = 8448 exactly.    Our estimate is close enough

Hence we get the required answer.

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Answer:

true

Step-by-step explanation:

Given the comopound inequality:

Let's graph the compound inequality.

Here x is greater than -1 but less than or equal to 7.

To graph the inequality, we have:

Also, x is less than or greater than 7, plot a closed dot on the point 7.

Then draw a straight line connecting both points.

Hence, we have the graph below:

Answer:

274.5

Step-by-step explanation:

I think it is 2, 0, 4 but it would be very helpful if you put in an image of the graph.

Have a great day :D

Answer:

1. Given

2. Corresponding Angles Theorem

3. ∠NPO ≅ ∠MQN (or something similar)

4. AA Similarity Theorem

Step-by-step explanation:

1. Line MQ || Line OP is the given statement.

2. ∠QNM on the left triangle corresponds to ∠PNO on the second triangle.

3. These two angles are cut by a transversal (Line MP), and thus are congruent.

4. ∠MQN and ∠NMQ are congruent to ∠NOP and ∠NPO respectively, so the triangles are similar.

The transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.

What do you mean by transformation of a graph ?

The modification of an existing graph or graphed equation to create a different version of the following graph is known as transformation.

The functions given are :

f(x) = x²

and

g(x) = (x - 1)² + 3

Now , we know that , the horizontal shift depends on the value of h. The horizontal shift is described as:

g(x) = f (x + h)

Then , the graph is shifted to left by h units.

and

g(x) = f (x - h)

Then , the graph is shifted to right by h units.

If we compare f(x) with g(x) , their is a difference of -1 , it meant shift is right by 1 units.

Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:

g(x) = f(x) + k

Then , the graph is shifted up by k units.

and

g(x) = f(x) - k

Then , the graph is shifted down by k units.

Here , if we compare f(x) with g(x) there is addition of 3 in g(x) , this meant the graph is shifted upward by 3 units.

The graph of the function is attached  below. Here , both of the functions are graphed.

Therefore , the transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.

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To make layla's favorite shade of purple, she needs 8 ounces of blue for every 14 ounces of red, and she need for 63 ounces of red, then the blue would be 36 ounces.

To make layla's favorite shade of purple, she needs 8 ounces of blue for every 14 ounces of red.

Based on the given conditions,

She needs ounces of blue = 8

For every ounces of red = 14

She need for 63 ounces of red = 63

Let us assume,

She need for ounces of blue = x

So,

We can write,

Need for 63 ounces of red ⇒ Every 14 ounces of red

she needs 8 ounces of blue ⇒ She need for X ounces of blue

Then,

\(\frac{8}{14}\) = \(\frac{x}{63}\)

We can solve the equation of \(\frac{8}{14}\) = \(\frac{x}{63}\)

Swap the sides,

\(\frac{x}{63}\) = \(\frac{8}{14}\)

Divide both sides of the equation by the coefficient of variable,

\(x\) = \(\frac{8}{14} *63\)

Simplify fractions,

x = 4*9

Calculate the product or quotient,

x = 36

Therefore,

To make layla's favorite shade of purple, she needs 8 ounces of blue for every 14 ounces of red, and she need for 63 ounces of red, then the blue would be 36 ounces.

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The correct option is cone and plane. A conic section is the intersection of a plane and a cone. The best definition of a conic section is "cone and plane".

The definition of conic section is a conic section is a shape that is formed when a right circular cone intersects a plane. Depending on the angle of the plane concerning the center line of the cone, the conic sections are classified into four types. They are a circle, parabola, ellipse, and hyperbola. Each type of conic section has a unique shape and properties.

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Answer:

2.848 pound

Step-by-step explanation:

On 5 pizzas = 14.24 pound cheese

On 1 pizza = 14.24/5 pound

=2.848 pound

For the given width length ratio and perimeter of rectangle, the length of rectangle is 80 cm.

The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Let the width of the rectangle be 3x, and the length be 4x (since the ratio of the width to the length is 3:4).

The perimeter of a rectangle is the sum of the lengths of all four sides, so we have:

Perimeter = 2(length + width)

Substituting the expressions for the length and width, we get:

280cm = 2(4x + 3x)

Simplifying the right-hand side, we get:

280cm = 14x

Dividing both sides by 14, we get:

x = 20

Therefore, the length of the rectangle is 4x = 4(20) = 80 cm

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The months in which the depths decreased are:

Between April and May

Between June and July

The change in depth between April and May is calculated as:

Change in depth = -0.28 - (-0.15) = -0.13 m

Thus, there was a decrease in depth between april and may

The change in depth between May and June is calculated as:

Change in depth = -0.08 - (-0.28) = 0.20 m

Thus, there was an increase in depth between May and June

The change in depth between June and July is calculated as:

Change in depth = -0.01 - (-0.05) = 0.07 m

Thus, there was a decrease in depth between June and July.

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The complete question is:

A scientist measures the depth of the water in a pond each month. The pond is considered full at 0 m. She compares her measures to the height of the water when the pond is considered full and records the change in depth in a table

Between which months did the depth of water decrease?

Answer:

\(\%Off-Campus = 45.5\%\)

Step-by-step explanation:

Given

----------------------Dorms ---- Off-Campus ---- Total

Freshman -------- 88  ------  ---------12   ------- 100

Sophomore  ------62  ---------------38  --------- 100

Junior --------------43 -----------------  57  ---------- 100

Senior -------------25  -----------------75  ------------ 100

Total ---------------218 -------------182  --------------400

Required

Determine the percentage of off-campus students

From the above table, we have that:

\(Off-Campus = 182\)

\(Total\ Surveyed = 400\)

The percentage is then calculated as follows;

\(\%Off-Campus = \frac{Off-Campus}{Total-Surveyed} * 100\%\)

\(\%Off-Campus = \frac{182}{400} * 100\%\)

\(\%Off-Campus = 0.455 * 100\%\)

\(\%Off-Campus = 45.5\%\)

Hence, option C answers the question

Answer:

oh 45%

Step-by-step explanation:

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.

You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).

Given,

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.

Let s represent the truck's speed and (s+20) represent the car's speed.

to determine each vehicle's time

Time = Speed / Distance

truck time = 350/s

Time in an automobile is 350/(s+20)

Truck time - car time = 2 hours

So,

(350/s) - [350/(s+20)] = 2

LCM is s(s+20)

[350(s+20) - 350s]/s(s+20) = 2

Cross multiplying,

350(s+20) - 350s = 2s(s+20)

Simplifying the equation,

350s + 7000 - 350s = 2s² + 40s

Now, we have quadratic equation to simplify,

2s² + 40s - 7000 = 0

Dividing the equation by 2

s² + 20s - 3500 = 0

Factorizing,

s= 50

s= -70 (impossible because of the sign)

Hence the truck's speed is s = 50 km/h.

The speed of the car is s + 20 = 70 km/h.

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Answer:  1. F(-1)=  8(-1)-8

                2. F(0)= 8(0)-8

                3 F(2)= 8(2)-16

Step-by-step explanation:

i think i got some wrong i haven't these math [problem  in a long time

Use the f-statistics and reject at least one of the hypothesis if the statistic exceeds the critical value.

Given,

Testing of joint hypothesis .

Here,

When testing a joint hypothesis, you should: use t-statistics for each hypothesis and reject the null hypothesis once the statistic exceeds the critical value for a single hypothesis. use the F-statistic and reject all the hypotheses if the statistic exceeds the critical value. use the F-statistics and reject at least one of the hypotheses if the statistic exceeds the critical value. use t-statistics for each hypothesis and reject the null hypothesis if all of the restrictions fail.

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Answer:

is goes to ¨¨not a function¨¨

Step-by-step explanation:

The set of all possible output values of a function is called the range. Option c, range, is the correct answer.

To understand this concept, let's break it down step by step:

1. A function is a relationship between inputs (also known as the domain) and outputs (also known as the range).
2. The domain refers to all the possible input values that can be used as input to the function.
3. The range, on the other hand, refers to all the possible output values that the function can produce.
4. For example, let's consider a function that takes the age of a person as input and returns their height. The domain of this function could be all the possible ages, while the range could be all the possible heights that correspond to those ages.
5. It's important to note that the range can vary depending on the function. In some cases, the range may be limited, while in others, it may be infinite.
6. By understanding the range of a function, we can determine all the possible output values that the function can produce.

In summary, the set of all possible output values of a function is known as the range.

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Which term describes the set of all possible output values for a function?

a. output

b. input

c. range

d. domain

The variance is 150.

We are given that the three bids are regarded as three independent random variables with a common uniform distribution on [0,10]. And we need to determine the variance of the accepted bid. The company agrees to accept the highest of three sealed bids on a property.

Hence, if X, Y, and Z represent the three independent random variables, the accepted bid is given byA = max (X,Y,Z)

We know that the variance of a uniform distribution on [0,10] is given byσ² = (b-a)²/12

Substituting a = 0, b = 10, we get σ² = 10²/12 = 25/3

Thus, the variance of each of X, Y, and Z is 25/3

Now, we need to find the variance of the accepted bid.

We can use the following formula to find the variance of a function of random variables: Var(g(X, Y, Z)) = E(g²(X, Y, Z)) - [E(g(X, Y, Z))]²

Since A = max (X,Y,Z), we haveA² = max (X,Y,Z)²

Using the identity,max (a,b)² = a² + b² - 2ab where a and b are any two real numbers, we haveA² = X² + Y² + Z² - 2XY - 2XZ - 2YZ

Thus, the variance of the accepted bid is given by Var(A) = E(A²) - [E(A)]²

Using the linearity of expectation, we haveE(A²) = E(X² + Y² + Z² - 2XY - 2XZ - 2YZ)E(X² + Y² + Z²) - 2E(XY) - 2E(XZ) - 2E(YZ)

Substituting E(X²) = E(Y²) = E(Z²) = 25/3 and E(XY) = E(XZ) = E(YZ) = 25/9, we getE(A²) = 3(25/3) - 2(25/9) = 50/3Also, E(A) = E(max (X,Y,Z))

Using the fact that the CDF of the maximum of two independent random variables is given by:

F_{max(X,Y)}(z) = F_X(z)F_Y(z)for all z, we haveF_A(z) = F_X(z)³ = z³/1000 since X, Y, and Z are identically distributed, and hence, have the same CDF.

Using this CDF, we can find the expected value of A by integrating z from 0 to 10:

E(A) = ∫₀¹₀ z(3z²/1000) dz= 3/400 ∫₀¹₀ z³ dz= 3/400 (10⁴/4)= 750/4

Hence,Var(A) = E(A²) - [E(A)]²= (50/3) - (750/4)²= (50/3) - 140625/16= [3200 - (7500/3)]/9= 150

Thus, the variance of the accepted bid is 150.

Therefore, the correct answer is 150.

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1 Pound is equal to 1.81 Australian Dollars

1 Pound sterling equals  1.81 Australian Dollar

Answer:

x-y

-18-(-15)

-18+15

-3

This question is Incomplete

Complete Question

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 350 grams and a standard deviation of 11 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.)

a. Highest 10 percent ________

b. Middle 50 percent __________to _______

c. Highest 80 percent _________

d. Lowest 10 percent _________

Answer:

a. 364.10 grams

b.

c. 340.74 grams

d.335.90 grams

Step-by-step explanation:

a. Highest 10 percent

Highest 10% = 90th percentile

The z score for the 90th percentile = 1.282

Using the z score formula

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

Mean = 350 grams

Standard deviation = 11 grams

1.282 = x -350/11

1.282 × 11 = x - 350

x = 14.102 + 350

x = 364.102 grams

The weight that corresponds in 2 decimal places to the highest 10% ≈ 364.10grams

b. Middle 50 percent

Middle 50 percent is found between the 25th and 75th percentile

Z score for 25th percentile = -0.674

Using the z score formula

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

Mean = 350 grams

Standard deviation = 11 grams

-0.674 = x -350/11

-0.674 × 11 = x - 350

x = -7.414 + 350

x = 342.586 grams

Approximately in 2 decimal ≈ 342.59 grams

Z score for 75th percentile = 0.674.

Using the z score formula

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

Mean = 350 grams

Standard deviation = 11 grams

0.674 = x - 350/11

0.674 × 11 = x - 350

7.414 = x - 350

x = 350 + 7.414

= 357.414 grams

Approximately in 2 decimal places is 357.41 grams

Therefore, the weight that corresponds to the middle 50 percent is between

342.59 grams to 357.41 grams

c. Highest 80 percent

Highest 80 percent = 20th percentile

Z score for 20th percentile = -0.842

Using the z score formula

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

Mean = 350 grams

Standard deviation = 11 grams

-0.842 = x -350/11

-0.842 × 11 = x - 350

x = -9.262 + 350

x = 340.738 grams

The weight that corresponds in 2 decimal places to the highest 80% ≈ 340.74 grams

d. Lowest 10 percent = 10th percentile

Z score for 10th percentile = -1.282

Using the z score formula

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

Mean = 350 grams

Standard deviation = 11 grams

-1.282 = x -350/11

-1.282 × 11 = x - 350

x = -14.102 + 350

x = 335.898 grams

The weight that corresponds in 2 decimal places to the lowest 10% ≈ 335.90 grams

The coordinates of P are (-1, -3)

How to find the coordinate of point P?

From the given information, we know that the ratio of the distance from Q to P to the distance from Q to R is 1:5 (i.e. 1/6: 5/6). This means that the ratio of the x-coordinate and y-coordinate differences is also 1:5.

We can use this information to set up a system of equations to find the coordinates of P.

Since Q (-2, -5) and R(4, 7)

Let's call the coordinates of P as (x,y)

Firstly, the x-coordinate of P can be found using the following equation:

(x-(-2))/(4-x) = 1/5

5(x+2) = (4-x)

5x + 10 = 4 -x

5x + x = 4 - 10

6x = -6

x = -6/6

x = -1

Similarly, the y-coordinate of P can be found using the following equation:

(y-(-5))/(7-y) = 1/5

5(y+5) = (7-y)

5y + 25 = 7 - y

5y + y = 7 - 25

6y = -18

y = -18/3

y = -3

Therefore, the coordinates of P are (-1, -3)

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The present value of the payments is smaller than the amount of the loan, so you will not be able to pay off the loan.

The present value of the payments refers to the current value of the future payments, considering the time value of money. In this case, the payments are made over a period of 8 months, and each payment is listed. To determine if the payments will be enough to pay off the credit card, we need to calculate the present value of these payments and compare it to the initial loan amount of $5,000.

Since the interest rate on the credit card is 1.5% per month, we need to discount each payment back to its present value. By discounting the payments, we can see the equivalent value of these payments in today's dollars. If the present value of the payments is equal to or greater than $5,000, it would be enough to pay off the loan. However, if the present value is smaller than $5,000, it means the payments will not be sufficient to pay off the loan.

In this case, without specific information about the discount rate used to calculate the present value, we cannot make an exact determination. However, based on the given information, which states that the present value of the payments is smaller than the amount of the loan, it suggests that the payments will not be enough to pay off the credit card debt.

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