In exercises5-16 (0, the differential equation is separable. Find the general solntion, in an explicit form if possible. 5. y′=(x2+1)yB​ 6. y′=2xy−1)7.y′=212y2A​​

1. p=-5

2.w=20

3.x=14

4. y= 17 over 10

In order to solve these, you want to combine the variables then isolate them on one side by adding/subtracting or multiplying/dividing whatever number is still with them.

4p + 8p + 12 = −48    

We combine 4p and 8p into 12p, and 12 is subtracted from both sides to remove it from the left side make -60 on the right side.

12p = -60

Now we divide both sides by 12, to remove the 12 from 12p, and we end up with p = -5

p = -5

9w + 33 = 12w – 27

-3w = -60

w = 20

−2x + 7 = −21

-2x = -28

x = 14

25 = 10y + 8

10y = 17

y = 1.7

Answer:

9.45 inches

Step-by-step explanation:

We should make a proportion for this one.

4.2/12=x/27

Now we cross multiply.

12x=113.4

Now we divide both sides by 12.

x=113.4/12

We solve 113.4/12.

x=9.45 inches

Answer:

4 ) {2,3}

5) {0,1,2,3,4,5}

6) { }

Answer:

P =4.71x-10.6

Step-by-step explanation:

R = 6.91x

C=2.2x+10.6.

P = R - C = 6.91x-2.2x -10.6 =4.71x-10.6

Answer:

Step-by-step explanation:

60=x+45

x=15

The number of miles that Hummer H1 can go would be = 230 miles.

To calculate the number of miles the vehicle can travel when a certain amount of gallons are given would be done following the steps below.

The number of miles for 1 gallon of gas = 10 miles

The number of miles for 23 gallons of gas = X miles

That is :

1 gallon = 10 miles

23 gallons = X miles

make X miles the subject of formula;

X miles = 23×10/1

= 230 miles.

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False.  We cannot use the normal distribution to approximate the sampling distribution of the average (x) for a small sample (n<30) if our sample has clear outliers.

The sampling distribution of the average, also known as the sampling distribution of the mean, is the distribution of all possible sample means that could be obtained from a population. In order to use the normal distribution to approximate the sampling distribution of the average, certain assumptions need to be met. One of these assumptions is that the data should follow a normal distribution or at least be approximately normally distributed.

If the sample contains clear outliers, it indicates that the data deviates significantly from the assumptions of normality. Outliers can affect the shape and properties of the distribution, making it non-normal. In such cases, using the normal distribution to approximate the sampling distribution of the average would not be appropriate because the underlying assumptions are violated. Alternative approaches, such as non-parametric methods, may be more suitable for analyzing data with outliers.

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The distance between the center and edge of a circle is known as the radius.

The distance between the center and edge of a circle is known as the radius. It is a fixed distance that extends from the center of the circle to any point on the circle's edge.

To calculate the radius, you need to measure the distance from the center of the circle to any point on its edge. You can use a ruler or a measuring tape to measure this distance.

Alternatively, if you know the circumference of the circle, you can use the formula:

radius = circumference / (2 × pi)

where pi is a mathematical constant approximately equal to 3.14.

The radius of a circle is an important parameter that helps to define its size and shape. It is also used in many calculations involving circles, such as finding the area or circumference of a circle, as well as in many real-world applications, such as in the design of wheels and gears.

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\(\\ \sf\longmapsto 500=50\times (1.23)^x\)

\(\\ \sf\longmapsto 1.23^x=10\)

\(\\ \sf\longmapsto 1.23^x=1.23^{11.12}\)(Used scientific calculator)

\(\\ \sf\longmapsto x=11.12\)

__________

\(\:\)

500 = 50 × \((1,23)^x\)

500 ÷ 50 = \((1,23)^x\)

10 = \((1,23)^x\)

\(\cancel{(1,23)}^{11,12}}\) = \(\cancel{(1,23)}^x\)

11,12 = x

Soo, Answer for Question 500 = 50 × \((1,23)^x\) its x = 11,12

To find m,

m= Y2-Y1 / X2-X1

m= 10-5 / 4-2

m= 5/2

m= 2.5

To find b,

Use coordinate (4,10)

y=mx+b

10=2.5(4)+b

10=10+b

b=0

y=2.5x

the answer is y=2.5x

Answer:

The least degree of the polynomial that assures an error smaller than 0.001 is 4.

The Lagrange error bound for the Taylor polynomial of degree n centered at x=2 for e^x is given by:

```

|e^x - T_n(x)| < \frac{e^2}{(n+1)!}|x-2|^{n+1}

```

where T_n(x) is the Taylor polynomial of degree n centered at x=2.

We want the error to be less than 0.001, so we have:

```

\frac{e^2}{(n+1)!}|x-2|^{n+1} < 0.001

```

We can solve for n to get:

```

n+1 > \frac{e^2 \cdot 1000}{|x-2|}

```

We know that |x-2| = 0.45, so we have:

```

n+1 > \frac{e^2 \cdot 1000}{0.45} \approx 6900

```

Therefore, n > 6899.

The least integer greater than 6899 is 6900, so the least degree of the polynomial that assures an error smaller than 0.001 is 4.

The fourth-degree Taylor polynomial centered at x=2 for e^x is given by:

```

T_4(x) = 1 + 2x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24}

```

We can use this polynomial to estimate e^1.45 as follows:

```

e^1.45 \approx T_4(1.45) = 4.38201

```

The actual value of e^1.45 is 4.38202, so the error in this approximation is less than 0.001.

Step-by-step explanation:

Answer:

for the first one I got y=-2x-2 the second part i got y=-x-1 or -1x-y-1=0  Correct me if I am wrong

Step-by-step explanation:

Use the slope formula

-4-4 =-8

  /               =-2

1 - -3=4

2. The second part use this formula y-y1=m(x-x1)

     y--4=-1(x-3)

y+4=-x+3

  -4      -4

y+0=-x-1

 y=-x-1      or -1x-y-1=0    I am not sure  

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

It would be 10.35

Step-by-step explanation:

Hope this helps! Pls give brainliest. :)

Answer:

10.35

Step-by-step explanation:

Given

A=LW

L=2.3

W=4.5

HENCE

A=(2.3)(4.5)=10.35

Answer:

answer is (14x+6) hope it helps

The client would receive 800 mL of fluid in 8 hours if they are receiving 1 L of fluid to run over 10 hours.

The mL of fluid the client would receive over 8 hours, we need to use the formula given below:Total volume ÷ Total time = Volume per hourThen, we will multiply the volume per hour by the given number of hours to calculate the volume of fluid for the given duration, which is 8 hours.Let's solve this problem using the formula.1 L is equal to 1000 mL. The client is receiving 1 L of fluid to run over 10 hours.

The volume per hour is:1000 ÷ 10 = 100 mL/hourNow, we can calculate the volume of fluid the client would receive in 8 hours:Volume per hour × Number of hours = 100 × 8 = 800 mL.

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Answer:

20 i think aHh

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Step-by-step explanation:

3⁶/3⁸

= 3 × 3 × 3 × 3 × 3 × 3/ 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3

= 1/ 3 × 3

= 1/9 (option C)

= 1/3²

= (1/3)² (option D)

= 3-² (option B)

There are approximately 2.97 billion droplets per acre being sprayed.

To calculate the number of droplets per acre, we need to first convert the diameter of the droplets from microns to inches (since we are using acres as our unit of area). There are 25,400 microns in one inch, so the diameter of the droplets in inches is 250/25,400 = 0.0098 inches.

Next, we need to calculate the area of one droplet. The formula for the area of a circle is A = πr², so the area of one droplet is A = π(0.0049)² = 0.0000754 square inches.

Finally, we can calculate the number of droplets per acre by dividing the total area of one acre (43,560 square feet) by the area of one droplet: 43,560 / 0.0000754 = 2.97 billion droplets per acre.

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May would therefore save $621,470.85 in interest costs if she opted for a 15-year simple interest mortgage ($798,750 - $177,279.15).

The sum of money that even a lender charges a loan for the usage of money over a certain period of time is known as interest. It is frequently represented as a proportion of the sum lent or borrowed and can be either simple or compound. Simple interest is determined by that of the principal amount alone, while interest expense is determined by the principal amount and the total amount of interest that has accrued. A key idea in banking, interest is utilised in a number of credit derivatives, including bonds, savings accounts, and loans.

given

May would save on interest costs if she chose a 15-year simple interest mortgage because the loan would be repaid sooner. Using the same technique as before but with n = 15 years, we can determine the interest costs for a 15-year mortgage:

PV is equal to PMT* [1 - (1 + r/12)(-n*12)] / (r/12)

Inputting the values provided yields:

355000 = PMT * [1 - (1 + 0.595%/12)^(-15*12)] / (0.595%/12)

PMT = $3,208.59

Over the course of the loan, the following would be paid in interest:

I equals PMT*n - PV.

I = $3,208.59 * 15 - $355,000

I = $177,279.15

May would therefore save $621,470.85 in interest costs if she opted for a 15-year simple interest mortgage ($798,750 - $177,279.15).

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The value of u is not provided, we cannot determine the exact value of y. None of the given options (a, b, c, d) can be chosen as the approximate value of y.

For the first question, you are given the model yhat = 2.1 + 1.0x^2 and you want to find the estimated marginal effect of x on y when x = 1.3. To find the estimated marginal effect, you need to take the derivative of yhat with respect to x. In this case, the derivative would be 2.0x.

Now, substitute x = 1.3 into the derivative:

2.0(1.3) = 2.6.

Therefore, the estimated marginal effect of x on y when x = 1.3 is 2.6.

For the second question, you are given the model \(lny = β₁ + β₂x^2 + u\), with parameter estimates

β₁ = 2 and

β₂ = 1.

To predict the value of y when x = 2, substitute the given values into the model:
\(lny = 2 + 1(2^2) + u\)
lny = 2 + 1(4) + u
lny = 2 + 4 + u
lny = 6 + u

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Answer:

x = -7

Step-by-step explanation:

\(8( - 2x - 11) = 24 \\ - 2x - 11 = 3 \\ - 2x = 3 + 11 \\ - 2x = 14 \div 2\)

\( x = - 7\)

a) The cost function C(x) can be represented as C(x) = 0.85x + 400, the revenue function R(x) can be represented as R(x) = 5x, and the profit function P(x) can be represented as P(x) = R(x) - C(x).

b)The break-even point occurs when the profit is zero, so we set P(x) = 0 and solve for x to find the break-even point. However, in this case, the club cannot exactly break-even due to the fixed facility rental fee.

C) The marginal profit when x = 100 can be found by taking the derivative of the profit function P(x) with respect to x and evaluating it at x = 100. The marginal profit represents the rate of change of profit with respect to the number of servings sold.

from selling x servings of pasta. It is calculated by subtracting the cost function C(x) from the revenue function R(x).

b) To find the

break-even point

, we set P(x) = 0 and solve for x. This means the profit is zero, indicating that the club is not making a profit nor incurring a loss. However, in this scenario, there is a fixed facility rental fee of $400, which means the club cannot exactly break-even. The break-even point can still be calculated by setting P(x) = -400 and solving for x, indicating the minimum number of servings required to cover the fixed cost.

The practical interpretation of the

marginal profit

at x = 100 is that it indicates how much the profit is changing for each additional serving sold when the club has already sold 100 servings. If the marginal profit is positive, it means that for each additional serving sold, the profit is increasing. If it is negative, it means that for each additional serving sold, the profit is decreasing.

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The probability of randomly selecting a 12th-grader with a score higher than 300 on the 2000 mathematics test is approximately 0.5.

Given that the scores of 12th-grade students on the 2000 mathematics test follow an approximately normal distribution with a mean of 300 and a standard deviation of 35, we can use the properties of the normal distribution to calculate the probability.

To find the probability that a randomly chosen student has a score higher than 300, we need to determine the area under the normal distribution curve to the right of the value 300. This represents the probability of a score being higher than 300.

Using statistical tables or a calculator with a cumulative distribution function for the normal distribution, we can find that the area to the right of 300 is approximately 0.5. This means that there is a 50% probability of selecting a student with a score higher than 300.

The normal distribution is symmetrical around its mean, so the probabilities of being below and above the mean are equal. Since the mean is 300, which is the cutoff point, the probability of a randomly selected student having a score higher than 300 is 0.5 or 50%.

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Answer:

x = 2.7

Step-by-step explanation:

5.4 = 2x

2x = 5.4

Divide both sides by 2.

x = 2.7

Answer: x= 2.7

1. Divide 2 on both sides

2. cancel terms who have the same numerator and denominator

A  water bottle would have 600 milimeters.

What is multiplication?

In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product. In the multiplication problem, 6 9 = 54, the numbers 6 and 9 are factors, and 54 is the product.

If one fluid ounce has approximately 30mm.

then 20 fluid ounce will have = 30 * 20

                                                 = 600 millimeters.

Hence, a water bottle would have 600 milimeters.

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Answer:

do you still need help with this ? its been 19 hours lol

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

my bad

Answer:

Step-by-step explanation:

i got 1.11111111111 hope it helps ( give me brainliest please)

The probability that the cook adds the right ingredients and cooks well is 0.75

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

Right ingredients = 9 times

Errors = 3 times

using the above as a guide, we have the following:

Total = 9 + 3

Evaluate the sum

Total = 12

The probability that the cook adds the right ingredients and cooks well is

P = Right ingredients/Total

So, we have

P = 9/12

Evaluate

P = 0.75

Hence, the probability is 0.75

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