A clownfish costs $3.60 to buy. An angelfish costs $5.80 to buy. Joy spends $42.00 on some clownfish and some angelfish. She buys at least one of each. How many of each type does she buy? What if she had $52 to spend on fish? How many of each type did she buy?

Answer:

If  [tex]K[/tex] is a constant of integration, then

[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]

Step-by-step explanation:

According to the information of the problem we know that

[tex]{\displaystyle \frac{dP}{dt} = P(a-bP) }[/tex]

Remember that in general a Bernoulli equation is an equation of the type

[tex]y' + p(x)y = q(x)y^n[/tex]

And the idea to solve the equation is to substitute

[tex]{ \displaystyle v = y^{1-n}}[/tex]

Now for this case

[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]

Then we substitute

[tex]v = P^{1-2} = P^{-1}[/tex]

Therefore

[tex]P = v^{-1}[/tex]

and if you compute the derivative of that you get that

[tex]{\displaystyle \frac{dP}{dt} = -v^{-2} \frac{dv}{dt}}[/tex]

Now you substitute that onto the original equation and get

[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]

[tex]{\displaystyle -v^{-2} \frac{dv}{dt} - v^{-1} = -bv^{-2}[/tex]

If you multiply everything by  [tex]-v^2[/tex]  you get that

[tex]{\displaystyle \frac{dv}{dt} + v = b }[/tex]

That's a linear differential equation and the solution would be

[tex]v = {\displaystyle \frac{b}{a} + Ke^{-at}} = P^{-1}[/tex]

Where [tex]K[/tex] is a constant of integration, then

[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]

The given logistic equation is a Bernoulli equation, which can be solved using a substitution of variables method.

The given differential equation is a Bernoulli equation, which is a nonlinear first-order ordinary differential equation of the form dy/dx = P(x)y + Q(x)y^n, where n is a constant. To solve it, we can use a substitution of variables by setting y = u^(1-n). Applying this substitution to the logistic equation, we get du/dx = (1-n)a*u + (1-n)b*u^(2-n), which can be solved using separation of variables method.

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Answer:

percentage error = 11.11 %

Step-by-step explanation:

Brandon poured w hat he estimated to be 32 ounces of oil into his car's engine . He later determined that he has actually poured 36 ounces from the marking on the container . The percentage error is computed below.

percentage error = approximate value - exact value/exact value × 100

approximate value = 32 ounces

exact value = 36 ounces

percentage error = |32 - 36| / | 36 | × 100

note we used the absolute value to eliminate negative signs

percentage error = 4/36 × 100

percentage error = 400/36

percentage error = 11.11 %

Answer:

121.875 if calculated so 121.875 if it shows it or less

Answer:

121.875

Step-by-step explanation:

To find the number you multiple 195 by 0.625 (0.625 is equivalent to 62.5%) which gets you 121.875

Answer:

p-value is greater than 0.05, hence we accept the null hypothesis.

Step-by-step explanation:

See attached images

Linda's monthly mortgage payment will be approximately $664.14.

Linda's combined monthly payment, including the mortgage and maintenance fee, will be $974.14.

We have

A)

Monthly Mortgage Payment:

Loan Amount: $100,000

Interest Rate: 7.1% per annum (APR)

Loan Term: 30 years (360 months)

Monthly Interest Rate = Annual Interest Rate / 12

= 7.1% / 12

= 0.0059

Number of Payments = Loan Term in years * 12

= 30 * 12

= 360

Monthly Mortgage Payment

= (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

Plugging in the values:

[tex]= (100,000 * 0.0059) / (1 - (1 + 0.0059)^{-360})[/tex]

= $664.14

B) Combined Monthly Payment:

Combined Monthly Payment

= Monthly Mortgage Payment + Monthly Maintenance Fee

= $664.14 + $310

= $974.14

Therefore,

Linda's monthly mortgage payment will be approximately $664.14.

Linda's combined monthly payment, including the mortgage and maintenance fee, will be $974.14.

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A) Linda's monthly mortgage payment is approximately $672.03.

B) Linda's combined monthly payment is approximately $982.03.

To determine Linda's monthly mortgage payment and her combined monthly payment, we can use the following steps:
A) Calculating the Monthly Mortgage Payment:-
We use the formula for the monthly mortgage payment on a fixed-rate mortgage:
[tex]\[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \][/tex]
Where:
- ( M ) is the monthly mortgage payment.
- ( P ) is the loan principal (amount borrowed), which is $100,000.
- ( r ) is the monthly interest rate, which is the annual rate divided by 12.
- ( n ) is the total number of payments (loan term in years multiplied by 12 months per year).
Given:
- [tex]\( P = 100,000 \)[/tex]
- Annual interest rate (APR) = 7.1% or 0.071
- Monthly interest rate [tex]\( r = \frac{0.071}{12} \approx 0.0059167 \)[/tex]
- Loan term ( n = 30 ) years, which is [tex]\( 30 \times 12 = 360 \)[/tex] months.
Substitute these values into the formula:
[tex]\[ M = 100,000 \times \frac{0.0059167(1 + 0.0059167)^{360}}{(1 + 0.0059167)^{360} - 1} \][/tex]  = $672.03.
B) Calculating the Combined Monthly Payment
The combined monthly payment is the sum of the monthly mortgage payment and the monthly maintenance fee.
Given:
- Monthly maintenance fee = $310
So, the combined monthly payment ( C ) will be:
[tex]\[ C = M + 310 \][/tex]
Let's compute these values.

A) Monthly Mortgage Payment
Linda's monthly mortgage payment is approximately $672.03.

B) Combined Monthly Payment
To find the combined monthly payment, we add the monthly mortgage payment and the monthly maintenance fee:
[tex]\[ \text{Combined Monthly Payment} = 672.03 + 310 = 982.03 \][/tex]
Therefore, Linda's combined monthly payment is approximately $982.03.

Answer: The type is Retrospective.

Step-by-step explanation: Observational Study is a type of research which measures determined characteristics of a population by studying individuals in a sample, without interfering or influencing the variables. There are 3 types of observational study:

According to the description given, the study above is a case-control study and the type is called Retrospective because it asks the individuals to tell about past habits, exposure to sunshine in this case. This type of study is not very reliable because it depends on the memory and the ability of the individuals to be honest and it can only prove association, not causation.

The type of observational study described in the question is a case-control study. The researcher selected women with and without osteoperosis, collected data on their exposure to sunshine, and compared the amount of exposure between the two groups.

The type of observational study described in the question is a case-control study. In a case-control study, the researcher selects subjects based on their disease status (in this case, women with or without osteoperosis) and compares their exposure to a risk factor (in this case, lack of exposure to sunshine). The researcher collected data on the exposure to sunshine over the previous twenty years for both groups and compared the amount of exposure between the two groups.

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Answer:

A. 615.44 cm²

Step-by-step explanation:

A = pi(r²)

= 3.14(14²)

= 3.14(196)

= 615.44 cm²

Final answer:

To find the approximate area of the pizza with a radius of 14 cm, use the formula for the area of a circle and substitute the given value, resulting in 615.44 cm².

Explanation:

The approximate area of the pizza can be calculated using the formula for the area of a circle:

A = πr²

Given that the radius is 14 cm, we substitute this into the formula:

A ≈ 3.14 x (14 cm)² = 615.44 cm²

Therefore, the approximate area of the pizza is 615.44 cm², which corresponds to option A.

Answer:

30 PS4's

Step-by-step explanation:

The manager chose 50/500 PS4's to sample

3/50 were defective

To find how many were defective in all 500, we multiply the fraction by a number that makes the 50 (the sample), into a 500(the total).

That number is 10

Whatever multiplication you do to the bottom of a fraction, you do to the top

3*10 / 50*10

30 / 500 are likely to be defective

Answer:

30

Step-by-step explanation:

Answer:

[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value using the alternative hypothesis is given by:

[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]  

Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge

Step-by-step explanation:

Information provided

4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9

We can find the sample mean and deviation with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\bar X=3.76[/tex] represent the sample mean

[tex]s=0.241[/tex] represent the sample standard deviation

[tex]n=10[/tex] sample size  

[tex]\mu_o =3.5[/tex] represent the value to check

[tex]\alpha=0.01[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test  if the new design increased the absorption amount of the sponge (3.5), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 3.5[/tex]  

Alternative hypothesis:[tex]\mu > 3.5[/tex]  

Since we don't know the deviation the statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value using the alternative hypothesis is given by:

[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]  

Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge

Answer:

between 3 and 60

Step-by-step explanation:

just did it on ed.

Answer: Between 3 and 60

Step-by-step explanation: Glad you figured it out! :)

Answer:

positive 5.5

Step-by-step explanation:

Answer:

-3x + 8 = y

-3x = y - 8

3x = 8 - y

x = (8-y)/3

Now interchanging x and y:-

y = (8-x)/3

Here, y is inverse function i.e. f⁻¹(x)

Hence, f⁻¹(x) = (8-x)/3

Since f⁻¹(x) is a linear expression of x, therefore it is a function.

Step-by-step explanation:

Answer:

Look at the answer of the pic

Answer:

(a)

The average length of the project is 33.9 weeks

The standard deviation of the project length is 2.8 weeks

(b)

The estimated probability that the project will be completed in 35 weeks or less is 0.65

Step-by-step explanation:

(a)

The average length of the project is;

E(P) = E(A+B+C+D)

      = 6.3 + 5.1 + 13.7 + 8.8

      = 33.9

The standard deviation of the project length;

SD(P) = √V(P)

         = √V(A+B+C+D)

         = √1.01 + 1.79 + 4.11 + 0.96

         = √7.87

         = 2.8

(b)

Normal distribution with mean 33.9 weeks and variance of 2.8² weeks.

The estimated probability that the project will be completed in 35 weeks or less is;

[tex]P(P \leq 35) = P( \frac{P-E(P)}{SD(P)} \leq \frac{35-33.9}{2.8} )[/tex]

[tex]P(P \leq 35) = P(z\leq0.3929)[/tex]

                 = 0.65  → Using Excel command (NORM.S.DIST(0.3929,TRUE))

To estimate the average length and standard deviation of a project, use a spreadsheet simulation model. Calculate the expected completion time and standard deviation for each activity. To find the probability of completing the project in a certain time frame, sum up the probabilities of activities that can be completed within that timeframe.

To estimate the average length of the project and the standard deviation of the project length, you can use a spreadsheet simulation model. Here are the steps you can follow:

For part (b), to find the estimated probability that the project will be completed in 35 weeks or less, you'll need to sum up the probabilities of all activities that can be completed within 35 weeks or less.

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Principal Balance: 2000

Compound Interest: 3%

Type: Yearly

2000 x 1.03 = 2060

Year 1 : £2060

2060 x 1.03 = 2121.8

Year 2: £2121.8

There will be £2,121.80 in the account after 2 years.

Answer:okStep-by-step explanation:

Answer:

The mean number of gerbils seen per day is 6.

The mean absolute deviation of the data is 2.29.

Step-by-step explanation:

The mean of a data set is the value that represents the entire data set. It is the average value.

The formula to compute the mean of a data set is:

[tex]\bar x=\frac{1}{n}\sum X[/tex]

The mean absolute deviation (MAD) of a data set is the average distance amid each value and the mean. The MAD provides us with an idea about the deviation in the data set.

The formula to calculate the value of MAD is:

[tex]MAD=\frac{1}{n}\sum |x-\bar x|[/tex]

The data set for the number of gerbils seen per day is:

S = {2, 3, 5, 7, 8, 8, 9}

Compute the mean of the data as follows:

[tex]\bar x=\frac{1}{n}\sum X[/tex]

  [tex]=\frac{1}{7}\times [2+3+5+7+8+8+9]\\\\=\frac{1}{7}\times 42\\\\=6[/tex]

The mean number of gerbils seen per day is 6.

Compute the mean absolute deviation of the data as follows:

[tex]MAD=\frac{1}{n}\sum |x-\bar x|[/tex]

          [tex]=\frac{1}{7}\times [|2-6|+|3-6|+|5-6|+|7-6|+|8-6|+|8-6|+|9-6|]\\\\=\frac{1}{7}\times 16\\\\=2.2857\\\\\approx 2.29[/tex]

Thus, the mean absolute deviation of the data is 2.29.

Final answer:

The mean of the data set (2, 3, 5, 7, 8, 8, 9) is 6, and the mean absolute deviation (MAD) is approximately 2.29.

Explanation:

Finding the Mean and MAD of a Data Set

The mean (average) of a data set is found by adding up all the numbers in the set and then dividing by the count of those numbers. In the provided data set (2, 3, 5, 7, 8, 8, 9), the mean is calculated as follows:

The mean absolute deviation (MAD) is found by calculating the absolute differences between each number in the set and the mean, averaging those absolute differences:

Therefore, the mean of the data set is 6, and the MAD is approximately 2.29.

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for detailed and step by step solution of the given problem.

a. The critical number of f is -5

b. The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).

c.  There is no relative extremum at x = -5.

d. Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).

(a) To find the critical numbers of the function,  find where the derivative is 0 or undefined.

To find the derivative of f(x):

[tex]f'(x) = (2/3)(x + 5)^(-1/3)[/tex]

The derivative is undefined at x = -5, since[tex](x + 5)^(1/3)[/tex] would be 0 in the denominator.

So -5 is a critical number of f.

(b) To find the intervals on which the function is increasing or decreasing,  examine the sign of the derivative on each interval.

Since f'(x) is always positive (except at x = -5, where it is undefined),

The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).

(c) To apply the First Derivative Test, look at the sign of the derivative near the critical point x = -5.

The derivative is undefined at x = -5, so the test is not applicable

Therefore, there is no relative extremum at x = -5.

Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).

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Answer: the value is true

Step-by-step explanation:

Answer:

  13 1/2

Step-by-step explanation:

X-4 1/6 = 9 1/3

Add 4 1/6 to each side

X-4 1/6+ 4 1/6 = 9 1/3 + 4 1/6

x = 9 1/3 + 4 1/6

  = 9 2/6 + 4 1/6

   13 3/6

    13 1/2

Answer:

  24 meters

Step-by-step explanation:

The Pythagorean theorem can be used to find the missing leg of the right triangle.

  AB² = BC² +AC²

  25² = 7² +AC²

  AC = √(625 -49) = √576

  AC = 24

The height to the top of the ladder is 24 meters.

Answer:

[tex]-\dfrac{2}{3}[/tex]

Step-by-step explanation:

When variable y is said to be proportional to another variable x, it is written as:

[tex]y \propto x[/tex]

To introduce the equality sign, we introduce what is called the constant of proportionality, say k and write the above as:

y=kx

Comparing the given equation:

[tex]y=-\frac{2}{3}x[/tex]

We can see that our constant of proportionality:

[tex]k=-\dfrac{2}{3}[/tex]

Answer:

If you mean how much is left after he ate 1/4 from the 2/3 then 5/12 of the pizza is left.

Step-by-step explanation:

Final answer:

Wakami ate 1/6 of the entire pizza by consuming 1/4 of the 2/3 of the pizza that was left.

Explanation:

To find out how much of the pizza Wakami ate, we need to calculate 1/4 of the 2/3 of the pizza that was left. This requires multiplying the two fractions together:

2/3 of the pizza left times 1/4 that Wakami eats = 2/3 times 1/4

To multiply fractions, you simply multiply the numerators (top numbers) and then multiply the denominators (bottom numbers):

(2 times 1) / (3 times 4) = 2 / 12

Now we simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 2:

2 / 12 = 1/6

So, Wakami ate 1/6 of the entire pizza.

Answer:

b) 4/52

Step-by-step explanation:

Since there are only 4 playing cards in a full deck that are labeled '2', and there are 52 cards in total - then there is a 4 out of 52 chance that a '2' card will be selected!

Answer:

b) 4/52

Step-by-step explanation:

There are only 4 "2" cards in a deck of 52, so you only have a 4/52 chance of pulling one, or about 8%.

hope this helps :)

Answer:

The center is located at (2, –1).  

The major axis is 8 units long.

The vertices are 4 units above and below the centre.

The foci are √7 units above and below the centre.  

Step-by-step explanation:

Assume the ellipse looks like the one below.

The properties of a vertical ellipse are

[tex]\textbf{Vertical ellipse}\\\dfrac{ (x - h)^{2} }{b^{2}} + \dfrac{(y - k)^{2}}{a^{2}} = 1\begin{cases}\text{Centre} = (h,k)\\\text{Dist. between vertices} = 2a\\\text{Vertices} = (h, k\pm a)\\\text{Dist. between covertices} = 2b\\ \text{Covertices}= (h\pm b, k)\\c = \sqrt{a^{2} - b^{2}}\\\text{Dist. of foci from centre} = c\\\text{Foci} = (h, k\pm c)\\\end{cases}[/tex]

A. Centre

TRUE. The centre is at (2,-1).

B. Major axis

TRUE

Length of major axis = 3 - (-5) = 3 + 5 = 8

C. Minor axis

False

Length of minor axis = 5 - (-1) = 5 + 1 = 6

D. Vertices

TRUE

Distance between vertices = 8 = 2a

a - 8/2 = 4

Vertices at (h, k ± a) = (2, -1 ± 4)

E. Foci

TRUE

c² = a² - b² = 4² - 3² = 16 - 9 = 7

c = √7

The foci are √7 above and below the centre.

F. Foci

False.

The foci are on a vertical line.

Answer:

x=0 i think

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I took the quiz

Answer:

Asymptotes, in mathematics, refer to a restriction at the domain set or the range set. It's drawn as a not solid line to indicate, graphically, the values that are not defined to the function.

So, when we express the domain and range sets of a function, we use parenthesis or brackets. In case of having asymptotes we use parenthesis, because that sing indicates an exclusion of the undefined value. On the other hand, the brackets indicates inclusion.

That means, if we use brackets to indicate asymptotes in an interval, that means the value is well defined for the function, which is false.

Answer:

[tex]P(E1/R)= 0.15[/tex]

Step-by-step explanation:

Hola!

La comañía en cuestión usa 4 empresas de transporte para realizar envios. Llamemos "E" al evento de que la empresa haya sido seleccionada para un envío:

E1: La empresa A1 realiza el envío ⇒ P(E1)= 0.15

E2: La empresa A2 realiza en envío ⇒ P(E2)= 0.30

E3: La empresa A3 realiza el envío ⇒ P(E3)= 0.35

E4: La empresa A4 realiza el envío ⇒ P(E4)= 0.20

Y también conoces las probabilidades de que un envío llegue con retraso, sabiendo cual es la empresa que realizó el envío. Llamemos "R" al evento que el envío llegó con retraso. Las probabilidades mencionadas son condicionales y se simbolizan de la siguiente manera:

P(R/E1)= 0.07

P(R/E2)= 0.08

P(R/E3)= 0.05

P(R/E4)= 0.09

Tienes que calcular la probabilidad de que un embarque que ha sido entregado con retraso, haya sido enviado por la empresa A1.

Esta probabilidad también es condicional, queremos saber la probabilidad de E1 sabiendo que ya ha pasado R, se simboliza de la siguiente manera:

[tex]P(E1/R)= \frac{P(E1nR)}{P(R)}[/tex]

Para poder calcularla necesitas averiguar el valor de la probabilidad de intersección entre E1 y R, P(E1∩R), y el valor de la probabilidad de R, P(R).

La probabilidad de R es una probabilidad marginal y es igual a:

P(R)= P(E1∩R)+P(E2∩R)+P(E3∩R)+P(E4∩R)

Para calcular los valores de las intersecciones debes aplicar la definición de probabilidad condicional:

[tex]P(A/B) = \frac{P(AnB)}{P(B)}[/tex] entonces P(A∩B)= P(A/B)*P(B)

Entonces:

[tex]P(R/E1)= \frac{P(RnE1}{P(E1)}[/tex] ⇒ P(E1∩R)= P(R/E1)*P(E1)= 0.07*0.15= 0.0105

P(E2∩R)= P(R/E2)*P(E2)= 0.08*0.30= 0.024

P(E3∩R)= P(R/E3)*P(E3)=0.05*0.35= 0.0175

P(E4∩R)= P(R/E4)*P(E4)= 0.09*0.20= 0.018

Ahora puedes calcular la probabilidad de que el envío llegue con retraso:

P(R)= 0.0105+0.024+0.0175+0.018= 0.07

Por último queda calcular la probabilidad solicitada:

[tex]P(E1/R)= \frac{0.0105}{0.07}= 0.15[/tex]

Espero que tengas un buen día!

Answer:

  225°

Step-by-step explanation:

Multiply radians by 180°/π to get degrees.

  (5π/4)×(180°/π) = (5/4)(180°) = 225°