Which ordered pair is a solution of the equation
y = 7x-2

Answer:

answer on the picture......

The biomass a year later is [tex]& \ y \approx 3.23 \times 10^7 \mathrm{~kg}[/tex]  and t=1.58 years to reach 4 times 107 kg of biomass.

The following differential equation: [tex]& \Rightarrow \frac{d y}{d t}=k y\left(1-\frac{y}{M}\right) \\[/tex]

[tex]& \Rightarrow \frac{d y}{d t}=k y\left(\frac{M-y}{M}\right)[/tex]

Using variable separable method:

[tex]$$\Rightarrow \frac{d y}{y(M-y)}=\left(\frac{k}{M}\right) d t$$[/tex]

Integrate both sides:

[tex]$$\begin{gathered}\Rightarrow-\int \frac{d y}{y(y-M)}=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{M}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{y-(y-M)}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int\left(\frac{1}{y-M}-\frac{1}{y}\right) d y=\int\left(\frac{k}{M}\right) d t\end{gathered}$$[/tex]

[tex]\Rightarrow-\frac{1}{M}(\ln (y-M)-\ln y)=\frac{k t}{M}+C \\[/tex]

Let C1 be a constant such that C1 = MC, therefore,

[tex]$$\begin{gathered}\Rightarrow-\ln (y-M)+\ln y=k t+C_1 \\\Rightarrow \ln \frac{y}{y-M}=k t+C_1 \\\Rightarrow \frac{y}{y-M}=e^{k t+C_1} \\\\\Rightarrow y=y e^{k t+C_1}-M e^{k t+C_1} \\\\\Rightarrow y e^{k t+C_1}-y=M e^{k t+C_1} \\\\\Rightarrow y=\frac{M e^{k t+C_1}}{e^{k t+C_1}-1} \\\\\Rightarrow y=\frac{M}{1-e^{-k t-C_1}} \\\Rightarrow y=\frac{M}{1-e^{-k t} e^{C_1}}\end{gathered}$$[/tex]

Let A be a new constant such that:

[tex]\Rightarrow y=\frac{M}{1-A e^{-k t}}[/tex]

Substitute the values of M and k, we'll get:

[tex]\Rightarrow y=\frac{7 \times 10^7}{1-A e^{-0.76 t}}[/tex]

Substituting the given initial condition:[tex]\Rightarrow y(0)=2 \times 10^7[/tex]

[tex]\Rightarrow 2 \times 10^7=\frac{7 \times 10^7}{1-A e^{-0.76(0)}} \\\\\\Rightarrow 2=\frac{7}{1-A} \\[/tex]

=2-2A=7

=A=-2.5

Therefore, [tex]\Rightarrow y=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}}[/tex]

On simplification, we'll get:

[tex]$$\begin{aligned}& \Rightarrow y \approx 32270466.08 \mathrm{~kg} \\& \Rightarrow y \approx 3.23 \times 10^7 \mathrm{~kg}\end{aligned}$$[/tex]

(b). Substitute the given value in the equation

[tex]$$\begin{gathered}\Rightarrow 4 \times 10^7=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4=\frac{7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4+10 e^{-0.76 t}=7\end{gathered}$$[/tex]

On simplification, we'll get t=1.58 years

Therefore, it will take for the biomass to reach 4 times 107 kg is 1.58 years.

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This is one way we can represent a linear equation:

[tex]y-y_1=m(x-x_1)[/tex]

We're given:

These functions give us information on two points, as they are represented as [tex]f(x)=y[/tex]:

First, solve for the slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

⇒ Plug in the two points:

[tex]m=\dfrac{-6-(-7)}{3-(-1)}\\\\m=\dfrac{-6+7}{3+1}\\\\m=\dfrac{1}{4}[/tex]

⇒ Plug this into [tex]y_2-y_1=m(x_2-x_1)[/tex]:

[tex]y-y_1=\dfrac{1}{4}(x-x_1)[/tex]

Now, there are two ways we can write this equation, as we are given two points:

(-1, -7)

⇒ [tex]y-(-7)=\dfrac{1}{4}(x-(-1))\\y+7=\dfrac{1}{4}(x+1)[/tex]

(3,-6)

⇒ [tex]y-(-6)=\dfrac{1}{4}(x-(3))\\y+6=\dfrac{1}{4}(x-3)[/tex]

[tex]y+7=\dfrac{1}{4}(x+1)[/tex] or [tex]y+6=\dfrac{1}{4}(x-3)[/tex]

A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck is a geometric distribution.

Given that,

A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck.

We have to find count how many times a card is drawn in this way until a jack is seen.

We know that,

A discrete probability distribution known as a geometric distribution can be used to describe the likelihood of experiencing success for the first time following a string of failures. Up until the first success, a geometric distribution can undergo an infinite number of trials.

So,

P(X=x)=qˣp.

Therefore, A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck is a geometric distribution.

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Answer: 75%

Step-by-step explanation: 4+3+5=12. 12-3=9. So the probability of not picking orange is 9/12, or 3/4. 3/4=75%. So the answer would be 75%

If you want to have $10,000 at the end of 3n years, you must deposit $86 at the end of the first 2n years and $98 at the end of each subsequent n years (12.25%).

Effective yearly interest rate is equal to (1 + (nominal rate divided by the number of compounding periods)). (Amount of compounding intervals) minus 1.

This would be: 10.47% = (1 + 10% x 12) x 12 - 1 for investment A.

It would be as follows for investment B: 10.36% = (1 + (10.1% 2)) 2 - 1.

The interest payment that the borrower pays the lender is determined by the interest rate. Lenders' quoted interest rates are yearly rates. The interest payment on the majority of house mortgages is computed monthly. As a result, the rate is divided by 12 before the payment is determined.

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From the provided topics to select, For the analytical data we need something where we can extract information from it. The answer is page bounce rate revenue and revenue per session.

In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.

The systematic computational analysis of data or statistics is known as analytics. It is employed for the identification, explanation, and dissemination of significant data patterns. It also involves using data patterns to make smart decisions.

Page bounce rate revenue and revenue per session are the topics which contains some data and facts from which an analysis process can extract some information for other uses.

So, The metrics for understanding analytical data are page bounce rate revenue and revenue per session.

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Answer: Its the same number with the sign changed..

Step-by-step explanation:

5 multiplied by negative 1 would be -5

And

negative 5 multiplied by negative 1 would be 5

Answer:

a) c[tex]\int\limits gradf.dr[/tex] = 1

b) c[tex]\int\limits gradf.dr[/tex] = 0

   (the limit symbol has a circle in the center for part b)

Step-by-step explanation:

c[tex]\int\limits gradf.dr[/tex] = f(q) - f(p)

a) c[tex]\int\limits gradf.dr[/tex] = f(1, 2) - f(0, 1)

                      =  61 - 60

                      = 1

b) If C is the circle of radius 1 centered at the point beginning at point (1,2), we can think of C as both beginnings and ending at point ( 1, 3).

c[tex]\int\limits gradf.dr[/tex] = f(1, 3) - f(1, 3)

                  = 68 - 68

                  = 0

Answer:

To write the equation in standard form, we need to isolate the variables on one side of the equation and the constants on the other side. We can do this by combining like terms and using the distributive property.

First, we distribute the 3 on the right side of the equation:

4y - 5x = 12x - 6y + 3

Then, we combine like terms:

4y - 5x = 12x - 6y + 3

= -x + 6y + 3

Finally, we move all the constants to the right side of the equation and all the variables to the left side:

x - 6y = -3

This is the standard form of the equation. In standard form, the equation has the form ax + by = c, where a and b are coefficients, and c is a constant. In this case, the coefficients are 1 and -6, and the constant is -3.

Answer:

17x - 10y = - 3

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

4y - 5x = 3(4x - 2y + 1) ← distribute parenthesis

4y - 5x = 12x - 6y + 3 ( subtract 4y - 5x from both sides )

0 = 17x - 10y + 3 ( subtract 3 from both sides )

- 3 = 17x - 10y , that is

17x - 10y = - 3 ← in standard form

The number of bags filled by the pet shop is 879 and the number of treats they gave to the groomer is 4.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the data given in the question,

Total number of dog treats in the shop = 6157

Number of treats per bag = 7

Extra treats will be given to the groomer.

Then, the number of bags will be,

6157/7 = 879.57

This means that a total of 879 bags are there, with 7 pieces of treats per bag.

So, the total number of treats in 879 bags will be,

879 × 7 = 6153

So, the amount of treats left for the groomer is,

6157 - 6153 = 4 treats.

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Answer:

a : c = 3 : 20

Step-by-step explanation:

Given ratios:

The value of b is 3 and 5.

The lowest common multiple of 3 and 5 is 15.

Multiply each ratio by a factor of 15 so that b is 15.

Multiply ratio a : b by 3:

⇒ a : b = 6 : 15

Multiply ratio b : c by 5:

⇒ b : c = 15 : 40

Therefore:

⇒ a : b : c = 6 : 15 : 40

So a : c is:

⇒ a : c = 6 : 40

Simplest form:

⇒ a : c = 3 : 20

The correct statement is-number of students in the data set

In research and data collecting, something that is being measured and whose values can change is referred to as a variable.

Given that we have a range of alternatives from January to December, the aforementioned example demonstrates how the student birth month is a variable. The student's ability to indicate whether they support particular political parties or not makes their political affiliation another variable. Since they are college students, the age of the student is another variable, with replies falling within a range of 20 to 25.

Since students will give different answers, whether they live at the same address or a different one, student address is also a variable.

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To solve this inequality, we can start by converting the mixed numbers to improper fractions. The mixed numbers in this inequality are 1/3 and -2 1/4. The negative sign in front of 2 1/4 indicates that the resulting fraction will be negative. To convert 1/3 to an improper fraction, we can multiply the denominator (3) by the whole number (1) and add the result to the numerator (1). This gives us 1/3 = 4/3. To convert -2 1/4 to an improper fraction, we can multiply the denominator (4) by the whole number (-2) and add the result to the numerator (1). This gives us -2 1/4 = -9/4.

Next, we can combine the two fractions on the left side of the inequality by adding their numerators and denominators. This gives us m + 4/3 + -9/4. We can then simplify this expression by combining like terms. This gives us m - 9/12 + 4/3. We can further simplify this expression by adding the fractions with unlike denominators. To do this, we can find a common denominator by multiplying the two denominators together, which gives us 12 * 3 = 36. We can then convert the fractions to have this common denominator by multiplying the numerator and denominator of each fraction by the appropriate value. For m - 9/12 + 4/3, we have m - (9 * 3)/(12 * 3) + (4 * 12)/(3 * 12), which simplifies to m - 27/36 + 48/36. We can then combine like terms to get m + 21/36.

Finally, we can solve for m by moving all of the terms with m to one side of the inequality and all of the other terms to the other side. To do this, we can subtract 21/36 from both sides of the inequality, which gives us m + 21/36 - 21/36 < -2 1/4 - 21/36. This simplifies to m < -2 1/4 - 21/36, which we can further simplify by converting -2 1/4 - 21/36 to an improper fraction. To do this, we can multiply the denominator (4) by the whole number (-2) and add the result to the numerator (1), which gives us -2 1/4 = -9/4. We can then add -9/4 and -21/36 to get -9/4 - 21/36 = -105/36. Finally, we can convert this to a mixed number by dividing the numerator (-105) by the denominator (36) and taking the quotient (-2) as the whole number and the remainder (27) as the numerator of the fraction. This gives us -105/36 =

Answer:

False.  They would form 4 right angles (90)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

y-4 = -3(x-2)

y - 4 = -3x + 6

y = -3x + 6 + 4

y = -3x + 10

Answer:

y = -3x+10

Step-by-step explanation:

Using the slope-intercept equation of a line

y = mx+b  where m is the slope and b is the y intercept

y = -3x+b

Substitute the point into the equation

4 = -3(2) +b

4 = -6+b

10 =b

y = -3x+10

By the slope formula, it is proved that the slope of AC is the same as the slope of DE thus option (D) is correct.

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

As per the given,

D(4,5) and E(5,3)

Slope = (3 - 5)/(5 - 4) = -2

A(6,8) and C(8,4)

Slope = (4 - 8)/(8 - 6) = -4/2 = -2

Since the slope of DE = slope of AC

Therefore, both lines will be parallel by the slope formula.

Hence "It is established using the slope formula that the slopes of AC and DE are the same".

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The complete diagram is below,

The solutions to the equation √( x + x² ) = 0 are x = 0 and x = -1.

Given equation in the question;

√( x + x² ) = 0

First, remove the radical of the left side of the equation by squaring both sides.

(√( x + x² ))² = 0²

x + x² = 0²

x + x² = 0

Next, factor the left side of the equation.

The common factor between x and x² is x

x( 1 + x ) = 0

Hence

x = 0

1 + x = 0

Subtract 1 from both sides

1 - 1 + x = 0 - 1

x = 0 - 1

x = -1

Therefore, the values of x are 0 and -1.

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Answer: 5(7+6s-9t)

Step-by-step explanation:

(note, this isn't the only expression that is equivalent but it's one of them)

You can notice that 35, 30, and 45 share a common factor of 5, and 5x7=35, 5x6=30, and 5x(-9)=-45, so:

5(7+6s-9t), which when you expand, it's equal to= 35+30s-45t

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1A) To find out how much the hot air balloon rose each minute, we need to find the rate at which it rose. The rate can be calculated by dividing the change in altitude by the change in time. In this case, the change in altitude is 70 meters - 44 meters = 26 meters, and the change in time is 2 minutes - 3 minutes = -1 minute (since the time is decreasing). The rate is therefore 26 meters/-1 minute = -26 meters/minute.

1B) The hot air balloon started at an altitude of 44 meters - (-26 meters/minute) * 3 minutes = 44 meters - (-78 meters) = 122 meters.

1C) To find the equation that describes the relationship between the altitude of the hot air balloon and the elapsed time, we can use the information that we have. The altitude at time t=0 is 122 meters, and the rate at which the altitude changes is -26 meters/minute. The equation is therefore A = -26t + 122.

The hot air balloon rise 13 m each minute.

The hot air balloon was 5 m above the ground at start.

The equation that describes the relationship between the altitude of the hot air balloon in meters is A = 13t + 5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have, After 3 minutes, the balloon was 44 meters above the ground.

After 2 minutes later, the hot air balloon had risen to 70 meters above the ground.

1. The rate of change

= (70-44)/ (5-3)

= 26/ 2

= 13 m / min

2. At start the hot air balloon is

= (44-13 x 3)

= 5 m above the ground

3. The equation that describes the relationship between the altitude of the hot air balloon in meters is

A = 13t + 5.

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The value of missing angles in the given figure are as follow:

m∠1= 56  ,m∠2= 56 and m∠3= 74.

As given in the question,

In the figure, MPQ is a triangle

We know that sum of the angles in the triangle is 180.

m∠ MPQ + m∠ PMQ + m∠1 =180

⇒58 + 66 + m∠1=180

⇒124 + m∠1= 180

⇒m∠1= 180 - 124

⇒m∠1=56

so m∠1=56.

∠1 and ∠2 are vertically opposite angles so ,

⇒m∠1= m∠2

therefore, m∠2=56.

Now in triangle QNO

∠QON + m∠2 + m∠3 =180

⇒50 + 56 +m∠ 3=180

⇒106 + m∠3= 180

⇒m∠3= 180 - 106

⇒m∠3=74

Therefore, the measure of the angles in the given figure are m∠1= 56  ,m∠2= 56 and m∠3= 74.

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Answer:

The correct answer is A. No, because 3(2) + 3 ≠ 15.

Step-by-step explanation:

because the total number of goals scored by Skylar and Wyatt was 15, and if Skylar scored 3 goals, then Wyatt would have scored 3 * 2 = 6 goals. Since the total number of goals scored by both players is 15, this scenario is not possible. Therefore, Skylar could not have scored 3 goals.

The required sample size of the given value is 577.

What is margin of error?

The formula to calculate the sample size  :-

n = (p(1-p)((Zα/₂)/E)²

Given :  Estimated proportion  p = 0.60

Margin of error : E = 0.04

Significance level : α = 1-0.95 = 0.05

Critical value : Zα/₂ = 1.96

Now, the required sample size will be :-

n = (0.60)(0.11)(1.96/0.04)²

= 6.6 * (0.0784)²

= 0.57744

Hence, the required minimum sample size of the given is 577.

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For a 90% confidence interval the upper and lower bound is 11.50 and 9.56 respectively.

Confidence interval means the probability that a population parameter will fall between a set of values.

The formula for confidence interval is C.I = u ± z (sd/[tex]\sqrt{n\\}[/tex] ) where u is the mean, sd is the standard deviation and z is the confidence level value. For an area of 90% around the mean, which makes 45% on each side, for the confidence level we will find the z-score at 0.45+0.5 = 0.95 area, and then double it since we need for both sides. At 0.95, the z-score is approximately 1.64. Thus, z is 3.28.

Plugging the values in the formula for C.I gives the upper bound as 10.53 + 0.968 = 11.50 and the lower bound as 10.53 - 0.968 = 9.56

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The probability, to the nearest 10 th of a percent, that both marbles drawn will be green is 0.02

Given :

A bag contains 4 red marbles, 7 blue marbles and 8 green marbles. If two marbles are drawn out of the bag

Probability :

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

total number of possible outcomes = 4 + 7 + 8

= 11 + 8

= 19

Total number of favourable outcomes = 7

probability = favourable outcomes / possible outcomes

= 7 / 19 * 18

= 7 / 342

= 0.02

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So a linear equation in the form p is P(n) = -$0.004*n + $79.

We have two data points:

6000 shirts can be sold for $55 each.

8000 shirts can be sold for $47 each.

Then we can define the relation:P(n).

Where P is the price, and n is the number of shirts.

Now, we know that we can model this as a linear relationship that passes through the points (6000, $55) and (8000, $47)

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, the slope is:

a = ($47 - $55)/(8000 - 6000) = -$0.004

Then our equation is:

P(n) = -$0.004*n + b

Now let's find the value of b, we know that:

P(6000) = $55= -$0.004*6000 + b

$55 = -$24 + b

b= $79

Our equation is:

P(n) = -$0.004*n + $79.

The linear equation P(n) = -$0.004*n + $79 has the form p.

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Answer:

37609

Step-by-step explanation:

You'd put the 3,419 inside the box and 11 outside the box.

But you'd need around 4 spaces inside the box for each number to be on top. And you'd need 2 spaces on the side. (Hopefully that makes sense)
Your answer should be 37609

False. The maximum likelihood estimator (MLE) is a method for estimating the parameters of a statistical model based on the maximization of the likelihood function. In the context of linear regression, the MLE would be the values of the parameters that maximize the likelihood of the observed data given the model.

The least squares estimator, on the other hand, is a method for estimating the parameters of a linear regression model by minimizing the sum of squared residuals, which is the difference between the observed response values and the fitted values predicted by the model. While the least squares estimator and the MLE can sometimes lead to similar estimates of the parameters, they are not the same thing and are derived using different principles.

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Answer:can you copy and paste it?

Step-by-step explanation: