Jesse the beetle crawls at a rate of 9 inches per minute, as modeled by the equation y=9x. His rate decreases by -8 inches per minute. Create two ordered pairs showing the distances he will crawl at 2 minutes and 7 minutes, respectively, at his new rate.

Sometimes, he may move backwards.

Answer:

Yes its a function....good job!!!

Step-by-step explanation:

The length of the unknown sides of the triangles are as follows:

CD = 10√2

AC = 10√2

BC =  10

AB = 10

Since, Triangle ACD

ΔACD is a right angle triangle.

Therefore, Pythagoras theorem can be used to find the sides of the triangle.

c² = a² + b²

where

c = hypotenuse side = AD = 20

a and b are the other 2 legs

lets use trigonometric ratio to find CD,

cos 45 = adjacent / hypotenuse

cos 45 = CD / 20

CD = 1 / √2 × 20

CD = 20 / √2 = 20√2 / 2 = 10√2

Hence,

20² - (10√2)² = AC²

400 - 100(2)  = AC²

AC² = 200

AC = √200 = 10√2

Triangle ABC

ΔABC is a right angle triangle too. Therefore,

AB² + BC² = AC²

Using trigonometric ratio,

cos 45 = BC / 10√2

BC = 10√2 × cos 45

BC = 10√2 × 1 / √2

BC = 10√2 / √2 =  10

Hence,

(10√2)² - 10² = AB²

200 - 100 = AB²

AB² = 100

AB = 10

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The required inequality expression is 8x + 6.50y ≤ 200

Maximum amount he can spend = $200

Cost of doll, = $6.50

Cost of car = $ 8.00

Mathematically, the maximum amount he can spend on restocking is cars and doll is :

(Cost of cars × number of cars) + (cost of doll × number of dolls) ≤ maximum amount

8x + 6.50y ≤ 200

Hence, the required inequality expression is : 8x + 6.50y ≤ 200

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Answer:  x = 200    

Step-by-step explanation:

x-30% of x=140

x = 200    

x-(30/100)*x=140   [Add the parentheses]

x-30x/100=140

100x-30x/100= 140

70x/100= 140

70x=140*100

70x=14000

x=14000/70

x=200                 [Correct]

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.

Which means that DB = CB

Which means that 10x + 16 = 5x + 20

10x - 5x = 20 - 16

5x = 4

x = 4/5

And so the length of CB is

5 * 4/5 + 20 = 4+20 = 24

Good LUCK :)

n = 0.9702. Rounding up to the nearest whole number, we get a minimum sample size of n = 1.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To calculate the minimum sample size needed to estimate the population mean ad price within a specified margin of error, we can use the following formula:

n = ((z*σ)/E)²

Where:

n = sample size

z = the z-score associated with the desired confidence level (in this case, 1.645 for 90% confidence)

σ = population standard deviation (0.6 in this case)

E = the desired margin of error (1 dollar in this case)

Plugging in the values, we get:

n = ((1.645*0.6)/1)²

n = 0.985²

n = 0.9702

Rounding up to the nearest whole number, we get a minimum sample size of n = 1.

Note that this result seems counterintuitive, as it suggests that only one ad needs to be surveyed to estimate the population mean within a dollar with 90% confidence. However, this is because the formula assumes that the population is normally distributed, which may not be the case for ad prices. In practice, it is generally a good idea to survey a larger sample size to ensure more accurate estimates.

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Answer:

17,280

Step-by-step explanation:

first, you find 5.6 % of 10,000 which is 560. Then you have to figure out how many years the interest was coming in which is 13 years. you multiply the 560 by 13 years to get 7,280 and add that to 10,000. that's how you get your final answer of 17,280

  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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The value of the ratio arc DC / arc AB is 3.

This means that arc DC is 3 times longer than arc AB.

To find the measure of arc AB, let's consider the properties of the circle and the chords.

Since AC and BC intersect at right angles at point P, and AB is equal to the radius of the circle, we can conclude that triangle APB is an isosceles right triangle with AP = BP (both are radii).

Therefore, angle APB = angle BPA = 45 degrees.

The measure of arc AB is equal to the measure of the central angle AOB, which is the sum of angles APB and BPA.

So, the measure of arc AB is 45 + 45 = 90 degrees.
To find the value of the ratio arc DC / arc AB, first note that arc DC is the remaining portion of the circle after removing arc AB.

Since the circle has a total of 360 degrees, the measure of arc DC is 360 - 90 = 270 degrees.

Now we can find the ratio:
(arc DC) / (arc AB) = 270 degrees / 90 degrees = 3

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Answer:

6 yards

Step-by-step explanation:

In order to solve this problem, we can take it one step at a time. In this question, we can assume that Igli's starting point is 0. If on the first play he gained 3 yards that means we add this value to the starting point.

0 + 3 = 3 yards.

Now his current position is 3 yards. In the next play, he lost 9 yards which means we must subtract that from his current position.

3 - 9 = -6 yards

Now his current position is -6 yards. In order to get back to the initial position of 0 we need to add the opposite amount of yards as his current position. Since his current position is -6 we need to add positive 6 yards to get him back to 0.

Answer:

(2u-7)(2u+3)

Step-by-step explanation

Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are -35/3, -140/3, - 560/3, -2240/3 and 7, -28, 112, - 448  

Four numbers forming a geometric sequence can be calculate as follows

these terms: a₁, a₂, a₃, a₄

a₁ = a₂ + 35

a₃ = a₄ + 560

Use the formula for the n-term:

a₂ = a₁r

a₃ = a₁r²

a₄ = a₁r³

replace

a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35

a₁r² = a₁r³ + 560  ⇒ a₁(1 - r)r² = 560

Subtracting from the first equation to  the second:

r² = 560/35

r² = 16

r = √16

r = ± 4

Use the first equation to find the first term:

a₁( 1 ± 4) = 35

1. a₁ = 35/-3 = -35/3

2. a₁ = 35/5 = 7

We have two sequences:

r = 4

-35/3, -140/3, - 560/3, -2240/3

r = -4

7, -28, 112, - 448  

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60% have a litle brother... it they are 24 then:

60% is to 24 as 100% is to x

so x = 24/(60%) = 24/0.6 = 40

the answer is 40

Answer:

Leon's puppy has gained the most weight.

The expression x³ - x when factored out is x(x -1)(x + 1)

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

X to the power of three - x

Express the expression properly

So, we have the following representation

x³ - x

The terms of the above expression are:

x³ and x

And the factor of x³ and x

Factor = x

So, we divide x³ and x by x

The results of these divisions are

x³/x = x²

x/x = 1

So, we have the following results

(x³ - x) = x(x² -1)

Express x² -1 as a difference of two squares

So, we have

(x³ - x) = x(x -1)(x + 1)

Hence, the factored expression is x(x -1)(x + 1)

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Answer:

125, 205, 390

Step-by-step explanation:

Answer:

125​ Supposedly

Step-by-step explanation:

The equation shows the relationship between variables and other quantities in a situation, by equating the constants of the situation.

What is an equation of variable?

The equation's unknown component is the variable. Variables alter when quantities change in any circumstance. It stands for an unidentified quantity, value, or number.

Equation properties include:

Consider a situation where a taxi driver charges a fee based on the distance of a taxi ride. This is presented as the equation,

y = 8x + 15

where variable(y) indicates the charge of the taxi and variable (x) represents the number of rides the taxi travelled.

And, the constant term 15 is the fixed amount which is charged by the taxi driver and 8 represents the rate by which the charge increases with respect to y.

Hence, the above-given equation shows the relationship between variables and other quantities in a situation.

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Answer:

The answer is b 2/5 times 1/4

Step-by-step explanation:

The expression equivalent to the given expression  -2(3x + 5y) is

given that

-2(3x + 5y)

expanding the parenthesis

-6x - 10y = 0

10y = 6x

y = 6x/10

y = 3x / 5

we can conclude that y = 3x/5 is equivalent to  -2(3x + 5y)

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The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The solution to the inequality will be -

x ≥ 3    or   x ≤ -1

We have the given inequality as -

|4x − 4| ≥ 8

We have the inequality as -

|4x − 4| ≥ 8

4x - 4 ≥ 8     or     4x - 4 ≤ - 8  

4x ≥ 12      or      4x ≤ - 4

x ≥ 3    or   x ≤ -1

Therefore, the solution to the inequality will be -

x ≥ 3    or   x ≤ -1

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The size of angle BCA is 45 degrees

A quadrilateral called a kite has two pairs of sides that are each the same length and are next to one another.

Where the two uneven sides meet, the two angles are equal. It can be thought of as two congruent triangles sharing a base. It has two diagonals that right-angle intersect with one another.

Given:

From the Figure we can see that

AB = BC and AD = DC = AC

and, ABC = 90 degrees

Now, In triangle ABC using Angle sum Property

A + B + C = 180

So,  A + 90 + C = 180

A + C = 90

As, AB = BC

Then, 2C = 90

C = 45

Hence, the angle is 45 degrees

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The Question attached here seems to be incomplete/ inappropriate. The complete Question is:

ABCD is a kite with AB = BC and AD = DC = AC, What is the size of angle  BCA

Step-by-step explanation:

22-14=8 so J=8

Answer: 123.30 miles

Step-by-step explanation:

Key: 1.25 in = 4.5 miles

14.5+19.75=34.25

34.25 divided by 1.25 = 27.40

27.40 x 4.5 = 123.30 miles <3