If (2, 3) is a point on locus whose equation is ax + 2y = 16 and also show that (0, 8) is another point on the locus.​

Answer:

Step-by-step explanation:

The sum of all possible values of $a$ is $1$.

To solve this problem, we need to use the given information to determine possible values of $a$ and $b$ in $g(x)=ax+b$ such that $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$.

First, we can simplify $f(g(x))$ and $g(f(x))$ as follows:

$$f(g(x))=3(ax+b)+2=3ax+3b+2$$

$$g(f(x))=a(3x+2)+b=3ax+ab+b$$

Next, we can set these two expressions equal to each other and simplify:

$$3ax+3b+2=3ax+ab+b$$

$$2b-ab=b$$

$$(2-a)b=b$$

Since $ab=20$, we have two cases to consider:

Case 1: $b=0$

In this case, we have $ab=20\implies a=0$ or $b=0$. Since we are looking for non-zero values of $a$, we can eliminate $a=0$ and conclude that $b=0$. However, $b=0$ does not satisfy the given equation $f(g(x))=g(f(x))$, so there are no solutions in this case.

Case 2: $b\neq 0$

In this case, we can divide both sides of $(2-a)b=b$ by $b$ to get:

$$2-a=1$$

$$a=1$$

Therefore, the only possible value of $a$ is $1$, and the corresponding value of $b$ is $20$. We can verify that $a=1$ and $b=20$ satisfy the given equation $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$.

You can learn more about sum at: brainly.com/question/31265134

#SPJ11

The volume of the container is  2216 liters

Using the general gas law, we have that;

PV = nRT

Such that the parameters are given as;

From the information given, we have that;

Substitute the values

3V = 4 × 8.31 × 200

Multiply the values, we have;

3V = 6648

Divide both sides by the coefficient of V, we get;

V = 2216 liters

Learn about volume at: https://brainly.com/question/1972490

#SPJ4

The farmer would have made a profit of 5% if he had sold the goat for 2100 shillings.

Let's use the given terms and find out the percentage profit if the farmer had sold the goat for 2100 shillings.
Calculate the cost price of the goat
We know that the farmer made a loss of 28% by selling the goat for 1440 shillings. Let's represent the cost price as "CP".

We can write the equation:
[tex]CP \times  (1 - loss% ) = selling price (SP)[/tex]
[tex]CP \times  (1 - 0.28) = 1440[/tex]
Solve for CP
[tex]CP \times 0.72 = 1440[/tex]
CP = 1440 / 0.72
CP = 2000 shillings
Calculate the percentage profit
Now we want to find out the percentage profit if the farmer had sold the goat for 2100 shillings.

We can write the equation:
[tex](SP_{new - CP)} / CP \times  100 = profit[/tex]
[tex](2100 - 2000) / 2000 \times  100 = profit%[/tex]
[tex]100 / 2000 \times  100 = profit%[/tex]
5% = profit%.

For similar question on profit.

https://brainly.com/question/29087694

#SPJ11

The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is  13.58

First using distance calculator we derived the length of TV and the length of VU.

Since TV = Height; and

VU = Base

and the triangle is a right triangle,

Then, area is given by 1/2 base x Height

Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264

So area = 1/2 * 6.40312 * 4.24264

Area = 13.58

Learn more about area:
https://brainly.com/question/27683633
#SPJ1

The interquartile range (IQR) of the given data set is 4.

Interquartile range (IQR) is a measure of variability in a data set that measures the spread of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

To find the interquartile range (IQR), we first need to find the median of the data set.

The median is the middle value of the dataset when the data is arranged in order. In this case, the data set is already in order, so the median is the middle value or the average of the two middle values:

Median = (26 + 28) / 2 = 27

Now, we need to find the first quartile (Q1) and the third quartile (Q3) of the data set.

Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.

Lower half: 22, 24, 26

Upper half: 28, 30

Q1 = median of the lower half = (24 + 26) / 2 = 25

Q3 = median of the upper half = (28 + 30) / 2 = 29

Now we can find the IQR:

IQR = Q3 - Q1 = 29 - 25 = 4

Therefore, the interquartile range (IQR) of the given data set is 4.

To know more about median

brainly.com/question/28060453

#SPJ1

Answer:

86 degrees fahrenheit

Step-by-step explanation:

(30°C × 9/5) + 32 = 86°F

(a) Miguel had the greatest spread in training times.

(b) The middle 50% of Adam's training times had the least spread.

(a) To find the greatest spread in training times, we need to calculate the range of each person's training times. Range is the difference between the maximum and minimum values. Comparing the ranges, we can say that Miguel had the greatest spread in training times since his range is the largest.

(b) The middle 50% of the training times refers to the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).

To find the least spread in the middle 50% of the training times, we need to compare the IQRs of each person. Adam's IQR is the smallest, which means the middle 50% of his training times had the least spread.

(c) The answers to parts (a) and (b) indicate that Miguel had a wider range of training times compared to Adam. However, Adam's middle 50% of training times had the least spread. This suggests that while Miguel's overall training times varied more, Adam's training times were more consistent within the middle range.

For more questions like Training click the link below:

https://brainly.com/question/8320293

#SPJ11

The ground speed of the ship is approximately 10 miles per hour.

To calculate the ground speed, we need to use vector addition. The ship's velocity can be broken down into two components: its speed in the easterly direction and its speed in the northerly direction. The easterly component is 8 miles per hour (since the ship is moving due east), and the northerly component can be found using trigonometry: northerly component = 8 * sin(60°) ≈ 6.93 miles per hour

Now, we need to take into account the effect of the currents, which are moving in a southerly direction. Again using vector addition, we can find the resultant velocity (i.e., the velocity of the ship relative to the ground) by adding the ship's velocity vector to the current's velocity vector. Since the current is moving due south, its velocity vector has no easterly component, but its southerly component is 4 miles per hour. resultant velocity = (8, 6.93) + (0, -4) = (8, 2.93)

Using the Pythagorean theorem, we can find the magnitude of the resultant velocity: |resultant velocity| = [tex]\sqrt{} (8^2 + 2.93^2)[/tex]≈ 8.6 miles per hour. Rounding to the nearest whole number, the ground speed of the ship is approximately 10 miles per hour.

Learn more about Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ4

Answer:

f(5) = 167

Step-by-step explanation:

To evaluate f(x) = 7x^2 - 8 when x = 5, we substitute 5 for x in the expression and simplify. Therefore, we have:

f(5) = 7(5)^2 - 8

f(5) = 7(25) - 8

f(5) = 175 - 8

f(5) = 167

So, f(5) = 167

a) Here is the chart showing the number of bacteria after 0 to 4 hours:

| Time (hours) | Number of bacteria |

|--------------|--------------------|

| 0 | 50 |

| 1 | 150 |

| 2 | 450 |

| 3 | 1,350 |

| 4 | 4,050 |

b) To write an expression that models the number of bacteria after a number of hours, n, we can use the formula:

In this case, the initial number of bacteria is 50, and the growth factor is 3 (since the number of bacteria triples every hour). Therefore, the expression that models the number of bacteria after n hours is:

c) To determine the number of bacteria that are present after 12 hours using the expression we derived in part b), we can substitute n = 12 into the expression:

= 26572050

The substitution is u = -x² + 9 and the evaluated value is -4.5(2/3)(-x² + 9)³/² + C.

To evaluate the given integral ∫9x√(-x² + 9dx),

we can use the substitution u = -x² + 9. This substitution will allow us to simplify the expression under the square root.

First, we can find du/dx by taking the derivative of u with respect to x: du/dx = -2x.

Next, we can solve for dx in terms of du by dividing both sides by -2x: dx = -du/(2x).

Using the substitution and the expression for dx in terms of du, we can rewrite the integral as:

∫9x√(-x² + 9dx) = -4.5∫√udu

Now, we can integrate the simplified expression √u using the power rule of integration:

-4.5∫√udu = -4.5(2/3)u³/² + C

Substituting back for u, we get:

-4.5(2/3)(-x² + 9)³/² + C

Therefore, the solution to the integral ∫9x√(-x^2 + 9dx) using the substitution u = -x^2 + 9 is:

-4.5(2/3)(-x² + 9)³/² + C

Learn more about derivative of integral : https://brainly.com/question/30398950

#SPJ11

The money multipliers are:

(a) 25.000

(b) 8.000

(c) 2.500

(d) 5.000

The money multiplier represents the amount of money the banking system can create through the lending process for every dollar of reserves held by the central bank. It is inversely related to the reserve requirement, which is the percentage of deposits that banks are required to hold as reserves.

When the reserve requirement is low, su

The money multiplier is given by the formula:

Money multiplier = 1 / Reserve requirement

(a) When the reserve requirement is 0.040, the money multiplier is:

Money multiplier = 1 / 0.040 = 25.000

(b) When the reserve requirement is 0.125, the money multiplier is:

Money multiplier = 1 / 0.125 = 8.000

(c) When the reserve requirement is 0.400, the money multiplier is:

Money multiplier = 1 / 0.400 = 2.500

(d) When the reserve requirement is 0.200, the money multiplier is:

Money multiplier = 1 / 0.200 = 5.000

Therefore, the money multipliers are:

(a) 25.000

(b) 8.000

(c) 2.500

(d) 5.000

Learn more about money multipliers

https://brainly.com/question/14986591

#SPJ4

Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.

First, we calculate the down payment:
10% of $25,625 = $2,562.50

Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50

Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69

Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82

So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82

Rounded to the nearest cent, the answer is option D: $27,735.14.

To know more about rounding-off:

https://brainly.com/question/28128444

#SPJ11

The population of the city after 5 years is approximately 7.94 million.

Assuming that the population of the city grows exponentially, we can use the formula:

P(t) = [tex]P0 * e^(^r^t^)[/tex]

Where:

- P(t) is the population after time t

- P0 is the initial population

- r is the annual growth rate expressed as a decimal

- t is the time elapsed in years

Using the given information:

- P0 = 6.47 million

- r = 2.91% = 0.0291

Let's calculate the population after 1 year:

[tex]P(1) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^1^)[/tex]

= 6.66 million (rounded to two decimal places)

So, the population of the city after one year is approximately 6.66 million.

We can also calculate the population after 5 years:

[tex]P(5) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^5^)[/tex]

= 7.94 million (rounded to two decimal places)

Learn more about Annual growth rate

brainly.com/question/23287647

#SPJ11

Answer:

new perimeter of Brandy deck is 46 feet .

Step-by-step explanation:

The new perimeter of Brandy deck is 46 feet.

The entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.

Using the given information,

Width = 7 Feet

Length = 12 feet

Perimeter = 2 (Width + Length)

[tex]= 2(7+12)[/tex]

[tex]=2(19)[/tex]

[tex]=38[/tex]

Perimeter when deck is 4 feet longer [tex]=38+ 4+4=46[/tex] Feet

Hence, the new perimeter of a deck is 46 feet.

Learn more about the perimeter of rectangle at:

brainly.com/question/24571594

At the coordinates (X, Y, Z) = (3, -2, 0), L(x, y, z) = C+35 + x - 12Cz is the linear approximation to the function f(Dy, Z) = Ce^2yz+32.

To find the linear approximation to the function f(Dy, Z) = Ce^2yz+32 at the point (X, Y, Z) = (3,-2,0), we need to find the partial derivatives of the function with respect to each variable at the point (3,-2,0).

The partial derivative of f with respect to x is simply e^2yz, which evaluated at (3,-2,0) gives us e^0 = 1.

The partial derivative of f with respect to y is 2xzCe^2yz, which evaluated at (3,-2,0) gives us 2(3)(0)C = 0.

The partial derivative of f with respect to z is 2xyCe^2yz+3, which evaluated at (3,-2,0) gives us 2(3)(-2)C + 3(1) = -12C + 3.

Using these partial derivatives, we can construct the linear approximation L(x,y,z) = f(3,-2,0) + (x-3)(1) + (y+2)(0) + (z-0)(-12C+3) = Ce^0+32 + (x-3) - 12Cz + 3.

Simplifying this expression, we get L(x,y,z) = C+35 + x - 12Cz.

Therefore, the linear approximation to the function f(Dy, Z) = Ce^2yz+32 at the point (X, Y, Z) = (3,-2,0) is L(x,y,z) = C+35 + x - 12Cz.

To learn more about coordinates visit;

brainly.com/question/16634867

#SPJ11

The measure of the other side of the right triangle is given as follows:

12 cm.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the other side has the length given as follows:

5² + x² = 13²

25 + x² = 169

x² = 144

x = 12.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

Calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix.

We can use a hypothesis testing approach to answer this question. The null hypothesis is that the true proportion of California residents who use Netflix is the same as the national proportion, or p = 0.55. The alternative hypothesis is that the true proportion of California residents who use Netflix is greater than 0.55, or p > 0.55.

We can use the sample proportion of Netflix users in California, which is 360/600 = 0.6, as an estimate of the true proportion p. The standard error of the sample proportion is:

SE = √[(p*(1-p))/n] = √[(0.55*(1-0.55))/600] = 0.024

The test statistic is:

z = (p - 0.55)/SE = (0.6 - 0.55)/0.024 = 2.08

Assuming a significance level of 0.05 and a one-tailed test (since the alternative hypothesis is one-sided), the critical z-value is 1.645.

Since our calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix. However, we should keep in mind that this conclusion is based on a sample of 600 adults from California, and there is always some degree of uncertainty involved in statistical inference based on samples.

To know more about hypothesis testing, refer to the link below:

https://brainly.com/question/30588452#

#SPJ11

The area of ΔEFG is approximately 6.7 square centimeters.

To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:

Area = (1/2)ab * sin(C)

In this case, a = g, b = e, and C = ∠F. Plug in the values:

Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)

Area ≈ 6.675 square centimeters

So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.

Learn more about area here: https://brainly.com/question/28470545

#SPJ11

Solving a system of equations we can see that he has 9 quarters and 16 dimes.

Let's define the variables:

x =  number of dimes

y = number of quarters.

There are 25 coins, so:

x + y = 25

The value is $3.85, so:

x*0.10 + y*0.25 = 3.85

So the system of equations is:

x + y = 25

x*0.10 + y*0.25 = 3.85

We can isolate x on the first equation to get:

x = 25 - y

Replacing that in the other one we get:

(25  -y)*0.10 + y*0.25 = 3.85

2.5 + y*0.15 = 3.85

y = (3.85 - 2.5)/0.15

y = 9

Then the other 16 coins are dimes.

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Answer:

a= 2.9cm

Step-by-step explanation:

area =25 so 17a=50

50/17=2.941176...

y = 6

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

The value of Y in the equation Y/4 = 3/2 is 6.

To find the value of Y, we'll use the following steps:

1. We start with the given equation:

Y/4 = 3/2.

2. Our goal is to isolate Y. To do this, we'll multiply both sides of the equation by 4, which is the denominator on the left side.

3. Multiplying both sides by 4 gives us: (Y/4) * 4 = (3/2) * 4.

4. On the left side, the 4s cancel out, leaving just Y: Y = (3/2) * 4.

5. Now, we simplify the right side by multiplying 3/2 by 4. We can think of 4 as 4/1, so the equation becomes: Y = (3/2) * (4/1).

6. Multiply the numerators (3*4) and denominators (2*1) separately: Y = (12/2).

7. Finally, simplify the fraction: Y = 6.

Learn more about Equation at

https://brainly.com/question/10413253

#SPJ11

To find the image of point P(-2,-2) translated 1 unit to the left and 3 units down, we subtract 1 from the x-coordinate and 3 from the y-coordinate to get coordinates of P' as: (-3, -5).

To translate a point to the left, we subtract from its x-coordinate, and to translate it down, we subtract from its y-coordinate.

Therefore, to translate P(-2, -2) 1 unit to the left and 3 units down, we subtract 1 from the x-coordinate and 3 from the y-coordinate to get P'(-3, -5) as the image of P after translation.

Therefore, the coordinates of P' are (-3, -5).

Learn more about translation on:

https://brainly.com/question/12861087

#SPJ1

Complete Question:

Point P' is the image of P(-2,-2) translated by 1 unit to the left and 3 units down. What are the coordinates of P'?

To determine the number of additional days that would make the cost equivalent for both Heather's Moving and Newton Rent-a-Truck, we can set up an equation:

Heather's Moving: 10 + 8x
Newton Rent-a-Truck: 80 + x

To find the point at which the costs are equal, we can set the equations equal to each other:

10 + 8x = 80 + x

Now, we can solve for x (additional days):

7x = 70
x = 10

So, the costs would be equivalent after 10 additional days. To find the total cost, we can plug the value of x back into either equation:

Total cost = 10 + 8(10) = 10 + 80 = $90.

Learn more about additional days: https://brainly.com/question/24900258

#SPJ11

Answer: Did not convert the minutes to hours

Step-by-step explanation:

The most obvious mistake here would be to not convert the minutes into hours.

Remember, the speed given, (7.5), is in miles per HOUR. Your time is given in MINUTES. a conversion is required. 45 minutes are 45/60 = 0.75 hrs.

NOW you can use S = DT to find your distance:

7.5 = D/0.75

.: D = 5.625 miles

Ann has failed to meet the condition called the "success-failure" condition.

In order to construct a confidence interval for the proportion (p), the sample must have at least 10 successes (planning to travel outside the state) and 10 failures (not planning to travel outside the state). In her sample of 29 students, she found 12 planning to travel (successes) and 17 not planning to travel (failures). Both numbers satisfy the success-failure condition, so she can construct the confidence interval for the proportion of students planning to travel outside the state during the coming summer.

More on  "success-failure" condition: https://brainly.com/question/31605067

#SPJ11

Answer:

C: The sample must be a random sample from the population

Step-by-step explanation:

took the test on edge

Gabriela will use 1620 square inches of wood to build the open box.

The amount of wood Gabriela will use depends on the surface area of the box, which is the sum of the areas of its six faces. Since the box is open on top, it will have five faces: four sides and a bottom.

The area of the bottom is the area of a rectangle with length 18 in. and width 15 in., which is:

Area of bottom = length x width = 18 in. x 15 in. = 270 in²

The area of each side is the product of the height and the length of the corresponding base, which is:

Area of each side = height x length = 15 in. x 18 in. = 270 in²

So the total surface area of the box is:

Total surface area = 2 x (Area of bottom) + 4 x (Area of each side)

= 2 x 270 in² + 4 x 270 in²

= 1620 in²

Therefore, Gabriela will use 1620 square inches of wood to build the open box.

Learn more about total surface area,

https://brainly.com/question/28178861

#SPJ11

To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:

u = rv + sw

Substituting the given values, we get:

(7, -10) = r(2, 1) + s(1,4)

Using the symbolic notation, we can write this as a system of equations:

7 = 2r + s
-10 = r + 4s

We can solve this system of equations by using the elimination method:

Multiply the second equation by 2:

7 = 2r + s
-20 = 2r + 8s

Subtracting the first equation from the second, we get:

-27 = 7s

Dividing both sides by 7, we get:

s = -27/7

Substituting this value of s into the first equation, we get:

7 = 2r - 27/7

Multiplying both sides by 7, we get:

49 = 14r - 27

Adding 27 to both sides, we get:

76 = 14r

Dividing both sides by 14, we get:

r = 38/7

Therefore, u = (7, -10) can be expressed as the linear combination:

u = (38/7)(2,1) + (-27/7)(1,4)

Using fractions where needed, the answer is:

u = (76/7, 38/7) + (-27/7, -108/7)
Visit here to learn more about the coordinates of vertices

brainly.com/question/28852734

#SPJ11

A reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.

To determine a reasonable estimate for the amount of flour and sugar combined, we first need to add the fractions 1/4 and 2/9. To do this, we need to find a common denominator. The least common multiple of 4 and 9 is 36. We can convert 1/4 to 9/36 by multiplying both the numerator and denominator by 9. We can also convert 2/9 to 4/36 by multiplying both the numerator and denominator by 4. Now we can add the fractions:

9/36 + 4/36 = 13/36

So Ellen mixed 13/36 kg of flour and sugar combined. To convert this to a decimal, we can divide the numerator by the denominator:

13 ÷ 36 ≈ 0.36

Therefore, a reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.

To know more about reasonable estimate, refer to the link below:

https://brainly.com/question/23707423#

#SPJ11