Solve the system by the method of your choice.
X=10+6y
X-6y=5

The function that models the number of bacteria, f(t), at time t, in hours, is f(t) = 100(∛4)^t

Based on the scatter plot, we can see that the data points roughly form an exponential curve.

Therefore, we can use the function of the form f(t) = ab^t to model the data, where a is the initial value of the function (the number of bacteria at t=0) and b is the growth factor.

To find the values of a and b, we can use the two data points given in the table: (0, 100) and (3, 400). Substituting these values into the equation, we get:

100 = ab^0  ->  a = 100

400 = ab^3

Dividing the second equation by the first equation, we get:

4 = b^3  ->  b = ∛4

Therefore, the function that models the number of bacteria, f(t), at time t, in hours, is f(t) = 100(∛4)^t

So the answer is f(t) = 100(∛4)^t.

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Answer:

50 employees can the company send to the conference

Step-by-step explanation:

2500:50= 50

The production cost for one lollipop is 5 dollars.

Let's assume the production cost for one lollipop is x dollars.

If Lewis sells one lollipop for 5 dollars, his profit = 5 - x dollars.

If Lewis sells three lollipops for 10 dollars,

Each lollipop would cost = 10/3 dollars ≈ 3.33 dollars.

So, if he sells three lollipops, his revenue would be 3 × 5 = 15 dollars, and his total cost would be 3 × x dollars = 3x dollars.

Therefore, his profit would be 15 - 3x dollars.

Since Lewis' profit is the same whether he sells one lollipop or three lollipops, we can set the two profit equations equal to each other and solve for x:

5 - x = 15 - 3x

2x = 10

x = 5

Therefore, the production cost for one lollipop is 5 dollars.

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To find the dimensions of the rectangular base, we can use the formula for the volume of a rectangular box:

Volume = Length x Width x Height

Given that the volume is 2860 and the height is 40 cm, we can rearrange the formula to solve for the dimensions of the base:

2860 = Length x Width x 40

Now, let's find possible dimensions by factoring 2860:

2860 = 2 x 2 x 5 x 11 x 13

To find the dimensions of the base, we need to divide these factors into the length and width in different combinations. Here are a few possible options:

Option 1:

Length = 2 x 5 x 11 = 110 cm

Width = 2 x 13 = 26 cm

Option 2:

Length = 2 x 2 x 11 = 44 cm

Width = 5 x 13 = 65 cm

Option 3:

Length = 2 x 2 x 13 = 52 cm

Width = 5 x 11 = 55 cm

These are just a few examples, and there could be other combinations of factors that give a volume of 2860 with a height of 40 cm.

Expression: 12x / 2

A coefficient is the number in front of a variable. In this problem, the coefficient is 12 because it is in front of the variable x.

Hope this helps!

Answer: $26.52

Step-by-step explanation:

1 Box of cereal is $2.37 so 6 boxes is equal to 6 * $2.37 = $14.22

1 Pound of apples is $4.10 so 3 pounds is equal to 3 * $4.10 = $12.30

Total = $14.22 + $12.30 = $26.52

The total purchase is  $18.90.

We have,

A discount would reduce the cost of the purchase. A tax increases the cost of the purchase.

The first step is to determine the total cost of the items purchased.

Total cost = (cost of lb of cheese x lb bought) + (cost of sliced ham x lbs bought) + (cost of bread x loaves bought) + (cost of a bag of potato chips x number of bags bought) + (cost of one salsa container x number of containers bought)

(1.99 x 1/2) + (3 x 3.29) + (1.59 x 2) + (2 x $3) + (1.39 x 1) = $20.39

Since, the total cost is greater than $20 she qualifies for the 10% discount

Total cost after the discount = (1 - 0.1) x $20.39

0.9 x $20.39= $18.35

Cost after the tax = (1 + 0.03) x $18.35

1.03 x $18.35 = $18.90

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complete question:

You have several purchases you need to purchase 1/2 lb of cheese, 3lbs sliced ham, 2 loaves of bread, 4 bags of potato chips, and 1 container of salsa. You have a coupon for $4.00 off of your purchase totals more than $15.00 or %10 off if the total is more than $20.00. The food sales tax is 3%. What is your total purchase?

Cheese:$1.99/lb

Sliced ham:$3.29/lb

Bread:$1.59/loaf

Potato chips:$1.99/ea Or 2 for $3.00

Salsa:$1.39/container

Be sure to include in your response.

The steps you followed to complete your computations.

The choice you made regarding which discount to use.

The total cost of your purchase.

The expression (fg)(x) is equal to 16x^4 + 72x^3 - 39x^2 + 5x.

To find (fg)(x), we need to evaluate the product of f(x) and g(x).

First, let's express f(x) and g(x) explicitly:

f(x) = 4x^2 + 19x - 5

g(x) = 4x^2 - x

Now, we can calculate their product:

(fg)(x) = f(x) * g(x)

= (4x^2 + 19x - 5) * (4x^2 - x)

To simplify the expression, we can use the distributive property and combine like terms:

(fg)(x) = 4x^2 * 4x^2 + 4x^2 * (-x) + 19x * 4x^2 + 19x * (-x) - 5 * 4x^2 - 5 * (-x)

Expanding and collecting like terms:

(fg)(x) = 16x^4 - 4x^3 + 76x^3 - 19x^2 - 20x^2 + 5x

Combining like terms:

(fg)(x) = 16x^4 + 72x^3 - 39x^2 + 5x.

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Answer:

cioè x ≥ 1; si avrà pertanto x > 0

Step-by-step explanation:

EXERCISE 2. Risolvere le seguenti disuguaglianze:

(1) | x−1 |< 3

(2) | x+1 |> 2

(3) | 2x+1 |< 1

(4) | x−1 |<| x+1 |

Caso: (a): | x−1 |< 3, risolvo

x−1 < 3

x ≥ 1

∪

−x+1 < 3

x < 1

, si avrà quindi

x < 4

x ≥ 1

cioè 1 ≤ x < 4 e

x > −2

x < 1

cioè −2 < x < 1. L’unione tra le due dà la soluzione −2 < x < 4

Caso: (b):

x+1 > 2

x ≥ −1

∪

−x−1 > 2

x < −1

, si avrà quindi

x > 1

x ≥ −1

cioè x > 1 e

x < −3

x < −1

cioè x < −3,

pertanto x < −3 ∪ x > 1

Caso: (c):

2x+1 < 1

x ≥ −1

2

∪

−2x−1 < 1

x < −

1

2

, si avrà quindi

x < 0

x ≥ −1

2

cioè −

1

2 ≤ x < 0 e

x > −1

x < −

1

2

cioè

−1 < x < −

1

2

. pertanto −1 < x < 0

Caso: (d): in questo caso,

−x+1 < −x−1

x < −1

∪

−x+1 < x+1

−1 ≤ x < 1

∪

x−1 < x+1

x ≥ 1

, si avrà quindi

0 < −2

x < 1

cioè non si hanno soluzioni e

x > 0

−1 ≤ x < 1

cioè 0 < x < 1 e

0 < 2

x ≥ 1

cioè x ≥ 1; si avrà pertanto x > 0

The coordinates of the pre-image, and the applied rotation transformation indicates;

3. a. The center of rotation is (0, 0), and the rotation is 90 degrees counter clockwise

b. The center of rotation is; (-1, 2), and the angle of rotation 90 degrees clockwise

A rotation transformation is one in which the the pre-image is rotated about a point, referred to as the center of rotation.

The coordinates of the vertices of the blue triangle are; (1, -1), (2, -1), (2, -3)

The coordinates of the corresponding vertices of the green triangle are; (1, 1), (1, 2), (3, 2)

The rotation transformation from the blue triangle to the green triangle therefore is (x, y) ⇒ (-y, x), which corresponds to a 90 degrees counterclockwise rotation about the origin.

b. The coordinates of the corresponding vertices of the orange triangle are; (-2, 0), (-1, 0), (-1, -2)

The 90 degrees clockwise rotation of a point (x, y) has an image at the point (y, -x)

The center of rotation can be found using the perpendicular bisectors method, which requires the perpendicular bisectors of the segment joining the corresponding points of the image and the pre-image as follows;

The equation of the line joining (1, 1), to (-2, 0) is; 3·y = x + 2

The slope is 1/3

The coordinates of the location of the perpendicular bisector is (1 + (-2))/2. (1 + 0)/2) = (-0.5, 0.5)

The slope of the perpendicular bisector = -3

The equation of the perpendicular bisector is; y - 0.5 = (-3)·(x - (-0.5))

y = -3·x - 1.5 + 0.5 = -3·x - 1

y = -3·x - 1

The equation of the line from (3, 2) to (-1, -2) is; y = x - 1

The slope of the perpendicular bisector is; -1

The midpoint is; (1, 0)

The equation is; y - 0 = -1·(x - 1)

y = -x + 1

The coordinate of the center of rotation is therefore;

-3·x - 1 = -x + 1

x = -1

y = -3 × (-1) - 1 = 2

The coordinate of the center of rotation is; (-1, 2)

The relative coordinates of the green triangle vertices with regards to the center of rotation are; (1 - (-1), 1 - 2)), (1 - (-1), 2 - 2), (3 - (-1), 2 - 2)

(1 - (-1), 1 - 2)) = (2, -1)

(1 - (-1), 2 - 2) = (2, 0)

(3 - (-1), 2 - 2) = (4, 0)

The coordinates following a 90 degrees clockwise rotation are;

(2, -1) ⇒ (-1, -2)

(2, 0) ⇒ (0, -2)

(4, 0) ⇒ (0, -4)

The coordinate of the image, relative to the origin  are therefore;

(-1 + (-1), -2 + 2) = (-2, 0)

(0 + (-1), -2 + 2) = (-1, 0)

(0 + (-1), -4 + 2) = (-1, -2)

The coordinates of the image corresponds with the coordinates of the orange triangle

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Answer: x=6

Step-by-step explanation:

Subtract x on both sides

-x - 1 = -7

Add 1 to both sides

-x = -6

Divide both sides by -1

x = 6

Answer:

c. 34.5 m

Step-by-step explanation:

Over horizontal ground, the range R for velocity v and launch angle θ is:

R=v^2sin2θ/g

=35^2sin16∘/9.8

= 34.5 meters (so the answer is (c))

a) Bonita Company's income from operations is $145,070.

b) Bonita Company's net income is $163,430.

c) the comprehensive income for Bonita Company is $173,310.

d) Since, we are not given the beginning balance of retained earnings, we cannot calculate the exact retained earnings balance at December 31, 2025.

Given that;

Presented below is information related to Bonita Company at December 31, 2025, the end of its first year of operations.

Sales revenue : 335,550

Cost of goods sold : 135,580

Selling and administrative expenses : 54,900

Gain on sale of plant assets: 30,790

Unrealized gain on available-for-sale debt investments: 9,880

Interest expense: 6,050

Loss on discontinued operations: 12,200

Dividends declared and paid: 5,060

(a) The cost of items sold, selling, and administrative expenses must be subtracted from the revenue from sales in order to determine the income from operations.

Revenue from operations is equal to sales revenue minus the cost of the goods sold plus selling and administrative costs.

Operations profit = $335,550 - $135,580 - $54,900 $145,070

was earned through operations.

As a result, Bonita Company's income from operations is $145,070.

(b) We must add or deduct all gains, losses, and expenses from the income from operations in order to determine the net income.

Net income is calculated as follows:

Income from operations - Loss on ceased operations - Gain on sale of plant assets - Unrealized gain on debt investments that are available for sale Net income equal

$145,070 + $30,790 + $9,880 + $6,050 + $12,200 - $5,060.

$163,430 in profit

As a result, Bonita Company's net income is $163,430.

(c) To determine the comprehensive income, we need to add or subtract all gains, losses, and expenses that are not included in net income. In this case, the only item that needs to be added is the unrealized gain on available-for-sale debt investments.

Comprehensive income = Net income + Unrealized gain on available-for-sale debt investments Comprehensive income

= $163,430 + $9,880

Comprehensive income = $173,310

Therefore, the comprehensive income for Bonita Company is $173,310.

(d) To calculate the retained earnings balance, we need to start with the beginning balance of retained earnings (which is not given in this problem) and add the net income, then subtract any dividends declared and paid.

Retained earnings balance = Beginning balance of retained earnings + Net income - Dividends declared and paid Retained earnings balance

= Beginning balance of retained earnings + $163,430 - $5,060

Retained earnings balance = Beginning balance of retained earnings + $158,370

Since, we are not given the beginning balance of retained earnings, we cannot calculate the exact retained earnings balance at December 31, 2025.

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Answer:

Step-by-step explanation:

The 40 degree angle we are given is called an angle of depression. Because of geometry and the fact that the base of the triangle and this dotted line are parallel to one another, the base angle inside the triangle is also 40. These are called alternate interior angles. The x represents the hypotenuse of the triangle. We can use right triangle trig to find it. The side measuring 500 is OPPOSITE the reference angle of 40 and the missing side is the HYPOTENUSE, so the trig ratio we will use is sin which is, according to SohCahToa, opposite side over hypotenuse; namely:

[tex]sin40=\frac{500}{x}[/tex]

Algebraically, we will multiply both sides by x and then divide by sin40 to get:

[tex]x=\frac{500}{sin40}[/tex]

Make sure your calculator is in degree mode and not radian mode and enter the problem as you see it above to get that

x = 777.9m, choice A.

The entire number is odd.

For any number n, the predecessor is n - 1 and the successor is n + 1.

We have,

To find the place value of the number in the thousand's place for the number obtained by adding 60 tens, 58 hundreds, and 685 ones, we can start by realizing that 60 tens are the same as 600, and 58 hundreds are the same as 5800.

Therefore, we have:

600 + 5800 + 685 = 7085

So the number is 7085.

The digit in the thousand's place is 0 since there is no digit in the thousand's place.

Therefore, the place value of the number in the thousand's place is 0.

To determine if the number is even or odd, we can look at the unit digit, which is 5.

Since 5 is an odd number,

The entire number is odd.

2.

The predecessor of a number is the number that comes before it, and the successor of a number is the number that comes after it.

To find the predecessor of a number, we subtract 1 from the number, and to find the successor, we add 1 to the number.

For example,

Let's say we want to find the predecessor and successor of the number 7.

The predecessor of 7 is 6, since 7 - 1 = 6.

The successor of 7 is 8, since 7 + 1 = 8.

In general,

For any number n, the predecessor is n - 1 and the successor is n + 1.

Thus,

The entire number is odd.

For any number n, the predecessor is n - 1 and the successor is n + 1.

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The altitude of the kite is 53 meters.

Now, First, we need to identify the right triangle formed by Bob, the kite, and the ground.

Here, The angle of elevation of the kite is, 58 degrees

Which is opposite to the altitude of the kite that we need to find.

And,  The length of the string is, 63 m

Which is the hypotenuse of the right triangle.

Hence, By Using trigonometry, we can use the sine function to solve for the altitude of the kite:

sin(58) = altitude / 63

Solving for the altitude, we get:

altitude = 63 x sin(58)

Altitude = 53 meters

Thus, the altitude of the kite is 53 meters.

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In the above scenario, The point that B is transformed to are coordinates (10, 6). This means that it is translated to the right by 9 units and upwards by 5 units.

In order to derive the new location of point B after the transformation by matrix A, we need to perform matrix multiplication of A with the column vector representing point B.

[tex]\left[\begin{array}{cc}8&2\\7&1\\\end{array}\right][/tex]   = [tex]\left[\begin{array}{cc}1\\1\\\end{array}\right][/tex]

[tex]\left[\begin{array}{cc}(8 * 1) + &(2 *1)\\(7 *1)&(1 *1)\\\end{array}\right][/tex] =  [tex]\left[\begin{array}{cc}10\\6\\\end{array}\right][/tex]

As a result, the converted point B is situated at (10, 6). As a result of the transformation provided by matrix A, point B has been translated to the right by 9 units (from x = 1 to x = 10) and upwards by 5 units (from y = 1 to y = 6).

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The equation of line p is x = 4 because it is parallel to the y-axis and passes through the point (4,7).

When a line is parallel to the y-axis, its slope is undefined. However, we know that line p passes through the point (4,7). Since it is parallel to the y-axis, we can conclude that its x-coordinate is always 4.

Therefore, the equation of line p is x = 4. This means that every point on the line will have an x-coordinate of 4 and can have any y-coordinate.

We can confirm this by checking that the point (4,7) satisfies the equation x = 4. Since the point lies on the line p, we can conclude that this is the equation for line p.

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Answer:

answer in explanation below

Step-by-step explanation:

79 to 83      5

84 to 88      3

89 to 93      1

94 to 98      6

          total = 15

Part A: Possible words to describe this data set include: discrete, unimodal, symmetric. Part B: the best measures of center and spread would be median and quartiles. Part C: the best measures of center and spread would be mean and standard deviation

Part A:

Data Set A: 1 3 3 2 4 0 4 3 3 5 2

This data set has a range of 5 with values ranging from 0 to 5. Possible words to describe this data set include: discrete, unimodal, symmetric.

Data Set B: 3 5 5 4 6 1 6 6 6 6 5

This data set has a range of 5 with values ranging from 1 to 6. Possible words to describe this data set include: discrete, bimodal, right-skewed.

Part B:

For Data Set A, the best measures of center and spread would be median and quartiles. The median would give an estimate of the center of the data, and the quartiles would give an estimate of the spread.

Part C:

For Data Set B, the best measures of center and spread would be mean and standard deviation. Mean would give an estimate of the center of the data, and standard deviation would give an estimate of the spread.

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1. The concentration will be 0.5 mg/L at 40 hours.

2. The complete table is:

3. We deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.

4. The intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20.

To get this, we will determine time when the concentration would be 0.5 mg/L. We will substitute value of the concentration and then solve the quadratic function for time (t):

c(t) = 20t/(t² + 4)

0.5 = 20t/(t² + 4)

0.5(t² + 4) = 20t

0.5t² + 2 = 20t

0.5t² + 2 - 20t = 0

t² + 4 - 40t = 0

t² - 40t + 4 = 0

Time t = 38.8998 ≈ 40 hours.

We will now complete table of values:

t        0    2      4     6     8         10        12        14     16        18      20

c(t)    0    5     4      3     2.35   1.92     1.62     1.4    1.23     1.10   1.00

Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes 0 for any value of t, we can logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.

Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.

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The volume of the silo is 17,128 cubic feet (ft³).

We have,

The volume of a cylinder is given by the formula:

V = πr²h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

V = 3.14 × 8.5² × 49

V ≈ 17,128

Rounding to the nearest whole number, the volume of the silo is 17,128 cubic feet (ft³).

Thus,

The volume of the silo is 17,128 cubic feet (ft³).

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The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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The surface area of a figure is obtained as the sum of the areas of all the parts that compose a figure.

The figure for this problem is composed as follows:

Considering the total surface area of 160 ft², the area of each missing face is given as follows:

2 x (24 + 8 + A) = 160

64 + 2A = 160

2A = 96

A = 48 ft².

Considering a rectangle with dimensions 12 ft and x, with area of 48 ft², the length of the missing edge is given as follows:

12x = 48

x = 4 ft.

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Answer:

Step-by-step explanation:

svsvse

Answer:

Let B be the number of balls Brandon had initially, and C be the number of balls Cody had initially.

We know that Brandon had 40% more balls than Cody, so:

B = 1.4C

We also know that Brandon gave 30% of his balls to Cody, so Cody received:

0.3B

And we know that Cody gave 50% of his balls to Brandon, so Brandon received:

0.5(0.3B) = 0.15B

Now, we can set up an equation to represent the final number of balls Cody had:

C + 0.3B - 0.5(0.3B) = C - 0.15B

And we know from the problem that Cody had 852 less balls than Brandon in the end, so:

C - 0.15B = B - 852

We can substitute B = 1.4C into this equation to get:

C - 0.15(1.4C) = 1.4C - 852

Simplifying this equation, we get:

0.79C = 852

Solving for C, we get:

C = 1078

And since B = 1.4C, we have:

B = 1.4(1078) = 1511.2

So Brandon initially had 1511 balls. However, since we're dealing with whole numbers of balls, we need to round to the nearest integer. Therefore, the final answer is:

Brandon initially had 1511 balls

Step-by-step explanation:

add me on sn ap = m_oonlight781

The cylinder's surface area is S = 452.4 cm²

Given data ,

Let the surface area of the cylinder with one base be S

Now , Surface area of cylinder = 2πr ( r + h )

To find the surface area of a cylinder, we need to calculate the sum of the areas of the curved surface (lateral surface) and the two circular bases.

where r = 8 cm

h = 5 cm

The formula for the lateral surface area of a cylinder is given by:

Lateral Surface Area = 2πrh

where r is the radius of the cylinder and h is the height.

The formula for the area of a circle is given by:

Base Area = πr²

Now , S = πr² + 2πrh

On simplifying , we get

S = π ( 8 )² + 2 ( π ) ( 8 ) ( 5 )

S = 64π + 80π

S = 452.389 cm²

Hence , the surface area is S = 452.4 cm²

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