Let f(x) = 4x² - 2x +11
The slope of the tangent line to the graph of f(x) at the point (3, 41)
Slope =
M=
B=

The total cost for 24 copper hearts would be $21.41.

To calculate the total cost for 24 copper hearts, we need to determine the total amount of copper used and then multiply it by the cost of copper per pound.

First, let's find out the total amount of copper used for 24 copper hearts. Each heart uses 0.75 square inches of copper, so for 24 hearts, the total amount of copper used would be:

0.75 square inches/heart [tex]\times 24[/tex]hearts = 18 square inches.

Next, we need to convert the square inches into cubic inches. Since we don't have information about the thickness of the hearts, we'll assume they are flat hearts with a thickness of 1 inch. Therefore, the volume of copper used for the 24 hearts would be:

18 square inches [tex]\times 1[/tex] inch = 18 cubic inches.

Now, we can calculate the total weight of copper used. Given that there is 0.323 pounds of copper per cubic inch, the total weight of copper for the 24 hearts would be:

18 cubic inches [tex]\times 0.323[/tex] pounds/cubic inch = 5.814 pounds.

Finally, we multiply the total weight of copper by the cost of copper per pound to find the total cost:

5.814 pounds [tex]\times[/tex] $3.68/pound = $21.41.

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a) The factored expression for h(t) is -16t(t - 10), obtained by factoring out a common factor of -16 and a common factor of t from the original expression -16t^2 + 160t.

b) Both the original expression -16t^2 + 160t and the factored expression -16t(t - 10) yield the same result of 144 when evaluated at t = 1, confirming the correctness of the factoring.

a) To factor out a common factor with a negative coefficient from the expression h(t) = [tex]-16t^2 + 160t[/tex], we can rewrite it as:

h(t) = [tex]-16(t^2 - 10t)[/tex]

Now, let's focus on factoring the quadratic expression inside the parentheses. We can factor out a common factor of t:

h(t) = -16t(t - 10)

Therefore, the factored expression for h(t) is -16t(t - 10).

b) To check the factoring by evaluating both expressions for h(t) at t = 1, we substitute t = 1 into the original expression and the factored expression and compare the results.

Using the original expression:

h(1) = [tex]-16(1)^2 + 160(1)[/tex]

h(1) = -16 + 160

h(1) = 144

Using the factored expression:

h(1) = -16(1)(1 - 10)

h(1) = -16(1)(-9)

h(1) = 144

Both expressions yield the same result of 144 when evaluated at t = 1. Therefore, the factoring is correct.

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Step-by-step explanation:

Use the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set model

Answer:

Step-by-step explanation:

no

they would be on different sides on the y axis

Answer:

Relative frequency of selecting a 2 = 8/50 = 0.16 = 16%

Step-by-step explanation:

You are selecting a random number between 1 and 5, and you perform this task 50 times.

Out of these 50 times, the outcome "2" appears 8 times.

Therefore the relative frequency of selecting the number 2 is:

f(2) = 8/50 = 0.16 which is 16%

Answer:

Step-by-step explanation:

To find the total revenue in each market, we can calculate the product of the sale volumes and sale prices per unit using matrices.

Let's represent the sale volumes as a matrix V and the sale prices per unit as a matrix P:

V = [6000 9000 1300]

[12000 6000 17000]

P = [3.50]

[2.75]

[1.50]

To calculate the total revenue in each market, we need to perform matrix multiplication between V and P, considering the appropriate dimensions. The resulting matrix will give us the total revenue for each product in each market.

Total revenue = V * P

Calculating the matrix multiplication:

[6000 9000 1300] [3.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[12000 6000 17000] [2.75] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Performing the calculation:

[60003.50 + 90002.75 + 13001.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[120003.50 + 60002.75 + 170001.50] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Simplifying the calculation:

[21000 + 24750 + 1950] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[42000 + 16500 + 25500] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

[47650] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[84000] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Therefore, the total revenue in Market I is GHS 47,650 and the total revenue in Market II is GHS 84,000.

The ratio of the amount charged in Mathematics to Consumer Studies is 4:5.

To find the ratio of the amount charged in Mathematics to Consumer Studies, we need to divide the amount charged in Mathematics by the amount charged in Consumer Studies.

The amount charged in Mathematics is R280 per month, while the amount charged in Consumer Studies is R350 per month.

Therefore, the ratio of the amount charged in Mathematics to Consumer Studies can be calculated as:

280 / 350

To simplify this ratio, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 70.

Dividing 280 by 70 gives us 4, and dividing 350 by 70 gives us 5.

So, the simplified ratio of the amount charged in Mathematics to Consumer Studies is:

4/5.

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Answer:

a. Y(t) = At³ + Be^t + Ct² + Dt + E

b. Y(t) = At + B + Ce^t + Dsin(t) + Ecos(t)

c. Y(t) = Aet + Bte^t + Csin(t) + Dcos(t)

d. Y(t) = At³ + Bt² + Ct + D + Ecos(2t) + Fsin(2t)

e. Y(t) = At² + Bt + C + Dsin(t) + Ecos(t) + Fsin(t) + Gcos(t)

f. Y(t) = Aet + Bte^-t + Ccos(t) + Dsin(t) + E + Ft + G

Answer:

The overall average nickel content of the rock samples is approximately 7.97%.

Step-by-step explanation:

To find the overall average nickel content of the rock samples, we need to take into account the number of samples from each location. Since we know the average nickel content of each set of samples, we can use a weighted average formula:

overall average nickel content = (total nickel content from first location + total nickel content from second location) / (total weight of samples from both locations)

To calculate the total nickel content from each location, we need to multiply the average nickel content by the number of samples:

total nickel content from first location = 8.43% x 1 sample = 8.43%

total nickel content from second location = 7.81% x 6 samples = 46.86%

To calculate the total weight of the samples from both locations, we need to add up the number of samples:

total weight of samples from both locations = 1 + 6 = 7

Now we can substitute these values into the formula and calculate the overall average nickel content:

overall average nickel content = (8.43% + 46.86%) / 7 ≈ 7.97%

Therefore, the overall average nickel content of the rock samples is approximately 7.97%.

Answer:

i believe by creating radii of equal lengths.

Step-by-step explanation:

it gives a path to create an angle congruent to angle APB. The angle APB would have the same radii (BP and AP) and the same width as the congruent angle that would be created.

Wish you good luck.

Answer:

PR = 10

RQ = 6

Step-by-step explanation:

We have cos R = 0.6

also, cos R = adjacent/ hypotenuse

= RQ/PR

⇒ RQ/PR = 0.6

⇒ RQ = 0.6 PR   -eq(1)

By pythagoras theorem,

PQ² + RQ² = PR²

given PQ = 8 and sub the value of RQ from eq(1):

8² + (0.6 PR)² = PR²

⇒ 64 + 0.36PR² = PR²

⇒ (1-0.36)PR² = 64

⇒ 0.64 PR² = 64

⇒ PR² = 64/0.64

⇒ PR² = 100

⇒ PR = 10

sub PR in eq(1):

RQ = 0.6*10

⇒ RQ = 6

The total volume of the dill spears is approximately 1013 cm³.

To find the total volume of the dill spears, we can use the formula for the volume of a cylinder, which is given by V = πr²h,

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

First, let's find the radius of the base.

Since the area of the base is given as 45 cm², we can use the formula for the area of a circle,

A = πr², to solve for the radius.

Rearranging the formula, we have r = √(A/π).

Given that the area of the base is 45 cm², we can substitute this value into the formula to find the radius:

r = √(45/π) ≈ 3 cm (rounded to the nearest centimeter)

Now that we have the radius and the height of the jar, we can calculate the volume of the jar using the formula V = πr²h:

V = π(3²)(13) ≈ 1173 cm³ (rounded to the nearest cubic centimeter)

However, we need to subtract the volume of the pickle juice that was drained from the jar.

We are given that the amount of pickle juice is 160 cm³, so the total volume of the dill spears is:

Total volume = Volume of jar - Volume of pickle juice = 1173 cm³ - 160 cm³ = 1013 cm³

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When 2 items are selected without replacement from a population of 6 items, there are 15 possible samples that can be formed. Option A.

To determine the number of possible samples when 2 items are selected at random without replacement from a population of 6 items, we can use the concept of combinations.

The number of combinations of selecting k items from a set of n items is given by the formula C(n, k) = n! / (k! * (n-k)!), where n! represents the factorial of n.

In this case, we have a population of 6 items and we want to select 2 items. Therefore, the number of possible samples can be calculated as:

C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5 * 4!) / (2! * 4!) = (6 * 5) / (2 * 1) = 15. Option A is correct.

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Answer:

8

Step-by-step explanation:

let x be the number,

according to the question,

-29 + 28 = -7 + x

1 + 7 = x

thus, x = 8

Answer:

30

Step-by-step explanation:

22/33=20/x

cross multiply

22x=33x20

22x=660

x=660/22

x=30

Are the given functions inverse: A. No.

In Mathematics and Geometry, an inverse function is a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine whether f(x) and g(x) are inverses, we would determine the corresponding composite function of f(x) and g(x) in simplified form as follows;

(fog)(x) = -5[-1/5(x) - 9] + 9

(fog)(x) = x + 45 + 9

(fog)(x) = x + 54

(gof)(x) = -1/5(-5x + 9) - 9

(gof)(x) = x - 9/5 - 9

(gof)(x) = x - 54/5

Since (fog)(x) and (gof)(x) are not equal to x, we can conclude that f(x) and g(x) are not inverses of each other.

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Answer:

(r q)(-3) = -3

(q r)(-3) = -3

Step-by-step explanation:

let x = 1

q(1) = -1 +2 = 1

r(1) = 1² = 1

(r q)(-3) = ?

(1×1)(-3) = -3

(q r)(-3) = ?

(1×1)(-3) = -3

The mean of the distribution used in this problem is 3.5.The answer is B. 3.5.

To find the mean of the distribution used in this problem, we need to calculate the expected number of troubles that can be repaired on the same day out of the first five reported. The likelihood of a trouble being repaired on the same day is given as 0.70.

The expected number of troubles repaired on the same day can be calculated by multiplying the probability of each event by the number of trials. In this case, we have five trials (the first five troubles reported) and a probability of 0.70 for each trial.

Expected number of troubles repaired on the same day = Probability of repair on the same day * Number of trials

= 0.70 * 5

= 3.5

This means that, on average, out of the first five troubles reported, we can expect 3.5 of them to be repaired on the same day based on the past data and the given likelihood. So, the correct answer is B. 3.5.

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Answer:

If Tonia eats 1/8 of the cake, then the fraction of the cake left is:

1 - 1/8 = 7/8

If Trinny eats 1/6 of the cake, then the fraction of the cake left is:

1 - 1/6 = 5/6

Since Tonia and Trinny have identical cakes, the amount of cake left is the same for both of them. Therefore, the amount of cake left is:

(7/8 + 5/6) / 2 = 41/48

So there is 41/48 of the cake left.

Vinay buys "two thousand seven" fruits.

To find the number of fruits that Vinay buys, we need to determine the place value of 2 in the number 37,523 and add 7 to it.

In the number 37,523, the digit 2 is in the thousands place.

The place value of 2 in the thousands place is 2,000.

Adding 7 to the place value of 2, we get:

2,000 + 7 = 2,007.

Therefore, Vinay buys 2,007 fruits.

In number names, we can write 2,007 as "two thousand seven."

So, Vinay buys "two thousand seven" fruits.

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What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D

Given that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.

We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..

ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.

In ΔABC, side between ∠A and ∠C is AC,

in ΔXYZ, side between ∠X and ∠Z is XZ.

Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.

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The coterminal of 4π/3 angle measure are 10π/3 and -2π/3

We add or subtract integer multiples of 2π.

So, 4π/3 + 2π = 10π/3 is one coterminal angle, and

4π/3 - 2π = -2π/3 is another coterminal angle.

To convert 125.67° to degree, minute, and second measure:

125.67° = 125° + 0.67°

Since there are 60 minutes in 1 degree, we can multiply 0.67 by 60 to get the minutes:

0.67° × 60 = 40.2'

Since there are 60 seconds in 1 minute, we can multiply 0.2 by 60 to get the seconds:

0.2' × 60 = 12"

So, 125.67° is equivalent to 125° 40.2' 12".

To find the degree measure equivalent to 10π/13 rounded to the nearest hundredth of a degree, we can divide 10π/13 by π and then multiply by 180° to convert from radians to degrees:

(10π/13) / π * 180° ≈ 138.46° (rounded to the nearest hundredth).

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Answer:

Step-by-step explanation:

To determine if the point (4,1) is a solution for the system of equations, we need to substitute the values of x and y from the point into both equations and check if the equations hold true.

For the first equation, y = -x + 5, we substitute x = 4 and y = 1:

1 = -(4) + 5

1 = -4 + 5

1 = 1

The equation holds true for the first equation.

For the second equation, y = 2x - 7, we substitute x = 4 and y = 1:

1 = 2(4) - 7

1 = 8 - 7

1 = 1

The equation also holds true for the second equation.

Since the point (4,1) satisfies both equations, it is indeed a solution to the system of equations.

Answer: (5, -1)

Step-by-step explanation:

To rotate a point counterclockwise by 90° about the origin, we swap the x and y coordinates and negate the new x-coordinate. For the point (-1, 5), we swap the x and y coordinates to get (5, -1). The x-coordinate becomes positive, and the y-coordinate becomes negative. Therefore, the coordinates of the image of the point (-1, 5) after a counterclockwise rotation of 90° about the origin are (5, -1).

I think you put down the same answer choice twice and instead meant to say (5, -1) instead of (-5, -1) twice.

The exact circumferences of the inscribed and circumscribed circles for the given polygons are 8π cm and 15π cm, respectively.

To find the exact circumference of a circle inscribed or circumscribed by a polygon, we can use the Pythagorean theorem to determine the diameter of the circle.

In the case of an inscribed polygon, the diameter of the circle is equal to the diagonal of the polygon. Let's consider the polygon with a diagonal of 8 cm. If we draw a line connecting two non-adjacent vertices of the polygon, we get a diagonal that represents the diameter of the inscribed circle.

Using the Pythagorean theorem, we can find the length of this diagonal. Let's assume the sides of the polygon are a and b. Then the diagonal can be found using the equation: diagonal^2 = a^2 + b^2. Substituting the given values, we have 8^2 = a^2 + b^2. Solving this equation, we find that a^2 + b^2 = 64.

For the circumscribed polygon with a diagonal of 15 cm, the diameter of the circle is equal to the longest side of the polygon. Let's assume the longest side of the polygon is c. Therefore, the diameter of the circumscribed circle is 15 cm.

Once we have determined the diameter of the circle, we can calculate its circumference using the formula C = πd, where C is the circumference and d is the diameter.

For the inscribed circle, the circumference would be C = π(8) = 8π cm.

For the circumscribed circle, the circumference would be C = π(15) = 15π cm.

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Answer:

P(5) = - 3

Step-by-step explanation:

to evaluate P(5) substitute x = 5 into P(x)

P(5) = (5)³ - 5(5)² - 2(5) + 7

      = 125 - 5(25) - 10 + 7

     = 125 - 125 - 3

    = 0 - 3

   = - 3

x < 4.1, as it represents the solution set for the given inequality. A.

The solution set of the inequality x < 4.1 can be determined by examining the given answer choices:

OA. x < 4.1:

This choice represents all values of x that are strictly less than 4.1.

It is a valid solution set for the given inequality.

OB. x < -4.1:

This choice represents all values of x that are strictly less than -4.1.

It is not a valid solution set for the given inequality.

OC. x > 4.1:

This choice represents all values of x that are strictly greater than 4.1.

It is not a valid solution set for the given inequality.

OD. x ≤ 4.1:

This choice represents all values of x that are less than or equal to 4.1.

It is not a valid solution set for the given inequality because the inequality is strict (x < 4.1), not inclusive.

OE. -4.1 < x < 4.1:

This choice represents all values of x that are strictly between -4.1 and 4.1.

It is not a valid solution set for the given inequality because it does not include the possibility of x being less than -4.1 or greater than 4.1.

OF. x < -4.1 or x > 4.1:

This choice represents two separate solution sets: one for x < -4.1 and another for x > 4.1.

It is not a valid solution set for the given inequality because it combines two separate possibilities.

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The solution to the simultaneous equations is x = 3 and y = 7

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

y = 2x + 1

y = 10 - x

Subtract the equations

So, we have

3x - 9 = 0

This gives

3x = 9

So, we have

x = 3

Next, we have

y = 10 - x

y = 10 - 3

Evaluate

y = 7

Hence, the solution is x = 3 and y = 7

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