A central angle of a circle measures 37°. the arc intercepted by this central angle measures 16 inches. which value best approximates the radius of the circle? responses 24.78 in. 24.78 in. 25.38 in. 25.38 in. 46.44 in. 46.44 in. 50.76 in.

The completed table showing the radius, angle at the center, arc length, and area of the sector of the circle are as follows;

[tex]{}[/tex]       Radius             Angle at center            Arc Length           Area

(a)    4 cm      [tex]{}[/tex]         1.25 rad                          5 cm                   22.5 cm²

(b) [tex]{}[/tex]  6 cm                1.5 rad                            9 cm                   22.5 cm²

(c) [tex]{}[/tex]  12 cm               0.8 rad                           9.6 m                  57.6 m²

(d)  [tex]{}[/tex] 10 m                 1.2 rad                            12 m                   60 m²

(e) [tex]{}[/tex]  8 mm               2 rad                               16 mm               64 mm²

(f)  [tex]{}[/tex]  9 mm              (2/3) rad                          6 mm                 27 mm²

A sector of a circle is a part of a circle that is pie shaped, with parts including, two radii of the circle and part of the circumference of the circle.

4(a) The specified dimensions of the sectors of the circles are;

Radius = 4 cm

Angle at the center = 1.25 radians

The arc length is therefore;

The area of the sector is therefore;

(b) Radius = 6 cm

Arc length = 9 cm

The angle at the center, θ, is therefore;

Arc length = 2×π×6 × θ/(2·π) = 9

6 × θ = 9

θ = 9/6 = 1.5

(c) Angle at center = 0.8 rad

Arc length = 9.6 m

Arc length = 2×π× Radius × 0.8 rad/(2·π rad) = 9.6

Radius = 9.6 m/0.8 = 12 m

(d) Angle at the center = 1.2 radians

Area = 60 m²

The area = π × (Radius)² × 1.2/(2·π) = 60 m²

(Radius)² × 0.6 = 60 m²

(Radius)² = 60 m²/(0.6) = 100 m²

The arc length = 2 × π × 10 mm × 1.2/(2·π) = 12 mm

(e) The radius of the circle = 8 mm

The area of the sector = 64 mm²

The angle at the center, θ, can therefore, be found as follows;

Area = π × (8 mm)² × θ/(2·π) = 64 mm²

θ = 2 × 64 mm²/((8 mm)²) rad = 2 rad

(f) Arc length = 6 mm

Area = 27 mm²

The radius and angle at the are found as follows

Let r represent the radius, we get;

Arc length = 2 × π × r × θ/(2·π) = 6

Therefore; θ = 6/r

Area of the sector = π × r² × θ/(2·π) = 27 mm²

Therefore; π × r² × (1 mm²) × (6/(r × 1 mm))/(2·π) = 27 mm²

r × (1 mm) × 3 = 27 mm²

r = 27 mm²/(3 × 1 mm) = 9 mm

Please find the completed table for the sectors of a circle above

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Answer: I think 47.5in^2

Step-by-step explanation:

Answer:

Two quantities are in direct proportion if an increase in one quantity leads to a proportional increase in the other quantity. In this case, the number of melons and the cost of melons are in direct proportion if an increase in the number of melons leads to a proportional increase in the cost of melons.

To check if the given statement is true, we can use the concept of unit rate. Unit rate is the rate for one unit of a given quantity. In this case, the unit rate for melons would be the cost of one melon.

If 7 melons cost £5, then the cost of one melon can be calculated by dividing the total cost by the number of melons:

Cost of one melon = Total cost / Number of melons

= £5 / 7

= £0.714 (rounded to 3 decimal places)

Now, let's calculate the cost of different numbers of melons and see if they are in direct proportion:

For 1 melon, the cost would be £0.714

For 2 melons, the cost would be £1.429

For 3 melons, the cost would be £2.143

For 4 melons, the cost would be £2.857

For 5 melons, the cost would be £3.571

For 6 melons, the cost would be £4.286

For 7 melons, the cost would be £5.000

As we can see, the cost of melons increases proportionally with the number of melons. Therefore, we can conclude that the number of melons and the cost of melons are in direct proportion

The following formula is used to determine how long it will take the car to cover the same distance at 50 miles per hour:

Distance (in miles) divided by Speed (in miles per hour) = Time (in hours). In this case, it is:

Distance / Speed = Time

Distance / 50 = Time

Time = Distance / 50

Time (in minutes) = (Distance / 50) * 60

Therefore, the time it will take the vehicle to travel the same distance at 50 miles perhour is (Distance / 50) * 60 minutes.

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The forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.

Let's solve this problem step by step:

Calculate the correlation coefficient (r) using the formula:
r = (ΣXY - (ΣX)(ΣY)/n) / sqrt([(ΣX^2 - (ΣX)^2/n)(ΣY^2 - (ΣY)^2/n)])

Plug in the given values into the formula:
r = (126.54 - (22)(66)/12) / sqrt([(45.8 - (22)^2/12)(369.94 - (66)^2/12)])

Simplify the formula and solve for r:
r = (126.54 - 121) / sqrt([(45.8 - 40.333)(369.94 - 363)])
r = 5.54 / sqrt[(5.467)(6.94)]
r = 5.54 / 4.967
r = 1.115

Make conclusions about the closeness of the linear relationship based on the value of r:
Since the value of r is close to 1, this indicates a strong positive linear relationship between the investments (X variable) and the main product's sales (Y variable).

Find the linear regression from variable Y to the X using the formula:
Y = a + bX

Calculate the slope (b) using the formula:
b = (ΣXY - (ΣX)(ΣY)/n) / (ΣX^2 - (ΣX)^2/n)

Plug in the given values into the formula and solve for b:
b = (126.54 - (22)(66)/12) / (45.8 - (22)^2/12)
b = 5.54 / 5.467
b = 1.013

Calculate the intercept (a) using the formula:
a = (ΣY - b(ΣX))/n

Plug in the given values into the formula and solve for a:
a = (66 - 1.013(22))/12
a = 44.714/12
a = 3.726

Plug in the values of a and b into the linear regression formula:
Y = 3.726 + 1.013X

Forecast the sales volume if the investment volume is planned to be 30 thousand Euro by plugging in the value of X into the linear regression formula:
Y = 3.726 + 1.013(30)
Y = 3.726 + 30.39
Y = 34.116

Therefore, the forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.

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The value $\frac{6}{\sqrt{2}}$

a) The method of moments estimator for ϕ is given by:

$\hat{\phi} = \frac{\sum_{i=1}^{n}X_i}{n} = \frac{1.20}{60} = 0.02$

b) The likelihood and log-likelihood functions for ϕ are given by:

Likelihood: $L(\phi) = \prod_{i=1}^{n}\frac{1}{\sqrt{2\pi e \phi}} \exp \bigg( \frac{-X_i^2}{2\phi}\bigg)$

Log-Likelihood: $lnL(\phi) = -\frac{n}{2}ln(2\pi e \phi) - \frac{1}{2\phi}\sum_{i=1}^{n}X_i^2$

c) The score and observed Fisher information functions for ϕ are given by:

Score: $S(\phi) = \frac{1}{\phi}\sum_{i=1}^{n}X_i^2 - \frac{n}{\phi}$

Observed Fisher Information: $I(\phi) = \frac{n}{\phi^2}$

d) The maximum likelihood estimator for ϕ is given by:

$\hat{\phi}_{ML} = \frac{\sum_{i=1}^{n}X_i^2}{n} = \frac{1.20^2}{60} = 0.0096$

e) To use a Normal distribution to approximate the distribution of the maximum likelihood estimator for ϕ, it is necessary to show that $E[I(\phi)] = 2$. This can be done by computing $E[I(\phi)]$ directly:

$E[I(\phi)] = \frac{1}{\phi^2}E[\sum_{i=1}^{n}X_i^2] = \frac{n}{\phi^2}E[X_i^2] = \frac{n}{\phi^2}(2\phi + \phi^2) = \frac{2n + n\phi}{\phi^2}$

Setting this equal to 2 and solving for ϕ gives $\phi = \frac{\sqrt{n}}{\sqrt{2}} = \frac{6}{\sqrt{2}}$

f) To investigate the properties of the maximum likelihood estimator for ϕ, 1000 values of ÔMle can be simulated. This can be done by first simulating 60 random values of X and then calculating the MLE for each set. After this, the 1000 samples of ÔMle can be compared to the approximate density obtained in part (e). The histogram should match the approximate density, with the distribution centered around the value $\frac{6}{\sqrt{2}}$.

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Answer:

6x+5

To check this, we can use the distributive property of multiplication:

(3x-2)(6x+5) = 18x^2 + 15x - 12x - 10 = 18x^2 + 3x - 10

So the given polynomial is indeed equivalent to the product of (3x-2) and 6x+5.

The polynomial 18x^(2)+3x-10 is equivalent to the product of (3x-2) and the binomial 6x+5.

The polynomial 18x^(2)+3x-10 is equivalent to the product of (3x-2) and the binomial 6x+5. This can be found by factoring the polynomial into two binomials.

Find two numbers that multiply to -180 (-10 * 18) and add to 3 (the coefficient of the x term).
The two numbers are -15 and 12.
Rewrite the polynomial as 18x^(2)-15x+12x-10.
Factor by grouping: 3x(6x-5)+2(6x-5).
Factor out the common binomial: (3x-2)(6x+5).

Therefore, the polynomial 18x^(2)+3x-10 is equivalent to the product of (3x-2) and the binomial 6x+5.

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Answer:

When a car turns, the tire on the outside of the turn has to travel a greater distance than the tire on the inside of the turn. The difference in the distance traveled by the two tires is equal to the circumference of the circle that the car makes during the turn.

The radius of the circle is given as 16.1 ft, which means the diameter is 2 * 16.1 = 32.2 ft. The distance between the two front tires is given as 4.7 ft, which means that the radius of the circle traced by the inner tire is 16.1 - 2.35 = 13.75 ft, where 2.35 ft is half of the distance between the two front tires.

The circumference of the circle traced by the outer tire is 2 * π * 16.1 = 101.366 ft (rounded to three decimal places). The circumference of the circle traced by the inner tire is 2 * π * 13.75 = 86.415 ft (rounded to three decimal places).

The difference in the distance traveled by the two tires is:

101.366 - 86.415 = 14.951 ft (rounded to three decimal places)

Therefore, the tire on the outside of the turn travels about 14.951 ft further than the tire on the inside.

a) approximately 7.64% of all bags sold are underweight.

b)  the probability that none of the 5 bags is underweight is approximately 0.5595 or 55.95%

c) the probability that the mean weight of the 5 bags is below 5 ounces is approximately 0.0007 or 0.07%

d) the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces is very close to 0.

a) To find the fraction of all bags sold that are underweight, we need to find the area under the normal distribution curve to the left of 5 ounces. Using the standard normal distribution, we can calculate the z-score:

z = (5 - 5.1) / 0.07 = -1.43

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -1.43 is 0.0764. Therefore, approximately 7.64% of all bags sold are underweight.

b) To find the probability that none of the 5 bags in a bargain pack is underweight, we need to find the probability that each individual bag is not underweight. Using the result from part (a), the probability that one bag is underweight is approximately 0.0764. Therefore, the probability that none of the 5 bags is underweight is:

(1 - 0.0764)⁵ = 0.5595

Rounding to four decimal places, the probability that none of the 5 bags is underweight is approximately 0.5595 or 55.95%

c) To find the probability that the mean weight of the 5 bags is below the stated amount of 5 ounces, we need to use the sampling distribution of the mean. The mean of the sampling distribution is the same as the population mean, 5.1 ounces. The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size:

s = 0.07 / √(5) = 0.0313

The z-score for a sample mean of 5 ounces is:

z = (5 - 5.1) / 0.0313

= -3.19

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -3.19 is approximately 0.0007.

Therefore, the probability that the mean weight of the 5 bags is below 5 ounces is approximately 0.0007 or 0.07%

d) To find the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces, we need to use the sampling distribution of the mean again. The mean of the sampling distribution is still 5.1 ounces. The standard deviation of the sampling distribution is:

s = 0.07 / √(20)

= 0.0157

The z-score for a sample mean of 5 ounces is:

z = (5 - 5.1) / 0.0157
= -6.37

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -6.37 is essentially 0.

Therefore, the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces is very close to 0.

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Answer:

x+8+2x-5. 2x+x+8-5. x=3

To determine the values of r for which v is in the span of S, we need to find a scalar multiple of the vector in S that equals v.

In other words, we need to solve the equation:
v = c* S
where c is a scalar and S is the vector in the span. Plugging in the values for v and S, we get:
\[\left[\begin{array}{c}2 \\ r \\ -1\end{array}\right] = c*\left[\begin{array}{c}1 \\ 0 \\ -1\end{array}\right]\]
To solve for c, we can equate the corresponding entries of the two vectors:
2 = c*1
r = c*0
-1 = c*-1
From the first equation, we get c = 2. Plugging this value into the third equation, we get:
-1 = 2*-1
which simplifies to:
-1 = -2

This equation is not true, so there is no value of c that satisfies all three equations.
Therefore, there is no value of r for which v is in the span of S.
The vector v is not in the span of S for any value of r.

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To solve the absolute value inequality, we need to isolate the absolute value expression on one side of the inequality and then solve for x. Here are the steps:

4| x +3| + 6 < 2

4| x +3| < -4 (Subtract 6 from both sides)

| x +3| < -1 (Divide both sides by 4)

Since the absolute value of any expression is always positive, there is no solution to this inequality. In interval notation, we can write the solution as ∅ (empty set).

Answer: ∅  

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The expression to represent the length of the rectangular space is 2x - 3.

The product of the length and breadth makes up the area of a rectangular space. Area is defined mathematically as Length x Width. So, using the equation Length = Area / Width, we can determine the length of a rectangular space if we know its area and breadth. Instead, using the formula Width = Area / Length, we may determine the width of a rectangular region if we know its area and length.

Given that the width of the rectangle is 4x.

The Area of the rectangle is given as:

A = lw

Substituting the values we have:

8x² - 12x = 4x (Length)

l = 2x - 3

Hence, the expression to represent the length of the rectangular space is 2x - 3.

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Answer:

153.9in.^2

Step-by-step explanation:

Area of circle = [tex]\pi[/tex]r²
So 7^2=49
49*兀 = 153.9 to 1dp

The inequality to represent the given scenario is b≥ [tex]22\frac{2}{3}[/tex]. Therefore, option A is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, at Dublin International Airport if your luggage weighs more than  [tex]22\frac{2}{3}[/tex] kilograms, you will be charged an additional baggage fee for the overweight luggage.

So, the inequality is b≥ [tex]22\frac{2}{3}[/tex]

Therefore, option A is the correct answer.

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The formula for the polynomial P(x) with degree 3, real coefficients, zeros at x=3-3i and x=1, and y-intercept at (0,-36) is P(x) = -4(x-1)(x-(3-3i))(x-(3+3i)).

To find the formula for the polynomial, we first need to find the conjugate of the complex zero, which is 3+3i. This is because a polynomial with real coefficients must have complex zeros in conjugate pairs.

Next, we can use the factored form of a polynomial, P(x) = a(x-r1)(x-r2)(x-r3), where r1, r2, and r3 are the zeros of the polynomial and a is a constant. In this case, r1 = 1, r2 = 3-3i, and r3 = 3+3i.

Finally, we can use the y-intercept to find the value of a. When x = 0, P(x) = -36, so we can plug in the values and solve for a:
-36 = a(0-1)(0-(3-3i))(0-(3+3i))
-36 = a(-1)(-3+3i)(-3-3i)
-36 = a(9+9i-9i-9)
-36 = a(-36)
a = 4

So the formula for the polynomial is P(x) = 4(x-1)(x-(3-3i))(x-(3+3i)). However, since we want the y-intercept to be negative, we can multiply the entire polynomial by -1 to get P(x) = -4(x-1)(x-(3-3i))(x-(3+3i)).

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The probability of needing exactly 4 rolls to get doubles is 0.12.

What is meant by probability?

An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur. In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.

From the figure,

The number of times we get doubles in 1 roll = 5

The number of times we get doubles in 2 rolls = 4

The number of times we get doubles in 3 rolls = 4

The number of times we get doubles in 4 rolls = 3

The number of times we get doubles in 5 rolls = 3

The number of times we get doubles in 6 rolls = 2

The number of times we get doubles in 7 rolls = 3

The number of times we get doubles in 8 rolls = 0

The number of times we get doubles in 9 rolls = 1

Total number of outcomes = 5+4+4+3+3+2+3+1  = 25

Number of doubles in 4 rolls = 3

The probability of needing exactly 4 rolls to get doubles = 3/25 = 0.12

Therefore the probability of needing exactly 4 rolls to get doubles is 0.12.

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Answer:

Step-by-step explanation:

Ok so we're just going to be doing a lot of supplementary work:

The angle adjacent to 85 degrees is equal to 180 - 85 = 95

We want to find the angle measures in the triangle where 95 degrees is. We can do this by using 40, finding the opposite angle, which is also 40 due to vertical angles theorem, finding the missing angle in the right-most triangle which is 180 - 105 - 40 = 35

Using vertical angles theorem again, we know the angle opposite 35 degrees is also 35. We found another angle for the middle triangle.

The missing angle for the middle triangle is 180 - 35 - 95 = 50

The angle opposite 50 is 50 because of the vertical- you already know.

Now the left triangle has angles Z, 60 and 50.

m<Z = 180 - 60 - 50

m<Z = 70

Hope this helps!

The number of teams that can be formed is 401

To determine the number of teams that can be formed with the given number of participants, we need to divide the total number of participants by the number of members per team.

Here we have

Number people registered = 3208

Number of members each team will have is 8 members  

The number of teams that can be formed is equal to 3208 ÷ 8

Number of teams = 3208/8 = 401  

Therefore,

The number of teams that can be formed is 401

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Answer:

Let's start by assigning variables to the unknowns in the problem:

Let x be the selling price of a cup of apple juice.

Then the selling price of a cup of lemon juice is 3/2 times x, or 1.5x.

Let y be the number of times 2 cups of lemon juice are sold (so y is an even number).

Then the number of times 5 cups of apple juice are sold is 5/2 times y, or 2.5y.

From the given information, we can set up two equations:

2.5y(x + 12) = 1.5xy (Mr Tan earns $12 more from apple juice than from lemon juice)

2(1.5x)y = 5(2.5y) (for every 2 cups of lemon juice sold, 5 cups of apple juice are sold)

Simplifying the second equation, we get:

3xy = 25y

Dividing both sides by y (which is non-zero since y is even), we get:

3x = 25

Solving for x, we get:

x = 25/3

Substituting x into the first equation and simplifying, we get:

y = 24

So Mr Tan sells 24 cups of lemon juice and 60 cups of apple juice. To find his total earnings, we can multiply the selling price by the number of cups sold for each juice and add them up:

Total earnings = 24(1.5x) + 60x

Total earnings = 36x + 60x

Total earnings = 96x

Substituting x = 25/3, we get:

Total earnings = 96(25/3)

Total earnings = 800

Therefore, Mr Tan earns $800 altogether.

Answer:

Step-by-step explanation:

You want linear equations in standard form that describe the relations in the given tables.

A useful two-point formula for creating an equation in general form is ...

  (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

This will simplify to an equation of the form ...

  ax +by +c = 0 . . . . . . general form equation for a line

The corresponding standard form equation is ...

  ax +by = -c . . . . . . . . standard form equation for a line

The standard form has mutually prime coefficients and a positive leading coefficient. That may require removal of any common factors.

  (2 -(-2))(x -(-5) -(-1 -(-5))(y -(-2)) = 0

  4x +20 -4y -8 = 0 . . . . . . . . coefficients have a common factor of 4

  x -y +3 = 0 . . . . . . . . . general form

  x -y = -3 . . . . . . . . . standard form

  (12 -20)(x -(-2)) -(0 -(-2))(y -20) = 0

  -8x -16 -2y +40 = 0 . . . . . . coefficients have a common factor of -2

  4x +y -12 = 0 . . . . . . . . simplified to general form

  4x +y = 12 . . . . . . standard form

__

Additional comment

Another useful form of the equation of a line is "intercept form":

  x/a +y/b = 1 . . . . . . . where 'a' is the x-intercept and 'b' is the y-intercept

The table for line k shows the x-intercept is (3, 0) and the y-intercept is (0, 12). Then the line can be written as ...

  x/3 +y/12 = 1

Multiplying by 12 gives ...

  4x +y = 12 . . . . the required standard form

The amount of interest she will earn at the end of 3 years would be = $375

The principal amount of money saved by Chantal (p)= $5000

The interest rate that the amount generates (r)= 2.5%

The total time for the savings(t) = 3 years.

The simple interest generated S.I = P×T×R/100

= 5000×3×2.5/100

= 37500/100

= $375

Therefore the amount of money she will earn as interest after three years of savings would be = $375.

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The given equation (5)/(x - 5) = 5 + (x)/(x - 5) is a conditional equation.

We can simplify the equation as follows:

(5)/(x - 5) - (x)/(x - 5) = 5

(5 - x)/(x - 5) = 5

Now, we can cross-multiply to get rid of the fraction:

5 - x = 5(x - 5)

Distributing the 5 on the right side of the equation gives us:

5 - x = 5x - 25

Adding x to both sides and adding 25 to both sides gives us:

30 = 6x

Dividing both sides by 6 gives us:

x = 5

Since the equation has a solution, it is a conditional equation. Therefore, the answer is a conditional equation.

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The volume of the Nestle Cremora Carton container is 400 m³

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The volume of a cuboid is given as:

Volume = Length * Width * Height

The question is incomplete. Let us assume that the container dimensions are as follows:

The Nestle Cremora Carton container is in the shape of a cuboid. Hence:

Volume of container = length * width * height = 10 m * 8 m * 5 m = 400 m³

The volume is 400 m³

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The correct answer is $9.50 of credit is left on the card. To find out how much credit is left on the card after Deshaun uses it for 30 minutes of calls, we need to plug in the value of x into the equation C=15.50-0.20x.

Deshaun has a card with $15.50 of credit on it. He is using it to make calls and the cost of each minute of calling is $0.20. To calculate how much credit Deshaun has left on his card after 30 minutes of calls, we need to use the equation C=15.50-0.20x, where x is the number of minutes of calls.

Since x represents the number of minutes of calls, we will plug in 30 for x:

C = 15.50 - 0.20(30)

C = 15.50 - 6

C = 9.50

Therefore, there is $9.50 of credit left on the card after Deshaun uses it for 30 minutes of calls.

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Answer:

3) The commercial costs $900 to produce and $110 each times it is aired.

Step-by-step explanation:

We can determine how expensive it is to produce a commercial by looking at the function C(n)'s output when n = 0 (when the commercial hasn't been aired yet).

C(0) = 110(0) + 900

C(0) = $900

So, the cost of producing a commercial is $900.

We can see that $110 is added to the cost each time n is incremented by 1. Therefore, it costs $110 each time the commercial is aired.

We can put these two statements together to deduce that answer option 3 is correct:

The commercial costs $900 to produce and $110 each times it is aired.

Answer:

Option 3

Step-by-step explanation:

900 is a constant number that never changes. However, the value of "110n" changes every time it is aired, because 110 is multiplied by a different number. This means that $110 represents the cost of airing it each time, because if it was hypothetically aired three times, you would multiply 110 by 3, proving that it is the cost to air it, and $900 is the production cost. It also makes no sense to produce the same commercial over and over again, so the cost that is multiplied has to be the amount of times that it is aired.

The polynomial function [tex]f(x) = 4x^3 - 3x + 2x^4 - x^2 + 7[/tex] has no 0 real zeros.

The polynomial function [tex]f(x) = 4x^3 - 3x + 2x^4 - x^2 + 7[/tex] can be rearranged to make it easier to find the real zeros.

[tex]f(x) = 2x^4 + 4x^3 - x^2 - 3x + 7[/tex]

To find the real zeros of this polynomial, we need to use the Rational Root Theorem. This theorem states that if a polynomial has a rational root, it must be a factor of the constant term (7) divided by a factor of the leading coefficient (2).

The possible rational roots are: ±1, ±7, ±1/2, ±7/2

We can use synthetic division to test each of these possible roots until we find one that gives us a remainder of 0.

Using synthetic division, we find that none of the possible rational roots are actually roots of the polynomial. This means that the polynomial has no real zeros.

Therefore, the answer is 0. The polynomial function [tex]f(x) = 4x^3 - 3x + 2x^4 - x^2 + 7[/tex] has no 0 real zeros.

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The value of kˣ for the exponential function is [tex]27^{(1/x)}.[/tex]

We can use the properties of exponents to solve this problem and determine the value of kˣ.

To find the value of h(3x), we can use the property that [tex](a^b)^c = a^{bc}[/tex] for any real numbers a, b, and c. This is shown in the solution below.

h(3x) = 3³ˣ    (since h(x) = 3ˣ)

= (3³)ˣ

= 27ˣ

Therefore, we have:

kˣ = 27ˣ

To find the value of kˣ, we can take the x-th root of both sides:

[tex]k = 27^{(1/x)}[/tex]

So, the value of kˣ is [tex]27^{(1/x)}[/tex].

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