1. Use substitution to determine which ordered pairs lie on the graph of the exponential function. f(x) = 3(4)2x

Answer:

420mm^3

Step-by-step explanation:

10mm×10.5mm=105mm

105mm×8mm=840mm^3

840mm^3÷2=420mm^3

The volume of this prism is calculated by this equation:

V = (area of a triangle)(height)

So plugging in the numbers it looks something like this

V = (10 x 10.5 x 1/2)(8)

V = (105 x 1/2)(8)

V = (52.5)(8)

V = 420 mm^3

The value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.

The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.

The connection between the four edges of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.

For the given figure we see the right triangle DHB.

Here, DH = 20 in and HB = 12 in.

Using the Pythagoras theorem we have:

DB² = DH² + HB²

DB² = 20² + 12²

DB² = 400 + 144

DB = 23.32

For the right triangle RHK we have:

HR = 16 and HK = 8.72

Using the Pythagoras theorem:

RK² = 16² + 8.72²

RK= 18.22

Also, KY = YK = 6.83 in.

Hence, the value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.

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Step-by-step explanation:

Refer to pic...........

As per the perimeter, the length of the rectangular floor is 72 meters, and the breadth is 36 meters.

Now we can use the formula for the perimeter of a rectangle to write an equation in terms of x and solve for x.

Perimeter of the rectangle = 2(length + breadth)

Given that the perimeter is 216 m, we can substitute the values of length and breadth in terms of x to get:

216 = 2(2x + x)

Simplifying this equation, we get:

216 = 2(3x)

Dividing both sides by 2, we get:

108 = 3x

Solving for x, we get:

x = 36

Now that we have the value of x, we can use it to find the length and breadth of the rectangular floor.

Length = 2x = 2(36) = 72 m

Breadth = x = 36 m

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The cost of the meal, including the 20% discount, 8% sales tax, and 15% tip, is $43.72.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

We are given that;

Items ordered= a 12 piece Grilled Tuscan Chicken Wings, Mozzarella

Fritta and Pan Sauteed Mussels.

Coupon percent off =20%

Sales tax= 8%

Waiter tip= 15%

Now,

Let's start by finding the cost of the appetizers and the pizza before any discounts or taxes are applied:

Grilled Tuscan Chicken Wings: let's assume this is $12

Mozzarella Fritta: let's assume this is $8

Pan Sauteed Mussels: let's assume this is $14

Craft Your Own Pizza: let's assume this is $10 for a small 2-topping pizza

So the total cost of the food before any discounts or taxes is:

$12 + $8 + $14 + $10 = $44

With the 20% coupon, we can apply a discount of:

0.2 x $44 = $8.80

So the new total before taxes is:

$44 - $8.80 = $35.20

Now we can calculate the sales tax on this amount:

0.08 x $35.20 = $2.82

Adding the sales tax to the discounted amount gives:

$35.20 + $2.82 = $38.02

Finally, we can calculate the total cost of the meal after adding the 15% tip:

$38.02 + 0.15 x $38.02 = $43.72

Therefore, by the given percentages the answer will be $43.72.

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Carlota's rate on a bicycle who is 74 miles away is approximately 6.1667 miles per hour.

Carlota's rate can be found by using the formula: rate = distance ÷ time. To find her rate for the first part of the trip, we can plug in the given values:

To find her rate for the second part of the trip, we need to subtract the distance and time she had already traveled from the total distance and time:

Then we can plug these values into the formula:

Since Carlota's rate is the same for both parts of the trip, we can simply use the overall distance and time to find her rate:

Therefore, Carlota's rate is approximately 6.1667 miles per hour.

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There are 15 blue counters in the bag.

Two quantities are compared to form a ratio. An equality of two ratios is a proportion.

We know that the initial ratio of red counters to blue counters was 4:5. Therefore, we can write:

4x : 5x

We also know that 10 more red counters were added to the bag. Therefore, the new number of red counters in the bag is:

4x + 10

The ratio of red counters to blue counters then became 6:5. Therefore, we can write:

(4x + 10) : y = 6 : 5

We can simplify this equation by cross-multiplying:

5(4x + 10) = 6y

20x + 50 = 6y

Dividing both sides by 6, we get:

y = (20x + 50)/6

Simplifying, we get:

y = (10x + 25)/3

Since y has to be a whole number, 10x + 25 has to be divisible by 3. The only value of x that satisfies this condition is x = 2.

Therefore, the initial number of red counters was 4x = 8, and the initial number of blue counters was 5x = 10.

After adding 10 more red counters, the new number of red counters was 18, and the new ratio of red counters to blue counters was 6:5.

To find the new number of blue counters, we can use the equation we derived earlier:

y = (10x + 25)/3

Substituting x = 2, we get:

y = (10(2) + 25)/3 = 15

Therefore, there are 15 blue counters in the bag.

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Answer:

To find the x-intercepts of the equation y = -(x+7)(x+4), we need to set y = 0 and solve for x. So, we have:

0 = -(x+7)(x+4)

This equation will be true if either (x+7) = 0 or (x+4) = 0. Solving each of these equations, we get:

x+7 = 0 => x = -7

x+4 = 0 => x = -4

Therefore, the x-intercepts of the equation y = -(x+7)(x+4) are x = -7 and x = -4.

Now, we know that the equations y = -(x+7)(x+4) and y = -(x-3) are equivalent. This means that they have the same solutions, or the same x-intercepts. So, we can use the x-intercepts we found for the first equation to determine the x-intercepts of the second equation.

To find the x-intercepts of the equation y = -(x-3), we set y = 0 and solve for x:

0 = -(x-3)

This equation will be true if (x-3) = 0, which gives us:

x-3 = 0 => x = 3

Therefore, the x-intercept of the equation y = -(x-3) is x = 3, which is different from the x-intercepts of the equation y = -(x+7)(x+4). This means that the two equations are not equivalent.

Step-by-step explanation:

Answer:

x-intercepts can be found below

Step-by-step explanation:

The equation:

[tex]y=-(x+7)(x+4)[/tex]

Can also be written as:

[tex]y=-1(x+7)(x+4)[/tex]

In order to find the x-intercepts, we must set each of the factors equal to 0.

[tex]-1=0[/tex]

[tex]x+7=0, x=-7[/tex]

[tex]x+4=0, x=-4[/tex]

The x-intercepts are:

[tex](0,0)[/tex]

[tex](-7,0)[/tex]

[tex](-4,0)[/tex]

The equation:

[tex]y=-(x-3)[/tex]

Can also be written as:

[tex]y=-1(x-3)[/tex]

In order to find the x-intercepts, we must set each of the factors equal to 0.

[tex]-1=0[/tex]

[tex]x-3=0, x=3[/tex]

The x-intercepts are:

[tex](0,0)[/tex]

[tex](3,0)[/tex]

To solve the equation 1/2 + a = 1 3/4, we need to convert the mixed number 1 3/4 to an improper fraction:

1 3/4 = 4/4 + 3/4 = 7/4

Now we can rewrite the equation as:

1/2 + a = 7/4

To isolate the variable a, we need to subtract 1/2 from both sides:

a = 7/4 - 1/2

To add these two fractions, we need to find a common denominator, which is 4:

a = (7/4 - 2/4)

a = 5/4

Therefore, a = 5/4.

To solve the equation 1/2 + ? = 7, we can follow a similar approach. We need to isolate the variable on one side of the equation, so we need to subtract 1/2 from both sides:

? = 7 - 1/2

We need to find a common denominator to add these two fractions, which is 2:

? = (14/2 - 1/2)

? = 13/2

Therefore, the missing number is 13/2.

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The Simple ratio and the ratio of the perimeters of two regular octagons are approximately 1.472

The formula for the area of the regular polygon is:

Area = (2 + 2[tex]\sqrt{2}[/tex]) × [tex]s^{2}[/tex]

Where, s = length of the side of a polygon

consider two equations for the two octagons,

48 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s1)^{2}[/tex]

147 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s2)^{2}[/tex]

The length of each polygon is

s1 = [tex]\sqrt{\frac{48}{(2 + 2\sqrt{2} )} }[/tex] ≈ 3.079cm

s2 = [tex]\sqrt{\frac{147}{(2 + 2\sqrt{2} )} } }[/tex] ≈ 4.532cm

The similarity ratio is,

s2 ÷ s1 ≈ 1.472

The ratio of perimeters is,

8s2 ÷ 8s1 = s2 ÷ s1 ≈ 1.472

Therefore, the similarity ratio and the ratio of the perimeters are both approximately 1.472.

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A performance task is any educational activity or assessment that calls for students to perform in order to demonstrate their comprehension, competency, and knowledge.

Mathematical activity includes the search for patterns as well as experimentation, description, fiddling, invention, picturing, conjecture, and guesswork.

A series of recurrent numbers, symbols, or shapes is referred to in mathematics as a pattern. Every kind of event or thing has a pattern that can be connected to it. A rule that distinguishes between items that are a part of a pattern and those that are not is known as a pattern.

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Complete question:

What is Performance task?

The remainder when f(x) is divided by x-1 is 0.

Remainder Theorem states that given a polynomial function and a value for x, the remainder when the polynomial is divided by (x-a) is equal to the value of the polynomial when x=a. This theorem can be used to quickly and accurately find the remainder of a division problem, making it a very useful tool.

The remainder theorem states that if a polynomial f(x) is divided by x-a, then the remainder is f(a). In this case, we want to find the remainder when f(x) is divided by x-1. Therefore, we need to find f(1).

f(1) = 2(1)^(3) + 3(1)^(2) - 12(1) + 7
f(1) = 2 + 3 - 12 + 7
f(1) = 0

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The given exponential functions are classified as exponential growth or exponential decay above.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to check whether the given functions represent exponential growth or decay.

We can write the classified functions as -

{ 1 }.   y = 500(0.30)ˣ                     exponential decay

{ 2 }.  y = 500(1.70)ˣ                      exponential growth

{ 3 }.  y = 0.3(500)ˣ                       exponential growth

{ 4 }.  y = 500(0.30)ˣ - 6               exponential decay

{ 5 }.  y = 0.3(1.7)ˣ - 2                    exponential growth

{ 6 }.  y = 500(0.30)ˣ ⁺ ⁸               exponential growth

{ 4 }.  y = 500(0.30)ˣ ⁻ ⁶               exponential decay

Therefore, the given exponential functions are classified as exponential growth or exponential decay above.

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Answer:

Step-by-step explanation:

Here's the long division of (2x³ + 3x² + 4x + 2) ÷ (x + 2):

2x^2 - x + 6

x + 2 | 2x^3 + 3x^2 + 4x + 2

- (2x^3 + 4x^2)

--------------

- x^2 + 4x

- (- x^2 - 2x)

-------------

6x + 2

- (6x + 12)

--------

-10

Therefore, the quotient is 2x^2 - x + 6, and the remainder is -10.

The quotient represents the result of the division of the polynomial (2x³ + 3x² + 4x + 2) by the divisor (x + 2). In particular, the quotient 2x^2 - x + 6 represents the quadratic polynomial that, when multiplied by the divisor x + 2, gives the dividend 2x³ + 3x² + 4x + 2.

In other words, we have:

(2x³ + 3x² + 4x + 2) = (x + 2)(2x^2 - x + 6) - 10

The remainder -10 indicates that the division is not exact, and that there is a "leftover" term of -10 when we try to divide the polynomial (2x³ + 3x² + 4x + 2) by (x + 2).

The measure of Angle D in a parallelogram is 88 degrees.

Explain about parallelogram ?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure.

Properties of a parallelogram:

According to the question:
Since EFDM is a parallelogram, we know that opposite angles are equal. Therefore,

Angle E = Angle M

Angle D = Angle F

We're given:

Angle E = 16x + 12

Angle D = 18x - 2

So we have:

Angle M = 16x + 12

Angle F = 18x - 2

The sum of the angles in a parallelogram is 360 degrees. Therefore, we have:

Angle E + Angle F + Angle D + Angle M = 360

Substituting the given values, we get:

(16x + 12) + (18x - 2) + (16x + 12) + (18x - 2) = 360

72x + 20 = 360

72x = 340

x = 5

Now we can find the values of Angle E, Angle D, Angle F and Angle M:

Angle E = 16x + 12 = 16(5) + 12 = 92 degrees

Angle D = 18x - 2 = 18(5) - 2 = 88 degrees

Angle F = Angle D = 88 degrees

Angle M = Angle E = 92 degrees

Therefore, the measure of Angle D is 88 degrees.

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The solution to the inequality 5(3y+1)<15 in interval notation is (-∞, 2/3).

To solve the inequality 5(3y+1)<15, we need to isolate the variable y on one side of the inequality. Here are the steps to do so:
1. Start with the given inequality: 5(3y+1)<15
2. Distribute the 5 on the left side: 15y+5<15
3. Subtract 5 from both sides: 15y<10
4. Divide both sides by 15: y<10/15
5. Simplify the fraction: y<2/3

Now, we can write the solution in interval notation. Interval notation uses parentheses or brackets to indicate the range of values that satisfy the inequality. In this case, the solution is all values of y less than 2/3, so we use the notation (-∞, 2/3).

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The correct domain for the function f(t)=(5)/(t^(2)+4) is {all reals}.

The domain of a function is the set of all possible inputs or values for the independent variable, t in this case. The function f(t)=(5)/(t^(2)+4) has a denominator of t^(2)+4. To find the domain, we need to determine the values of t that would make the denominator equal to zero, as those values would make the function undefined.

t^(2)+4=0
t^(2)=-4
t=±√(-4)

Since the square root of a negative number is not a real number, there are no real values of t that would make the denominator equal to zero. Therefore, the domain of the function is {all reals}.

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The probability that there are not greater than 859 defective products in 359 packages is 0.9999.

We are given that;

Distribution: X 0 3 4 1 2 Р 0.02 0.14 0.34 0.36 0.14 1

0(X) = 0.9635 2

Now,

We need to know the probability of success for each package, which is the probability of having a defective product. Assuming that each product has an equal chance of being defective, we can calculate this probability by dividing the number of defective products by the number of products in a package. In this case, we have:

[tex]p = \frac{0.02 + 0.14 + 0.34 + 0.36 + 0.14}{4} = 0.25[/tex]

This means that each product has a 25% chance of being defective, and each package has a binomial distribution with n=4 and p=0.25.

To find the average and the standard deviation of the number of defective products in a package, we can use these formulas³:

[tex]$$E(X) = np$$$$\sigma(X) = \sqrt{np(1-p)}$$[/tex]

Plugging in the values of $n$ and $p$, we get:

[tex]$$E(X) = 4 \times 0.25 = 1$$$$\sigma(X) = \sqrt{4 \times 0.25 \times (1-0.25)} = \sqrt{0.75} \approx 0.866$$[/tex]

Therefore, the average number of defective products in a package is 1, and the standard deviation is 0.866.

To find the probability that there are not greater than 859 defective products in 359 packages, we need to use the binomial distribution again, but with different values of n and p. In this case, we have:

[tex]$$n = 359 \times 4 = 1436$$$$p = 0.25$$[/tex]

We want to find the probability that [tex]$X \leq 859$[/tex], where [tex]$X$[/tex] is the number of defective products in 1436 trials. We can use this formula:

[tex]$$P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i}p^i(1-p)^{n-i}$$Plugging in the values of $n$, $p$, and $k$, we get:$$P(X \leq 859) = \sum_{i=0}^{859} \binom{1436}{i}0.25^i(1-0.25)^{1436-i}$$[/tex]

Therefore, by probability the answer will be 0.9999.

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Answer:

151 tables

Step-by-step explanation:

If 1 table is used for 6 guests then for 901 guest we need to divide 901 by 6

901÷6= 150.15

Rounding of the answer 151 tables needed

In response to the given query, the result we have is As a result, the expressions following statement may be used to explain how long Interstate 90 is: 2m + 153.5

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

Let L represent the length of I-90. We are informed that

L = 2m + 153.5

where m is Interstate 15's length.

As a result, the following statement may be used to explain how long Interstate 90 is:

2m + 153.5

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Answer: I remember this question very well. I believe that the correct answer is 99.7%

68% of data falls between 15 and 25.

95% of data falls between 10 and 30.

99.7% of data falls between 5 and 35.

{-2 2 22}

a) The characteristic polynomial of A is given by:
$$p_A(\lambda) = \lambda^3 - 5\lambda^2 + 18\lambda + 36$$
b) The two eigenvalues of A are:
$$\lambda_1=2, \lambda_2=-4, \lambda_3=9$$
c) A basis for the eigenspace corresponding to the smallest eigenvalue $\lambda_2=-4$ is given by the set of vectors:
$$\begin{bmatrix} 0\\1\\0 \end{bmatrix}, \begin{bmatrix} 2\\0\\1 \end{bmatrix}$$
d) A basis for the eigenspace corresponding to the largest eigenvalue $\lambda_3=9$ is given by the set of vectors:
$$\begin{bmatrix} 1\\0\\-4 \end{bmatrix}, \begin{bmatrix} -2\\2\\22 \end{bmatrix}$$

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The equation that can be used to determine the area of the glass is A = 2 1/2 x 4.

A rectangle is a 2-dimensional quadrilateral with four right angles. A rectangle has two diagonals of equal length which bisect each other. The sum of interior angles is 360 degree and opposite sides are parallel

The area of the rectangle is the product of the length and the width.

Area of a rectangle = length x width

A = 4 x 2 1/2

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The cost of producing 2000 bagels is $796.8.

To determine the cost of producing 2000 bagels, we need to plug in the value of x into the given equation and solve for C(x).
C(x) = 300 + 0.25x - 0.4(x/1000)^3
C(2000) = 300 + 0.25(2000) - 0.4(2000/1000)^3
C(2000) = 300 + 500 - 0.4(2)^3
C(2000) = 300 + 500 - 0.4(8)
C(2000) = 300 + 500 - 3.2
C(2000) = 796.8

Therefore, the cost of producing 2000 bagels is $796.8.

In general terms, profit is nothing more than revenues minus costs. This mathematically expressed is:

Profit = Revenues - Costs

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Answer:

A: x

Step-by-step explanation:

So with problems like this when it saids f(g(x) it wants you to plug those values in. In some cases you have a value where the x is but you don't so you can't solve g(x) so you move on to the next step. You plug in g(x)= x-1/2 everywhere there is a x in f(x). So our equation would be 2(x-1/2) + 1. Then you solve by canceling the 2 by dividing it out so we would have x-1 +1. Then you combine like terms which -1 +1 is 0 so our final answer would be x.

We can write the mean absolute deviation as -

1.63.

Absolute deviation or mean absolute deviation is the measure of how far a given data element is from a given mean value of the data.

Given is that Suzie's Desserts offers its customers 5 dessert options. The prices are: $5.00 $9.00 $9.00 $6.00 $6.00 $9.00 $9.00.

The formula for absolute deviation is -

[tex]$\frac {1}{n} \sum \limits_{i=1}^n |x_i-m(X)|[/tex]

We can calculate the mean as -

(5 + 9 + 9 + 6 + 6 + 9 + 9)/7 = 7.57

We can write the  absolute deviation as -

Absolute deviation =

1/7(5 - 7.57 + 9 - 7.57 + 9 - 7.57 + 6 - 7.57 + 6 - 7.57 + 9 - 7.57 + 9 - 7.57) = 1.63

Therefore, we can write the mean absolute deviation as -

1.63.

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The total number of trips between the zone: a. 1 and 6 is 10863 trips. b. 3 and 10 is 12617 trips. c. 5 and 10 is 11215 trips. d. 4 and 9 is 15560 trips.

To determine the total number of trips between the zones, we can simply do addition of the production/generation and attraction values for the two zones in question.  Based on the values in the table:

a. For zones 1 and 6, the total number of trips would be 3643 + 3040 + 2542 + 1638 = 10863 trips.

b. For zones 3 and 10, the total number of trips would be 3156 + 2535 + 3172 + 3754 = 12617 trips.

c. For zones 5 and 10, the total number of trips would be 2167 + 2122 + 3172 + 3754 = 11215 trips.

d. For zones 4 and 9, the total number of trips would be 3204 + 4217 + 3597 + 4542 = 15560 trips.

Therefore, the total number of trips between the zones are: a. 10863 trips between zones 1 and 6 b. 12617 trips between zones 3 and 10 c. 11215 trips between zones 5 and 10 d. 15560 trips between zones 4 and 9.

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The quadrilateral with the specified value for x has a 45° angle.

A polygon with four sides, four angles, and four vertices is called a quadrilateral.

The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.

The exterior angles of the given quadrilateral are x°, 3x°, x°, and 3x°.

We are aware that a quadrilateral's total exterior angles are 360°.

Now, x°+3x°+x°+3x°=360°

8x°=360°

x°=45°

Therefore, the quadrilateral with the specified value for x has a 45° angle.

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