Trinity has 20 quarters and nickels worth a total of $2.00. How many of each coin does she Include introductory statements as well as a concluding statement.​

Let us represent the unknown number by x.

From the problem statement, it is given that the sum of the square of the number (x²) and 15 is the same as eight times the number (8x).

Thus, the equation becomes:

x² + 15 = 8x

To find the solution, we need to first bring all the terms to one side of the equation:

x^2-8x+15=0

Next, we need to factorize the quadratic expression:

x^2-3x-5x+15=0

x(x-3)-5(x-3)=0

(x-3)(x-5)=0

From the above equation, x = 3 or x = 5.

Therefore, the two numbers are 3 and 5 respectively.

The numbers are 3 and 5.

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Answer:

135,309,862,740 is your answer.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$12000\\ r=rate\to 5.3\%\to \frac{5.3}{100}\dotfill &0.053\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=12000\left(1+\frac{0.053}{4}\right)^{4\cdot 5}\implies A=12000(1.01325)^{20}\implies A\approx 15613.98\)

A-1 = (ATA)-1AT, and therefore ATA is also invertible.

If A is invertible, it means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. This means that A has an inverse, denoted by A-1.

Now, let's consider the matrix ATA. To show that it is also invertible, we need to find a matrix C such that (ATA)C = C(ATA) = I. We can do this by substituting B = A-1 into the equation and multiplying both sides by A:ATAA-1 = AIA-1 = AA-1 = I

This means that C = A-1 is the inverse of ATA, so (ATA)-1 = A-1. Now, let's substitute this back into the equation to find A-1:A-1 = (ATA)-1AT = A-1ATA-1AT = A-1IT = A-1

Thus, we have shown that A-1 = (ATA)-1AT, and therefore ATA is also invertible.

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The nurse should run the pump at 111.1 ml/hr.

To infuse a 1000ml bag of lactated ringers over 9 hours, the nurse must determine the hourly rate at which the fluid should be infused. This can be done by dividing the total volume of the fluid (1000 ml) by the number of hours it will take to infuse it (9 hours).

So, the hourly rate would be:

1000 ml ÷ 9 hours = 111.1 ml/hr.

Therefore, the nurse should run the pump at 111.1 ml/hr in order to infuse the 1000ml bag of lactated ringers over 9 hours.

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By using Pythagorean theorem and derivatives, we find the distance between the boy and the balloon is increasing at a rate of 16 ft/s, 5 seconds after the boy passes under the balloon.

We can use the Pythagorean theorem to relate the distance between the boy and the balloon, the height of the balloon, and the distance the boy has traveled:

distance^2 = height^2 + (distance traveled by the boy)^2

Taking the derivative with respect to time, we have:

2(distance)(rate of change of distance) = 2(height)(rate of change of height) + 2(distance traveled by the boy)(rate of change of distance traveled by the boy)

Simplifying and solving for the rate of change of distance, we get:

rate of change of distance = [(height)(rate of change of height) + (distance)(rate of change of distance traveled by the boy)] / distance

At the moment the boy passes under the balloon, we have:

distance = 40 ft

height = 40 ft

rate of change of height = 4 ft/s (since the balloon is rising at a speed of 4 ft/s)

distance traveled by the boy = 16 ft/s x 5 s = 80 ft

rate of change of distance traveled by the boy = 16 ft/s (since the boy is cycling at a constant speed of 16 ft/s)

Substituting these values into the equation above, we get:

rate of change of distance = [(40 ft)(4 ft/s) + (40 ft)(16 ft/s)] / 40 ft = 16 ft/s

Therefore, the distance between the boy and the balloon is increasing at a rate of 16 ft/s, 5 seconds after the boy passes under the balloon.

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PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction. The solution to the Expression (3^0 * 8^2)^-2 is 1/4096.

The expression (3^0 * 8^2)^-2, the order of operations, which is typically referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Simplify the exponent expressions within the parentheses:

(3^0 * 8^2) = (1 * 64) = 64

Step 2: Rewrite the expression with the simplified value:

(64)^-2

Step 3: Apply the exponent rule for a negative exponent:

(64)^-2 = 1 / (64)^2

Step 4: Evaluate the expression within the parentheses:

(64)^2 = 64 * 64 = 4096

Step 5: Rewrite the expression with the simplified value:

1 / 4096

Therefore, the solution to the expression (3^0 * 8^2)^-2 is 1/4096.

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Answer:

A

Step-by-step explanation:

The only side that you dont have to use the Pythagorean theorem is LQ and that measure is 2. So A is the correct answer.

The equation of the line that is parallel to y = -3x + 6 is: y = -3x - 20.

The equation of the line that is perpendicular to y = -3x + 6 is: y = 1/3x + 20/3.

Recall the following facts:

Given the equation of a line as y = -3x + 6, the slope of the line is m = -3. This implies that, the line that is parallel to y = -3x + 6 will have the same slope of m = -3, and the slope of the line that is perpendicular to y = -3x + 6 will be m = 1/3.

To write the equation of the perpendicular line, substitute m = 1/3 and (a, b) = (-8, 4) into y - b = m(x - a):

y - 4 = 1/3(x - (-8))

y - 4 = 1/3x + 8/3

y = 1/3x + 8/3 + 4

y = 1/3x + 20/3

To write the equation of the parallel line, substitute m = -3 and (a, b) = (-8, 4) into y - b = m(x - a):

y - 4 = -3(x - (-8))

y - 4 = -3x - 24

y = -3x - 24 + 4

y = -3x - 20

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Answer:

129

Step-by-step explanation:

8^2 + 9 (12/3 x 2) -7  Parentheses first 12 : 3 is the same as 12/3

    8^2 + 9 (4x2)-7 Parentheses:

      8^2 + 9 (8) - 7 Exponent 8 x 8:

        64 + 9(8) - 7     Multiply:

         64 + 72- 7     Add :

             136 - 7    Subtract:

                 129

The answer is 129.

Hope this helps :)

Answer:

2812/39

Step-by-step explanation:

74 • (76/78)

76/78 = 38/39

74 • 38/39 = 2812/39

red line is crimson because itit tha national colour of nepal

Answer:

8×3×2=48

Step-by-step explanation:

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Answer:

48 cubic meters

Step-by-step explanation:

Answer:

  0.90

Step-by-step explanation:

You want the probability of A or B given the counts in the Venn diagram shown.

The probability of A or B will be the total number of counts in the circles divided by the total number of counts shown on the chart.

  P(A or B) = (25 +5 +15)/(25 +5 +15 +5) = 45/50 = 90/100

  P(A or B) = 0.90

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In this case, the probability of either event A or B occurring is 0.53 or 53%, assuming that events A and B cannot occur simultaneously.

The probability of either event A or B happening can be found using the formula P(A or B) = P(A) + P(B) - P(A and B). In this case, the probability of event A occurring is 5/25, and the probability of event B occurring is 5/15. Since we do not know if events A and B can occur simultaneously, we will assume they can't (i.e., they're mutually exclusive), making P(A and B) = 0. So, P(A or B) = 5/25 + 5/15 - 0 = 0.2 + 0.33 = 0.53, or 53% when rounded to the nearest hundredth as a decimal.

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First pick: Random apple

2 out of the 5 apples are red. Therefore, the probability of choosing a red apple is:

Second pick: Red apple removed

We're left with 4 apples, one of which is red.

Therefore, the probability of choosing the red apple from this bowl is:

To get the probability of the two events happening right next to each other, we mulitply both probabilities:

Meaning that the probability that both apples chosen will be red is 1/10, or 10%

The question is an illustration of Pythagoras theorem

The length of the hypotenuse is 11.8 cm

The legs of the right triangle have the following measures

Leg 1 = 7 cm

Leg 2 = 9.5 cm

So, the length of the hypotenuse (h) is calculated using the following Pythagoras theorem.

\(h = \sqrt{Leg\ 1^2 + Leg\ 2^2}\)

This gives

\(h = \sqrt{7^2 + 9.5^2}\)

Evaluate the squares

\(h = \sqrt{139.25}\)

Evaluate the exponent

\(h = 11.8\)

Hence, the length of the hypotenuse is 11.8 cm

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Answer:11.8

Step-by-step explanation:

Y E S

The dimensions of a different sector with the same area and perimeter are An alternative sector's radius is 6.42 inches. An alternative sector has an arc length of 16.52 inches.

The distance between two places along a segment of a curve is known as the arc length.

Sector radius, r = 8.26 inches

Sector arc length = 12.84 inches

Sector perimeter = 2r + length of the arc

The specified sector's perimeter is equal to 2 x 8.26 x 12.84 x 29.36 inches.

The circle's circumference is 2 + 8.26 + 16.52.

The specified circle's area is A = 8.262 * 68.2276.

Sector area, A = 53.0292 inch2

Consequently, we have;

2R plus A equals 29.36 inches

A·R = 53.0292 × 2

that provides;

R² + 53.0292 = 14.68·R

R² - 14.68·R + 53.0292 = 0

using a graphing calculator to factor yields;

(R - 6.42)·(R - 8.26) = 0

R = 6.42 or R = 8.26

R = 8.26 is the measurement for the first sector.

Due to the distinctions between the sectors, we have;

R = 6.42 inches is the radius of the other sector.

The length of the arc, A = 29.36 - 2R

∴ A = 29.36 - 2 × 6.42 = 16.52

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a) To find the first three elements of the sequence defined by an = n^2 - 3n + 2, we simply substitute n = 0, 1, 2 into the expression for an and simplify: a0 = 2, a1 = 0, a2 = 0.

b) To show that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2, we can use mathematical induction. Assume the relation holds for some arbitrary k >= 2. Then we can show that it also holds for k+1 by substituting k+1 into the expression and using the fact that an = (k+1)^2 - 3(k+1) + 2 = k^2 - k + 2 + 2k. After simplification, we arrive at the expression for ak+1 in terms of ak and ak-2, showing that the relation holds for k+1.

a) To find the first three elements of the sequence, we simply substitute n = 0, 1, 2 into the expression for an and simplify:

a0 = (0)^2 - 3(0) + 2 = 2

a1 = (1)^2 - 3(1) + 2 = 0

a2 = (2)^2 - 3(2) + 2 = 0

Therefore, the first three elements of the sequence are 2, 0, 0.

b) To show that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2, we need to show that the expression for an can be written in terms of the previous two terms of the sequence, a(n-2) and a(n-1), using the given recurrence relation.

We can write:

an = n^2 - 3n + 2

  = (n-2)^2 - 3(n-2) + 2 + 2(n-2)

  = (n-2)^2 - 3(n-2) + 2n

Next, we can substitute n-2 for n in the expression for a(n-2) to get:

a(n-2) = (n-2)^2 - 3(n-2) + 2

Finally, we can substitute n-1 for n in the expression for a(n-1) to get:

a(n-1) = (n-1)^2 - 3(n-1) + 2

Now, we can use these expressions to write an in terms of a(n-2) and a(n-1) as follows:

an = (n-2)^2 - 3(n-2) + 2n

  = a(n-2) + 2(n-1) - (n-1)^2 + 3(n-1)

  = 2a(n-2) - a(n-1) + 2

Therefore, we have shown that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2.

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Answer:

x = 38°

y = 90°

Step-by-step explanation:

x is an inscribed angle, so, 78/2=39

y is an inscribed angle of which connects two endpoints of the diameter, so y = 90°

Answered by GAUTHMATH

Answer:

10

Step-by-step explanation:

\( {14}^{2} = ( {9}^{2} + {x}^{2} )\)

\(196 = 81 + {x}^{2} \)

\(196 - 81 = {x}^{2} \)

\(115 = {x}^{2} \)

\(x = \sqrt{115} \)

X = 10.7

The correct choice is OB. The series diverges.

The given series is: 1, 1, -1, ...

To determine whether the geometric series converges, we need to check if the absolute value of the common ratio between consecutive terms is less than 1.

The common ratio between consecutive terms is -1/1 = -1.

The absolute value of the common ratio is |-1| = 1.

Since the absolute value of the common ratio is equal to 1, which is not less than 1, the geometric series diverges (choice OB).

Therefore, the correct choice is OB. The series diverges.

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\( \huge{ \blue{ \frac{4}{3} = \frac{20}{n} }}\)

\( \bold{ = \frac{3 \times 20}{4n} }\)

\( = \frac{60}{4} \)

\( \huge{ \bold{ \gray{ \boxed{ = \boxed{15}}}}}\)

\( \huge{ \orange{20 + 15}}\)

\( \huge{ \bold{ \red{ \boxed{ = \boxed{35}}}}}\)

\( \huge{ \bold{ \green{ \boxed{ \boxed{ \underline{c. \: 35}}}}}}\)

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For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.

Non occurrence patterns identifies the absence of events when detecting a pattern.

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Answer:

-25

Step-by-step explanation:

Since product mean multiply, we multiply (3-4) and (blank), which we'll call "n".

(3-4)n = 25

subtract in parentheses

(-1)n = 25

remove parentheses

-1n = 25

swap signs

n = -25

Answer:

hai :D

Step-by-step explanation:

Also try D

The probability that the second smallest integer from a set of six distinct integers is picked at random is the same as the probability that the first smallest is 1.

This can be expressed mathematically as:

P(second smallest) = P(first smallest).

The probability of the first smallest integer is the number of combinations that result in the first smallest number divided by the total number of possible combinations of six distinct integers.

For example, if we have six distinct integers in a set, A, B, C, D, E, and F, the probability of A being the first smallest is the number of combinations that result in A being the smallest divided by the total number of combinations.

The combinations that result in A being the smallest are {A, B, C, D, E, F}, {B, A, C, D, E, F}, {C, A, B, D, E, F}, and so on. That’s a total of 6 combinations out of the total possible number of combinations, which is 6 x 5 x 4 x 3 x 2 x 1 = 720.

Therefore, P(first smallest) = 6/720 = 1/120. Similarly, the probability of the second smallest number being the same is also 1/120.

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Answer:

9 degrees Celsius

Step-by-step explanation:

I graphed the function on the graph below to find the maximum of the parabola. The maximum is at (9,200), which means at 9 degrees Celsius, there are 200,000 fish.

The temperature at which there will be maximum number of fishes is given by the point (9, 200), is it is 9 degrees.

Given data:

To find the temperature that will result in the maximum number of fish, determine the x-value (temperature) at the vertex of the quadratic function.

The given function is P(x) = -2(x - 9)² + 200, where P(x) represents the fish population in thousands and x represents the water's temperature.

The general form of a quadratic function is y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

The vertex form of the function is P(x) = -2(x - 9)² + 200.

Comparing this to the general form, the vertex of the parabola is at the point (9, 200).

Hence, the temperature that will result in the maximum number of fish is 9 degrees (the x-value of the vertex).

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