Miguel deposited a certain amount of money in the bank. The bank paid him interest after one year at which point he had $757.12. After the next year he had $787.40. How much money did Miguel originally put into the bank? (Answer to the nearest dollar.)

Answer:

-3 and 4

Step-by-step explanation:

if y=0 then just look in the x axis

Answer:

P(A) =  0.5

P(B) = 0.33

P(A ∩ B) = 0

P( A ∪ B) = 0.83

Step-by-step explanation:

Tot = 6 + 18 + 12 = 36

P(A) = 18/36 = 0.5

P(B) = 12/36 = 0.33

P(A ∩ B) = 0

P( A ∪ B) = P(A) + P(B) - P(A and B)

= 0.5 + 0.33 - 0

= 0.83

The output of the combinatorial circuit is ¬(p ∧ (¬r ∨ q))

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

The figure of the combinatorial circuit

From the figure, we have the following features

Hence, the output is ¬(p ∧ (¬r ∨ q))

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The percentage of the books at the library are fiction books is 93%.

The percentage of the books at the library are fiction books is calculated as follows;

Total number of books = 2,790 (fiction) + 210 (non-fiction) = 3,000

Percentage of fiction books = (number of fiction books) / (total number of books) x 100%

Percentage of fiction books  =  (2,790 / 3,000) x 100

Percentage of fiction books = (0.93)  x 100

Percentage of fiction books  = 93%

Thus, the percentage of the books at the library are fiction books is determined by applying percentage formula.

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The equation of a line is not unique to its graph; this means that multiple lines can have the same slope and y-intercept. Therefore, this equation is a possible match, making option D the correct answer.

The equation of the graph shown below could be `y = 3x - 2`.

We are given an equation of the line that can fit the graph shown.

To determine which equation it is, we can compare the graph to each of the answer choices:

A. y = -10:

This is the equation of a horizontal line that is 10 units below the x-axis.

It is not the equation of the graph shown.B. 2x - 3y = -9:

To convert this equation to slope-intercept form, we need to solve for y:

2x - 3y = -93y = 2x + 9y

= (2/3)x + 3

This is the equation of a line with a slope of 2/3, meaning it has a positive slope.

The graph shown has a negative slope, so this equation is not a match.C.

-4x + 2y = -6:

To convert this equation to slope-intercept form, we need to solve for y:

-4x + 2y = -62y

= 4x - 6y

= 2x - 3

This is the equation of a line with a slope of 2, meaning it is steeper than the graph shown.

This equation is not a match.D. y = 3x - 2:

This equation is already in slope-intercept form, meaning it has a slope of 3 and a y-intercept of -2.

The graph shown has a slope of -3 and a y-intercept of -2.

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Answer:

d = -4.3

Step-by-step explanation:

-2d = 8.6

d is being multiplied by -2. You want d alone, so divide both sides of the equation by -2.

-2d/-2 = 8.6/-2

d = -4.3

Answer: the car travels 2,870 meters with 52,700 joules of energy.

Step-by-step explanation:

The given car uses 756 joules of energy every second. So, it would use x amount of energy to travel for t seconds. We know that the car uses 52,700 joules of energy. Let's find the time first.T = E ÷ P = 52,700 ÷ 756 = 70 seconds.

Now, we can calculate the distance covered by the car with this amount of energy.

Distance = Speed × Time = 41 m/s × 70 s = 2,870 meters.

Therefore, the car travels 2,870 meters with 52,700 joules of energy.

The height is  (x + 1) /x⁴ + 4x³ + 3x² + 8. Option D

From the information given, we have that the formula for calculating the volume of a rectangular prism is expressed as;

Volume = area × height

Then, we have that;

Area = x³ + 3x² + 8

Volume = x⁴ + 4x³ + 3x² + 8x + 4

Now, substitute the values, we get;

x⁴ + 4x³ + 3x² + 8x + 4 =  x³ + 3x² + 8 × height

Divide both sides by the coefficient of the height, we have;

Height =  x⁴ + 4x³ + 3x² + 8x + 4 /x³ + 3x² + 8

Factor the expression;

Height = (x + 1) /x⁴ + 4x³ + 3x² + 8

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The Real number solutions for $a$ that satisfy the given equation are:

\[a = \sqrt[3]{\frac{25}{192}}.\]

To find all real numbers $a$ that satisfy the given equation, let's simplify the equation and solve for $a$.

Starting with the given equation:

\[\frac{1}{64a^3 + 7} - 7 = -\frac{64a^3}{64a^3 + 7}.\]

First, let's eliminate the denominators by multiplying both sides of the equation by $(64a^3 + 7)$:

\[(64a^3 + 7) \cdot \left(\frac{1}{64a^3 + 7} - 7\right) = (64a^3 + 7) \cdot \left(-\frac{64a^3}{64a^3 + 7}\right).\]

Simplifying each side of the equation:

\[1 - 7(64a^3 + 7) = -64a^3.\]

\[1 - 448a^3 - 49 = -64a^3.\]

\[448a^3 - 64a^3 = 1 + 49.\]

\[384a^3 = 50.\]

Dividing both sides of the equation by 384:

\[a^3 = \frac{50}{384}.\]

\[a^3 = \frac{25}{192}.\]

To solve for $a$, we need to take the cube root of both sides:

\[a = \sqrt[3]{\frac{25}{192}}.\]

Therefore, the real number solutions for $a$ that satisfy the given equation are:

\[a = \sqrt[3]{\frac{25}{192}}.\]

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The plane flew at the first speed (111 mph) for 2 hours, and the remaining time of the trip (5 - 2 = 3 hours) was flown at the second speed (122 mph).

Let's assume the plane flew at the first speed (111 mph) for x hours.

Since the total duration of the trip was 5 hours, the time flown at the second speed (122 mph) can be calculated as (5 - x) hours.

To find the time flown at each speed, we can set up an equation based on the distance traveled.

The total distance traveled during the trip is 588 miles.

The distance covered at the first speed is given by the formula: Distance = Speed [tex]\times[/tex] Time.

So, for the first part of the trip, the distance covered is 111x miles.

The distance covered at the second speed is: Distance = Speed [tex]\times[/tex] Time.

For the second part of the trip, the distance covered is 122(5 - x) miles.

Since the total distance is 588 miles, we can set up the equation:

111x + 122(5 - x) = 588

Simplifying the equation:

111x + 610 - 122x = 588

-11x + 610 = 588

-11x = -22

x = 2.

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Answer:

$2,403.02

Step-by-step explanation:

To calculate the amount of interest earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded monthly, we can use the compound interest formula:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ I=P\left(1+\frac{r}{n}\right)^{nt}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ interest earned. \\ \phantom{ww}$\bullet$ $P =$ principal amount. \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form). \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year. \\ \phantom{ww}$\bullet$ $t =$ time (in years). \\ \end{minipage}}[/tex]

Given values:

Substitute the values into the formula and solve for I:

[tex]I=12585\left(1+\dfrac{0.035}{12}\right)^{12 \cdot 5}-12585[/tex]

[tex]I=12585\left(1.00291666...\right)^{60}-12585[/tex]

[tex]I=12585(1.19094282...)-12585[/tex]

[tex]I=14988.015...-12585[/tex]

[tex]I=2403.01550...[/tex]

[tex]I=\$2403.02[/tex]

Therefore, the interest earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded monthly is $2,403.02 (to the nearest cent).

The two lines are neither parallel nor perpendicular.

To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes. Let's examine the given lines and analyze their slopes:

Line 1: y + 1 = -5x

We can rewrite Line 1 in slope-intercept form (y = mx + b) by isolating y:

y = -5x - 1

From this equation, we can identify that the slope of Line 1 is -5.

Line 2: y = (1/5)x - 2

Line 2 is already in slope-intercept form, and we can observe that the slope of Line 2 is 1/5.

Compare the slopes: The slopes of Line 1 and Line 2 are -5 and 1/5, respectively. Since the slopes are not equal (they are not the same value), the lines are not parallel.

Determine perpendicularity: To determine if the lines are perpendicular, we need to check if the product of their slopes is -1. Multiplying the slopes of Line 1 and Line 2, we have:

(-5) * (1/5) = -1

Since the product is -1, the lines would be perpendicular. However, in this case, the product of the slopes is -1/5, not -1. Therefore, the lines are not perpendicular either.

Hence, the two lines given by the equations y + 1 = -5x and y = (1/5)x - 2 are neither parallel nor perpendicular.

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The order of the rotational symmetry for the figure is: Option B: 4 or more

The number of positions where a figure can be rotated and still look exactly the same as it did before the rotation is called the symmetry order. For example, he can rotate the star along the vertex five times and see the same thing each time. So its symmetry order is 5.

Looking at the given figure, we see a number from 1 to 4 on the image.

Now, it will seem like the figure can be easily rotated but to be rotated to get the exact same shape we currently have, it will have to be rotated at least 4 or more times due to the complex nature.

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The number of hours worked this week is 119.

If we start with a number N, and we reduce it by a percentage X, then the new number is:

N' = N*(1 - X/100%).

Here we know that last week, you worked for a total of 140 hours, and this week you worked 15% less, then the number of hours you worked this week is:

N' = 140*(1 - 15%/100%)

N = 140*(1 - 0.15)

N =  119.

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Comparing the two conditional relative frequencies:

0.4286 is approximately equal to 0.43 (rounded to two decimal places)

0.4500 is approximately equal to 0.45 (rounded to two decimal places)

The correct answer is: 0.41 to 0.43.

To compare the conditional relative frequencies of a male preferring hip hop music to a female preferring hip hop music, we need to calculate the relative frequencies within each gender group.

The conditional relative frequency is calculated by dividing the frequency of the specified group (in this case, the number of males or females preferring hip hop music) by the total frequency of that gender group.

For males:

Conditional Relative Frequency of Males Preferring Hip Hop = Frequency of Males Preferring Hip Hop / Total Frequency of Males.

= 21% / 49%

= 0.4286 (rounded to four decimal places)

For females:

Conditional Relative Frequency of Females Preferring Hip Hop = Frequency of Females Preferring Hip Hop / Total Frequency of Females

= 23% / 51%

= 0.4500 (rounded to four decimal places)

Comparing the two conditional relative frequencies:

0.4286 is approximately equal to 0.43 (rounded to two decimal places)

0.4500 is approximately equal to 0.45 (rounded to two decimal places)

Therefore, the correct answer is:

0.43 to 0.45

The conditional relative frequency of a male preferring hip hop music falls within the range of 0.43 to 0.45 when compared to the conditional relative frequency of a female preferring hip hop music.

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The inside of the bronchioles are covered in cilia and mucus that trap and remove dust and other foreign particles. The Option B.

The bronchioles which are small air passages in the lungs are lined with specialized structures called cilia and produce mucus. The cilia are tiny hair-like structures that constantly beat in coordinated motions, creating a wave-like movement.

The mucus which i a sticky substance is produced by goblet cells and acts as a protective layer. Together, the cilia and mucus form a defense mechanism that helps trap and remove dust, pollen, bacteria and other foreign particles that enter the airways during breathing.

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a.) The sample space for this scenario would be: Option A.

GG, GB, GR, BG, BB, BR, RG, RB, RR

b The probability distribution for X is:

X | 0 | 1 | 2 |

P(X) | 1/3 | 2/3 | 0 |

GG: There are no red crayons selected. X = 0.

GB, BG, RG: Only one red crayon is selected. X = 1.

GR, RB: One red crayon and one non-red crayon are selected. X = 1.

BB: There are no red crayons selected. X = 0.

BR, RB: One red crayon and one non-red crayon are selected. X = 1.

RR: Two red crayons are selected. X = 2.

The probability distribution for X would be as follows:

X = 0: P(X = 0) = 2/6 = 1/3

X = 1: P(X = 1) = 4/6 = 2/3

X = 2: P(X = 2) = 0/6 = 0

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The expected number of investigators who will report that 3, 4, or 5 people are consumers of rice is 57 investigators.

The binomial distribution B(n, p) describes the behavior of a count X of successes in n independent trials, each with its own boolean-valued outcome: success (with probability p) or failure (with probability q = 1-p).

We want to find the probability that an investigator reports 3, 4, or 5 people are consumers of rice. The probability P(X=k) for a binomial distribution is given by the formula:

P(X=k) = C(n, k) * p^k * q^(n-k)

So we want to find P(X=3) + P(X=4) + P(X=5) :

P(X=3) = C(10, 3) * (0.5)^3 * (0.5)^(10-3)

= 0.117

P(X=4) = C(10, 4) * (0.5)^4 * (0.5)^(10-4)

= 0.205

P(X=5) = C(10, 5) * (0.5)^5 * (0.5)^(10-5)

= 0.246

The expected number of investigators who will report three or less of the people interviewed consumed is :

= P(X=3) + P(X=4) + P(X=5)

= 0.117 + 0.205 + 0.246

= 0.568

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Full question is:

Suppose that half the population of a town are consumers of rice. Each of 100 investigators interviews 10 individualas to see wheather they are consumers of rice. How many investigators do you expert to report that three or more but less than six people are consumers of rice?

Step-by-step explanation:

arithmetic sequence :

a1 = 7

d = 3

an = an-1 + d = a1 + (n-1)×d

the formula for the sum of an arithmetic sequence is

n/2 × (2×a1 + (n-1)×d)

40 is a12 (n = 12), as 40-7 = 33, 33/3 = 11, 11 plus 1 from a1 is 12.

we have the sum of 12 terms.

12/2 × (2×7 + 11×3) = 6 × (14 + 33) = 6×47 = 282

so, we have :

the sum = 282

A = 12

B = 7 + (n-1)×3 = 7 + 3n - 3 = 4 + 3n

areu supposed.to substituted the numbers under each question into the equation?

Answer:

average rate of change of the function = 3

Step-by-step explanation:

average rate of change function is defined as,

f(b) - f(a) / b - a where [a,b] is the interval

according to the question [a,b] = [2, 2+h]

f(2) = 3(2) + 7 = 13

f(2+h) = 3(2 + h) + 7 = 6 + 3h + 7 = 13 + 3h

by substituting the values in the function,

average rate of change function = 13 + 3h - 13 / 2 + h - 2 = 3h / h = 3

To copy angle ABC onto ray DE to create angle FDE, the correct sequence of steps are:

1.Step 1: Draw ray DE.

2. Step 2: Place the compass at point D and set the width to any convenient width.

3. Step 3: Without changing the width, draw an arc that cuts both rays DE and DC. Label the intersection point F.4. Step 4: Place the compass at point B and set the width to the same amount.

5. Step 5: Without changing the width, draw an arc that intersects with ray BC.

6. Step 6: Without changing the width, draw an arc that intersects with the previously drawn arc at point G.

7. Step 7: Draw a line from point D to point G.

8. Step 8: Draw a line from point F to point E.
9. Step 9: The created angle FDE is the copy of angle ABC.

Thus, the correct sequence of steps needed to copy angle ABC onto ray DE to create angle FDE are:

Draw ray DE, place the compass at point D and set the width to any convenient width, without changing the width, draw an arc that cuts both rays DE and DC, label the intersection point F, place the compass at point B and set the width to the same amount, without changing the width, draw an arc that intersects with ray BC, without changing the width, draw an arc that intersects with the previously drawn arc at point G, draw a line from point D to point G, draw a line from point F to point E, the created angle FDE is the copy of angle ABC.

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Answer:

Step-by-step explanation:

Answer: 12 | Constant Function

Step-by-step explanation:

The function always produces the value 3 * 4, which is 12, regardless of the input x. Thus the answer is 12 and is a constant function.

The different 2-member groups that are possible is 28

From the question, we have

Total number of members, n = 8

Numbers to selection, r = 2

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 8 and r = 2

Substitute the known values in the above equation

Total = ⁸C₂

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 8!/(6! * 2!)

Evaluate

Total = 28

Hence, the number of ways is 28

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The statements that are correct about the function that have been shown are;A, B, C, F

A mathematical function called an exponential function has the independent variable in the exponent. Its general form is:

f(x) = a^x

where "x" is the variable and "a" is the base, a positive constant. The exponential function's appearance and behavior depend on the base "a".

The function grows exponentially when the base "a" is greater than 1. The function expands quickly as "x" grows in value. As "x" rises, the growth rate becomes steeper.

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Answer:

27p^2

Step-by-step explanation:

1:Take out the constants.

(9x3)pp

2:simplify 9 x 3 to 27

27pp

3:Use product rule: x^a x^b=x^a+b

27p^2

The answer is:

[tex]\sf{p^{12}}[/tex]

Work/explanation:

When multiplying numbers with the same base, we can just add their exponents.

This can be shown with the following exponent law:

[tex]\sf{x^m\cdot x^n=x^{m+n}}[/tex]

Similarly:

[tex]\sf{p^9\times p^3=p^{9+3}=p^{12}}[/tex]

Hence, the answer is p¹².

A possible arrangement of the whole numbers 0 through 9, at most one time, to create an accurate number line is: 0 - 3 - 1 - 2 - 4 - 7 - 6 - 5 - 9 - 8.

To create an accurate number line using the whole numbers 0 through 9, at most one time, we need to arrange the numbers in ascending order from left to right.

To maintain the right spacing, each number should be spaced at an acceptable interval. Here is one possible configuration:

0 - 3 - 1 - 2 - 4 - 7 - 6 - 5 - 9 - 8.

In this arrangement, each number appears exactly once, and they are placed in sequential order with equal spacing between them.

This creates an accurate number line representing the whole numbers 0 through 9.

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The values on the graph of the velocity of the body, indicates that we get;

a. t = 2 seconds and t = 7 seconds

b. 3 ≤ t ≤ 6

c. Please find attached the speed of the body in the interval 0 ≤ t ≤ 10 created with MS Excel

b. Please find attached the acceleration of the body in the interval 0 ≤ t ≤ 10

Velocity is the rate of change of the position of an object with respect to a specified reference frame and time.

The figure is a velocity time graph, and the velocity of an object is the rate of change of the displacement with time, such that when graph is above the horizontal axis, the velocity is positive, and when the velocity is below the horizontal axis, the velocity is negative, therefore, we get;

a. When the velocity of the changes sign, the direction of the body reverses. The points at which the velocity changes sign, which are the x-intercepts are at t = 2, and t = 7

b. The speed is constant when the velocity remains the same, which are locations on the graph, where the graph is an horizontal line. Therefore, the interval at which the body is moving at a constant velocity is; 3 ≤ t ≤≤6

c. The speed of a body is its absolute velocity, which can be found from the graph by taking the absolute value of the velocity at each point on the graph as follows;

The points on the resulting graph will therefore be; (0, 0), (1, 4), (3, 4), (6, 4), (8, 4) and (10, 0).

Please find attached the speed of the body in the interval 0 ≤ t ≤ 10

d. The acceleration is the rate of change of the velocity of the body with time. The acceleration of the body which has a velocity graph consisting of straight lines is a piecewise constant graph, such that we get;

From t = 0 to t = 1, a = (4 - 0)/(1 - 0) = 4

From t = 1 to t = 3, a = (4 - (-4))/(1 - 3) = -4

From t = 3 to t = 6 , a = (-4 - (-4))/(6 - 3) = 0
From t = 6 to t = 8, a = (4 - (-4))/(8 - 6) = 4

From t = 6 to t = 10, a = (0 - 4)/(10 - 8) = -2

Please find attached the graph of the acceleration of the body, created with MS Excel

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