Given AMHNAOJP. Determine
the angles and sides of AOJP.
22cm
HJ 56
24cm
50
N
28cm
M
P
J

You will have approximately $1929.29 available to spend in 6 years.

To calculate the future value of your deposit after 6 years, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)^Time

Plugging in the values:

Present Value (PV) = $1491

Interest Rate = 5.07% = 0.0507

Time = 6 years

Future Value = $1491 * (1 + 0.0507)^6

Calculating the expression:

Future Value = $1491 * (1.0507)^6

Future Value ≈ $1929.29

Therefore, you will have approximately $1929.29 available to spend in 6 years.

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Answer:

√185 = 13.6

Step-by-step explanation:

Distance² = (x' - x)² + (y' - y)²

Distance² = (-7 - 4)² + (5 - -3)² = (-11)² + (8)² = 121 + 64 = 185

Distance = √185

Answer:

25/4

Step-by-step explanation:

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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Answer:

5/3

Step-by-step explanation:

5×(10×1/3)

=10×5/3

=since 5×(10×1/3) gives 50/3 so thus 10×5/3.

The fraction is therefore 5/3

Answer

1,049.18 and 20,125.18

Step-by-step explanation:

increase: 19,076*0.055 = 1,049.18

new price: 19,076*1.055 = 20,125.18

The height of the cylinder is 3.6 inches.

We know that the volume of a cylinder of radius R and height H is:

V = pi*R²*H

where pi = 3.14

We know that the radius is R = 5in and the volume is 284.7 inches cubed, replacing that in the formula above we will get:

284.7 in³= 3.14*(5 in)²*H

Solving that for H we will get:

H= (284.7 in³)/ 3.14*(5 in)²

H = 3.6 inches.

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Answer:

x=$3

Step-by-step explanation:

2x+5=3x+2

-2 from both sides

2x+3=3x

-2x from both sides

3=x

The equation of the circle graphed in this problem is:

(x - 5)² + y² = 16.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

For the circle graphed, we have that:

Hence the equation of the circle graphed is:

(x - 5)² + y² = 16.

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Answer:

13

Step-by-step explanation:

∠Q ≅ ∠ P ⇒ RP = RQ = 13

Answer:

(a) hundreds = 817

(b) hundredths = 817.09

(c) 3 d.p = 817.086

(d) 4 s.f. = 817.1

(e) whole number = 817

Answer:

Step-by-step explanation:

α + β = -b/a

αβ = c/a

α² + β² = (α + β)² - 2αβ

           \(= (\frac{-b}{a})^{2}-2\frac{c}{a}\\\\= \frac{b^{2}}{a^{2}}-\frac{2c}{a}\\\\=\frac{b^{2}}{a^{2}}-\frac{2c*a}{a*a}\\\\=\frac{b^{2}-2ca}{a^{2}}\)

9514 1404 393

Answer:

Step-by-step explanation:

The first two problems can be solved in your head by working backward from the end result.

__

1. After 3/2 is added, the result is 4. Then we must be adding 3/2 to 4 -3/2 = 5/2. We notice that 5/2 already has the numerator 3 more than the denominator, so the fraction of interest is 5/2.

__

2. If 3/8 is added to a number giving a result of 1, the number must be 1 -3/8 = 5/8. That is 5 times 1/8. The number of interest is the reciprocal of 1/8, so is 8.

__

3. Let x represent the speed of the faster car. Then x-3 is the speed of the slower car, and the two times are ...

  time = distance/speed

  390/x = 372/(x-3)

  390(x -3) = 372x . . . cross multiply

  18x = 1170 . . . . . . . add 1170-372x

  x =  65 . . . . . . . . . . divide by 18

The speeds of the cars are 65 mph and 62 mph.

The value of the cosine of ∠L in triangle LMN is approximately 0.98 using Pythagorean Theorem.

To find the cosine of ∠L in triangle LMN, we first need to use the Pythagorean theorem to find the length of side LM, since only have the lengths of NM and LN:

\(LM^2 = LN^2 - NM^2\\LM^2 = 40^2 - 9^2\\LM^2 = 1521\)

\(LM = \sqrt{1521}\)

LM = 39

Now that we know the length of all three sides of the triangle, we can use the cosine rule to find the cosine of ∠L:

cos(L) = \((LM^2 + LN^2 - NM^2)\) / (2 x LM x LN)

cos(L) = \((39^2 + 40^2 - 9^2)\) / (2 x 39 x 40)

cos(L) = 0.975

Rounding to nearest hundredth:

cos(L) = 0.98

Therefore, the value of cosine of ∠L in triangle LMN is approximately 0.98.

The ratio of the neighbouring side to the hypotenuse is known as the cosine of an angle in a right triangle. As L is not a straight angle in this situation, its value must be determined using the cosine method. Whether a triangle is a right triangle or not, the cosine rule can be used to relate the lengths of its sides and angles.

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The probability of selecting at least one red marker probability = \(\frac{1}{5}\)

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%.

Given that,

In the box contains ,

Black markers are = 5

Blue markers are = 3

Red markers are = 2

The given scenario will not affect the required probability as the selection of the second one is a case of future.

We need to find the probability of the first marker is red.

The probability is,

Probability =  \(\frac{red marker}{total markers}\)

Total markers = 5 + 3 +2

= 10

Probability = \(\frac{2}{10}\)

Probability = \(\frac{1}{5}\)

The probability of selecting at least one red marker probability = \(\frac{1}{5}\)

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Answer:

only C is a function cause a function has only 1 same value.

Answer:3:2 is the answer i am very sure

Step-by-step explanation:

26400 is what they travel in feet in a day divide that by 24 and that should be your answer

The expressions that accurately represents the area of the entire figure are:

C: (3x)(2x) - x²

D: x(3x) + x(2x)

To find the area of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.

From the given information:

side length of smaller square = x

area of smaller square = x * x = x²

side length of larger square = 2 * x = 2x

area of larger square = 2x * 2x = 4x²

Total area = area of smaller square + area of larger square

Total area = x² + 4x² = 5x²

Option C:

(3x)(2x) - x² =  6x² - x² = 5x²

Option D:

x(3x) + x(2x) =  3x² + 2x² = 5x²

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Answer:

1) \(16\frac{2}{3}\)% or 20%

Step-by-step explanation:

Given that:

An experiment which is carried out by flipping a coin and rolling six sided die.

The outcomes can be:

{H1, H2, H3, H5, H6, T1, T1, T2, T3, T5}

As per question statement:

Number of outcomes having tails and an odd number greater than one is 2 (i.e. T3 and T5)

Total number of outcomes here is 10.

Therefore, to find the percentage, we use the following formula:

\(\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\times 100\)

\(\Rightarrow \dfrac{2}{10}\times 100 = 20\%\)

As per question statement, the answer is 20%.

If we consider all the outcomes, i.e.

{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

Total number of outcomes = 12

The percentage will come out be :

\(\Rightarrow \dfrac{2}{12}\times 100 = 16\frac{2}{3}\%\)

Step-by-step explanation:

Probabibility = 1/6 * 1/6 = 1/36 = 2.77%.

The system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

Carlos graphed the system of equations that can be used to solve the equation x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

To graph this system of equations, we need to set the equation equal to zero. So, the equation becomes:

x^3 - 2x^2 + 5x - 6 + 4x^2 - 14x - 12 = 0

Combining like terms, we get:

x^3 + 2x^2 - 9x - 18 = 0

To graph this equation, you can use a graphing calculator or plot points manually. Here are the steps to manually plot the graph:

1. Choose a range for x, for example, from -5 to 5.
2. Pick a few values for x within the chosen range and substitute them into the equation to find the corresponding y-values.
3. Plot the points (x, y) on a coordinate plane.
4. Connect the plotted points to create a smooth curve.

By following these steps, you can graph the system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

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Answer:

this question is not factorable with rational number so either trick question and the answer is no solution or it is typed wrong

Step-by-step explanation:

Answer: 122.81

Step-by-step explanation:

If 86 seals dove for a combined total depth of 10,578 meters, each seal would have dove an average of 122.81 meters (10,578 meters / 86 seals)

\(10578 \div 86 = 122.81\)

Both the decorative light strands will change change the colors at the same time again after 448 seconds

In the above question, it is given that,

Two strands of decorative lights, red and blue is one strand and green and yellow is another are hanged

Strand one changes colors in = 16 seconds

Strand two changes colors in = 28 seconds

We need to find, after how many seconds will the strands change color at the same time again

To find this, we will take the LCM(Lowest Common Multiple) of both strands time

Factors of 16 = 2 x 2 x 2 x 2

Factors of 28 = 2 x 2 x 7

LCM( 16 and 28) = 2 x 2 x 2 x 2 x 2 x 2 x 7 = 448

Therefore, It can be concluded that, both the decorative light strands will change change the colors at the same time again after 448 seconds

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Answer:

Graph A

Step-by-step explanation:

I had this question in my class and got it right with answer A :')