What is the least common multiple (LCM) of 8 and 10?

After 4 years, with an initial deposit of $6,000 at a 1.5% annual interest rate compounded monthly, Isabel will have approximately $6,370.07 in her account.

Calculating Compound Interest

To calculate the amount of money Isabel will have in her account after 4 years with an initial deposit of $6,000 at an annual interest rate of 1.5% compounded monthly, we can use the compound interest formula:

V(t) = P(1 + r/n)nt

P = principal amount (initial investment) = $6,000

r = annual interest rate (as a decimal) = 0.015

n = number of times the interest is compounded per year = 12

t = number of years the money is invested or borrowed for = 4

Substituting these values into the formula, we get:

V(4) = $6,000(1 + 0.015/12)12(4)

This simplifies to:

V(4) = $6,000(1 + 0.00125)48

Calculating the value inside the parentheses first:

1 + 0.00125 = 1.00125

Then raising it to the 48th power gives us:

1.0012548 ≈ 1.061678

Multiplying this by the principal:

V(4) ≈ $6,000 × 1.061678 ≈ $6,370.07

After 4 years, Isabel's account will have approximately $6,370.07.

Answer:$6,370.07

Step-by-step explanation:

Answer:

the answer is x = 9 cm

Step-by-step explanation:

The correct equation of the parabola in intercept form is [tex]2 (x+2)^2 -50[/tex].

To derive this equation, we will use the fact that the parabola passes through the given point (1,32) and has x-intercepts at -7 and 3.

[tex]y = k*(x+7)(x-3)[/tex]

[tex]y = k *(x^2 + 4x - 21)[/tex]

[tex]32 = k ( 8 * -2)32 = -16* kk = 32/-16 = -2[/tex]

[tex]y = -2(x+7)(x-3)[/tex]

[tex]= -2(x^2 + 4x - 21)[/tex]

[tex]= -2(x^2 +4x ) -42[/tex]

[tex]= 2(x^2 + 4x + 4) - 42 - 8[/tex]

[tex]= 2 (x+2)^2 -50[/tex]

Answer:

Red kite has maximum altitude with 23.1 feet higher.

Step-by-step explanation:

Given : Emma enjoys flying kites. her red kite has a maximum altitude of 117.46 meters, and her black kite has a maximum altitude of 362.26 feet.

one foot is the same as 0.3048 meters.

To find : Which kite has a higher maximum altitude, and how many feet higher is it?

Solution :

First we have to convert meter into feet.

We have given, 1 feet = 0.3048 meters.

[tex]1 \text{ meter }=\frac{1}{0.3048} \text{ feet}[/tex]

So, red kite has a maximum altitude of 117.46 meters

In feet, red kite has a maximum altitude of

[tex]117.46\text{ meter }=\frac{117.46}{0.3048}=385.36 \text{ feet}[/tex]

Now, Red kite has a maximum altitude of 385.36 feet

Black kite has a maximum altitude of 362.26 feet.

385.36>362.26 feet.

Difference is 385.36-362.26=23.1 ft.

Therefore, Red kite has maximum altitude with 23.1 feet higher.

The mean of the quiz scores is given by the equation M = 86 %

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the quizzes be represented as M

Now , the equation will be

Let the number of quizzes be n = 5

Let the scores of each quizzes be represented by set A

Set A = { 95% , 95%, 80%, 85%, 75% }

So , the mean of the quizzes M = sum of the quizzes / number of quizzes

Substituting the values in the equation , we get

The mean of the quizzes M = ( 95% + 95% + 80% + 85% + 75% ) / 5

The mean of the quizzes M = ( 430/5 )

The mean of the quizzes M = 86 %

Therefore , the value of M is 86 %

Hence , the mean of the quizzes is 86 %

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Let the number of water pumps be n and the time taken to fill the pool is t.

Now, we can see that higher the number of water pumps, lesser the time to fill the pool.

It means quantities  vary indirectly.

Thus, [tex]n=\frac{k}{t} , \text{ where k is the constant of variation}[/tex]

Now, we have been given that It takes four identical water pumps 6 hours to fill a pool.

Thus, we have

[tex]4=\frac{k}{6} \\ \\ k=24[/tex]

Hence, constant of variation is 24.

Now, we have to find the time that  three pumps will take to fill the same pool.

[tex]3=\frac{24}{t} \\ \\ 3y=24\\ \\ y=\frac{24}{3} \\ \\ y=8[/tex]

Hence, it will take 8 hours to fill the pool by three identical pumps.

the length of side VY is equal to the height, which is 19.4 units. The formula for the perimeter of a rectangle is given as `2 * (base + height)`.

It's correctly stated that the base of the rectangle is `3y + 1`, and the height is `2y + 3`. The perimeter is given as `90 units`.

To find the dimensions, we set up an equation using the formula for the perimeter:

  90 = 2 * [(3y + 1) + (2y + 3)]

  This equation represents that the perimeter is equal to twice the sum of the base and height.

The equation is then simplified:

  90 = 2 * [5y + 4]

  By dividing both sides by 2, it becomes:

  5y + 4 = 45

  Solving for y:

  5y = 45 - 4

  5y = 41

  y = 41 / 5

  y = 8.2 units

  So, the value of y is correctly determined as 8.2 units.

With the value of y known, the base and height expressions are evaluated:

  Base: `3y + 1 = 3 * 8.2 + 1 = 24.6 + 1 = 25.6 units`

  Height: `2y + 3 = 2 * 8.2 + 3 = 16.4 + 3 = 19.4 units`

The dimensions of the rectangle are correctly calculated as follows:

  Base: 25.6 units

  Height: 19.4 units

  It's also mentioned that the length of side VY is equal to the height, which is 19.4 units.

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The height of the drive-in movie theater screen can be determined using proportions and similar triangles. The total height of the screen is found to be 11.7 feet.

To find the height of the screen, you'll need to use similar triangles, as the triangle formed by your line of sight to the top and bottom of the screen is similar to the triangle formed by the screen and the ground. The proportion of the vertical distance from your eye to the ground and the horizontal distance from you to the screen is equal to the proportion of the height of the screen and the horizontal distance from you to the screen. Hence, you can calculate the height of the screen using a cross-multiplication.

So, we have the equation: 5.7/11 = h/11, where h is the height of the screen from your eye level. Solving this gives us h=5.7 feet. Thus, the total height of the screen is the height from the ground to your eye level plus the height of the screen from your eye level. So, the total height = 5.7 feet + 6 feet = 11.7 feet.

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Answer:

There is likely an association because 0.8 is not similar to ≈ 0.33.

The probability that the result is a multiple of 5 and a multiple of 2 is 6/11

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For this case, we're given that:

Take E = Event of spinner's spin resulting in multiple of 5 or multiple of 2

S = results of Sample

Then, favorable results (in favor of E) are: 2,4,5,6,8,10 (total 6 in count)

All possible results are 1, 2, ... , 11  (total 11 in count)

Thus, we get:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{6}{11}[/tex]

Thus, the probability that the result is a multiple of 5 and a multiple of 2 is 6/11

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In a spinner numbered 1 through 11, there is only one number (10) that is both a multiple of 5 and a multiple of 2. As there are 11 possible outcomes in a single spin, the probability of spinning and landing on 10 is 1/11.

The subject of this question is mathematical probability. Given that there is a spinner with 11 equal areas numbered 1 through 11, we are asked to find the probability of landing on a number that is both a multiple of 5 and a multiple of 2 when the spinner is spun once.

Firstly, we identify the numbers which are both multiples of 5 and 2 between 1 and 11. In this case, only one such number exists, which is 10. Hence, there is only one favorable outcome. The total number of outcomes are 11 (as the spinner has 11 equal areas).

Probability is defined as 'number of favorable outcomes' divided by the 'total number of outcomes'. In this case, since there is 1 favorable outcome (i.e. landing on '10') and 11 possible outcomes (any of the numbers 1 to 11), the probability is therefore 1/11.

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Answer:

The answer is A) 2.

Step-by-step explanation:

The best way would be to use intervals of 2.

We know that the shortest persons 48 inches and the tallest 60 inches.

The difference between the tallest person and the shortest is:

60 - 48 = 12 inches

Since the difference is small, we might use intervals smaller than 12 because if we used intervals of 12, we wouldn't know for sure the heights of the other students, and we would have to estimate their heights.

Using intervals of 8 would be the same, we would have to estimate the heights of most students.

Using 5 , would also not be a good choice because 5 is not a multiple of 48, 60 or 12, therefore, that

Therefore, 2 would be the best option, as you don't have to estimate and the intervals would match the shortest and tallest height.

Eliminate parentheses using the distributive property.

... 5x = 10x -10x +15

Collect terms, then divide by the coefficient of x.

... 5x = 15

... x = 3

Answer:

B

Step-by-step explanation:

imagine math

Answer:

Option: A is the correct answer.

      A)  Period: 3 , amplitude : 1.5

Step-by-step explanation:

We know that Period of a function is the smallest value such that the function repeats after a fixed time.

and also the amplitude of the function is the height above or below the mid-line.

After looking at the graph we see that the period of the function is: 3

Since the function is repeating itself after every x=3.

Also, the mid-line of the function is: y= -0.5.

Hence, the height above the mid-line is: 1+0.5 = 1.5

        Hence, amplitude= 1.5