What principal will amount to 20,790 in 2 years at the simple interest of 5% per annum?​

Answer:

84 Sq in

Step-by-step explanation:

area of the composite figure = Area of square + Area of triangle

\( = {9}^{2} + \frac{1}{2} \times (9 - 7) \times 3 \\ \\ = 81 + \frac{1}{2} \times 2 \times 3 \\ \\ = 81 + 3 \\ \\ = 84 \: {in}^{2} \)

I am very unsure what your question is, but the simple tip is to divide it by two each year as it is decreasing by a half..

To find the number of copies sold in subsequent years, you can use the formula:

N = N0 * (1/2)^t

where N is the number of copies sold in a given year, N0 is the initial number of copies sold (in this case, 600,000), t is the number of years since the book was released.

For example, to find the number of copies sold in the second year after the book was released:

N = 600,000 * (1/2)^1

N = 300,000

So, 300,000 copies were sold in the second year. To find the number of copies sold in subsequent years, you can continue to plug in values of t and solve for N.

The total change in temperature, in degrees Fahrenheit, for the package of food is 50°F

The initial temperature of the package of food as given in the question is -15°F

At noon, the temperature of the package of food was changed to 35° F

We need to find out the total change in temperature which is

Temperature of food package at noon - The initial temperature of the package of food

By substituting the values given in question we get

                       = 35° - (-15° F)

Which is a simple integer problem

                      = 35 - (-15)

                     = 35 + 15

                     =   50 F

Hence, the total change in temperature, in degrees Fahrenheit, for the package of food is 50° F

An integer is the range 0, a wonderful natural number or a poor integer with a minus signal. The poor numbers are the additive inverses of the corresponding advantageous numbers. in the language of arithmetic,

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The range of the data set would remain the same when the number 9 replaces one of the 2's in the set.

In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;

Range = Highest number - Lowest number

For the initial data set, we have the following range:

Range = 16 - 1

Range = 15.

For the new data set when the number 9 replaces one of the 2's, we have the following range:

Range = 16 - 1

Range = 15.

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Answer:

Below

Step-by-step explanation:

To find the slope of a line, we use the formula:

slope = (change in y-coordinates) / (change in x-coordinates)

In this case, if Akio recorded the distance he rode on his bike ride in hours, the slope of the line for the first two hours would be the change in the y-coordinates (distance) divided by the change in the x-coordinates (time) between those two points.

To find the slope of the line for all five hours, we will need to know the specific coordinates of all five points, otherwise, it's impossible to calculate the slope.

The slope of a line represents the rate of change in the y-coordinates (distance) per unit of change in the x-coordinates (time). In this situation, the slope represents Akio's speed, since the change in distance is divided by the change in time. A positive slope indicates an increase in distance over time, which means Akio is getting faster, whereas a negative slope indicates a decrease in distance over time, which means Akio is getting slower.

It's worth noting that a slope of zero would mean that there is no change in distance over time, which would mean that Akio isn't moving.

Answer:

So they have a 24 dollar design fee, and 2 dollars per hat. You have to calculate the cost of 4 hats that are 2 dollars each, plus the design fee of 24 dollars

Step-by-step explanation:

Answer:

90 notebooks and folders

Step-by-step explanation:

Find the least common multiple (LCM) or 18 and 15!

18 x 5 = 90

15 x 6 = 90

Therefore, your answer is 90

Hope this helps!

The speed of the moving body that is being referred to here is 80 kilometer per hour.

The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.

                                \(Distance = speed * time\)

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The volume common to two spheres, each with radius r, if the distance between their centres is r/2 is V = (11/12)×π×r³.

The attached diagram shows 2 circumferences with radius r and separated centres by r/2.

Let´s call circumferences  1 and 2; by symmetry, rotating area A will produce a volume V₁ identical to a V₂, Obtained by rotating area B ( both around the x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) × r × x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) × r × x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) × r × (r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

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Answer:

14 Inches

D= R + R

Add the radius by itself to get the diameter

Answer:

—1 ...........................

Answer:

5:8

5 to 8

Step-by-step explanation:

There are 8 students total and 3 boys wear glasses so there is 5 girls left that wear glasses.

Hope this helps :)

the point on the plane 7x - y + 7z = 70 nearest to the origin is (x, y, z) = (490/99, -70/99, 490/99).

What is Origin?

Origin is the beginning, middle, or beginning of something, or where one comes from. An example of origin is when an idea comes to you while you are sleeping. An example of an origin is the soil where oil comes from. An example of ancestry is your ethnicity.

To find the point on the plane 7x - y + 7z = 70 nearest to the origin, we can use the concept of perpendicular distance. The point on the plane closest to the origin will lie along the line perpendicular to the plane that passes through the origin.

The equation of the plane is 7x - y + 7z = 70. We can rewrite it in the form Ax + By + Cz + D = 0, where A, B, C are the coefficients of x, y, z respectively, and D is a constant.

In this case, A = 7, B = -1, C = 7, and D = -70.

The direction ratios of the line perpendicular to the plane are equal to the coefficients of x, y, z in the plane equation. Therefore, the direction ratios are (7, -1, 7).

Let's assume the coordinates of the point closest to the origin on the plane are (x, y, z).

The line passing through the origin and perpendicular to the plane can be parametrically represented as:

x = 7t

y = -t

z = 7t

Substituting these values into the equation of the plane, we get:

7(7t) - (-t) + 7(7t) = 70

49t + t + 49t = 70

99t = 70

t = 70/99

Substituting the value of t back into the parametric equations, we get:

x = 7(70/99) = 490/99

y = -(70/99) = -70/99

z = 7(70/99) = 490/99

Therefore, the point on the plane 7x - y + 7z = 70 nearest to the origin is (x, y, z) = (490/99, -70/99, 490/99).

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Answer:

39%, 0.42, 11/25

Step-by-step explanation:

First, let's convert the percentage and the fraction into decimals, to make out lives so much easier.

39% = 0.39

11/25 = 0.44

Now, we reorder.

0.39, 0.42, 0.44

Finally, we convert the percentage and the fraction back into their original forms, and adjust the order.

39%, 0.42, 11/25

-hope it helps

The equation cos (α - β) × cos (α + β) ≠ cos² α - cos² β. Then the given equation is incorrect.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

The equation is given below.

cos (α - β) × cos (α + β) = cos² α - cos² β

Then show whether the equation is correct or incorrect.

Taking the left-hand side, then we have

\(\cos(\alpha-\beta)*\cos(\alpha +\beta) = (\cos \alpha \cos\beta + \sin \alpha \sin \beta ) (\cos \alpha \cos\beta - \sin\alpha \sin\beta )\\\\\cos(\alpha-\beta)*\cos(\alpha +\beta) = \cos ^2 \alpha \cos ^2\beta - \sin ^2 \alpha \sin ^2\beta\)

The left-hand side does not equal to the right-hand side.

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Step-by-step explanation:

As far as I understand, they can use all 26 letters (alphabet) and all 10 digits (0, 1, ..., 9), and the password looks like this:

letter-letter-letter-letter-letter-letter-number-number (6 letters, 2 numbers).

▪︎ They can reuse the letters, so they can choose the 1st letter out of 26 possible letters, then they still can choose the 2nd letter out of 26 (it's ok if they have both A's for example, they can reuse them) and so on. So each time they can choose one letter out of 26. Thus, it's 26*26*26*26*26*26.

▪︎ The same thing with numbers. Each time they can choose one number out of 10, so it's 10*10.

▪︎ Therefore, the answer is 26*26*26*26*26*26*10*10 = 30,891,577,600. That's almost 31 billion passwords.

There should be 12 emails total.

7.200 and 2.683 are the variance and standard deviation, respectively.

Calculation of expected number of emails, variance and standard deviation:

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There are 70 ways to assign 4 runners from a group of 8 to run the legs of the race.

Permutation and combination are two fundamental concepts in mathematics that deal with counting and arranging objects.

This is a combination problem. The formula for calculating the number of combinations of r items from a set of n items is:

nCr = n! / (r! * (n-r)!)

where n! represents the factorial of n, or the product of all positive integers up to and including n.

In this problem, we want to choose 4 runners from a group of 8, without regard to order. So we can use the combination formula as follows:

8C4 = 8! / (4! * (8-4)!)

= (8765) / (4321)

= 70

Therefore, there are 70 ways to assign 4 runners from a group of 8 to run the legs of the race.

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Answer:

vertical angle s

Step-by-step explanation:

cause the form a 180º angel

The correct option is D) 48. As the correlation coefficient ranges from -1 to +1, if the value of eta result is close to 1 or -1, it indicates strong correlation between the two variables. Therefore, the eta result 48 indicates strong relationship between dependent and independent variable.

In order to determine a strong relationship between dependent and independent variable, the correlation coefficient is computed.

It ranges between -1 and +1. Correlation coefficient ranges from -1 to +1 where -1 indicates perfect negative correlation and +1 indicates perfect positive correlation. On the other hand, 0 indicates no correlation.

Therefore, higher the value of correlation coefficient stronger the correlation or relationship between the two variables. The following eta results indicate strong relationship between dependent and independent variable: Option D) 48

As the correlation coefficient ranges from -1 to +1, if the value of eta result is close to 1 or -1, it indicates strong correlation between the two variables. Therefore, the eta result 48 indicates strong relationship between dependent and independent variable.

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Answer:

Step-by-step explanation:

Answer:

The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, the commentary will spotlight one practice connection in depth. Possible secondary practice connections may be discussed but not in the same degree of detail.

Answer:the best predicted value of ý when the twin born first has an IQ of 109 is 107.50

Step-by-step explanation:

Given the regression equation:

ŷ = -2.59 + 1.01x

We need to predict the value of ý when x (IQ score of the twin born first) is 109.

So we substitute x = 109 into the regression equation:

ŷ = -2.59 + 1.01(109)

ŷ = -2.59 + 110.09

ŷ = 107.50

Therefore, the best predicted value of ý when the twin born first has an IQ of 109 is 107.50.

Out of the given differential equations, only equation 3 is separable, and equation 4 is linear. The rest are nonlinear and neither separable nor linear.

The first-order differential equation dy/dx + exy = x2y2 is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term x2y2 in the equation makes it nonlinear, and the term exy makes it non-separable.

The differential equation y + ex * sin(x) = x3y' is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term ex * sin(x) and the term y' (derivative of y) make it nonlinear, and the term y makes it non-separable.

The differential equation ln(x) - x2y = xy' is separable but not linear. The terms ln(x) and x2y make it nonlinear, but it can be separated into two parts, one containing x and y and the other containing x and y'. Therefore, it is separable.

The differential equation dy/dx + cos(y) = tan(x) is linear but not separable. The terms cos(y) and tan(x) make it nonlinear, but it can be written in the form dy/dx + P(x)y = Q(x), where P(x) = cos(y) and Q(x) = tan(x). Therefore, it is a linear differential equation.

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The p-value for a standardized test statistic of z = -1.86 with the alternative hypothesis Ha: p < 0.5 is 0.0322.

To find the p-value for the standardized test statistic of z = -1.86 with the alternative hypothesis Ha: p < 0.5, we need to find the area under the standard normal distribution curve to the left of z = -1.86.

We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can use the following steps:

1) Calculate the cumulative distribution function (CDF) of the standard normal distribution at z = -1.86. This gives us the area under the curve to the left of z = -1.86.

CDF(-1.86) = 0.0322

2) Since the alternative hypothesis is one-tailed (p < 0.5), we need to find the area in the left tail of the standard normal distribution. Therefore, the p-value is the same as the area under the curve to the left of z = -1.86.

p-value = 0.0322

So the p-value for a standardized test statistic of z = -1.86 with the alternative hypothesis Ha: p < 0.5 is 0.0322.

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Answer:

On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.

- sorry I answered late! but I just did the test and got a 100 :)

The equation that represents the relationship between the number of days and the number of pages  Lila reads is y = 42x

If Lila read 84 pages in 2 days and 210 pages in 5 days, the number of pages "y" and the number of days "x" can be express in coordinate form as shown:

(2, 84) and (5, 210)

To get the required equation, we will find the equation of the line passing through the coordinate points as shown:

y = mx + b

m is the slope

b is the y-intercept;

Get the slope

\(m =\frac{210-84}{5-2}\\m=\frac{126}{3}\\m=42\\\)

Get the y-intercept:

84 = 42(2) + b

84 = 84 + b

b =0

Get the required equation:

Recall that y = mx+ b

y = 42x + 0

y = 42x

Hence the equation that represents the relationship between the number of days and the number of pages  Lila reads is y = 42x

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Answer:

4.222222 or jus 4.2 with - over the 2 to indicate multiple 2's

Answer:

4.875

Step-by-step explanation:

Pretty simple, just divide the numerator by the denominator.

The linear function of the profit p in terms of the number of computers(x) sold per month is:

F(p)= 4x +1300;

Profit made on selling 450 computers a month = 2500

profit made on selling 600 computers a month= 3100

Then let F(p) be the function representing the profit in terms of the computers sold

Where the number of computer sold are a variable of x

Then,

F(p): 450x = 2500

F(p): 600x = 3100

Using two-point form as both are proportional

y - 3100 = 3100-2500/600-450(x-450)

y - 3100 = 600/150(x-450)

y-3100= 4(x-450)

y-3100= 4x - 1800

y=4x + 3100 - 1800

y = 4x + 1300

where y=F(p) i.e the profit made on the sale of x number of computers per month.

so,

F(p)= 4x +1300;

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