How much simple interest is made on an investment of $800 for 7 years at 6%

The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

Learn more about trigonometric ratio here: brainly.com/question/28016662

#SPJ1

The height of the triangle found using Heron's formula and the formula for the area of a triangle is 7 ft

The area of a triangle is the half the product of the base length and the height of the triangle.

The area of the triangle is A = √(s·(s - 14)·(s - 11)·(s - 7))

The above formula is the Heron's formula for finding the area of a triangle of the form;

A = √(s·(s - a)·(s - b)·(s - c)), where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter of the triangle therefore;

s = (a + b + c)/2

The comparison of the Heron's formula for finding the area of a triangle and the specified formula for the area of the triangle, indicates that we get;

a = 14, b = 11, and c = 7

s = (14 + 11 + 7)/2 = 16

Therefore; A = √(16·(16 - 14)·(16 - 11)·(16 - 7)) = √(1440) = 12·√(10)

A = 12·√(10)

The area of a triangle = (1/2) × Base length × Height

Where the base length is one of the lengths of the sides of the triangle

Therefore;

Height₁  = 12×√(10)/((1/2) × 14) ≈ 5.42

Height₂  = 12×√(10)/((1/2) × 11) ≈ 7

Height₃  = 12×√(10)/((1/2) × 7) ≈ 10.84

The option that corresponds to the possible height of the triangle is 7 ft

Learn more about Heron's formula here: https://brainly.com/question/1527791

#SPJ1

Answer:

c. 80,000 products

Step-by-step explanation:

Year 1 = 20000

20000 * 0.75 = 15000

Year 2 = 15000

15000 * 0.75 = 11250

Year 3 = 11250

11250 * 0.75 = 8437.5

Etc.

20000 + 15000+ 11250 + 8437.5 = 54687.5

If you continue this, you'll eventually reach 80000

80000 products can the company expect to eventually sell.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

Given,

The company sells 20,000 products in the first year

a=20000

each year it can expect to sell only 75% of the quantity it will have sold the year before

r=75/100=0.75

Sum of Geometric sequence S=a/1-r

S=20000/1-0.75

S=20000/0.25

S=80000

Hence, 80000 products can the company expect to eventually sell.

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ5

Check the picture below.

Answer:

4/15

Step-by-step explanation:

Bag A

3 red marbles and 6 blue marbles.  = 9 marbles

P(blue) = blue/total =6/9 = 2/3

Bag B

6 green marbles and 4 yellow marbles.  = 10 marbles

P(yellow) = yellow/total=4/10 = 2/5

P(blue,yellow) = 2/3 * 2/5 = 4/15

Answer:

I don't know what the unit of measurement is, so I'll say the distance is 21. As for the average speed, its average speed is 8 per second.

Step-by-step explanation:

Distance: 21

Speed: 7

There :3

Answer:

m=1/3

Step-by-step explanation:

slope is rise over run

go up 1 over 3

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

To know more about logarithm visit:

https://brainly.com/question/30085872

#SPJ1

Answer:

The number of edges

Step-by-step explanation:

quad means 4 so all quadrilaterls have 4 sides.

The irrational solution of an exponential function, 3⁽¹⁻⁴ˣ⁾ = 4ˣ in exact form, is equals to the 0.190 in a decimal rounded to three decimal places.

The exponential function is a mathematical function of the form f(x) = aˣ , where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The most commonly used exponential base is the transcendental number e, which is approximately equal to 2.71828.

We have given an exponential equation is

3⁽¹⁻⁴ˣ⁾ = 4ˣ

Require to solve this Exponential equation.

Now, 3⁽¹⁻⁴ˣ⁾= 4ˣ

taking logarithm both sides we get,

ln ( 3⁽¹⁻⁴ˣ⁾ ) = ln(4ˣ)

=> (1-4x) ln(3) = xln(4) [using ln( aˣ)= x ln(a) ]

=> ln (3) - 4x ln (3) = x ln (4)

=> ln (3) = x ln(4) + 4x ln(3)

=> ln (3) = x[ ln (4) + 4 ln (3) ]

=> x = ln (3) / [ ln (4) + 4 ln (3) ]

=> x ~ 0.190

Therefore, solution set is ln (3) / [ ln (4) + 4 ln (3) ].

To learn more about Exponential function, refer:

https://brainly.com/question/2456547

#SPJ4

Answer: The best problem solving strategy to solve this problem with is a formula. Additionally Brandon had $12.50 before going to the store.

Step-by-step explanation: Formula and Solving it

He Spent $2.50 on pencils.

Amount left after buying a pencil = x - 2.50

Next, he spent half of the amount left in his pocket.

He spent (x - 2.50)/2 on notebook and paper.

So the total amount he spent = 2.50 + (x -2.50)/2

Amount left when he got home =$ 5.00

That means, x - Total amount spent = 5

=> x - (2.50 + (x -2.50)/2 ) = 5

=> x - 2.50 -x/2 + 2.50/2 = 5

=> x/2 - 2.50/2 = 5

=> x/2 = 5 + 2.50/2

=> x/2 = 6.25

=>x = $12.5

the equation of the line that is parallel to the line - x + 2 y = 7 is - x - y + 7 = 0.

We know that, if the lines are parallel, then their slopes are equal.

We have the line:

- x + 2 y = 7

Slope = - 1

Now, we have the point ( 4, 3)

So, the equation of the line will be:

y - y₁ = m ( x - x₁ )

Substituting the values, we get that:

y - 3 = - 1 ( x - 4 )

y - 3 = - x + 4

x + y - 3 - 4 = 0

x + y - 7 = 0

- x - y + 7 = 0

Therefore, the equation of the line that is parallel to the line - x + 2 y = 7 is - x - y + 7 = 0.

Learn more about equation here:

https://brainly.com/question/1214333

#SPJ9

Answer:

1.5 inches

Step-by-step explanation:

Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts

Step-by-step explanation:

Answer:

C on Edge 2021

Step-by-step explanation:

Answer

Your answer should be C.

Step-by-step explanation:

Answer:

x=0, y=4 and z=0.

Explanation:

Given the system of linear equations:

From the third equation:

Substitute z=-4x into the first and second equations.

Solve the two results simultaneously.

Substitute y=4 to solve for x.

Finally, recall that: z=-4x

Therefore x=0, y=4 and z=0.

Answer:

Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day

Step-by-step explanation:

To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.

Let's calculate his average time per day:

Average time per day = Total time / Number of days

Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:

Average time per day = 6 hours / 5

Average time per day = 1.2 hours per day

To convert hours to minutes, we'll multiply the average time per day by 60:

Average time per day = 1.2 hours * 60 minutes

Average time per day = 72 minutes per day

Therefore, Clarence's average time per day is 72 minutes.

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

<95141404393>

No, the two events A and B are not independent. Event A is heavy traffic and Event B is bad weather. They both are dependent to each other.

Suppose that two events are denoted by A and B. They are said to be an independent event if and only if:

\(P(A \cap B) = P(A)P(B)\)

It is because

\(P(A|B) = P(A)\\P(B|A) = P(B)\)

and therefore, using chain rule and above facts gives:

\(P(A \cap B) = P(A)P(B)\)

Let event,

Event A = heavy traffic

Event B = bad weather

Only when one event affects the other is a pair of occurrences considered to be independent.

The two occurrences are not independent in this case.

Heavy rains, snowfall, and other extreme weather conditions cause traffic systems to fail, resulting in gridlock. This is seen in all major metropolitan areas.

As a result, the two activities are not independent, since weather conditions impact traffic.

To learn more about the independent event, refer to the link;

https://brainly.com/question/13488890

#SPJ1

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Answer:

g(x)=x-2/x^2-9

If there is more than one value, separate them with commas.

Step-by-step explanation:

A simple event has one outcome or sometimes a collection of outcomes.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

A simple event is an event in which the outcome can be specified without further information or division.

For example, the event "rolling a die" has 6 possible outcomes, each of which is a simple event (rolling a 1, rolling a 2, etc.).

Hence, A simple event has one outcome or a collection of outcomes.

To learn more about the probability visit,

brainly.com/question/251701

#SPJ1

Answer:

the answer is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is 2, because it is the only factor that can go with both of the numbers.

Step-by-step explanation:

please do a brainliest to me

Consider the continuous random variable x that has a uniform distribution over the interval from 40 to 44. The variance of 'x' is approximately C: 1.155.

The variance of a continuous uniform distribution over the interval [a, b] is determined by the formula given as follows:

Var(x) = (b-a)^2 / 12

For the given distribution, a = 40 and b = 44, so the variance is calculated by putting these values into the above formula:

Var(x) = (44 - 40)^2 / 12 = 1.155

Therefore, the variance of 'x' is approximately 1.155

You can learn more about variance at

https://brainly.com/question/28426562

#SPJ4

Answer:

D

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))

Answer:

1⅔

Step-by-step explanation:

multiply by reciprocal

Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.

The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.

The given x=1+12+ dx=dt 0+12(1) =12

Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12

(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).

To learn more about parametric equations here

https://brainly.com/question/28537985

#SPJ4

Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)

x(t), y(t), z(t) =