mark invested a certain amount at 5 % simple interest per year after 10 year he received an interest of 50000 how much did he invest​

Answer: 4

Step-by-step explanation:

1 third of 30 is 10 and 2/5s of 10 is 4

Solution :

a). The researcher in the experiment recruited 12 adults wo are healthy to conduct the study. So the individuals are the "healthy adults".

The treatment is the "reading technology" and the response variable in the experiment is the time taken to get a deep sleep.

b). Here, in this research study every participant are randomly assigned to the treatment, i.e. the e-book or the print book at night. So we can say that a true experimental research design has been made to conduct this experiment.

c). It is very important to select the e-reader night or the print book at random order for the participant in order to reduce bias and also to remove any effect of the confounding variable.

The randomization of the participants means the random assignment of the treatments.

Note that the size of angle x = 115°. This is a problem relating to the sum of angles in a circle. See the computation below.

The sum of angles in a circle is always equal to 360 degrees or 2π radians.

This means that the sum of the measures of the angles formed by any number of rays or line segments that meet at a common point, or vertex, and whose endpoints lie on the circle, will always add up to 360 degrees or 2π radians. This property is often used in geometry and trigonometry to solve problems involving circles and angles.

With regard to the above problem,

We are given three angles in a circle named as follows:

a) 81°

b) 164°

c) x

The above rule state that

81 + 164 + x = 360°

thus, x = 360 - 81 - 164

x = 360 -245

x = 115°

Thus the value of ∠x is  115°

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Full Question:

See attached image.

The coordinates of the intersection of the diagonals of abcd with the given vertices are (0,2).

The equation of diagonal AC is the equation of the line joining

(−4,6) and (4,−2)

Using the two point formula of a line, we have

           (y−6) / (x+4) = 6−(−2) / (−4−4)

                       x + y = 2

The equation of diagonal BD is the equation of the line joining

(5,6) and (−5,−2)

Using the two point formula of a line, we have

           (y−6) / (x−5) = 6−(−2) /  5−(−5)

                           5y = 4x+10

Multiply equation x + y = 10 by 5 to get 5x+5y=10

Replace 5y=4x+46 using 5x+5y=10

        5x + (4x+10) = 10

        5x + 4x +1 0 = 10

           9x + 10 = 10

               9x=0

                 x=0

Substitute x=0 in eqn(1), To get 0+y=2

                                                         y=2

The point of intersection of the diagonals of the given quadrilateral is (0,2)

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Answer:

O a=0

Step-by-step explanation:

The value of angle ABC is 26°

What is a value ?

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value.

Values are the benchmarks or ideals by which we judge the acts, traits, possessions, or circumstances of others. Values that are embraced by many include those of beauty, honesty, justice, peace, and charity.

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value.

to find the ∠ABC

we know ∠CAB = 64° and ∠BCA = 90°

let ∠ABC be x

x + 64 + 90 = 180

x = 180 - 64 - 90

  = 26°

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Answer:

30 inches

Step-by-step explanation:

Answer:

ans is 58°

Step-by-step explanation:

it is a straight line so the angle is 180°

so the angle of CED is

CED + 122° = 180°

CED = 180 - 122 = 58°

Answer:

7

Step-by-step explanation:

7²÷3²-2 = 49/9-2 =49/7 =7

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer: 21:9 and 42:18

Step-by-step explanation:

14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.

21:9 is our simplified ratio multiplied by 3 on both sides.

42:18 is our simplified ratio multiplied by 6 on both sides.

But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.

The answer is ,The polygon has 3 sides

Answer:

Step-by-step explanation:

The sides of a 30-60-90 triangle are in the ratio 1:√3:2

The side opposite the 30° angle is (12√6)÷2 = 6/√6.

The side opposite the 60° angle is √3×6/√6 = 6/√2 =3√2.

The sides of a 45-45-90 triangle are in the ratio 1:1:√2

The hypotenuse is 3√2, so the side opposite the 45° angle is 3.

x = 3

To find the length of the third side of a right triangle when two sides are given, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's assume the two given sides are 'a' and 'b', and the unknown third side is 'c' (the hypotenuse).

Using the Pythagorean theorem:

c² = a² + b²

Substituting the given values:

c² = 4² + 5²

c² = 16 + 25

c² = 41

To find the length of 'c', we need to take the square root of both sides:

c = √41

So, the length of the third side is √41 (approximately 6.40) when rounded to two decimal places.

Therefore, the possible length of the third side of the right triangle is √41.

Step-by-step explanation:

We will use a phayragoras theorem

a^2 +b^2= c^2

let side1=4 be a

let side2=5 be b

let the 3rd side be the hypotnuous=c

therfore 4^2+5^2=c^2

=16+25=c^2

=41=c^2.

therfore c=√41

Yes, it appear that the mean work week has increased for women at the 5% level.

We are informed that a 25-year-old mother of three worked an average of 80 hours per week according to a 1955 Life Magazine report.

Imagine a study was conducted to find out if the average workweek has risen. The results of a survey given to 75 women are as follows. The sample's standard deviation was 10, and the sample's mean was 83. It should be noted that the test statistic is 2.598.

Now, at 5% level of significance the t table gives critical value of 1.668 at 74 degree of freedom for one-tail test. Since our test statistics is more than the critical value of t as 2.598 > 1.668, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

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However, I can still give you some general steps to solve a math problem in 200 words.

Step 1: Read the problem thoroughly and understand what it's asking you to find. This may involve identifying the given information and what you need to find. Also, identify any constraints on the problem, like time or cost.

Step 2: Plan how to solve the problem. Think about what mathematical operations or formulas you can use to find the answer. Make a list of the steps you need to take to solve the problem. Also, determine the units for your answer.

Step 3: Solve the problem. Use the mathematical operations or formulas you've identified in step 2 to find the answer. Show all of your work, including any calculations, so that you can easily check your work later.

Step 4: Check your answer. Make sure that your answer makes sense and that it satisfies any constraints given in the problem. Also, check that your units are correct. If your answer doesn't make sense, go back and review your work to see if you made an error.

Step 5: Reflect on what you've learned. Think about what you did well and what you could improve upon in future problem-solving situations. This will help you become a more effective problem solver in the future.

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A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

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Using distributive property, the equivalent expression is 45 - 16x

To find the equivalent expression of 13 - 8(2x - 4), we need to simplify the expression using the distributive property and then combine like terms.

First, we distribute the -8 to the terms inside the parentheses:

13 - 8(2x - 4) = 13 - 16x + 32

Next, we combine the constant terms:

13 - 16x + 32 = 45 - 16x

Therefore, the equivalent expression of 13 - 8(2x - 4) is 45 - 16x.

Overall, finding the equivalent expression of an algebraic expression can help simplify calculations and make solving equations easier.

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Answer:

4m = 56

Step-by-step explanation:

4 * m = 56

4m = 56

4/4m = 56/4

m = 14

Answer:

If 20 is 100% then 20 divided by 4 equals 5 so 20 lbs. - 5 lbs. = 15 lbs. the baker has 15 pounds of sugar left.

Step-by-step explanation:

This is a wonderfully easy problem. So, you start off by dividing the pounds of sugar by the denominator which is 4. So:

20 / 4 = ?

Then you that product and multiply it by the numerator, which is 3 in this case and you get your answer.

Thanks!

The phrase "all free variables of a formula ϕ(u1, . . . , un) are among u1, . . . , un" refers to a property of a logical formula ϕ with variables u1, u2, ..., un. In logic and formal systems, variables are used to represent unspecified elements or objects.

When a variable is considered "free" in a formula, it means that it is not bound by any quantifiers or other logical operators in the formula. In other words, it is a variable that is not restricted in any way within the formula.

The given statement implies that all the free variables in the formula ϕ(u1, . . . , un) are explicitly listed among the variables u1, u2, ..., un. In other words, the formula ϕ does not contain any additional free variables beyond the ones explicitly mentioned.

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5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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The parabola x = √(y - 9) opens upwards.The given parabolic equation is x = √(y - 9). Let's identify the direction of opening of this parabola.The general form of the equation of a parabola is y = a(x - h)² + k.

Comparing this to the given equation, we can see that h = 0 and k = 9. The vertex is therefore (h, k) = (0, 9). Now, let's determine whether the parabola opens upwards or downwards.

If the coefficient of (x - h)² is positive, the parabola opens upwards, and if it's negative, the parabola opens downwards. In this case, since the coefficient of (x - h)² is 1, which is positive, the parabola opens upwards.

Therefore, the parabola x = √(y - 9) opens upwards.

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Answer:

f(x)=(x+3)(x+2)(x-3)(x-4)

Step-by-step explanation:

Answer: f(x)=(x+3)(x+2)(x-3)(x-4)

Step-by-step explanation:

The type of relationship that angle a and angle b have is that they are complementary.

A right angle equals the measure of 90 degrees. If two angles equals a right angle, then their sum equals 90 degrees. Complementary angles have a sum of 90 degrees, therefore, if two angles form a right angle, then they are a pair of complementary angles.

In the image given, angle a and angle b form a right angle. Thus, the sum of angle a and angle b equals 90 degrees. This means they are complementary angles.

Therefore, the type of relationship that angle a and angle b have is that they are complementary.

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Answer:

The null and alternative hypothesis are:

\(H_0: \mu=135\\\\H_a:\mu\neq 135\)

P-value = 0.0162.

Yes, there is enough evidence to support the claim that the corn yield is significantly different from 135 bushels per acre.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the corn yield is significantly different from 135 bushels per acre.

Then, as it is a two-tailed test (we are looking if the yield has changed) the null and alternative hypothesis are:

\(H_0: \mu=135\\\\H_a:\mu\neq 135\)

The significance level is 0.05.

The sample has a size n=50.

The sample mean is M=138.4.

The standard deviation of the population is known and has a value of σ=10.

We can calculate the standard error as:

\(\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{50}}=1.414\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{M-\mu}{\sigma_M}=\dfrac{138.4-135}{1.414}=\dfrac{3.4}{1.414}=2.4\)

This test is a two-tailed test, so the P-value for this test is calculated as:

\(\text{P-value}=2\cdot P(z>2.4)=0.0162\)

As the P-value (0.0162) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the corn yield is significantly different from 135 bushels per acre.

Answer:

(a) Top-left graph

(b) 1/3

Step-by-step explanation:

Think about what the graph of \(f(x)=\frac{x}{6}\) looks like. It is a diagonal line with a positive slope of \(\frac{1}{6}\), so if you take the area under that line from 0 to 2, you get a triangle! Hence, the top-left graph is the correct graph.

Since the area is just a triangle, we know that our base is 2-0=2 and our height is 2/6 = 1/3, so, geometrically, the integral is:

\(\displaystyle \int\limits^2_0 {\frac{x}{6}} \, dx=\frac{2(\frac{2}{6})}{2}=\frac{2}{6}=\frac{1}{3}\)

If you want to do it the standard way using antiderivatives:

\(\displaystyle \int\limits^2_0 {\frac{x}{6}} \, dx=\frac{1}{12}x^2 \biggr|^2_0=\frac{1}{12}(2)^2-\frac{1}{12}(0)^2=\frac{4}{12}=\frac{1}{3}\)

As you can see, we arrive at the same answer!