How would I go about doing this? Any help is appreciated.

A student takes out two loans to help pay for college expenses. The total amount of money borrowed is $12600. Both loans have interest that accrues annually. The first loan has an interest rate of 3.5%, and the second loan has an interest rate of 4.5%. After the first year, the interest from both loans total $500.5. Find the initial amount borrowed at 3.5%. Round to the nearest dollar.

Answer:

no it is not

Step-by-step explanation:

8 × 1 does not equal 2

Answer:

The probability is  \(P(2) = 0.426\)

Step-by-step explanation:

From the question we are told that

         The probability of  success is \(p = 0.26\)

          The number of hits is  n =  7

Generally this probability follows a binomial distribution given there can only be two outcome i.e the probability of success and the probability of failure

       The probability of failure is  \(q = 1- p\)

substituting values

               \(q = 1 - 0.26\)

               \(q = 0.74\)

Now the probability of  exactly 2 hits in his next 7 at bats is mathematically evaluated as

     \(P(2) = \left n} \atop {}} \right. C_2 *p^{2} * q^{n- 2}\)

substituting values

    \(P(2) = \left 7} \atop {}} \right. C_2 *p^{2} * q^{7- 2}\)

Here \(\left 7} \atop {}} \right. C_2\) means 7  combination 2 and using a calculator(reference calculator soup website) to compute, the value obtained is  

          \(\left 7} \atop {}} \right. C_2 =21\)

So

     \(P(2) = 21 *(0.26)^{2} * (0.74)^{5}\)

     \(P(2) = 0.426\)

The customer will pay $6.30 for the 60 local calls that all lasted 3 minutes.

To find out how much the customer will pay, we need to calculate the total cost for all the local calls.
Step 1: Calculate the total number of minutes for all the calls
Since the customer made 60 local calls and each call lasted 3 minutes, we can multiply 60 by 3 to get the total number of minutes.
60 calls * 3 minutes/call = 180 minutes
Step 2: Calculate the total cost for all the minutes
The customer pays $0.035 per minute for local calls. To find the total cost, we can multiply the total number of minutes by the cost per minute.
180 minutes * $0.035/minute = $6.30

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Answer:

  x = 5

Step-by-step explanation:

The only thing the circle does for you is tell you that the angle between the lines marked 3 and 4 is a right angle. A tangent line is always at right angles to the radius at that point.

So, you have a 3-4-x right triangle. The Pythagorean theorem applies:

  3² +4² = x²

  9 + 16 = x² = 25

  x = √25

  x = 5

_____

Comment on the answer

This is a 3-4-5 right triangle. You will meet them a lot, so it is useful to remember these side ratios form a right triangle.

Answer:

0.343, 0.424, 0.443

Step-by-step explanation:

Answer:

I exactly don't know the answer

By multiplicatiοn it can be determined that he uses 308 cm οf string.(οptiοn D).

In mathematics, multiplicatiοn is nοthing but repeated additiοn οf numbers. It is a methοd οf finding the prοduct οf twο οr mοre numbers. It can be οperated between whοle numbers , integers, fractiοns. The sign οf multiplicatiοn is "×" .

Aasim uses 11 centimeters οf string tο tie each newspaper. He ties 28 newspapers.

Here we will use the multiplicatiοn methοd.

In this system twο numbers are multiplied.                                    11

       fοr 1 newspaper he needs = 11cm string                               × 28  

then fοr 28 newspaper he needs = (11×28 ) cm οf string.             8 8                                                                                                          

                                                                                                        2  2 ×

                                                                                                        308

Hence, he needs 308cm οf string.

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\(\huge\sf\blue{Solution:-}\)

Here is a Parallelogram RSTU.

Given,

Height = 16.5 inches

Base = 15.3 inches

★Area of Parallelogram is = Base × Height

So, Area = 15.3 × 16.5 => 252.45 inches² or 252.5 inches²

________________________________________

Answer:

252.5

Step-by-step explanation:

{Be careful}

The area: \(15.3\times16.5\times\frac{1}{2}\times2\)

\(=252.5\) inches²

I hope this helps you

:)

The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

We know that the method to find the axis of the symmetry of the parabola is given by:

x = - b / 2 a

We have the general equation of the parabola as:

y = a x² + b x + c

We have the equation of the parabola as:

y = - 4 x² + 24 x - 35

Comparing from this equation, we get that:

a = - 4

b = 24

c = - 35

Now, substituting the values, we get that:

x = - 24 / 2 (- 4)

x = - 24 / - 8

x = 24 / 8

x = 3

Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

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If the expression  (4k + 8)/4 simplifies to an expression of the form ak + b, then the value of a/b is 1/2

The expression is (4k + 8) / 4

The expression is the mathematical statement that consist of the different variables, numbers and the mathematical operator. The mathematical operators are addition, subtraction, division and multiplication.

The given expression is (4k + 8)/ 4

Solve the expression

(4k + 8) / 4 = 4k/4 + 8/4

Divide the terms

=k + 2

The result is in the form of ak + b

The value of a = 1

The value of b = 2

The value of a/b = 1/2

Therefore, the value of the expression a/b is 1/2

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Answer:

Step-by-step explanation:

Step-by-step explanation:

D.12

A.26

........................

Answer:

D and A

Step-by-step explanation:

D= 132

A is larger than 132

Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

----------------------------------------------------------------------------------------------------------

    -y = -7x

+

    y = -4x + 3

----------------------------------------------------------------------------------------------------------

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer:

Sin is opposite side divided by hypotenuse.

Tan is opposite side divided by adjacent side.

The conversation between sin x and tan x is given as tan x = sin x / √(1 - sin² x).

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The trigonometry expression is given below.

sin x and tan x

We know that the relation between tangent and sine of an angle is given as,

tan x = sin x  / cos x             ...1

And we know that the relation between sine and cosine of an angle is given as,

cos x = √(1 - sin² x)          ...2

From equations 1 and 2, then we  have

tan x = sin x / √(1 - sin² x)

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Step-by-step explanation:

1/4

90%

1.5

0.005

6/10

25%

2/10

49.5

3/4

0.4

Answer:

F(4) is 1/2

F(x) = 4 when x is 8

Step-by-step explanation:

\(\text{If the quadratic equation is a perfect square, then}\\\\~~~~~\text{Discriminant} = 0\\\\\implies 12^2 - 4 \cdot 1 \cdot c = 0 \\\\\implies 144 -4c =0\\\\\implies 4c = 144\\\\\implies c = \dfrac{144}4\\\\\implies c = 36\)

Answer:

The question is an incomplete question

Answer: I think it’s B

Step-by-step explanation:

Answer:

answer b

Step-by-step explanation:

Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

9514 1404 393

Answer:

  112 m²

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

Here, we have four identical triangles. Their total area is ...

  SA = 4A = 4(1/2)bh = 2bh

  SA = 2(8 m)(7 m) = 112 m² . . . . pyramid surface area

The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;

If we perform a 180° rotation about the point O the following happens

Ray \(\overleftrightarrow{EF}\) maps unto ray \(\overleftrightarrow{GH}\)

Ray \(\overleftrightarrow{GH}\) maps unto ray \(\overleftrightarrow{FE}\)x

\(\overleftrightarrow{FG}\) maps unto itself

Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.

The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.

The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;

The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.

Whereby the center of rotation of the line \(\overleftrightarrow{EF}\) is equidistant from both the line \(\overleftrightarrow{GH}\) which is parallel to the line \(\overleftrightarrow{EF}\), the image of the line \(\overleftrightarrow{EF}\) maps to the line \(\overleftrightarrow{GH}\) following a 180° rotation about the point O, and the rotation of the line \(\overleftrightarrow{FG}\) about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;

∠x ≅ 40° (A rotation transformation is a rigid transformation)

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Answer:

Step-by-step explanation:

the consecutive are 39,40,41 and the smallest here is 39

Hope this helped

Answer:

- 7

Step-by-step explanation:

Line is passing through the points (2,-11) and (8,-53)

Slope of the line = [-53 - (-11)]/(8 - 2)

= (-53+11)/6

= -42/6

= -7

The sum that Mahesh borrowed was Rs. 22,800, the interest that Mahesh has to pay was Rs. 6,492, the interest that Rakesh has to pay was Rs. 7,550, and the percentage by which Rakesh pays more interest than Mahesh was 16.3%.

a) Sum borrowed by Mahesh

Let us suppose that the principal sum borrowed by Mahesh from the bank at 9% per annum is Rs. x.

Hence, we can write that

Simple Interest = (P × R × T )/ 100

= (x × 9 × 3)/100

= 27x/100

Therefore, the amount that Mahesh has to pay after 3 years, including the interest, is

A = P + SI

= x + 27x/100

= 127x/100

Again, Mahesh invests the same amount of Rs. x to Rakesh at 10% per annum, which is compounded annually, for three years.

Hence, the total amount after three years that Rakesh has to pay Mahesh is:

Amount after 3 years = x (1 + R/100)³

= x (1 + 10/100)³ = 1.331 x

Therefore, Mahesh made a profit of Rs. 7,550 by investing Rs. x at 10% per annum, compounded annually, for three years.

Hence, we can write that

Compound Interest = Amount - Principal

CI = 1.331x - x = 0.331x

Therefore, 0.331x = Rs. 7,550=>

x = Rs. 22,800

Thus, Mahesh borrowed Rs. 22,800 from the bank.

b) Interest that Mahesh has to pay

Interest = P × R × T/100

= Rs. 22,800 × 9 × 3/100 = Rs. 6,492

Therefore, Mahesh has to pay Rs. 6,492 as interest.

c) Interest that Rakesh has to pay

The total amount that Rakesh has to pay to Mahesh is Rs. 30,350 [= (22,800 + 7,550)].

Therefore, interest that Rakesh has to pay = Total Amount - Principal

= Rs. 30,350 - Rs. 22,800 = Rs. 7,550

Therefore, Rakesh has to pay Rs. 7,550 as interest.

d) Percentage by which Rakesh pays more interest than Mahesh

Let us calculate the percentage difference between the interest paid by Rakesh and the interest paid by Mahesh.

Thus, the percentage difference can be calculated as

% Difference = (|Interest paid by Rakesh - Interest paid by Mahesh|/ Interest paid by Mahesh) × 100

% Difference = (|7,550 - 6,492|/6,492) × 100

% Difference = 16.3%

Therefore, Rakesh pays more interest than Mahesh by 16.3%.

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The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

D) Slope of Funcation B = - Slope of Function A

Step-by-step explanation:

The equation for the line is:

y=mx+b

Where m is the slope and b is the y-intercept

In this question, we are only interested in the slope.

For function A, we can see that the equation is f(x) = -2x + 1

Going back to the equation, we can see that -2 is the slope

Now for function B, we need to find the slope by looking at the graph.

To do this, you need to remember that the slope is y/x, or rise over run. (This is saying that every time the y happens, the x also happens. For example, if the slope is 1/2, every time the line goes up 1 unit, it goes to the right 2 units)

So for the function, we can see that when you move to the right 1 unit (run), you also move up 2 units (rise), so the slope would be

2

Comparing the slope of both the functions

Function A is -2

and

Function B is 2

So the answer is D

Thus;

Expressing 2.7g to milligram(mg); we have:

Answer:

D. 19.25^2

Step-by-step explanation:

A = 5.5

H = 3.5

A = 19.25^2