Select the locations on the number line to plot the points 4 1/ 3 and −1 1/3 .

1. Another term for adding money to an account is - contribute

One should contribute to his account. This phrase means, one should add money to his account. Contribution is addition of money in account.

2. Which situation allows you to have the most saved ?

A) having a set amount set aside for savings each time you are paid- this can be the most possible answer. Technically a person should save 20% to 25% of his income and this amount increases with income. So, each time when you are paid, set aside the savings amount.

It's 25 easy how I got my answer I looked on my fingers and put 5 fingers up and i did it 5 times and got 5.10.15.20.25 that's 5 times

Final Answer:

The answers are:
1. B. 5.76 x 10¹⁴ miles
2. D. $15,494.70

Explanation:

Let's solve each of these questions step by step.
Question 1:
First, we'll calculate the distance to the star in miles, given its distance in light years.
One light year is approximately 5.88 x 10¹² miles.
The star is 9.8 x 10¹ light years from Earth.

To find the distance in miles, we multiply the distance in light years by the length of one light year in miles:
Distance in miles = (5.88 x 10¹² miles/light year) * (9.8 x 10¹ light years)

To multiply these numbers in scientific notation, we multiply the coefficients (5.88 and 9.8) and then add the exponents of 10 (12 and 1).
Coefficient multiplication: 5.88 * 9.8
Using a calculator or doing the multiplication by hand, we find that 5.88 * 9.8 is approximately 57.624.
Exponent addition: 12 + 1 = 13

So the distance in miles is approximately 57.624 x 10¹³ miles.

However, in scientific notation, the coefficient should be between 1 and 10. Therefore, we need to adjust the coefficient from 57.624 to 5.7624 and increase the exponent by 1 to keep the same value.
Distance in miles = 5.7624 x 10¹⁴ miles

To make it approximately and match the answer choices, we can round the coefficient to 5.76.
Distance in miles ≈ 5.76 x 10¹⁴ miles

The closest answer to our computed value is:
B. 5.76 x 10¹⁴ miles

Question 2:
Next, let's use the compound interest formula to find the balance in the account after 33 years.
The compound interest formula is:
[tex]A = P (1 + r/n)^{(nt)[/tex]
where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.

We're given:
P = $1,600.00
r = 7% annual interest = 0.07 (as a decimal)
n = 2 (since interest is compounded semiannually)
t = 33 years

Plugging these values into the formula gives us:
[tex]A = 1600.00 * (1 + 0.07/2)^{(2*33)[/tex]
Let's break it down:

Interest rate per compounding period: 0.07/2 = 0.035
Number of compounding periods: 2*33 = 66

Now substitute these values:
A = 1600 * (1 + 0.035)⁶⁶

We calculate (1 + 0.035)^66 using a calculator:
(1 + 0.035)⁶⁶ ≈ (1.035)⁶⁶ ≈ 9.682

So the final balance is:
A ≈ 1600 * 9.682 ≈ 15491.2

The closest answer to our computed value is:
D. $15,494.70

Hence, the answers are:
1. B. 5.76 x 10¹⁴ miles
2. D. $15,494.70

Answer:

C.),F.),andD.) Are correct

Step-by-step explanation:

Option: C, D and F are the correct options.

C.   [tex](\dfrac{36}{4})^x[/tex]

D.   [tex]9\cdot 9^{x-1}[/tex]

F.  [tex]\dfrac{36^x}{4^x}[/tex]

We are asked to find the expression which is equivalent to:

                                        [tex]9^x[/tex]

C)

 [tex](\dfrac{36}{4})^x[/tex]

We know that:

[tex](\dfrac{36}{4})^x=9^x[/tex]

Since, 36/4=9

Hence, option: C is correct.

D)

[tex]9\cdot 9^{x-1}=9^{1+x-1}[/tex]

Since,

[tex]a^m\cdot a^n=a^{m+n}[/tex]

Hence,

[tex]9\cdot 9^{x-1}=9^x[/tex]

Hence, option: D is correct.

F)

[tex]\dfrac{36^x}{4^x}[/tex]

We know that:

[tex]\dfrac{36^x}{4^x}=(\dfrac{36}{4})^x[/tex]

Since, we know that:

[tex]\dfrac{a^n}{b^n}=(\dfrac{a}{b})^n[/tex]

Hence, we have:

[tex]\dfrac{36^x}{4^x}=9^x[/tex]

Since, 36/4=9

Hence, option: F is the correct answer.

Answer:

The real answer is 846 ^-^ I got it right

The volume of the rectangular prism is 105.57

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

Where l, h and w represent the length, height and width respectively.

Given that;

Length of the prism is 2 times the width L = 2w

the width is 4 times the height  w = 4h

Now let’s plug these values;

the surface area equation, it becomes;

A = 2(2w(w) + w(w/4) + w/4(2w))

A = 2(2w^2 + w^2/4 + w^2/2)

A = 1/2(7w^2)

792 x2 = 7w^2

w = 15.04

The volume of a rectangular prism=Length X Width X Height

V = 2w x w x w/4

V x 2 = w³

V = 15.04³/2

V = 105.57

Thus, the volume is 105.57.

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The measure of the side IJ is the longest one so the largest angle is ∠H. Then the correct option is B.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Three survey markers are located on a map at points H, I, and J. A triangle is formed by connecting these markers by string so that HI = 150 feet, HJ = 245 feet, and IJ = 365 feet.

If the side is the largest one then its opposite angle will be the largest one.

The measure of the side IJ is the longest one so the largest angle is ∠H. Then the correct option is B.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

x + y = 5

x + y = 6

5 ≠ 6

The system of equations has many solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 is an equation.

2x + 4 - 5x is an equation.

We have,

x + y = 5 _____(1)

x + y = 6 ______(2)

Now,

Solving (1) and (2) we get,

5 = 6

This is not true.

This means that,

We have many solutions.

If we get,

x = y

0 = 0

n = n ( n can be any value)

The system of equations will have no solutions.

Thus,

x + y = 5

x + y = 6

5 ≠ 6

The system of equations has many solutions.

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We know that a two-way frequency table is constructed when we have to deal with two variables ( which is also known as a bivariate data)

Here we have two variables as wore a tie or not and the second variable is: Received compliment or not.

Hence, on the basis of the information provided to us in the question we see that the two-way frequency table is obtained as follows:

                                               Wore tie          Do not wore tie     Total

Receive compliment                 25                         5                       30

Do not receive compliment       9                         11                       20

        Total                                 34                         16                       50

The considered data given about the frequencies of events can be used to fill the two-way frequency table. The values will be 25 and 5 in first row, and 9 and 11 in second row.

Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ... , Y_n[/tex]

List them in title of the rows and left to the columns. There will be [tex]n \times k[/tex] table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  [tex]X_i[/tex]  and [tex]Y_j[/tex]  (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

We're given that:

If we take:

A = event of Lea wearing a tie on a day

A' = event of Lea not wearing a tie on a day

B = event of Lea getting a compliment on a day

B' = event of Lea not getting a compliment on a day

then, we're given that:

[tex]n(A' \cap B') = 11\\n(B) = 30\\n(A') = 16[/tex]

Also, total number of days = S = 50

On each of those 50 days, she either wore a tie or not.

If she didn't put on a tie on 16 out of 50 days, then she wore tie for 50-16=34 days.

Thus, we get n(A) = 34

Similarly, we get n(B') = 50 - n(B) = 50 - 30 = 20

[tex]\begin{array}{cccc}&A&A'&\rm Total\\B&n(B\cap A)&n(B\cap A')&n(B)=30\\B'&n(B' \cap A)&n(B' \cap A')=11&n(B')=20\\\rm Total & n(A)=34 & n(A')=16 & S=50 \end{array}[/tex]

Using the total of the third row, we get:

[tex]n(B' \cap A) + 11 = 20\\n(B' \cap A) = 9[/tex]

Similarly, now using second column's total, we get:

[tex]n(B \cap A) + n(B' \cap A) = 34\\n(B \cap A) + 9 = 34\\n(B \cap A) = 25[/tex]

Now using second row's total, we get:

[tex]25 + n(B \cap A') = 30\\n(B\cap A') = 5[/tex]

Thus, we get:

[tex]\begin{array}{cccc}&A&A'&\rm Total\\B&n(B\cap A)=25&n(B\cap A')=5&n(B)=30\\B'&n(B' \cap A)=9&n(B' \cap A')=11&n(B')=20\\\rm Total & n(A)=34 & n(A')=16 & S=50 \end{array}[/tex]

Thus, finally, we can say that:

                                                  Wore a tie,               Didn't wore a tie

Got a compliment                         25                                    5

Didn't got a compliment               9                                      11

Thus, the values will be 25 and 5 in first row, and 9 and 11 in second row.

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 the  sine and cosine  are co-functions

So

sin (theta) = cos (90 - theta)------> This implies that  the angles sum to 90°

therefore

( x + 22)  + (2x - 7)  =  90    simplify

3x + 15  = 90     subtract  15 from both sides

3x  =  75      divide both sides by 3

x  = 25

 The answer Part 1) is x=25°

 Part 2) Given cos x=12/13 and sin x =5/13

What is ratio for ​ tanx ​ ?

 we know that

tan x = sinx / cos x

tan x  =   (5/13) / (12/13)   =  (5/13) * (13/12)  =  5/12

the answer Part 2) is 5/12

Solving Q1: Given BE = ED and AE = EC.

Considering triangles ΔAED and ΔCEB;

1. AE = EC (given)

2. ∠AED = ∠CEB (vertical angles)

3. ED = EB (given)

ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)

∠DAE = ∠BCE and AD = BC (using CPCTC)

⇒ AD║BC (Converse of Alternate Interior angles theorem)

Similarly consider triangles ΔABE and ΔCDE;

1. AE = CE (given)

2. ∠BEA = ∠DEC (vertical angles)

3. BE = DE (given)

ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)

∠ABE = ∠CDE and AB = CD (using CPCTC)

⇒ AB║CD (Converse of Alternate Interior angles theorem)

Since we have AB║CD, AB = CD and AD║BC, AD = BC.

Therefore, quadrilateral ABCD is a parallelogram.

****************************************************************************************************

Solving Q2: The parallelogram has the angle measures shown in the diagram.

It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.

Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.

Using Angle-Side-Angle congruence of triangles, both the triangles would be congruent too.

Using CPCTC, we can say opposite sides of quadrilateral would be congruent.

Therefore, all sides in given quadrilateral are equal.

Hence, Given quadrilateral is a Rhombus.

The tax has only made Susan worse off by $10 or 5.7% because Rebecca is the one who is going to pay for the dog sitting and not Susan (who is going to have an income of $165 after-tax).

Further Explanation:

Income Tax: It is the additional payment that an individual needs to pay on the amount of income he/she generates. Here $10 is the tax on the income which Susan is going to generate by dog sitting the dog of Rebecca.

Here, it can be seen that Susan is the one who is earning from the transaction and not Rebecca. So, Rebecca is should not bear any tax payable to the government since both of them agree to a price of $175 so that is the only amount which Rebecca is going to pay for dog sitting. Also, if Susan herself pays the whole amount of tax, it still would not bother her because her expectation from dog sitting was $150 which is still lesser than what she expected in the first place.

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Answer details:

Grade: Senior School

Subject: Taxation

Chapter: Tax imposed on various services.

Keywords: Income tax, payment of tax, dog sitting during the wedding, dog sitter, worse off condition of Rebecca and Susan.

Using continuity concepts, it is found that K = 320 makes the function continuous.

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

A function f(x) is said to be continuous at x = a if:

[tex]\lim_{x \rightarrow a^{-}} = \lim_{x \rightarrow a^{+}} = f(a)[/tex]

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

The piece-wise function given is:

[tex]f(x) = \frac{5x^4 - 20x^3}{x-4}, x \neq 4[/tex]

[tex]f(x) = K, x = 4[/tex]

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

The definition for x different of 4 can be simplified, as follows:

[tex]f(x) = \frac{5x^4 - 20x^3}{x-4} = \frac{5x^3(x - 4)}{x - 4} = 5x^3[/tex]

Thus, the simplified definition is:

[tex]f(x) = 5x^3, x \neq 4[/tex]

[tex]f(x) = K, x = 4[/tex]

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

For the lateral limits, x is close to but not exactly 4, so the first definition is used.

[tex]\lim_{x \rightarrow 4^-} = \lim_{x \rightarrow 4} 5x^3 = 5(4)^3 = 5 \times 64 = 320[/tex]

[tex]\lim_{x \rightarrow 4^+} = \lim_{x \rightarrow 4} 5x^3 = 5(4)^3 = 5 \times 64 = 320[/tex]

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

For continuity, it is needed that:

[tex]f(4) = 320[/tex]

Thus:

[tex]K = 320[/tex] makes the function continuous.

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Answer: $475

Step-by-step explanation:

Given : A seller buys an item from a manufacturer for $9,500 he increases cost by %5 percent.

i.e. The original cost of item = $9,500

Mark up percentage = 5% = 0.05

The formula given to find the mark up value is :_

[tex]\text{Mark up}=\text{Original cost * percentage mark up}\\\\\Rightarrow\ \text{Mark up}=9500\times0.05=\$475[/tex]

Hence, the mark up value = $475

Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 10

2. C) y equals negative 1 divided by 8 x squared

3. D) x equals negative 1 divided by 32 y squared

4. C) x2 = -5.3y

5. C) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)

6. None from the choices, it should be

Center: (0, 0); Vertices: the point negative two square root two comma zero and the point 2 square root two comma zero; Foci: Ordered pair negative square root 6 comma zero and ordered pair square root 6 comma zero

7. B) A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at the point zero comma seven and zero comma negative seven. The minor axis has endpoints at negative six comma zero and six comma zero.

8. D) x squared divided by 16 plus y squared divided by 25 equals 1

9. D) Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)

Answer:

the answer is letter C

Step-by-step explanation:

Answer:

220cos40

Step-by-step explanation:

cos40=x/220

(220)cos40=x/220(220)

220cos40=x