Find the interest earned and the future value of an annuity with annual payments of $1,400 for 18 years into an account that pays 4% interest per year.

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right] }[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}8&3\\-7&2\end{array}\right] \cdot\left[\begin{array}{ccc}8&3\\-7&-6\end{array}\right] \\\\=\left[\begin{array}{ccc}(8)(8)+(3)(-7)&(8)(3)+(3)(-6)\\(-7)(8)+(2)(-7)&(-7)(3)+(2)(-6)\end{array}\right] \\\\=\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right][/tex]

Answer:

D

Step-by-step explanation:

43, 6

-70, -33

Answer:

(3a-1)(3a+1)

Step-by-step explanation:

We can quickly see with this problem that it is the difference of two squares as 9a^2 is (3a)^2 and 1 is 1^2 and therefore can factorise quickly using this rule.

x^2-y^2 = (x-y)(x+y) where x = 3a and y = 1

ANSWER

[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]

EXPLANATION

We want to simplify completely:

[tex]9 {a}^{2} - 1[/tex]

We express the two terms as difference of two squares;

[tex] {(3 {a})^{2} } - {1}^{2} [/tex]

Recall and apply the following identity;

[tex]{x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

We apply this identity to obtain:

[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]

Answer:

[tex]y=\tan \frac{1}{2} \pi[/tex]

Step-by-step explanation:

The given graph has a period of [tex]2\pi[/tex], because the graph repeats after every [tex]2\pi[/tex] units.

The formula for finding the period of a tangent function is

[tex]T=\frac{\pi}{b}[/tex]

We substitute the period to get;

[tex]2\pi=\frac{\pi}{b}[/tex]

This implies that;

[tex]b=\frac{\pi}{2\pi}[/tex]

Therefore[tex]b=\frac{1}{2}[/tex]

Hence the function represented by the graph is

[tex]y=\tan \frac{1}{2} \pi[/tex]

Answer:

2294 balls is the approximate number of balls

Step-by-step explanation:

Find the volume occupied a ball of radius 3inches

Volume of a sphere=4/3 [tex]\pi[/tex]×r³

where r is the radius in inches

4/3× [tex]\pi[/tex]×3³ = 36 [tex]\pi[/tex]

=113.11 in³

Find volume of a rectangle prism

v=l×w×h where l is length of prism, w is width of prism and h is height of prism

L=10ft=10×12=120 inches

w=5ft=5×12=60 inches

h=3ft= 3×12= 36 inches

v=120×60×36=259200 in³

Number of balls needed

N=volume occupied by a single ball/volume of the rectangular prism

N=259200/113.11 =2291.57⇒2292 balls

Check the picture below.

let's notice that 89/36 =>  2 and 17/36, namely 2π or two revolutions and then a bit more, the 17/36 slack, so then -89π/36 = - 2π - 17π/36.

the positive angle will of course be 2π - 17π/36 = 55π/36.

Answer:

No solution

Step-by-step explanation:

Rearrange into quadratic form: 3x² + 0x - 3 = 0

Quadratic formula: when ax² + bx + c = 0: x = (-b ± √(b² - 4ac))/2a

Plug in: x = 0 ± √(0 - 4*3*3))/2a

From this, we can conclude that this equation has no solution, as 0 - 4*3*3 will definitely be negative, and a negative number can not be square rooted.

The mean, or average, of the data set is 3 defective toys per sample group. Therefore set 0.3 and 0.5 are the most accurate representations.

Option C) 0.3

[2 1 | 1 0 ] • x = [5 | 10]

We multiply by the inverse of

[2 1 | 1 0 ]

det( [2 1 | 1 0] ) = -1

=> [2 1 | 1 0 ]^(-1) = (-1)•[0 -1 | -1 2 ] =

= [0 1 | 1 -2]

=> [2 1 | 1 0 ] • x = [5 | 10]

=> x = [2 1 | 1 0 ]^(-1) • [5 | 10]

=> x = [0 1 | 1 -2] • [5 | 10]

=> x = [0+10 | 5-20]

=> x = [10 | -15]

Answer:

900 cuboc unit

Step-by-step explanation:

Volume of pryamid= 1/3× area× height

= 1÷3×15^15×8

= 900cubic unit

For this case we have by definition, that the area of a square base pyramid is given by:

[tex]V = \frac {L ^ 2 * h} {3}[/tex]

Where:

L: It's the side of the square base

h: It's the height of the pyramid

We have that[tex]L = 15 \ units[/tex], then [tex]L ^ 2 = 15 ^ 2 = 225 \ units ^ 2[/tex]

Substituting:

[tex]V = \frac {225 * 8} {3}\\V = 600 \ units ^ 3[/tex]

Finally, the volume of the pyramid is [tex]600 \ units ^ 3[/tex]

Answer:

[tex]600 \ units ^ 3[/tex]

ANSWER

40°

EXPLANATION

The opposite sides of a rhombus are parallel.

This implies that, the diagonal is a transversal.

This means that,

m<1 and m<2 are alternate interior angles.

Since alternate interior angles congruent,

m<1 =m<2=40°

The correct choice is C.

Answer:

D.

Step-by-step explanation:

For this case we have:

Let k> 0:

To graph [tex]y = f (x) + k,[/tex] the graph k units is moved up.

To graph [tex]y = f (x) -k[/tex], the graph moves k units down.

Let h> 0:

To graph[tex]y = f (x-h)[/tex], the graph moves h units to the right.

To graph [tex]y = f (x + h),[/tex] the graph moves h units to the left.

So, we have:

[tex]y = f (x) = - \sqrt [3] {x}[/tex]

Shifted 7 units up and 4 to the right means:

[tex]k = 1\\h = 4[/tex]

[tex]y = f (x) = - \sqrt [3] {x-4} +7[/tex]

Answer:

Option B

Answer:

D. 40%

Step-by-step explanation:

You can fill in the table completely

[tex]\begin{array}{cccc}&\text{Hamburgers}&\text{Pizza}&\text{Total}\\\text{Adults}&0.24&0.36&0.6\\\text{Children}&0.11&0.29&0.4\\\text{Total}&0.35&0.65&1\end{array}[/tex]

From this table you can state that the probability that a randomly selected person is a child is 0.4 that is 40%.

The percentage of the people surveyed are children is:

                               40%

We are given a table as follows:

                            HAMBURGERS               PIZZA             TOTAL

ADULTS                   0.24                              0.36                0.6

CHILDREN                0.11                               0.29                 0.4

TOTAL                      0.35                              0.65                   1

Now we are asked to find the percent of students that were surveyed.

From the table we may see that the probability of children who were surveyed are:

     0.11+0.29=0.40

( since, the second column gives the total of the probability of children)

Hence, in percentage form it is given by:

0.40×100=40%

          Hence, the answer is:

               40%

Answer: W = 700 divided by a+18

Step-by-step explanation:

a) We can plug in $358 into A(w), since A(w) represents the amount of money Dale needs. So,

358 = 700 - 18w

Subtract: -342 = -18w

Divide: w = 19 weeks

b) We can plug in 6 into w, since w represents the number of weeks Dale saves money. So,

A(w) = 700 - 18(6)

Multiply: A(w) = 700 - 108

Subtract: A(w) = $592

Answer:

[tex]9y^2-4x^2-36y+16x-16=0[/tex]

Step-by-step explanation:

The given hyperbola has equation:

[tex]\frac{(y-2)^2}{4}-\frac{(x-2)^2}{9}=1[/tex]

We multiply through by 36 to get:

[tex]9(y-2)^2-4(x-2)^2=36[/tex]

We expand to get:

[tex]9(y^2-4y+4)-4(x^2-4x+4)=36[/tex]

[tex]9y^2-36y+36-4x^2+16x-16=36[/tex]

[tex]9y^2-36y-4x^2+16x-16=0[/tex]

The equation of the hyperbola in general form is:

[tex]9y^2-4x^2-36y+16x-16=0[/tex]

Answer: A

48+ 36 = 84  

84/4 = 21 groups  

there are 21 groups of 4 balloons  

5 unit to left, 3 units down is the correct answer.

Answer:

(x - 3)(4x² + 6x + 9)

Step-by-step explanation:

This is a difference of cubes which factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

8x³ = (2x)³ ⇒ a = 2x

27 = 3³ ⇒ b = 3

Hence

8x³ - 27

= (2x)³ - 3³

= (2x - 3)( (2x)² + (2x × 3) + 3²)

= (2x - 3)(4x² + 6x + 9)

Answer:

80%

Step-by-step explanation:

(54-30)/30 *100 = 80%

Let's call trade balance b, exports e and imports i.

We now construct formula.

[tex]b=\Delta{ei}=e-i[/tex]

Put in the data from last year.

[tex]b=968-1658=\boxed{-690}[/tex]

U.S trade balance for that year is -690 billion dollars.

Answer:

9 ft

Step-by-step explanation:

The ladder is 15 foot

The height the ladder reaches from the bottom of the wall is 12 ft

The distance (x) from the bottom of the wall to the foot of the ladder is:

Applying the Pythagorean theorem;

x = [tex]\sqrt{15^2 - 12^2}[/tex] = 9 ft

A 15 foot ladder needs to be placed at a distance of 9 foot from the base of the house so that it exactly reaches the top of a 12 foot wall.

In this case;

Therefore;

We are going to find the distance of the ladder from the base of the house on the ground which is the other leg.

Using Pythagoras theorem;

[tex]a^{2} + b^{2} = c^{2}[/tex]

Taking the horizontal distance of the ladder from the wall as b

Then;

[tex]b^{2} = c^{2} -a^{2}[/tex]

therefore,

[tex]b^{2} = 15^{2} -12^{2}[/tex]

[tex]b^{2} = 225 -144[/tex]

[tex]b^{2} = 81[/tex]

[tex]b = \sqrt{81} \\b= 9 ft[/tex]

Hence; the ladder needs to be placed at a distance of 9 foot from the base of the house.

Keywords: Right triangle, Pythagoras rule

Level; High school

Subject: Mathematics

Topic: Pythagoras theorem

Answer:

see explanation

Step-by-step explanation:

The length of the arc is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{90}{360}[/tex] ← r = 1

      = 2π × [tex]\frac{1}{4}[/tex] = [tex]\frac{\pi }{2}[/tex] ≈ [tex]\frac{3.14}{2}[/tex] = 1.57

Answer:

D. 12

Step-by-step explanation:

Answer:

D 12

Step-by-step explanation:

8h > 64

Divide each side by 8

8h/8 > 64/8

h > 8

H must be greater than 8

The only value in your list greater than 8 is 12

Answer:

D

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Answer:

commutative property: the property stating that changing the order in which two numbers are added or multiplied does not change the value of the sum or product

equivalent: having the same amount, value, area, volume, or force

evaluate: to determine the value of

like terms: terms consisting of the same variables, raised to the same exponent

Step-by-step explanation:

TRUST me this is RIGHT

To analyze whether two algebraic expressions are equivalent, you can use an interactive tool such as an algebra solver or calculator to compare the results of the expressions for various values of x. Simplify the expressions if possible, compare the simplified expressions, and verify the results by substituting different x-values.

To determine if the expressions 7x – 4 and 6x – 4 – x are equivalent, you can use an interactive tool like an online algebra solver or calculator. This process usually involves comparing the results of the expressions for multiple values of x.

Step 1:

Firstly, simplify the expressions if possible. For the second expression, 6x – 4 – x, you can simplify it as 5x – 4.

Step 2:

Now, compare the simplified expressions, you can see that 7x - 4 and 5x - 4 are not equivalent as the coefficients of x (7 and 5) are not equal.

Step 3:

Last, for verification, you can substitute different values of x into both equations and see if the outputs are the same. If the outputs are different then, the equations are not equivalent.

https://brainly.com/question/953809

#SPJ11

Answer:

maybe you add then all up

Answer:

The correct answer is last option

x¹⁶y²²

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾

(Xᵃ)ᵇ = Xᵃᵇ

To find the correct answer

It is given an expression {X⁶Y⁸}³/X²Y²

By using identities we can write,

{X⁶Y⁸}³/X²Y² = X⁶ˣ³ Y⁸ˣ³/X²Y²

 = X¹⁸Y²⁴/X²Y²

 = X⁽¹⁸ ⁻ ²⁾ * Y⁽²⁴ ⁻ ²⁾

 = X¹⁶Y²²

Therefore the correct answer is last optionX¹⁶Y²²

Answer:

$47, 17.5%

Step-by-step explanation:

When she buys the $20 book, she can get 40% off either the $15, $12, or $10 book.  She'll save the most by getting 40% off the $15 book.

Then, when she buys the $12 book, she'll get %40 off the $10 book.

The total she pays is:

20 + (0.60)(15) + 12 + (0.60)(10)

20 + 9 + 12 + 6

47

Without the discounts, the cost of the books would have been:

20 + 15 + 12 + 10

57

So she saves $10.  10 out of 57 is approximately 17.5%.

Since supplementary angles add up to 180°, you would subtracted the measurement that you have from 180°.

Ex.

180-x= y

X being the measurement that you have, and y being the missing measurement.

Answer:

2

Step-by-step explanation:

Given Data:

total distance= 850 miles

gas tank holds gas= 15 gallons

mileage = 72/3.2 miles/gallon

if

72 miles uses= 3.2 gallon

then

850 miles uses= x gallons

by cross-multiplication we get

72x=3.2(850)

x=37.778

i.e. 850 miles will use 37.7778 gallon of gas

Asgas tank holds 15 gallons

number of times gas tank is used up= 37.3/15

                                                            = 2.518

rounding off

number of times gas tank is used up=3

As they filled the gas tank at the start of the road trip, hence 3-1=2

ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION =2 !

Answer:

20 cents.

Step-by-step explanation:

You can drop 2 zeros from both the price and the amount of pencils. If 1000 pencils costs 20.00 dollars then 10 pencils cost .20 dollars or 20 cents.