Real Numbers: Mastery Test

The dimensions of the picture size to fit in the frame are 14 inches by 11 inches.

It is known the frame is 17 inches tall but this includes 1.5 inches of the wooden frame. This means that 3 inches of the frame (1.5 inches x 2) do not count for the size of the picture.

We already know the picture can be 14 inches tall and the total area is 238 square inches including the 1.5 wooden frame.

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Answer:

$1,585

Step-by-step explanation:

Simple interest formula:

A = P(1 + rt)

where:

Given:

Substituting given values into the formula:

⇒ A = 1000(1 + 0.0325 · 18)

       = 1585

Answer:

12

Step-by-step explanation:

the ratio of the 2 numbers = 3 : 4 = 3x : 4x ( x is a multiplier ) , then

3(3x) + 2(4x) = 68 , that is

9x + 8x = 68

17x = 68 ( divide both sides by 17 )

x = 4

smaller number = 3x = 3 × 4 = 12

Answer:

16pi km² / 8pi km

Step-by-step explanation:

r = 4

A = pi(r²)

4² = 16

A = 16pi km²

C = 2r(pi)

2r = 8

C = 8pi km

option A

hope it's correct and really helps...!!!

Answer: the answer is A i got 100% on my

test

Step-by-step explanation:

There are 1.5625 grams of the radioactive substance that would remain after 60 seconds.

The exponent of a number represents the total time required to multiply that number. 8 8 8 may be stated as 83 since 8 is multiplied by itself three times. In this case, 3 is the 'exponent' or 'power' that indicates how many times 8 is multiplied by itself, and 8 is the 'base' that represents the integer being multiplied.

The exponent is given as:

y = a (1 - r)ˣ

As per the question, we have

a = 100, and r = 0.50 and x = 6

Substitute the known values in the above formula, and we get

y = 100 × (1-0.50)⁶

y = 100 × (0.50)⁶

y = 100 × 0.015625

Apply the multiplication operation, a

y = 1.5625

So, after 60 seconds, 1.5625 grams of the radioactive substance would remain.

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I'll do the first two questions of each activity to get you started. The remaining unanswered questions will follow similar steps compared to the other questions in the same activity group.

=======================================================

Activity 5, Problem 1

To find the mean, we first add up the values

4+8+2+8+5+9 = 36

Then we divide over n = 6 because there are 6 values in this data set.

36/n = 36/6 = 6

=======================================================

Activity 5, Problem 2

Follow the same idea as the previous problem.

Add the values:  9+8+8+13+12 = 50

Divide by the number of values: 50/n = 50/5 = 10

=======================================================

Activity 6, Problem 1

The median is the middle-most number. Think of a median of a highway or freeway.

In order to find the median, we first need to sort the data values from smallest to largest.

The original set {7,3,9,9,2,5,8} sorts to {2, 3, 5, 7, 8, 9, 9}

If we erased the first and last items, we get this smaller subset

{3, 5, 7, 8, 9}

repeat again to get

{5,7,8}

At this point its clear the middle most value is 7

But if you wanted, you could cross the first and last values from the list to end up with {7}

=======================================================

Activity 6, Problem 2

We could do the same trick as the previous problem, but I'll use a slightly different route this time.

We'll need to sort {10,8,4,11,9} into {4, 8, 9, 10, 11}

There are n = 5 items in that set. The middle slot would be at slot n/2 = 5/2 = 2.5 = 3

The value 9 is in slot 3 of the sorted items.

=======================================================

Activity 7, Problem 1

The mode is the most frequent value of a set. It repeats the most often.

The set {5,6,7,3,5,4} sorts to {3,4,5,5,6,7}

The value "5" shows up the most. It shows up twice when everything else shows up exactly once only.

=======================================================

Activity 7, Problem 2

Using the same idea in the previous problem, the set {7,4,11,9,7,3} has the mode 7 because it shows up the most of any other value.

Here's the sorted set: {3,4,7,7,9,11}

Sorting is optional with finding the mode in contrast to being mandatory when it comes to finding the median.

Answer:

i think the answer is 144

Step-by-step explanation:

ohhh so first we should try finding the slope here. since we know the points are (3.5 , 21) and (6.5, 69) we can use the formula to look for the slope

the formula is:

y2 - y1 / x2 - x1

lets substitute

69 - 21 / 6.5 - 3.5

48 / 3

16

f(x) = 16x + b

now we just substitute

btw i dont think we need to find b because this inst a linear equation? im not sure but yea i dont think we need to find the y-intercept

so anyways

f(9) = 16(9)

= 144

Answer:

[tex] (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656{x}^{} + 46656 [/tex]

Step-by-step explanation:

we want to solve the following binomial:

[tex](x + 6 {)}^{6} [/tex]

There is a handy way to expand powers of binomials which is known as binomial theorem . and it describes the algebraic expansion of powers of a binomial. binomial theorem is given by

[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0 }^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

comparing (x+6)⁶ to (a+b)ⁿ , we get

now substitute them on the formula which yields:

[tex] \displaystyle (x + 6 {)}^{6} = \sum _{k = 0 }^{n} \binom{6}{k} {x}^{6 - k} \cdot {6}^{k} [/tex]

converting the summation notation into sum yields:

[tex] \displaystyle (x + 6 {)}^{6} = \binom{6}{0} {x}^{6 - 0} \cdot {6}^{0} + \binom{6}{1} {x}^{6 - 1} \cdot {6}^{1} + \binom{6}{2} {x}^{6 - 2} \cdot {6}^{2} + \binom{6}{3} {x}^{6 - 3} \cdot {6}^{3} + \binom{6}{4} {x}^{6 - 4} \cdot {6}^{4} + \binom{6}{5} {x}^{6 - 5} \cdot {6}^{5} + \binom{6}{6} {x}^{6 - 6} \cdot {6}^{6} \\ \implies(x + 6 {)}^{6} = \binom{6}{0} {x}^{6 } \cdot 1 + \binom{6}{1} {x}^{5} \cdot {6} + \binom{6}{2} {x}^{4} \cdot 36+ \binom{6}{3} {x}^{3} \cdot 216 + \binom{6}{4} {x}^{2} \cdot 1296+ \binom{6}{5} {x}^{} \cdot 7776+ \binom{6}{6} {x}^{0} \cdot 46656 \\ \implies(x + 6 {)}^{6} = 1 \cdot {x}^{6 } \cdot 1 + 6 \cdot{x}^{5} \cdot {6} + 15 \cdot {x}^{4} \cdot 36+ 20 \cdot {x}^{3} \cdot 216 + 15 \cdot{x}^{2} \cdot 1296+ 6 \cdot {x}^{} \cdot 7776+ 1 \cdot {x}^{0} \cdot 46656 \\ \implies \boxed{ (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656 {x}^{} + 46656 }[/tex]

and we're done!

Answer:

  isosceles obtuse triangle

Step-by-step explanation:

The attached graph shows a plot of the three lines.

The triangle is an isosceles obtuse triangle in the 2nd quadrant.

_____

It is convenient to let a graphing calculator plot these lines. If you're going to plot them by hand, it usually works best to choose values of the variables for the variable that has the largest coefficient (3 in two of the equations). That way, you're not trying to plot coordinates that contain fractions.

Answer:

1t = 1000kg

22.69 x 1000= 22690 kg

22690 kg ÷ 100 = 226.9

I would usually round it to 227 but I would say 226, since they are asking how many full bags she sold.

Answer:

6 in

Step-by-step explanation:

4×12×w=288

48×w=288

/48. /48

w=6

Answer:

y = 4

Step-by-step explanation:

because 5 x 4 = 20 and 20 × 4 = 80 and so on y is equal to four

Answer:

16.4 units to the nearest tenth.

Step-by-step explanation:

sin 66 = 15 / x

x *  sin 66 = 15

x = 15 / sin 66

= 16.4196

Done!

Answer: 40

Step-by-step explanation: The total number of points from the first 8 games is 7+4+3+6+8+3+1+5=37.

We have to make this a multiple of 9 by scoring less than 10 points.

The closest multiple of 9 is 45. 45-37=8.

Now we have to add a number to get a multiple of 10.

The next multiple is 50 we added 5, multiplying these together you get 8 x 5 is 40.

Answer:

23

Step-by-step explanation:

[tex]368/16=23[/tex]

Answer:

60 degrees

Step-by-step explanation:

well, angle x is on a line with a little square that means 90 degrees and a 30 degree angle, so you would simply add those two angles together 90+30=120 and then subtract by 180 because a straight line is always 180 degrees which is 180-120=60 degrees.

point grab lol

Answer:

the guy above if right it is D

Step-by-step explanation:

I did the work on Acellus and pick D IT GAVE ME A CHECK MARK

The reason that supports the statement 7 in the given proof is D. Subtraction property of equality.

Subtraction property of equality is defined as, if an equation is of the form,

a = b,

then any number subtracted from both sides makes the equation same.

a - c = b - c

Here, given a proof for the value of x.

In the 6th step, by substitution,

55 = 5x + 10

This is an equation.

We need term in x on one side and a constant term on other side.

For that, if we subtract both sides by 10,

55 - 10 = 5x + 10 - 10

45 = 5x

So here the subtraction property of equality is used.

Hence the correct option is D.

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Answer:

1

Step-by-step explanation:

5-3x=2

5-3(1)=2

2+3=5

Answer:

1

Step-by-step explanation:

5-3•_=2

The only number that would fit in this equation is 1.

Answer:

The answer is 1,568 in a multiplication problem.

4 x 4 x 4 = 64

3.5 x 7 = 24.5

64 x 24.5 = 1,568

Let me know if this was not what you were looking for, I may or may not be able to change it.

Answer:

x=8, y = 0

Step-by-step explanation:

Substitution is easier for this problem.

3x + y = 24 ---> y = 24 - 3x

x^2 + y = 64

Substitute y

x^2 + 24 - 3x = 64

x^2 - 3x = 40

Factor out x

x(x-3) = 40

Pretty much you can guess and check

x = 8

If x = 8, y = 0

or

x^2 - 3x = 40

Complete the square

x^2 - 3x + 2.25 = 42.25

(x-1.5) ^2 = 42.25

Square root both sides

x - 1.5 = 6.5

x=8

x - 1.5 = -6.5

x = -5

Check

x = -5 doesn't work, so x = 8 and y = 0

Answer:

B.

Step-by-step explanation:

1) the given equation is provided in slope-interception form, then

2) the interseption is '-3', it means the point (0;-3) - the correct answer is either B or C;

3) the slope of the given line is more that 1 (3/2>1), it means the angle is [45°;90°], then the line of the answer B is satisfies this condition.*

4) finally, the correct answer is B.

* - if to substitute the point (2;0) then it will be true equality 0=0.

Answer:

The answer is D : y= −0.15x^2 + 2x + 5.5

Step-by-step explanation:

i got it right on my test

The quadratic equation represented by the table is y = -0.15x² + 2x + 5.5

An equation is an expression that shows the relationship between two or more numbers and variables.

Quadratic function is in the form y = ax² + bx + c; where a, b and c are constants.

From the table, at point (0, 5.5):

5.5 = a(0)² + b(0) + c          (1)

From the table, at point (1, 7.35):

7.35 = a(1)² + b(1) + c          (2)

From the table, at point (2, 8.9):

8.9 = a(2)² + b(2) + c          (3)

From 1, 2 and 3:

a= -0.15, b = 2, c = 5.5

The quadratic equation represented by the table is y = -0.15x² + 2x + 5.5

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Answer:

x+y=4

Step-by-step explanation:

hello :

note :  by identity  you have   x²-y² = (x-y)(x+y)

in this exercice : 2x²-2y² = 2(x²-y²) = 2 (x-y)(x+y)

means :   2 (x-y)(x+y) = 40

but x-y = 5

so : 2(5)(x+y) =40

x+y=40/10

x+y=4

Answer:

radius = 9.5 cm

Step-by-step explanation:

If 2 chords intersect then the product of the parts of 1 chord is equal to the product of the parts of the other chord, that is

PT × TQ = ST × TR

PT × 3 = 4 × 12 = 48

3 PT = 48 ( divide both sides by 3 )

PT = 16

then

diameter = PT + TQ = 16 + 3 = 19 cm

radius = 19 ÷ 2 = 9.5 cm

Answer:

Area of a triangle

[tex] \frac{bh}{2} \\ 10 \times 10 = 100 \\ 100 \div 2 = 50 \\ the \: triangles \: have \: the \: same \: area \: and \: there \: are \: 4 \: triangles \: so \\ 4(50) = 200 \\ now \: we \: find \: the \: are \: of \: the \: rectangular\: base \: \\ area = bh \\ b = 10 \\ h = 10 \\ 10(10) = 100 \\ no w \: we \: add \: the \: area \: of \: the \: triangles \: and \: the \: square \\ 200 + 100 = 300 \: {in}^{2} [/tex]

Answer:

5.9 or 5.85 unrounded

Answer:

  (c)  The two quantities are equal.

Step-by-step explanation:

The sine of an angle is equal to the cosine of its complement. In a right triangle, the acute angles are complementary, which means ...

  sin(A) = cos(B)

The two quantities are equal.

Answer:

Step-by-step explanation:

Sin(A) = opposite / hypotenuse

opposite = 4

hypotenuse = 5

Sin(A) = 4/5 = 0.8

Cos(B) = adjacent / hypotenuse.

adjacent = 4

hypotenuse = 5

Cos(B) = 4/5 = 0.8

Believe it or not, this will always happen if you take Sin(A) and find that Cos(90 - A) are equal

Take a simpler case. Suppose you are working with a 30 60 90 triangle.

Cos(60) = Sin(90 - 60) = 1/2