Simplify the expression. Write your answer as a power.
64⁴/64³
The simplified expression is

The difference of the grandson's age in years and the grandfather's age in years is 77. Therefore, the age of the grandson is 7 years.

A grandson's age in months is equal to his grandfather's age in years.

Recall,

12 months = 1 year

Hence,

let

x = age of grandson in month

It is the same age in years for the grandfather.

Therefore,

x = age of grand father in years

The difference of the grandson's age in years and the grandfather's age in years is 77. Therefore,

x - x / 12 = 77

12x - x/12 = 77

11x / 12 = 77

cross multiply

11x = 924

x = 924 / 11

x = 84

Therefore, the grandson age in in years is 84 / 12 = 7 years.

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Answer:

See below

Step-by-step explanation:

She could have each student in the class write his or her name on a slip of paper and put it in a bowl. Then, she could shake the bowl and pull out any slip of paper with a student's name on it. After 3 times, the random sample would be over, and Mrs. Purdue would have her 3 representatives.

The equation of line is y = ( 1/4 )x , with slope m = 1/4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 0 )

Let the second point be Q ( 8 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 0 ) / ( 8 - 0 )

Slope m = 2/8 = 1/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 0 = ( 1/4 ) ( x - 0 )

y = ( 1/4 )x

Hence , the equation of line is y = ( 1/4 )x

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Answer:

Mean - 17.222222222222

Median - 17

Mode - 12

Step-by-step explanation:

lets arrange this is least to greatest.

2, 4, 12, 12, 17, 18, 28, 29, 33

to find the mean(even though you dont need it), you add all the numbers up and devide by the amount of numbers.

so -> 2 + 4 + 12 + 12 + 17 + 18 + 28 + 29 + 33 = 155

and there are 9 numbers, so 155 / 9 = 17.2 and a lot more 2s

to find the median, you arrange from least to greatest vice versa, then find the middle number.

2, 4, 12, 12, 17, 18, 28, 29, 33

the middle number is 17, so the mean is 17

to find the mode, you have to find the number that is most repeated.

2, 4, 12, 12, 17, 18, 28, 29, 33

the number that is repeated the most is 12, so your mode is 12.

Hope this helped!!!

In triangle ABC, If A is located at (-1,2), A' will be located at (-3, 6)

To answer the question, we need to know what dilation is

Dilation is a form of transformation in which the size of an object is increased or decreased by a factor.

For any object with coordinates (x,y) dilated by a factor k, the new coordinates of the dilated object is (kx, ky).

Given that triangle ABC is going to be dilated by a scale factor of 3 and A is located at (-1, 2).

Since

The new coordinates of A' = (kx, ky)

= (3 × -1, 3 × 2)

= (-3, 6)

So, A' will be located at (-3, 6)

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Answer:

Mean:  The sum of all data values divided by the total number of data values.

Median: The middle value when all data values are placed in order of size.  If there is an even number of data values, the median is the mean of the middle two values.

Mode: The most frequently occurring data value.

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Question 3

[tex]\textsf{Mean}=\dfrac{69 + 70 + 71 + 73 + 74 + 75 + 76 + 76 + 76 + 86}{10}=74.6[/tex]

Ordered data values:  69, 70, 71, 73, 74, 75, 76, 76, 76, 86

Median = (74 + 75) / 2 = 74.5

Mode = 76

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Question 4

[tex]\textsf{Mean}=\dfrac{3 + 5 + 5 + 5 + 6 + 6 + 7 + 8 + 8}{9}=5.9\: \sf (nearest \:tenth)[/tex]

Ordered data values:  3, 5, 5, 5, 6, 6, 7, 8, 8

Median = 6

Mode = 5

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Question 5

[tex]\begin{aligned}\textsf{Mean} & =\dfrac{11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 16 + 16 + 17 + 18 + 19 + 20 + 23}{15}\\ & =15.5 \: \sf (nearest\:tenth)\end{aligned}[/tex]

Ordered data values:  11, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 18, 19, 20, 23

Median = 15

Mode = 12, 13, 14, 16

Answer:

see explanation

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

the median is the middle value of a set of data. If there is no exact middle value then it is the average of the values on either side of the middle.

the mode is the value that occurs most often in the data set

A data set can have more than 1 mode

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

(3)

(a)

mean = [tex]\frac{74+73+75+76+71+69+70+76+76+86}{10}[/tex] = [tex]\frac{746}{10}[/tex] = 74.6

(b)

Arrange the data in ascending order

 69  70  71  73  74  75  76  76  76  86

                              ↑ middle

median = (74 + 75) ÷ 2 = 149 ÷ 2 = 74.5

(c)

mode = 76

(4)

(a)

mean = [tex]\frac{6+8+8+5+6+7+5+3+5}{9}[/tex] = [tex]\frac{53}{9}[/tex] ≈ 5.9 ( to 1 dec. place )

(b)

3  5  5  5  6  6  7  8  8

                 ↑ middle

median = 6

(c)

mode = 5

(5)

(a)

mean = [tex]\frac{12+13+18+23+14+17+14+16+13+16+15+19+11+20+12}{15}[/tex] = [tex]\frac{233}{15}[/tex]  ≈ 15.5 ( to 1 dp )

(b)

11  12  12 13  13  14  14  15  16  16  17  18  19  20  23

                                      ↑ middle

median = 15

(c)

the mode is multimodal

modes are 12, 13, 14, 16

Step-by-step explanation:

[tex] = {4}^{3} \times {4}^{x} [/tex]

[tex] = {4}^{3 + x} [/tex]

[tex] = {4}^{x + 3} [/tex]

Answer:

2xa(5x^2 + 3a).

Step-by-step explanation:

We are factorising:-

Divide the left side by 2xa and place the result in the parentheses:

10x^3a+6xa^2 = 2xa(5x^2 + 3a )

Answer:

2xa(5x² +3a-1)

Step-by-step explanation:

10x³a+ 6xa²-2xa=2xa-2xa

10x³a+ 6xa²-2xa=0

Factor 10x³a+ 6xa²-2xa:

2ax(5x² + 3a -1)

Answer:

-1/2

Step-by-step explanation:

it has to be a negative number since

every other number is negative

its a fraction since the numbers are decreasing

96 divided by 48 is 2

so the number being multiplied or ration must be -1/2

Answer:

[tex] \frac{2}{9} \: is \: less \: than \: \frac{1}{3} [/tex]

and

[tex] \frac{1}{3} + \frac{1}{6} \: must \: be \: more \: than \: \frac{1}{3} [/tex]

Step-by-step explanation:

Let the number be X

3×X=3X

Increased by 2

3X+2>0≤-3

Using the binomial distribution, we have that:

a) The distribution is given by:

b) 0.3125 = 31.25%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, we have that:

The distribution is given by the probability of each outcome, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{4,0}.(0.5)^{0}.(0.5)^{4} = 0.0625[/tex]

[tex]P(X = 1) = C_{4,1}.(0.5)^{1}.(0.5)^{3} = 0.25[/tex]

[tex]P(X = 2) = C_{4,2}.(0.5)^{2}.(0.5)^{2} = 0.375[/tex]

[tex]P(X = 3) = C_{4,3}.(0.5)^{3}.(0.5)^{1} = 0.25[/tex]

[tex]P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.0625[/tex]

The probability of at least 3 daughters is given by:

[tex]P(X \geq 3) = P(X = 3) + P(X = 4) = 0.25 + 0.0625 = 0.3125[/tex].

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Answer:

(x + 3)^2 + (y - 3)^2 = 5^2

Step-by-step explanation:

They're not really much to show work. Looking at the graph we need to find the origin which is (h  ,k), and the radius.

(h , k) = (-3 , 3)

The radius is r = 5 because counting it from origin to the edge.

Plug that into the formula equation: (x - h)^2 + (y - k)^2 = r^2

(x - (-3))^2 + (y - 3)^2 = 5^2

(x + 3)^2 + (y - 3)^2 = 5^2

Answer:

23.5

Step-by-step explanation:

let's take the number as X

2X+20=66.3

2X=66.3-20

X=23.15

Using the normal distribution, it is found that the sections that are one standard deviation from the mean are 34 and 40.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 37, \sigma = 3[/tex]

The measures that are one standard deviation from the mean are given by X when Z = -1 and Z = 1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1 = \frac{X - 37}{3}[/tex]

X - 37 = -3

X = 34

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1 = \frac{X - 37}{3}[/tex]

X - 37 = 3

X = 40

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Answer:

Step-by-step explanation:

Relation between sugar and flour

Table

[tex]\left[\begin{array}{ccc}sugar(tsp)&flour(cups)\\12&2\\18&3\\36&6\\48&8\\54&9\end{array}\right][/tex]

Answer:

Step-by-step explanation:

Remark

The key to this question is the second entry. Numerically the sugar is divided by 6 to get the flour. Never mind the units. Just deal with the ratio itself.

Formula

Flour = Sugar / 6

Solution

Sugar = 12

Flour = 12/6 = 2

Flour = 18/6

Flour = 3

Flour = 6

6 = sugar/6               multiply by 6

6*6 = 6* sugar/6

36 = sugar

Sugar = 48

Flour = 48/6 = 8 cups of flower

Flour = 9

9 = sugar / 6

9*6 = sugar

Sugar = 54.

Multiplication is the process of multiplying. The amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given a medicine provides 3.6 milligrams of medicine. Therefore, the amount of medicine the dog will have in a week is,

The amount of medicine = 3.6milligrams × 7 = 25.2 milligrams

Hence, the amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.

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The area of the reflective material is:  284 square yards.

A rectangle is a quadrilateral with four sides and four right-angles.

it has two lines of symmetry.

Analysis:

To find the area of the reflecting material we find the area of the following shapes: trapezium + rectangle + triangle

bigger base of trapezium = 2 + 6 + 2 = 10 yard

smaller base of trapezium = 6

length of rectangle = 18 yard

width of rectangle : 2+6+2 = 10 yard

base of triangle is =  10 yard

Area of reflective material = 1/2(6+10) + 18x10 + 1/2(10)(8) = 284 square yards

In conclusion, the area of reflective material is : 284 square yards.

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Answer:

m<A > m<B > m<C

Step-by-step explanation:

In triangles, the measure of angles is proportional with the side length's they see,

The angle with the biggest the biggest measure sees the biggest side length

in triangle ABC the side lengths are given as

BC = 14, CA = 13 and AB = 5

from this, we can conclude:

m<A > m<B > m<C

Answer:

x=11800

Step-by-step explanation:

make a proportion:

2360/.2=X/1

2360(1)=.2x

x=11800

Answer:

$0.70 per ounce

Step-by-step explanation:

Concepts + Application

The unit price of an object, in this case, is the total amount of money spent divided by how many ounces there are. We're given the total amount of money as $4.20 and the number of ounces as 6. Thus, we just divide 4.20 by 6.

Solution

Parallel lines are the top & bottom lines - labelled 10 & 2

A = 0.5(2+10) x 2

=12 units^2

Hope this helps!

The sampling type in this study, where a researcher recruits 60 paired volunteers and asks them to rate their satisfaction after product use, is B. paired data.

A paired data test or sampling is used when the researcher is interested in the difference between two variables for the same subject.

For instance, in this experiment, the researcher wants to find the satisfaction level of the volunteers who used the shampoo and conditioner separately or combined.

Thus, the sampling type in this study, where a researcher recruits 60 paired volunteers and asks them to rate their satisfaction after product use, is B. paired data.

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Answer:

  2mn

Step-by-step explanation:

The expanded form of the square can be found using the distributive property.

__

  (m -n)² = (m -n)(m -n) = m(m -n) -n(m -n) . . . use the distributive property

  = m² -mn -nm +n² . . . . use it again

  = m² -2mn +n² . . . . . . combine like terms

The missing term is 2mn.

Answer:

720

Step-by-step explanation:

Three-fourths of 960 are simply three fourths times 960, which can be written as follows:

Three/fourths x 960

Furthermore, you can convert "three" to "3" and "fourths" to "4" and then the equation and answer are:

3/4 x 960 = 720

The average velocity of the object after during the first three seconds is: 48m/s

The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.

Instantaneous velocity  is the speed of an object at a particular point in time.

Average velocity is the velocity of an object after covering a certain distance for a period of time

Analysis:

Given

initial height = 600 feet

Height with respect to time = f(t) = -16[tex]t^{2}[/tex] + 600

a) Height at t = 0 = 600 feet

    Height at t = 3 seconds = f(3) = -16[tex](3)^{2}[/tex] + 600 = 456 feet

Distance travelled  = 600 - 456 = 144 feet

Average velocity = distance travelled/time taken  = 144/3 = 48 feet/seconds

b) instantaneous velocity at time t = [tex]\frac{df(t)}{dt}[/tex] = [tex]\frac{d(-16t^{2} + 600) }{dt}[/tex] = -32t

  when instantaneous velocity equal average velocity

     -32t = -48

      t = 1.5 seconds

In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.

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Answer:

True

Step-by-step explanation:

Straight angles are straight lines which equal 180 degrees

Answer:

true it is equals 180 for that angle