What is the length of an edge of a cube whose total surface area is equal to 150 square feet?

The inverse of the equation y = x^2 + 9 is [tex]x = \sqrt{y - 9[/tex]

The equation is given as:

y = x^2 + 9

Subtract 9 from both sides

x^2 = y - 9

Take the square root of both sides

[tex]x = \sqrt{y - 9[/tex]

Hence, the inverse of the equation y = x^2 + 9 is [tex]x = \sqrt{y - 9[/tex]

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Answer:

20

Step-by-step explanation:

a c will have the same angle as b d

The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).

Formation of the linear equation for the drinks bought by Maria:

The total number of drinks bought by the Maria is 13.

Lets say 'm' represents the number of medium drink.

's' represents the number of small drink.

Total drinks comprises of medium drinks and small drinks.

Thus,

s + m = 13, is the first linear equation.

Now medium drinks cost $3.

Total cost for purchasing medium drinks = (price of one medium drink)×(total number of medium drinks)

Total price for medium drinks = 3×m

Similarly,

Total cost for purchasing small drinks = (price of one small drink)×(total number of small drinks)

Total price for small drinks = 2×s

Total cost = total cost of medium drink + total cost of small drink

          32  = 3×m + 2×s, is second linear equation.

From equation first substitute the value of 'm' in second equation to fine the total number of drink.

32 = 3×(13 - s) + 2×s

32 = 39 - 3s + 22

s = 7

Put s = 7 in first equation and calculate 'm'.

m = 13 -7

m = 6

Therefore, The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

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The population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

According to the question,

The population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

The sample proportion p, is a point estimate of the population proportion.

Hence, the correct answer is point estimate. Thus, the population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

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The volume of the shape will be 50cm3.

It should be noted that the volume van be found by multiplying the area by the height. The volume will be:

= 10 × 5

= 50cm³

The standard deviation volume will be:

= 0.1 × 50

= 5cm

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rhumbos

it is the most precise name because it gives more information about the quadrilateral

38.2% of the cubes are without chocolate coated.

Given that,

The length ,l= 10 inch

The width ,b=10 inch

The height, h=5 inch

We know that the lateral surface area of the cuboid or rectangular block,

SA= 2(lh+lb+hb)

⇒ SA = 2( 10*5 +10*10+5*10)

⇒ SA =2*200=400 [tex]inch^{3}[/tex]  

The volume of the cuboid,V= 10*10*5 =500 [tex]inch^{3}[/tex]

The block of candy is then cut into another small cube 1 inch per side.

length,l=1 inch

width, b=1 inch

height,h=1 inch

So, the surface area of each small cube ,sa= 2(1+1+1) = 6 [tex]inch^{3}[/tex]

Volume of each candy,v= 1*1*1=1 [tex]inch^{3}[/tex]

So, the total number of candy= 500/1 =500 nos.

There is chocolate on each and every piece on the exterior inch. But those who are totally within do not.

A cube measuring 8 inches by 8 inches by 3 inches makes up the inside.

So, the total no of boxes that have no chocolate =8*8*3=192 boxes

So, the percentage = 192*100/500= 38.2 %

Therefore, it is concluded that 38.2% of cubes are without chocolate.

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The equation that represents the relation is y = 8 - 0.5x

The given parameters are:

Start = 8m

Rate = 1/2 m/s

The linear equation that represents the submarine movement is:

y = Start - Rate * x

This gives

y = 8 - 1/2 * x

Evaluate

y = 8 - 0.5x

Hence, the equation that represents the relation is y = 8 - 0.5x

See attachment for the graph

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The total amount of Chandra's investments after 8 years exists $110.03.

The formula for calculating the compound interest exists defined as;

[tex]$A = P(1+r/n)^{nt[/tex]

where, P exists the amount invested = $75

r exists the rate. = 0.048

t exists the time = 8 years

n = 12 (monthly)

The formula for calculating the compound interest,

[tex]$A = P(1+r/n)^{nt[/tex]

Substitute the value in the above equation, and we get

[tex]$A = 75(1+0.048/12)^{96[/tex]

A = 75(1.467)

A = 110.03

Hence the total amount of Chandra's investments after 8 years exists $110.03

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hi

we have an aroithmetic serie of first term 1 and  pace  2

so sum of 12 first terms, namming  1 as  S1 and  12th term as  S12

S12 =  1 + 2*11 = 23

formula of summ :      number of term *  (  final term + first term) / 2

So sum of terms  from S1 +S12 =    12   ( S12 +S1 )  / 2  =  12 * ( 23+1) /2

12*  12=  144

-

The independent variable that caused a change in the dependent variable is called cofounding variable.

Given the Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called _____ variables.

These are variables in statistics other than the dependent and independent variables which can also be important to a researcher because it affects the dependent variable.

Confounding variables can also be called influences, external factors or third variables because they mostly affect the outcome of a research and prevent a researcher from achieving its objectives.

Hence, Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called cofounding variables.

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The maximum number of floors that this building can have is 6

The given parameters are:

Elevators = 4

Stops = 3

At least one elevator stops on 2 floors

The maximum number of floors is calculated as:

Maximum = Elevators * Stops/2

This gives

Maximum = 4 * 3/2

Evaluate

Maximum = 6

Hence, the maximum number of floors that this building can have is 6

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The coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)

The functions are given as:

y = x + 1

2x + y = 4

x + y = 5

Next, we plot the graph of the lines (see attachment)

From the attached graph, the coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)

Rewrite the equations in slope intercept form

y = x + 1 ⇒ Slope = 1

y = -2x + 4 ⇒ Slope = -2

y = -x + 5 ⇒ Slope = -1

The equations y = x + 1 and y = -x + 5 have their slopes to be opposite reciprocals

This means that the lines are perpendicular (they form a right angle)

Hence, the triangle is a right triangle

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Answer:

$96.

Step-by-step explanation:

5/6  costs 80

Multiply both parts by 6/5:

5/6 * 6/5 ( = 1 ) costs 80 * 6/5

= 16 * 6

= $96.

Applying exponential properties, the simplified base for the function is given as follows:

[tex]f(x) = 2(3)^{2x}[/tex]

The function is represented by the following definition:

[tex]f(x) = 2\sqrt[3]{27^{2x}}[/tex]

As an exponent, the function is given by:

[tex]f(x) = 2(27)^{\frac{2x}{3}}[/tex]

27 can be simplified as follows:

27 = 3 x 3 x 3 = 3³

Hence:

[tex]f(x) = 2(3^3)^{\frac{2x}{3}}[/tex]

Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:

[tex]f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}[/tex]

Hence the simplified base for the function is given as follows:

[tex]f(x) = 2(3)^{2x}[/tex]

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Answer:

25k x 3

Step-by-step explanation:

The given limit indicates that there is a vertical asymptote at x = 2.

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator. When x tends to these values laterally, the limit of f(x) goes to infinity.

In this problem, the function is:

[tex]f(x) = \frac{x^2 - 4x - 12}{x - 2}[/tex]

The vertical asymptote is:

x - 2 = 0 -> x = 2.

Hence:

[tex]\lim_{x \rightarrow 2^+} f(x)[/tex] and [tex]\lim_{x \rightarrow 2^-} f(x)[/tex] are either positive infinity or negative infinity.

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The coordinates of the fourth vertex are (6, -2)

The coordinates of three vertices of a rectangle are given as: (3,7), (-3,5), and (0,-4).

Calculate the slope of the first two coordinates using

m = (y2 - y1)/(x2 - x1)^2

Substitute the known values in the above equation

d = (7 - 5)/(3 + 3)

Let the fourth coordinate be (x, y)

Calculate the slope of the other two coordinates using

m = (y2 - y1)/(x2 - x1)^2

Substitute the known values in the above equation

m = (y + 4)/x

Equate both slope equations

(y + 4)/x = (7 - 5)/(3 + 3)

Simplify the fraction

(y + 4)/x = 1/3

Cross multiply

x = 3y + 12

Let y = -2

So, we have:

x = 3 *-2 + 12

Evaluate

x = 6

Substitute x = 6 and y = -2 in (x, y)

This gives (6, -2)

Hence, the coordinates of the fourth vertex are (6, -2)

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Answer:

a  =   1.5 in.

Step-by-step explanation:

Use the Pythagoras Theorem:

1.7^2 = a^2 + 0.8^2

a^2 = 1.7^2 - 0.8^2

      = 2.25

a  =   1.5 in.

Answer:

a = 1.5 in.

Explanation:

Using Pythagoras theorem:

a² + b² = c²

insert values

a² + 0.8² = 1.7²

a² = 1.7² - 0.8²

a² = 2.89 - 0.64

a² = 2.25

a = √2.25

a = 1.5

Answer: Option (4)

Step-by-step explanation:

From the diagram, we know that

[tex]\sin 60^{\circ}=\frac{BC}{15}\\\\\cos 60^{\circ}=\frac{AB}{15}[/tex]

This means we can eliminate options 1 and 2.

Now, if we multiply both sides by 15, we get

[tex]15\cos 60^{\circ}=7.5[/tex].

This gives us Option (4).

Answer:

Step-by-step explanation:

already

The information about the coordinate plane shows that the slope of XV is 1.

From the information, the slopes of the diagonals are negative reciprocals. Therefore, the slope of UW is -1 and the slope of XV is 1.

The diagonals of kite UVWX are perpendicular.

It should be noted that negative reciprocals in a kite create a perpendicular bisector. So the two lines share a midpoint so they are perpendicular.

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Answer:

Step-by-step explanation:

The slope of XV is

1

The slope of UW is

–1

The slopes of the diagonals are

negative reciprocals

The diagonals of kite UVWX are

perpendicular

.

Step-by-step explanation:

Let the number of stamps of John be x.

Then number of Minghua's stamps:

John's: x

Minghua's: (3/2)x

Answer: 6.5

Step-by-step explanation:

Since all squares are rhombi, and diagonals of a rhombus intersect at right angles, this means that

[tex]13x+5.5=90\\\\13x=84.5\\\\x=6.5[/tex]

The probability of randomly getting a red or green counter is:

P = 39%/100% = 0.39

We know that 40% of the counters are red or white. Then 60% of the counters are blue or green.

Now we know that the ratio of red to white is 3:5

Then the percentage of red counters is:

(3/8)*40% = 15%

And the ratio of blue to green is 3:2

Then the percentage of red counters is:

(2/5)*60% = 24%

Then the percentage of counters that are either red or green is:

15% + 24% = 39%

Then the probability of randomly getting a red or green counter is:

P = 39%/100% = 0.39

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Answer:

No

Step-by-step explanation:

So to determine whether this is a function, we first need to know what a function is. A function is defined as for each input, there is only 1 output.

This output doesn't have to be unique and other inputs can output this output, but it only matters that each input outputs only one output.

So let's look at what you provided and specifically these two points:

(3, 5)

(3, -3)

This input 3, outputs 5 and -3, which is not a function since this input outputted 2 different outputs. One thing to note is had you provided the two points: (3, 5), (3, 5) instead then it would still be a function because the input outputted the same output of 5 both times.

The standard deviation is approximately 0.01307. See the explanation below.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.

Step 1: First, lets calculate the variance.

The formula for variance is:

[tex]\sigma^2 = \frac{\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]

To get the variance ( s2 ) we must first get the mean. Our mean is 0.99892.

We subtract each value by the mean and square the difference.

(0.978-0.99892)² = 0.0004376464

(0.982-0.99892)² = 0.0002862864

(0.983-0.99892)² = 0.0002534464

(0.984-0.99892)² = 0.0002226064

(0.987-0.99892)² = 0.0001420864

(0.988-0.99892)² = 0.0001192464

(0.989-0.99892)² = 9.84064e-05

(0.99-0.99892)² = 7.95664e-05

(0.992-0.99892)² = 4.78864e-05

(0.992-0.99892)² = 4.78864e-05

(0.993-0.99892)² = 3.50464e-05

(0.994-0.99892)² = 2.42064e-05

(0.996-0.99892)² = 8.5264e-06

(0.997-0.99892)² = 3.6864e-06

(1-0.99892)² = 1.1664e-06

(1.001-0.99892)² = 4.3264e-06

(1.006-0.99892)² = 5.01264e-05

(1.007-0.99892)² = 6.52864e-05

(1.011-0.99892)² = 0.0001459264

(1.015-0.99892)² = 0.0002585664

(1.015-0.99892)² = 0.0002585664

(1.015-0.99892)² = 0.0002585664

(1.018-0.99892)² = 0.0003640464

(1.02-0.99892)² = 0.0004443664

(1.02-0.99892)² = 0.0004443664.

Step 2: Add all these numbers above

0.0004376464+0.0002862864+0.0002534464+0.0002226064+0.0001420864+0.0001192464+9.84064e-05+7.95664e-05+4.78864e-05+4.78864e-05+3.50464e-05+2.42064e-05+8.5264e-06+3.6864e-06+1.1664e-06+4.3264e-06+5.01264e-05+6.52864e-05+0.0001459264+0.0002585664+0.0002585664+0.0002585664+0.0003640464+0.0004443664+0.0004443664

=0.00410184

Step 3: Now we divide the sum by how many numbers there are. In this case we have 25.

We'll call this number n.

So n=25

For a sample (use 0.00410184 divided by (n-1) ):

So s2 =0.00410184 divided by 24

s2 = 0.00017091

Step 4 - Solve for Standard deviation:

The standard deviation is the square root of the variance. Our variance is 0.00017091.

So we only apply a square root on the variance.

= √ 0.00017091

s = 0.0130732551

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Full Question:

A statistical process control monitoring system samples the inside diameter of ball bearing every hour. Measurements were taken every hour for 25 hours. The target thickness, T, is the average.

0.992 1.015 0.988 0.996 1.015 1.000 0.989 0.994 1.018 0.997 1.020 1.007 1.006 0.982 1.001 0.992 1.020 0.993 0.978 0.984 0.990 1.015 0.983 1.011 0.987

What is the population standard deviation, σ?

Answer:

  r = 5

Step-by-step explanation:

Solving radical equations often results in extraneous solutions. These can be avoided by using a graphing calculator for the solution.

The attached shows that the value of r that makes both sides of the equation have the same value is r = 5.

Check:

  √(5·5 -9) -3 = √(5 +4) -2   ⇒   4 -3 = 3 -2 . . . true

Solution of an equation like this is typically done by isolating the radical expressions, then squaring the equation.

We can add 3, square the equation, then isolate the radical and square again:

  [tex]\displaysyle \sqrt{5r-9}-3=\sqrt{r+4}-2\\\\\sqrt{5r-9}=\sqrt{r+4}+1\qquad\text{add 3}\\\\5r-9=(r+4)+2\sqrt{r+4}+1\qquad\text{square both sides}\\\\(4r-14)^2=4(r+4)\qquad\text{subtract $(r+5)$ and square again}\\\\16r^2-116r+180=0\qquad\text{rewrite in standard form}\\\\4(4r -9)(r -5) = 0\qquad\text{factor}\\\\r=\{\dfrac{9}{4},\ 5\}\qquad\text{solutions to the factored form}[/tex]

Trying these values in the original equation, we get ...

  √((5(9/4) -9) -3 = √(9/4 +4) -2   ⇒   1.5 -3 = 2.5 -2 . . . . . false

  √(5(5) -9) -3 = √(5 +4) -2   ⇒   4 -3 = 3 -2 . . . . . true

The solution is r = 5.

Answer:

Step-by-step explanation:

Elasticity Demand

(Q1 - Q2)/(Q1 + Q2)

(P1 - P2)/(P1 + P2)

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