The scale on a scale drawing is 1 : 30. What should you do with each measurement on the drawing to get the actual dimensions? Provide an example of a drawing that uses this scale. Include both the original and new dimensions.

Answer:

c = 468 / 13

Step-by-step explanation:

If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.

Answer:

468/13 = c

Step-by-step explanation: Further explanation :

[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]

Answer:

-9

Step-by-step explanation:

4 + (-13)

=> 4 - 13

=> -9

Answer:

Step-by-step explanation:

Equation of a circle is given by

( x - h)² + ( y - k)² = r²

where r is the radius and

( h , k) is the center of the circle

From the question the radius R = 1/3

the center ( h ,k ) = (4/3 , -8/3)

Substituting the values into the above equation

We have

[tex](x - \frac{4}{3} )^{2} + {(y - - \frac{8}{3}) }^{2} = ({ \frac{1}{3} })^{2} [/tex]

We have the final answer as

[tex](x - \frac{4}{3} )^{2} + {(y + \frac{8}{3}) }^{2} = \frac{1}{9} [/tex]

Hope this helps you

Answer:

-3

Step-by-step explanation:

Since you are subtracting a negative, it turns positive so it will be.

-4+1

-3

Answer:

-3

Step-by-step explanation:

-4-(-1) = -4 + 1 = -3

Answer: a. $40,800 b. 36

Step-by-step explanation:

Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].

[tex]\sigma= \$14,900[/tex]

a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.

Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]

= 40,800

hence, the point estimate of the mean salary for all college graduates in this town = $40,800

b.  Since  lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.

Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]

Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.

z-value for 99% confidence level  = 2.576

So,

[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]

The sample size used for the analysis =36

Answer:

[tex]p(x)[/tex] and [tex]q(x)[/tex] have the same domain and the same range.

Step-by-step explanation:

[tex]p(x) = 6-x[/tex] and

[tex]q(x) = 6x[/tex]

First of all, let us have a look at the definition of domain and range.

Domain of a function [tex]y =f(x)[/tex] is the set of input value i.e. the value of [tex]x[/tex] for which the function [tex]f(x)[/tex] is defined.

Range of a function [tex]y =f(x)[/tex] is the set of output value i.e. the value of [tex]y[/tex] or [tex]f(x)[/tex] for the values of [tex]x[/tex] in the domain.

Now, let us consider the given functions one by one:

[tex]p(x) = 6-x[/tex]

Let us sketch the graph of given function.

Please find attached graph.

There are no values of [tex]x[/tex] for which p(x) is not defined so domain is All real numbers.

So, domain is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]

Its range is also All Real Numbers

So, Range is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]

[tex]q(x) = 6x[/tex]

Let us sketch the graph of given function.

Please find attached graph.

There are no values of [tex]x[/tex] for which [tex]q(x)[/tex] is not defined so domain is All real numbers.

So, domain is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]

Its range is also All Real Numbers

So, Range is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]

Hence, the correct answer is:

[tex]p(x)[/tex] and [tex]q(x)[/tex] have the same domain and the same range.

Answer:

q =  5000/x  + 6

Step-by-step explanation:

D´= dq/dx  =  - 5000/x²

dq = -( 5000/x²)*dx

Integrating on both sides of the equation we get:

q = -5000*∫ 1/x²) *dx

q = 5000/x + K   in this equation x is the price per unit and q demanded quantity and K integration constant

If when  1006 units are demanded when the rice is 5 then

x = 5     and   q = 1006

1006  =  5000/5 +K

1006 - 1000 = K

K = 6

Then the demand function is:

q =  5000/x  + 6

Answer:

I found the answer on Yahoo

Step-by-step explanation:

P[rains in spain] = 1/9

P[hurricane in hartford & rain in spain] = 0.03*1/9 = A

P[hurricane in hartford & no rain in spain] = 0.02*8/9

P[hurricane in hartford] = 0.03*1/9 + 0.02*8/9 = 0.19/9 = B

P[rain in spain | hurricane in hartford] = A/B = 3/19 <---------

Answer:

A

Step-by-step explanation:

In the second step, they added 5 to both sides to get rid of the -5 on the left side. Since the same thing was done to both sides (addition), the answer is the addition property of equality.

Answer:

Addition property of equality

Step-by-step explanation:

The equation is like:

=> x - 5 = -14

=> x - 5 + 5 = -14 + 5

=> x = -9

Since, we add 5 to both sides to solve for "x", the answer is "Addition Property of Equality".

Hope this helps.

Answer:

[tex]\frac{2}{5}[/tex] • [tex]\frac{3}{7}[/tex] = [tex]\frac{6}{35}[/tex]

Answer: 0.171

Step-by-step explanation:

First, do 2/5 which would equal 0.4

Second, so 3/7 which would equal 0.428571428571429

Lastly multiply the two answers together to get 0.171428571428571

Answer:

-2 degrees

Step-by-step explanation:

Our original temperature is 15. We're asked to find the temperature at 11:00 P.M., which is 17 less than 15. We can set up the equation 15 - 17 to get -2. This is your answer.

Answer:

The temperature was -2 degrees  Fahrenheit

Step-by-step explanation:

The starting temperature was 15 degrees

It fell 17 degrees

15 -17 = -2

The temperature was -2 degrees  Fahrenheit

Answer:

yes

Step-by-step explanation:

every negative any positive number is an integer

Answer:

Step-by-step explanation:

No.  Integers do not have fractions in them.

-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer

Answer:

Width: 32 inches.

Length: 64 inches.

Step-by-step explanation:

Let's say that the width of the rectangle is x inches, so the length is 2x inches.

If 2x + 4 and x - 1, the perimeter is 198 inches. That means that two times the width plus two times the length is 198 inches.

2(2x + 4) + 2(x - 1) = 198

4x + 8 + 2x - 2 = 198

6x + 6 = 198

x + 1 = 33

x = 32.

That means that the width of the original rectangle is 32 inches, and the length is 32 * 2 = 64 inches.

Hope this helps!

Answer:

[tex]B' = (-96,-24)[/tex]

Step-by-step explanation:

Given

[tex]A(0,6)[/tex]

[tex]B(-8,-2)[/tex]

[tex]C(8,-2)[/tex]

Required

Determine the coordinates of B' if dilated by a scale factor of 12

The new coordinates of a dilated coordinates can be calculated using the following formula;

New Coordinates = Old Coordinates * Scale Factor

So;

[tex]B' = B * 12[/tex]

Substitute (-8,-2) for B

[tex]B' = (-8,-2) * 12[/tex]

Open Bracket

[tex]B' = (-8 * 12,-2 * 12)[/tex]

[tex]B' = (-96,-24)[/tex]

Hence the coordinates of B' is [tex]B' = (-96,-24)[/tex]

Answer:

Bit late but the answer is (-4,-1)

Step-by-step explanation:

Took the test in k12

Answer:

exact form: x=-56/3

mixed number form: -18 2/3

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

b . sphere

Step-by-step explanation:

Answer:

40.63

Step-by-step explanation:

31.25+9.38= 40.63

Hope this helps

Answer: 40.63

Look at the image for shown work.

Answer:

1, 7

Step-by-step explanation:

Because the product is 0, either (x-1) or (x-7) is equal to 0. That means that x = 1, or 7

Answer: There are 15 friends.

Step-by-step explanation:

We know that there is N friends (N is the number that we are looking for)

Each friend weights 1/20 ton.

Now, the weight of the N friends together is N times 1/20 ton.

Then we have:

N*(1/20) ton = 3/4 ton

We solve this for N.

First multiply both sides by 20.

20*N*(1/20) = N = 20*(3/4) = 60/4 = 15

Answer:

I can find the total number of people by dividing the total weight by the weight of one person.

Step-by-step explanation:

Answer:

Step-by-step explanation:

if we shift 13 units right and 6 units down we get the reqd. graph.

Answer:

see explanation

Step-by-step explanation:

Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)

• If k > 0 then shift left by k units

• If k < 0 then shift right by k units

Thus y = (x - 13)² represents a shift to the right of 13 units

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Thus

y = (x - 13)² + 6 is the graph of y = x² translated 13 units right and 6 units up

Answer:

Three

Step-by-step explanation:

Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores

The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.

Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:

(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)

This is the vector equation; getting the parametric form is just a matter of delineating

x(t) = 1 + t

y(t) = 3t

z(t) = 6 + t

The vector equation for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5 is v =(1+t)i + (3t)j + (6+t)k

The parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5

The parametric equation of a line through the point A(x, y, z) perpendicular to the plane ax+by+cz= d is expressed generally as:

A + vt where:

A = (x, y, z)

v = (a, b, c) (normal vector)

This can then be expressed as:

s = A + vt

s = (x, y, z) + (a, b, c)t

Given the point

(x, y, z) = (1,0,6)

(a, b, c) = (1, 3, 1)

Substitute the given coordinate into the equation above:

s = (1,0,6) + (1, 3, 1)t

s = (1+t) + (0+3t) + (6+t)

The parametric equations from the equation above are:

x(t) = 1+t

y(t) = 3t

z(t) = 6+t

The vector equation will be expressed as v = xi + yj + zk

v =(1+t)i + (3t)j + (6+t)k

Learn more here: brainly.com/question/12850672

Answer:

Option (2)

Step-by-step explanation:

If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.

By using this property,

Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.

By applying Pythagoras theorem in right triangle KNJ,

(KJ)² = (KN)² + (NJ)²

(33)² = (6√10)² + (NJ)²

NJ = [tex]\sqrt{1089-360}[/tex]

NJ = [tex]\sqrt{729}[/tex]

    = 27 units

Since, GJ = 2(NJ)

GJ = 2 × 27

GJ = 54 units

Option (2) will be the answer.

Answer:

256 outcomes.

Step-by-step explanation:

Each time you flip the coin you have two possible outcomes, it can either come up with heads or tails.

You're going to flip the coin eight times so the first time you can have 2 possible outcomes, the second time you have 2 possible outcomes, the third time you have 2 possible outcomes, etc.

Since you are going to do this eight times you are going to multiply each of the outcomes, so you will have:

Possible outcomes = 2×2×2×2×2×2×2×2= 256

Thus, there are 256 different outcomes in total.

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▹ Answer

x = 5

▹ Step-by-Step Explanation

The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.

Hope this helps!

CloutAnswers ❁

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Answer:

The x value is 5

Step-by-step explanation:

The x value is the value going across

Starting where the two axis meet, we go 5 units to the right

That is the x value

Answer:

Thus percentile lies between 53.3% and 55.6 %

Step-by-step explanation:

First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N

where n is the ordinal rank of the given value

N is the number of values in ascending order.

The data in ascending order is

0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3

1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5

Number of observation = 45

4.9 lies between 3.3 and 5.5

x*n = 24 observation x*n = 25 observation

x*45= 24 x*45= 25

x= 0.533 x= 0.556

Thus percentile lies between 53.3% and 55.6 %

Answer:

B) 5

Step-by-step explanation:

Proportions:

8 ⇒ 10

20 ⇒ 5x

5x = 20*10/8

5x = 25

x = 25/5

x = 5

Answer:

The bearing is N 55.62° W

Step-by-step explanation:

ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots.

It then turns 90° towards the south after one hour.

Still maintain the same speed and direction for two hours.

The bearing is just the angle difference from the ship current location to where it started.

Let the speed be km/h

Distance covered in the first round

= 15*1

= 15km

Distance covered in the second round

=15*2

= 30 km

Angle at C = (90-80)+90

Angle at C = 10+90= 100

Let the distance between the port and the ship be c

C²= a² + b² -2abcos

C²= 15²+30²-2(15)(30)cos 100

C²= 225+900+156.28

C²= 1281.28

C= 35.8 km

Using sine formula

30/sin x= 35.8/sin 100

30/35.8 * sin 100 = sinx

0.838*0.9848= sin x

0.8253= sin x

Sin ^-1 0.8253 = x

55.62° = x

The bearing is N 55.62° W

Answer:

  6

Step-by-step explanation:

Jana had a total of 3+3+3+3 = 12 muffins. Half that number is 3+3 = 6 muffins.

Jana put 6 muffins on the plate.