Which of the following statements about a variable are true?

A variable cannot be subtracted.
A variable is represented by a letter.
A variable represents a quantity.
A variable cannot be multiplied.

Answer:

The initial temperature was To = -14 degrees

Step-by-step explanation:

Solution:-

- We will take the starting temperature to be = Ti

- The final temperature, Tc = 16 degrees

- We are given that there is a drop of 10 degrees from initial temperature To. We can mathematically express this as:

                                 To - 10

- Then there is a rise of 40 degrees after the drop of 10 degrees. The mathematical expression would be:

                                 To - 10 + 40

- The current temperature is Tc. We can equate the expression developed to final temperature:

                                 To - 10 + 40 = Tc

- Solve for To:

                                 To = 16 - 40 + 10

                                 To = -14 degrees

Answer:

-14 degrees

Step-by-step explanation:

In this question, we are asked to calculate the starting temperature if we know what the temperature is now and the kind of temperature change that has happened.

Now, since we do not know the initial temperature , let’s call it x

from the question, it dropped by 10 and increased by 40 and finally with a temperature of 16.

mathematically

x-10+40= 16

x+30 = 16

x = 16-30

x = -14

Answer: $43.28

Step-by-step explanation: To find the sales tax, first convert 8.25% to a decimal. 8.25% as a decimal is 0.0825.

Now simply multiply 0.0825 x 39.98 which equals about 3.30

So, the total sales tax is $3.30

Now add $3.30 to $39.98 which equals a total cost of $43.28

Answer:25

Step-by-step explanation:

15x 2/5=25

Answer:

$37.50

Step-by-step explanation:

[tex]\frac{2}{5}[/tex] of Aiden's money is $15. Half of [tex]\frac{2}{5}[/tex] is [tex]\frac{1}{5}[/tex], so you have to find half of $15 to find out what [tex]\frac{1}{5}[/tex] of Aiden's money is.

15/2 = 7.5. [tex]\frac{1}{5}[/tex] of Aiden's money is $7.50.

7.5 × 5 = 37.5, so Aiden had $37.50 before he put some into his piggy bank.

Answer:

P = 54 so

arc AC = 150

Step-by-step explanation:

The measure of AC on circle P in degrees is 118degrees

To get the measure of the arc AC on the circle, we will use the formula for calculating the angle at a point.

The sum of the angle at a point is 360 degrees, hence:

arc AB + arcBC + arcCD + arc DE + arcEA = 360

If ∠APE and ∠EPD are congruent, this means that arc DE = arcEA. The equation becomes:

arc AB + arcBC + arcCD + arc DE + arcDE = 360

Substitute the given angles into the expression:

arc AB + arcBC + arcCD +2arcDE = 360

126 + 74 + 42 + 2arcDE = 360

242  + 2arcDE = 360

2arcDE = 360 - 242

2arcDE = 118

arcDE = 118/2

arcDE = 59

arcAC = 2(arcDE)

arcAC = 2(59)

arcAC = 118 degrees

Hence the measure of AC on circle P in degrees is 118degrees

Learn more here: https://brainly.com/question/24356953

Answer:

[tex]Q(t) =[/tex] [tex]100(2)^t[/tex]

Step-by-step explanation:

please see the attached files for more details

Answer: Option 'B' and 'D' are correct.

Step-by-step explanation:

Since we have given that

Let the age of Lilian be 'x'

Let the age of Kylie be 'x+3'.

Let the age of Joan be 'x+3-2=x+1'.

So, According to question, we get :

Total sum of all three birthday celebrants today would be

[tex]x+x+3+x+1=3x+4[/tex]

If we put 52, we get that

[tex]3x+4=52\\\\3x=52-4\\\\3x=48\\\\x=\dfrac{48}{3}=16[/tex]

If we put 55, we get that

[tex]3x+4=55\\\\3x=55-4\\\\3x=51\\\\x=\dfrac{51}{3}\\\\x=17[/tex]

Hence, Option 'B' and 'D' are correct.

Using algebra, we express each person's age in variables, create a relationship between them, and find that the only option that can represent their combined age as a sum of 3L + 4 is 52. Therefore, option B is the correct answer.

To solve this problem, we can begin by assigning variables to each person's age and then creating equations based on the information provided. Let's let the variable L represent Lillian's age, K represent Kylie's age, and J represent Joan's age.

From the problem, we know that:

Joan is 2 years younger than Kylie: J = K - 2

Kylie is 3 years older than Lillian: K = L + 3

Now, using the second equation, we can express Joan's age in terms of Lillian's:

Substitute the value of K from the second equation into the first: J = (L + 3) - 2

This simplifies to: J = L + 1

Now we can express the combined age of Joan, Kylie, and Lillian:

Combined age: J + K + L

Substitute J and K with the expressions in terms of L: (L + 1) + (L + 3) + L

Add them: 3L + 4

Now, we have to check which option is divisible by 3 when 4 is subtracted from it because the combined age should be in the form 3L + 4. Among the options given:

A. 51 - 4 = 47 (Not divisible by 3)

B. 52 - 4 = 48 (Divisible by 3)

C. 53 - 4 = 49 (Not divisible by 3)

D. 54 - 4 = 50 (Not divisible by 3)

E. 55 - 4 = 51 (Not divisible by 3)

The correct answer is option B, which makes the combined age of Joan, Kylie, and Lillian equal to 52 years.

Answer:

Other numerator.

Answer:

multipy the numerator by the other numerator

Narancia out~!

Answer:

The answer is 1,275,120

Step-by-step explanation:

The goal of this is to determine the number of strings of strings of six lowercase letters from the English alphabet that contain the letters a and b in positions consecutive with a preceding b, with all the letters distinct.

Now,

As the letters  a and b are consecutive, the possible string outcomes are in this form:

ab_ _ _ _

_ab_ _ _

_ _ab_ _

_ _ _ ab_

_ _ _ _ ab

As seen here, ab can denoted in five locations as in C (5, 1) = 5 ways

we use the permutation for the order of the letters to be needed.

so,

n= 24, r =4

p (24, 4) = 24ǃ /( 24 - 4)ǃ

= 24ǃ /20ǃ

=255,024

Now, the number of possible strings is 5* 255.024 = 1,275,120.

In conclusion there are 1,275,120 number of strings of six lowercase letters from the English alphabet contain the letters a and b in consecutive positions with a preceding b, with all the letters distinct.

Answer:

Step-by-step explanation:

25

Answer:

27             X

__    =      __

40           100

cross multiply divide. meaning 27*100 = 40*X. -> 2700 = 40*X. also meaning the answer is 2700 divided by 40 = X.

plug 2700/40 into a calculator. answer 67.5%

Step-by-step explanation:

We have to find the percent of change :

50 pounds to 35 pounds

Original amount = 50 pound

New amount= 35 pounds

Since, New amount is less than the original amount,

this is a percentage of decrease.

Change in amount =35 -50  = -15 pound

percentage change= change of amount/original amount x 100

substitute the given values we have:

percentage change= -15/50 x 100

simplify:

percentage change= -30%

Therefore the decrease is 30%

Brainliest????

Answer:

V = 11 times 9 times 7

Step-by-step explanation:

To answer this question, a dimensional analysis must be done.

The volume has cube length as a unit, that is, l ^ 3

We analyze each option

V = base * height * height

ignoring what each one means, we know that each one is measured in length therefore:

V = L * L * L = L ^ 3 that is to say that in this way the volume can be found.

The other way is:

V = base + height + height

If we replace, we have to:

V = L + L + L = L, and the volume does not have units of length, therefore this option is not viable.

Which means that the option of V = 11 times 9 times 7 is correct.

I must mention, that the true way to calculate the volume in this case would be:

V = Base area * height

V = (base + height / 2) * height

Answer:

  see below

Step-by-step explanation:

The angle where chords cross is the average of the intercepted arcs. Here, that is ...

  (37° +46°)/2 = (83°)/2 = 41.5°

Angle SUT is 41.5°.

_____

Comment on the error

The measure of an arc cannot be arbitrarily said to be the same as the angle where the chords cross. It will be the same if (a) the chords cross at the circle center, or (b) the opposite intercepted arc has the same measure. Neither of these conditions hold here.

Answer:

1) A

2) 41.5°

Step-by-step explanation:

SUT would have been 46° if U was the centre

Angle SUT = (37+46)/2

= 83/2

= 41.5

Answer:

Jackie is incorrect. Since 2 pints equal 1 quart, she would need to multiply 12 by 2 to get the correct answer of 24 pints.

Answer:

2 5/18

Step-by-step explanation:

multiply across.

Answer:

improper fraction is 77/18 mixed number form 4 5/18 decimal form 4.27 thank me later

Step-by-step explanation:

Answer:

  $18,200

Step-by-step explanation:

We want ...

  f(x) = g(x)

  53 +.105x = 235 +.095x . . . . use given expressions

  .01x = 182 . . . . . . .  subtract 53+.095x

  x = 182/.01 = 18200 . . . . . divide by the coefficient of x

Each must sell $18,200 for their weekly pay to be the same.

Answer:

237 centimeters

Step-by-step explanation:

A foot = 30 centimeters

We know 1 meter or 1m is equivalent to around 3 feet. The exact measurement of a meter is 3.28 feet. So 1m = 100 centimeters because one foot equals 30 centimeters. .28 of a foot is 10 cm.

2 meter = 200 cm

.37 = 37 centimeters because each 0.01 in a meter = 1 cm. And there are 100 cm in a meter so we can accurately say 2.37 meters are 237 cm.

P.S

Have an Amazing Day! I Hope This Helps and Good Luck!

-Faker/Tosrel

Answer:

3 cans

Step-by-step explanation:

We need to find the area of the deck

A = 9 1/9 * 3

Changing to an improper fraction

9 1/9 = (9*9+1)/9 = 82/9

A = 82/9 *3 = 82/3

Changing back to  a mixed number

82/3 = 27  1/3

Each can covers 10 m^2

We will need 3 cans

Answer:

3 cans

Step-by-step explanation:

3*9 1/9=27.3 meters^2

the closest  number of cans for 27.3 meters^2 is 3 because

1 can=10 meters^2

2 cans=20 meters^2

3 cans=30 meters^2

so by estimating 3 cans would be the closest compared to 20 and 10.

Answer:

It is c

Step-by-step explanation:

Answer:

Total cost of t-shirts = $393

Step-by-step explanation:

A company charges a fixed rate of $8 for the printing of pattern on the whole order of t-shirts.

It also charges a variable rate of $11 for each t-shirt.

So the equation for the total cost of the t-shirts becomes,

Total cost of t-shirts = $8 + $11n

Where n is the number of t-shirts.

We are given n = 35 t-shirts

So the total cost of t-shirts are,

Total cost of t-shirts = $8 + $11(35)

Total cost of t-shirts = $8 + $385

Total cost of t-shirts = $393

You will need 592 square inches of cardboard to build the box.

To determine how much cardboard is needed to build the box, we calculate the surface area of the box.

The box has six faces: two of each dimension.

Calculating the area of each pair of faces:

Two faces of (12 in x 8 in):

2 x (12 x 8) = 2 x 96 = 192 square inches

Two faces of (12 in x 10 in):

2 x (12 x 10) = 2 x 120 = 240 square inches

Two faces of (8 in x 10 in):

2 x (8 x 10) = 2 x 80 = 160 square inches

Sum the areas of all faces:

192 + 240 + 160 = 592 square inches

Answer:

The maximum dimension for box will be side length as 26.667 inches and height will be 6.667 inches and volume will be 4741 cu inches.

Step-by-step explanation:

Given:

With dimensions as

40x40 square and sides are folded in square corners.

To Find:

Maximum volume that will yield and maximum dimension for box

Solution:

Consider, a box with 40 x 40 dimensions as follows and

let a x side length square corners are cut and folded up and a new figure is formed .and for that what will be the maximum volume and dimension.

Now,

as the there 2 corner for each side i.e. 2 square on side length

Resultant length will be 40-2x

So volume is given by ,

[tex]V=l^2*h[/tex]

[tex]=(40-2x)^2*x[/tex]

[tex]V=(40^2-2*2x*40+4x^2)*x[/tex]

[tex]V=(1600-160x+4x^2)*x[/tex]

[tex]V=4x^3-160x^2+1600x[/tex]

To get Maximum volume differentiate w.r.t 'x'

[tex]V'=12x^2-320x+1600[/tex]

[tex]V"=24x-320[/tex]

Now solve for x with help of quadratic equation we get ,

12x^2-320x+1600

=4(3x-20)(x-20)

Therefore ,

3x-20=0 or x-20=0

x=20/3 or x=20

x=16.666 or x=20

Now use this values in a 2nd derivative equation,

V"=24(6.667)-320)

V"=160-320

V"=-160 <0 ,................equation(1)[Here maximum volume will be presented]

For X=20

V"=24*20-320

V"=480-320

=160>0 ..................Equation(2)[here minimum volume will presented]

Comparing equation 1 and 2 we get ,

Take as x=20/3 as the folded square length as it is gives minimum value for 2nd derivative.

So

[tex]V=(40-2x)^2*x[/tex]

[tex]V=[40-2(20/3)]^2*20/3[/tex]

[tex]V=[40-40/3]^2*6.667[/tex]

=[tex][26.667]^2*6.667[/tex]

=4740.95

=[tex]4741 cu inches.[/tex]

So side lengths =40-2x=40-2*20/3

=40(1-1/3)

=40(2/3)

=26.667 inches

And the height will be x=20/3=6.667 inches.

Answer:

71.75 milliroentgens per hour

Step-by-step explanation:

The  intensity(I) of Radiation varies inversely as the square of the distance (D) from the machine.

This is written as:

[tex]I \propto \frac{1}{D^2} \\$Introducing the constant of Variation k$\\I = \frac{k}{D^2} \\$When D=3 meters, I=62.5 milliroentgens per hour$\\62.5= \frac{k}{3^2}\\k=62.5 X 9 =562.5\\$Substituting K=562.5 into the variation equation$\\I = \dfrac{562.5}{D^2} \\$Therefore, When D=2.8 meters$\\Intensity,I = \dfrac{562.5}{2.8^2}=$71.75 milliroentgens per hour$[/tex]

Answer: The correct answer is option B: There are between 15 and 20 green pieces in all 5 packages

Step-by-step explanation: The most important factor has been given which is, "Which statement about the candy pieces in the remaining packages is best supported by this information."

The information given is such that, the first package she opened had 4 green pieces and on this basis we can safely assume that all other packages have 4 green pieces as well. The second package had 3 green pieces and this based on this too we can safely assume that all other packages had 3 green pieces. Hence, all 5 packages can either have a total of 4 x 5 green candies which equals a total of 20 green pieces or, all 5 packages can have a total of 3 x 5 green candies which equals a total of 15 green pieces.

So according to Suzi's experiment, there are between 15 and 20 green pieces in all 5 packages.

Answer:

1,404,928 is the volume of a cube with a side length that measures 112 ft

Answer:

1,404,928 is the volume

each person has about 19 each

all you have to do is 49-2=38

38 divided by 2 = 19

Horatio has 30 video games and Preston has 19

Set up an equation:

x = Games horatio has

Since theres two people we will give x the coefficient of 2

You get 11 from how much more horatio has

49 is the total

The Equation

49 = 2x + 11

Solve

49 = 2x + 11

-11        - 11

38 = 2x

19 = x

Preston has 19 video games and since horatio has 11 more horatio has 30 video games

Answer:

p = 0.52392

Step-by-step explanation:

Here we have

p = 23% = 0.23

[tex]\hat p[/tex] = 208/800 = 0.26

n = 800

q = 1-p = 0.77

α = 5% = 0.05

Here we have

Z test given by

[tex]z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}[/tex]

From which we have

From the Cpdf we have Probability = 0.0219, z = 2.016

Therefore from the z score = 0.0683, p = 0.52392 from z table.

Answer:

K = 51

Step-by-step explanation:

Since the triangles are similar, the angles are the same measure.

<K = <F

We can find angle F since the angles of a triangle add to 180

D + G + F = 180

59+70 +F = 180

Combine like terms

129+F = 180

Subtract 129 from each side

129-129+F = 180-129

F = 51

K = F = 51

Answer:

51°

Step-by-step explanation:

Angle K corresponds to Angle F

Angle F = 180 - 70 - 59

Angle F = 51°

Answer:

25

Step-by-step explanation:

5^2

This means multiply 5 two times

5*5

25

Answer:

5

Step-by-step explanation:

You see if A is a scale representation of B then 2cm rep 5cm.

thereby, We can say that 1cm rep 2.5cm in the scale.

1cm rep 2.4cm

=12.5cm

12.5 ×1\2.4 =5cm

x=5cm

Answer: A

Step-by-step explanation:

We need to get the denominators to be same first before we can do anything to the numerator.

The LCD (lowest common denominator) is [tex]3x^{3}[/tex]. To find the LCD, multiply the denominators together: [tex]x^{3}[/tex] · [tex]3x[/tex] = [tex]3x^{3[/tex].

Below, we are trying to get the denominators to equal the same or to [tex]3x^{3}[/tex].

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

[tex]\frac{12}{3x^{3} } - \frac{2x^{3}-x^{2} }{3x^{3} }[/tex]

Now that the denominators are the same, we can subtract the numerators from each other.

[tex]\frac{ 12 - (2x^{3} -x^{2})\\}{3x^{3} } \\[/tex]

[tex]\frac{12-2x^{3} +x^{2} }{3x^{3} }[/tex]

Now, we can just reorganize the variables.

Answer:  A or [tex]\frac{-2x^{3} + x^{2}+12 }{3x^{3} }[/tex]