The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month). Water costs 0.20 dollars per liter.

[tex]x+y=12\\\dfrac{x}{y+3}=\dfrac{1}{2}\\\\x=12-y\\2x=y+3\\\\2(12-y)=y+3\\24-2y=y+3\\3y=21\\y=7\\\\x=12-7=5\\\\\dfrac{x}{y}=\dfrac{5}{7}[/tex]

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Work Shown:

3 & 1/2 = 3 + 1/2 = 3 + 0.5 = 3.5

3.5% = 3.5/100 = 0.035

r = 0.035 is the decimal form of [tex]3\frac{1}{2}\%[/tex] which is used along with

to get the following

A = P*(1+r/n)^(nt)

A = 500*(1+0.035/12)^(12*0.5)

A = 508.81405074594

A = 508.81

Extra info: Gabe earned A-P = 508.81 - 500 = 8.81 dollars in interest.

Answer:

Option (B)

Step-by-step explanation:

From the figure attached,

ΔABC is a right triangle.

Cosine and Sine ratios from the given triangle will be,

SinA = [tex]\frac{\text{Opposite side}}{Hypotenuse}[/tex]

        = [tex]\frac{a}{c}[/tex]

CosB = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{a}{c}[/tex]

Therefore, both the ratios (Sine and Cosine) will be equal as [tex]\frac{a}{c}[/tex]

Option (B) will be the correct option.

Answer:

Average = 2000

Step-by-step explanation:

Given numbers are:

1,000 2,300 2,600

To find:

First round off the numbers to nearest 1000 and then find Average.

Solution:

1000 is already in thousands so no need to round off.

To round off a number to nearest thousand, we need check the digit on hundred's place.

So, 2300 will be rounded off as 2000.

and 2600 will be rounded off as 3000.

Now, the numbers whose average is to be calculated are 1000, 2000, 3000.

Formula for average is given as:

[tex]Average = \dfrac{\text{Sum of all numbers}}{\text{Count of numbers}}[/tex]

applying the formula:

[tex]Average = \dfrac{1000+2000+3000}{3}\\\Rightarrow Average = \dfrac{6000}{3}\\\Rightarrow \bold{Average = 2000}[/tex]

So, the average after rounding off to nearest 1000 is 2000.

Answer:

15.56

Step-by-step explanation:

Total flour available=35 cups

Each cake=2 1/4 cups

Find how many cakes Pauline can bake with 35 cups of flour

Let the number of cakes she can bake with 35 cups of flour=x

x=35 cups / 2 1/4 cups

=35÷9/4

=35×4/9

=140/9

=15 5/9 cakes

=15.56 cakes approximately

Surface area of sphere is what referred to as Total surface area or lateral surface area because here the surface is curved everywhere.

[tex] \large{ \boxed{ \rm{ \orange{Surface \: area \: of \: sphere = 4\pi {r}^{2} }}}}[/tex]

Total surface area of other 3-D shapes:

Lateral surface area of these shapes:

━━━━━━━━━━━━━━━━━━━━

Answer:

m∠D = 97.34°

Step-by-step explanation:

Concept used"

sum of all angles of Quadrilateral is 360 degrees.

If any Quadrilateral is inscribed in circles then sum of opposite angle of that Quadrilateral is 180 degrees

________________________________________________

Given

Quadrilateral ABCD is inscribed in a circle

thus,

pair of opposite angles will be

m∠A and m∠C

m∠B and m∠D

thus,

m∠B + m∠D = 180

Thus,

m∠A + m∠C = 180

64+  (9x - 1) = 180

9x = 180 - 63 + 1 = 118

x = 118/9 = 13.11

thus, value of

m∠B is (6x + 4)°

m∠B = (6*13.11 + 4)°  = 82.66°

m∠B + m∠D = 180

82.66 + m∠D = 180

m∠D = 180 - 82.66 = 97.34°

Thus,

m∠D is 97.34°

Answer:

Problem 1)  frequency:  160 heartbeats per minute, period= 0.00625 minutes (or 0.375 seconds)

Problem 2) Runner B has the smallest period

Problem 3) The sound propagates faster via a solid than via air, then the sound of the train will arrive faster via the rails.

Step-by-step explanation:

The frequency of the football player is 160 heartbeats per minute.

The period is (using the equation you showed above):

[tex]Period = \frac{1}{frequency} = \frac{1}{160} \,minutes= 0.00625\,\,minutes = 0.375\,\,seconds[/tex]

second problem:

Runner A does 200 loops in 60 minutes so his frequency is:

[tex]\frac{200}{60} = \frac{10}{3} \approx 3.33[/tex]   loops per minute

then the period is: 0.3 minutes (does one loop in 0.3 minutes)

the other runner does 200 loops in 65 minutes, so his frequency is:

[tex]\frac{200}{65} = \frac{40}{13} \approx 3.08[/tex]   loops per minute

then the period is:

[tex]\frac{13}{40} =0.325\,\,\,minutes[/tex]

Therefore runner B has the smaller period

Answer:

x = all real numbers.

Step-by-step explanation:

3 x minus 8 = negative x + 4 (x minus 2)

3x - 8 = -x + 4(x - 2)

3x - 8 = -x + 4x - 8

3x - 8 = 3x - 8

3x - 3x = -8 + 8

0 = 0

Since the result is a true statement, but 0 = 0, x is equivalent to all real numbers.

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

x = -13

Step-by-step explanation:

2x-3x+5=18

Combine like terms

-x +5 = 18

Subtract 5 from each side

-x +5-5 = 18-5

-x = 13

Multiply each side by -1

x = -13

Answer:

[tex]\huge \boxed{{x=-13}}[/tex]

Step-by-step explanation:

[tex]2x-3x+5=18[/tex]

[tex]\sf Combine \ like \ terms.[/tex]

[tex]-1x+5=18[/tex]

[tex]\sf Subtract \ 5 \ from \ both \ sides.[/tex]

[tex]-1x+5-5=18-5[/tex]

[tex]-1x=13[/tex]

[tex]\sf Multiply \ both \ sides \ by \ -1.[/tex]

[tex]-1x \times (-1)=13 \times (-1)[/tex]

[tex]x=-13[/tex]

Answer:

Perimeter = 8x - 12

Step-by-step explanation:

The perimeter of a square is:

p = 4(side length)

on this case:

p = 4(2x-3)

p = 4*2x + 4*-3

p = 8x - 12

Answer:

Step-by-step explanation:

Amount charges by plumber =  £ 167.00

Call out fee = £ 18.50

Charge excluding the call out fee = 167 - 18.50 = £ 148.50

Total hours worked = 9 hours

Charge per hour = charge excluding the call out fee ÷ total hours

                           = 148.50 ÷ 9

                          = £ 16.50

Answer:

The answer is

Step-by-step explanation:

[tex]1 \frac{2}{5} + \frac{3}{4} [/tex]

To solve the question first convert the mixed fraction to an improper fraction

That's

[tex]1 \frac{2}{5} = \frac{7}{5} [/tex]

So we have

[tex] \frac{7}{5} + \frac{3}{4} [/tex]

Find the LCM of the fractions

The LCM of 5 and 4 is 20

That's

[tex] \frac{7}{5} + \frac{3}{4} = \frac{7(4) + 3(5)}{20} = \frac{28 + 15}{20} [/tex]

[tex] = \frac{43}{20} [/tex]

= 2.15

We have the final answer as

Hope this helps you

Answer:

2 pi •10•210

Step-by-step explanation:

Khan academy

Answer:

Option (4)

Step-by-step explanation:

By the theorem of inscribed angles and the intercepted arc,

"In a circle, angles subtended by the same arc always measure the same and the arc measures the double of the inscribed angle."

If an inscribed angle in a circle measures 75° then all inscribed angles by the same arc will measure 75°.

In addition to this, measure of arc subtended by these inscribed angle will measure double of the inscribed angle (150°)

Therefore, Option (4) will be the answer.

Answer:

10.5 pounds of apples

Step-by-step explanation:

4 devided by 14 = 3.5

3.5* 3 = 10.5

Answer:

  This is the other ray that will make up the angle ∠AYZ and will complete the construction.

Step-by-step explanation:

The point of the construction is to copy the angle. That is, the end result must be an angle with identical measure to the original. The construction so far has no angle at Y. Drawing ray YA will complete the construction and create the desired angle. That is, YA ...

  This is the other ray that will make up the angle ∠AYZ and will complete the construction.

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Since we are to find the probability that 2 randomly selected points from Q,R,S,T and W are non-collinear

Non collinear points are points that doesn't lie on the same straight line. From the diagram given, the two point that are non colliear are (QR, QS, QT and QW making 4 2random non collinear points. Hence out expected number of outcome is 4.

For the total possible outcome, we are to find the number of ways we can randomly select two points from the 5 points given and this can be done using the combination rule.

This can therefore be done in 5C2 number of ways.

5C2 = 5!/(5-2)!2!

5C2 = 5!/3!2!

5C2 = 5*4*3*2*1/3*2*2

5C2 = 5*2

5C2 = 10 different ways

Hence the total possible outcome is 10

Therefore, the probability that 2 randomly selected points from Q,R,S,T and W are noncollinear will be 4/10 = 2/5

Answer:

a 1000 times// just divide them

Answer:

10,000 times Larger

Step-by-step explanation:

To determine the multiple larger for 86,000,000 than 8,600, we simply will use the division operation and the result will be the multiple.

86,000,000 / 8,600 = 10,000

Hence, the number 86,000,000, is 10,000 times larger than 8,600.

Another method is simply to look at the additional zeroes that 86,000,000 has in comparison to 8,600.  Since we can see that 86 is the only non-zero digit within the two numbers, we can use the properties of the decimal system to compare.  Note that 86,000,000 has 6 zeroes, while 8,600 has two zeros.  This means that we will need 4 zeroes as part of our tens multiple, so we can say that 10,000 is the multiple.  Once again, we see that 86,000,000 is 10,000 times larger than 8,600.

Cheers.

Answer:

Step-by-step explanation:

(9-5)/6-4)= 4/2= 2

y - 5 = 2(x - 4)

y - 5 = 2x - 8

y = 2x - 3 is the solution

Answer:

the answer is y = –2x – 5 hope this helps:) give brainliest if it does

Step-by-step explanation:

i got it right on edge

Answer:

890 if it’s 178 bags per garden bed

Step-by-step explanation:

since 1 raised garden bed is supposedly 178 bags, 5 would be 890 since it’s just 5x178. if it’s not 178 bags (which would make sense since 178 is a big number), just multiply 5 by that number and if it’s a decimal round up to the next whole number if it’s about how many bags Bismah needs to buy, since you can’t by 1/2 of a bag

Bismah will need a total of 890 bags of soil for all the 5 raised garden. beds.

Multiplication is one of the basic operations in mathematics where a number is added repeatedly to itself up to the times as the value of the other number.

That is, if a number p is multiplied to another number q, p × q, implies that p is added repeatedly to itself q times or q is added repeatedly to itself up to p times.

Number of garden beds Bismah has raised = 5

Number of bags of soil needed for a garden bed = 178 bags

Number of  bags of soil needed for 5 garden bed = 178 × 5 bags

                                                                                   = 890 bags

Hence Bismah would need 890 bags of soil for the 5 raised garden beds in the community garden.

To learn more about Multiplication, click on the link given below :

https://brainly.com/question/24327297

#SPJ5

Answer:

Step-by-step explanation:

[tex]5\frac{1}{6}=\frac{(5*6)+1}{6}=\frac{31}{6}[/tex]

Answer:

31/6 (improper fraction).

Step-by-step explanation:

5 1/6 = (6 × 5) + 1/6 = 31/6

31/6 is the improper fraction.

Answer:

34.5

Step-by-step explanation:

5 times x(2.3) = 11.5.

11.5 times 3 is 34.5

you put 2.3 in place of x because x was the unknown value, but now that we know it is 2.33 we plug it in.

Answer:

14000 pounds :)

Step-by-step explanation:

Answer:

14000 pounds

Step-by-step explanation:

Formula:

multiply the mass value by 2000

Answer:

[tex]\huge\boxed{Step \ 3}[/tex]

Step-by-step explanation:

In Step # 3, We need to divide rather than to subtract. So, the first mistake is done in step 3.

Answer:

[tex]\Large \boxed{\mathrm{Step \ 4}}[/tex]

Step-by-step explanation:

[tex]20 +20 \div 4-2[/tex]

Division should be performed first, not subtraction.

[tex]20+5-2[/tex]

Answer:

Step-by-step explanation:

Let n and r represent the output in liters per hour of the Nguyen and Reed family sprinklers, respectively. Then we have ...

  15n +25r = 1175 . . . . total sprinkler output

  n + r = 55 . . . . . . . . . sum of two output rates

The second equation tells us we can substitute n = 55 -r into the first equation:

  15(55 -r) +25r = 1175

  10r = 1175 -825 . . . . . . subtract 825

  r = 350/10 = 35 . . . . . . divide by 10

  n - 55 -35 = 20 . . . . . . find n from r

Nguyen family's sprinkler: 20 L per hour

Reed family's sprinkler: 35 L per hour

Answer:

The values of the angles are;

m∠DEA = 62°, m∠ADB = 45°

Step-by-step explanation:

Specify an arc or an angle three letters  

Angle opposite an arc on the circumference

m DA ≅ m CB = 62°  (Arc between parallel lines are congruent)

∠CAB = 1/2 × m CB = 1/2 × 62° = 31° (Angle at the center = 2 × Angle st the circumference)

∠DBA = 31° (Angle at the center m DA = 2 × Angle st the circumference)

m∠DAB = 104° (Given)

∠ADB = 180° - m∠DAB - ∠DBA = 180° - 104° - 31° = 45° (Interior angles of triangle ΔADB

m∠ADB = 45°

∠AEB = 180 - ∠CAB - ∠DBA = 180° - 31° - 31° = 118°

∠AEB ≅ ∠COD (Vertically opposite angles)

∠DEA ≅ ∠CEB (Vertically opposite angles)

∠AEB + ∠COD + ∠DEA + ∠CEB = 360° (Sum of angles at a point)

118° + 118° + ∠DEA + ∠CEB = 360°

∠DEA + ∠CEB = 360° - 118° - 118° = 124°

Given that ∠DEA = ∠CEB we have;

2 × ∠DEA = 124°

∠DEA = 124°/2 = 62°

m∠DEA = 62°.

Answer:

36 lbs

Step-by-step explanation:

let the weight of each boy's backpack be B and the weight of each girl's backpack be G.

Given that the total weight of all (i.e 10 boys' and 10 girls') backpacks equals 600 lbs,  i.e.

10B + 10G = 600   (simplifying by dividing both sides by 10)

B + G = 60 ------- eq 1

Also given that a girl's backpack is 1.5 times LESS than a boy's backpack.

written another way, we can say that a boy's backpack is 1.5 times MORE than a girl's backpack, or:

B = 1.5G   (rearranging)

B - 1.5G = 0     ------ eq 2

We can solve eq 1 and eq 2 by elimination,

(eq 1) - (eq 2)

(B + G) - (B - 1.5G) = 60 - 0

B + G - B + 1.5G = 60

G  + 1.5G = 60

2.5G = 60   (divide both sides by 2.5)

G = 60 / 2.5

G = 24 lbs   (substitute this into equation 1)

B + G = 60

B + 24 = 60

B = 60 - 24

B = 36 lbs

Answer:

[tex]\boxed{\sf 200 \ feet^2}[/tex]

Step-by-step explanation:

The 3D shape is a square-based pyramid.

The surface area of a square-based pyramid is given as:

[tex]\sf SA=2 \times (base \ length) \times (slant \ height) + (base \ length)^2[/tex]

Plug in the values.

[tex]\sf SA=2 \times 10 \times 5 + 10^2[/tex]

[tex]\sf SA=100 + 100[/tex]

[tex]\sf SA=200[/tex]

Answer:

length=4 cm

Step-by-step explanation:

Area of rectangle= length * width

48=l*12

length=48/12

length=4 cm