During a catered lunch =, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?

Answer:

30 crayons

Step-by-step explanation:

Let x be the number of crayons he started with

gave out 14 crayons

x-14

Got 12 back

x-14+12

Gave out 11 after lunch

x-14+12 -11

This equals 17

x-14+12 -11 =17

Combine like terms

x-13 = 17

Add 13 to each side

x -13+13 =17+13

x = 30

Answer: 30

Step-by-step explanation:

For this problem work backwards. Start from 17 and add 14. You should get 31. Then subtract 12, which equals 19. Finally add 11 to 19, which equals 30. Basically you are doing the inverse operation to get your answer. Hope this helps!

Answer:

The perimeter of the Rhombus is 100 cm

Step-by-step explanation:

First of all, we will need to find the length of the other diagonal.

let’s call the diagonals p and q

Mathematically, the area of the Rhombus is;

pq/2 = Area of Rhombus.

Let’s call the missing diagonal p

So;

(p * 14)/2 = 336

14p = 672

p = 672/14

p = 48 cm

Now, we can find the perimeter of the Rhombus using these diagonals.

Mathematically;

P = 2 √(p^2 + q^2)

Substituting these values, we have;

P = 2 √(14)^2 + (48^2)

P = 2 √(2500)

P = 2 * 50

P = 100 cm

The perimeter of the rhombus is the sum of its side lengths

The perimeter of the Rhombus is 100 cm

The length of one of its diagonal is given as:

[tex]p= 14[/tex]

And the area is given as:

[tex]A = 336[/tex]

Assume the other diagonal is q.

The area of the rhombus is represented as:

[tex]A = \frac{pq}2[/tex]

So, we have:

[tex]336 = \frac{14q}2[/tex]

This gives

[tex]336 = 7q[/tex]

Divide both sides by 7

[tex]48 = q[/tex]

Rewrite as:

[tex]q = 48[/tex]

The perimeter (P) of the rhombus is calculated as:

[tex]P =2\sqrt{p^2 + q^2[/tex]

So, we have:

[tex]P =2\sqrt{48^2 + 14^2[/tex]

Evaluate the squares

[tex]P =2\sqrt{2500[/tex]

Take positive root of 2500

[tex]P =2 \times 50[/tex]

[tex]P =100[/tex]

Hence, the perimeter of the Rhombus is 100 cm

Read more about areas and perimeters at:

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Answer: (-6,8)

Step-by-step explanation:

Translation rules are

Left c units : [tex](x,y)\to(x-c,y)[/tex]

Down c units : [tex](x,y)\to(x,y-c)[/tex]

The image point of (-5,9) after a translation left 1 unit and down 1 unit will be:

[tex](-5,9)\to(-5-1,9-1)=(-6,8)[/tex]

Hence, the image point is (-6,8).

Answer: D

Step-by-step explanation:

The common difference is  -2/3  so using the last term which is -8/27 multiply it by -2/3 to find the next terms.

[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]    

[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]  

[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]  

Answer:

2 in

Step-by-step explanation:

18/3=6 , 6 is the scale factor

12/6=2

Answer:

width= 2

Step-by-step explanation:

18 inches is the original height and we are now reducing that to 3 inches.

In order to do that, we have to divide 18 by 3 which equals 6.

Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which  equals 2.

Your final answers should be: width= 2

Hello!

Answer:

[tex]\huge\boxed{x = 27}[/tex]

Given:

3x - 4y = 65 where y = 4;

Substitute in 4 for "y":

3x - 4(4) = 65

Simplify:

3x - 16 = 65

Add 16 to both sides:

3x - 16 + 16 = 65 + 16

3x = 81

Divide both sides by 3:

3x/3 = 81/3

x = 27.

Hope this helped you! :)

Answer:

x=27

Step-by-step explanation:

3x-4y=65

Let y=4

3x - 4(4) = 54

3x -16 = 65

Add 16 to each side

3x -16+16 = 65+16

3x = 81

Divide each side by 3

3x/3 =81/3

x =27

Hey There!!~

Your best answer choice is B). x > 1.

Good Luck!!

Answer:

$6488.19

Step-by-step explanation:

To solve this problem we use the compounded interest formula:

[tex]amount = principal(1 + (r \n))^({n}{t})[/tex]

a = $2600(1+(0.0675/1))¹*¹⁴

a = $6488.19

Answer:

P = 27.2c-7.2d

Step-by-step explanation:

It is given that,

The width of a rectangle is (8.3c-8.4d)

The length of a rectangle is (5.3c+4.8d)

The perimeter of a rectangle is equal to the sum of its all sides i.e.

P = 2(l+b)

P = 2(8.3c-8.4d+5.3c+4.8d)

P = 2[(8.3c+5.3c)+(4.8d-8.4d)]

P = 2(13.6c-3.6d)

⇒P = 27.2c-7.2d

Hence, the expression that represents the perimeter of the rectangle is 27.2c-7.2d.

Answer:

1. tan A = 1/(tan B)

Step-by-step explanation:

By definition,

tangent A = opposite / adjacent = a / b

and

tangent B = opposite / adjacent = b / a

Therefore tangent A = a/b = 1/tan(B)

Answer: Tan a=tan b

I belive

Step-by-step explanation:

Answer:

When two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°

Step-by-step explanation:

Based on the Inscribed Angles Theorem, the measure of an intercepted arc is twice the measure of the inscribed angle that intercepts it in a circle.

Consequently, the theorem also Holds that the measure of two inscribed angles intercepting the same arc, are congruent. In other words, both angles together are the same, and their sum would give you the measure of the arc they both intercept.

In the diagram shown in the attachment below, we have 2 inscribed angles, angle A and B. They both intercept the same arc of 75°.

Therefore, we can conclude that the measure of both angles equal 75°, which is the same as the measure of the arc they intercept.

Angle A = Angle B

m<A + m<B = measure of intercepted arc = 75°

Answer:

:

"(100 + 3) (100 + 7)

Now, by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = 3 , b = 7

= (100)² + (3+7)*100 + (3*7)

= 10000 + 1000 + 21

= 11021

.

(110 - 7) (110 - 3)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = (-7) , b = (-3)

= (110)² + { (-7) + (-3) }*110 + {(-7)*(-3)}

= 12100 + (-10)*110 + 21

= 21200 - 1100 + 21

= 11021

.

➖➖➖➖➖➖➖➖➖➖

.

(90 + 5) (90 + 6)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 90 , a = 5 , b = 6

= (90)² + (5+6)*90 + (5*6)

= 8100 + 990 + 30

= 9120

.

(100 - 5) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = (-5) , b = (-4)

= (100)² + { (-5) + (-4) }*100 + 20

= 10000 + (-9)*100 + 20

= 10000 - 9000 + 20

= 10020 - 900

= 9120

.

➖➖➖➖➖➖➖➖➖➖

.

(100 + 4) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = 4 , b = (-4)

= (100)² + { 4 + (-4) }*100 + 4*(-4)

= 10000 + (4 - 4)*100 - 16

= 10000 + 0*100 - 16

= 10000 - 16

= 9984

.

(90 + 14) (90 + 6)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 90 , a = 14 , b = 6

= (90)² + (14 + 6)*90 + (14*6)

= 8100 + 20*90 + 84

= 8100 + 1800 + 84

= 9984"

This answer was in another question

This answer was given by BloomingBud

Step-by-step explanation:

Answer:

1) 9120 2) 11021

Step-by-step explanation:

95 * 96 = (100-5)(100-4) = 10000 - 500 - 400 + 20 = 9120

103 * 107 = (100+3)(100+7) = 10000 + 300 + 700 + 21 = 11021

Answer:

3.625 gpm

Step-by-step explanation:

Answer:

Graph D

Step-by-step explanation:

(h)t = -16t^2 + 80

At time t = 0 the screwdriver is at 0+80 =80 ft

As time increases the height will decrease so we can eliminate graph B

We know this is a downward parabola by the - in front of the t^2 so we can eliminate graph A

We need to find where it meets the x axis

0 = -16t^2 + 80

-80 = -16t^2

5 = t^2

t = sqrt(5)

t =2.23

This is Graph D

Answer:

Cada uno de ellos gana:

S/. 24

S/. 36

Step-by-step explanation:

Planteamiento:

a + b = 60

a = 12 + b

Desarrollo:

sustituyendo el valor de la segunda ecuación del planteamiento en la primer ecuación del planteamiento:

(12+b) + b = 60

2b + 12 = 60

2b = 60 - 12

2b = 48

b = 48/2

b = 24

de la segunda ecuación del planteamiento:

a = 12 + b

a = 12 + 24

a = 36

Check:

24 + 36 = 60

Answer:

convert into a whole number 6

if an ordered pair is a solution, it should satisfy the equation.

see the first option

[tex]y=3x[/tex] , if you put $x=4$ and $y=12$

you'll get $12=12$ which is true.

now the last option, $y=8-x$ put $x=4$ and $y=12$

$12=8-4\implies 12\ne4$ thus it is not a solution.

So option 4 is correct

Answer:

Last one:

Step-by-step explanation:

y = 8 - x

12 = 8 - 4

12 = 4 (impossible)

Answer:

x = 15

Step-by-step explanation:

We need to find the value of x in the equation 3x – y = 18 when y = 27.

To find the value of x, put y = 27 in the above equation.

So,

3x - 27 = 18

3x = 45

x = 15

So, the value of x is 15.

Answer:

72°

Step-by-step explanation:

From the figure given, angle D intercepts arc ABC. According to the Inscribed Angle Theorem:

m < D = ½(ABC) = ½(AB + BC)

Thus,

[tex] 56 = \frac{1}{2}(AB + 40) [/tex]

Solve for AB

[tex] 56 = \frac{AB + 40}{2} [/tex]

Multiply both sides by 2

[tex] 56*2 = \frac{AB + 40}{2}*2 [/tex]

[tex] 112 = AB + 40 [/tex]

Subtract both sides by 40

[tex] 112 - 40 = AB + 40 - 40 [/tex]

[tex] 72 = AB [/tex]

Arc AB = 72°

Answer:

$26532.98

Step-by-step explanation:

Given:

Sum is:

Answer:

25/4 laps or (6.25 laps)

Step-by-step explanation:

1 lap = 1 1/5 miles

kellyn plans to jog 7 1/2 miles

                                                      1  lap

number of laps = 7 1/2 miles x  --------------   = 25/4 laps or (6.25 laps)

                                                    1 1/5 miles

Answer:

Nina can run:

13 1/2 km in 1 hour

Step-by-step explanation:

4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2

proportions:

9/2 hours ⇔  1/3 hour

N hours ⇔ 1 hour

N = (9/2)*1 / (1/3)

N = (9/2) / (1/3)

N = (9*3) / (2*1)

N = 27/2

27/2 = 26/2 + 1/2 = 13 + 1/2 = 13 1/2

Nina can run:

13 1/2 km/h

13 1/2 km in 1 hour

Nina can run [tex]13\frac{1}{2}[/tex] km in an hour

The distance Nina can run in an hour can be determined by dividing the distance she can run in 1/3 of an hour by 1/3

Distance Nina can run in an hour = distance run ÷ [tex]\frac{1}{3}[/tex]

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

Convert the mixed fraction to an improper fraction [tex]\frac{9}{2}[/tex] × 3 = [tex]\frac{27}{2}[/tex]

Convert the improper fraction back to an mixed fraction = [tex]13\frac{1}{2}[/tex] km

To learn more about fractions, please check:

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Answer:

7 m

Step-by-step explanation:

Use the pythagorean theorem.

a^2+b^2=c^2

7.5 is your hypotenuse and 3 is one of your legs.

7.5^2 - 3^2 = 47.25

the sqrt of 47.25 is 6.873863542, therefore the nearest meter it reaches is 7.

Answer:

40°

Step-by-step explanation:

The circumference of a circle is equal to 360°

The arc AB is 180°, the arc AC is given as 100° so the arc CB is 80° and since <A is an inscribed angle it is equal to the half of the arc it sees

80 ÷ 2 = 40

Answer:

The correct option is;

a. Accountant

Step-by-step explanation:

The given data are;

Career,                                                                   Average Salary

Veterinarian,                                                          $56,000

Personal trainer,                                                    $18,000

Accountant,                                                           $43,000

Paralegal,                                                              $34,000

Architect,                                                               $50,000

Photographer,                                                       $19,000

Pharmacist,                                                            $44,000

Secretary,                                                              $30,000

Surveyor,                                                               $36,000

Webmaster,                                                           $49,000

Among the options given, which are, accountant (salary, $43,000), paralegal (salary, $34,000), photographer (salary, $19,000), and surveyor (salary, $36,000), the accountant, with a salary of $43,000, requires the most education.

Answer:

First. 115°

Second. 65°

Third. 65°

Fourth. 7

Fifth. 425.25

First

angle DAB = angle ADC (since this is an isosceles trapezoid)

Second

In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)

180-115 is 65°

Third

(Same reason as second)

Fourth

The side 3x+4 is same as the opposite side

So 3x + 4 = 25

on solving you get x = 7 in

Fifth

[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]

area = 1/2 × 13.5 (20+43)

area = 1/2 × 13.5 × 63

Thus area is 425.25

Answer:

Step-by-step explanation:

1)As ABCD is isosceles trapezium,

∠ADC= ∠DAB

∠ADC = 115°

2) AD //BC

∠ADC + ∠DCB = 180°   {co interior angles}

115 + ∠DCB = 180

 ∠DCB = 180 - 115

 ∠DCB = 65°

3) As ABCD is isosceles trapezium,

∠CBA = ∠DCB

∠CBA = 65°

4) As ABCD is isosceles trapezium, non parallel sides are congruent.

AB = DC

3x + 4 = 25 in

3x = 25 - 4

3x = 21

x = 21/3

x = 7 in

5) height = 13.5 in

a= 43 in

b= 20 in

Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]

                   [tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]

Answer:

5/3

Step-by-step explanation:

5×(10×1/3)

=10×5/3

=since 5×(10×1/3) gives 50/3 so thus 10×5/3.

The fraction is therefore 5/3

Answer:

0.0276

Step-by-step explanation:

The computation of the probability that the next driver is texting while driving is shown below:

= Fourth pull failure × fifth pull success

where,

Fourth pull failure is (1 - 0.52)^4

And, the fifth pull success is 0.52

Now placing these values to the above formula

So,

= (1 - 0.52)^4 × 0.52

= 0.0276

Hence, the probability is 0.0276

Step-by-step explanation:

Let the rate of the plane be x

The rate of the wind be y

Against the wind

Resultant velocity = x-y

1650/3 = x - y

550 = x - y

With the wind

Resultant velocity = x + y

3480/4 = x + y

870 = x + y

Solve equation simultaneously

Add both equations

870+550 = x+y+x-y

1420 = 2x

x = 710

x + y = 870

y=870 - 710

y = 160

The rate of jet in still air = 710 mph

The rate of wind = 160 mph

HOPE IT HELPS!

PRETTY PLEASE MARK ME BRAINLIEST :-)

Answer:

No it's not.

Step-by-step explanation:

[tex]1 \frac{1}{3} = \frac{4}{3} = 1.333333[/tex]

Integers are set of numbers consisting

It doesn't consist

Hope this helps ;) ❤❤❤

Answer:

[tex]\boxed{\sf No}[/tex]

Step-by-step explanation:

[tex]\displaystyle 1 \frac{1}{3} =1.3333333...[/tex]

Integers are whole numbers that can be positive or negative. Integers do not include fractions and decimals.