The sum of three numbers is 52. The difference of the largest and the smallest is 48, and the sum of the two smaller numbers is 11, Find the numbers.

Answer:

the last one 3(x+4) = 3x + 12

Step-by-step explanation:

Answer: 0.0208

Step-by-step explanation:

Given: The length of time to find a parking spot on the UW campus is normally distributed with a mean of 4.75 minutes and a standard deviation of 1.35 minutes.

Let x = time taken to find parking spot

The probability that a randomly selected driver takes less than 2 minutes to find a parking spot on the UW campus will be :

[tex]P(x<2)=P(\dfrac{x-\mu}{\sigma}<\dfrac{2-4.75}{1.35})\\\\=P(Z<-2.037)\ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=1-P(Z<2.037)\\\\=1- 0.9792=0.0208\ \ \ \text{[By p-value table]}[/tex]

Hence, the probability than a randomly selected driver takes less than 2 minutes to find a parking spot on the UW campus.= 0.0208

Answer:

Step-by-step explanation:

For all Plato users.

We have to find the sum of the series has been given as.

[tex]\sum_{k=1}^{8}5(\frac{4}{3} )^{k-1}[/tex] -----(1)

If the series has been given as,

[tex]\sum_{n=1}^{k}a(r)^{n-1}[/tex] -------(2)

It's a geometric series with first term 'a' and common ratio 'r'.

Comparing both the expressions (1) and (2),

[tex]a=[/tex] 5

[tex]r=\frac{4}{3}[/tex]

Number of terms 'n' = 8

Sum of the k terms of this series is given by,

Sum = [tex]\frac{a(r^k-1)}{r-1}[/tex]

       = [tex]\frac{5[(\frac{4}{3})^8-1)]}{\frac{4}{3}-1 }[/tex]

       = [tex]\frac{5(9.98872-1)}{\frac{1}{3}}[/tex]

       = [tex]\frac{44.9436}{\frac{1}{3} }[/tex]

      = 134.83

Therefore, Option (B) is the correct option.

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Depreciation formula :

Amount x (1-rate)^time

125 x (1-0.005)^5

124 x 0.995^5 = 121.91

Answer: $121.91

Answer:

-3m+7.5=4.5m

Step-by-step explanation:

Answer:

85%

Step-by-step explanation:

Answer:

85%

Step-by-step explanation:

What I would do is how much she would score if the test was a 25 question test. She would have scored 21.33. Now add this to her current score. 64+21.33 = 85.33. The rounded answer is 85.

Answer:

Length of the person = 1.9 m

Step-by-step explanation:

Actual length of the lorry = 9.5 m

Length of the lorry as per scale = 10 cm

Scale factor used to get the actual length of the lorry = [tex]\frac{\text{Actual length}}{\text{Length on scale}}[/tex]

                                                                                         = [tex]\frac{9.5}{10}[/tex]

                                                                                         = 0.95 : 1

Let the actual length of the person = x meters

Length of the person as per scale = 2 cm

Scale factor used to get the length of person is same.

Therefore, relation between the actual length of the person and scale length will be,

[tex]\frac{x}{2}= \frac{0.95}{1}[/tex]

x = 2 × 0.95

x = 1.9 meters

Answer and Step-by-step explanation:

This problem involves the use of trigonometric functions.

First, we will use the tangent trig function, and then the sine trig function.

[tex]tan(32) = \frac{x}{15}[/tex]

We solve for x by multiplying both sides by 15.

15(tan(32)) = x

Put this into a calculator and solve.

x = 9.373

Now, we solve for y.

[tex]sin(32) = \frac{9.373}{y}[/tex]

We multiply by y on both sides first.

y(sin(32)) = 9.373

Now, we divide each side by sin(32).

[tex]y = \frac{9.373}{sin(32)}[/tex]

Put this into a calculator and solve.

y = 17.6877

x = 9.373

y = 17.6877

These are your answers.

#teamtrees #WAP (Water And Plant)

Answer:

(a) [tex]y = \frac{4}{x^2}[/tex]

(b) [tex]x = \frac{2}{5}[/tex]

Step-by-step explanation:

Given

Variation: Inverse proportional.

This is represented as:

[tex]y\ \alpha\ \frac{1}{x^2}[/tex]

See attachment for table

Solving (a):

First convert variation to equation

[tex]y = k\frac{1}{x^2}[/tex]

From the table:

[tex](x,y) = (1,4)[/tex]

So, we have:

[tex]4 = k * \frac{1}{1^2}[/tex]

[tex]4 = k * \frac{1}{1}[/tex]

[tex]4 = k * 1[/tex]

[tex]4 = k[/tex]

[tex]k = 4[/tex]

Substitute 4 for k in [tex]y = k\frac{1}{x^2}[/tex]

[tex]y = 4 * \frac{1}{x^2}[/tex]

[tex]y = \frac{4}{x^2}[/tex]

Solving (b): x when y = 25.

Substitute 25 for y in [tex]y = \frac{4}{x^2}[/tex]

[tex]25 = \frac{4}{x^2}[/tex]

Cross Multiply

[tex]25 * x^2 = 4[/tex]

Divide through by 25

[tex]x^2 = \frac{4}{25}[/tex]

Take positive square roots of both sides

[tex]x = \sqrt{\frac{4}{25}[/tex]

[tex]x = \frac{2}{5}[/tex]

Answer:

55 minutes

Step-by-step explanation:

The amount of time that is needed to pass to change 6:30 into 7:05 is 35 minutes. The amount of time that is needed to pass to change 3:55 to 4:15 is 20 minutes. If you add the time Joe practiced on Monday and Tuesday altogether it's 55 minutes.

Hope I could help! :)

Answer:

$1.50 is 105 Naira

Step-by-step explanation:

If the exchange rate is 1:70, that means that in order to get the amount of Naira equal to some amount of US dollars, you would multiply the number of US dollars by 70. And so we get...

1.5 x 70 = 105 (Naira)

Answer:

105 Naira

Step-by-step explanation:

Please see the attached image.

I hope this helps!

Answer:

D

Step-by-step explanation:

Because the term 7x^3 is to the third power, the curve moves like x^3. This means that as x approaches infinity and -infinity, it approaches infinity and -infinity respectively. The answer is D.

Answer:

-5/2+-2

Step-by-step explanation:

Answer:x=-5/11

Step-by-step explanation:

2x+2+20x=−8

Step 1: Simplify both sides of the equation.

2x+2+20x=−8

(2x+20x)+(2)=−8(Combine Like Terms)

22x+2=−8

22x+2=−8

Step 2: Subtract 2 from both sides.

22x+2−2=−8−2

22x=−10

Step 3: Divide both sides by 22.

22x/22=-10/22

Answer:  The width of the playing field = 45 ft

length of playing fiels =  86ft

Step-by-step explanation:

Step 1

Perimeter of rectangular field is given as 2 ( L+ b)

Let the width be represented as  x

such that the length = 41 ft longer than the width be  x+ 41

To find the length and breadth

Step 2

Perimeter = 2( L+ b)= 2l + 2b

Perimeter =  2 (x+41 ) + 2 x = 262

2x + 82 + 2x= 262

4x+ 82= 262

4x= 262 - 82

4x= 180

x= 180/4

x= 45

width= 45 ft

length = x+ 41= 45+ 41= 86ft

Answer:

1. Yes

2. No

3. Yes

Step-by-step explanation:

We have three equations where x is equal to -4. We are then asked if -4 are a solution to these equations.

To solve we need to substitute the x in every equation for -4. Start :

1.

3(2(-4) - 4) = -36

3(-8 - 4) = -36

-24 - 12 = -36

Therefore -4 is a solution.

2.

5(-4) - 6(-4) - (-4) = 18

-20 + 24 + 4 = 18

4 + 4 = 18

8 ≠ 18

Therefore -4 is not a solution.

3.

5 - 2(3(-4) - 1) = 31

5 - 2(-12 - 1) = 31

5 - 2(-13) = 31

5 + 26 = 31

Therefore -4 is a solution.

Answer:

∠U = 26°

∠V = 35°

∠W = 119°

Step-by-step explanation:

Given:

∠U = (x+9)°

∠V = (2x+1)°

∠W = (7x)°

Find:

Value of each angle

Computation:

Using angle sum property

∠U + ∠V + ∠W = 180°

(x+9)° + (2x+1)° + (7x)° = 180°

10x + 10 = 180

x = 17

So,

∠U = (x+9)° = 17 + 9 = 26°

∠V = (2x+1)° = 34 + 1 = 35°

∠W = (7x)° = 7 x 17 = 119°

Answer:

whats your snap ill help

Step-by-step explanation:

Answer:

1508.6 steps

Step-by-step explanation:

one mile = 5280 feet

42 inches = 3.5 feet

5280 / 3.5 = 1508.57

Answer:

The answer is -3x + 3

Answer:

Y>2x-4

B

Have a great day, hope this helps

Answer:

1) 7 x (6+y)

2)(  y x 6) + (y x 7)

3) 6(y+7)

4) (y x 6) + y^2

I hope im right !

Step-by-step explanation:

( 7 * 6 ) + ( 7 * y) ➡ 7 (6 +y)

y(6 + 7) ➡ ( y * 6 ) + ( y * 7)

( 6 * y) + ( 6 * 7) ➡ 6 ( y + 7)

y( 6 + y) ➡ ( y * 6 ) + y²

Hope it will help :)

9514 1404 393

Answer:

  (b)  540 boxes

Step-by-step explanation:

The 28 foot depth of the trailer will accommodate 18 boxes (leaving 1 ft unfilled).

The 8 1/2 foot width of the trailer will accommodate 5 boxes (leaving 1 ft unfilled).

The 9 1/6 foot height of the trailer will accommodate 6 boxes (leaving 1/6 ft unfilled).

The collection of boxes filling the trailer is 18 deep, 5 wide, and 6 high, for a total of ...

  18 × 5 × 6 = 540 boxes

_____

In each case, the number of boxes that will fit is the dimension divided by the dimension of the box. The result is the integer part of the quotient. For example, ...

  (28 ft)/(3/2 ft/box) = 56/3 box = 18 2/3 box . . . 18 boxes will fit

Answer:

Using graph for units

D=1/2(6)(9)=27 sq units

E=1/2(7)(6)=21 sq units

F=1/2(6)(8)=24 sq units

Step-by-step explanation:

Answer:

D=27 units, E=21 units, F=24 units

Step-by-step explanation:

The formula for area of a triangle is (BASE * HEIGHT)/2

For triangle D, the base is 9 units and the height is 6 units. Then you can apply the formula and do 9*6 which is 54 and then do 54/2 which is 27 units.

Similarly, the base for E is 6 units, and the height is 7 units. So you do 6*7 which is 42 and then do 42/2 which is 21 units.

Again, the base for F is 6 units, and the height is 8 units. Then again, using the formula, we can do 6*8 which is 48 and then do 48/2, which is 24 units.

Hopefully this helped!

Answer:

Explanation:

-5b = 10a

-5b / -5 = 10a / -5

Answer:

The answer is below

Step-by-step explanation:

Chancellor Manufacturing makes two pumps for use in household reef aquariums. The Standard pump (Model A) requires 4.5 lbs of stainless steel while the Deluxe lightweight pump (Model B) 3.0 lbs of stainless steel. There are 63 lbs of stainless steel available during this production period. The combined production of both pumps must be at least 12 pumps. There are orders for at least 6 of the lightweight Model B. Lastly, management has decided that no more than 15 Model B pumps be produced.

The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210.

Solution:

a) Let x represent model pump A and let y represent model pump B.

Since There are 63 lbs of stainless steel available, hence:

4.5x + 3y ≤ 63

Both pumps must be at least 12 pumps. Therefore:

x + y ≤ 12

There are orders for at least 6 of the lightweight Model B:

y ≥ 6

Also,  no more than 15 Model B pumps be produced:

y ≤ 15

The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210. The cost equation is:

Minimize Cost = 150x + 210y

b)

Hence the LP formation is:

Minimize Cost = 150x + 210y

4.5x + 3y ≤ 63

x + y ≤ 12

y ≥ 6

y ≤ 15

x ≥ 0.

c) The LP problem was solved using geogebra online graphing tool.

The points that satisfy the problem are:

(0, 6), (0,12), (6, 6)

At (0,6); cost = 150(0) + 210(6) = 1260

At (0,6); cost = 150(0) + 210(12) = 2520

At (6,6); cost = 150(6) + 210(6) = 2160

Hence the minimum cost is at (0, 6)