Twelve people waited more than 45 minutes.
How many people waited between 10 and 30 minutes?

Step-by-step explanation:

step 1. all the side length are different therefore all of the internal angles are different.

step 2. a triangle with all different angles is scalene.

step 3. all of the angles are less than 90°

step 4. a triangle with all angles less than 90° is acute.

Answer:

D) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/6.

Step-by-step explanation:

The Number of boxes = 6

Box containing a prize = 1

Probability of success, p = box containing a price / number of boxes = 1 /6

Number of trials = 5

Probability of success on exactly 2 trials, r = 2

Hence,

P(r = 2) = nCr * p^r * (1-p)^(n-r)

n = 5 ; r = 2 ; p = 1/6

Using a binomial probability calculator :

P(r = 2) = 0.1608

Answer:

what

Step-by-step explanation:

did you have a stroke?

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)

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 :)

Answer:

1

Step-by-step explanation:

. It is read as 2 raised to zero. Now let see how to solve such problem For example 3^5 then it means 3×3×3×3×3 = 243 Now back to question Anything raised to zero is always 1 Hence 2^0= 1

Depreciation formula :

Amount x (1-rate)^time

125 x (1-0.005)^5

124 x 0.995^5 = 121.91

Answer: $121.91

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:

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:

Explanation:

-5b = 10a

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

Answer: just turn them into decimals and use a calculator then turn them back into fractions in simplified form

Step-by-step explanation:

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:

8 times 9 or 72 devide 9 is 8

Step-by-step explanation:

that th answer

Answer:

The factors of 72 are 1,2,3,4,6,8,9,12,18,24,36,72

Step-by-step explanation:

9 is a factor of 72 because 9×8=72

Answer: positive I think

Step-by-step explanation:

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 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:

-3m+7.5=4.5m

Step-by-step explanation:

Answer:

The answer is 4w^2 + 8w - 3

Step-by-step explanation:

Umm I hope it's right

Answer:

The left graph is a positive slope (yellow box)

The middle graph has no slope (green)

The right graph has a negative slope (purple)

Step-by-step explanation:

The left graph has a positive slope because the slope increases left to right. We can see this because the line starts at the origin at zero (0, 0), and increases.

The right graph has a negative slope because the slope decreases left to right. We can see this because it starts a value greater than zero, and gradually decrease to zero.

The middle graph contains no slope because it is a straight horizontal line. If we were to calculate the slope, (rise/run) of two points, the slope is the same in every point. It is constant.

The correct answer is,

The left graph is a positive slope (yellow box)

The middle graph has no slope (green)

The right graph has a negative slope (purple)

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Here, we have.

The left graph has a positive slope because the slope increases left to right. We can see this because the line starts at the origin at zero (0, 0), and increases.

The right graph has a negative slope because the slope decreases left to right. We can see this because it starts a value greater than zero, and gradually decrease to zero.

The middle graph contains no slope because it is a straight horizontal line. If we were to calculate the slope, (rise/run) of two points, the slope is the same in every point. It is constant.

Hence, The correct answer is,

The left graph is a positive slope (yellow box)

The middle graph has no slope (green)

The right graph has a negative slope (purple)

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Answer:

a. – 4 or –3

b. –4 or –2

c. 4 or –3

d. 7 or 4

Step-by-step explanation:

To factorize the above expression, multiply the first and last term together, then find two factors of the result such that their sum will result to the middle term of the expression.

Now, we shall give the answers to the question.

a. x² + 7x + 12 = 0

x² + 3x + 4x + 12 = 0

Factorise

x(x + 3) + 4(x + 3) = 0

(x + 4)(x + 3) = 0

x + 4 = 0 or x + 3 = 0

x = 0 – 4 or x = 0 – 3

x = – 4 or –3

Therefore, the roots of the equation are – 4 or –3

b. t² + 6t + 8 = 0

t² + 2t + 4t + 8 = 0

Factorise

t(t + 2) + 4(t + 2) = 0

(t + 4)(t + 2) = 0

t + 4 = 0 or t + 2 = 0

t = 0 – 4 or t = 0 – 2

t = –4 or –2

Therefore, the roots of the equation are –4 or –2

c. 2n² – 2n – 24 = 0

Divide through by 2

n² – n – 12 = 0

n² + 3n – 4n – 12 = 0

Factorise

n(n + 3) – 4(n + 3) = 0

(n – 4)(n + 3) = 0

n – 4 = 0 or n + 3 = 0

n = 0 + 4 or n = 0 – 3

n = 4 or n = –3

Therefore, the roots of the equation are 4 or –3

d. y² – 11y + 28 = 0

y² – 4y – 7y + 28 = 0

Factorise

y(y – 4) – 7(y – 4) = 0

(y – 7)(y – 4) = 0

y – 7 = 0 or y – 4 = 0

y = 0 + 7 or y = 0 + 4

y = 7 or 4

Therefore, the roots of the equation are 7 or 4.

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.

First, we determine the value of the 5 installments using a 5% annual compounded rate.

We calculate the future value, and then the present value:

FV= {A*[(1+i)^n-1]}/i

A= annual payments

FV= {60,000*[(1.05^5) - 1]} / 0.05

FV= $331.537.88

PV= FV/(1+i)^n

PV= $259,768.60

At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.

Now, if the annual rate is 6% continuously compounded.

First, we need to calculate the effective interest rate:

r= e^i - 1

r= effective inerest rate

r= e^0.06 - 1

r= 0.0618

FV= {60,000*[(1.0618^5) - 1]} / 0.0618

FV= 339,443.23

PV= 339,443.23/1.0618^5

PV= $251,509.01

At an annual rate of 6% compounded continuously, she should choose the $255,000.

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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Answer:

The answer would be 0.05

Step-by-step explanation:

This is because it is PER Cent so 5% is 0.05 of 1

Answer:

1/20 and 0.05

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Answer:

Minimum = 23,040

Q1 = 30315

Q2 = 31975

Q3 = 31975

Maximum = 33650

Step-by-step explanation:

Ordered data:

23040, 24050, 26520, 28730, 30170, 30460, 30930, 31300, 31860, 31920, 32030, 32320, 32340, 32590, 32700, 32720, 33020, 33190, 33280, 33650

The five number summary :

Minimum = 23,040

Lower quartile (Q1) = 1/4(n+1)th term

n = 20

Q1 = 1/4* (21)th term

Q1 = 5.25 ; (5th + 6th) term / 2

Q1 = (30170 + 30460) / 2 = 30315

Median (Q2) :

Q2 = 1/2* (21)th term

Q2 = 10.5 ; (10th + 11th) term / 2

Q2 = (31920 + 32030) / 2 = 31975

Upper Quartile (Q3) :

Q3 = 3/4* (21)th term

Q3 = 15.75 ; (15th + 16th) term / 2

Q 3 = (32700 + 32720) / 2 = 32710

Maximum : 33650

Answer:

slope=2

Step-by-step explanation:

the line is negative since it's downwards, and the slope goes 2 down and 1 right to meet the next point. -2/1=-2

The slope of the given graph is -2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Points from the graph (1, 0) and (0, 2).

So, the slope of line

= ( 2- 0) / (0 -1)

= 2 / (-1)

= -2/1

= -2

Hence, the slope of graph is -2.

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Answer:

whats your snap ill help

Step-by-step explanation:

Answer:

0.125⅓×0.25½

(125/1000)⅓×(25/100)½

(5³/10³)⅓ × (5²/10²)½

5/10 × 5/10

1/2×1/2

1/4