Mark can dig a ditch in 4 hours. Greg can dig the same ditch in 3 hours. How long would it take them to dig it together?

Answer:

1/36

Step-by-step explanation:

1/6x1/6=1/36

Answer:

26

Step-by-step explanation:

Let's find first the lower quartile in both A and B

steps:

73 and 75 are the smallest consecutive numbers

The lower quartile in A is 74

47 and 49 are the smallest consecutive numbers

The lower quartile in B is 48

Answer:

29

Step-by-step explanation:

To find the lower quartile of each you need to find the median to split them into 2 groups (upper and lower quartile).

Lower quartile of Set A: 73, 75, 79, 81, 84, 85

Lower quartile of Set B: 47, 49, 51, 51, 55, 56

Now you find the median of the 2

Set A: 80

Set B: 51

Lastly you subtract A & B and get 29

plan B would share less

because, 20% of 1700 is 340 and 30% of 1450 is 435

I hope this helps!!

Answer:

plan A

Step-by-step explanation:

Plan A

1700-8450=6750*.20=1350+1700=3050

Plan B

1450-8450=7000*.30=2100+1450=3550

Answer=Plan A

Answer:

multiply 5/7 by 3

Step-by-step explanation:

Simplify equation:     14 - 7y + 5 = 1 + 3y + 24

     simplify again:  19 - 7y = 25 + 3y

     add -25  and 7y to both sides:   -6 = 10y

     y = -6/10   or -0.6

2.  After 30 minutes, richie has delivered 1/3 of the papers, so they have to deliver the remaining 2/3.  Since they can deliver them all in 40 minutes, would the answer be 2/3 of 40?  I'm not sure about this.

Answer:

a. Distance = 400 - 200t

b. see attached graph

c. A travelled 180 km, B travelled 220 km, both took 2 hours.

Step-by-step explanation:

Given

distance = 400

A = 90 km/h

B = 110 km/h

A & B drive towards each other

Solutions

a) equation

Let

t = elapsed time in hours,

D(t) = distance between two drivers

D(t) = 400 - (A+B) t  

D(t) = 400 - 200t  ......................(1)

b. graph : for graph, see attached figure.

c. Distance and time

Time:

solve for t with the distance D(t) = 0 using equation (1)

0 = 400 - 200 t

200t = 400

t = 2   hours

distance travelled by A = 2 hours * 90 km/h  = 180 km

distance travelled by B = 2 hours * 110 km/h  = 220 km

Answer:

10 s'mores

Step-by-step explanation:

20 ÷ 2 = 10

but only if she has enough of the other ingredients too :)

Answer:

10 smore's

Step-by-step explanation:

If 2 graham crackers is required to make 1 smore

then 20 graham crackers will make 10 smore's

2 x 10 = 20

Answer:

A function is a relation in which each input has only one output.

Step-by-step explanation: In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.

A function is a coordinate grid containing a U-shape with arrows on both ends that open to the right, and in which the bottom portion of the U passes through the origin which is the correct answer would be an option (A).

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

A function is a coordinate grid with a U-shaped pattern, arrows on both ends that open to the right, and the origin at the bottom of the U.

Because there is only one output of the relation, y, for any input x (1, 2, 3, or 0), is a function of x. Because the input y = 3 contains multiple outputs, including x = 1 and x = 2, x is not a function of y.

Therefore, the function is a coordinate grid containing a U-shape with arrows on both ends that open to the right, and in which the bottom portion of the U passes through the origin.

Hence, the correct answer would be option (A).

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Answer:

D. 35

Step-by-step explanation:

20-5>25 = 20>25 incorrect

30-5>25 = 25>25 incorrect

35-5>25 = 20>25 correct

Answer:

x=7

Step-by-step explanation:

4/3x-1/3=9

Add 1/3 on both sides

4/3x=28/3

Multiply the reciprocal

(3/4)(4/3)x=28/3(3/4)

x=7

Hope this helps !!

Answer:

1 hour 12 minutes or 1.2 hours

Step-by-step explanation:

You add fractions to get this.

1 room/3 hours + 1 room / 2 hours = 1 room / x

0.33333333+0.5 = 1 room / x

0.83333333 = 1 / x    Multiply both sides by x

0.83333333x  = 1      Divide by 0.8333333

x = 1/0.833333

x = 1.2 hours or

x = 1 hour and 12 minutes  

Answer:

[tex]\text{Domain of}R_1=\{-2,0,2,4\}[/tex]  and [tex]\text{Range of}R_1=\{-3,-1,0\}[/tex]

[tex]\text{Domain of}R_2=\{-3,-1,0,3\}[/tex]  and [tex]\text{Range of}R_2=\{-1,0,1,2,3\}[/tex]

Step-by-step explanation:

Domain is the set of input values or x-values.

Range is the set of output values or y-values.

According to the relation mapping diagram, the relation is

[tex]R_1=\{(-2,-3),(-2,-1),(0,0),(2,0),(4,-3)\}[/tex]

So,

[tex]\text{Domain of}R_1=\{-2,0,2,4\}[/tex]

[tex]\text{Range of}R_1=\{-3,-1,0\}[/tex]

In the graph 5 points are plotted. So, the relation is  

[tex]R_2=\{(-3,1),(-1,-1),(0,0),(3,2),(3,3)\}[/tex]

So,

[tex]\text{Domain of}R_2=\{-3,-1,0,3\}[/tex]

[tex]\text{Range of}R_2=\{-1,0,1,2,3\}[/tex]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

[tex]$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $[/tex]

Also

[tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]

I think you mean [tex]210x^6y^4[/tex]

We can deduce that this term will be located somewhere in the middle. So I will calculate [tex]k= 5; k=6 \text{ and } k =7[/tex].

For [tex]k=5[/tex]

[tex]$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$[/tex]

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just [tex]x^{n-k} y^k[/tex]

For [tex]k=6[/tex]

[tex]$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$[/tex]

Answer:

1,000 feet

Step-by-step explanation:

The closer to a square a rectangle is, the greater the area. So the 5,000 feet should be divided into 5 equal sections to create 2 squares with the river making one side.  (Like the letter "E").

5,000/5=1,000

Answer:

d.which is number of candle's in a box

Answer:

number of candies in a box

Step-by-step explanation:

Answer: to find this answer .we need to do pegothogs property

Step-by-step explanation:

30° + 90° = 90 (because it is right angle )

120° - 90° = 30°

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Answer:

The probability that computers work more than 41 minutes is 0.15866 or 15.87%.

Step-by-step explanation:

We are given that a computer tallied the time to work for 200 days and found it reasonable to the normal curve. The mean is 35 minutes, and the standard deviation with six minutes.

Let X = the time taken by computer to work for 200 days.

So, X ~ Normal([tex]\mu=35, \sigma^{2} =6^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                               Z  =  [tex]\frac{X-\mu}{\sigma }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 35 minutes

           [tex]\sigma[/tex] = standard deviation = 6 minutes

Now, the probability that computers work more than 41 minutes is given by = P(X > 41 minutes)

      P(X > 41 minutes) = P( [tex]\frac{X-\mu}{\sigma }[/tex] > [tex]\frac{41-35}{6 }[/tex] ) = P(Z > 1) = 1 - P(Z [tex]\leq[/tex] 1)

                                                                = 1 - 0.84134 = 0.15866

The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.84134.

Answer:

r]

Step-by-step explanation:

Answer:

Standard deviation=4

Step-by-step explanation:

Standard deviation = square root of variance

Standard deviation=√variance

Variance=standard deviation square

Variance=standard deviation^2

From the question

Variance=16

Standard deviation=?

Standard deviation=√variance

=√16

=4

Standard deviation=4

check:

If standard deviation=4

Variance=standard deviation^2

=4^2

=16

Therefore,

Standard deviation=√variance

[tex]4[/tex]

Variance of the variable [tex]=16[/tex]

Standard deviation [tex]=\sqrt{16}[/tex]

                                [tex]=\boldsymbol{4}[/tex]

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Answer:

-8q +18

Step-by-step explanation:

-3 ( 2q -6) -2q

Distribute

-6q+18-2q

Combine like terms

-8q +18

Answer:

[tex]\huge\boxed{a_n=1\cdot(-2)^{n-1}}[/tex]

Step-by-step explanation:

[tex]a_n=a_1r^{n-1}[/tex]

We have the geometric sequence: 1, -2, 4, -8, ...

Find the common ratio:

[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}[/tex]

[tex]a_1=1,\ a_2=-2[/tex]

substitute:

[tex]r=\dfrac{-2}{1}=-2[/tex]

Substitute

[tex]a_1=1;\ r=-1[/tex]

to

[tex]a_n=a_1r^{n-1}[/tex]

[tex]a_n=1\cdot(-2)^{n-1}[/tex]

Answer:

[tex]a_{n}=1 (-2)^{n-1}[/tex]

Step-by-step explanation:

Hi there!

Let's do it,

1)[tex]1,-2,4,-8[/tex]  

First let's find the q, the common ratio by dividing the second term by the anterior one.

-2:1 =-2

4:-2=-2

So the common ratio is -2. Plugging in on the General formula:

[tex]a_{n}=a_{1}q^{n-1}[/tex]

[tex]a_{n}=1 (-2)^{n-1}[/tex]

The lines around the angle is saying that they are corresponding. so the angle of b is 25

Answer:

[tex]\boxed{<b = 25}[/tex]

Step-by-step explanation:

Two angles in the same sector/segment have congruent measures.

So, <b = 25 (These are the two angles in the same segment).

Answer: {-7, 2}

Step-by-step explanation: This type of equation is called a polynomial equation and in order to solve for x, we would first factor the left side.

Notice that the left side of the equation is a trinomial in a special

form that can be factored as he product of two binomials.

As our first term for each binomial, we have the factors of x², x · x

and as the second term, we have the factors of -14 that add to 5.

In this case, the factors are +7 and -2.

So we have (x + 7)(x - 2) = 0.

If (x + 7)(x - 2) = 0, that means that either x + 7 = 0 or x - 2 = 0.

Solving for x in each equation, we have x = -7 or x = 2.

We can write our answer as the solution set {-7, 2}.

The solution of quadratic equation is,

⇒ x = - 7, 2

We have to given that,

An equation is,

⇒ x² + 5x - 14 = 0

We can factorized the above quadratic equation as,

⇒ x² + 5x - 14 = 0

⇒ x² + (7 - 2)x - 14 = 0

⇒ x² + 7x - 2x - 14 = 0

⇒ x (x + 7) - 2 (x + 7) = 0

⇒ (x + 7) (x - 2) = 0

This gives,

x + 7 = 0

x = - 7

x - 2 = 0

x = 2

Therefore, The solution of quadratic equation is,

⇒ x = - 7, 2

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It's point A. 4 vertical units away from point M.

Answer: Point A

Step-by-step explanation:

Point M has the same x value as point A and point A is 4 units below it.

Hope it helps <3

Answer:

any way since the sides are the same leangth

Step-by-step explanation:

Answer:

f(x) = 28 + 10x²

For f(1) substitute 1 into f(x)

That's

f(1) = 28 + 10(1)²

= 28 + 10

f(27) = 28 + 10(27)²

= 28 + 7290

Hope this helps you

Answer:

1) TRIANGULAR PRISM

3) d. 144 cm3

Step-by-step explanation:

1) When figuring out what shape a net is, look at the two shapes that are different. In this case, its the triangles. Then take a look at the other shapes. If it has a rectangle base then you know its a prism. If it has a different shpes base then you know its pyramid. Now just combine the two key words you found. Triangle + Prism = Triangular Prism

2) A solid is something that is firm and stable. So it is not a liquid or solid. Pretty much everything that you listed is a solid.

3) The formula for finding the volume of a triangular prism is bxhxl divided by 2. So it would be 8x3x12= 288 divided by 2= 144 cm3

Answer:

Triangular prism.

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

24 ÷ [ 33- (1+2)^2]

= 24 / ( 33 - 3^2)

= 24 / 24 = 1.

21 + 3 (2-2^2)

= 21 + 3(2 - 4)

= 21 + 3 * -2

= 21 - 6

= 15.

[(14+√4)÷2^3] - 14

= [ (14 + 2) / 8] - 14

= 16/8 - 14

= 2 - 14

= -12.

20 + [18÷(4+1)] - (3^2 + 2)

= 20 + [18÷ 5] - (9 + 2)

= 20 + 3.6 - 11

= 23.6 - 11

= 12.6.

Answer: (0.4016, 0.4984).

Step-by-step explanation:

Let p be the proportion of voters will vote for Candidate A for president.

Formula for confidence interval for proportion:

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

, here [tex]\hat{p}[/tex]= sample proportion

n= sample size.

z* =two-tailed critical z- value.

As per given, we have

n= 700

[tex]\hat{p}[/tex] = 0.45

Critical two-tailed z-value for 99% confidence interval = 2.576

Then, the required 99% confidence interval for p would be:

[tex]0.45\pm (2.576)\sqrt{\dfrac{0.45(1-0.45)}{700}}\\\\=0.45\pm(2.576)\sqrt{0.000353571428}\\\\=0.45\pm (2.576)(0.0188035)\\\\=0.45\pm0.04844\\\\=(0.45-0.048437,\ 0.45+0.048437)\\\\=(0.401563,\ 0.498437)\approx(0.4016,\ 0.4984)[/tex]

Hence, the required confidence interval (0.4016, 0.4984).

Answer:

The correct option is;

[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex]

Step-by-step explanation:

The given expression is presented as follows;

[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )[/tex]

Which can be expanded into the following form;

[tex]\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n[/tex]

From which we have;

[tex]\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}[/tex]

[tex]\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}[/tex]

Therefore, substituting the value of n = 50 we have;

[tex]\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}[/tex]

[tex]\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}[/tex]

Which gives;

[tex]4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}[/tex]

[tex]3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}[/tex]

[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}[/tex]

Therefore, we have;

[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex].