Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]
A. 28.93 units²
B. 29.98 units²
C. 29.79 units²
D. 30.73 units²

Answer:

The volume of the pyramid is 867 inch^3

Step-by-step explanation:

Here in this question, we are interested in calculating the volume of a square based pyramid.

Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.

V = a^2h/3

where a represents the length of the side of the square and h is the height of the pyramid

From the question, the length of the side of the square is 17 in while the height is 9 in

Plugging these values, we have ;

V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch

Answer:

x = -1

Step-by-step explanation:

the line of the simetry is x = -1

Answer:

Its x = -1 because it splits the diamond shape perfectly at x -1

Step-by-step explanation:

Answer:

37,139

Step-by-step explanation:

Given the following :

Population in 2002 = Initial population (P0) = 22,800

Growth rate (r) = 5% = 0.05

Growth in 2012 using the exponential growth function?

Time or period (t) = 2012 - 2002 = 10years

Exponential growth function:

P(t) = P0 * (1 + r) ^t

Where P(t) = population in t years

P(10) = 22800 * (1 + 0.05)^10

P(10) = 22800 * (1.05)^10

P(10) = 22800 * 1.62889

P(10) = 37138.797

P(10) = 37,139 ( to the nearest whole number)

Answer:

  the sides are different lengths as shown in the diagram

Step-by-step explanation:

Plotting the three points, you can see by "inspection" that the middle length side (PQ) is longer than the shortest side (QR) and shorter than the longest side (PR). You could use the distance formula to show this, or you can use a scale to measure the drawing.

A triangle with three unequal sides is a scalene triangle. ∆PQR is scalene.

To build the fleet of ships, Astrid must consider each of the given rates (i.e.  the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.

Given that:

Required quantities

[tex]Wood = 40\ tons[/tex]

[tex]Sailors = 300[/tex] per ship

Available quantities

[tex]Wood = 4\ tons[/tex] daily

[tex]Days = 100[/tex] at most

First, we calculate the total tons of woods Astrid can receive.

[tex]Total = Days \times Wood\ Available[/tex]

[tex]Total = 100 \times 4[/tex]

[tex]Total = 400\ tons[/tex] ---- in 100 days

Next, we calculate the number of ships that can be made from the 400 tons.

[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]

So, we have:

[tex]Ships = \frac{400}{40}[/tex]

[tex]Ships = 10[/tex]

This means that Astrid can build up to 10 ships

The number of sailors the ship can accommodate is:

[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]

So, we have:

[tex]Sailors = 10 \times 300[/tex]

[tex]Sailors = 3000[/tex]

It means the 10 ships can accommodate 3000 sailors.

3000 sailors is greater than 2100 sailors.

So, we can conclude that she can build enough ship for the 2100 sailors.

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Answer:

280 tons

Step-by-step explanation:

:)

Answer:

2+n = 8

Step-by-step explanation:

2+ something must equal 8.

8 minus 2 = 6

n=6

Answer:

According to question,

2+ n =8

=) n = 8-2

=) n =6

hope you understand.

Answer:

The y-values repeat in various functions (for example: quadratic function: y=x²; y=4 for x=2 and for x=-2)  

Hello there! :)

Answer:

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

Given the equation:

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.

Answer:

height = 4cm

Step-by-step explanation:

volume = п r² h

п = 3.14   (aprox.)

r = radius

h = height

volume = 616cm³

then:

616 = 3.14 * 7² * h

616 = 3.14*49*h

616 = 153,86 * h

h = 616 / 153.86

h = 4

height = 4cm

Answer:

Your answer is

Step-by-step explanation:

Hope this helps....

Have a nice day!!!!

Answer:

4

Step-by-step explanation:

8 ^ 2/3

Rewriting 8 as 2^3

( 2^3) ^ 2/3

We know that a^ b^c = a^ (b*c)

2 ^ ( 3 * 2/3)

2 ^ 2

4

Answer:

52 / 5424 = 0.00958..

198 / 8549 = 0.0231 ..

Step-by-step explanation:

52 / 5424

First of all, you need to add 0 plus a coma → 0.

52 becomes 520, but this value is smaller than 5424, so we need to add another 0

5200 → another 0 → 52000

So now, we have 52000 / 5424.

We start,  5424 . 10 = 54240, we are higher than 52000, so let's try 9

5424 . 9 = 48816, great!

52000 - 48816 = 3184

This is smaller than 5424, so we need a zero, again. But we do not add 0 to the result, because we are in the decimal side

31840 → 31840 / 5424. We would try 6,

5424 . 6 = 32544. It's bigger!, We use 5

5424 . 5 = 27120!

31840 - 27120 = 4720. We get another 0

47200, and we try 8.

5424 . 8 = 43392

47200 - 43392 = 3808.

So we are going to add 0, until we have four digits that can be divided by 5424 and decimals are infinte.

52 / 5424 = 0.00958..

198 / 8549 → Need to add, the first 0 to convert 198 to 1980

1980 = 0. → Another zero

19800 = 0.0 → 19800 / 8549

We try 2 → 8549 . 2 = 17098

19800 - 17098 = 2702 → we add 0

27020 / 8549 → We try 3

8549 . 3 = 25647 → 27020 - 25647 = 1373 → we add 0

13730 / 8549 → We use 1 → 13730 - 8549 = 5181

As decimal are infinite, we can express the result as:

198 / 8549 = 0.0231 ..

Answer:

(2a, b )

Step-by-step explanation:

Given the endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ [tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

Here (x₁, y₁ ) = N(2a, 2b) and (x₂, y₂ ) = P(2a, 0), thus

midpoint = [ [tex]\frac{1}{2}[/tex](2a + 2a), [tex]\frac{1}{2}[/tex](2b + 0 ) ] = (2a, b )

Answer:

Step-by-step explanation:

The function is f(x)=x^2 + ax + b

Derivate the function:

● f'(x)= 2x + a

Solve the equation f'(x)=0 to find a

The minimum is at (3,9)

Replace x with 9

● 0 = 2×3 + a

● 0 = 6 + a

● a = -6

So the value of a is -6

Hence the equation is x^2 -6x+b

We have a khown point at (3,9)

● 9 = 3^2 -6×3 +b

● 9 = 9 -18 + b

● 9 = -9 +b

● b = 18

So the equation is x^2-6x+18

Verify by graphing the function.

The vetex is (3,9) and it is a minimum so the equation is right

Answer:

Step-by-step explanation:

Given that ;

The Acme Company lost 650 hours due to accidents on the job in the first quarter of the year

The average hourly wage of the employees who contributed to the lost hours was $15.00 . i.e the direct labor cost = $15.00

The company benefits add 25% to the wages. = 0.25

The loaded labor cost = $15.00/hr × 0.25 = $3.75/hour

If we add the additional cost of benefit, then we have the loaded labor cost to be =  $15.00/hour + $3.75/hour

= $18.75 / hour

However, the direct labor costs that the workers continued to receive without working. for the  first quarter of the year by using the cost-of-lost-hours formula is  :

= 650 hours × $15.00 / hours

= $9750

The hidden costs can be estimated from the Acme company's contributions to the employee. Given that the company benefits add 25% to the wage of the employee, therefore, this wage must be incorporated in order to find out the total wage cost for the lost work hours in the Acme company.

As a result of the company benefits, the fully loaded labor cost is 650 hours  × $18.75 /hour which gives $12187.5.

Consequently, it is pertinent to determine the cost for  additional benefits that the workers are receiving even though they are not working, this is achieved by the difference in the $9750 direct cost paid to labor and the benefits amount of $12187.5

i.e

the cost for additional benefits that the workers are receiving even though they are not working = $12187.5 - $9750 = $2437.5

Other ways the hidden cost can be estimated is by take note of the amount paid to the employee on the day the employee had  an emergency, amount paid to the rescue team involved. etc

Answer:

Sector

Step-by-step explanation:

A sector of a circle is the portion of circle enclosed by two radii and arc

Answer:

3x +10y  is greater than or equal to 250.

Step-by-step explanation:

The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.

Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.

Answer:

3n + 10c > 250

Step-by-step explanation:

I confirmed it in grandpoint

Answer:

The correct option is;

c. Plot a point not on the original line segment

Step-by-step explanation:

The steps to copy a line segment are;

1) Plot a point that will be an endpoint of the new line segment

2) With the compass pin at the beginning of the original line segment, open the compass width to the end of the original line segment

3) With the adjusted compass width from the above step place the compass pin at the plotted point of the new line segment and draw an arc in the region the new line segment is to be located

4) Select a point on the arc where the other end of the new line will be

5) From the selected point from the above step, draw a line to the point plotted as the beginning of the new line segment

6) The length of the line drawn above is the same as the length of the original line segment.

Hey there! I'm happy to help!

First, let's find the length of GA. We can just subtract all of the other sides from the perimeter to find this.

172-56-56-35=25

We see that E'M' is 14 and EM is 35.

35/14=2.5

This means that all of the sides on the big pinball machine are 2.5 times bigger than those of the smaller one.

So, we take the length of GA and then divide it by 2.5 to see how big G'A' is.

25/2.5=10

Therefore, the length of G'A' is 10 inches.

I hope that this helps! Have a wonderful day! :D

The order of a matrix is m×n where m is the number of rows and n is the number of columns.

can you count and find what are m and n here?

Answer:

Step-by-step explanation:

Number of rows X Number of columns

Rows = 3

Columns = 2

answer = 3x2

Answer:

  all reals

Step-by-step explanation:

Simplified, you have ...

  20 -3n = 20 -3n

The equation is a tautology, true for all values of n.

The solution set is "all reals."

Answer:

Step-by-step explanation:

Hello,

[tex]2n^2+n-4=0\\\\\Delta=b^2-4ac=1^2-4*2*(-4)=1+32=33>0[/tex]

So there are 2 distinct real solutions.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

Given:

Number of red balls, n(R) = 3

Number of green balls, n(G) = 9

Number of yellow balls, n(Y) = 2

Number of orange balls, n(O) = 2

Number of purple balls, n(P) = 4

Two balls are drawn one at a time with replacement.

To find:

Probability of drawing a green ball and an orange ball ?

Solution:

Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20

Formula for probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Probability that a green ball is drawn at first:

[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Green) = \dfrac{9}{20}[/tex]

Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]

[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]

Answer: [tex](y-1)=\dfrac{3}{2}(x+3)[/tex]

Step-by-step explanation:

Slope of the given line passing through (-2,-4) and (2,2) :

m=  [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]=\dfrac{2-(-4)}{2-(-2)}\\\\=\dfrac{2+4}{2+2}=\dfrac{6}{4}\\\\=\dfrac{3}{2}[/tex]

Parallel lines has same slope . That means  slope of required line would be [tex]\dfrac{3}{2}[/tex].

Equation of a line passing through (a,b) and has slope 'm' is given by :_

[tex](y-b)=m(x-a)[/tex]

Now, Equation of a line passing through(-3, 1) and has slope '[tex]\dfrac{3}{2}[/tex]' is given by

[tex](y-1)=\dfrac{3}{2}(x-(-3))\\\\\Rightarrow\ (y-1)=\dfrac{3}{2}(x+3)\ \ \to \text{Required equation in point slope form.}[/tex]

Sandy got 350 out of 2400.

Her portion is 350/2400 which can be reduced to:

35/240 = 7/48

The portion is 7/48

Answer:

None

Step-by-step explanation:

All of the fractions listed are not a whole or more than a whole. They are all parts of a whole, therefore she did not spend more than an hour on any of them

Answer:

cooking and swimming

Step-by-step explanation:

Answer:

53 1/3 km/h

Step-by-step explanation:

average speed = (total distance)/(total time)

average speed = distance/time

time * average speed = distance

time = distance/(average speed)

250 km at 75 km/h

distance = 250 km

time = (250 km)/(75 km/h) = 3.33333... hours

350 km at 70 km/h

distance = 350 km

time = (350 km)/(70 km/h) = 5 hours

200 km at 30 km/h

distance = 200 km

time = (200 km)/(30 km/h) = 6.6666...  hour

total distance = 250 km + 350 km + 200 km = 800 km

total time = 3.33333... hours + 5 hours + 6.66666... hours = 15 hours

average speed = (total distance)/(total time)

average speed = (800 km)/(15 hours)

average speed = 53 1/3 km/h

The average speed of whole journey of the train is 45 km/hr

Average speed is the ratio of total distance travelled to total time taken. It is given by:

Average speed = total distance / total time

Given that a train travels 250 km with a average speed of 75 km/hr, hence:

75 = 250/time

time = 3.33 hours

It the travel 200 km with average speed of 30km/hr, hence:

30 = 200/time

time = 6.67 hours

The total distance = 200 km + 250 km = 450 km

The total time = 3.33 hr + 6.67 hr = 10 hours

Average speed = total distance/total time = 450 km/10 hours = 45 km/hr

The average speed of whole journey of the train is 45 km/hr

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Answer:

900 outfits

Step-by-step explanation:

You just have to multiply them all together :)

Answer:

[tex]slope=3[/tex]

Step-by-step explanation:

Use the following equation the find the slope:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope". Insert the known values:

[tex](-10_{x1},8_{y1})\\\\(-15_{x2},-7_{y2})\\\\\\\frac{-7-8}{-15-(-10)}\\\\\frac{-7-8}{-15+10}[/tex]

Solve:

[tex]\frac{-7-8}{-15+10}=\frac{-15}{-5}[/tex]

Simplify. Two negatives make a positive:

[tex]\frac{-15}{-5}=\frac{15}{5}[/tex]

Simplify fraction by dividing top and bottom by 5:

[tex]\frac{15}{5}=\frac{3}{1} =3[/tex]

The slope is 3.

:Done

The slope of the line that passes through the points (-10, 8) and  (-15, -7) is 3 and thsi can be determined by using the point-slope formula.

Given :

The line that passes through the points (-10, 8) and  (-15, -7).

The following steps can be used in order to determine the slope of the line that passes through the points (-10, 8) and  (-15, -7):

Step 1 - The slope formula when two points are given is:

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.

Step 2 - Substitute the known terms in the above formula.

[tex]\rm m = \dfrac{-7-8}{-15+10}[/tex]

Step 3 - Simplify the above expression.

[tex]\rm m = \dfrac{15}{5}[/tex]

m = 3

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Answer:

I hope this will help!

Step-by-step explanation:

Answer:

The answer is option 1.

Step-by-step explanation:

You have to apply Indices Law :

[tex] \frac{ {a}^{m} }{ {a}^{n} } ⇒ {a}^{m - n} [/tex]

So for this question,

[tex] \frac{ {7}^{ - 3} }{ {7}^{ - 5} } = {7}^{ - 3 - ( - 5)} = {7}^{ - 3 + 5} = {7}^{2} [/tex]

Answer :

7²

[tex] \frac{ {7}^{ - 3} }{ {7}^{ - 5} } = \\ {7}^{ - 3 - ( - 5)} = \\ {7}^{ - 3 + 5} = {?}^{2} [/tex]