Apply the distributive property to factor out the greatest common factor.
{25p + 50q} =

Answer:

33.69°

Step-by-step explanation:

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Answer:

33.69°

Step-by-step explanation:

Let's take ∡CBA as y

Tan y =  [tex]\frac{opposite}{adjacent}[/tex]

         =  [tex]\frac{6}{9}[/tex]

         = 0.6666

y = 33.69°

Solution 1

Solution 2

Solution 3

#1

#2

Cancel by 4

#3

Answer:

15

Step-by-step explanation:

Let the probability of picking an orange = P(O), and the probability of picking a strawberry = P(S),

Based on the question, he picked an orange first and the probability of picking that is

P(O) = 12/50

Then he picked a strawberry on the second pick, the probability of picking the strawberry is P(S) and we'll find that later.

The probability of picking orange then strawberry with replacement is

P(O) × P(S) = 9/125

Substitute the P(O)=12/50,

12/50 × P(S) = 9/125

P(S) = 3/10

Then by finding the number of strawberry candies, we'll just have to multiply P(S) with the total number of candies, i.e.

Number of strawberry candy

= 3/10 × 50

= 15

Step-by-step explanation:

as the graphic shows, we are dealing with a special rhombus : a square.

this is proven by the fact that the angle on one side of the diagonal at the corner is 45°. so, the other side must be 45° too, and so we have 90° angles at the corners.

what is not clear to me is : what is 6 cm long ? a half-diameter, or the whole diameter ?

I assume the half-diameter.

what the graphic is trying to suggest is that we have 4 little right-angled triangles that are also isoceles triangles (their legs are equally long).

every leg is 6 cm long (based on my assumption above).

because they are right-angled, the area of each of these little triangles is leg×leg/2

6×6/2 = 18 cm²

we have 4 triangles, so the total area is

4×18 = 72 cm²

if 6 cm stands for the whole diagonal after all, then the only change is the length of the legs, which would be then 6/2 = 3 cm.

then we would have

3×3/2 = 4.5 cm² for a single triangle

and

4×4.5 = 18 cm² for the whole area.

Answer:

0

Step-by-step explanation:

The median of this data set is 0. To find the median, you must arrange the data points from least to greatest (which is already done in this data set), then you must locate the central number, if there is no specific central number, you find the number inbetween these two central numbers, in this case 0 and 0, which is 0.

Answer:

the answer is 1/27. C :))

Answer: p=11

Step-by-step explanation:

-3(p-4) = -2p+1

-3p+12=-2p+1

+2p +2p

-p+12=1

-12 -12

(-1)-p=-11 (-1)

p = 11

Check answer:

-3(11-4)=-2(11)+1

-3(7)=(-22)+1

-21 = -21

Answer:

702 pounds

Step-by-step explanation:

9 * 78 = 702

Answer:

If Maria has 9 boxes that each weigh 78 pounds, in total the boxes would weigh 702 pounds.

Step-by-step explanation:

9 x 72 = 702 pounds

Your welcome! :)

The total amount which Todd will have after 4 years is $1,178

The total amount which Alexis will have after 4 years is $1,184

1050 + 32(4)=

1050 + 128

= $1,178.

For Alexis

(P x T x R)/100

(1050 x 4 x 3.2)/100

=13400/100

=$134 interest after 4 years.

Therefore, 1050 + 134

=$1,184.

Here is the constructed frequency distribution table:

Number of visits   Number of students

0 - 1                            5

2 - 3                             9

4 - 5                           11

6 - 7                            5

8 - 9                            8

10 - 11                         2

A frequency table is used to arrange a large amount of data using their frequency. The class width is the difference between the upper boundary and the lower boundary.

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Answer:

  9 1/2 inches

Step-by-step explanation:

The scale of a map is the ratio of map distance to represented distance. This can be used to write a proportion.

__

  map distance/represented distance = 1 in/(30 mi) = x/(285 mi)

where x represents the map length of the southern border.

Multiplying by 285 mi, we have ...

  x = (285 mi)(1 in)/(30 mi) = 9.5 in

The border is 9.5 inches on the map.

Answer:

12 feet

Step-by-step explanation:

3 times 4 is 12

you would multiply by 4 because of the 4 sides of the window

Answer:

Step-by-step explanation:

According to the drawing we can see the lines

The required length of the rectangle is 12/5 feet and the width is 9/5 feet.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's denote the length of the rectangle as L and the width as W.

From the problem statement, we know that:

3L = 4W (equation 1)

We also know that the perimeter P is given by:

P = 2L + 2W = 8 2/5 feet

Multiplying both sides by 5 to get rid of the fraction, we get:

10L + 10W = 42

Dividing by 2, we get:

5L + 5W = 21 (equation 2)

Now we can use equations 1 and 2 to solve for L and W.

First, we can substitute equation 1 into equation 2 to get an equation in terms of W:

5L + 15L/4 = 21

Multiplying both sides by 4, we get:

20L + 15L = 84

35L = 84

L = 84/35 = 12/5 feet

Now we can substitute the value of L into equation 1 to get the value of W:

3L = 4W

3(12/5) = 4W

W = 9/5 feet

Therefore, the length of the rectangle is 12/5 feet and the width is 9/5 feet.

Learn more about models here:
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Answer:

Varies - possibly not enough information

Step-by-step explanation:

How many doses per day?

Do you only need to know the amount of oz. for "today"?

Does this need to be expressed in decimal form?

If the patient is ordered to take 2- 2/3 oz. per day, you have your answer.

Decimal form: 2-2/3 = 8/3 = 2.667 oz.  

Answer:

[tex]\fbox{ Option D ➫ \: 416 \: cm²}[/tex]

Step by step explanation:

Given:

height of prism h = 18 cm

length of base of triangle b = 10cm

height of triangle h' = 2 cm

side A of triangle = 5 cm

side B of triangle = 7 cm

To find:

Surface area of prism = ?

Solution:

[tex]Area \: of \: base \: triangle = \: \frac{1}{2}\cdot{b}{h'} \\ Area \: of \: base \: triangle = \frac{1} {\not2}\cdot{10} \times \not{2} \\ Area \: of \: base \: triangle = 10 \: {cm}^{2} [/tex]

[tex] \fbox{Area \: of \: base \: triangle \: (B) = 10 \: cm²}[/tex]

[tex]Perimeter \: of \: base \: triangle = Side A + Side B + base b \\ Perimeter \: of \: base \: triangle = 5 + 7 + 10 \: cm \\ Perimeter \: of \: base \: triangle = 22 \: cm[/tex]

[tex] \fbox{Perimeter \: of \: base \: triangle (p) \: = 22 \: cm}[/tex]

[tex]Surface \: area \: of \: prism = 2B+ \: ph \\ Surface \: area \: of \: prism = 2 \times 10+ \: 22 \times 18 \\ Surface \: area \: of \: prism = 20 + 396\\ Surface \: area \: of \: prism = 416 \: {cm}^{2} [/tex]

[tex]\fbox{Surface \: area \: of \: prism = 416 \: cm²}[/tex]

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Answer:

D. 416 cm²

Step-by-step explanation:

Let S be the surface area of the prism

     B be the area of the base of the prism

     A be the lateral area of the prism

_______

formula :

S = 2B + A

__________

The base is a triangle ,then B the area of the base :

[tex]B=\frac{10 \times 2}{2}=10 \mathrm{~cm}^{2}[/tex]

_______

formula :

A = (Perimeter of the base) × (the height of the prism)

__________

then ,

[tex]\begin{aligned}A &=(10+5+7) \times 18 \\&=22 \times 18 \\&=396cm^2\end{aligned}[/tex]

Conclusion:

[tex]\begin{aligned}S &=2 B+A \\&=2 \times(10)+396 \\&=20+396 \\&=416 \mathrm{~cm}^{2}\end{aligned}[/tex]

Answer:

See below ~

Step-by-step explanation:

Distance Formula

Finding the side lengths

Perimeter

Answer:

the answer is D

Step-by-step explanation:

Answer:

  (a)  3/8x +3/8y

  (d)  5/8x -5/8y -1/4x +y

  (e)  5/8x - 1/4x + y - 5/8y

Step-by-step explanation:

An equivalent expression can be found by simplifying the given expression, removing parentheses and combining like terms.

__

  (x -y)(5/8) -1/4x +y

  = 5/8x -5/8y -1/4x +y . . . . . use distributive property

  = 5/8x -1/4y +y -5/8y . . . . . . reorder terms

  = (5/8 -1/4)x +(1 -5/8)y . . . . . group like terms

  = 3/8x +3/8y

Answer:

1.65x

Step-by-step explanation:

multiply 3x107 to get 321.

multiply 5x106 to get 530.

divide 530 by 321 to get 1.65x

Answer:

81 [ft].

Step-by-step explanation:

1) the basic formula is: h=gt²/2, where g - acceleration due to gravity, t - elapsed time;

2) if the final velocity is 72, g=32, then it is possible to calculate elapsed time:

[tex]t=\frac{V}{g}=\frac{72}{32}=\frac{9}{4} [sec].[/tex]

3) if g=32, t=9/4, then the required height is:

[tex]h=\frac{32*(\frac{9}{4} )^{2} }{2}=\frac{16*81}{16}=81[ft].[/tex]

The height of the building comes to be 81 feet.

Initial velocity u= 0 feet/sec

Final velocity v= 72 feet/sec

The acceleration due to gravity g =32ft /sec²

Height of the building h= suppose h

The equation of a motion is:

[tex]v^{2} =u^{2} +2gh[/tex]

Where u and v are the initial and final velocities.

[tex]72^{2} =0+2*32*h\\144 = 64h\\h=81[/tex]

So, the height of the building = 81 feet.

Therefore, the height of the building comes to be 81 feet.

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Answer:

12, 60

Step-by-step explanation:

To solve this question, we can use a system of equations

1) x + y = 76

2) y - 3x = 12

Then, we can use the second equation to isolate y and substitute it into the second equation

y = 3x + 12

x + (3x + 12) = 76

4x + 12 = 76

4x = 64

x = 16, y = 60

Answer:

6

Step-by-step explanation:

based in

Vincent Van Gogh’s most popular painting, The Starry Night was created by Van Gogh at the asylum in Saint-Rémy, where he’d committed himself in 1889. Indeed, The Starry Night seems to reflect his turbulent state of mind at the time, as the night sky comes alive with swirls and orbs of frenetically applied brush marks springing from the yin and yang of his personal demons and awe of nature.

Answer:

The answer is 12 cm.

Step-by-step explanation:

Verified by correct test results.

The length of the hypotenuse of the given right triangle would be 12cm.

Given is that the length of the shorter leg of a 30-60-90 Special Right Triangle is 6 cm long.

The base length is the shortest distance of the right - angled triangle. We can find the hypotenuse using the cosine function as -

cos(60) = b/h

h ={b/cos(60)}

h = 6/(1/2)

h = 6 x 2

h = 12 cm

Therefore, the length of the hypotenuse of the given right triangle would be 12cm.

To solve more questions on triangles, visit the link-

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f(x) = 2x³+3x²-4x-5

let x + 2 = 0

x = 2

f(x) = 2(2)*3 + 3(2)*2 - 4(2) - 5

= 2 × 8 + 3 × 4 - 4 × 2 - 5

= 16 + 12 - 8 - 5

= 15

↪Then the reminder is 15

☆...hope this helps...☆

_♡_Mashi_♡_

Answer:

9 units

Step-by-step explanation:

Line O bissects AC at its midpoint, creating a right angle. So, we know that AB is exactly 1/2 of AC.

Algebraically:

AB = AC/2

AB = 18/2

AB = 9 units

Hope this helps!

Answer:

AB = 9

Step-by-step explanation:

Perpendicular line from the center of the cirlcle to the chord bisects the chord.

AB = 18/2

AB = 9

Answer:

The answer is 27.6

Step-by-step explanation:

I've attached a picture with the labelled figured and working steps. Hope it'll help =)