Simplify the radical expression. Use absolute value symbols if needed.
√400x^2y^6

A. 20|x|y^3
B. 20|x|y^4
C. 20|xy^3|
D. 20xy^4

Answer: $1500 was invested in the account earning 8%.

$3300 was invested in the account earning 12.5%.

$1850 was was invested in the account earning 7.5%.

Step-by-step explanation:

Let x represent the amount invested in the account earning 8%.

Let y represent the amount invested in the account earning 12.5%.

Let z represent the amount invested in the account earning 7.5%.

Penelope invested $6650 into theee investment accounts, earning 8%, 12.5%, and 7.5% simple interest per year. It means that

x + y + z = 6650- - - - - - - - - - -1

Interest earned from the $x investment is

8/100 × x = 0.08x

Interest earned from the $y investment is

12.5/100 × x = 0.125y

Interest earned from the $z investment is

7.5/100 × x = 0.075z

If the annual interest earned totaled $671.25, it means that

0.08x + 0.125y + 0.075z = 671.25- - - - - - - 2

The amount invested at 12.5% was $300 more than twice the amount invested at 8%. It means that

y = 2x + 300

Substituting y = 2x + 300 into equation 1 and equation 2, it becomes

x + 2x + 300 + z = 6650

3x + z = 6650 - 300

3x + z = 6350- - - - - - - - - 4

0.08x + 0.125(2x + 300) + 0.075z = 671.25

0.08x + 0.25x + 37.5 + 0.075z = 671.25

0.33x + 0.075z = 671.25 - 37.5

0.33x + 0.075z = 633.75- - - - - - - 5

From equation 4, z = 6350 - 3x

Substituting z = 6350 - 3x into equation 5, it becomes

0.33x + 0.075(6350 - 3x) = 633.75

0.33x + 476.25 - 0.225x = 633.75

0.33x - 0.225x = 633.75 - 476.25

0.105x = 157.5

x = 157.5/0.105

x = 1500

y = 2x + 300

y = 2(1500) + 300

y = 3300

Substituting x = 1500 and y = 3300 into equation 1, it becomes

1500 + 3300 + z = 6650

z = 6650 - 4800

z = 1850

Answer:

The area is 36

Step-by-step explanation:

hope it helps :3

multiple the length x width

6x6=36

Answer:

The length of ST to the nearest tenth of a foot is 5.2 ft

Step-by-step explanation:

Here we have

∡T = 90°

∡R = 64°

RS = 5.8 ft

To answer the question, we have apply sine rule as follows;

[tex]\frac{a}{Sin\alpha } = \frac{b}{sin\beta } = \frac{c}{sin\gamma}[/tex]

Therefore, for triangle RST, we will have;

[tex]\frac{RS}{SinT } = \frac{ST}{sinR } = \frac{RT}{sinS}[/tex]

Therefore;

[tex]\frac{5.8}{Sin90 } = \frac{ST}{sin64 }[/tex] from which

[tex]{ST}{ } = \frac{5.8 \times sin64}{Sin90 } = 5.213 \, ft[/tex]

Therefore, the length of ST to the nearest tenth of a foot = 5.2 ft.

Answer: 53 degrees

Step-by-step explanation:

Answer:

19.66 or 19.7 units

Step-by-step explanation:

[tex]sin \: 24 \degree = \frac{8}{x} \\ \\ 0.4067366431 = \frac{8}{x} \\ \\ x = \frac{8}{0.4067366431} \\ x = 19.6687467 \\ x \approx 19.7 \: units \\ [/tex]

Answer:12

Step-by-step explanation:

Given

A quarter and a spinner is played simultaneously so

A quarter can show two outcomes i.e. head and tail

While spinner can show 6 outcomes from 1 to 6

So there can be [tex]2\times 6=12[/tex] possible outcomes

(H,1),(H,2) ,(H,3) ,(H,4) ,(H,5) ,(H,6) ,(T,1) ,(T,2) ,(T,3) ,(T,4) ,(T,5) ,(T,6)

Answer:

Point Form:

( − 2 , 3 )

Equation Form:

x  =  − 2 ,  y  =  3

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Answer:

x = -2, y = 3

Step-by-step explanation:

x + 3y = 7

2x + 4y = 8

Make the x term the same for both equations by multiplying the first equation by 2.

Now you have two equations with the same x terms.

2x + 6y = 14

2x + 4y = 8

Take the larger equation from the smaller to remove the x terms from the equations.

2x + 6y = 14

                   -

2x + 4y = 8

2y = 6

y = 3

Put the known y term back into the equations to find the y term

3(3) + x = 7

9 + x = 7, x = -2

12 + 2x = 8

2x = -4, x = -2

Step-by-step explanation:

This sequence is by adding 4 you get the next number

Addition is the function

Answer:

212

Step-by-step explanation:

volume of new figure = sum of the two individual figures

volume of one cuboid=l*b*h

volume of first cuboid=92

volume of second  cuboid=120

sum of two figures=212

hope this helps

plzz mark me brainliest

Answer:

212 is the answer

Step-by-step explanation:

First to find the area of the first figure, you must use the formula for volume: length times width times height.

so: 23(2)(2) is equal to 92.

then for the second figure: 8(5)(3) is equal to 120.

now you add the two answers.

92+120=212

Answer:

Actual dimension of the field = 42 ft × 21 ft

Equation : [tex]y=\frac{7}{2}x[/tex]

Step-by-step explanation:

Scale for the drawing of a rectangular playing field is,

2 inches = 7 feet

Or 1 inch = 3.5 feet

If length of the playing field on drawing = 12 in

Then actual length of the field = 12×3.5 = 42 feet

And width on the drawing = 6 inches

Therefore, actual width of the field = 6×3.5 = 21 feet

If 'x' is the dimension of a scale drawing and 'y' be the corresponding dimension of the actual field,

[tex]\frac{x}{y}=\frac{2}{7}[/tex]

[tex]y=\frac{7}{2}x[/tex]

Answer: The​ student's estimate is off by  

4%

Answer:

Jeff rode 4 1/2 miles

Step-by-step explanation:

a simple way to do this is divide 9 by 2 to get 4 1/2

Answer:

Step-by-step explanation:

If it is hard to multiply fractions, you can always convert it into decimal form.

1/2 is equivalent to 0.5

Since he went around the trail 9 times, you have to multiply 0.5 times 9 which equals 4.5.

That means Jeff rode 4 1/2 miles

Hope this helps!

Answer:

The exact probability that all three marbles drawn  will be red is [tex]\frac{1}{56}[/tex]

Step-by-step explanation:

Number of red marbles = 5

Number of blue marbles = 4

Number of Green marbles = 7

Total Number of marbles = 5+4+7=16

We are given that three marbles  are drawn out of the bag

Probability of getting 1 red marble on first draw=[tex]\frac{5}{16}[/tex]

Probability of getting 1 red marble on second draw= [tex]\frac{4}{15}[/tex]

Probability of getting 1 red marble on third draw=[tex]\frac{3}{14}[/tex]

So,the exact probability that all three marbles drawn  will be red=[tex]\frac{5}{16} \times \frac{4}{15} \times \frac{3}{14}=\frac{1}{56}[/tex]

Hence The exact probability that all three marbles drawn  will be red is [tex]\frac{1}{56}[/tex]

Final answer:

The exact probability of drawing three red marbles consecutively from a bag containing a mix of 16 marbles is 1 in 56, calculated by multiplying the probabilities of each draw without replacement.

Explanation:

The question asks for the exact probability that all three marbles drawn from a bag containing 5 red marbles, 4 blue marbles, and 7 green marbles will be red. To find this probability, we use the formula for conditional probability without replacement.

First, calculate the total number of marbles, which is 5 + 4 + 7 = 16 marbles. The probability of drawing a red marble first is 5 out of 16. Once a red marble is drawn, there are now 15 marbles left, and 4 of them are red. So, the probability of drawing a second red marble is 4 out of 15. Further, if a second red marble is drawn, there are now 14 marbles left, and 3 of them are red, making the probability of drawing a third red marble 3 out of 14.

The combined probability of all three events (drawing three red marbles in a row) happening is the product of their individual probabilities:

P(3 red marbles) = (5/16) * (4/15) * (3/14) = 60 / 3360 = 1/56

Therefore, the exact probability of drawing three red marbles in a row from the bag is 1 in 56.

Answer:

1/5

Step-by-step explanation:

We need to fill in the circles; on the left, we need to put the number of students who play an instrument. That information is given: it's 25.

In the middle, we need the number of students who both play an instrument and speak a foreign language: again, we know that's 16.

On the right, we need the number of students who speak a foreign language; that's 30.

Finally, there are 9 students who participate in neither of these activities, so place "9" outside the circles but still in the rectangle.

See the attachment.

Probability is basically (# times specific event can occur) / (# times general event will occur). Here, the specific event is getting a student who plays an instrument and speaks a foreign language, which is 16. The general event is just selecting a student; since there are 80 total students, that number would be 80.

Our probability is thus:

16 / 80 = 1/5

Answer:

16/41

Step-by-step explanation:

Outside both: 9

Intersection (both): 16

0nly "Play instrument": 25

Only "Speak Foreign language": 30

Total: 80

P(Language/Instrument)

= n(both)/n(Instrument)

= 16/(25+16)

= 16/41

Answer:

3k -10

Step-by-step explanation:

8k - 6 -5k -4 = (8-5)k -(6+4) = 3k -10

The expression (8k - 6) - (5k + 4) is equivalent to the expression 3k - 10.

The equivalent is the expressions that are in different forms but are equal to the same value.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ (8k - 6) - (5k + 4)

Simplify the expression, then the value of the expression will be

⇒ (8k - 6) - (5k + 4)

⇒ 8k - 6 - 5k - 4

⇒ 3k - 10

Then the expression (8k - 6) - (5k + 4) is equivalent to the expression 3k - 10.

More about the equivalent link is given below.

https://brainly.com/question/889935

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The total surface area of the composite figure will be 134 square units.

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]

That ∑ sign shows "sum"

We are given that;

The dimensions of figure

Now,

The area of the shared face is already calculated as 20 square units. So, to find the total surface area, we subtract this from the sum of the surface areas:

TSA=(60+94)−20

TSA=154−20

TSA=134

Therefore, the area of the figure will be 134 square units.

Learn more about area of a composite figure here:

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Answer: The face that is shared with the rectangular prism is

✔ 2(5)

.

The area of each base of the rectangular prism is

✔ 10

square units.

The lateral area (excluding the shared face) for the rectangular prism is

✔ 18

square units.

The total surface area of the composite figure will be

✔ 66

square units.

Step-by-step explanation:

Answer:

Each member in the group that went to the candy store named  Sugar Shack

received a larger portion of a candy bar because each member in the group got  5/7 of a candy bar.

Step-by-step explanation:

Okay so first I am a visual learner so I drew a picture! I started with Sweet Dreams. I drew 4 candy bars and split each candy bar in 6 pieces. Each friend got 1/6 of each candy bar. This means if someone went to Sweet Dreams they got a total of 4/6 of a candy bar. Which is equivalent to  2/3. I then converted that into a decimal which is about .66 and then I went on to Sugar Shack. I then drew 5 candy bars split in 7ths. Each person got a seventh out of each candy bar. This means they got a total of 5/7. I then converted that into a decimal which is about .714. Since .71 is greater than .66 that means people at Sugar Shack got a larger portion. Hope this helps!!! Good luck on the assignment!

Each member in the group that went to the candy store named Sugar Shack received a larger portion of a candy bar because each member in the group got 0.71 of a candy bar.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

Two candy stores are offering free same-sized candy bars to groups of friends.

Both groups shared the candy bars equally among their members.

A group of six friends went to Sweet Dreams and received four candy bars to share.

That means,

the share of one member = 4/6 = 2/3 or 0.67

A group of seven friends went to Sugar Shack and received five candy bars to share.

That means,

the share of one member = 5/7 = 0.71.

Therefore, each member in the group got 0.71 of a candy bar.

To learn more about the fractions;

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Answer:

x = -31

Step-by-step explanation:

x-19=2x+12

Subtract x from each side

x-x-19=2x-x+12

-19 = x+12

Subtract 12 from each side

-19-12=x+12-12

-31 =x

Answer:

The next three terms of the sequence are 182.3, 273.5 and 410.3 respectively (all rounded to the nearest tenth value)

Step-by-step explanation:

A geometric sequence is one in which successive members are multiples of a constant common ratio.

From the sequence, we can identify that;

First term a = 36

common difference = 2nd term/first term = 3rd term/second term = 4th term/3rd term

Hence, common difference d = 54/36 = 81/54 = 1.5

The next three terms of the sequence are the 5th, 6th and 7th term respectively.

For the 5th term, we have 4th term × common ratio = 121.5 × 1.5 = 182.3

For the 6th term, we have 5th term × common ratio = 182.3 × 1.5 = 273.5

For the 7th term, we have 6th term × common ratio = 273.5 × 1.5 = 410.3

Steps to solve:

-4(r + 3) = -42

~Distribute

(-4 * r) + (-4 * 3) = -42

~Simplify

-4r - 12 = -42

~Add 12 to both sides

-4r - 12 + 12 = -42 + 12

~Simplify

-4r = -30

~Divide -4 to both sides

-4r/-4 = -30/-4

~Simplify

r = 7.5

Best of Luck!

Answer:

7.5

Step-by-step explanation:

(-4) (7.5 + 3)= -42

Answer:

The ratio of the height of the cone to the height of the cylinder is 3 to 1

The ratio of the height of the cone to the radius of the sphere is 4 to 1

Step-by-step explanation:

First we need to know the volume of a cylinder, a cone and a sphere:

V_cylinder = pi*r^2*h

V_cone = (1/3)*pi*r^2*h

V_sphere = (4/3)*pi*r^3

If they have the same volume:

The ratio of the height of the cone to the height of the cylinder is:

V_cone / V_cylinder = 1

(1/3)*pi*r^2*h1 / pi*r^2*h2 = 1

(1/3) * h1 = h2

h1 / h2 = 3

So the ratio is 3 to 1

The ratio of the height of the cone to the radius of the sphere is:

V_cone / V_sphere = 1

(1/3)*pi*r^2*h / (4/3)*pi*r^3 = 1

h / 4r = 1

h / r = 4

So the ratio is 4 to 1

Answer:Here

Step-by-step explanation:

Answer:

22.75

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

Harry stains his shirt during the dinner.

Step-by-step explanation:

P (Harry stains his shirt during the dinner) [tex]=[/tex] [tex]\frac{1}{5}[/tex] [tex]= 0.2[/tex]

P (Larry stains his shirt during the dinner) [tex]= 15%[/tex]% [tex]= 0.15[/tex]

[tex]0.2 > 0.15[/tex]

It is more likely that Harry stains his shirt during the dinner.

Answer:

4

Step-by-step explanation:

1) to find hcf, first look at what both 12 and 16 are divisible by

12 and 16 are divisible by 2

so

12/2=6

16/2=8

now we have 6,8

6 and 8 are divisible by 2 as well

6/2=3

8/2=4

3,4 is what we are left with

since we had to divide these numbers by 2 both times, multiply them.

2*2=4

4 is the hcf

Answer: 77/50

Step-by-step explanation:

Decimal: 1.54

Fraction: 77/50

Percentage: 154%

Answer:175

Step-by-step explanation:

250-75 is 75 I believe this is correct

Step-by-step explanation:

Putting values of x and y

2 = 4 + 2

2 = 6

= 6-2

= 4

Answer:

[tex] 2.226 \times {10}^{8} [/tex]

Step-by-step explanation:

[tex](5.3 \times {10}^{4} )(4.2 \times {10}^{3} ) \\ = 5.3 \times 4.2 \times {10}^{4 + 3} \\ = 22.26 \times {10}^{7} \\ = 2.226 \times {10}^{8} [/tex]

Answer:C

Step-by-step explanation:

Answer: 7 glasses

Step-by-step explanation:

Hi, to answer this question, first, we have to subtract the amount of juice poured (1/8) to the amount of remaining juice before he poured some (1).

1-1/8 = 7/8 remaining juice

Since he pours the same amount into more glasses until the pitcher is empty, we have to divide the remaining juice (7/8) by the amount poured in each glass (1/8).

7/8 ÷ 1/8 = 7 glasses

Feel free to ask for more if needed or if you did not understand something.

Answer:

140 inches

Step-by-step explanation:

The formula for volume or a rectangular prism is v=lwh

Length = 14

Width= 10

Height= 1

Multiplying them together gives you the volume which is 140