Divide 500 in the ratio 4:5:1

Answer:

20% of students prefer to go to the aquarium

50% of teachers prefer to go to the aquarium

Step-by-step explanation:

1.

8 students prefer the aquarium out of 40 students.

Set up an equation:

Variable x = percentage of students

8/40 = x/100

Cross multiply:

8 × 100 = 40 × x

800 = 40x

20 = x

Divide:

20%

Check your work:

40 students × 20%

Convert percentage into decimal:

40 × 0.20

8

8 students prefered the aquarium so this is correct!

2.

5 teachers prefer the aquarium out of 10 teachers.

Set up an equation:

Variable x = percentage of teachers

5/10 = x/100

5 × 100 = 10 × x

500 = 10x

50 = x

50%

Check your work:

10 × 0.50

5

Correct!

Answer:

D. y - 7 = 11(x - 5)

Step-by-step explanation:

Use point slope form, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Plug in the given slope and point:

y - y1 = m(x - x1)

y - 7 = 11(x - 5)

So, the correct answer is D. y - 7 = 11(x - 5)

Answer:

general term - 7n+4

5th term - 7(5) + 4 = 39

6th term - 7(6) + 4 = 46

Step-by-step explanation:

I Think Its C

Answer:

2√10

Step-by-step explanation:

Given the following data;

Area of square = 40

Mathematically, the area of a square is calculated by using the formula;

Area, A = s²

Where;

s is the length of sides of a square.

Substituting into the formula, we have;

40 = s²

s = √40

s = √4 * √10

s = 2 * √10

s = 2√10

Answer:

B

Step-by-step explanation:

Use pythagorean theorem

4^2+5^2=AC^2, AC= 6.4

7^2+9^2=CB^2, CB=11.4

=========================================================

Explanation:

Let

r = area devoted to residential use

This variable is some positive real number, and it represents the area in acres.

Your teacher says that " the area devoted to business use is 7,200 acres less than the area devoted to residential use"

This means the expression r-7200 represents the area for business use

Note the jump from 25% to 65% is 65/25 = 2.6, meaning that we multiply by 2.6 when going from the business area to the residential area.

So we'll multiply by 2.6 to go from r-7200 to r

We'll have this equation

2.6(r-7200) = r

because it's effectively saying

2.6*(business area) = residential area

--------------------------

Let's isolate r

2.6(r-7200) = r

2.6r-2.6*7200 = r

2.6r - 18720 = r

2.6r - r = 18720

1.6r = 18720

r = 18720/(1.6)

r = 11700

We'll use 11700 acres for the residential portion.

And also r-7200 = 11700-7200 = 4500 acres are set aside for the business district.

--------------------------

The largest region (residential) uses 11700 acres of land.

Note the jump from 10% to 65% involves a multiplier of 6.5 because 65/10 = 6.5

So if g is the amount of government land used, then,

6.5g = r

6.5g = 11700

g = 11700/(6.5)

g = 1800

1800 acres of land are for government use

This is why the answer is choice B.

The area, in acres, devoted to government use is 1800.

Option (B) is correct.

To find the area.

Percentage, a relative value indicating hundredth parts of any quantity.

Given that:

Let

r = area devoted to residential use

This variable is some positive real number, and it represents the area in acres.

This means the expression r-7200 represents the area for business use

Note the jump from 25% to 65% is 65/25 = 2.6, meaning that we multiply by 2.6 when going from the business area to the residential area.

To multiply by 2.6 to go from r-7200 to r

The equation is

2.6(r-7200) = r

because it's effectively saying

2.6*(business area) = residential area

--------------------------

Let's isolate r

2.6(r-7200) = r

2.6r-2.6*7200 = r

2.6r - 18720 = r

2.6r - r = 18720

1.6r = 18720

r = 18720/(1.6)

r = 11700

We'll use 11700 acres for the residential portion.

And also r-7200 = 11700-7200 = 4500 acres are set aside for the business district.

The largest region (residential) uses 11700 acres of land.

Note the jump from 10% to 65% involves a multiplier of 6.5 because 65/10 = 6.5

So if g is the amount of government land used, then,

6.5g = r

6.5g = 11700

g = 11700/(6.5)

g = 1800

So, the area, in acres, devoted to government use is 1800.

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Answer:

y=-4x+2

Step-by-step explanation:

Hi there!

We want to find out which equation represents a line with a slope of -4 and a y intercept of (0,2)

The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We have everything we need to plug into the equation, let's just label the values to avoid confusion

m=-4

b=2 (when you substitute the y intercept as b, b is the value of y in the point)

Now substitute into the equation

y=-4x+2

Hope this helps!

Answer:

144 = c - 379

Step-by-step explanation:

"144 is the same as 379 less than c"

144 = c - 379

Answer and Step-by-step explanation:

This can be written in an equation like this:

144 = c - 379

The question is saying that 144 is the same answer as the result of 379 less than c (or c minus 379). This is why we equal 144 to the result of c minus 379.

#teamtrees #PAW (Plant And Water)

Answer:

48 ÷ 60 = 4/5

Step-by-step explanation:

4/5 is the answer

Answer:

[tex]\frac{1}{30}[/tex]

Step-by-step explanation:

We require the number of minutes in a day.

i hour = 60 minutes

24 hours = 24 × 60 = 1440 minutes ( 24 hours in 1 day )

Then

fraction = [tex]\frac{48}{1440}[/tex] ( divide numerator/ denominator by 12 )

            = [tex]\frac{4}{120}[/tex] ( divide numerator/ denominator by 4 )

            = [tex]\frac{1}{30}[/tex]

9514 1404 393

Answer:

  A.  1/2

Step-by-step explanation:

The points on a unit circle are (cos(θ), sin(θ)), where θ is the angle from the +x axis to to the ray from the origin through that point.

If the point is (√3/2, 1/2), then sin(θ) = 1/2.

Answer:

1050

Step-by-step explanation:

Let x = full capacity

[tex]\frac{3}{5} x=\frac{2}{7} x+330[/tex]

Move the variable to the left side by subtracting both sides by [tex]\frac{2}{7} x[/tex]

[tex]\frac{3}{5} x-\frac{2}{7}x=\frac{2}{7} x+330 -\frac{2}{7}x[/tex]

[tex]\frac{3}{5} x-\frac{2}{7} x=330[/tex]

Combine the like terms (don't forget about common denominator)

[tex]\frac{21}{35} x-\frac{10}{35} x=330[/tex]

[tex]\frac{11}{35} x=330[/tex]

Multiply both sides by [tex]\frac{35}{11}[/tex] to isolate the x

[tex](\frac{35}{11})\frac{11}{35} x=330(\frac{35}{11})[/tex]

[tex]x = 1050[/tex]

Answer:

-8 and 3

Step-by-step explanation:

The slope of the line will be - 8, the equation is y=-8x+3

Answer:

the answer is 0.31/ 5.1/8.57.1% /207067

Step-by-step explanation:

ascending order from the smallest to the largest

Answer:

(4) 644,000

Step-by-step explanation:

643,581

The 3 is in the thousands place

We look at the hundreds place

5

It is 5 or greater so we round the thousands place up 1

644000

Answer:

3 hours 30 minutes

Step-by-step explanation:

Jan :2 hours

her husband : 1 hour 30 minutes

2hr + 1 ½ hrs = 3 ½ hrs...that is 3 hours 30 minutes....?

Step-by-step explanation:

14.99 - 11.53= 3.46+1.95 =4.41

Answer:

Step-by-step explanation:

y = x³

x = ∛y

Switch x and y:

y = ∛x

f⁻¹(x) = ∛x

f⁻¹(12) = ∛12 ≅ 2.29

check:

x = 2.29

f(x)  = 2.29³ ≅ 12

Step-by-step explanation:

Recall that 1 dozen = 12 so 4 dozen cookies has a total of 48 cookies. We are going to use the following ratios to solve the problem:

[tex]\left(\dfrac{3\:\text{eggs}}{48\:\text{cookies}}\right)[/tex] and [tex]\left(\dfrac{48\:\text{cookies}}{3\:\text{eggs}}\right)[/tex]

a) [tex]12\:\text{eggs}×\left(\dfrac{48\:\text{cookies}}{3\:\text{eggs}}\right) = 192\:\text{cookies}[/tex]

b) 18 dozen cookies = 216 cookies

[tex]216\:\text{cookies}×\left(\dfrac{3\:\text{eggs}}{48\:\text{cookies}}\right) = 13.5\:\text{eggs}[/tex]

Answer:

Sin X = 12 / 37

Step-by-step explanation:

Given a right angled triangle, we are to obtain the Sin of the angle X ;

Using trigonometry, the sine of the angle X , Sin A is defined as the ratio of the angle opposite X to the hypotenus of the right angle triangle.

In the right angle triangle :

Sin X = opposite / hypotenus

Opposite = 12 ; hypotenus = 37

Sin X = 12 / 37

Answer:

y<=(-2x+4)

Step-by-step explanation:

The equation of line is y=-2x+4. For the region left of it, y<=(-2x+4)

Answer:

Amanda's box is in this case, the bigger one. Then subtract the Amanda's by Mary's. The Larger box is 70cm^3 larger then the smaller box.

Step-by-step explanation:

Amanda's box: 13.5*10*10= 1350cm^3

Mary's box: 20*8*8= 1280cm^3

1350-1280=70

The larger box is 70cm^3 larger then the smaller box.

If you have any questions regarding my answer tell me in the comments, i will come answer them. Have a good day.

Answer:

d = 6 , a₁ = - 6 and a₁₀ = 48

Step-by-step explanation:

The nth term of an arithmetic progression is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₃ = 6 and a₇ = 30 , then

a₁ + 2d = 6 → (1)

a₁ + 6d = 30 → (2)

Subtract (2) from (1) term by term to eliminate a₁

4d = 24 ( divide both sides by 4 )

d = 6

Substitute d = 6 into (1)

a₁ + 2(6) = 6

a₁ + 12 = 6 ( subtract 12 from both sides )

a₁ = - 6

Then

a₁₀ = - 6 + (9 × 6) = - 6 + 54 = 48

----------------------------------------------------

Answer:

d=6

a=-6

Step-by-step explanation:

use the formula for the nth term which is

Tn=a+(n-1)d..you will have to create two equations then solve them as a simultaneous equation

T3=6 and T7=30

T3=a+(3-1)d

6=a+2d........... first equation

T7=a+(7-1)d

30=a+6d.......... second equation

then solve them as a simultaneous equation

a+2d=6

a+6d=30

-4d/-4=-24/-4

d=6

a+2d=6

a+2(6)=6

a=6-12

a=-6

I hope this helps

Answer:

B opition is right

Step-by-step explanation:

The domina a function of

.・。.・゜✭・Srry but which language is this!?

Answer : 19.6cm

I hope this helps you! Have a good day!

Answer:

Step-by-step explanation:

If the length of a tree's shadow is 32.25 meters. The height of the tree to the nearest hundredth of a meter will be : 9.84m

Given:

Malika height=1.45 meters

Length =32.25 meters

Width =27.5 meters

Height of the tree=x

Proportion:

1.45 : 32.25 :: x : 27.5

Now let determine the height of the tree

32.25-27.5/1.45=32.25/x

4.75/1.45=32.25/x

Cross multiply

4.75x=32.25×1.45

4.75x=46.7625

Divide both side

x=46.7625/4.75

x=9.84m

Inconclusion  if the  length of a tree's shadow is 32.25 meters. The height of the tree to the nearest hundredth of a meter will be : 9.84m

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Answer:

1. 0.5

Step-by-step explanation:

The probability of flipping a coin and landing on heads or tails is 100%. So 3)1 would be incorrect. In probability, we learned that just because something was picked more than once, it does not lower the chances of the thing being picked again. So 5)0 would be incorrect. The chances of getting tails are 50% also 0.5 and the chances of getting heads are 50% also 0.5. So 1 is correct.

There is a 0.5 percent chance that the following coin will land on its side.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

The sample space, which is typically represented using set notation, contains a list of all the potential ordered outcomes as elements. A sample space with all possible outcomes exists for a series of five fair coin tosses. The example of a fair coin toss is 2*2*2H,T.

{HHHHH,HHHHT,HHHTH,HHTHH,HTHHH........TTTTT} The likelihood that the next coin will land on its side is always equal to It doesn't matter if previous results were TTTTT, HHHHH, or TTHT. The probability that the next number will be a tails is therefore still 0.5 in each of these cases as well as all others.

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Answer:

there is a 20% chance of getting a red marble

Step-by-step explanation:

Answer:

there is a 1/5 percent chance or 20%

Step-by-step explanation:

Hope this helps!