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scoundrel [369]
2 years ago
15

A formula for 6 gallon of light green paint use 3/8 gallons of white paint. Liam has 9/16 gallon of white paint. Does liam have

enough white paint to make 8 gallons of light green paint? If not, how many more does he need?
Mathematics
1 answer:
FromTheMoon [43]2 years ago
3 0

Answer:

Yes he have enough white paint.

Step-by-step explanation:

We are given

6 gallons of light green paint use → \frac{3}{8} gallons of white paint

using the unitary method

1 gallons of white paint → 6*8/3 gallons of light green paint

                                        → 16 gallons of light green paint

but Liam have 9/16 gallons of white paint

9/16 gallons of white paint → 16* 9/16 gallons of light green paint

                                             → 9 gallons of light green paint

Yes Liam have enough white paint to make 8 gallons of light green paint.  

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Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1
TiliK225 [7]

Answer:

1. Western erodes 2 ft/yr; Dunes builds up at 5 ft/yr

2. Sometime in 2006

3. Solve simultaneous equations

Step-by-step explanation:

1. Erosion patterns

(a) Western Beach

In 15 yr, Western Beach erodes from 100 ft to 70 ft.

The rate of erosion is 30 ft/15 yr = 2 ft/yr.

(b) Dunes Beach

In 15 yr, Dunes Beach builds up from 20 ft to 95 ft.

The rate of buildup is 75 ft/15 yr = 5 ft/yr.

2. Beaches with equal width

From the table, it appears that the beaches will have the same width sometime in year 11 (2006).

3. Best approximation

The graph below also shows that it happens part way through year 11 (2006).

We could get an even better solution by calculating the equations of the two lines and solving the simultaneous equations.

5 0
2 years ago
Help with maths question please
mars1129 [50]
<h3>✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽</h3>

➷ Substitute -3 into g(x)

g(-3) = 2(-3) + 4

Solve:

g(x) = -2

Substitute this value into f(x)

f(-2) = 3(-2)^2

Solve:

f(-2) = 12

The answer is B. 12

<h3><u>✽</u></h3>

➶ Hope This Helps You!

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6 0
2 years ago
12. If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95% confident that th
atroni [7]

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

Step-by-step explanation:

We have the following info given:

Confidence= 0.95 the confidence level desired

ME =0.03 represent the margin of error desired

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

The confidence level is 95% or 0.95, the significance is \alpha=0.05 and the critical value for this case using the normal standard distribution would be z_{\alpha/2}=1.96

Since we don't have prior information we can use \hat p= 0.5 as an unbiased estimator

Also we know that ME =\pm 0.03 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

6 0
2 years ago
Chris wonders whether the planes that fly over his house follow any sort of pattern. For two months, he
KatRina [158]

Answer:

Kindly check explanation

Step-by-step explanation:

From the relative frequency below:

For NORTH - SOUTH:

Monday - Thursday = 115 ; has a relative frequency of 75.16%,

Hence, we can obtain the row total since it amounts to 100% thus;

75.16% of row total = 115

0.7516× row total = 115

Row total = 115 / 0.7516 = 153.00

Hence, Friday - sunday:

Row total - (Monday-Thursday)

153 - 115 = 38

FOR EAST - WEST:

Monday - Thursday = 21 ; has a relative frequency of 25.30%,

Hence, we can obtain the row total since it amounts to 100% thus;

25.30% of row total = 21

0. 253 × row total = 21

Row total = 21 / 0.253 = 83.00

Hence, Friday - sunday:

Row total - (Monday-Thursday)

83 - 21 = 62

x = (38 / 100) × 100%

x = 0.38 × 100%

x = 38.00 %

5 0
2 years ago
A metal alloy is a metal made by blending 2 or more types of metal. A jeweler has supplies of two metal alloys. On alloy is 30%
tensa zangetsu [6.8K]

Answer:

He should combine 1 kg of 30% alloy and 3 kg of 10% alloy.

Step-by-step explanation:

Let x = mass of 30% ally.

Let y = mass of 10% alloy.

He needs 4 kg of alloy, so the first equation, dealing with masses, is

x + y = 4

Now we deal with the amount of gold.

He uses x mass of 30% gold alloy. The amount of gold in that mass is 0.3x.

He uses y mass of 10% gold alloy. The amount of gold in that mass is 0.1y.

The total mass of gold is 0.3x + 0.1y. We are told the told the end alloy is 4 kg of 15% gold alloy. That contains 0.15(4) kg = 0.6 kg of gold.

The second equation is

0.3x + 0.1y = 0.6

Now we put together the two equations as a system of equations.

x + y = 4

0.3x + 0.1y = 0.6

Multiply both sides of the second equation by -10.

-3x - y = -6

Add this equation to the first original equation.

         x + y = 4

+     -3x - y = -6

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

        -2x    = -2

            x    = 1

Now substitute x = 1 in the first original equation and solve for y.

x + y = 4

x + y = 4

y = 3

Answer: He should combine 1 kg of 30% alloy and 3 kg of 10% alloy.

6 0
2 years ago
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