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It will take 7 minutes and 30 seconds to melt at a temperature of 40°C.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The amount of time it takes an ice cube to melt varies inversely to the air temperature this can be written as,

Time ∝ 1/(Temparature).

Time = K(1/Temp).

At 30 degrees Celsius, the ice will melt in 10 minutes.

10 = K(1/30).

K = 300.

Now, the time required to melt the ice at 40°C is,

Time = 300(1/40).

Time = 7.5 minutes or 7 minutes 30 seconds.

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Answer:

x>3

y≥2x-5

Step-by-step explanation:

graph them

Answer:

7% of 150= 10.5 :)

Step-by-step explanation:

150/x=100/7

(150/x)*x=(100/7)*x       - we multiply both sides of the equation by x

150=14.2857142857*x       - we divide both sides of the equation by (14.2857142857) to get x

150/14.2857142857=x

10.5=x

x=10.5

now we have:

7% of 150=10.5

Answer:

F) The rates are not equivalent.

Step-by-step explanation:

Consider the rates 45 mile in 8 minutes and 4 minutes to travel 25 mile. Select the statement(s) that are true. Multiple select question.

We find the unit rates

a) 45 mile in 8 minutes , we find the unit rate in miles per minute

8 minutes = 45 miles

1 minute = x

8 × x = 45 miles × 1 minute

x = 45 miles/8 minutes

x = 5.625 miles/ minute

b) 4 minutes to travel 25 miles. Find the unit rate is minutes per mile

25 miles = 4 minutes

1 mile = x

25miles × x = 4 minutes × 1

x = 4 minutes/25 miles

x = 0.16 minutes/mile

Hence, the correct option is

F) The rates are not equivalent.

Answer:

40%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Y= -6

X=-2

Answer:

D. 43x + 72 ≤ 1,128

Step-by-step explanation:

She  has $1,128

Total price $72

43x since its unit rate for each

43x + 72 is less than or equal to $1,128

Answer:

D. 43x + 72 ≤ 1,128

Step-by-step explanation:

Good luck! Hope this helped :)

Answer:

fghjgfvgh

yguhyu

Step-by-step explanation:

Answer:

frank traveled 2760-1400 = 1360 miles

traveled 16 hours

This means he drove: 1360 miles / 16 hours = 85 miles per hour.

Answer:

a) $4000

b) $2000

Step-by-step explanation:

a)

interest = Principal x rate as decimal x time

interest = 20,000 x 0.05 x 4

interest = 4000

b)

interest = Principal x rate as decimal x time

interest = 20,000 x 0.05 x 2

interest = 2000

you save $2000 if you pay after 2 years

Answer:2,500

Step-by-step explanation:

Answer:

$40

Step-by-step explanation:

You find the LCM (least common multiple). To do this, you can use prime factorization.

(there is an below that shows the prime factorization tree for 8 and 10)

so, the only common prime factor is 2. you use the 2 and multiply with the remaining prime factors.

5*2 --> for 10

2*2*2 -->for 8

becomes

5*2*2*2

if you multiply that out, it becomes 40.

Another method is to just think: "What can they both become after being multiplied by a number?"  or "What can 8 and 10 both be?"

Anyway, the answer is 40. Hope this helps!

Answer:

Both angles have a measure of 134degrees, y = 27degrees.

Step-by-step explanation:

As per what is given in the problem:

There are 2 parallel lines, both are intersected by a transversal.

Remember the theorem, when two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent.

The is meanse that:

3y + 53 = 7y - 55

Solve using inverse operations:

3y + 53 = 7y - 55

     +55         +55

3y + 108 = 7y

-3y            -3y

108 = 4y

/4      /4

27 = y

Now, substitute back in to find the value of the angle:

3y + 53

y = 27

3 ( 27 ) + 53

81 + 53

= 134

Since the angles are alternate exterior, they are congruent, hence both angles have a measure of 134degrees.

Answer:

1/6 or 0.16666... can be written rounding off to three decimal digits such as:

Step-by-step explanation:

As we know that

[tex]1\div 6\:=\:0.16666\dots \:[/tex]

In order to round off three decimal places (or digits ), we need to check:

Therefore, 1/6 or 0.16666... can be written rounding off to three decimal digits such as:

The fraction 1/6 expressed as a decimal number is 0.167

Fractions are expressed as the ratio of two integers. For example, a/b is a fraction where a and b are integers

Given the fraction 1/6, we are to express it as a decimal.

First, we can express it as a percentage as shown:

1/6 * 100 = 100/6

1/6 = 16.7%

Expressing as a decimal number

16.7% = 0.167

Hence the fraction 1/6 expressed as a decimal number is 0.167

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Answer:

y=mx+b :)

Step-by-step explanation:

Answer:

19.2

Step-by-step explanation:

Cross multiply to get 96=5n

n=19.2

Answer:

n= 96/5 or 19.2 or 19 1/5

Step-by-step explanation:

Answer:

- 749.5i + 10821.5

−2669.5

−4168.5

Step-by-step explanation:

Given tgat:

Number of stores in 2003 (y2) = 1078

Number of stores in 1999 (y1) = 4076

1999 = i = 9

2003 = 13

y - y1 = m(x - x1)

m = slope = (y2 - y1) / (i2 - i1)

m = (1078 - 4076) / 13 - 9

m = - 2998 / 4

m = - 749.5

y - 4076 = - 749.5(i - i1)

y - 4076 = - 749.5(i - 9)

y - 4076 = - 749.5i + 6745.5

y = - 749.5i + 10821.5

Prediction for 2008 and 2010

2008 ; i = 18

y = - 749.5(18) + 10821.5

y = −2669.5

2010 ; i = 20

y = - 749.5(20) + 10821.5

y = − 4168.5

Answer:My suggestion is practice what you learned after each class for like 10-20 min and pay close attention in class. Wish you the best of luck.

Step-by-step explanation:

Answer: 1, 2, 5

Step-by-step explanation: Move the decimal two times to the left if you divide by 100.

Answer:

1. w=-24

2. g=3

Step-by-step explanation:

Answer:

The mean would get bigger becuase you are adding in a bigger number there for the mean would increase.The standard deviation would change as well because then again you are adding a bigger number and standard diviation is basically the difference between the gratest and least.  For #2 no the median wouldn't chnage becuase the 70 is going in place for the 7 so it would just fill it's spot and wouldn't effect the data set.

Step-by-step explanation:

The median would be a better choice for the measure of center becuase the mean is telling you the average and the median is actully telling you where the middle of the data set is.

The mean is the average of a group of data. The data set  added up and divided by the number of data. The mean is sensitive to extreme data.

When 7 is changes to a 70 then mean and standard deviation both changes.

For the given data set median be a better choice for the measure of center than the mean because mean is sensitive to extreme data and median is the point at which half the data are above and half the data are below.

The median is the point at which half the data are above and half the data are below. Medians are less sensitive to extreme scores . Therefore, median is center point of data set.

Standard deviation shows how much variation there is from the mean. A low SD indicates that the data points tend to be close to the mean, whereas a high SD indicates that the data are spread out over a large range of values.

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Answer:

4.87 to the fourth power

Step-by-step explanation:

0.000487 in Scientific Notation:

4.87  * 10^-4

Answer:

g(7) = 4

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

What g(7) is saying is that we are trying to find the y-value when x = 7. According to the graph, when x = 7, y would equal 4. Therefore, g(7) = 4 and our coordinate would be (7, 4).

You need to know that g(7) means that x = 7. Look at the graph. When x is 7, what is the value of y?

The point (7,4) indicates that g(7) = 4.

Answer:

a. x=100 b. x=30

Step-by-step explanation:

A: <1 and <2 are supplementary by consecutive interior angles theorem

x + x-20 = 180

2x-20=180

2x=200

x=100

B: <1 and <2 are congrunt by corresponding angles postulate

3x-5=x+55

2x=60

x=30

Answer:

Area of triangle ABC = 10

Option C is correct.

Step-by-step explanation:

We need to find area of triangle ABC

We are given A(2,1) B(4,7) and C(6,3)

The formula used to find [tex]Area \ of \ triangle=\frac{1}{2}base\times height[/tex] ABC is:

In the given triangle base= AC and height = BC

First we need to find the distance between A and C and B and C

The formula used to find distance between AC [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have [tex]x_1=2, y_1=1, x_2=6, y_2=3[/tex]

Putting values and finding distance

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-2)^2+(3-1)^2}\\Distance=\sqrt{(4)^2+(2)^2}\\Distance=\sqrt{16+4}\\Distance=\sqrt{20}[/tex]

find distance between BC [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have [tex]x_1=4, y_1=7, x_2=6, y_2=3[/tex]

Putting values and finding distance

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-4)^2+(3-7)^2}\\Distance=\sqrt{(2)^2+(4)^2}\\Distance=\sqrt{4+16}\\Distance=\sqrt{20}[/tex]

So, We have height = [tex]\sqrt{20}[/tex] and base = [tex]\sqrt{20}[/tex]

Finding area of triangle

[tex]Area \ of \ triangle=\frac{1}{2}base\times height\\Area \ of \ triangle=\frac{1}{2}\sqrt{20} \times \sqrt{20} \\Area \ of \ triangle=\frac{1}{2}\times 20\\Area \ of \ triangle=10[/tex]

So, Area of triangle ABC = 10

Option C is correct.

Answer:

Step-by-step explanation:

Answer:

D,E

Step-by-step explanation:

Answer:

Step-by-step explanation:

if 45x-b is an equation then b value is the y coordinate of y-intercept (where graph touches the y axis)

Answer:

x=k/y

w=k/t

5=k/√49

5=k/7

k=5×7

k=35