At 7:45 a.m. Mike began walking to school. He arrived at his school at 8:20 a.m. How long did it take him to walk to school?
A. 15 minutes
B. 25 minutes
C. 35 minutes
D. 40 minutes
E. 65 minutes

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

If two figures are similar. then the ratio of its areas is equal to the scale factor squared

In this problem we have a tile with a length of 1 foot by a width of 1 foot

The area of the tile is equal to

[tex]A=LW[/tex]

substitute the values

[tex]A=(1)(1)=1\ ft^{2}[/tex]

Let

z-------> the scale factor

x------> the area of 1/2 tile

y------> the area of the original tile

so

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

substitute

[tex]z^{2} =\frac{(1/2)}{1}[/tex]

[tex]z=\frac{\sqrt{2}}{2}[/tex] -----> scale factor

therefore

To find the area of 1/2 tile must multiply the dimensions of the tile by the scale factor

so

[tex]L=1*\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\ in[/tex]

[tex]W=1*\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\ in[/tex]

Calculate the area

[tex]A=\frac{\sqrt{2}}{2}*\frac{\sqrt{2}}{2}=\frac{1}{2}\ ft^{2}[/tex]

Martin's method is incorrect because to find the area of 1/2 tile, he multiplies the dimensions by 1/2

so

[tex]L=1*\frac{1}{2}=\frac{1}{2}\ in[/tex]

[tex]W=1*\frac{1}{2}=\frac{1}{2}\ in[/tex]

the area will be

[tex]A=\frac{1}{2}*\frac{1}{2}=\frac{1}{4}\ ft^{2}[/tex]

Answer:

Step-by-step explanation:

Given are two functions

[tex]y=\sqrt{x} :\\f(x) =\sqrt{x}[/tex]

We have to compare and contrast these two functions.

On comparing we have both are the same.

FIrst one is written as y = form while second function is written as function of x

Sometimes we use y and sometimes we use f(x) in practice.

In both the cases, x is the independent variable and normally marked on x axis and y or f(x) the dependent variable marked on vertical y axis.

The rectangle's length is 12 cm, and the width is 9 cm, calculated by setting up a system of equations using the given perimeter and the relationship between length and width.

To find the length and width of the rectangle when given its perimeter and a relationship between its length and width, we can set up a system of equations. First, let's denote the length of the rectangle as L and the width as W. According to the question, the width is 3 centimeters more than half the length, so we have W = ½L + 3.

Since the perimeter (P) of a rectangle is given by P = 2L + 2W, and we know the perimeter is 42 centimeters, we can set up an equation: 42 = 2L + 2(½L + 3). Simplifying this, we get 42 = 2L + L + 6 or 42 = 3L + 6. Subtracting 6 from both sides gives us 36 = 3L or L = 12 centimeters for the length.

Now we can find the width using the previous relationship W = ½L + 3. Substituting the value of L, we get W = ½(12) + 3 = 6 + 3 = 9 centimeters for the width.

Therefore, the length is 12 centimeters and the width is 9 centimeters.

Answer:

128 Shoppers prefer bananas.

Step-by-step explanation:

In the question it is given that 400 shoppers were surveyed to determine their favorite fruit.

Among all of them 32% people like bananas.

So to find out how many people prefer bananas, we just calculate 32% of 400.

32% of 400

[tex]\frac{32}{100}[/tex] × 400

0.32 × 400 = 128

128 Shoppers prefer bananas.

Answer:

Two triangles are said to be congruent by ASA congrency criterion if the two angles and side between them are equal or congruent.

Refer to the image attached.

To prove: [tex]\Delta ABC \sim \Delta XYZ[/tex]

Given: [tex]AB \cong XY, \angle A \cong \angle X[/tex]

Now, we can observe that the side AB is between the angles A and B and the side XY is between the angles X and Y.

Since it is given that  [tex]AB \cong XY, \angle A \cong \angle X[/tex], so the condition [tex]\angle B \cong \angle Y[/tex] should be known to shows these triangles congruent.  

Answer:

its B

Step-by-step explanation:

To find the missing dimension of a triangle given the height and area, we can use the formula for the area of a triangle: Area = 1/2 * base * height. We're given the height as 7 inches and the area as 21 square inches. Plugging these values into the formula, we can solve for the base using algebraic manipulation.

To find the missing dimension of a triangle given the height and area, we can use the formula for the area of a triangle: Area = 1/2 * base * height. We're given the height as 7 inches and the area as 21 square inches. Plugging these values into the formula, we get: 21 = 1/2 * base * 7. Solving for the base, we can multiply both sides of the equation by 2 and divide by 7 to get the base: base = (21 * 2) / 7 = 6 inches.

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Final answer:

By using the area formula for a triangle, A = (b × h) / 2, with the provided height of 7 inches and area of 21 square inches, the base is calculated to be 6 inches.

Explanation:

To find the missing dimension of a triangle, given the height and area, we can use the formula for the area of a triangle A = (b × h) / 2, where A is the area, b is the base, and h is the height. Given that the height h is 7 inches and the area A is 21 square inches, we can rearrange the formula to solve for the base b:
Area = (base × height) / 2 → 21 = (b × 7) / 2 → b = (21 × 2) / 7 → b = 6

The missing dimension, the base of the triangle, is 6 inches, provided height of 7 inches and area of 21 square inches.

Answer:

40

Step-by-step explanation:

Given that Anita divides 1438 by a multiple of 10

i.e. she might have divided by 10 or 20 or 30 .....

The tenth column is 3

So quotient value would be

30+d for some d in the unit column

It may be 31 or 32.....

Say it is 31, then 1438/31 =46.38 and

1438/39 = 36.87

i.e she must have divided by 40 only

Verify:

1438/40 =35 as quotient and 38 as remainder.

So she divided by 40

From the table we have the points (-4, -2) and (-2, -10).

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute:

[tex]m=\dfrac{-10-(-2)}{-2-(-4)}=\dfrac{-10+2}{-2+4}=\dfrac{-8}{2}=-4[/tex]

The slope of the linear function is -4. The correct option is B. -4.

The slope of a function is the rate of change of the dependent variable with respect to the change of the independent variables.

Therefore, the slope is change in the y variable with respect to the change in the x variable.

Let's find the slope of the linear function as follows:

slope = y₂ - y₁ / x₂ - x₁

Therefore,

slope = m = -10 + 2 / -2 + 4

slope = - 8 / 2'

Therefore,

slope = -4

The correct option is B. -4 .

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Answer: True

Step-by-step explanation:

I don’t have one I know the answer because I am currently taking the quiz right now.

The solution to the given equation is 6. Therefore, the correct answer is option B.

The given equation is x+6=x+x.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, x+6=2x

Transpose x to other side of the equation, we get

2x-x=6

x=6

Therefore, the correct answer is option B.

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Answer:

Sally walks at a speed of 2 kilometers per hour.

Step-by-step explanation:

Given data

We can find the speed (v) of Sally using the following expression

v = d/t = (1/2 km) / (1/4 h) = 2 km/h

Sally walks at a speed of 2 kilometers per hour.

Answer:

m∠x = 63°

m∠y =45°

m∠z = 72°

I hope this helps! :)

Answer:

Step-by-step explanation:

It is given that ABCD is a parallelogram, thus by using the properties of parallelogram, we have

∠A=∠C (Opposite angles of parallelogram are equal)

⇒∠x=63°

Thus, the measure of angle A that is x is 63°.

Now, ∠ABC+∠BCD=180°(Corresponding angles of parallelogram)

⇒∠ABD+∠DBC+63=180

⇒∠DBC=180-135

⇒∠DBC=45°

Thus, y=∠DBC=45° (Alternate angles)

and z=∠DBA=72° (Alternate angles)

Hence, the measure of angle x, y and z are 63°, 45° and 72° respectively.

Show that n is odd →∃m∈ℤ,n2=8m+1

Let k be an integer so that n=2k+1. Then n2=(2k+1)2=4k2+4k+1=2(2k2+2k)+1.

But this isn't equal to 8m+1, so can I change that into 4(2m)+1?

The mean is the sum of data given to the total sample size.. The mean, median, mode, and range are -25, -28.-28, and 40 respectively

The mean is the sum of data given to the total sample size.

Mean = Sum of data/sample size
Mean =  -11-28-17-25-28-39-6-46/8
Mean =  -200/8
Mean = -25

Calculate the median

Median is the middle number after rearrangement

-46, -39, -28, -28, -25, -17, -11, -6
From the arrangement, the median of the data is -28

Calculate the mode

The mode is the value with the highest frequency. From the data given, the mode is -28

Range:

Range = highest value - lowest value

Range = -6 - (-46)
Range = 40

Hence the mean, median, mode and range are -25, -28.-28 and 40 respectively

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Answer :- First option is correct.

Microeconomics is the study of psychology of individuals at small scale.

In microeconomics, price of goods helps to determine the quantity supplied and the quantity demanded.

Quantity demanded is determined by

1. Desire of any good 2. Willingness to buy that good 3.Ability to buy a good

Other than that quantity supplied is determined by

1.Production cost [supply can increase with decrease in cost of production]

2. Productivity [supply can increase with increase in number of workers or hard working workers]

3.Technology[supply can increase with increase in the use of new technology related to production]

4.Govt regulation [it can either restrict or advertise the goods that can either increase or decrease the supply of that good respectively.]

5.Taxes and subsidies [implication of taxes can decrease the supply but by implication of subsidies supply can increase]etc.

So, Ist option is correct that the quantity supplied is determined by production cost and quantity demanded is determined by desire for the product.

The speed of the polar bear is found by dividing the distance swam (390 meters) by the time it took (150 seconds). This results in a speed of 2.6 meters per second.

The subject of your question is related to the calculation of speed, which falls under Physics. The polar bear swims 390 meters in 150 seconds. To find the speed, we apply the basic formula which is Speed = Distance/Time. Here, the distance is 390 meters, and the time is 150 seconds.

So if we divide 390 by 150, we get 2.6 meters per second. This means the speed of the polar bear is 2.6 m/s.

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Answer:

Percentage of amount paid for labor, parking space and busing are 12%, 39% and 49% respectively.

Step-by-step explanation:

The stadium pays the amount for labor = $14000

Amount paid for leasing a parking space = $45000

and to provide busing to and from the parking space = $57000

Total amount paid = $14000 + $45000 + $57000

                              = $116000

Percentage of amount paid for labor = [tex]\frac{\text{Amount paid for labor}}{\text{Total amount paid}}\times 100[/tex]

= [tex]\frac{14000}{116000}\times 100[/tex]

=12.06

≈ 12%

Percentage of amount paid for parking space

= [tex]\frac{\text{Amount paid for parking space}}{\text{Total amount paid}}\times 100[/tex]

= [tex]\frac{45000}{116000}\times 100[/tex]

= 38.79%

≈ 39%

Percentage of amount paid for busing = [tex]\frac{\text{Amount paid for busing}}{\text{Total amount paid}}\times 100[/tex]

= [tex]\frac{57000}{116000}\times 100[/tex]

= 49.14%

≈ 49%