A student pays for 8.9 pounds of apples with a $10 bill. How much change does the student receive?

Answer:

The slope of the line passing through these points is 3.

Step-by-step explanation:

A first order function is given by the following formula:

[tex]y = ax + b[/tex]

In which a is the slope.

In this problem, we have that:

The line passes through the point (5,5). This means that when x = 5, y = 5. So

[tex]5a + b = 5[/tex]

[tex]b = 5 - 5a[/tex]

The line also passes through the point (6,8). This means that when x = 6, y = 8. So:

[tex]6a + b = 8[/tex]

[tex]b = 5 - 5a[/tex]

So

[tex]6a + 5 - 5a = 8[/tex]

[tex]a = 3[/tex]

The slope of the line passing through these points is 3.

Adding 10 to every observation in a sample, the sample mean would be 10 more the precious one and the standard deviation will remain the same.

"It is an average of a set of data."

"For a sample of observation [tex]x_1,x_3,x_2,...,x_n[/tex] the mean of the sample is,

[tex]\Rightarrow \bar{X}=\frac{x_1+x_3+x_2+...+x_n}{n}[/tex]"

"It is a measure of how dispersed the data from the mean."

[tex]\Rightarrow \sigma=\sqrt{\frac{\Sigma(x_i-\bar{X})^2}{N}}[/tex]

where, [tex]\bar{X}[/tex] is the mean of sample and N is the size of sample

For given question,

Let [tex]x_1,x_3,x_2,...,x_n[/tex] be a sample observation.

We need to check if we add 10 to all of the observations in a sample, then does this change the sample mean. Also we have to check how does it change the sample standard deviation.

Let [tex]\bar{X}[/tex] be the mean of [tex]x_1,x_3,x_2,...,x_n[/tex]

[tex]\Rightarrow \bar{X}=\frac{x_1+x_3+x_2+...+x_n}{n}[/tex]

We add 10 to all of the observations in a sample.

[tex]\Rightarrow x_1+10,x_3+10,x_2+10,...,x_n+10[/tex]

The mean of above sample would be,

[tex]=\frac{(x_1+10)+(x_3+10)+(x_2+10)...+(x_n+10)}{n}\\\\=\frac{10n + (x_1+x_3+x_2+...+x_n)}{n}\\\\ =\frac{10n}{n} +\frac{x_1+x_3+x_2+...+x_n}{n}\\\\ =10 + \bar{X}[/tex]

This means, if we add 10 to every observation in a sample then the sample mean we 10 more the precious one.

In case of standard deviation,

adding 10 to every observation will not change the [tex](x_i-\bar{X})[/tex] factor.

This means, the standard deviation will remain the same.

Therefore, adding 10 to every observation in a sample, the sample mean would be 10 more the precious one and the standard deviation will remain the same.

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Final answer:

Adding 10 to each observation in a sample raises the sample mean by 10 but does not change the sample standard deviation, which measures the variability or spread of the data from the mean.

Explanation:

When you add 10 to all of the observations in a sample, you increase the sample mean by 10. This is because the mean is the average of all the values, and increasing each value by 10 raises the average by the same amount. However, this adjustment does not affect the sample standard deviation because standard deviation is a measure of variability or spread of the data from the mean, and adding a constant to each data point does not change the spread of the data relative to each other.

To understand how this works, suppose we have a sample with observations such as 3, 7, and 4. The sample mean is (3+7+4)/3 = 4.67.

If we add 10 to each observation, we get 13, 17, and 14. The new mean is,

(13+17+14)/3 = 14.67,

which is the original mean plus 10. However, the differences between each observation and the mean remain the same

(13-14.67 = -1.67, 17-14.67

= 2.33, and

14-14.67 = -0.67),

Meaning the spread has not changed, and thus the standard deviation remains the same.

Answer:

C. The difference in length between Cassie’s longest and shortest practice sessions was greater than the difference in length between Jacqueline’s longest and shortest sessions.

Step-by-step explanation:

The slope of the blue curve measures the plane's rate of descent. the unit of measurement for the slope of the curve is feet per minute. at point a, the slope of the curve is -2,500, which means that the plane is descending at a rate of 2,500 feet per minute. at point b, the slope of the blue curve is , which means that the plane is at a rate of feet per minute

As you are measuring altitude against time, the slope of the curve measures the plane's rate of climb or descent.

At t = 0, the plane is at an altitude of 11 kilometer. It is descending all the time until at t = 10 the plane reaches ground level.  At both points the plane is descending.  Whereas at point A, the tangent line shows the rate of descent as 2 km over 2 minutes = 1 km per minute.

At point B, the tangent line shows the rate of descent as 2 km over 4 minutes = ½ km per minute.

Grade:  9

Subject:  Mathematics

Chapter:  Math and Graphing Assessment

Keywords:  feet per minute, The slope of the blue curve, the unit of measurement, the plane, the slope

The slope of the curve on a position versus time graph represents the instantaneous velocity of the plane. The unit of measurement is typically meters per second or feet per minute, and the slope at a given point can be calculated using a tangent line at that point.

The slope of the blue curve is related to the instantaneous velocity of the plane on a position versus time graph. The unit of measurement for the slope of the curve is meters per second (m/s) or feet per minute depending on the system being used. At point A, the slope indicates the rate at which the plane's velocity is at that moment in time. The steeper the slope of the curve at a particular point, the faster the plane is moving at that instant. At point B, a different slope value would imply a different instantaneous velocity.

To calculate the slope at any point, you would draw a straight line tangent to the curve at that point, which represents the instantaneous velocity. The slope is calculated as the 'rise over run'—the change in position (displacement) over the change in time. If we had specific numerical values at points A and B, we could calculate and state the exact rates of change in the plane's position, hence giving us the instantaneous velocities at those points.

Answer:

Mr. Chang

Step-by-step explanation:

29.99 * .20= 5.998

29.99- 5.998 = she payed 23.99

25* .10= 2.50

25-2.50= he payed 22.50

Therefore he payed more

Step-by-step explanation:

To calculate the probability that at least one dog will be adopted out of nine visits to an animal shelter, given a single visit adoption probability of 0.20, you use the complementary probability principle: 1 minus the probability of no adoptions in nine visits (0.80^9).

The question asks to calculate the probability that at least one dog will be adopted out of nine visits to an animal shelter, given that the probability of adopting a dog on any visit is 0.20. To find this, we need to use the concept of complementary probability, which states that the probability of at least one event occurring is equal to 1 minus the probability of the event not occurring at all. Here, the event not occurring at all means no dogs are adopted in nine visits.

First, let's find the probability of not adopting a dog on a single visit, which is 1 - 0.20 = 0.80. Next, to find the probability of not adopting a dog in nine visits, we raise this number to the ninth power: 0.80^9. Lastly, to find the probability of at least one adoption in nine visits, we subtract this value from 1.

So, the calculation goes as follows:

Performing the arithmetic gives us the answer.

1 liter = 100 centiliter

0.31 * 100 = 31

31 centiliters = 0.31 liters

1 liter = 100 centiliter

0.31 * 100 = 31

31 centiliters = 0.31 liters

The height of the statue is 97.6 meters

The Breakdown

To determine the height of the statue, we can use trigonometry and create a right triangle with the sailor, the tip of the torch, and the top of the statue.

Assuming the height of the statue is "h" (in meters). The distance between the sailor and the statue is the sum of the initial distance and the additional distance sailed, which is 110 meters.

In the first observation, the angle of elevation is 25 degrees. This means that the tangent of the angle is equal to the height of the statue divided by the initial distance between the sailor and the statue:

tan(25°) = h / initial distance

Similarly, in the second observation, the angle of elevation is 43 degrees and 50 minutes. We need to convert this angle to decimal degrees before using it in calculations. 50 minutes is equal to 50/60 = 5/6 degrees.

So, the angle of elevation in decimal degrees is 43 + 5/6 = 43.8333 degrees.

Now, we can use the tangent function again to relate the height of the statue to the new distance between the sailor and the statue:

tan(43.8333°) = h / (initial distance + 110)

We have two equations with two unknowns (h and initial distance). We can solve this system of equations to find the height of the statue.

Solving the first equation for the initial distance:

initial distance = h / tan(25°)

Substituting this value into the second equation, we get:

tan(43.8333°) = h / (h / tan(25°) + 110)

Now, we can solve this equation for h:

h = (tan(43.8333°) × 110) / (1 - tan(43.8333°) / tan(25°))

Using a calculator, we find that:

tan(43.8333°) ≈ 0.957

tan(25°) ≈ 0.466

Substituting these values into the equation:

h = (0.957 × 110) / (1 - 0.957 / 0.466)

h ≈ 97.6 meters

Therefore, the height of the statue is 97.6 meters.

You would end up paying $2.84 in sales tax.

63.20*0.45=$2.84.

Hope this helps!

4.5% = 0.045

63.20 x 0.045 = 2.844

tax = $2.84

Answer:

The slope of the line is 1/2.

Step-by-step explanation:

2 x − 4 y = 10 (Subtract  2 x from both sides.)

− 4 y = − 2 x + 10 (Divide both sides by -4.)

y = − 2 x − 4 + 10 − 4  (Simplify.)

y = 1/2 x − 5 /2

y=1/2

Answer:

the slope is equal to [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

we have

[tex]2x-4y=10[/tex] -----> equation of the line in standard form

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b  is the coordinate y of the y-intercept

Convert the equation of the line into slope intercept form

[tex]2x-4y=10[/tex] -----> isolate the variable y

[tex]4y=2x-10[/tex]

[tex]y=\frac{2}{4}x-\frac{10}{4}[/tex]

Simplify

[tex]y=\frac{1}{2}x-\frac{5}{2}[/tex]

therefore

the slope is equal to

[tex]m=\frac{1}{2}[/tex]

The amount of the tax per unit imposed by the government, based on the examples provided, is $4 per unit. This specific tax impacts the supply curve and the market's equilibrium, affecting both the consumers' and suppliers’ prices.

The question you're asking about centers on the concept of tax per unit, which is a specific type of tax that governments impose on goods or services. In the information provided, various scenarios are described where a tax is imposed, which affects the prices and the quantity traded of the good. For instance, the imposition of a specific tax of $4 means the supply curve shifts vertically upwards by this amount. The resulting changes in market conditions illustrate how the tax burden is shared between consumers and suppliers.

In the most relevant example, both the government and supplier receive $4 per unit after the imposition of the tax. Therefore, the amount of the tax per unit imposed by the government is $4, which is option (b) in the context of your question.

Answer:

Graph is attached below

Step-by-step explanation:

[tex]24x+25=-6y+7[/tex]

To graph the given equation , first we need to solve the equation for y

[tex]24x+25=-6y+7[/tex]

Subtract 7 on both sides

[tex]24x+18=-6y[/tex]

Divide both sides by -6

[tex]y=-4x-3[/tex]

To graph the given equation , make a table.

Assume some random number for x  and find out y

x         y=-4x-3

-1           1

0           -3

1             -7

Now graph all the points and join it by a line

(-1,1)(0,-3)(1,-7)

The graph is attached below

The solution to the inequality x - 7.67 ≥ 8.4 is x ≥ 16.07, which is found by isolating x on one side of the inequality.

To solve this inequality, we need to isolate x on one side. The inequality is x - 7.67 ≥ 8.4. To get x by itself, we have to remove 7.67 from the left side of the inequality. We can do that by adding 7.67 to both sides of the inequality.

So, the revised equation is x - 7.67 + 7.67 ≥ 8.4 + 7.67. After simplifying, we get x ≥ 16.07. This is the solution to the inequality.

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A. We are given that the combination is 1 letter and 8 digits, so the total number of unique combinations would be the product of each possibilities.

Total unique ID’s = 26 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10

or can also be written as

Total unique ID’s = 26 * 10^8

Solving:

Total unique ID’s = 2.6 x 10^9

B. Let us now calculate the total unique ID’s if there is only 1 letter followed by 3 digits.

Total unique ID’s = 26 * 10^3

Total unique ID’s = 26,000

Since there are 48,000 students and only 26,000 unique ID’s, therefore it is not enough.

NO.

Final answer:

The answer explains the calculation of unique student IDs at a university and determines if a specific ID format is sufficient for a given student count.

Explanation:

(a) To calculate the number of unique student IDs, we multiply the possibilities for each part: 26 possibilities for a letter and 10 possibilities for each of the eight digits:

Total unique student IDs = 26 x (10)^8 = 26 x 100,000,000 =26 x 10^8

(b) For a university with 43,000 students, one letter followed by three digits would have:

Total unique IDs = 26 x (10)^3 = 26 x 1,000 = 26,000, which is more than 43,000 students - so no, it would not suffice.

let cat food = x

 total plus 5% = 105% = 1.05

1.05 * (11.50 + X) = 16.80

12.075 + 1.05x = 16.80

1.05x = 16.80-12.075

1.05x = 4.725

x = 4.725 / 1.05

x= 4.50

 the cat food cost $4.50

11.50 +4.50 = 16.00

16.00 * 0.05 = 0.80

16.00 + 0.80 = 16.80

Answer:

The common ratio r is -7.

Step-by-step explanation:

The common ratio of a geometric sequence is the division of the term [tex]a_{n+1}[/tex] by the term [tex]a_{n}[/tex].

In this problem, we have that:

[tex]a_{1} = 2, a_{2} = -14, a_{3} = 98, a_{4} = -686[/tex].

So the common ratio r is:

[tex]r = \frac{-14}{2} = \frac{98}{-14} = \frac{-686}{98} = -7[/tex]

The common ratio r is -7.

BODMAS stands for Brackets of Division, Multiplication, Addition, and Subtraction.

In the given equation, the simplified value is -1.

The given equation is:

[tex]8 - 13 - ( - 4)[/tex]

Step 1: In the equation, brackets are present. The brackets will open and the negative sign will be changed to a positive sign, (-) (-) = +.

The equation now becomes:

[tex]8 - 13 + 4[/tex]

Step 2: Based on the BODMAS, after division and multiplication, addition comes.

Solving for the same, we get:

[tex]8 - 9[/tex]  [Becaue, -13 + 4 = -9 (+)(-) = (-)]

Step 3: The final value of subtracting -9 from 8, we get:

[tex]8 - 9[/tex]   = -1.

Therefore, for the given equation, [tex]8 - 13 - ( - 4)[/tex], the simplified answer is -1.

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Answer:

6.31 m

Step-by-step explanation:

The surface area (S) of a sphere is a function of its radius (r) according to the following expression.

[tex]S=4\pi r^{2}[/tex]

We can rewrite it to solve for the radius given the surface area.

[tex]S=4\pi r^{2}\\r^{2} =\frac{S}{4\pi} \\r=\sqrt{\frac{S}{4\pi}}[/tex]

When S = 500 m², the radius is

[tex]r=\sqrt{\frac{500m^{2} }{4\pi}}=6.31 m[/tex]

Let L be the length of the ladder, and consider the 75 degree angle.  Thinking in terms of trig, the "opposite side" of the triangle formed by the ladder, the ground and the wall is 23 ft.  Your job is to determine the length of the ladder, which is the same as the length of the hypotenuse of the triangle.

The sine function relates these two lenths:

                     opp. side           23 ft

sin 75 deg = ----------------  =  --------------

                       hyp                    hyp

                                             23 ft                     23 ft

Solving for hyp,   hyp = ----------------------  =  ------------ = 23.8 ft                                                                    sin 75 deg             0.956

The minimum ladder length would be 23.8 ft, which rounds up to 24 ft.

Check:  is (23.8 ft)(sin 75) = 23 ft?  Yes.

Using trigonometry, the shortest possible length of the ladder given that the wall height is 23 feets and makes an angle of 23° with the ground ls 24 feets

Recall from trigonometry :

Using :

Sin(75°) = 23 / hypotenus

Cross multiply :

Hypotenus × 0.9659258 = 23

Divide both sides by 0.9659258

Hypotenus = (23 / 0.9659258)

Hypotenus = 23.81 feets

Therefore, the height of the ladder rounded to the nearest feet is 24 feets.

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