Alex can run 5/4 miles in 1/12 hour. At this rate, how far can he run in 1 hour?

Answer:

Let x be the number of animated DVDs Sammi borrowed and y be the number of superhero DVDs she borrowed.

The total number of minutes of all DVDs is 1,200, so we have:

90x + 120y = 1,200

And the total number of DVDs borrowed is 11, so we have:

x + y = 11

To solve this system of linear equations, we can use substitution method. Solving for y in the second equation, we get:

y = 11 - x

Substituting this expression for y into the first equation, we have:

90x + 120(11 - x) = 1,200

Expanding the right side, we get:

90x + 1320 - 120x = 1,200

Combining like terms, we get:

-30x = -120

Solving for x, we get:

x = 4

Since x is the number of animated DVDs, Sammi borrowed 4 animated DVDs. Substituting this value of x back into the expression for y, we have:

y = 11 - x = 11 - 4 = 7

So Sammi borrowed 7 superhero DVDs.

The solution means that Sammi borrowed 4 animated DVDs and 7 superhero DVDs, which lasted for a total of 1,200 minutes. This method was relatively simple and efficient, as it only involved solving for one variable and then using substitution.

Answer:

36

Step-by-step explanation:

length=6

width=3

height=2

6 x 3 x 2 = 36

The metric system is an international system of measurement that uses the base unit of the meter to measure length or distance. The meter is defined as the length of the path traveled by light in a vacuum during a specific fraction of a second.

It is an essential unit of the International System of Units (SI) and is used to measure distance, length, height, and width in most countries worldwide.

The meter is equivalent to approximately 39.37 inches, making it a longer unit of measurement than the inch, which is used in the imperial system of measurement. The metric system is based on a decimal system, which makes it easier to convert between units of length. For instance, one kilometer (km) is equal to 1,000 meters, and one centimeter (cm) is equal to 0.01 meters.

The metric system is widely used in science, industry, and daily life. It is the standard system of measurement used in most countries worldwide, except for the United States, which primarily uses the imperial system of measurement. However, it is essential to understand the metric system, as it is becoming increasingly popular in many fields and is a fundamental part of global communication.

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Answer:

$ 645.85

Step-by-step explanation:

First you would plug 6,500 into P. The plug 2.5% as 0.025 into i. And plug the years (5) into n.

A = 6500 (1 + 0.025)^5 = 7354.15

That is the amount that would be in the account at the end of the 5 years.

Then you take the cost of the car (8,000) and subtract the money left in the account (7,354.15).

8000 - 7354.15 = 645.85

Your final answer would be rounded to the nearest cent, or the hundredths place.

The comparison between A and B is as follows:A < B.

We are given that:120 % of A is equal to 150 => (120/100)A = 150

Divide both sides by 120/100: A = 150 × 100/120 = 125

And, 105 % of B is equal to 165 => (105/100)B = 165

Divide both sides by 105/100: B = 165 × 100/105 = 157.14

Therefore, A = 125 and B = 157.14

Compare A and B:It can be seen that B is greater than A. Therefore, B > A. Hence, the comparison between A and B is as follows:A < B.

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Answer:

hello there i think the answer is c

Step-by-step explanation:

Cost of 15 notebooks = Rs 145

Cost of 1 book = 145/15 = Rs 9.66

Answer:

$17.50

Step-by-step explanation:

Yes, the conditions for inference are met. The teacher conducts 50 trials, which is large enough to meet the large counts condition (np ≥ 10 and n(1-p) ≥ 10).

The teacher's attempt to make the number cube unfair by inserting lead weights raises the question of whether the proportion of rolls that will land on a 1 has changed. To determine if she was successful, the teacher rolls the cube 50 times and keeps track of the number of times she rolls a 1. The data shows that she rolled a 1 15 times.

To determine if the data provides convincing evidence that the proportion of rolls that will land on a 1 is greater than one-sixth, we need to check if the conditions for inference are met.

The 10% condition requires that the sample size is less than 10% of the population size. Since we do not know the population size, we cannot determine if this condition is met.

The large counts condition requires that both the number of successes (15) and the number of failures (35) are greater than or equal to 10. This condition is met.

The randomness condition requires that the sample is random. Since the teacher rolled the cube, it is assumed that the rolls were random.

Therefore, the conditions for inference are met. We can use a hypothesis test to determine if the data provides convincing evidence that the proportion of rolls that will land on a 1 is greater than one-sixth.

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Answer:

B. A linear, partial variation

Step-by-step explanation:

We know that speed = distance / time. From the table we have a linear function, and it's indirect, or partial.

a) The actual distance between towns K and L is: 100 km

b) As shown in the attached file

c) The bearing of town L from town K is 117 degrees.

The scale of the map is given as:

1 cm to represent 50 km

Now, when we measure the distance between K and L on the map, we see that it gives us a distance of 2 cm.

Using the scale of 1 cm: 50 km, we can say that:

Actual distance between towns K and L = (2 * 50)/1 = 100 km

b) Using a compass and it’s 3cm aiming down {South} as seen in the attached photo. Then a line was drawn aiming {South} with a ruler. On the end of the line the (x) point was put there to get the mark.

c) Measuring the angle gives the bearing of town L from town K which is 117 degrees.

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Answer:

1. variable by itself with a coefficient of 1 on one side of the equation and all the other variables and constants on the other side.

2.Because solving an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns.

Step-by-step explanation:

3x =4xyz - 12y

+12           +12

3x + 12y

----------

4xy

3x + 12y

---------- =z

4xy

Answer:

Answer:

Please find attached the graph of the function created with MS Excel showing the relevant points required to draw an approximate graph of the function on a graph paper

Step-by-step explanation:

The given quadratic function is f(x) = -2·x² + 7·x + 4

The range of the input (x) values = -1 ≤ x ≤ 5

The coefficient of the quadratic is negative -2, the graph is n shape

The intercept form of the function is given as follows;

-2·x² + 7·x + 4 = -1 × (2·x² - 7·x - 4)

-1 × (2·x² - 7·x - 4) = -1 × (2·x² + x - 8·x - 4)

-1 × (2·x² + x - 8·x - 4) = -1 × (x · (2·x + 1) - 4·(2·x + 1))

∴ -1 × (x · (2·x + 1) - 4·(2·x + 1)) = -1 × (2·x + 1)·(x - 4)

∴ f(x) = -2·x² + 7·x + 4 = -1 × (2·x + 1)·(x - 4)

At the x-intercepts, (2·x + 1) = 0 or (x - 4) = 0, which gives;

x = -1/2 or x = 4

Therefore, the x-intercepts are (-1/2, 0), (4, 0)

The equation in vertex form is given as follows;

f(x) = -2·x² + 7·x + 4 = -2·(x² - 7·x/2 + 2)

By applying completing the squares method, to x² - 7·x/2 - 2, we get;

Where x² - 7·x/2 - 2

x² - 7·x/2 = 2

x² - 7·x/2 + (-7/4)² = 2 + (-7/4)² = 81/15

(x - 7/4)² = 81/16

∴ (x - 7/4)² - 81/16 = 0 = x² - 7·x/2 - 2

∴ x² - 7·x/2 - 2 = (x - 7/4)² - 81/16

-2·(x² - 7·x/2 + 2) = -2·((x - 7/4)² - 81/16) = -2·(x - 7/4)² + 81/8

The vertex = (7/4, 81/8)

When x = 0, we get;

f(0) = -2 × 0² + 7 × 0 + 4 = 4

The y-intercept = (0, 4)

The sketch of the function should pass through the x-intercepts (-1/2, 0), (4, 0), the y-intercept (0, 4), and the y-intercept (0, 4), and the vertex, (7/4, 81/8) on a graph sheet

Please find attached a drawing of the function of the function created with MS Excel

Answer:

Sorry

Step-by-step explanation:

I not know this one

Answer:

all together there is 141 candies in all

The correct answer for the equation or inequality is 2.1319

A mathematical assertion that two expressions are equal is known as an equation. It consists of two mathematical expressions, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). Equations are used to represent relationships, locate unknown quantities, and solve problems.

To solve the equation \(6^z = 45.6\), you can use the logarithm to find the value of z. Here's a step-by-step explanation:

1. Write the equation as a logarithmic equation: z = \(log6(45.6)\)
2. To solve for z, use the change of base formula: z = \(log(45.6) / log(6)\).
3. Calculate the value of z using a calculator: z = 2.1319.

So, the correct answer is 2.1319.

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Answer:

1, 2

2, 5

3, 8

4, 11

5, 14

Step-by-step explanation:

you just plug each n value into the n

Answer:

I believe that it is the first one.

Step-by-step explanation:

Answer:

118.54

Please make me brainiest

Explain

22×3.14÷2= 34.54

8×13= 104-20= 84

84+34.54= 118.54

Step-by-step explanation:

most of the solution is already written there.

in words :

you define 2 variables for the 2 unknown quantities.

per definition we pick

M = number of medium packs

L = number of large packs

in order to solve a system of 2 variables we need 2 different equations about these 2 variables (for 3 variables we need 3 equations and so forth).

she bought 10 packs.

that much we know. and we know how much she paid for these 10 packs in total.

and we know the individual prices for a single pack of medium and of large size.

so,

M + L = 10

we don't know how many of each, but the total number of packs is 10. so, that's what we are writing down, and it becomes our first equation to solve the 2 variables.

and combining our knowledge about individual prices and the total cost we say

1.80M + 2.40L = 21.60

in other words, we still don't know how many of each size she bought, but the sum of the unknowns "weighted" by their individual prices is known in the form of total cost.

and this is then our second equation.

to summarize these equations again :

M + L = 10

1.80M + 2.40L = 21.60

the first equation is the easiest to transform, and we use it to express one variable by the other (apply the same change to both sides, like here subtracting L from both sides) :

M = 10 - L

this identity we can now use in the second equation :

1.80×(10-L) + 2.40L = 21.60

you know, when you multiply 2 expressions, you need to multiply every term of one expression with every term of the other expression. so, we get

1.80×10 - 1.80L + 2.40L = 21.60

18 - 1.80L + 2.40L = 21.60

when you add 2 terms of the same variable, you can simply add the factors of the variable. so, we get

18 + 0.60L = 21.60

when transforming an equation, it is important to always apply the same changes on both sides. so, here, we subtract 18 from both sides :

0.60L = 3.60

now dividing both sides by 0.60 :

L = 6

and from

M = 10 - L

we get

M = 10 - 6 = 4

so, she bought 4 medium packs and 6 large packs.

Answer: Point A: −12 3

explanation: I hope that helps

A. The sand will not fit into the tank because the volume of the sand is higher than that of the container

B. the difference in the volume of the first and second tank is 70in³

C. The measurement of the tank that will hold exactly 375 is 5in × 7in × 10.7 in

A prism is a solid shape that is bound on all its sides by plane faces.

The volume of a prism is expressed as;

volume = base × height

The volume of the tank = 5×7×9

= 315 in³

The volume of the sand is 375 .

Therefore the volume of the sand is greater than that of the tank, this means the sand will not fit into the tank.

B. The height of the second tank = 9+2 = 11

The volume of the second tank = 5×7 × 11 = 385

therefore the difference in the volume of the first and second tank = 385-315

= 70in³

C. If the tank has thesame base, then the height will be

375 = 5× 7 × h

375 = 35h

h = 375/35

h = 10.7 in

therefore the measurement of the tank that will hold exactly 375 is 5in × 7in × 10.7 in

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Answer:

the answer is y = x + 1

have a good day :3

Answer: $11 per hour

Step-by-step explanation:

Divide $82.50 by 7.5 hours to get your hourly pay or the rate of your pay.

Using proportions, it is found that he was supposed to read the book in 10 days.

40 pages - x days

25 pages - x + 6 days

Applying line multiplication, as it is an inverse rule of three:

\(40x = 25(x + 6)\)

\(40x = 25x + 150\)

\(15x = 150\)

\(x = \frac{150}{15}\)

\(x = 10\)

He was supposed to read the book in 10 days.

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Approximately 20.30% of the total area is below the standard normal curve between z = -1.6 and z = -0.65. 

To discover the rate of the entire region beneath the standard normal curve between z=-1.6 and z=-0.65, we got to discover the region to the cleared out of z=-0.65 and the range to the cleared out of z=-1.6. At that point subtract the two ranges. 

Using a standard normal distribution table or a calculator capable of calculating normal probabilities, we can find the regions to the left of z = -0.65 and z = -1.6 respectively.

The area to the left of z = -0.65 is 0.2578 (rounded to four decimal places).

The area to the left of z = -1.6 is 0.0548 (rounded to four decimal places).

In this manner, the rate of add-up to the region between z = -1.6 and z = -0.65 is

Rate of add up to zone = (range cleared out of z = -0.65 - zone cleared out of z = -1.6) × 100D44 = (0.2578 - 0.0548) × 100D44 = 20.30D 

Therefore, approximately 20.30% of the total area is below the standard normal curve between z = -1.6 and z = -0.65. 

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The equation in point-slop form of the line line having the slope m=-1 and that contains the point (-2,3)  is y-3=-1(x+2)

Given,

The slope m = -1

The point = (-2,3)

We know the point-slope form,

\(y-y_{1}=m(x-x_{1})\\\)

Substitute the values in the equation

y-3=-1(x-(-2))

y-3=-1(x+2)

Hence, the equation in point-slop form of the line line having the slope m=-1 and that contains the point (-2,3)  is y-3=-1(x+2)

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Answer:

x=5

Step-by-step explanation:

Desmos is a tool to finding your answer to this equation. Its a graphing calculator