0.04 divided by 1.68

The rate of change of y with respect to x is 35 words per minute.

The rate of change of y with respect to x can be found by taking the slope of the line that represents the relationship between x and y. To find the slope, we can use the formula:

slope = change in y / change in x

Using the given information, we can calculate the slope as:

slope = (525 - 140) / (15 - 4) = 385 / 11 = 35

Therefore, the rate of change of y with respect to x is 35 words per minute.

Final answer:

Jeremy's rate of change in typing speed is 35 words per minute, calculated by dividing the change in words typed by the change in time (385 words/11 minutes).

Explanation:

The student is asking about the rate of change of the words typed with respect to time spent typing. To calculate this, we will use the given values: 140 words in 4 minutes and 525 words in 15 minutes. The rate of change, essentially being the slope of the line that represents the relationship between words typed (y) and the time (x), can be calculated by finding the ratio of the change in words to the change in time:

This means that Jeremy types at an average speed of 35 words per minute.

Final answer:

The ratio of red cards to other cards that Brent counted (10 red cards, 10 black cards, 20 blue cards) is 1:3 after summing black and blue cards to find the total number of other cards and simplifying the ratio.

Explanation:

Brent counted 10 red cards, 10 black cards and 20 blue cards. The question is what is the ratio of red cards to other cards. To calculate the ratio, we need to determine the total number of cards that are not red, which would be the black and blue cards combined.

First, we sum the black and blue cards:

10 black cards + 20 blue cards = 30 other cards.

Now, we set up the ratio of red cards to other cards:

10 red cards : 30 other cards, which simplifies to 1 : 3 when both sides of the ratio are divided by 10, the greatest common divisor.

Therefore, the ratio of red cards to other cards is 1:3.

To find the individual cost of a hot dog and hamburger from a concession stand, we set up a system of equations from the given information and solve it to get the cost of one hot dog as $1.25 and one hamburger as $2.00.

To find the cost of one hot dog and one hamburger, we set up a system of equations based on the information given:

Let's denote the cost of one hot dog as d and the cost of one hamburger as h. We can then rewrite the given information as:

Solving this system of equations, we can multiply the first equation by 2 and the second equation by 3, and subtract them, cancelling out the hamburger terms:

Subtracting the first equation from the second gives:

Thus, one hamburger costs $2.00. Plugging this back into the first equation, we get:

Which simplifies to:

Therefore, one hot dog costs $1.25.

Answer:

There are 14 bags in 3.5 boxes.

Step-by-step explanation:

Given : Lettuce is packaged in four bags to a box. If there are 3.5 boxes of lettuce in a cooler.

To find : How many bags of lettuce would there be?

Solution :

Lettuce is packaged in four bags to a box.

i.e, In 1 box there are 4 bags.

If there are 3.5 boxes of lettuce in a cooler.

In 3.5 boxes number of bags are [tex]4\times 3.5=14[/tex]

Therefore, There are 14 bags in 3.5 boxes.

The probability that a couple will have a girl a boy a girl and a boy in this specific order is 1/16

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

If the couple will give birth to a boy and a girl, hence the total outcome of the event is 2

Pr(having a boy) = 1/2

Pr(having a girl) = 1/2

Pr(a girl, a boy, a girl and a boy) = 1/2 * 1/2 *1/2 * 1/2

Pr(a girl, a boy, a girl, and a boy) = 1/16

Hence the probability that a couple will have a girl a boy a girl and a boy in this specific order is 1/16

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Step 1

Find the equation of the line perpendicular to [tex] y = 4x + 5 [/tex] that pas through the origin

we know that

the slope of the equation [tex] y = 4x + 5 [/tex] is

[tex] m1=4 [/tex]

if two lines are perpendicular

then

the product of their slopes is equal to [tex] -1 [/tex]

[tex] m1*m2=-1 [/tex]

the slope of the line perpendicular is equal to

[tex] m2=-\frac{1}{m1} \\\\ m2=-\frac{1}{4} [/tex]

with m2 and the origin find the equation of the line

[tex] y-y1=m(x-x1)\\ y-0=(-\frac{1}{4} )*(x-0)\\ y=-\frac{1}{4} x [/tex]

Step 2

Solve the system

[tex] y = 4x + 5 [/tex]---> equation [tex] 1 [/tex]

[tex] y=-\frac{1}{4} x [/tex]-----> equation [tex] 2 [/tex]

Multiply equation [tex] 1 [/tex] by [tex] -1 [/tex]

Adds equation [tex] 1 [/tex] and equation [tex] 2 [/tex]

[tex] -y = -4x - 5 [/tex]

[tex] y=-\frac{1}{4} x \\ ----- [/tex]

[tex] 0=-4x-\frac{1}{4} x-5\\ \\ \frac{17}{4} x=-5\\ \\ x=-\frac{20}{17} [/tex]

[tex] y = 4x + 5 [/tex]

[tex] y = 4*(-\frac{20}{17}) + 5 \\ \\ y=\frac{5}{17} [/tex]

the solution is the point [tex] (-\frac{20}{17} ,\frac{5}{17} ) [/tex]

[tex] (-\frac{20}{17} ,\frac{5}{17} ) [/tex]=[tex] (-1.176 ,0.294 ) [/tex]

therefore

the answer is

the point is [tex] (-\frac{20}{17} ,\frac{5}{17} ) [/tex]

see the attached figure

The point [tex]\boxed{(-1.176,0.294)}[/tex] on the line [tex]y=4x+5[/tex] is the closest point to the origin.  

Further explanation:

The general form of linear function is as follows:

[tex]\boxed{y=mx+c}[/tex]

A linear function has one independent variable and one dependent variable. The independent variable is [tex]x[/tex] and the dependent variable is [tex]y[/tex].

Here, [tex]c[/tex] is the constant term and [tex]m[/tex] is the slope and gives the rate of change of dependent variable.  

The point slope form of a line is given as follows:

[tex]\boxed{y-y_{1}=m(x-x_{1})}[/tex]  

where [tex](x_{1},y_{1})[/tex] is the point on the line and [tex]m[/tex] is the slope of the line.

It is given that the equation of the line is as follows:

[tex]y=4x+5[/tex]

where [tex]4[/tex] is the slope of the line.

Consider the slope of the line [tex]y=4x+5[/tex] as [tex]m_{1}=4[/tex].

We first find the line perpendicular to the line [tex]y=4x+5[/tex] that passes through the origin as shown in Figure 1 in the attachment below.

If two lines are perpendicular then the product of their slopes is [tex]-1[/tex]  that is [tex]m_{1}\tiimes m_{2}=-1[/tex].

And [tex]m_{2}[/tex] is the slope of the perpendicular line.

Calculated the value of [tex]m_{2}[/tex] as follows:

[tex]\begin{aligned}m_{1}\times m_{2}&=-1\\m_{2}&=-\dfrac{-1}{m_{1}}\\&=\dfrac{-1}{4}\\&=-0.25\end{aligned}[/tex]

Therefore, the slope of perpendicular line is [tex]-0.25[/tex].

We have the point [tex](0,0)[/tex] on the line and the slope of the line.

Thus, the equation of line is,

[tex]\begin{aligned}y-y_{1}&=m_{2}(x-x_{1})\\y-0&=(-0.25)(x-0)\\y&=-0.25x\end{aligned}[/tex]  

The equation of the perpendicular line is as follows:

[tex]\boxed{y=-0.25x}[/tex]        .......(2)

Substitute [tex]y=-0.25x[/tex] in equation (1).

[tex]\begin{aligned}-\dfrac{x}{4}&=4x+5\\-\dfrac{x}{4}-4x&=5\\-\dfrac{17x}{4}&=5\\-17x&=5\times 4\\x&=-\dfrac{20}{17}\\x&\approx-1.176\end{aligned}[/tex]  

Now, put the value of [tex]x[/tex] in equation (2) to get the value of [tex]y[/tex] as,

[tex]\begin{aligned}y&=-0.25\times (-1.176)\\&=0.294\end{aligned}[/tex]  

Therefore, the closest point is [tex]\boxed{(-1.176,0.294)}[/tex].

Learn more

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Linear equations

Keywords: Linear equations, slope of a line, equation of the line, function, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open intervals, sets, range domain, codomain.

Amount earn as commission on real state building is $5,520

What information do we have?

Amount of real state house = $92,000

Percentage of Commission on sale = 6%

Amount earn as commission = Amount of real state house × Percentage of Commission on sale

Amount earn as commission = 92,000 × 6%

Amount earn as commission = 92,000 × 0.06

Amount earn as commission = $5,520

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The​ half-life of this radioactive isotope is 135.897 days and this can be determined by using the formula of half-life.

Given :

The formula of the half-life is given by:

[tex]\rm A =P \left(\dfrac{1}{2} \right)^{\dfrac{t}{t_{1/2}}}[/tex]

where A is the final concentration, P is the initial concentration, t is the time period, and [tex]\rm t_{1/2}[/tex] is the half-life.

Now, substitute the known values in the above formula.

[tex]\rm 0.13P =P \left(\dfrac{1}{2} \right)^{\dfrac{400}{t_{1/2}}}[/tex]

Simplify the above expression.

[tex]\rm 0.13 = \left(\dfrac{1}{2} \right)^{\dfrac{400}{t_{1/2}}}[/tex]

Take the log on both sides.

[tex]\rm log(0.13) = {\dfrac{400}{t_{1/2}}} \times log\left(\dfrac{1}{2} \right)[/tex]

[tex]\rm t_{1/2} = \dfrac{400\times log(0.5)}{log(0.13)}[/tex]

Simplify the above expression in order to evaluate the [tex]\rm t_{1/2}[/tex].

[tex]\rm t_{1/2} = 135.897\;days[/tex]

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The half-life of a radioactive isotope is calculated by using the decay formula and solving for the known half-life, given that 13% of the original isotope remained after 400 days.

To determine the half-life of a radioactive isotope, we first need to understand that half-life is the time required for half of a sample of a radioactive isotope to decay. From the problem, it stated that after 400 days, only 13% of the original isotope remained. The formula for decay is N = N0 * (1/2)^(t/T), where N is the final amount, N0 is the initial amount, t is the time elapsed, and T is the half-life.

Given that N/N0 is 0.13 after 400 days, we can rewrite the decay formula to solve for T. By substituting the values into the equation, i.e., 0.13 = (1/2)^(400/T), we can use the laws of logarithms to solve for T. So then we will get the half-life (T) of the isotope.

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The annual depreciation expense for the meat processor's refrigerator, using the straight-line method, is $2,600.

Straight-line Depreciation Calculation

The straight-line depreciation method spreads the cost of an asset evenly over its useful life. To calculate the annual depreciation expense for the refrigerator, we follow this formula: (Cost of the asset - Residual value) / Estimated useful life.

In this case, the numbers provided are a cost of $48,000, a residual value of $9,000, and an estimated useful life of 15 years. Using these values, the calculation is as follows:

(48,000 - 9,000) / 15 = 39,000 / 15 = $2,600 per year.

Therefore, the annual depreciation expense that the meat processor would record for this refrigerator is $2,600.

To find the different options for a car model with multiple customizable features, you multiply the number of choices for each feature. For this model, with 10 colors, 2 options each for transmission, four-wheel drive, and air conditioning, and 3 speaker options, there are 240 different combinations.

To calculate the number of different options for this model of a car, we need to consider all the features that can be selected and multiply the number of choices for each feature together. For the color, there are 10 options. For each of the features, such as automatic transmission, four-wheel drive, and air conditioning, there are 2 choices: with or without. Finally, for the radio-CD speakers, there are 3 options: two, three, or four speakers. Multiplying these choices together gives us the total number of different options:

10 (colors) × 2 (transmission) × 2 (four-wheel drive) × 2 (air conditioning) × 3 (radio-CD speakers) = 240 different options.

So, there are 240 different options available for this model of a car.

Final answer:

To find the total number of different options for the car, we multiply the number of choices for each feature resulting in 240 different options.

Explanation:

The student is asking about the number of different option combinations for a specific model of a new car. The car can be customized with ten colors, automatic transmission or not, four-wheel drive or not, air conditioning or not, and can have two, three, or four radio-CD speakers. To determine the total number of different options, we multiply the number of choices for each feature:

Therefore, the total number of different options is calculated as follows:

10 (colors) × 2 (transmission) × 2 (drive) × 2 (air conditioning) × 3 (speakers)

= 240 different options.

The trivial lower-bound classes for the problems provided include O(n) for finding the largest element in an array, O(n^2) for graph completeness, O(2^n) for subset generation, and O(n log n) for distinctness checking. Some of these bounds are tight, such as O(n) and O(2^n), while others may not be.

For each of the following problems, we can establish a trivial lower-bound class and discuss whether it is tight:

Where the above figure is given as the attendant derivatives F', the maximum value attained by F is 400.

It is to be noted that:

Max occurs at x=50 where F'(x) = 0.

We need to find value for F(50) using fundamental theorem of calculus:

[tex]\int_{50}^{50} F' dx = F(50) - F(20)[/tex]

= F (50) -100
F(50) = 100 + A

Where A is the estimated Area under the graph.

If we assume the shaded region is close to a right triangle then the Area is

(1/2) x 30 x 20

= 300

Thus,

F (50) = 100 + 300

= 400

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The area of each strip of paper is 15/8 square inches.

The area of each strip of paper can be calculated by multiplying the length and width of the strip. In this case, the length is 2 1/2 inches and the width is 3/4 inches. To multiply fractions, multiply the numerators together to get the numerator of the product, and multiply the denominators together to get the denominator of the product. So, the area of each strip is:

(2 1/2 inches) x (3/4 inches) = (5/2 inches) x (3/4 inches) = 15/8 square inches.

Answer:

6, 6, 2

Step-by-step explanation:

Factor 72:

72 = 2³ × 3²

Look for groups of 3 numbers whose products are 72 and their sums:

2, 4, 9: sum 15

8, 9, 1: sum 18

8, 3, 3: sum 14

6, 6, 2: sum 14

6, 4, 3: sum 13

12, 6, 1: sum 19

12, 3, 2: sum 17

18, 4, 1: sum 23

18, 2, 2: sum 22

24, 3, 1: sum 28

36, 2, 1: sum 39

72, 1, 1: sum 74

Jim knows the sum, but he can't guess the ages. that means the sum must be 14 for which there are two sets of ages which have a product of 72:

8, 3, 3 and 6, 6, 2

Then when he says "my youngest", that means one age is less than the other two. The only choice is 6, 6, 2.

The mathematical  sentence written with a greater than, a less than sign, or a not equal sign is know as Inequality.

Inequalities are mathematical formulas in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is substituted by a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

As, the mathematical  sentence written with a greater than, a less than sign, or a not equal sign.

The definition of inequality is that two things are NOT equal. One of the items could be less than, greater than, less than or equal to the other things, or greater than or equal to the other things.

So, the statement is Inequality statement.

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