Alejandro is learning how to play guitar. One day out of the week, he attends a 45-minute lesson. The remaining days of the week, he practices guitar for 25 minutes per day. What total number of minutes does Alejandro spend at his lesson and practicing in 3 weeks?

Answer:

Step-by-step explanation:

Given the above model, we can state that it's predictions were accurate.

The model uses the variable x which represents no. of years from 1970 to 2010

2010 -1970 = 40
P + (x/2) = 44

P + 40/2 = 44

P + 20 = 44
P = 44 - 20
p = 24

The model, it predicted 24% of the population would be smoking in this city in the year 2010. Whereas the data from the graph tell us that

28 %  of the adults actually smoked in the city in 2010. Hence the model is accurate .

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Full Question:

The mathematical model

p+ x/2 =44

Describes the percentage, p, of adults who smoked cigarettes x years after 1970

Does the mathematical model underestimate or overestimate the percentage of adults who smoked cigarettes in 2010? By how much?

The equation in slope-intercept form for the line that has slope of -2/5 and y-intercept of -4 is written as: y = -2/5x - 4.

The slope-intercept form for any given straight line or linear relationship can be expressed as y = mx + b, where:

m = slope of the line

b = the y-intercept

Given the following:

slope (m) = -2/5.

y-intercept (b) = -4

To write the equation, substitute m = -2/5 and b = -4 into y = mx + b:

y = -2/5x - 4

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The statement that is true about the given circle equation is:

Option A: The circle is centered at (−6, 3) and has a radius of 11.

The standard form for finding the equation of a circle is given by the expression:

(x - h)² + (y - k)² = r²

where:

(h, k) represents the coordinates of the center of circle

r represents the radius of the circle

We are given the equation of the circle as:

(x - 6)² + (y - 3)² = 121

Now, 121 can also be written as 11². Thus, the equation of the circle can be rewritten as:

(x - 6)² + (y - 3)² = 11²

Comparing with the standard form of equation of a circle gives:

Coordinates of center = (-6, 3)

Radius = 11

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There are 2000 milligrams in 2 grams of a substance, and it constitutes 40% of a 5-gram sample.

Convert grams to milligrams:

2 grams = 2 * 1000 milligrams

2 grams = 2000 milligrams

Calculate the percentage in a 5-gram sample:

Percentage = (2000 milligrams / 5000 milligrams) * 100

Percentage = (2 / 5) * 100

Percentage = 0.4 * 100

Percentage = 40%

Thus, there are 2000 milligrams in 2 grams of a substance, and it constitutes 40% of a 5-gram sample.

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​2 grams = ​ milligrams

How many milligrams are there in 2 grams of a substance, and what is the percentage of this amount in a 5-gram sample?

Therefore here, (5⁴)². 5⁶. (5⁸)².(5⁶)². (5⁸)² simplifies to 5⁸².

The integer's basic form is represented by its smallest equivalent fraction. How to determine the simplest form: Look for shared components in the denominator and numerator.

By applying the exponentiation laws, let's us gradually simplify this an expression is:

[tex](5^4)^2 = 5^(4*2) = 5^85^6 * 5^8 = 5^(6+8) = 5^1425^6 = (5^2)^6 = 5^(2*6) = 5^1225^8 = (5^2)^8 = 5^(2*8) = 5^16[/tex]

When all of these simplifications are put back into the original statement, we get the following:

[tex](5^4)^2. 5^6. 5^8. 25^6. 25^8 = 5^8 * 5^14 * 5^12 * 5^16 * 5^16[/tex]

Using the rule that is  [tex]a^b * a^c = a^(b+c)[/tex],

The first three terms can be combined to create:

[tex]5^8 * 5^14 * 5^12 * 5^16 * 5^16 = 5^(8+14+12) * 5^(16+16) = 5^50 * 5^32[/tex]

Using the same rule again, we can combine these two terms:

5⁵⁰* 5³²

= 5⁵⁰⁺³²

= 5⁸²

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The interquartile range of the data will be 0.215.

The lower half is:

7.86, 7.87, 7.99, 8.03

The median of the lower half is:

(Q1) = (7.87 + 7.99) / 2 = 7.93

The upper half is:

8.06, 8.08, 8.09, 8.20, 8.43

The median of the upper half is:

(Q3) = (8.09 + 8.20) / 2 = 8.145

The IQR is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215

Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955

Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795

None of the data points fall outside these thresholds, so there are no outliers in this data set.

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Answer:

157,000

Step-by-step explanation:

π r² h

Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

we should expect 4 white horses among the next 20 horses that come to board. we can solve by equation .

what is equation ?

An equation is a mathematical statement that uses symbols and variables to show that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables, constants, and mathematical operations such as addition

In the given question,

Out of the 15 horses currently boarded, 3 are white. This means that the proportion of white horses among the currently boarded horses is:

3 / 15 = 0.2 or 20%

Therefore, if we assume that the next 20 horses that come to board will have a similar distribution of coat colors, we can expect approximately 20% of them to be white.

So, the expected number of white horses among the next 20 horses that come to board is:

20 x 0.2 = 4

Therefore, we should expect 4 white horses among the next 20 horses that come to board.

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The Length of the arc in the circle shown is calculated to one decimal place, in terms of pi, as approximately 3.6π cm.

The length of an arc in a given circle can be calculated by applying the formula as expressed below:

Length of arc (s) = ∅/360 * 2πr, where:

Reference angle = ∅

Radius of the circle = r.

Given the parameters:

Radius (r) = 16 cm

Reference angle (∅) = 40 degrees.

Plug in the values:

Length of the arc (s) = 40/360 * 2 * π * 16

Length of the arc (s) = 3.6π cm

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Answer:

To calculate the length of the minor arc AB in terms of pi, you need to know the measure of the central angle that intercepts the arc and the radius of the circle. Do you have that information?

Step-by-step explanation:

Answer:

To find the coordinates of the point of intersection between the two lines, we can solve the system of equations by elimination or substitution. Here, we will use the elimination method.

First, we will multiply the first equation by 10 and the second equation by 4, in order to eliminate the y term:

- 70x + 40y = 230

- 32x - 40y = 76

Adding these two equations, we get:

- 102x = 306

Dividing both sides by 102, we get:

- x = 3

Now we can substitute this value of x into either equation to find the value of y. Using the first equation:

- 7(3) + 4y = 23

- 21 + 4y = 23

- 4y = 2

- y = 1/2

Therefore, the point of intersection is (3, 1/2).

Answer:

Step-by-step explanation:

Answer:

f(x) = x^3 - x^2 + 16x - 16

Step-by-step explanation:

If a polynomial has the zeros 1, 4i, and -4i, then it must have the factors (x - 1), (x - 4i), and (x + 4i). This is because a factor of (x - a) produces a root of x = a.

To find the polynomial, we can multiply these factors together:

(x - 1)(x - 4i)(x + 4i)

= (x - 1)(x^2 - (4i)^2)

= (x - 1)(x^2 + 16)

= x^3 + 16x - x^2 - 16

So the polynomial function in standard form with real coefficients whose zeros include 1, 4i, and -4i is:

f(x) = x^3 - x^2 + 16x - 16

The expression "the cube root of the product of x and y, less twelve" can be mathematically represented as ³√(xy) - 12.

To understand this expression, let's break it down step by step:

Product of x and y:

We multiply the values of x and y together to find their product, denoted as xy.

Cube root of the product:

We take the cube root of the product obtained in the previous step.

The cube root of a number x is the value that, when raised to the power of 3, equals x. In this case, we take the cube root of xy, represented as ³√(xy).

Subtract twelve:  

Finally, we subtract twelve from the result obtained in the previous step, ³√(xy). This gives us the expression ³√(xy) - 12.

The expression ³√(xy) - 12 represents a mathematical operation involving the cube root of the product of x and y, followed by subtracting twelve from the result.

This can be useful in various mathematical contexts, such as solving equations or modeling real-world problems.

It's important to note that the expression is dependent on the values of x and y.

By substituting specific values for x and y, we can evaluate the expression to obtain a numerical result.

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The correct option is the last one, the mean will decrease.

For a set of N values {x₁, x₂, ..., xₙ} the mean is defined as the sum of the N values divided by N, this is:

mean = (x₁ + x₂ + ... + xₙ)/N

Now, here the mean is 3, and a family with 7 children (more than the mean) moves away.

That will cause a decrease in the mean, because we are removing one of the larger values.

The correct option is the last one.

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Answer:

False.

Step-by-step explanation:

A integer in math is defined as a whole number. Therefore, the presence of fractions (which, in this case, is 1/2) and decimals, would mean that the term is in fact, not a integer.

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This is a word problem involving supplementary angles. To solve it, we need to follow these steps:

Identify the given information and the unknown quantity. In this problem, we are given that an angle is 590 less than six times its own supplement. The unknown quantity is the measure of the angle.

Write an equation that relates the given information and the unknown quantity. We can use the fact that supplementary angles are two angles with a sum of 180°1. Let x be the measure of the angle. Then its supplement is 180 - x. The equation is:

x=6(180−x)−590

Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:

xx7xxx​=6(180−x)−590=1080−6x−590=490=7490​=70​

Therefore, the measure of the angle is 70°.

The relative frequency of customers ordering five hot dogs is 7%, option B is correct.

To find the relative frequency of customers ordering five hot dogs, we need to divide the frequency of customers who ordered five hot dogs by the total number of customers.

The total number of customers is the sum of the frequencies in the table:

Total frequency = 90 + 45 + 18 + 18 + 14 + 13 = 198

The frequency of customers ordering five hot dogs is 14, so the relative frequency is:

Relative frequency of customers ordering five hot dogs = (frequency of customers ordering five hot dogs) / (total frequency) = 14 / 198 = 0.0707

To express this as a percentage, we can multiply by 100:

Relative frequency of customers ordering five hot dogs = 0.0707 * 100% = 7.07%

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Answer: 5

Step-by-step explanation:

They are the points

Answer:

x = 23°

Step-by-step explanation:

We Know

The 67° angle + the x must be equal to 90°

Find the x.

Let's solve

67° + x = 90°

x = 23°

Answer:

To solve for z in terms of x and y using the given equations:

x + y = z ........(1)

y - z = x ........(2)

From equation (2), we get:

y - x = z (by adding z on both sides)

Substituting this value of z in equation (1), we get:

x + y = y - x

2x = 0

x = 0

Substituting x = 0 in equation (2), we get:

y - z = 0

y = z

Therefore, the solution is:

z = y

We cannot determine a specific value of z without knowing the values of x and y.

The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

To obtain measures of spread, we can use the dot plot to visualize the frequency of each observation in the data-set, and then calculate the interquartile range (IQR).

For a group of 15 students, we can find the quartiles as follows:

The first quartile (Q1) is the median of the first half of the data-set, which consists of the first seven students.

Looking at the dot plot, the fourth dot represents the median of the first half. For Bus 14, Q1 = 12. For Bus 18, Q1 = 9.

The third quartile (Q3) is the median of the second half of the data-set, which consists of the last seven students. Looking at the dot plot, the eleventh dot represents the median of the second half. For Bus 14, Q3 = 18.

For Bus 18, Q3 = 16.

We can then calculate the IQR as the difference between Q3 and Q1:

For Bus 14, IQR = Q3 - Q1 = 18 - 12 = 6.

For Bus 18, IQR = Q3 - Q1 = 16 - 9 = 7.

Based on the IQR values, we can conclude that Bus 14 is more consistent than Bus 18, as it has a lower IQR.

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The team made approximately 773 runs in the match.

Let's start by setting up an equation to represent the information given in the problem.

Let's call the total runs made by the team "T".

37% of T = 286

To solve for T, we can start by converting the percentage to a decimal:

37% = 0.37

0.37T = 286

Now we can solve for T by dividing both sides of the equation by 0.37:

T = 286 ÷ 0.37

T ≈ 773.0

Therefore, the team made approximately 773 runs in the match.

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The rise and run of the line is shown in the image below, where: slope of the line (m) = -3/4.

The slope refers to how steep a line is. To find the slope of a line on coordinate plane, find the rise and the run of the line, then find their ratio.

Slope of a line (m) = change in y / change in x = rise / run

The red line in the image below represents the rise of the line while the blue line represents the run of the line.

The rise = 3 units

The run = 4 units

Therefore, we have:

Slope (m) = rise/run = -3 units / 4 units

Slope (m) = -3/4.

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the value of 4% as a fraction is 1/25

4/100 is the fraction, but when 4 is divided into 100, it gives you 1/25 in simplest form.

Keyboards A and B are significantly different from one another

The F ratio has been found to be 4.30, equating to the MS between treatments divided by MS error resulting in a value of 2082/484. In order to seek out the critical value for F at an alpha level of 0.05 within degrees of freedom between treatments (2) and degrees of freedom error (3), we must consult the F-table, revealing it to be 5.14.

We reach the conclusion that rejecting the null hypothesis would not prove necessary as there appears to be no great significance when it comes down to the number of errors made with the three concerned keyboards.

Tukey's HSD signifies 2.0, indicating any distinction of means exceeding such scores is considered noteworthy. Calculating pairwise comparisons can enlighten us as to which keyboards are significant from one another:

Comparing Keyboard A versus Keyboard B: The difference was calculated using |25-6| / ✓(484/6*(1/6+1/6)) = 3.03, determining its significance surpassing Tukey's HSD (2.0).

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Answer:

Step-by-step explanation:

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