a) is linearly dependent and set b) is linearly independent.
By inspection, we can determine whether the given sets are linearly dependent by looking at the relationship between the vectors in each set. If one vector can be written as a linear combination of the other vectors in the set, then the set is linearly dependent.
For set a) \( \left\{\left[\begin{array}{l}1 \\ 3\end{array}\right],\left[\begin{array}{l}2 \\ 6\end{array}\right]\right\} \), we can see that the second vector is simply 2 times the first vector. This means that the second vector can be written as a linear combination of the first vector, and therefore the set is linearly dependent.
For set b) \( \left\{\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right],\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right],\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]\right\} \), we can see that none of the vectors can be written as a linear combination of the other vectors in the set. This means that the set is linearly independent.
Therefore, by inspection, we can determine that set a) is linearly dependent and set b) is linearly independent.
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b. Use the factors to write an expression for the height and width in terms of the length.
If the length of the rectangle is represented by x, then the height and width can be represented by the factors a and b, respectively. Therefore, the expression for the height and width in terms of the length can be written as:
Height = a * x
Width = b * x
These expressions can be used to find the height and width of the rectangle if the length and the factors are known.
For example, if the length is 10 and the factors are 2 and 3, then the height would be 2 * 10 = 20 and the width would be 3 * 10 = 30.
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A golf course charges a cart fee of $5 for members and $10 for nonmembers. Last Sunday, the number of members with carts was at least twice the number of nonmembers. The golf course had collected at most $300 in cart fees.
If x is the number of members and y is number of nonmembers. Using the inequalities below, tell which graph represents the possible solution for the number of each kind of golfer?
Plot the coordinates on the graph to obtain the graph of the system of inequalities.
What is graphing method to solve the equation?As Math World correctly notes, to solve a system of linear equations by graphing, we simply graph both equations in the same coordinate plane and locate the intersection of the two lines.
The visual technique actually just requires three easy actions to complete: Slope-Intercept Form should be applied to both equations.
Each linear equation's graph should be shown in the same coordinate plane. Identify the system's solution.
If the lines cross, the system's solution may be found by using the coordinates of the crossing point. The problem cannot be solved if the lines are parallel.
Let us suppose number of members =x.
Let us suppose the number of non members = y.
The system of equation for the following situation is:
5x + 10y ≤ 300
x ≥ 2y
Substitute different values of x to obtain different values of y.
Plot the coordinates on the graph to obtain the graph of the system of equations.
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The enrollment at high school R has been increasing by 15 students per year.Currently High School R has 200 students attending.High school T currently has 400 students,but it’s enrollment is decreasing in size by average of 10 students per year. If the two schools continue their current enrollment trends over the next few years, how many years will it take the schools to have the same enrollment.
So it will take 20 years for High School R and High School T to have the same enrollment.
What is enrollment?Enrollment is the process of registering for classes at a college or university. The process usually involves submitting an application and providing transcripts and other documents to the school.
The enrollment at High School R is increasing by 15 students per year while High School T is decreasing by 10 students per year. To figure out how many years it will take for both schools to have the same enrollment, we need to calculate the difference between the two schools.
High School R currently has 200 students and High School T has 400 students. The difference between the two schools is 200 students (400-200 = 200).
Since High School R is increasing by 15 students per year and High School T is decreasing by 10 students per year, it will take 20 years for the two schools to have the same enrollment.
To calculate this, we divide the difference between the two schools (200 students) by the difference between the two schools' enrollment growth (15 students - 10 students = 5 students). This gives us 200/5 = 40. Since 40 years is too long, we divide 40 by 2 and get 20, which is the answer. So it will take 20 years for High School R and High School T to have the same enrollment.
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Rafael is in charge of planning a reception for 3200 people. He is trying to decide which snacks to buy. He has asked a random sample of
people who are coming to the reception what their favorite snack is. Here are the results.
Favorite
Snack
Brownies
Pretzels
Potato chips
Other
Based on the above sample, predict the number of the people at the reception whose favorite snack will be brownies. Round your answer to
the nearest whole number. Do not round any intermediate calculations.
Number of
People
27
19
74
60
Answer:
To predict the number of people whose favorite snack is brownies, we need to use the proportion of people in the sample who said brownies were their favorite and apply it to the total number of people attending the reception.
The total number of people in the sample is:
27 + 19 + 74 + 60 = 180
The proportion of people in the sample who said brownies were their favorite is:
27/180 = 0.15
To predict the number of people at the reception whose favorite snack will be brownies, we can multiply the total number of people attending the reception by the proportion of people in the sample who said brownies were their favorite:
3200 x 0.15 = 480
Therefore, we can predict that approximately 480 people at the reception will have brownies as their favorite snack.
If Tamara has 70 dollars, she buys a dress for 10$, A drink for 4.99, a snack for 4 dollars, and a necklace for 20$, how much does she have left?
Answer:
Tamara has $31.01 left
Step-by-step explanation:
Tamara has $70
Dress - $10
Drink - $4.99
Necklace - $20
Snack - $4
Add all of these costs up then subtract them by 70
10 + 4.99 + 20 + 4 = 38.99
70 - 38.99 = 31.01
[tex]70 - (10+4.99+4+20) = 70 - 38.99 = \$ \ 31.01[/tex]
A 6 th degree polynomial with a root of multiplicity 4 at x=3, and a root of multiplicity 2 at x=-1, can be written as the function y=(x-3)^(a)(x-b)^(c) where:
The answer of function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].
A 6th degree polynomial with a root of multiplicity 4 at x=3, and a root of multiplicity 2 at x=-1, can be written as the function[tex]y=(x-3)^4(x+1)^2[/tex].
This is because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times, and the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.
Therefore, the values of a, b, and c in the function y=(x-3)^(a)(x-b)^(c) are:
a = 4, because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times.
b = -1, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.
c = 2, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.
So, the function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].
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Suppose you are testing the following claim: "More than 47% of car crashes occur within 2 miles of the motorists home." Express the null and alternative hypotheses in symbolic form for a hypothesis test (enter as a percentage).
H0:pH0:p (Enter percentages, not decimals. Example 99%, not 0.99)
Ha:pHa:p (Enter percentages, not decimals. Example 99%, not 0.99)
Use the following codes to enter the following symbols:
≥≥ enter >=
>> enter >
≤≤ enter <=
<< enter <
≠≠ enter !=
The null hypothesis (H0) is the hypothesis that is assumed to be true until there is evidence to suggest otherwise. In this case, the null hypothesis is that the percentage of car crashes that occur within 2 miles of the motorist's home is less than or equal to 47%. The alternative hypothesis (Ha) is the hypothesis that is being tested and is the opposite of the null hypothesis. In this case, the alternative hypothesis is that the percentage of car crashes that occur within 2 miles of the motorist's home is greater than 47%.
To express the null and alternative hypotheses in symbolic form, we can use the following symbols:
H0: p <= 47% (The percentage of car crashes that occur within 2 miles of the motorist's home is less than or equal to 47%)
Ha: p > 47% (The percentage of car crashes that occur within 2 miles of the motorist's home is greater than 47%)
Note that we are using the symbol <= for less than or equal to, and > for greater than. These symbols are used in hypothesis testing to express the null and alternative hypotheses in symbolic form.
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A student solved the equation x²+ 5x -60 = 5x +4. The student's work is shown below.
Determine if the student made an error. If so, explain their error AND solve for the correct solutions.
Answer:
x = -8, 8
Step-by-step explanation:
The student did make an error. When factoring [tex]x^2-64[/tex], they used incorrect factors. Using FOIL method, the students factored equation would become [tex]x^2 +32x-32x-1024 = x^2-1024[/tex], which is not [tex]x^2-64[/tex].
Instead, the factors 8 and -8 should be used.
[tex]x^{2} +5x-60=5x+4\\x^2 +5x - 64=5x\\x^2-64=0\\(x+8)(x-8)=0\\x=-8, 8[/tex]
Answer: x = ±8
Step-by-step explanation:
The given equation is:
x² + 5x - 60 = 5x + 4
The student's work shows that they simplified the equation correctly to:
x² - 64 = 0
However, their factorization of the resulting equation is incorrect. Factoring x² - 64 using difference of squares we get:
(x + 8)(x - 8) = 0
So, the solutions for x are x = -8 and x = 8. The student's solutions of x = ±32 are incorrect.
Therefore, the student made an error in factoring the equation, and the correct solutions for x are x = -8 and x = 8.
A person starts walking from home and walks:
5 miles East
4 miles Southeast
6 miles South
3 miles Southwest
4 miles East
Round your answers to 2 decimal places.
This person has walked a total of _____ miles.
Find the total displacement vector for this walk:
If this person walked straight home, they'd have to walk _____ miles.
This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.
To find the total displacement vector for this walk, we can use the Pythagorean Theorem to find the magnitude of the displacement vector and the direction of the displacement vector.
First, let's find the magnitude of the displacement vector:
d = √((Δx)² + (Δy)²)
Where Δx is the change in the x-direction and Δy is the change in the y-direction.
Δx = 5 + 4cos(45°) + 0 + 3cos(225°) + 4 = 9.83 miles
Δy = 0 + 4sin(45°) + 6 + 3sin(225°) + 0 = 2.17 miles
d = √((9.83)² + (2.17)²) = √(96.58 + 4.71) = √(101.29) = 10.06 miles
So, the magnitude of the displacement vector is 10.06 miles.
Next, let's find the direction of the displacement vector:
θ = tan⁻¹(Δy/Δx) = tan⁻¹(2.17/9.83) = 12.58°
So, the direction of the displacement vector is 12.58°.
Therefore, the total displacement vector for this walk is 10.06 miles at an angle of 12.58°.
If this person walked straight home, they'd have to walk 10.06 miles.
This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.
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I need help on number 14 please please
Answer:
A. 5 cm
Step-by-step explanation:
AB = BC
x + 3 = 3x - 1
x - 3x = -1 - 3
-2x = -4
x = -4/-2
x = 2
BC = 3x - 1 = 3(2) - 1 = 6 - 1 = 5
A small plane lands at a point 331 miles east and 86 miles north of the point at which it took off. Find the distance the plane flew and the direction. Distance
=∣
miles Direction
=
degrees North of East Question Help:
□
Message instructor
The direction the plane flew is 14.6 degrees North of East.
So, the final answer is:
Distance = 342 miles
Direction = 14.6 degrees North of East
The distance the plane flew can be found using the Pythagorean Theorem, which states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c^2 = a^2 + b^2. In this case, the distance east (331 miles) is one side of the triangle and the distance north (86 miles) is the other side.
So, we can plug in the values and solve for c:
c^2 = 331^2 + 86^2
c^2 = 109561 + 7396
c^2 = 116957
c = √116957
c = 342 miles
Therefore, the distance the plane flew is 342 miles.
To find the direction, we can use trigonometry. The direction is the angle between the east-west line and the line connecting the starting point and the landing point. We can use the tangent function to find this angle:
tan θ = opposite/adjacent
tan θ = 86/331
θ = tan^-1(86/331)
θ = 14.6 degrees
Therefore, the direction the plane flew is 14.6 degrees North of East.
So, the final answer is:
Distance = 342 miles
Direction = 14.6 degrees North of East
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Let A and B be events with P(A)=0.6, P(B)=0.4, and P(B|A)=0.4. Find P(A and B)
The probability of A and B, using conditional probability, is given as follows:
0.24 = 24%.
How to obtain the conditional probability?The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which the probabilities are listed and explained as follows:
P(B|A) is the probability of the event B happening, given that the event A happened.[tex]P(A \cap B)[/tex] is the probability of both the events A and B happening.P(A) is the probability of the event A happening.To obtain the probability of A and B, the needed parameters are already given in the problem, and are as follows:
P(B|A) = 0.4.P(A) = 0.6.Hence the probability of A and B is calculated as follows:
P(A and B) = P(A) x P(B|A)
P(A and B) = 0.6 x 0.4
P(A and B) = 0.24.
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write an equivalent expression to 8k - (5 + 2k) without parentheses
Answer:
8k - (5 + 2k) can be simplified by distributing the negative sign to the terms inside the parentheses:
8k - 5 - 2k
Then, we can combine like terms by adding the constants -5 and 8k:
6k - 5
Therefore, an equivalent expression to 8k - (5 + 2k) without parentheses is 6k - 5.
Help with this question
What is the volume for the prism? 4 m 1.5 m 2 m
Answer: 12 [tex]m^{3}[/tex]
Step-by-step explanation:
Volume = length x width x height
Volume = 4 m x 1.5 m x 2 m
Volume = 12 cubic meters
Solve and show your solution on the grid: 2 /3 × 3 /5
The product of 2/3 and 3/5 is 2/5
Solving fractions on the grid:To represent a fraction on a grid, we need to divide the grid into equal parts based on the denominator of the fraction, and then shade in a number of those parts based on the numerator of the fraction.
Here we have
=> 2/3 × 3/5
To solve 2/3 × 3/5, we multiply the numerators together and the denominators together
=> [ 2/3 × 3/5 ] = 6/15
=> [ 2/3 × 3/5 ] = 2/5
This multiplication can be represented as given in the picture
Therefore,
The product of 2/3 and 3/5 is 2/5
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Use the table below to calculate the average percent change in population in California from 2000-2009.
If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
Answer:
Step-by-step explanation: your hot
Describe the graph of y = 1/2 x − 10 − 3 compared to the graph of y = 1 x .
The graph of y = [1/2(x -10)] - 3, compared to the graph of 1/x, represents these following transformations:
Horizontal compression by a scale factor of 2.Translation right 10 units.Translation down 3 units.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The translations for this problem are given as follows:
x -> x - 10: shift right 10 units.y -> y - 3: shift down 3 units.Additionally, there was a multiplication by 2 in the domain, meaning that the parent function was horizontally compressed by a factor of 2.
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HELP LpEASE 25 POINTS
Area of circle A is 113.04 in²
Area of circle B is 200.96 in²
Area of circle C is 452.16 in²
Area of circle B is 254.34 in²
The number of times that the area of Circle D greater than Circle A is 2.25
What are the areas of the circles?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 3.14
R = radius
here, we have,
Area of circle A = 3.14 x 6² = 113.04 in²
Area of circle B = 3.14 x (6 + 2)² = 200.96 in²
Area of circle C = 3.14 x (8 + 4)² = 452.16 in²
Area of circle B = 3.14 x (12 - 3)² = 254.34 in²
Number of time that is the area of Circle D greater than Circle A = 254.34 in² / 113.04 in² = 2.25
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Complete question:
The radius of Circle A is 6 in. The radius of Circle B is 2 in. greater than the radius of Circle A. The radius of Circle C is 4 in. greater than the radius of Circle B. The radius of Circle D is 3 in. less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
Prove the following statement. Your work should be legible, and all of your logic should be clear and justified. Sin^4 (A) – cos^4 (A) = 1 - 2 cos^2 (A)
we have proven the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) using the identity sin^2(A) + cos^2(A) = 1 and basic algebraic manipulation. Our work is legible, and our logic is clear and justified.
To prove the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A), we can use the following steps:
Step 1: Use the identity sin^2(A) + cos^2(A) = 1 to express sin^4(A) in terms of cos^4(A).
sin^4(A) = (1 - cos^2(A))^2
Step 2: Expand the expression on the right hand side.
sin^4(A) = 1 - 2cos^2(A) + cos^4(A)
Step 3: Rearrange the terms to get the expression on the left hand side.
sin^4(A) - cos^4(A) = 1 - 2cos^2(A)
Step 4: Verify that the expression on the left hand side is equal to the expression on the right hand side.
1 - 2cos^2(A) = 1 - 2cos^2(A)
Therefore, the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) is proven to be true.
In conclusion, we have proven the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) using the identity sin^2(A) + cos^2(A) = 1 and basic algebraic manipulation. Our work is legible, and our logic is clear and justified.
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DETAILS PREVIOUS ANSWERS LARCOLALG 10 2.1.047. Find the slope -intercept form of the equation of the line that has the given slope m and passes through the given point. m=-(1)/(6),(8,0)
The slope-intercept form of the equation of the line that has a slope of -1/6 and passes through the point (8,0) is y = -1/6x + 4/3.
To find the slope-intercept form of the equation of the line that has the given slope m and passes through the given point, we can use the point-slope form of a linear equation and then rearrange it to the slope-intercept form.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
Where m is the slope and (x₁, y₁) is the point that the line passes through.
In this case, m = -1/6 and the point is (8, 0).
Plugging these values into the point-slope form, we get:
y - 0 = -1/6(x - 8)
Simplifying and rearranging to the slope-intercept form, we get:
y = -1/6x + 8/6
y = -1/6x + 4/3
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I need help on number 14 please please
Given - two tangent lines are drawn from the point B
To find - the value of BC
Explanation - when tangent lines are drawn for outside of the circle then the length of line formed is equal
We get
AB=BC
[tex]x+3 =3x-1\\x-3x=-1-3\\-2x=-4\\x=2[/tex]
BC= [tex]3x-1 =3(2)-1=6-1=5[/tex]
The length of BC = 5
Final answer - The option A is correct, the length is 5
You poured five bowls of cereal to find out the number of fruit flavored pieces you get in a bowl. The fruit flavored pieces numbered 3,23,20,23, and 21.
The average number of fruit flavored pieces you get in a bowl is 18.
Find the number of fruitTo find the number of fruit flavored pieces you get in a bowl, you can calculate the average of the fruit flavored pieces in the five bowls you poured.
Here's how:
1: Add the number of fruit flavored pieces in each bowl: 3 + 23 + 20 + 23 + 21 = 90
2: Divide the total number of fruit flavored pieces by the number of bowls: 90 / 5 = 18
Therefore, the average number of fruit flavored pieces you get in a bowl is 18.
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Dakota is able to drive his car 32.5 miles per gallon of gasoline. Write and solve an inequality that could be used to determine the minimum number of gallons of gasoline Dakota would need to drive 117 miles to his brother's house. Then interpret the solution. Explain your reasoning. Input Field 1 of 1 Skip to input field.
Answer:
Step-by-step explanation: first if you do x/32.5 ≤ 117 = 3802.5 and also we know that 1 mile= 32.5, so if you take 32.5 * 117 it also equals 3802.5
so it will take him a minimum of 3802.5 gallons to drive 117 miles
Dakota would need at least 3.6 gallons of gasoline to drive 117 miles to his brother's house.
What is the inequality?A statement that compares two numbers or expressions using an inequality symbol, such as (less than), > (greater than), (less than or equal to), or, is known as an inequality in mathematics (greater than or equal to).
Let x be the volume of gasoline required for Dakota to travel 117 miles to his brother's home. The minimum value of x can be calculated using the inequality shown below:
x ≥ 117 / 32.5
Here, we calculate the bare minimum amount of gasoline Dakota would require to travel 117 miles by dividing the whole distance (117 miles) by the miles per gallon (32.5 miles/gallon).
The inequality is reduced to: x ≥ 3.6
Dakota would therefore require 3.6 gallons of fuel to travel 117 miles to his brother's house.
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I NEED TO FINISH THIS TEST I HAVE ONLY 3 MINUTES LEFT!!
What is this number in standard form?
(8×10) + (2×1/100) +( 9×1/1,000)
heres the answer:
8x10=80
2x1=2/100= 0.02
9x1=9/1000= 0.002
0.002+0.02+80=
80.002!!
Write the vector in the form \( \langle a, b\rangle \). The vector is (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
The vector in the form \( \langle a, b\rangle \) is simply the given vector with the values of a and b identified and simplified as necessary.
To write the vector in the form \( \langle a, b\rangle \), we need to identify the values of a and b from the given vector. The value of a corresponds to the x-component of the vector, and the value of b corresponds to the y-component of the vector.
If the given vector is \( \langle 3, -4\rangle \), then the value of a is 3 and the value of b is -4.
If the given vector is \( \langle \frac{5}{2}, \sqrt{3}\rangle \), then the value of a is \(\frac{5}{2}\) and the value of b is \(\sqrt{3}\).
If the given vector is \( \langle -2\sqrt{2}, 7\sqrt{3}\rangle \), then the value of a is \(-2\sqrt{2}\) and the value of b is \(7\sqrt{3}\).
In all of these cases, the values of a and b are either integers or fractions, and any radicals are simplified as much as possible.
So, the vector in the form \( \langle a, b\rangle \) is simply the given vector with the values of a and b identified and simplified as necessary.
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What you guys are doing is not fair. Give. Me answer
Answer: stop being a brat
Step-by-step explanation:
An online keyboarding course collects data comparing each students age to their typing speed. The equation of the line of best fit representing this data is y=-1.4x+117.8 , where x is the age (years) and y is the typing speed (words per minute). What is the expected typing speed of a student who is 17 years old?
Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.
What does speed feel like?It functions by dividing distance by speed. The time can also be calculated by dividing the distance traveled by the speed. You can determine the third input if you know the first two. For instance, we may get the speed as 120 x 2 = 60 miles per hour if a car travels 120 miles in two hours.
The equation of the line of best fit is:
y = -1.4x + 117.8
where x is the age in years and y is the typing speed in words per minute. To find the expected typing speed of a 17-year-old student, we can substitute x = 17 into the equation:
y = -1.4(17) + 117.8
y = -23.8 + 117.8
y = 94
Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.
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Tres situaciones en las que se hace necesario el uso de números negativos
Answer:
Aquí hay tres situaciones en las que se hace necesario el uso de números negativos:
Temperaturas: Las temperaturas pueden ser positivas o negativas, dependiendo de si estamos midiendo la temperatura por encima o por debajo del punto de congelación del agua. Por ejemplo, si la temperatura es de -10°C, significa que hace 10 grados bajo cero.
Deudas: Cuando una persona toma un préstamo o usa una tarjeta de crédito, puede acumular una deuda que debe ser pagada en el futuro. Esta deuda se representa con un número negativo, ya que representa el dinero que se debe.
Altitud: Cuando se mide la altitud de un lugar, puede ser por encima o por debajo del nivel del mar. Si la altitud es por debajo del nivel del mar, se representa con un número negativo. Por ejemplo, la altitud del Mar Muerto es de aproximadamente -430 metros.
A solid with the volume 100 cubic units is is dilated by a scale factor of k find the image for each given value of k
To find the image for each given value of k, we need to multiply the original volume (100 cubic units) by the scale factor (k).
What is volume?Volume is a measure of the amount of space occupied by an object or substance. It is expressed as a numerical value, usually in cubic units, such as milliliters (mL) or cubic centimeters (cc). It is also used to measure the capacity of a container, such as a bottle, or a tank.
Dilation is a transformation that changes the size of a shape. When a solid is dilated by a scale factor of k, the new solid will be k times larger than the original solid. For example, if a solid has a volume of 100 cubic units and is dilated by a scale factor of 2, the image solid will have a volume of 200 cubic units (2 x 100).
To find the image for each given value of k, we need to multiply the original volume of the solid (100 cubic units) by the scale factor (k). We can use the equation V = kV0, where V0 is the original volume and V is the new volume, to calculate the new volume of the solid.
For example, if k = 3, the new volume will be 3 x 100 = 300 cubic units. If k = 4, the new volume will be 4 x 100 = 400 cubic units. In general, for any given value of k, the new volume will be k times the original volume.
To summarize, when a solid with a volume of 100 cubic units is dilated by a scale factor of k, the image solid will have a volume of k times the original volume (V = kV0). Therefore, to find the image for each given value of k, we need to multiply the original volume (100 cubic units) by the scale factor (k).
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