The explicit formula of the arithmetic sequence in this problem is given as follows:
[tex]a_n = 40 - 7n[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The explicit formula of an arithmetic sequence is given as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
From the recursive formula, each term is the previous term subtracted by 7, hence the common difference is given as follows:
d = 7.
The first term of the sequence is given as follows:
[tex]a_1 = 33[/tex]
Hence the explicit formula is obtained as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]a_n = 33 - 7(n - 1)[/tex]
[tex]a_n = 40 - 7n[/tex]
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suppose you take a random sample of size 25 from a population with mean of 120 and a standard deviation of 15. your sample has a mean of 115 and a standard deviation of 13.8. which of the following has a mean of 120 and a standard deviation of 3?
3 has a mean of 120 and a standard deviation of 3.
Describe standard deviation using an example?
The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.
The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.
mean of sample means = true mean = 120
std dev of sample mean = true std / sqrt(n)
= 15/5 = 3
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FILL IN THE BLANK if the dollar price of the euro increases from $1.50 to $2.00, the dollar is _______ and european goods are ____expensive to americans. (5 points)
The dollar is weakening in comparison to the euro, making European goods more expensive for Americans. American consumers must spend more to purchase the same amount of goods from Europe.
When the dollar price of the euro increases from $1.50 to $2.00, it means that the euro has strengthened relative to the dollar. This means that the dollar has weakened in comparison to the euro. This weakened dollar results in American consumers needing to spend more to purchase European goods. As the dollar price of the euro increases, it takes more dollars to purchase the same amount of euros, meaning the same amount of goods from Europe will cost more dollars. This means that European goods become more expensive to Americans as the dollar price of the euro increases. This is a result of the weakened dollar and the strengthened euro in comparison to each other.
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if a to b ratio, b to c ratio, c to d ratio, are given, then express a to d in terms of given ratios
The ratio of a to d can be expressed by multiplying the ratio of a to b, b to c, and c to d. Therefore, a to d = (a to b) x (b to c) x (c to d).
The ratio of a to d can be determined by using the given ratio of a to b, b to c, and c to d. To begin, the ratio of a to b can be expressed as a:b, the ratio of b to c can be expressed as b:c, and the ratio of c to d can be expressed as c:d. Then, the ratio of a to d can be determined by multiplying the ratios of a to b, b to c, and c to d. This can be written as (a:b) x (b:c) x (c:d). Therefore, the ratio of a to d can be expressed as (a:b) x (b:c) x (c:d). For example, if the ratio of a to b is 2:3, the ratio of b to c is 4:5, and the ratio of c to d is 6:7, then the ratio of a to d would be (2:3) x (4:5) x (6:7) or 24:35.
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Calculate the angle EOD in the figure above
2. Calculate the angle DOC In the angle above
Answer:
Step-by-step explanation: Hello!
To find angle EOD, you are already given two angle measurements. The measure of angle AOB is 55 degrees and the measure of angle BOC is 30 degrees. The important thing that you have to remember to solve this problem is that vertical angles are congruent. (I won't be explaining the definition of vertical angles, but you can find a lot of images and explanations online). This means the two angles formed by two lines intersecting each other in any way is always congruent. Angles AOB and EOD are congruent by the definition of vertical angles. This means that the measure of angle EOD is 55 degrees.
Now, you have to find the measurement of angle DOC. By the definition of straight lines, you know that the angles formed by a straight line all add up to 180 degrees. This means that:
EOD + DOC + COB = 180 degrees. You are already given two of these measurements. (Angle EOD which you just figured out and Angle COB which was already given). Fill these numbers in the equation.
55 + DOC + 30 = 180. Combine like terms (55 + 30)
85 + DOC = 180. Then subtract 85 from both sides using the subtraction property of equality.
(85 - 85) + DOC = (180 - 85)
DOC = 95.
The measure of angle DOC = 95.
You can check this by substituting the new measurement for angle DOC back into the equation.
Does 55 + 30 + 95 = 180?
85 + 95 = 180
180 = 180.
The measure of angle DOC is 95 degrees and the measure of angle EOD is 55 degrees.
given a n percent chance of something happening, find the probability of it happening at least n times out of k
P(at least n times) = 1 - (1 - p)^k, where p is the probability of the event happening and k is the number of trials.
The probability of an event happening at least n times out of k trials can be calculated using the formula P(at least n times) = 1 - (1 - p)^k. Here, p is the probability of the event happening, and k is the number of trials. The formula is based on the principle that the probability of an event happening at least n times is equal to one minus the probability of it happening less than n times. The probability of it happening less than n times is calculated by taking the probability of the event happening once, and then multiplying it by itself k times. This is because each trial is independent, and the probability of the event happening for each trial is the same. The result of this multiplication is then subtracted from one, which gives us the probability of it happening at least n times out of k trials
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You have agreed to loan some money to a friend at a simple interest rate of 153% per year. Your friend hasn't taken this class; all they know is that they can pay you back $500 in 2 weeks.
How much money do you give your friend today so that the repayment of $500 in 2 weeks is equivalent to a simple interest loan with a rate of 153% per year? Round your answer to the nearest dollar.
The amount of money gives to my friend today so that the repayment of $500 in 2 weeks is equivalent to a simple interest loan with a rate of 153% per year is, $477.10
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
Given that,
Loan agreed on simple interest rate = 153% per year
He knows that he can pay me back $500 in 2 weeks or 2/52 years
Suppose, money given to him = P
So, simple interest of amount P in 2 weeks
I = P × 125 ×(2/52) /100
= 0.048P
Total repayment = P + 0.048P
He can pay back only $500
Total repayment = $500
P + 0.048P = $500
1.048P = 500
P = 477.10
Hence, the loan amount is $477.10
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Use determinants to decide if the set of vectors is linearly independent. -2 The determinant of the matrix whose columns are the given vectors is (Simplify your answer:) Is the set of vectors linearly independent? A The set of vectors is linearly dependent; because the determinant exists_ 0 B. The set of vectors is linearly independent; because the determinant exists_ O
c: The set of vectors is linearly independent, because the determinant is not zero_ 0
D: The set of vectors is linearly dependent, because the determinant is not Zero.
The determinant of a matrix is a scalar value that can be used to determine if a set of vectors is linearly independent.
It is calculated by taking the product of the elements in each row or column and subtracting the product of the elements in the other row or column. For example, if we have a matrix with two columns and two rows, A and B, the determinant can be calculated using the following formula: det(A) = (A11*A22) - (A12*A21). If the determinant is equal to zero, then the set of vectors is linearly dependent, as this implies that all of the elements in the matrix are multiples of each other. On the other hand, if the determinant is non-zero, then the set of vectors is linearly independent. This can be seen because all of the elements in the matrix are not multiples of each other and thus the set of vectors cannot be expressed as a linear combination of each other.
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for the sequence 11,13,15,_,_,_, find the formula for the nth term
Answer:
aₙ = 9 + 2n
Step-by-step explanation:
Formula for the nth term of an arithmetic sequence, aₙ with a common difference of d and first term of a₁ is
aₙ = a₁ + d(n-1)
The common difference is the difference between two consecutive terms and is a constant
Here d = 13- 11 = 15-13 = 2
First term is 11
nth term:
aₙ = 11 + 2(n-1)
aₙ = 11 + 2n -2
aₙ = 9 + 2n
So if you wanted the 10 term say it would be
a₁₀ = 9 + 2x 10 = 9 + 20 = 29
In a city library, the mean number of pages in a novel is 525 with a standard deviation of 200.
Furthermore, 30% of the novels have fewer than 400 pages. Suppose that you randomly select 50 nov from the library.
What is the probability that at least 20 of the novels have fewer than 400 pages?
The probability that at least 20 of the novels have fewer than 400 pages is 1 - 0.2266 = 0.7734 or 77.34%.
What is the normal distribution and the cumulative distribution?
The normal distribution, also known as the Gaussian distribution or bell curve, is a probability distribution that describes the distribution of a continuous random variable.
The cumulative distribution function (CDF) is a function that gives the probability that a random variable is less than or equal to a certain value
To solve this problem, we can use the normal distribution and the cumulative distribution function (CDF) of a normal distribution. The normal distribution is a probability distribution that describes how many novels have a certain number of pages.
The mean number of pages in a novel is given as 525 and the standard deviation is 200. We know that 30% of the novels have fewer than 400 pages, which corresponds to a z-score of (400 - 525) / 200 = -0.75.
We can use the cumulative distribution function (CDF) to find the probability that at least 20 of the novels have fewer than 400 pages. The CDF of a normal distribution gives the probability that a random variable is less than or equal to a certain value.
The probability that at least 20 of the novels have fewer than 400 pages is the same as the probability that at most 30 of the novels have more than 400 pages. Using a standard normal table or software, we can find the probability that a standard normal random variable is less than -0.75 as P(X< -0.75) = 0.2266, this is the probability that less than 30 novels have more than 400 pages.
Hence, the probability that at least 20 of the novels have fewer than 400 pages is 1 - 0.2266 = 0.7734 or 77.34%.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equations that are equivalent are:
2 + x = 5
x + 1 = 4
-5 + x = -2
How to Determine Equivalent Equations?If any two or more equations are equivalent, they would have the same value when evaluated.
To find which equations are equivalent, solve to find the value of x in each given equation.
A. 2 + x = 5
x = 5 - 2
x = 3
B. x + 1 = 4
x = 4 - 1
x = 3
C. 9 + x = 6
x = 6 - 9
x = -3
D. x + (-4) = 7
x = 7 + 4
x = 11
E. -5 + x = -2
x = -2 + 5
x = 3
The equivalent equations are:
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are y-1/7x-2 & x-7y=4 parallel perpendicular intersecting but not perpendicular
y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.
Two lines are parallel if they have the same slope (or no slope at all), and two lines are perpendicular if the product of their slopes is -1. To determine if lines are parallel or perpendicular, you can find their slopes and check if they are equal or if the product of their slopes is -1.
The first line y-1/7x-2 can be rewritten in slope-intercept form y = mx + b as y = 1/7x + 2
The second line x-7y=4 can be rewritten in slope-intercept form y = mx + b as y = x/7 - 4/7
The slopes of the two lines are 1/7 and -1/7 respectively. The product of the slopes of two lines is 1/49 which is not -1, that means that the two lines are not perpendicular. Also, the slopes are not equal, which means that the lines are not parallel.
Therefore, the two lines y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.
Find the surface area of the solid.
The surface area of the cuboid is 94 m² while The surface area of the triangular pyramid is 259.695 in²
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Surface area is the sum of each area of the solid surface.
7) For the cuboid:
Surface area = 2(3 m * 4 m) + 2(3 m * 5 m) * 2(4 m * 5 m) = 94 m²
The surface area of the cuboid is 94 m²
8) For the triangular pyramid:
Surface area = 3(1/2 * 17.4 in * 8.7 in) + (1/2 * 8.7 in * 7.5 in) = 259.695 in²
The surface area of the triangular pyramid is 259.695 in²
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What type equation is this is it a rational ?
Answer:
A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials, \frac{P(x)}{Q(x)}. Q(x)P(x). These fractions may be on one or both sides of the equation.
if we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the ---select--- point determined by t
If we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the terminal point determined by t.
What is a terminal point?
The ray that has been rotated around the origin to form an angle with the stationary ray that is the initial side of the angle is the ray that has reached its terminal point. The most typical acute-angle measurements are represented by the sine and cosine values.
The coordinates of the terminal point come from the coordinates of the reference point (positive or negative depending on the quadrant.)
We know that a unit circle is the circle of radius 1 which is centered at the origin in the xy-plane.
General equation of a unit circle is: x^2+ y^2 = 1
Starting at the point (1,0),
If t≥0, then, t is the distance along the unit circle in clockwise direction
If t<0, then mod t is the distance along the unit circle in clockwise direction.
Here, role="math" , localid="1648202152711"t is a real number by which a point P(x,y) is generated. This point is known as the terminal point which is determined by the real number t.
Hence, if we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the terminal point determined by t.
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I just need the answer and an explanation as to why it is that answer please and thank you
Triangles that are congruent have the same size and form.Triangle HGK is congruent to triangle KHJ.
What do congruent and similar mean? Triangles that are congruent have the same size and form.Three pairs of matching sides are equivalent in two triangles according to the Side-Side-Side (SSS) Theorem.Side-Angle-Side (SAS) Theorem: Two triangles have two pairs of matching sides and two pairs of corresponding angles that are congruent.The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. Using labels: Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle HG = HK and GK = KJTo learn more about congruent refer to:
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Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle HG = HK and GK = KJ
What do congruent and similar mean?Triangles that are congruent have the same size and form.
Three pairs of matching sides are equivalent in two triangles according to the Side-Side-Side (SSS) Theorem.
Side-Angle-Side (SAS) Theorem: Two triangles have two pairs of matching sides and two pairs of corresponding angles that are congruent.
The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. Using labels:
Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle
HG = HK and GK = KJ
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Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.
log √7=
Log 23/6=
The values would be
log √7= 0.291
log 23/6= 0.585
What is a logarithm?
A logarithm is a mathematical function that calculates the power to which a given number (called the base) must be raised to produce a given value. The most common base used in logarithms is base 10, but logarithms can be defined with any base. If the base of a logarithm is not specified, it is assumed to be base 10. The logarithm of a number is represented by the symbol log.
log √7 = (1/3)log7
Log 23/6 = log(23) - log(6)
The logarithm of a number is the exponent to which the base must be raised to produce that number. If the base of the logarithm is not specified, it is assumed to be base 10.
The square root of 7 is around 2.646, and log2.646 is around 0.874, so
log √7 = (1/3)log7 = (1/3)*0.874 ≈ 0.291
The logarithm of 23 is around 1.363 and the logarithm of 6 is around 0.778, so
Log 23/6 = log(23) - log(6) = 1.363 - 0.778 = 0.585
Hence, the values would be
log √7= 0.291
log 23/6= 0.585
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The number of bacteria in a culture is modeled by
Answer:
Bacteria Growth The number N of bacteria in culture is modeled by N= 250e^kt where t is the time in hours. If N = 280 when t= 10, estimate the time required for the population to double in size.
Step-by-step explanation:
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A bag of Starburst candies can be considered an SRS of the whole population of Starburst candies; Since there are 4 flavors. the probability that each Starburst is cherry flavor IS % 0.25. Each bag of Starburst contains 200 candies Suppose we buy = one bag of Starburst X v the number of cherry Ilavor Starburst candies in the pag 1. Is this binomial distribution? 2. What is n? What is p? 3. What is the mean of X? Interpret: 4. What is the standard deviation of X?_ Interpret 5. What is the probability of getting exactly 60 cherry filavored starburst?
6. What is the probability of getting at most 60 cherry flavored starburst
1. Yes, this is a binomial distribution.
2. n = 200, p = 0.25.
3. The mean of X is 50. This means that we can expect to get 50 cherry flavored Starburst candies on average.
4. The standard deviation of X is 7.07. This means that the number of cherry flavored candies is likely to be close to the mean of 50, but it could vary by up to 7.07 in either direction.
5. The probability of getting exactly 60 cherry flavored Starburst is 0.108.
6. The probability of getting at most 60 cherry flavored Starburst is 0.619.
A bag of Starburst candies can be considered an SRS of the whole population of Starburst candies since there are 4 flavors. The probability that each Starburst is cherry flavor is 0.25. Since we are buying one bag of Starburst, the number of cherry flavored candies in the bag can be represented by a binomial distribution with n = 200 and p = 0.25. This means that the mean of X (the number of cherry flavored candies) is 50. The standard deviation of X is 7.07, which means that the number of cherry flavored candies is likely to be close to the mean of 50, but could vary by up to 7.07 in either direction. The probability of getting exactly 60 cherry flavored Starburst is 0.108, and the probability of getting at most 60 cherry flavored Starburst is 0.619.
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the measure of angle a is 5 times the measure of its supplement. what is the measure of each angle? enter your answers in the boxes.
The measure of an angle which is 5 times its supplement is 150.
Supplementary Angles. When the sum of the measures of two angles is 180 then the angles are called supplementary angles. When two angles are supplementary, each angle is said to be the supplement of the other.
thus, x and y two angle which sum is 180 then x and y supplement to each other.
According to the problem,
The measure of an angle which is 5 times its supplement.
Supplementary angles means , sum of angles is 180.
⟹x=5(180 −x)
⟹x=5×180 −5x
⟹6x=5×180
⟹x=5×30
=150
Hence, x=150
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X=
6±√(-6)²-4(1)(1)
___________
2(1)
The zeroes of the quadratic equation are [tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex] and [tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex] for the given quadratic equation.
What is quadratic equation?A second-degree algebraic equation known as a quadratic equation can be found in mathematics (having one or more variables raised to the second power). Ancient Babylonian cuneiform texts from the time of Hammurabi demonstrate a knowledge of how to solve quadratic equations, but it seems that ancient Egyptian mathematicians were not familiar with this technique.
They have played a significant role in the physics of accelerated motion, such as free fall in a vacuum, ever since Galileo's time. The general quadratic equation in one variable is written as ax2 + bx + c = 0, where a, b, and c are arbitrary constants (or parameters) and an is not equal to 0.
Given to solve the quadratic equation
[tex]{\displaystyle x={\frac {6\pm {\sqrt {(-6)^{2}-4(1)(1)}}}{2(1)}}}[/tex]
[tex]{\displaystyle x={\frac {6\pm {\sqrt {36-4}}}{2}}}[/tex]
[tex]{\displaystyle x={\frac {6\pm {\sqrt {32}}}{2}}}[/tex]
[tex]{\displaystyle x={\frac {6-4{\sqrt {2}}}{2}}}[/tex]
[tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex]
x = 0.171573
[tex]{\displaystyle x={\frac {6+4{\sqrt {2}}}{2}}}[/tex]
[tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex]
x = 5.828427
Thus, the zeroes of the quadratic equation are [tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex] and [tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex] for the given quadratic equation.
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A sociologist develops a test to measure attitudes towards public transportation, and n = 80 randomly selected subjects are given the test. Their mean score is = 84 and their standard deviation is s = 15.4. Find the margin of error E for the 95% confidence interval for the mean score of all such subjects, and round to the nearest tenth.
Answer:
Step-by-step explanation:
t%5Bc%5D=2.055
ME=SE%2At%5Bc%5D
ME=4.118%2A2.055
ME=8.463
.
.
.
(67.7,84.7)
Super is a ride-sharing company. The Chief of Operations wants the revenue (output value) to be seven times the cost of service operations (input cost). Suppose that each regular car earns a value of $1500 per month and premium cars earn $2500 per unit per month. The monthly cost of operating a regular car is $100 per month and $500 per premium car. Super currently has 19 regular cars. How many premium cars do they need to achieve a productivity ratio of 7? (Enter your response rounded to whole number.)
Super would need 2 premium cars to achieve a productivity ratio of 7.
How to find the productivity ratio?Let's call the number of premium cars "x".
The total revenue from the regular cars would be $1500 * 19 = $28,500 per month.
The total revenue from the premium cars would be $2500 * x.
The total cost of the regular cars would be $100 * 19 = $1900 per month.
The total cost of the premium cars would be $500 * x.
The Chief of Operations wants the revenue to be 7 times the cost of service operations, so we can write the following equation:
($28,500 + $2500x) / ($1900 + $500x) = 7
Expanding and simplifying the equation, we get:
$2500x + $28,500 = 7($1900 + $500x)
$2500x + $28,500 = $13,300 + 7$500x
$11,200 = 6$500x
$11,200 / $6,500 = x
x = 1.723
Rounding up, Super would need 2 premium cars to achieve a productivity ratio of 7.
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ivan had scores of 62, 75 and 90 on three of four tests. if his average on all four tests was 80.5, his score on the fourth test was
The score of fourth test is 95
what is mean?The mean, also known as the average or the arithmetic mean, is a measure of central tendency that represents the sum of a set of values divided by the number of values in that set. It is one of the most common ways to summarize a set of data and is often used as a reference point for other measurements such as standard deviation. It is represented by the Greek letter "mu" (µ) for population mean and "x bar" for sample mean.
Given mean of the score is 80.5
mean of score is given as (∑ score) / n
where ∑ score is sum of score of all marks and n is the number of test he had attempted
∑ score = 62 + 75 +90 +x
where x is marks in fourth subject
so ∑ score = mean * 4
=> 227 + x = 80.5 *4
=> x = 322 -227
so x = 95
so the marks of the fourth test is 95.
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The percentage of battery remaining, y, on a tablet's battery after x hours can be represented by the given graph.
coordinate grid with the x axis labeled time in hours and the y axis labeled percent of battery remaining, with a line that passes through the points 0 comma 40 and 4 comma 0
What is the meaning of the y-intercept in the context of the problem?
After 40 hours, the tablet will have 0 percent of battery left.
The tablet will not have any battery remaining after 4 hours.
The tablet starts with 40 percent of battery remaining.
The tablet loses 4 percent of battery every hour.
The meaning of the y-intercept of the linear function is given as follows:
The tablet starts with 40 percent of battery remaining.
How to interpret the y-intercept of a linear function?The two most important features of a linear function are the slope and the intercept, and their meaning is explained as follows:
Slope: rate of change of the output variable relative to the input variable.Intercept: value assumed by the output variable when the input variable assumes a value of zero.When x = 0, y = 40, hence the intercept of this function is of 40, representing the initial value of 40 of the percentage of battery remaining.
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−4≤−2(y−1)<2
Step 2 of 2 : Graph the solution set.
Answer:
draw a line between an empty point at 0 and a filled point at 3
Step-by-step explanation:
To graph this inequality we first want to isolate the y variable to make it a bit easier to deal with. This is a compound inequality and when isolating the y variable instead of just doing an operation on both sides, we do it to all sides which follows the same principle of maintaining equality.
We start with the original inequality:
[tex]-4 \le -2(y-1) < 2[/tex]
From here we divide by -2 on all sides, but since we're dividing by a negative we would flip the way the inequality is pointing so we get:
[tex]2\ge y-1 > -1[/tex]
From here we add 1 to all sides.
[tex]3 \ge y > 0[/tex]
Although generally we would write this as:
[tex]0 < y \le 3[/tex]
Now to graph this we would draw a hole on the number line at the point zero, and a filled point on the number line at 3, since 3 is included (since less than or equal to 3) and then just connect the two points. I'll include an image that demonstrates this.
The length and breadth of a cuboid shaped paper are 1m and 60 cm respectively. If 1920 small cubes of 5 cm each can be placed in the box, find the height of box.
Answer:
h = 40 cm
Step-by-step explanation:
1. Let's calculate the total volume of 1920 cubes, size 5 x 5 x 5 cm:
V one = 5 cm x 5 cm x 5 cm = 125 cm³
V all = 1920 x 125 = 240,000 cm³
2. Divide this volume by the area of the paper to get the height, given that 1 m = 100 cm:
S paper = 100 cm x 60 cm = 6,000 cm²
h = V all / S paper = 240,000 / 6,000 = 40 cm
a norman window has the shape of a rectangle surmounted by a semicircle. (thus the diameter of the semicircle is equal to the width of the rectangle. see exercise 1.1.72.) if the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
The dimensions that maximize the area of the window are:
Width: 8.4 ftHeight: 4.2 ftWhat is diameter of the semicircle?If any of the following values are known, the diameter of a semicircle can be easily determined: Surface, bounds, or circumference. The diameter (d) is equal to ((8A/)) units if A is the semicircle's area. The semicircle's diameter (d) is calculated using the formula 2P/(+2) units if P is its perimeter. The equation (x - h)2 + (y - k)2 = r 2 is often solved for y to get a pair of equations with the form y = r 2 - (x - h)2 + k. A positive square root equation explains the upper semicircle, and a negative square root equation describes the lower semicircle.We have a Norman window, where the rectangle's width and the semicircle's diameter are the same.The rectangle's perimeter is made up of its two heights, one width, and half of its circumference.The perimeter can be expressed as follows if w is the semicircle's diameter (and the rectangle's breadth) and h is the other side of the rectangle:[tex]$P=2 h+w+\frac{\pi \cdot w}{2}=30$[/tex]
[tex]$2 h+(1+0.5 \pi) w=30$[/tex]
[tex]$h=\frac{30-(1+0.5 \pi) w}{2}=15-(0.5+0.25 \pi) w$[/tex]
With the restriction for the perimeter [tex]$(\mathrm{P}=30)$[/tex], we can express h in function of w. Now, we can express the area only in function of w and maximize its value:
[tex]& A=A_c / 2+A_r=\frac{1}{2} \cdot \frac{\pi w^2}{4}+h w=\frac{\pi w^2}{8}+\left[15-\left(\frac{1}{2}+\frac{\pi}{4}\right) w\right] \cdot w \\[/tex]
[tex]& A=15 w-\left(\frac{1}{2}+\frac{\pi}{4}-\frac{\pi}{8}\right) w^2=15 w-\left(\frac{1}{2}+\frac{\pi}{8}\right) w^2[/tex]
To maximize the area, we derive and equal to 0 :
[tex]$\frac{d A}{d w}=15(1)-\left(\frac{1}{2}+\frac{\pi}{8}\right)(2 w)=0$[/tex]
[tex]$$15-(1+\pi / 4) w=0$$[/tex]
[tex]$w=\frac{15}{1+\pi / 4} \approx 8.4$[/tex]
Now, we can calculate the height as:
[tex]$$h=15-(0.5+0.25 \pi) w$$[/tex]
[tex]$$h \approx 15-(1.2854) \cdot 8.4=15-10.8=4.2$$[/tex]
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Answer:
-9,-6,6,12
Step-by-step explanation:
A students tuition was $4263 a loan was obtained for 4/7 of the tution how much was the Loan?
0.125 less than 0.127
Answer: 0.002. 0.127 - 0.125 is 0.002
