a) The table of the discrete function is given as follows:
Basketballs - Spending
0 - $0
1 - $15
2 - $30
3 - $45
4 - $60
5 - $75
6 - $90
7 - $105.
b) With the spending of $105, the number of basketballs purchased was of 7.
What are discrete and continuous functions?Discrete and continuous functions depends on the values assumed by the input values of the function, as follows:
Discrete functions: assumes integer values.Continuous functions: assumes real values.In this problem, we have that the number of basketballs purchased is a countable amount, assuming only integers, hence it is a discrete function.
The proportional relationship means that each basketball costs $15, and hence the table is constructed considering it.
Hence the number of basketballs purchased with a cost of $105 is given as follows:
105/15 = 7 basketballs.
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Solve for p: 3+ 10p - 8p = 17
Joseph bought a brand new car 6 years ago for $22,250. The table below shows v(n), the value of the car t years since it was purchased
What is the correlation coefficient between 1 and v(n), and what does the coefficient indicate?
The correlation coefficient is -0.955 and indicates a very weak linear association
The correlation coefficient is -0.913 and indicates a very weak linear association
The correlation coefficient is -0.913 and indicates a strong negative linear association
The correlation coefficient is -0.955 and indicates a strong negative linear association
F.
G
H.
J
t
0
1
2
3
4
5
6
v(t) $22,250 $16.200 $11.700 $8,100 $6,300 $4.950 $3.825
5
Answer:
Step-by-step explanation:
The correlation coefficient between 1 and v(n) is -0.913, and this coefficient indicates a strong negative linear association. The correlation coefficient is a measure of the strength and direction of the relationship between two variables. In this case, the correlation coefficient is -0.913, which indicates a strong negative relationship between 1 and v(n). This means that as the value of 1 increases, the value of v(n) decreases, and vice versa. This relationship is linear, which means that it can be described by a straight line. Overall, the correlation coefficient indicates a strong negative linear association between 1 and v(n).
What percent is equal to the part-to-whole ratio 9:80?
1. In linear equation with two variables "ax + by = c", a and b cannot be equal to
(a) One
(b) Zero
(c) Integer
(d) Rational number
In linear equation with two variables "ax + by = c", a and b cannot be equal to Zero. which is the correct answer would be an option (A).
In a linear equation with two variables "ax + by = c", a and b can be any real numbers, including zero and integers. They can also be irrational numbers or rational numbers.
There is no restriction on the values of a and b in this equation.
As per the question, the following are all valid linear equations :
x + 0y = 2 ⇒ x = 2
0x + y = 1 ⇒ y = 1
Here above linear equations having only one variable so a and b cannot be equal to zero.
Thus, in a two-variable linear equation, a and b cannot be equal to zero.
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Carlos graphed the system of equations that can be used to solve x cubed minus 2 x squared 5 x minus 6 = negative 4 x squared 14 x 12. On a coordinate plane, 2 functions are shown. The functions intersect at (negative 3, negative 66), (negative 2, negative 32), and (3, 18) What are the roots of the polynomial equation? –3, –2, 3 –3, 2 18, 32 18, 32, 66
Answer: A
Step-by-step explanation: the other guy is wrong
s i have 24 vanilla wafer cookies to put in a bag how many bags can i fill if i put the same number in each
She can put it into 2, 4, and 8 bags such that wafer cookies will same number in each bag.
What is a number system?A way to express or represent numbers is through the number system.
The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.
We often employ decimal numbers because they are so widely used.
The base of the decimal number system, which uses ten digits from 0 to 9, is 10.
A system of writing numbers is known as a number system. It is a mathematical notation that uses digits or other symbols to consistently express the numbers in a given set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
Given,
Number of wafer cookies = 64
To put into 2 bags = 64/2 = 32 in each bag.
To put into 4 bags = 64/4 = 16 in each bag.
To put into 8bags = 64/8 = 8 in each bag.
The complete question is : Lindy has 64 vanilla wafer cookies to put in bags. How many bags can she fill if she puts the same number in each bag and uses them all? Find all the possibilities. Explain your reasoning.
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Rewrite the given equation in logarithmic form. Then, select all of the equations with an equivalent solution. 8e^x-5=0
The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:
x = ln(5/8).
How to define the logarithmic form of the exponential equation?The exponential function in this problem is defined as follows:
8e^x-5 = 0.
The equation can be sorted isolating the exponential as follows:
8e^x = 5.
e^x = 5/8.
The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:
ln(e^x) = ln(5/8).
As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:
ln(e^x) = x.
Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:
x = ln(5/8).
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{ ( 2 , 3 ) , ( − 2 , 5 ) , ( 4 , 4 ) , ( − 4 , 5 ) , ( x , y ) }
Answer:
Its gotta be (6, 5)
Step-by-step explanation:
If we look at the sequence, the x coordinates are 2, -2, 4, -4. In the first & third x coordinates, there is an increment of 2 i. e. first 2 and then 2+2=4 so the fifth x coordinate should be 4+2=6.
The y coordinates are 3, 5, 4, 5. In the first and third y coordinates, there is an increment of 1 i. e. first 3 and then 3+1=4 so the fifth y coordinate should be 4+1=5.
The sequence goes like this
(2, 3), (-2, 5), (4, 4), (-4, 5), (6, 5), (-6, 5), (8, 6), (-8, 5), and so on
Percents, decimals, and fractions
Answer:
1.) 0.25
2.) 0.50
3.) 0.125
4.) 2.25
Step-by-step explanation:
When turning percentages into decimals, you move the decimal point two places to the left.
EX:
25%
25.0 (move the decimal point two places to the left)
2.5
.25
0.25 (add any zeros if necessary)
Hope this helps!!
Tip:It doesn't matter where the decimal point is in a percentage, as long as you move the point two places to the left, you are still turning it into a decimal.
Min Kurata deposited $875 for 3 months at 4% and made no other deposits or withdrawals. How much simple interest did his money earn? What is the amount in the account?
Hello,
I hope you and your family are doing well!
To find the amount of simple interest earned by Min Kurata's money, we can use the formula:
I = P * r * t
Where I is the amount of interest earned, P is the principal (the initial amount deposited), r is the annual interest rate, and t is the time in years.
In this case, the principal is $875, the annual interest rate is 4%, and the time is 3 months. Since the time is given in months, we need to convert it to years by dividing it by the number of months in a year (12):
t = 3 months / 12 months/year = 0.25 years
Plugging these values into the formula gives:
I = $875 * 0.04 * 0.25 = $35
So Min Kurata's money earned $35 in simple interest.
To find the total amount in the account, we can add the amount of interest to the principal:
total amount = $875 + $35 = $910
So the total amount in the account after 3 months is $910.
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y is directly proportional to the cube of x. If y = 20 when x is 3 find y when x is 5
The solution is y = 2500/27
The value of y is 2500/27 when x = 5
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the proportionality constant be represented as = k
Now , the value of k is calculated by
y is directly proportional to the cube of x
Substituting the values in the equation , we get
y ∝ x³
On simplifying the equation , we get
y = kx³ where k is the proportionality constant
Now ,
when x = 3 , y = 20
Substituting the values in the equation , we get
20 = k ( 3 )³
20 = k x 27
Divide both sides by 27 , we get
k = 20/27
So , the proportionality constant k = 20/27
Now , when x = 5 ,
y = 20/27 ( 5 )³
y = ( 20 x 5 x 5 x 5 ) / 27
y = 2500/27
Therefore , the value of y is 2500/27
Hence ,
The value of y is 2500/27 and the proportionality constant is 20/27
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Prove that tanx sinx + cosx = secx
The proof that tan(x) sin(x) + cos(x) = sec(x) is represented by the trigonometric equation sec(x) = sec(x)
How to prove the trigonometric equationFrom the question, we have the following parameters that can be used in our computation:
tan(x) sin(x) + cos(x) = sec(x)
Express tan(x) as sin(x)/cos(x)
So, we have the following representation
sin(x)/cos(x) * sin(x) + cos(x) = sec(x)
Evaluate the products
So, we have the following representation
sin²(x)/cos(x) + cos(x) = sec(x)
Take the LCM
[sin²(x) + cos²(x)]/cos(x) = sec(x)
Express sin²(x) + cos²(x) as 1
So, we have
1/cos(x) = sec(x)
Evaluate
sec(x) = sec(x)
Hence, the equation has been proved
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Write the equation for a line parallel to y=-x + 7 that
passes through (7,-2).
Pls help!! Asap
Answer:
the slope is same, so y=-x+5 (x=7, y=-2 insert)
What are the significant digits?
2.6 × 10'-15'
( -15 is an exponent btw)
Therefore, the number of significant figures is 4.
What are Significant Figures?Significant figures are the digits of a number that are meaningful in terms of accuracy or precision. These digits indicate the precision of a calculation or measurement.
What are Significant Figures Rules?Non-zero digits are always significant.Zeros between non-zero digits are always significant.Leading zeros are never significant.if we have trailing zeros then they are only significant if the number contains a decimal point.Given:
exponential notification is,
2.6 ×[tex]10^{-15}[/tex]
=365500
(real number)
= 3.655 × [tex]10^{5}[/tex]
(scientific notation)
= 3.655e5
(scientific exponential notation)
Therefore, the number of significant figures is 4.
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a 52-foot ladder is leaning against a vertical wall. if the bottom of the ladder is being pulled away from the wall at the rate of 8 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall?
The rate of change of the area of the triangle, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall is 26 square feet per second.
Let's call the distance between the bottom of the ladder and the wall x. We can express the area of the triangle in terms of x as follows:
Area = (1/2) * 52 * x
The area of the triangle is changing at a rate of 8 square feet per second as x changes at a rate of 8 feet per second. We can find the rate of change of the area with respect to x by taking the derivative of the area expression with respect to x:
d(Area)/dx = (1/2) * 52 = 26
Therefore, the rate of change of the area of the triangle, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall is 26 square feet per second.
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if lin and diego want to run a race where they will both finish when the timer hits 30 seconds exactly but diego runs 5.5 meters per 1 second and lin runs 4 meters per 1 second how long of a head start should lin get?
Lin needs a 45-meter head start as Lin will travel 120 meters in 30 seconds, and Diego will travel 165 meters in 30 seconds.
Time = 30 sec
Lin's speed = 4m/s
Diego's speed = 5.5m/s
Distance travelled by ,
Lin = speed * time = 4 * 30
= 120 m
Diego = 5.5 * 30
= 165
Therefore, Diego will travel 45 m more than Lin in 1 sec.
Therefore, the head start should be of 45m.
The most crucial scientific notion is measurement is speed . Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance.
The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
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Roxanne drew an indigo line that was 11 4/5 inches long. Then she drew a white line that was 6 3/5 inches long. How much longer was the indigo line than the white line?
The indigo line is longer than the white line by 5.2 inches.
What is a line?A line is a one-dimensional figure that has length but no width.
The length of the indigo line can be represented as I and the length of the white line as W.
The length of the indigo line is 11 4/5, i.e., I = 11 4/5 = 11.8
The given length of the white line is 6 3/5, i.e. W = 6 3/5= 6.6
The difference in length between the indigo and white lines is given by
I-W = 11.8 - 6.6 = 5.2
Hence, the indigo line is 5.2 inches longer than the white line.
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Which of the following choices is not an example of a unit rate?
earnings per hour dollars per pound calories per serving $25.50 for 5 gallons
Examples of unit rates are Dollars per pound calories and earnings per hour. The rest is not the unit rate.
What is the unit rate?
An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. 70 yards in 10 seconds and 7 yards in 1 second are both ratios, although only the latter is a unit rate.
Earnings per hour are a unit rate since it is calculated for an hour.
Dollars per pound calories is a unit rate.
Serving $25.50 for 5 gallons is not a unit rate, the cost is for 5 gallons. If the cost is for 1 gallon then it will unit rate.
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Please factorize [tex]\ln ^2\left(4-x\right)+\ln \left(4-x\right)\ln \left(x+\frac{1}{2}\right)-2\ln ^2\left(x+\frac{1}{2}\right)=0[/tex]
Answer:
[ln (4 - x) - ln (x + 1/2)] × [ln (4 - x) + 2 ln (x + 1/2)] = 0----------------------------------
Given equation:
ln² (4 - x) + ln (4 - x) ln (x + 1/2) - 2 ln² (x + 1/2) = 0Substitute:
ln (4 - x) = p, ln (x + 1/2) = qThen we have:
p² + pq - 2q² = p² - q² + pq - q² = (p + q)(p - q) + q(p - q) = (p - q)(p + q + q) = 0(p - q)(p + 2q) = 0Substitute back:
ln² (4 - x) + ln (4 - x) ln (x + 1/2) - 2 ln² (x + 1/2) = 0 [ln (4 - x) - ln (x + 1/2)] × [ln (4 - x) + 2 ln (x + 1/2)] = 0Suppose that the function y = f(x) is decreasing on the interval (2,4). What can be said about the graph of y = - f(x)?
Answer:
Good question
yes so the answer will be on your screen in
3
2
1
here it is
Step-by-step explanation:
did u get it
hamid is playing a trivia game with multiple choice questions. each question has 222 correct answers among 555 answer choices. hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random. what is the probability that hamid guesses both answers correctly? round your answer to two decimal places.
10 is the probability that hamid guesses both answers correctly .
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
the likelihood that Hamid will correctly guess both answers
= 2/5x1/4 = X
= 0.4x0.25 = X
= 0.1 = X
= 0.1x 100 = 10
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Which equation is equivalent to 1\5x-3-2\3
The equivalent equation of the equation given as 1/5x - 3 - 2/3 is 1/5x - 11/3
How to determine the equivalent equationFrom the question, we have the following parameters that can be used in our computation:
1\5x-3-2\3
The fractions can be properly expressed as
1/5x - 3 - 2/3
Next, we evaluate the difference between -3 and -2/3
So, we have the following representation
1/5x - 3 - 2/3 = 1/5x - (9 + 2)/3
Evaluate the like terms
So, we have the following representation
1/5x - 3 - 2/3 = 1/5x - (11)/3
Remove the brackets
This gives
1/5x - 3 - 2/3 = 1/5x - 11/3
Hence, the equivalent equation is 1/5x - 11/3
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*NEED HELP ASAP* See screenshot below.
The equation that gives the tree's height at any time in slope-intercept form is y = (9/2)x + 5. Select 2nd option
How to write equation in slope-intercept form the tree's height at any time?
The slope-intercept form equation of a line can be given as y = mx + c
where m is the slope and c is the y-intercept
Let y and x represent the height and time respectively
slope (m) = y2-y1 / x2-x1
where x1 = 2, y1 = 14 and x2 = 4, y2 = 23 (from table)
m = 23-14 / 4-2 = 9/2
y = mx + c
14 = (9/2 )×2 + c
14 = 9 + c
c = 14-9 = 5
put m = 9/2 and c = 5 into y = mx + c. Thus, the equation will be:
y = (9/2)x + 5
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Function h is an input-output machine that uses the rule 9r - 1. Write the machine's
function using function notation.
Function notation form of function h is h(r) = 9r - 1
How to write the machine's function using function notation?Function notation is a way of expressing a mathematical function using a special notation that assigns a specific symbol (called the "function name") to represent the function.
This function name is typically a single letter, such as f, g, or h, and it is followed by a set of parentheses that contain the input value(s) for the function.
Given: Function h is an input-output machine that uses the rule 9r - 1
The function h can be represented using function notation as follows:
h(r) = 9r - 1
This function takes an input value r and applies the rule 9r - 1 to it, producing an output value.
For example, if we input the value 3 into the function, it would produce the output value h(3) = 9×3 - 1 = 26
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The nth term of a sequence is
2n² + 4n 3
Work out the 10th term of the
sequence.
Answer:
The 10th term of this sequence is 243.
Step-by-step explanation:
Given expression: [tex]2n^2 + 4n + 3 = a_n[/tex]
If n is the term number, then substitute 10 for n and compute.
[tex]2n^2 + 4n +3 = a_n[/tex]
[tex]2(10)^2 + 4(10) + 3 = a_{10}[/tex]
[tex]2(100) + 40 + 3 = a_{10}[/tex]
[tex]200 + 40 + 3 = a_{10}[/tex]
[tex]243 = a_{10}[/tex]
∴ The 10th term of the sequence is 243
⭐if this response helped you, please mark it the "brainliest"!⭐
Answer:
243
Step-by-step explanation:
Multiply 3 by 1, 4 by 10 and 2 by 100
2×100 + 4×10 + 3x1= 243
1. $3.96 x 5
2. 0.023 x 40
3. 0.67 x 61
4. $19.99 x 6
5. 0.13 x 57
6. 0.041 x 15
Answer:
1. $19.80
2. 0.92
3. 40.87
4. 119.94
5. 7.41
6. 0.615
Step-by-step explanation:
1. $3.96 x 5 = $19.80
2. 0.023 x 40
⇒ 0.023 x 10 = 0.23
⇒ 0.23 x 4 = 0.92
3. 0.67 x 61
⇒ 0.67 x 1 = 0.67
⇒ 0.67 x 60 = 40.2
⇒ 0.67 + 40.2 = 40.87
4. $19.99 x 6
⇒ 19.99 x 6 = 119.94
5. 0.13 x 57
⇒ 0.13 x 50 = 6.5
⇒ 0.13 x 7 = 0.91
⇒ 6.5 + 0.91 = 7.41
6. 0.041 x 15
⇒ 0.041 x 10 = 0.41
⇒ 0.041 x 5 = 0.205
⇒ 0.41 + 0.205 = 0.615
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Select the correct answer. If ( x + 4 ) is a factor of polynomial p, which statement must be true? A. p ( - 4 ) > 0 B. p ( 4 ) = 0 C. p ( - 4 ) = 0 D.
Only if (C) p(-4) = 0 will x + 4 be the polynomial p's factor.
What are the factors?A factor is a number that completely divides another number.
To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
There is therefore no residual after division.
The numbers you multiply together to obtain another number are called factors.
A factor is therefore another number's divisor.
So, this is only true if, and only if, x + 4 is a factor of the polynomial p.
x + 4 = 0
x = -4
Comply with the polynomial equation that is:
p(-4) = 0
Therefore, only if (C) p(-4) = 0 will x + 4 be the polynomial p's factor.
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Complete question:
If (x + 4) is a factor of polynomial p, which statement must be true?
A.p(4) = 0
B. p(-4) > 0
C. p(-4) = 0
D. p(4) < 0
Alexis is `56` inches tall.
What is her height in centimeters?
the answer is 142.24 cm
Answer:
142.24 centimeters tall
Step-by-step explanation:
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How do news paper work?
Practice identifying solutions to linear equations.
This equation has one solution.
5(x – 1) + 3x = 7(x + 1)
What is the solution?
Answer: x=12
Step-by-step explanation: PEMDAS
first solve the parentheses. that would make the equation 5x-5+3x=7x+7. Since there are no exponents, we don't need to do the e. no multiplication or division. so now we add and subtract to get x. first ill subtract 3x from both sides. 5x-5=4x+7. now subtract 5x from both sides. -5=-x+7. after that, subtract 7 from both sides. -12=-x. then divide by -1 so we can get only x and not a negative x. 12=x. so, the answer is x=12.
