which number is bigger and why? (7/9 and 5/8) [word problem in attachment]
The player who has the better record between Jamal and Brian as required in the task content is; Jamal.
Which player has the better record of Jamal and Brian?It follows from the task content that the player who has the better record between Jamal and Brian is to be determined.
Since it is given that Jamal and Brian 7/9 and 5/8 of their free throws respectively;
It follows that when expressed as a percentage; we have;
For Jamal;
7 / 9 × 100% = 77.78%
For Brian;
5 / 8 × 100% = 62.5%.
Ultimately, the player who has the better record for free throws is; Jamal since he has a greater percentage success rate for free throws.
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What value of C will make the following system a dependent system (one in which the lines coincides)15x +20y= -106x + 8y= c
ANSWER
C = -4
EXPLANATION
Given:
15x +20y= -10
6x + 8y= c
Thus we have:
a1 = 15x, b1 = 20y, c1 = -10
and
a2 = 6x, b2 = 8y, c2 = c
The condition now is:
\(\frac{a_1}{a_2}\text{ = }\frac{b_1}{b_2}\text{ = }\frac{c_1}{c_2}\)i.e:
\(\frac{15x}{6x}=\frac{20y}{8y}\text{ = }\frac{-10}{c}\)Determine c using the x
\(\begin{gathered} \frac{15x}{6x}=\frac{-10}{c} \\ \frac{5}{2}\text{ = }\frac{-10}{c} \\ 5c\text{ = -20} \\ c\text{ = -}\frac{20}{5} \\ c\text{ = -4} \end{gathered}\)Determine c using the y
\(\begin{gathered} \frac{20y}{8y}\text{ = }\frac{-10}{c} \\ \frac{10}{4}\text{ = }\frac{-10}{c} \\ 10c\text{ = -40} \\ c\text{ = }\frac{-40}{10} \\ c\text{ = -4} \end{gathered}\)Hence, the value of C that will make the systems a dependent system is -4.
A probability model consists of the sample space and the way to assign probabilities.
A probability model consists of the sample space and the way to assign probabilities. The sample space is the collection of all possible outcomes of a random experiment. It can be finite, countably infinite, or uncountably infinite.
A probability model is a way of assigning probabilities to events in the sample space.The probability of an event is a measure of the likelihood that the event will occur. The probability of an event is always between 0 and 1, inclusive. A probability of 0 means that the event will never occur, while a probability of 1 means that the event is certain to occur. If an event has a probability of 0.5, then it is just as likely to occur as not to occur.The probability of an event can be calculated using different methods, depending on the type of experiment. For example, if the experiment is a coin toss, then the probability of getting heads is 0.5, and the probability of getting tails is also 0.5. If the experiment is rolling a six-sided die, then the probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on.In summary, a probability model consists of the sample space and the way to assign probabilities. It is a mathematical framework used to quantify uncertainty in various fields such as statistics, physics, economics, and engineering. The probability of an event is a measure of the likelihood that the event will occur and is always between 0 and 1, inclusive.
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Which of the following is an improper integral?
A) the integral from 0 to 3 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
B) the integral from 1 to 3 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
C) the integral from negative 1 to 0 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
D) None of these
Answer:
A) \(\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx\)
General Formulas and Concepts:
Calculus
Discontinuities
Removable (Hole) Jump Infinite (Asymptote)Integration
IntegralsDefinite IntegralsIntegration Constant CImproper IntegralsStep-by-step explanation:
Let's define our answer choices:
A) \(\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx\)
B) \(\displaystyle \int\limits^3_1 {\frac{x + 1}{3x - 2}} \, dx\)
C) \(\displaystyle \int\limits^0_{-1} {\frac{x + 1}{3x - 2}} \, dx\)
D) None of these
We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.
Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.
∴ our answer is A.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Verify that the given values of x solve the corresponding polynomial equations: a) 6x^2−x^3=12+5x;x=4 b) 9x2−4x=2x3+15;x=3
a) \(6x^2−x^3=12+5x;x=4\) For verifying that the given values of x solve the corresponding polynomial equations, we have to substitute the given values of x in the equation. x = 3 does not solve the equation.Hence, both the given values of x do not solve the corresponding polynomial equations.
If we get true equations, it means the given values of x solve the corresponding polynomial equations. Now, we will put the value of x in the equationa)\(6x^2−x^3=12+5xPut x = 46(4)^2 - (4)^3 = 12 + 5(4)64 - 64 ≠ 32\)
Thus, x = 4 does not solve the equationb)
\(9x^2 − 4x = 2x^3 + 15; x = 3Put x = 39(3)^2 - 4(3) = 2(3)^3 + 153(27) - 12 ≠ 45\)
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Solve the system of linear equations using the substitution method.
X = 5 and 2x + y = 10
A. (5, -5)
B. (5, 0)
C. (2, -2)
D. (2, -1)
Answer:
B
Explanation:
x = 5
2x + y = 10
Substitute x = 5 into 2x + y = 10
2(5) + y = 10
10 + y = 10
y = 0
Hence, coordinates are (5,0).
What is |3456|? Absolute Value
Answer:
It’s just 3456.
Step-by-step explanation:
Absolute value is the positive version of whatever digit you have. So if there is a positive, it would remain a positive, If it were a negative, it would be a negative
Answer:
Step-by-step explanation:
It is 3456.
The absolute value is positive 3456.
If it was |-3456| it would still be positive.
Company g also sells fat quarters. the mean and standard deviation of the number of defects on a fat quarter that can be sold by company g are 0.40 and 0.66, respectively. the fat quarters sell for $5.00 each, but are discounted by $1.50 for each defect found.
(c) what are the mean and standard deviation of the selling price for the fat quarters sold by company g?
The mean and standard deviation of the probability distribution is:
Y will be 0.4899 and 0.699 respectively.
What is Probability Distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.
According to the given question,
From the given probability distribution, it should be noted that the probability distribution for y will be:
Y 0 1. 2
Probability 0.63. 0.25. 0.12
The mean of Y will be:
Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)
Mean = 0 + 0.25 + 0.25
Mean = 0.49
The variance will be 0.4899.
Therefore, the standard deviation will be:
standard deviation = ✓0.4899
Standard Deviation = 0.699.
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Look at this chart. a bar chart titled percentage of americans over age 65 shows years on the x axis and percentage on the y axis from 0 to 25. 1950, 8. 1970, 10. 1990, 12. 2020, 16. 2040, 20. 2060, 27. based on this chart, why is the social security administration facing a funding problem? life expectancy is increasing slower than expected, so people are not living as long as thought. younger people are no longer paying as many retirement taxes as in past generations. the number of elderly americans is growing quickly, so more money is going out than coming in. an unequal amount of taxes is being allocated to medicare and medicaid services.
The bar chart reveals that the funding issue faced is because: C. the number of elderly Americans is growing quickly, so more money is going out than coming in
What is a Bar Chart?In a bar chart, frequency of a data point is represented by the bars or bins.
In the bar chart described, it shows that the percentage of elderly Americans is increasing from 8% in 1950, to 27% in 2060. This implies that more money would be needed to cater for the growing dependents population of which elderly people make up the percentage of dependents.
Therefore, the funding issue faced is because: C. the number of elderly Americans is growing quickly, so more money is going out than coming in.
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Answer: C
Source? Trust me bro
A dog is chained to a pole. If the dog can run within an area of 380 ft.², how long is the chain?
ty if you could help :)
Answer:
The chain is around 11 feet in length.
Step-by-step explanation:
Area of a circle = π × r²
380 ft² = π × r²
121 ft² = r²
11 ft = r
Find the difference ("subtract") between (x+7) & (3x+4)
After subtraction (3x+4) - (x+7), the resultant answer is 2x-3.
What is subtraction?One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.
Removal of items from a collection is represented by the operation of subtraction.
For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.
So, we have:
(x+7) and (3x+4)
We have to subtract as:
(3x+4) - (x+7)
Now, subtract as follows:
(3x+4) - (x+7)
3x+4 - x-7
2x-3
Therefore, after subtraction (3x+4) - (x+7), the resultant answer is 2x-3.
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a report states that 38% of home owners had a vegetable garden. how large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4% with 95% confidence?
The required sample size is 566
What is Confidence interval?In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.
Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. The confidence interval is used to find lower and upper values of unknown population parameter and is given by:
n = (Z² × p × (1-p)) / E²
Z=1.96 from standard normal distribution table
n = (1.96² × 0.38 × (1-0.38)) / 0.04²
n = 566
The required sample size is 566
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PLZ HELP ME PLZZZZZZZZZZZZZZZZZZZZZZ
Answer and Step-by-step explanation:
Ok, so all we have to do is input the values into the equation.
We are told Adam bought 2 mechanical pencils and 8 spiral notebooks, which cost $13
and that
Kia bought 3 mechanical pencils and 5 spiral notebooks, which cost $12.50.
Adam: 2p + 8n = 13
Kia: 3p + 5n = 12.5
This is the answer.
#teamtrees #WAP (Water And Plant)
Answer: Adam: 2p + 8n = 13
Kia: 3p + 5n = 12.5
Step-by-step explanation:
Help please (Image attached)
The value of the infinite series as n tends to 0 is: 0
How to estimate infinite series?Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.
From the infinite series, we want to find the value of the series as n tends to 0.
We are given the series as:
x/2ˣ
At x = 0, we have:
0/2⁰ = 0/1 = 0
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Which shows the solution to the equation x² = 121? Select all that apply.
A. 11
B. 12
C. -11
D. -12
x+5y=-5 find x and y intercept
Answer:
x= (5,0) y= (0,1)
Step-by-step explanation:
sherry had $125.05 in her checking account She made deposit of $28.35 and $78.88 how much money was in sherry account after the deposit
Answer:
$17.82
Step-by-step explanation:
\(125.05 - 28.35 = 96.7 \\ 96.7 - 78.88 = 17.82\)
Answer: $232.48
Step-by-step explanation: an equation you could use would be:
125.25+(28.35+78.88)
Add parentheses: 28.35+78.88= 107.23
Add the rest: 125.25+107.23= 232.48
combine like terms (6n+7y)+(5+6n)+(-3y-3)
Answer:
12n + 4y + 2
Step-by-step explanation:
6n+6n
7y-3y
5-3
apologies if this is incorrect :)
What is the radius of a circle that has a circumference of 3.14 meters
Step-by-step explanation:
radius of circle = 1/2 meter
Answer:
the answer is 0.5meters
7h-15h+40 = -72
What do I do after this to get a complete answer
Answer:
Let me finish it :
7h - 15h + 40 = -72
(7h - 15h) + 40 = -72
-8h + 40 = -72
-8h = -72 - 40
-8h = -112
h = 8
So the value of h is 8
━━━━━━━━━━━━━━━━━
Hope it helps!
Hey there!
7h - 15h + 40 = -72
COMBINE the LIKE TERMS
-8h + 40 = -72
SUBTRACT 40 to BOTH SIDES
-8h + 40 - 40 = -72 - 40
CANCEL out: 40 - 40 because it gives you 0
KEEP: -72 - 40 because it helps solve for the h-value
NEW EQUATION: -8h = -72 - 40
SIMPLIFY IT!
-8h = -112
DIVIDE -8 to BOTH SIDES
-8h/-8 = -112/-8
CANCEL out: -8/-8 because it gives you 1
KEEP: -112/-8 because it helps solve for the h-value (it gives you the result of it!)
NEW EQUATION: h = -112/-8
SIMPLIFY IT!
h = 14
Therefore, your answer is: h = 14
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
The table shows values for functions f(x) and g(x) . x f(x) g(x) 1 14 14 3 −2 −4 5 5 −3 7 9 7 9 6 6 11 11 −3 What are the known solutions to f(x)=g(x) ? Select each correct answer. Responses 1 1 5 5 7 7 9 9 11 11
After observing the table of the given five functions, we know that the solution would be when f(x) = g(x) at x =1.
What are functions?A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable).
In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The polynomial function of degree zero is a constant function.
Linear Function: The first-degree polynomial function.
Quadratic Function: The degree of two polynomial functions.
Cubic Function: The degree of three polynomial functions.
So, the table is shown:
x f(x) =4x+1 g(x) = 3ˣ⁺¹ ⁻ ⁴
-3 -11 -35/9
-2 -7 -11/3
-1 -3 -3
0 1 -1
1 5 5
2 9 23
3 13 77
We must resolve the equation f(x) = g. (x)
We must determine the value of x such that f(x) = g. (x).
You can see from the provided table that when x = 1
f(x) =5, g(x) = 5
Therefore, after observing the table of the given five functions, we know that the solution would be when f(x) = g(x) at x =1.
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Correct question:
The table shows values for functions f(x) and g(x)
x f(x)=4x+1 g(x)=3x+1−4
−3 −11 −359
−2 −7 −113
−1 −3 −3
0 1 −1
1 5 5
2 9 23
3 13 77
What is the solution to f(x)=g(x) ?
Select each correct answer.
−3
−2
−1
0
1
2
3
8.1 Tangent Lines find the side of of triangle KLJ
Answer:
x=12
Step-by-step explanation:
tangent forms 90° with the touch point at circle
(x+8)^2 = 256+x^2
x^2 + 16x + 64 = 256 + x^2
16x = 192
x= 12
really confused on
this one :(
Answer:
C/Point B is between points A and C
Step-by-step explanation:
When graphed, the lines are parellel.
you devise an experiment to measure the temperature of some water in a cup. you measure the temperature using an extremely precise thermometer precisely 5 times, and it appears to be a little different in a random way each time. you decide to use a mean value as a best estimate. how would you determine the uncertainty?
To determine the uncertainty associated with the mean temperature estimate based on the five measurements, you can calculate the standard deviation of the data. The standard deviation measures the average amount of variation or spread in the temperature measurements.
Here's how you can calculate the uncertainty:
1. Take the five temperature measurements and calculate their mean (average) temperature.
2. Calculate the difference between each measurement and the mean temperature.
3. Square each difference obtained in step 2 to eliminate negative values.
4. Calculate the average of the squared differences obtained in step 3. This is called the variance.
5. Take the square root of the variance calculated in step 4. This is the standard deviation.
The standard deviation provides a measure of the uncertainty associated with the mean temperature estimate. It indicates how much the individual measurements deviate from the mean, giving you an idea of the variability in the data.
It's important to note that this method assumes the temperature measurements follow a normal distribution and that the measurements are independent and unbiased. If there are concerns about the assumptions or if the data doesn't meet these criteria, alternative statistical techniques may be needed to estimate the uncertainty.
Solve the equation to find the value of x. log2(5x-4)=4
The given equation is
\(\log _2(5x-4)=4\)To solve for x, the logarithm to indices relationship will be applied
That is
\(\begin{gathered} \log _ab=x \\ \Rightarrow b=a^x \end{gathered}\)Hence
\(\begin{gathered} \log _2(5x-4)=4 \\ \Rightarrow5x-4=2^4 \end{gathered}\)This is simplified to get
\(\begin{gathered} 5x-4=16 \\ 5x=16+4 \\ 5x=20 \\ x=\frac{20}{5} \\ x=4 \end{gathered}\)Therefore, the value of x = 4
The ratio of boys to girls in the show are 11 to 17. If there are a total of 132 boys, what is the total of students in the show?
Answer:
216 studentsStep-by-step explanation:
The ratio of boys to girls:
b/g = 11/7If there are a total of 132 boys, then number of girls is:
132/g = 11/7g = 132*7/11g = 84Total number of students:
b + g = 132 + 84 = 216Which is defined using the undefined terms point and line?
A) angle
B) circle
C) parallel lines
D) ray
Answer:
i would say circle cause there no evan lines angles or points in it
Step-by-step explanation:
The object which is defined using undefined terms of points and lines is option D)
D) Ray
Reason for electing the above option is as follows;
Undefined terms are terms that are not required to be given formal definition in them selves and they include the terms set, plane, line, and point
A point is a dimensionless marker of position and it is indicated in geometry by a capital letter. In geometry, a point is the most elementary entity
A line is an infinitely long and straight geometric object that is defined and named by any two points located on it
A ray is a subset of a line that extends long straight infinitely in one direction, and has a starting point
Therefore, the geometrical object defined by a point and a line is a ray and the correct option is option D)
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A normal thyroid will take up about 12% of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount
It would take approximately 48.12 days for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount.
To determine the time it takes for the radioactive iodide taken up by the thyroid to decay to 0.01% of the original amount, we can use the concept of radioactive decay and the half-life of iodine-131.
Half-life of iodine-131: 8.02 days
Fraction of iodide taken up by a normal thyroid: 12%
Fraction remaining after decay: 0.01% (or 0.0001) of the original amount
Let's assume we start with 100 units of radioactive iodide taken up by the thyroid. After the first half-life (8.02 days), half of the iodide will decay, so we'll have 50 units remaining. Since a normal thyroid takes up 12%, we multiply the remaining units by 0.12 to find the amount taken up: 50 units × 0.12 = 6 units.
Now, we have 6 units remaining in the thyroid, and we'll repeat the process for subsequent half-lives until we reach 0.01% of the original amount.
1st half-life: 50 units remaining (0.12 taken up)
2nd half-life: 25 units remaining (0.12 taken up)
3rd half-life: 12.5 units remaining (0.12 taken up)
4th half-life: 6.25 units remaining (0.12 taken up)
5th half-life: 3.125 units remaining (0.12 taken up)
6th half-life: 1.5625 units remaining (0.12 taken up)
After 6 half-lives, the remaining iodide in the thyroid is approximately 1.5625 units, which is 0.015625% of the original amount (100 units).
To calculate the time it takes for the radioactive iodide taken up by the thyroid to decay to 0.01% of the original amount, we need to multiply the half-life by the number of half-lives
Time = Half-life × Number of half-lives
= 8.02 days × 6
= 48.12 days
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-- The given question is incomplete, the complete question is
"Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of NaI, in which only a small fraction of the iodide is radioactive. (c) A normal thyroid will take up about 12% of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount?" --
Billy likes to go cycling.
His bike has wheels of diameter 80 cm.
He has a counter on his bike which
counts the number of revolutions
the wheels make.
One day the counter shows 350 revolutions.
How far has Billy cycled?
Give your answer to the nearest metre.
Answer:
560 metres
Step-by-step explanation:
80 cm in metres is 0.8 metres.
After 1 revolution any point on the wheel will be back to the original position before moving. 0.8 times 2, which gives us 1.6 metres. In 1 revolution the bike travels 1.6 metres.
Now 1.6 metres times 350 gives us 560.
So the answer is 560 metres.
A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
Answer: 5 cents
Step-by-step explanation:
Let's assume the ball costs "x" dollars.
According to the problem, the bat costs a dollar more than the ball, which means the bat costs "x+1" dollars.
Together, the bat and ball cost $1.10.
So, we can add the cost of the ball and bat:
x + (x+1) = 1.10
Combining like terms, we get:
2x + 1 = 1.10
Subtracting 1 from both sides:
2x = 0.10
Dividing both sides by 2:
x = 0.05
Therefore, the ball costs 5 cents.