The time that runner takes to finish the race is 2.133 minutes.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The speed of the runner is given as 3/8 miles per minute.
The remaining distance to be travelled is 7/8 miles.
Then, the time taken by the runner is the ratio of distance to be travelled to the speed. It can be written as follows,
Time taken by runner = (7/8)/(3/8)
= 7/3
= 2.133
Hence,the time taken by the runner to finish the race is 2.133 minute.
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It is an association between two sets of objects which is paired according to a certain rule. A. Domain B. Range C. Relation D.Function
Relation is an association between two sets of objects which are paired according to certain rule.
As given in the question,
Given statement is:
Association between the two given sets of objects that are paired according to the certain rule.
Explanation of each option for the given statement:
A. Domain : Domain represents all the input values of any relation.
It is not correct option.
B. Range : It represents all the output values of any relation.
It is not correct option.
C. Relation : It represents the association between two sets which are collection of ordered pairs ( x, y ) where each input value is associated with output value.
It is the correct option.
D. Function : It represents each input is uniquely related to output value.
Not a correct option.
Therefore, relation is an association between two sets of paired objects with certain rule.
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pharmacy technicians are concerned about the rising number of fraudulent prescriptions they are seeing. a small pharmacy sees 1,500 new prescriptions a month, 28 of which are fraudulent. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
The mean and standard deviation of sampling distribution are 0.0187 and 0.010 respectively
The mean is a measure of location which tells us the average of observation.
Standard deviation tells us how dispersed a data is or how much variation our data contains.
According to question,
The population size : N = 1500
Number of fraudulent in a month : 28
Population proportion : P = 28/1500
=> P = 0.0187
Sample size: n = 180
Sample proportion : p = 28 / 180
=> p = 0.156
Therefore The mean of sampling distribution for the sample size 28,
μ = P
=> μ = 0.0187
The standard deviation will be
=> σ = [tex]\sqrt{\frac{p(1-p)}{n}}[/tex]
Substituting the value,
=> σ = [tex]\sqrt{\frac{0.0187(1-0.0187)}{180}}[/tex]
=> σ = 0.010
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Help, I don't understand how to do this and it's due tomorrow. (Correct answer shown.)
The minimum value of the function occurs between 4 and 5.
What is a function?A function is a relation where every input is connected to only one possible output from a set of available inputs.
Given the table of values.
Note that the value of the function is a minimum of between 4 and 5.
Hence, the minimum value of the function occurs between 4 and 5.
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Irina predicted that she would sell 75 books, but she actually sold 95 books. Which expression would find the percent error? Use the table below to help answer the question.
Answer:
21%
Step-by-step explanation:
Approximate number = 75
exact number = 95error
approximate number - exact number| ÷ exact number error = |(75-95)| / 95 = |20| / 95 = 0.21percentage of error = 0.21 x 100% = 21%
The answer should be correct! Hope it helps!!! Mark as Brainliest. It would make my day! Thank you :)
What is the surface area of this triangular prism?
5 cm
8 cm
3.5 cm
7.2 cm
Answer:130.09
Step-by-step explanation:
Using the formulas
A=2AB+(a+b+c)h
AB=s(s﹣a)(s﹣b)(s﹣c)
s=a+b+c
2
Solving forA
A=ah+bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=5·7.2+8·7.2+3.5·7.2+1
2·﹣54+2·(5·8)2+2·(5·3.5)2﹣84+2·(8·3.5)2﹣3.54≈130.08536
The values for random variables in a Monte Carlo simulation area. selected manually.b. generated randomly from probability distributions.c. taken from forecasting analysis.d. derived secondarily using formulas.
The values for random variables in a Monte Carlo simulation area that were chosen at random from probability distributions are the right answer.
What is Monte Carlo Simulation ?
The Monte Carlo Method, also referred to as the Monte Carlo Simulation or a multiple probability simulation, is a mathematical method for predicting potential outcomes of an uncertain event. To help people make better decisions when faced with uncertainty, John von Neumann and Stanislaw Ulam developed the Monte Carlo Method during World War II.
Therefore, the values for random variables in a Monte Carlo simulation area that were generated at random from probability distributions are the right answer.
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The correct response is the set of values for random variables in a Monte Carlo simulation region that were randomly selected from probability distributions.
In order to represent uncertainty in a model that represents a real system and computes the values of model outputs, a Monte Carlo technique is used. During World War II, John von Neumann and Stanislaw Ulam created the Monte Carlo Method to aid people in making better judgments when faced with uncertainty.
As a result, the correct response is the random values for random variables that were produced using probability distributions in a Monte Carlo simulation area.
A circle has a circumference of 6. It has an arc of length 1. What is the central angle of the arc, in degrees?
Answer:
60 degrees
Step-by-step explanation:
The arc length is 1/6th of the total ....the angle will be 1/6th of the total 360° of the circle
1/6th X 360 = 60 °
Answer:
60 degrees
Step-by-step explanation:
1.) Figure out which portion of the circle that the arc is. Since the total circumference is 6, and the arc is 1, that means that the arc is 1/6 of the circle.
2.) Now, figure out the measure of the angle. Since the total angle measure in a circle is 360 degrees, we multiply 1/6*360 to figure out the measure. This is equal to 60 degrees.
Solve for x. Round to the nearest tenth of a degree, if necessary.
Check the picture below.
[tex]tan(x)=\cfrac{\stackrel{opposite}{50}}{\underset{adjacent}{42}}\implies tan(x)=\cfrac{25}{21}\implies x=tan^{-1}\left( \cfrac{25}{21} \right)\implies x\approx 50^o[/tex]
Make sure your calculator is in Degree mode.
The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had 76 passengers - 12 in first class and 64 in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class. We can use a simulation to see if this result is likely to happen by chance. How would you use random digits to imitate one repetition of the process? What variable would you measure?
We will use certain constraints to imitate the repetition of the process as mentioned below
To simulate one repetition of the procedure using random digits, we shall perform as follows:
from a line of the random digits table, ten one and two-digit numbers could be selected with the following conditions;
1. skipping repeated numbers
2. skipping numbers from 77 to 99
here the numbers 01 to 12 i.e. first-class passengers in the group of selected random numbers are to be counted.
As we know, numbers represent first-class passengers while numbers to represent coach-class people.
Hence, using this we can use random digits
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A landscape artist plans to draw a pair of mountains, so he takes some measurements and draws the figure below. (Note: the peaks are NOT right angles, and sides of the mountains are parallel). Find the measurement of x, y, and z. Explain your reasoning and show your work.
The angle measures in this problem are given as follows:
x = 88º. y = 55º.z = 37º.How to obtain the angle measures?The sides of the mountains are parallel, which means that the angles of these sides have the same measures, as follows:
y = 55º, as the measure on the first mountain is parallel to the measure of 55º in the second mountain.z = 37º, as the measure of 37º on the first mountain is parallel to the measure of z on the second mountain.Then the measure of x is obtained considering that angles x, y and z form a ray, that is, the sum of their measures is of 180º, hence:
x + y + z = 180
x + 55 + 37 = 180
x = 180 - (55 + 37)
x = 88º.
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he points (12,10) and (30,25) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
The slope of the two points passing through points (12,10) and (30,25) will be 5 / 6.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. the slope is defined as the ratio of the rise to the run.
Given that points (12,10) and (30,25) form a proportional relationship.
The slope of the line passing through the two points will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 25-10 ) / ( 30-12 )
Slope = 15 / 18
Slope = 5 / 6
Therefore, the slope of the two points passing through points (12,10) and (30,25) will be 5 / 6.
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The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph of the function.
Initially, as xxx increases, yyy
.
The slope of the graph is equal to
for all xxx between x=0x=0x, equals, 0 and x=3x=3x, equals, 3.
Starting at x=3x=3x, equals, 3, the function value yyy
as xxx increases.
The slope of the graph is equal to
for xxx between x=3x=3x, equals, 3 and x=5x=5x, equals, 5.
For xxx between x=0x=0x, equals, 0 and x=4x=4x, equals, 4, the function value yyy
000.
For xxx between x=4x=4x, equals, 4 and x=8x=8x, equals, 8, the function value yyy
000.
if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?
At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, the value of a margin of error of x is 1.534%.
In the given question, at a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, then we have to explain how should we interpret that.
The given confidence interval = 95%.
We can write it as CI = 0.95.
An approval rating is 55%.
We can write it as(p) = 0.55
A margin of error is x.
Let the value of sample size n = 1000.
So the margin of error;
ME = z× {p(1-p)}/√n
The value of z for confidence interval of 95% is 1.96.
Now putting the value
x = 1.96× {0.55(1-0.55)}/√1000
x = 1.96× {0.55×0.45}/31.623
x = 1.96× 0.2475/31.623
x = 1.96×0.00783
x = 0.01534
x = 1.534%
So the margin of error should be 1.534%.
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The right question is:
At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?
A study was conducted to compare the proportion of drivers in boston and new york who wore seat belts while driving. Data were collected, and the proportion wearing seat belts in boston was 0. 581 and the proportion wearing seat belts in new york was 0. 832.
z = -2.51 is the required test statistic.
What is the test statistic?A statistic employed in statistical hypothesis testing is known as a test statistic.
A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.
The probability value, or p-value, indicates the likelihood that your data could have been true under the null hypothesis.
This is accomplished by estimating the probability of your test statistic, which is the figure obtained from a statistical analysis of your data.
So, we have to use: Ha: pB < pNY
This implies that the alternative thesis is revised as follows:
Ha: pB - pNY < 0
In contrast to the null hypothesis:
H₀: pB - pNY = 0
This is the test statistic:
z = X - μ/a
Now, pB = 0.581, pNY = 0.832.
It follows that: X = 0.581 - 0.832 = -0.251
The test for the null hypothesis is 0.
This follows to: μ = 0
Standard deviation: 0.1
This follows to: s = 0.1
Test statistic:
z = X - μ/a
z = -0.251-0/0.1
z = -2.51
Therefore, z = -2.51 is the required test statistic.
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Complete question:
A study was conducted to compare the proportion of drivers in Boston and New York who wore seat belts while driving. Data were collected, and the proportion wearing seat belts in Boston was 0.581 and the proportion wearing seat belts in New York was 0.832. Due to local laws at the time the study was conducted, it was suspected that a smaller proportion of drivers wear seat belts in Boston than New York.
Find the test statistic for this test using Ha: pB < pNY. (Use standard error = 0.1.)
Find the Laplace transform F(s) = L{f(t)} of the function f(t) = sin^2 (wt), defined on the interval t >= 0. F(s) = L {sin^2 (wt)} = For what values of S does the Laplace transform exist
The laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].
Given,
[tex]f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}[/tex]
applying laplace transform on both sides,
[tex]L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex]
The range for values of s for which F(s) exists is when F(s)≥0
[tex]\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0[/tex]
using formula to find roots,
[tex]s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi[/tex]
Thus, the laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].
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A strand of hair grows at a constant rate of 1/2 inch per month. A different strand of hair grows at a constant rate of 4 inches per year.
Find out if this is or isn't a proportional relationship ?
I WILL GIVE BRAINLIEST
Answer:This is not a proportional relationship.
Step-by-step explanation:
Please help need this done asap
2. 2x-7=3 Addition Property
3. 2x=10 Division Property
4. x = 5
Answer:
I hope I helped
I have not been taught on this topic yet but I manage to answer the question if the answer is wrong it isn't my fault I haven't been taught yet.
I wish you a happy day
Step-by-step explanation:
1.)4x – 7 = 2x + 3
4x – 2x – 7 = 2x – 2x + 3 (subtraction property)
2x – 7 = 3
2x – 7 +7 = 3 + 7(addition property)
2x = 10(division property)
x = 5(reflexive property)
help me please/............................................ . . . . . . . . . . . .
The value of x=11 and the value of an angle ∠RDB=45°.
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Angle can also refer to the measurement of an angle or a rotation. This measurement is the ratio of the length of a circular arc to its radius.
By using the secant-secant theorem,
(13x+7-60)/2=5x-10
13x-53=10x-20
3x-53=-20
3x=33
x=11
m ∠RDB=5(11)-10
=45°
Hence, the value of x=11 and the value of an angle ∠RDB=45°.
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How can you balance the equation
Ba(C2O4) + K(IO3) → Ba(IO3)2 + K2(C2O4)
the big numbers in the parenthesis are supposed to be subscripts. Also the compound IO3 is supposed to be Iodine and oxygen separate I think.
The balanced equation is Ba(C₂O₄) + 2K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄).
What is an equation?An equation is a combination of different variables, in which two expressions are equal to each other.
The given equation is,
Ba(C₂O₄) + K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄)
Since, there are 2 atom of potassium on right side and also (IO₃) is two times.
To balance the equation, Coefficient of K(IO₃) should be 2.
The equation can be represented as,
Ba(C₂O₄) + 2K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄)
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PLEASE HELP ASAPPP. WILL GIVE BRAINLIEST AND 5.0 STAR RATING.
Answer:
$21.6
Step-by-step explanation:
[tex]720*\frac{3}{100} =720*0.03=21.6[/tex]
If 6a = 5b, what are the following ratios?
2a:7b
Answer:
If 6a = 5b then the ratio of 2a : 7b is 5 : 21
Explanation:
Given that 6a = 5b
We have to find the ratio of 2a : 7b
Let us first solve the given expression and find values of a and b
6a = 5b
So we have found that a = 5 and b = 6
Finding ratio of 2a : 7b
2a : 7b = 2(5) : 7(6)
2a : 7b = 10 : 42
On simplifying to lowest terms,
2a : 7b = 5 : 21
Thus the ratio of 2a : 7b is 5 : 21
My question is below!
Answer:
Below
Step-by-step explanation:
s = small box number volume = 6s
L = large box number volume = 15L
6s + 15 L =243
AND s = L +2
An investigator wants to estimate caffeine consumption in high school students. How many students would be required to estimate the proportion of students who consume coffee? Suppose we want the estimate to be within 5% of the true proportion with 95% confidence.
Alpha = _____
Z = _____
p = _____
Effect Size = _____
n = _____
The value of alpha is 0.025. The Z-value is 1.96. The P(z) is 0.5. The effect size is 0.05. The Sample size for the study is 384.
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.
Here,
All the calculations attached in image.
z= 1.96
p = 0.5
q = 1-p = 0.5
E = 0.05
sample size =
(z^2).(pq)=(1.96^2).(0.5)(.0.5)
384.16,
round up
n for study =385
Alpha has a value of 0.025. There is a 1.96 Z-value. P(z) equals 0.5. The impact factor is 0.05. The Sample size for the study is 384.
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caitlin won a bag full of money. she has 49 bills in all. she counts $1,430. there are twenty dollar bills and fifty dollar bills in the bag. how many of each bill does caitlin have?
Answer:
30 I think but I'm not positive
Step-by-step explanation:
a mother is 21 years older than her son. in 6 years, she will be 5 times as old as her son. where is the father?\
The father is with the son's mother.
Given that,
a mother is 21 years older than her son.
Let us consider M be the age of the mother and S be the age of the son
which implies that,
M = S + 21 ---------------(1)
and in 6 years, mother will be 5 times as old as her son
i.e. M + 6 = 5(S + 6)
M = 5S + 24 ------------- (2)
so equation (1) and (2) implies that,
S + 21 = 5S + 24
21 = 4S + 24
S = - 3/4
That means son is - 3/4 years old or - 9 months.
The time at which we know the father will be with son's mother.
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help me with this i cant figure out the second part
The value of c that will make the expression x² + 24x + c a perfect trinomial is 144.
The perfect squared trinomial as a perfect binomial is (x + 12)²
How to find the value of c in the expression?An expression obtained from the square of the binomial equation is a perfect square trinomial.
In other words, perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial.
If a trinomial is in the form ax² + bx + c is said to be a perfect square, if and only if it satisfies the condition b² = 4ac.
Therefore,
x² + 24x + c
where
a = 1b = 24c = ?Therefore,
b² = 4ac
24² = 4 × 1 × c
4c = 576
divide both sides by 4
c = 576 / 4
c = 144
Therefore,
c = 144
The perfect squared trinomial as a perfect binomial is as follows:
x² + 24x + 144
x² + 12x + 12x + 144
x(x + 12) + 12(x + 12)
(x + 12)(x + 12)
(x + 12)
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For what type of variable does it make sense to construct a confidence interval about a population​ proportion?.
A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.
Given,
We must determine the kind of variable needed in the given problem to build a confidence interval for a population proportion.
Considering that;
The percentage of the entire population that possesses a specific quality is known as the population proportion (which is qualitative in nature). Therefore, a qualitative variable with two alternative outcomes must be used to generate the confidence interval for the population proportion.
Therefore, the nature of the various types of variables is used to choose the correct option. A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.
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Question is incomplete. Completed question is given below;
What type of variable is required to construct a confidence interval for a population proportion?
A. Quantitative
B. Qualitative with any number of possible outcomes
C. Continuous
D. Qualitative with 2 possible outcomes
E. Discrete
F. Qualitative with 3 or more possible outcomes
Can someone please help me? I need help
BTW this is algebra 2
Answer:
Step-by-step explanation:
1. is .4444444 or 4/9
All you do for this is enter -2 as x for 4(3)^x
2. is x^24 or answer (4)
this is because you will multiply the exponents starting with -4 till you get 24.
-4 x -1 = 4
4 x 6 = 24
3. sorry I have to go for this one, plug in any number into x and experiment with the 4 answers till one of them gives you the same solution
y varies directly as x. y = 18 when x = 5. Find x when y = 36.
Answer:
Step-by-step explanation:
y varies directly as x.
y = 18 , x = 5
y =36 then x also double,
x = 10
what is the statement of |4×+12|=0
Step-by-step explanation:
4x+12=0
4x= -12
x = -3
.........