In this case, the population consists of an insurance company's policyholders. The sample consists of his 200 policyholders under study. The sample size is 200.
H0: µ ≥ $5,000
Ha: µ < $5,000 (claimed)
As we can see that the sample size is 200, which is way greater than 30, so a z-test is appropriate here.
z(test) = (4800 - 5000) / (1300 / √200) = -2.1757
p (z = -2.1757) = 0.0148
The critical z-value for the left-sided test at α = 0.05 is -1.645
The tested value of z is less than the critical value, so we reject the null hypothesis. The hypothesis drawn here ( null hypothesis) will be rejected as an alternate decision because the p-value is less than the significance level (0.05).
At the 0.05 significance level, the prevention plan effectively reduced the average amount of harm. Insurers should continue these plans and try to improve them where possible.
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classify the following sequence as either arithmetic or geometric. then state the common difference or ratio and find the missing terms. explain your reasoning.
_,-9,_,3,9
-15_, -9, -3_, 3, 9...
First of all we understand about what is sequence ?
A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function. Sequences can be both finite and infinite.
Now we know that
Arithmetic = each new term differs from the previous term by a fixed amount.
an = a1 + d (n − 1)
Geometric = each element after the first is obtained by multiplying the previous number by a constant factor
an = a1 (r)^(n − 1)
Given pattern is
_,-9,_,3,9
find out the blanks by following a pattern ..
The term to term rule of a sequence describes how to get from one term to the next.
There is the difference of +6
hence The common different is +6.
-15_, -9, -3_, 3, 9...
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Necesito esto pa mañana ayudaaaa
Using the absolute value function, we have that:
1) The table is:
x = 0, |x| = 0.x = 1, |x| = 1.x = 2, |x| = 2.x = 3, |x| = 3.x = -1, |x| = 1.x = -2, |x| = 2.x = -3, |x| = 3.2) The graph is given at the end of the answer.
3) The rule is: g(x) = |x - 3|.
4) The rule is: D(x) = |x| - 5.
5) The rule is: K(x) = |x - 3| - 5.
What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin.
Hence, applying the rule, the table is completed as follows:
x = 0, |x| = 0.x = 1, |x| = 1.x = 2, |x| = 2.x = 3, |x| = 3.x = -1, |x| = 1.x = -2, |x| = 2.x = -3, |x| = 3.The function is graphed at the end of the answer.
A translation right of 3 units is given by:
f(x - 3).
Hence:
g(x) = |x - 3|.
A translation down 5 units is given by:
f(x) - 5.
Hence:
D(x) = |x| - 5.
For item 5, the function was shifted 5 units down and 3 right, hence it is given by:
K(x) = |x - 3| - 5.
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Through any three points there is exactly one plane containing them
Answer:
j
Step-by-step explanation:
kl
Which sequence of numbers is in order from least to greatest?
(Edpuzzle)
The sequence is -2 1/4, - 1.2, -0.7, 2 1/2, 2 3/4.
what is sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
We have given number as
-2 1/4 = -2.25
-1.2
-0.7
2.5
2.75
So, the arrangement from least to greatest is -2 1/4, - 1.2, -0.7, 2 1/2, 2 3/4.
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Sandy collected 10 pounds of apples at an apple orchard. She is determined to eat 20% of the apples remaining every day after the day she went to the orchard. Write an exponential function to model this scenario and use it to estimate how many pounds of apples she has left after 1 week.
The pounds of apple left after 1 week is 2.1 pounds.
How many pounds of apple would be left?The pounds of apple would decline each day that Sandy eats it.
An exponential function is a function that is used in mathematics with the form: f ( x ) = [tex]a^{x}[/tex]
Where:
x is a variablea is a constantThe pounds of apple left = initial pounds of apple x (1 - rate at which she eats it)^number of days
10 x (1 - 0.2)^number of days
10 x 0.8^7 = 2.1 pounds
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What is -2x + 4 = -10 ?
Answer:
x=7 -2x+4=-10
-2x+4-4=-10-4
Step-by-step explanation:
this should be right pick me brainliest
Confirmed Solution:
[tex]x=7[/tex]
Further Explanation:
Displayed Above
Hope this helps!
Sue has 20 biscuits in a tin.
There are: 12 plain biscuits
5 chocolate biscuits
3 currant biscuits
Sue takes at random two biscuits from the tin.
Work out the probability that the two biscuits were not the same type.
=======================================================
Explanation:
Define the following three events:
A = plain biscuitB = chocolate biscuitC = currant biscuitNotation like P(A) = 12/20 means the probability of event A (aka picking the plain biscuit) is 12/20 since there are 12 plain biscuits out of 20 total. I'll leave the fraction un-reduced so we can see where the 12 and 20 come from. Going from 12/20 to 3/5 has us lose vital information about the original values.
Notation like AB means a plain biscuit was selected first and then a chocolate biscuit is selected second in that exact order. I'm assuming the first selection is not replaced. This makes the probability of the second selection dependent on the first.
So,
P(AB) = P(A)*P(B given A) = (12/20)*(5/19) = 3/19
P(AC) = P(A)*P(C given A) = (12/20)*(3/19) = 9/95
P(BC) = P(B)*P(C given B) = (5/20)*(3/19) = 3/76
The last step is to add those results to get the probability of event AB, event BC or event AC of occurring. Addition is possible since the events are mutually exclusive.
P(AB)+P(AC)+P(BC) = 3/19 + 9/95 + 3/76 = 111/380
I've skipped a few steps, so let me know if you need to see the finer details. Also feel free to ask about any questions in general if they come up.
Johnny manziel of texas a&m is the first freshman to win the heisman trophy. players are given 3 points for every first-place, 2 points for every second-place vote, and 1 point for every third-place vote. manziel received 892 total votes for first, second, and third place, for a total of 2029 points. if he had 4 fewer than twice as many second-place votes as first-place votes, how many votes did he receive for each place
Using a system of equations, it is found that the number of votes that he received for each place is given as follows:
First: 454Second: 229Third: 209.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: number of first place votes that he received.Variable y: number of second place votes that he received.Variable z: number of third place votes that he received.He received 892 total votes, hence:
x + y + z = 892.
Total of 2029 points, hence:
3x + 2y + z = 2029.
He had 4 fewer than twice as many second-place votes as first-place votes, hence:
x = 2y - 4.
Replacing in each of the first two equations:
x + y + z = 892.
2y - 4 + y + z = 892
3y + z = 896.
3x + 2y + z = 2029
3(2y - 4) + 2y + z = 2029
8y + z = 2041.
Multiplying the first equation by -1, and subtracting the second equation from the first, we have that:
5y = 1145
y = 1145/5
y = 229.
The other amounts are given as follows:
z = 2041 - 8y = 2041 - 8(229) = 209.x = 2y - 4 = 2(229) - 4 = 454.Hence the number of votes that he received for each place is given as follows:
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The amplitude of a periodic function is 2.5 and its minimum value is 0 . What is the function's maximum value?
(F) -2.5 (G) 0 (H) 2.5 (I) 5.0
The maximum value of the periodic function will be 2.5 if the amplitude of a periodic function is 2.5 and its minimum value is 0 option (H) 2.5 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The amplitude of a periodic function = 2.5
The minimum value = 0
The maximum value = the amplitude = 2.5
Thus, the maximum value of the periodic function will be 2.5 if the amplitude of a periodic function is 2.5 and its minimum value is 0 option (H) 2.5 is correct.
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If the length of a rectangle is four less than twice its width and the perimeter is
220 inches, what is the width of the rectangle?
The width of the rectangle with a perimeter of 220 inches is 38 inches.
What is the width of the given rectangle?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The perimeter of a rectangle is expressed as;
P = 2( length + width )
Given the data in the question;
Let x represent the width of the rectangle.
Width of the rectangle = xLength = 2x - 4Perimeter = 220 inchesTo solve for the width ( x ), plug the given values into the perimeter formula above and solve for x.
P = 2( length + width )
220 = 2( (2x - 4 ) + x )
220 = 2( 2x - 4 + x )
220 = 2( 3x - 4 )
220 = 6x - 8
6x = 220 + 8
6x = 228
x = 228/6
x = 38
Therefore, the width of the rectangle x is 38 inches.
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By 8:00 a.m., the snack bar had made $3,256 in sales. By noon, the snack bar’s total sales were $8,821. About how much money did the snack bar take in each hour between 8:00 a.m. and noon?
$814.00
$1,391.25
$2,205.25
$5,565.00
Answer:
b) $1,391.25
Step-by-step explanation:
Noon is at 12pm, so 8am-12pm will be 4 hours.
8821-3256=5565, so the snack bar made $5565 in 4 hours, to find how much it made in 1 hour we need to divide 5565 by 4.
5565/4=1391.25
Use the diagram below for questions 15-17.
15. If m/1 = (7x-19), and m/2 = (x + 5)°, find m/2.
16. If m/1 = (6x + 25)°, and m/4= (10x - 11)°, find m/1.
17. If m/4= (3x + 7)°, and m25= (9x - 43)°, find m/UPS
18. If ZW and ZV are supplementary angles and m/V = 49°, find m/W.
S
19. If 21 and 22 are vertical angles, <2 and <3 are complementary angles,
and m/3 = 56°, find m/1.
20. If 21 and 22 form a linear pair and m/1 is 18 degrees less than fives
times the measure of 22, find m/1.
Gina Wilson (All Things
The angle measures for this problem are given as follows:
15. m<2 = 18º.
16. m<1 = 79º.
17. m<UPS = 151º.
18. m<W = 131º.
19. m<1 = 34º.
20. m<1 = 147º.
Item 15Using the angle addition postulate, we have that an angle of 90º is split into two angles, angle 1 and angle 2, hence:
m<1 + m<2 = 90º.
We use this equation to solve for x as follows:
7x - 19 + x + 5 = 90
8x - 14 = 90
8x = 104
x = 104/8
x = 13º.
Hence the measure of angle 2 is given as follows:
m<2 = x + 15 = 18º.
Item 161 and 4 are vertical angles, meaning that they are congruent, hence we can solve for x as follows:
6x + 25 = 10x - 11
4x = 36
x = 9º.
Hence the measure of angle 1 is given as follows:
m<1 = 6(9) + 25 = 79º.
Item 17Angles 4 and 5 are supplementary, meaning that the sum of their measures is of 180º, hence we solve for x as follows:
3x + 7 + 9x - 43 = 180
12x = 216
x = 216/12
x = 18.
The measure of angle UPS is:
m<UPS = m<4 + 90º = 3(18) + 7 + 90 = 151º.
Item 18From the explanation of supplementary angles in item 17, we have that:
m<W + 49º = 180º
m<W = 131º.
Item 19Complementary angles are angles whose sum of the measures is of 90º, hence:
m<2 + m<3 = 90º
m<2 + 56 = 90
m<2 = 34º.
Vertical angles are congruent, hence:
m<2 = m<1 = 34º.
Item 20The measures of the angles are:
m<1 = 5x - 18.m<2 = x.Angles that form a linear pair are supplementary, hence:
m<1 + m<2 = 180
5x - 18 + x = 180
6x = 198
x = 198/6
x = 33.
Then the measure of angle 1 is given by:
m<1 = 5(33) - 18 = 147º.
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In the diagram, AOC = 144 degrees, APC = 145 degree and onis the center of the circle. Find BAD.
===========================================================
Explanation:
Central angle AOC is 144 degrees. This means arc ABC is 144 degrees because the central angle subtends this arc.
The remaining bit of the circle is 360-144 = 216 degrees. If we placed point E somewhere on the edge of the circle, toward the bottom, then major arc AEC is 216 degrees in measure.
Notice how inscribed angle ADC subtends this 216 degree arc. So according to the inscribed angle theorem, angle ADC is half of the 216 degree arc at 216/2 = 108 degrees.
Angle APD = 180 - (angle APC) = 180 - 145 = 35 degrees
------------------------
Focus solely on triangle ADP. We have these interior angles
A = unknownD = 108P = 35The three interior angles must add to 180
A+D+P = 180
A+108+35 = 180
A+143 = 180
A = 180-143
A = 37 which is the measure of angle BAD.
0.116=? (16 keeps on going)
When written as a fraction, 0.116 can be found to be the equivalent of 29 / 250
How to find the equivalent fraction?The value of 0.116 has 3 decimals after the decimal point. This means that it is a thousandth decimal.
The fraction form is therefore:
= 116/1,000
You can then take this to be simplest form:
= (116 / 2) / (1,000 / 2)
= 58 / 500
= (58 / 2) / (500 / 2)
= 29 / 250
In conclusion, 0.116 = 29/250
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Clayton wonders what types of sports the students at his school like to play. So, he plans to ask a small sample of them. Pick all the ways of sampling the students that would produce a representative sample.
All the ways of sampling the students that would produce a representative sample are Simple random sampling, Strafied random sampling, Systematic sampling, Cluster sampling, Convenience sampling.
Sampling : In statistics, quality assurance, and survey methodology, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population.
Given that Clayton wonders what types of sports the students at his school like to play. So, he plans to ask a small sample of them.
Explanation:
Let us assume that there are 3000 students in Clayton's school and he has to choose a sample of 20 students.
1) Simple random sampling - Pick 20 of the students of the school from the 3000 students there are in his school.
2) Strafied random sampling - Divide all the students of the school into 4 grades and randomly pick 5 students from each of the grades.
3) Systematic sampling - Pick evert 7th student who enters the school premises until 20 students are picked.
4) Cluster sampling - Pick several 1st period classes of the school then randomly pick students from those classes.
5) Convenience sampling - Ask 20 students from all the 3000 students in the school recess.
Therefore, All the ways of sampling the students that would produce a representative sample are Simple random sampling, Strafied random sampling, Systematic sampling, Cluster sampling, Convenience sampling.
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Identify each function as linear, quadratic, or exponential. Explain your reasoning.
a. y=3(x+1)²
The equation is a quadratic equation.
Linear equation is a equation whose degree is 1. Degree is defined as the highest power of the variable in a polynomial function.
Quadratic equation is a equation whose degree is 2.
Exponential equation is a equation in which the variable appear a exponents.
Now we have been the equation that is,
[tex]y=3(x + 1)^{2}[/tex]
Expanding this we would get
y = 3([tex]x^{2}[/tex] + 1 + 2x)
y = 3[tex]x^{2}[/tex] + 2x + 3
Here the highest power is 2 that is the degree is 2 . Thus this equation is a quadratic equation.
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Write each expression in simplest form. (x¹/₂y⁻²/₃)⁻⁶
The given expression can be simplified by using the rule of negative exponent.
In the expression, there are two terms with negative exponent. The second base term y has a negative exponent -2/3. The second negative exponent -6 is applied to both base terms.
The rule states that the negative exponent can be solved by reciprocating the base term i.e. a^-x=1/a^x.
Solving the negative exponent for y,
Hence, x^1/2y^-2/3=x^1/2/y^2/3.
Solving the second negative exponent -6 that applies to both terms, applying the same rule i.e. a^-x=1/a^x.
(x^1/2/y^2/3)^-6=(y^2/3/x^1/2)^6
Multiplying the powers and simplifying,
y^2/3*6/x^1/2*6=y^4/x^3
The simplest form of the expression (x^¹/₂y^⁻²/₃)^-6 is y^4/x^3.
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There are 250 cars in a car park.165 of them are Toyota. What is the probability that the first car to leave the car park is: a)a Toyota b)not a Toyota?
Answer:
Toyota
Step-by-step explanation:
im not sure im a 5th grder that just guessed
Answer:
a) 33/50 b) 17/50
Step-by-step explanation:
total cars = 250
toyotas = 165
The probablity of the first car to leave being a toyota is
165/250
Simplify it to 33/50
The probability of the first car to leave not being a toyota is
(250 - 165)/250
= 85/250
= 17/50
What are the domain and points of discontinuity of the rational function? Are the points of discontinuity removable or non-removable? What are the x - and y -intercepts of the rational function?
a. y=1/x²-16
points of discontinuity are x = -4&x = +4.
x = +4 is removable discontinuity
The x- intercept is x = 0The y- intercept is y= -(1/16).
How to find the points of discontinuity of the rational function & find the x - and y -intercepts of the rational function?points of discontinuity:
In rational functions, points of discontinuity are defined as fractions with undefined or zero as their denominator. When the denominator of a fraction is 0, the fraction is no longer defined and shows up as a hole or break in the graph.
points of discontinuity removable:
A point on the graph that is removable discontinuity is one that may be filled in with a single value despite not existing.If an is zero for a factor in the denominator that shares a factor with a factor in the numerator, a removable discontinuity at x=a in the graph of a rational function occurs.
points of discontinuity non removable:
A function's break that cannot be repaired with a single point is referred to as a non-removable discontinuity. It cannot be filled in with a single point, a vertical asymptote (a vertical line that the graph approaches but never crosses because the function is undefined at that x-value) is non removable.
given that y=1/x²-16
write 16 as a 4²
[tex]y = \frac{1}{ {x}^{2} - {4}^{2} } [/tex]
[tex]y = \frac{1}{(x + 4)(x - 4)} [/tex]
now,
domain : x !=4.
points of discontinuity are
(x+4) = 0 (x-4) = 0
x = -4 x = +4
Here x = +4 is removable discontinuity.
The x- intercept is
if x = 0, then
[tex]y = \frac{ 1}{ - 16} [/tex]
The y- intercept is
if y = 0
x = 0.
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If n=23, represent 25 and 27 in terms of n
Help!!
Step-by-step explanation:
25= n+2.27=n+5I hope this helped you
Each of Mrs. White's two children received $50 for their savings account. The original amounts in their savings accounts
were $500 and $300, respectively. Which savings account had a greater percent of increase?
The child that will have a greater percentage of increasing amounts is; The child with original amount of $500
What is the percentage increase?
The amount that has increased from the initial number to the final number in terms of 100 parts of the original is essentially what the concept of percentage increase refers.
We are given that the original amount found in their savings account are;
First child; A = $500
Second child; B = $300
Thus the first child denoted by A has greater amount in savings compared to the second child and as such child A will have a greater percentage of increasing amounts.
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Answer: The older child.
Step-by-step explanation: The original amounts in their savings accounts
were $500 and $300, respectively.
Determine whether each statement is always, sometimes, or never true.
ln e x ≥ 1
[tex]ln(e^x) \geq 1[/tex] is sometimes true, by seen by operations on logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
When x < 1, the given equation is false.For example, let x = 0.1
Then, [tex]ln(e^{(0.1)}) = 0.1 < 1[/tex]
But, when x > 1, the given equation is true.For example, let x = 2
Then, [tex]ln(e^2) = 2 > 1[/tex]
Hence, [tex]ln(e^x) \geq 1[/tex] is sometimes true, by seen by operations on logarithm.
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Solve each equation.
3 log x-log 6+log 2.4=9
3 log (x) - log (6) + log (2.4) = 9 => x = 1357.28, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
3 log (x) - log (6) + log (2.4) = 9
=> 3 log (x) - 0.778 + 0.38 = 9
=> 3 log (x) = 9 - 0.38 + 0.778 = 9.398
=> log (x) = 3.13267
Since, generally the base of log is 10, raising them to 10.
=> [tex]10^{log_{10}(x)} = 10 ^{3.13267}[/tex]
=> x = 1357.28
Hence, 3 log (x) - log (6) + log (2.4) = 9 => x = 1357.28, by properties of logarithm.
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What is 81826 dived by 160 to the 2nd power?
Answer:
3.19 or 3.2 if round
Step-by-step explanation:
160^2 = 25600
81826 / 25600= 3.19
A used-boat dealership buys a boat for 2600 then sells it for 4100 whats the percent increase? please help!!!
The percentage increase from the boat price of 2600 to 4100 is 57.69%
How to determine the percentage increase?The given parametes are
Cost price = 2600
Selling price = 4100
The percentage increase in the price of the boat is calculated as
Percentage increase = (Selling price - Cost price)/Cost price * 100%
Substitute the known values in the above equation
So, we have
Percentage increase = (4100 - 2600)/2600 * 100%
Evaluate the difference in the above equation
So, we have
Percentage increase = 1500/2600 * 100%
Evaluate the quotient in the above equation
So, we have
Percentage increase = 0.5769 * 100%
Evaluate the product in the above equation
So, we have
Percentage increase = 57.69%
Hence, the percentage increase from the boat price of 2600 to 4100 is 57.69%
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Answer:
60% (Rounded to the first decimal)
Step-by-step explanation:
How many times does 2600 go in 4100:
4100/2600 = 1.6
ABCD is a Rhombus. Solve the following problems. If AE = 8, then find AC
The AC in Rhombus ABCD is 16 cm.
In question it is not given that what is E, so, let suppose that E is intersecting point of diagonals AC and BD of rhombus with side AB, BC, CD and DA.
Rhombus :Rhombus is a parallelogram with four equal sides and sometimes one with no right angles.
As it is given that AE =8 cm.
And, we know that AC is diagonal rhombus,
so, as E is middle point of diagonal AC
Then, AC = 2 × AE
AC = 2 × 8
Hence, AC = 16 cm.
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Find three consecutive odd integers such that the sum of the smallest number and middle number is 27 less than three times the largest number.
The three consecutive odd integers are 17, 19 and 21 respectively.
Linear equationsLinear equations are equations that has a leading degree of 1. Given the three consecutive odd numbers to be
2x+1, 2x+3 and 2x+5
If the sum of the smallest number and middle number is 27 less than three times the largest number, then;
2x + 1 + 2x + 3 = 3(2x+5) - 27
Simplify
4x + 4 = 3(2x) + 3(5) - 27
4x + 4 = 6x + 15 - 27
4x - 6x = 15 - 27 - 4
-2x = -16
x = 16/2
x = 8
Determine the numbers
Smallest number = 2x + 1
Smallest number = 2(8) + 1 = 17
Middle number = 2x + 3
Middle number = 2(8) + 3
Middle number = 19
Largest number = 2(8) + 5
Largest number = 21
Hence the three consecutive odd integers are 17, 19 and 21 respectively.
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whats the easiest way to solve division
the easiest way to solve division is to first use calculator if you don't have it you can count the number by dividing them
a pine tree is shaped like a cone with a radius of 8 feet and a volume of 3887.2 cubic feet. what is the height of the pine tree?
The height of the pine tree shaped like a cone is 58.03 feet.
What is curverd surafce area of a cone?The curved surface of a cone is when we only consider the surface area of the sides.
We know the general formula for the volume of a cone is (1/3)πr²h.
Given, the volume of a pine tree shaped like a cone is 3887.2 cubic feet also given that it has a radius of 8 feet,
∴ We can obtain the height of the pine tree by equating given volume with the formula and substituting the value of radius.
So, (1/3)π(8)²h = 3887.2.
(1/3).(3.14).(64)h = 3887.2.
(200.96/3)h = 3887.2.
h = (3887.2×3)/200.96.
h = 11661.6/200.96.
h = 58.03 feet.
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Alisha and Lowesha share £50 in the ratio 2:3. How much does Lowesha get?
Answer:
she got 30 dollars.
Step-by-step explanation:
2x3x=50
5x=50
5x/5=50/5
=10
10*3=30 dollars