Answer:
[tex]a_n=(-2)^{n-1}[/tex]
Step-by-step explanation:
So a geometric sequence can be explicitly defined as: [tex]a_n = a_1(r)^{n-1}[/tex]. IN this case we're given r, but we don't know what a_1 is. We can find this by lugging in 4 as n, and -8 as a_n, since they're given values
Plug known values in:
[tex]-8 = a_1(-2)^{4-1}[/tex]
Subtract the values in the exponent
[tex]-8 = a_1(-2)^3[/tex]
Simplify the exponent
[tex]-8 = a_1 (-8)[/tex]
Divide both sides by -8
[tex]1=a_1[/tex]
So the nth term can be defined as: [tex]a_n = 1(-2)^{n-1}[/tex], and since the 1 is redundant, the equation can simply be defined as: [tex]a_n=(-2)^{n-1}[/tex]
If the farmer isn't present, the fox cannot be left with either the dog or the goose, or both. if need be, the goose can be left with the grain provided the dog is present because the dog will guard the grain and won't eat the goose. help the farmer cross the river.
Answer:
See below
Step-by-step explanation:
Take fox across
go back to get goose
take goose across
take fox BACK
grab dog.....take dog across
go back get grain and take it across
go back get fox and take it across
ales volume last weekend for four samples, each consisting of five car dealerships, were as follows: Data Point 1 2 3 4 5 Sample 1 37 15 43 25 21 Sample 2 38 31 12 19 28 Sample 3 16 21 45 32 25 Sample 4 19 10 45 37 22 What is the standard deviation of the distribution of sample means
The sample standard deviation of sample 1 is 11.54, of sample 2 is 10.21, of sample 3 is 11.25, of sample 4 is 14.15.
Given
Data point sample 1 sample 2 sample 3 sample 4
1 37 38 16 19
2 15 31 21 10
3 43 12 45 45
4 25 19 32 37
5 21 28 25 22
We have to find the sample standard deviation of each sample.
We have to first mean of each sample.
Sample mean of 1=141/5=28.2
Sample mean of 2=128/5=25.6
Sample mean of 3=139/5=27.8
Sample mean of 4=133/5=26.6
Sample standard deviation=[tex]\sqrt{}[/tex]∑[tex](x-x bar)^{2}/n-1[/tex]
∑[tex](x-x bar)^{2}[/tex] is calculated in the figure.
Sample standard deviation of sample 1=[tex]\sqrt{532.8/4}[/tex]
=[tex]\sqrt{133.2}[/tex]
=11.54
Sample standard deviation of sample 2=[tex]\sqrt{417.2/4}[/tex]
=[tex]\sqrt{104.3}[/tex]
=10.21
Sample standard deviation of sample 3=[tex]\sqrt{506.8/4}[/tex]
=[tex]\sqrt{126.7}[/tex]
=11.25
Sample standard deviation of sample 4=[tex]\sqrt{801.2/4}[/tex]
=[tex]\sqrt{200.3}[/tex]
=14.15.
Hence the sample standard deviation of sample 1 is 11.54, sample standard deviation of sample 2 is 10.21, sample standard deviation of sample 3 is 11.25, sample standard deviation of sample 4 is 14.15.
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Determine if each of the following functions from {a,b, c,d} to itself is one-to-one and/or onto. Check ALL correct answers. (a) f(a)
The answer is . one-to-one.
What is the domain of a set?The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range. Domain: all x-values that are to be used (independent values).
(a) The function is onto because a, b, c, and d are members of its codomain. All points are converted into various points, making it a one-to-one relationship. The response is that it is one-to-one and onto ( A and C).
(b) It is onto because a, b, c, and d are members of the function's codomain. All points are converted into various points, making it a one-to-one relationship. The response is that it is one-to-one and onto (A and B).
(C) The element b is not onto since it is not a part of the function's codomain. All points are converted into various points, making it a one-to-one relationship. One-to-one is the right response.
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The complete question is -
Determine if each of the following functions from {a,b,c,d} to itself is one-to-one and/or onto.
Check ALL correct answers.
(a) f(a)=d,f(b)=a,f(c)=c,f(d)=b
A. onto.
B. neither one-to-one nor onto.
C. one-to-one.
f(a)=b,f(b)=a,f(c)=c,f(d)=d
A. one-to-one.
B. onto.
C. neither one-to-one nor onto.
f(a)=c,f(b)=d,f(c)=a
A. one-to-one.
B. onto.
C. neither one-to-one nor onto.
The art club had an election to select a president nine out of the 12 members of the our club voted in the election what percentage of the members voted
Answer:
75%
Step-by-step explanation:
9 divided by 12 is 0.75, so 9 is 75 percent of 12.
I hope this helps, have a good day!
Find the value of x in 1:x=6 1/4
Answer:
x = [tex]\frac{4}{25}[/tex]
Step-by-step explanation:
1 : x = 6 [tex]\frac{1}{4}[/tex] ← change to improper fraction
1 : x = [tex]\frac{25}{4}[/tex] , then
[tex]\frac{1}{x}[/tex] = [tex]\frac{25}{4}[/tex] ( cross- multiply )
25x = 4 ( divide both sides by 25 )
x = [tex]\frac{4}{25}[/tex]
Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
If the length,breadth, height of cuboid are 16 m, 5 m,4 m , slant height of pyramid is 10m, height be 6 m then the surface area of composite figure be 444 [tex]m^{2}[/tex].
Given that the length,breadth,height of cuboid are 16m,5 m, 4m and slant height be 10 m and height be 6 m.
Surface area is basically sum of area of all the sides of a figure.
Surface area of composite figure = area of cuboid less area of common side + area of 2 slant sides of pyramid+area of two triangles.
=2(lb+bh+hl)-(lb)+2(slant height*breadth of cuboid)+2[1/2* length of cuboid* height of triangle)
=2(16*5+5*4+4*16)-16*5+2(10*5)+2[1/2*16*6]
=2(80+20+64)-80+2*50+2(48)
=2(164)-80+100+96
=328-80+196
=248+196
=444[tex]m^{2}[/tex]
Hence the surface area of composite figure having a cuboid and pyramid on top is 444[tex]m^{2}[/tex].
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14. Ashley is holding a fair six-sided die and a fair
coin. If Ashley rolls the die once and then flips
the coin, what is the probability that the die will
show a 5 and the coin will come up tails?
Answer:
1/12
Step-by-step explanation:
Landing on the 5 is a 1/6 chance, landing on tails is a 1/2 chance, multiply, and you get 1/12
Using the defects method, which of these relationships represents the law of cosines if the measure of the included angle between the sides a and b of ∆abc is more than 90°? a. area of square c2 = -area of square a2 − area of squareb2 area of defect1 area of defect2 b. area of square c2 = area of square a2 area of squareb2 area of defect1 − area of defect2 c. area of square c2 = area of square a2 area of squareb2 − area of defect1 − area of defect2 d. area of square c2 = area of square a2 area of squareb2 area of defect1 area of defect2 e. area of square c2 = area of square a2 − area of squareb2 area of defect1 − area of defect2
The relationship that represents the law of cosines if the measure of the included angle between the sides a and b is D. area of square c² = area of square a² area of squareb² area of defect1 area of defect2
What is the law of cosine?It should be noted that the cosine law is simply used to solving triangles.
The law simply states that c² = a² + b² - 2abcosC.
The correct option that illustrates this is D.
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Answer:
c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2
Step-by-step explanation:
A sample of 148 college students at a large university reports getting an average of 6.85 hours of sleep last night with a standard deviation of 2.12 hours.
a.Verify that it is reasonable to use the t-distribution to construct a confidence interval for the average amount of sleep students at this university got last night.
b. Construct a 98% confidence interval for the average amount of sleep students at this university got last night. Use two decimal places in your margin of error.
c.. Provide an interpretation of your interval in the context of this data situation.
d.. Suppose you want to conduct a similar study at your university. Assuming that the standard deviation of this sample is a reasonable estimate of the standard deviation of sleep time at your university, how many students do you need to survey to estimate the mean sleep time of students at your university with 95% confidence and a margin of error of 0.5 hours?
The solution for the questions is mathematically given as
a)
t-distribution.
b)
the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952, 7.3048 )
c) the value of the [tex]\mu_0[/tex] is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_0; otherwise, reject H _0.
d)
you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.
What is the distribution to use?Generally, the equation for is mathematically given as
a.
In this case, the standard deviation of the population is unknown.
As a result, we make use of the t-distribution.
b)
We wish to generate a confidence interval with a 98 percent likelihood for the mean.
Because of this,
[tex](\bar{X}-t_{n-1,\alpha/2}\frac{s}{\sqrt{n}},\bar{X}+t_{n-1,\alpha/2}\frac{s}{\sqrt{n}})[/tex]
[tex](6.85-t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}},6.85+t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}})[/tex]
[tex](6.85-t_{147,0.01}\frac{2.12}{12.1655},6.85+t_{147,0.01}\frac{2.12}{12.1655})[/tex]
(6.3952,7.3048)
Therefore, the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952 , 7.3048 )
c )
If the value of the mu _0 is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_o; otherwise, reject H_0.
d . Here, we want to determine the sample size
Therefore,
[tex]n=t_{n-1,\alpha/2}^2\frac{s^2}{E^2}[/tex]
[tex]n=t_{148-1,0.05/2}^2\frac{2.12^2}{0.5^2}[/tex]
[tex]n=t_{147,0.025}^2\frac{2.12^2}{0.5^2}[/tex]
[tex]n=2.6097^2\frac{2.12^2}{0.5^2}[/tex]
n=122.4364
In conclusion, you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.
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How can you use the converse of the Pythagorean Theorem
to tell if a triangle is a right triangle?
Answer:
Yes. If the squares of the 2 short sides add up to the square of the hypotenuse, the triangle contains a right angle. Hope this helped.
The product of two fractions is 9/3/ 5. if one of them is 9/ 3/7. find the other
The other fraction is [tex]1\frac{1}{55}[/tex].
The calculation to find out other fractionProvided that ,
One fraction = [tex]9\frac{3}{7}[/tex] = [tex]\frac{66}{7}[/tex]
The product of their fraction = [tex]9\frac{3}{5}[/tex] = [tex]\frac{48}{5}[/tex]
We have to find out the other fraction.
When one fraction and their product are given, the formula to find out another fraction = product / one fraction
So, the other fraction = [tex]\frac{48}{5}[/tex] / [tex]\frac{66}{7}[/tex]
= [tex]\frac{48}{5} * \frac{7}{66}[/tex]
= 336/330
= 56/55 [divided both the numerator & denominator by 6]
= [tex]1\frac{1}{55}[/tex]
Therefore it is concluded that the other fraction is [tex]1\frac{1}{55}[/tex] .
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Rewrite the ratio 15: 39 as an equivalent ratio of the form 1 : n.
Give any decimals in your answer to 1 d.p.
Answer:
n = 2.6
Step-by-step explanation:
Hello!
We can create an equation with equivalent fractions. Remember that a ratio can also be represented as a fraction.
[tex]a:b = \frac ab[/tex]We can create two fractions that are equivalent to each other given the ratios.
[tex]\frac{15}{39} = \frac 1n[/tex]Solve for n[tex]\frac{15}{39} = \frac 1n[/tex][tex]\frac{5}{13} = \frac 1n[/tex][tex]5n = 13[/tex][tex]n = \frac{13}{5}[/tex][tex]n = 2.6[/tex]The value of n is 2.6.
a rectangle has a lengths and width of twelve and eight units, respectively. Using only multiplication show in a diagram which of the solutions below represent the perimeter of the entire rectangle
96 units
384 units
None of these
20 units
40 units
192 units
Answer:
40 units
Step-by-step explanation:
lengths:
12+12=24
width:
8+8=16
perimeter:
2l+2w
2(12)+2(8)
24+16=40
give the volume of the triangular prism shown
A-440in^3
B-528in^3
C-880in^3
D-264in^3
Answer:
D. 264 in³
Step-by-step explanation:
The missing edge dimension can be found using the Pythagorean theorem. Then the volume can be found using the appropriate formula.
Edge dimensionThe missing dimension and the two given for the top triangle will satisfy the Pythagorean theorem. If the missing dimension is represented by 'a', then we have ...
a² +8² = 10²
a = √(100 -64) = 6 . . . . inches
VolumeThe area of the top triangle is ...
A = 1/2bh . . . . where b and h are the base and height dimensions
A = 1/2(6 in)(8 in) = 24 in²
The volume of the triangular prism is ...
A = Bh . . . . . where B is the area of the triangular base, and h is the prism height
A = (24 in²)(11 in) = 264 in³
The volume of the triangular prism shown is 264 in³.
1. Which of the statements is NOT true about the illustration?
Angle DME is another name for angle 3.
MDis congruent to AE.
Angle 3 is congruent to angle 5.
MEis parallel to AD.
Answer: Option (1)
Step-by-step explanation:
[tex]\angle DMA[/tex] is another name for angle 3, but not [tex]\angle DME[/tex].
thanks!!
1) Now is your chance to find examples of sinusoids. Come up with some examples of natural or man-made phenomena that repeat at predictable intervals.
Search the Internet to find descriptions, and post the link as well as your analysis of why the behavior is periodic. You do not have to find an equation or write one. Examples already given in the lessons for this unit are off limits, so look for something new.
As you ride a ferris wheel, your distance from the ground varies sinusoidally with time. When the last passenger boards the ferris wheel and the ride starts moving, let your position be modeled by the diagram provided.
2) Let t be the number of seconds that have elapsed since you began moving. It takes you 5 seconds to reach the top of the wheel (38 feet above the ground) and 20 seconds to make a complete revolution. The diameter of the wheel is 30 feet.
Work with your classmates to answer the following questions:
What is the lowest you go as the ferris wheel turns?
Why is this number always greater than zero?
Write the equation of a sinusoid that describes this motion.
Predict your height above the ground when t = 3, t = 8, t = 15, and t = 19.
The examples of sinusoids include sound and water waves.
How to illustrate the information?Simple harmonic motion such as that of a pendulum or a weight attached to a spring results in a sinusoidal relationship between position and time.
The angle will be formed after t time of the starting of the motion.
θ = wt = 2πt/20 = πt/10
Radius of the wheel = 30/2 = 15 feet
Distance from the ground = (15 - 15cosθ) + 8 = (15 - 15cosπt/10) + 8
= 23 - 15cos(πt/10)
As we know the minimum value of the cos is -1
-1 ≤ cos(πt/10) ≤ 1
8 ≤ 23 - 15cos(πt/10) ≤ 38
The lowest distance = 8 feet
It should be always greater than zero as the lowest point of what should be above the ground.
d = 23 - 15cos(πt/10)
Plug t = 3 in the above equation:
d(3) = 14.18 feet
For t = 8
d(8) = 35.13 feet
For t = 15
d(15) = 23 feet
For t = 19
d(19) = 8.73 feet
Thus, the lowest distance is 8 feet, and the lowest point of what should be above the ground and the equation is d = 23 - 15cos(πt/10).
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Write a paragraph summarizing the data set , 12,13,14,15,16,17,18,19,20,21,22,23,24,25. Included unit measure,the number of data , the shape of the distribution, value of appropriate measure of center , value of appropriate measure of spread
The number of observation given in the following data set 14. This is also called the size of the population.
What is the description for the above data?It is important to note that the above data possess the minimum value of 12 and the maximum value of 25. As indicated in the attached image, the data set is normally distributed.
The measures of central tendency are given as follows;
Median = 18.5; Mean = 18.5Standard Deviation = 4.03112887Variance = 16.25Mid Range = 18.5The quartiles are given as follow:Q1 --> 15
Q2 --> 18.5
Q3 --> 22
IQR = 7
Mean Absolute Deviation (MAD) = 3.5
Min = 12
Max = 25.
It is to be noted that the above indictors are called Descriptive Statistics.
What is the purpose of descriptive statistics?
The features of a sample or data set, such as a variable's mean, standard deviation, or frequency, are described or referred to as descriptive statistics.
We can better grasp a data sample's constituent parts by using inferential statistics.
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help me please guys!!!
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathsf{|-8| + 9 = }[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\textsf{The additive inverse of }\mathsf{|-8|}\textsf{ is positive 8.}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathsf{|-8| + 9}[/tex]
[tex]\mathsf{= \bold 8 + 9}[/tex]
[tex]\mathsf{= 17}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{17}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{|-8 + 9| =}[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\textsf{We will convert your equation to }\mathsf{-8 + 9}\textsf{ because it can make the equation}\\\textsf{a lot easier to solve.}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathsf{|-8 + 9|}[/tex]
[tex]\mathsf{= -8 + 9}[/tex]
[tex]\text{Start at }\rm{-8}\text{ and go \boxed{up} 9 spaces to the right and you have your answer.}[/tex]
[tex]\mathsf{= 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
please help me im in a rush
Answer:
Step-by-step explanation:
A = 4 ft
B = 10 ft
C = 8 ft
D = 6 ft
b) Area of rectangle = length * width
Area of 2 triangle = base * height
Area of right triangular prism = area of 2 triangles +area of left rectangle + area of middle rectangle + area of right rectangle
= 6 * 8 + 4* 6 + 4 * 10 + 4 * 8
= 48 + 24 + 40 + 32
= 144 ft²
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Formulas:}[/tex]
[tex]\huge\text{Area of rectangle is: }\huge\boxed{\rm{\bold{w}idth \times \bold{h}eight = \bold{a}rea}}[/tex]
[tex]\huge\text{Area of triangle is: }\huge\boxed{\rm{\dfrac{1}{2} \times \bold{b}ase \times \bold{h}eight = \bold{a}rea}}[/tex]
[tex]\huge\textbf{Now, that we have that out of the}\\\\\huge\textbf{way, we can label your given equation:}[/tex]
[tex]\rm{A \rightarrow 4\ \boxed{\rm{ft}}}\\\\\rm{B \rightarrow 10\ \boxed{\rm{ft}}}\\\\\rm{C \rightarrow 8 \ \boxed{\rm{ft}}}\\\\\rm{D \rightarrow 6\ \boxed{\rm{ft}}}[/tex]
[tex]\huge\textbf{What should your equation look like?}[/tex]
[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]
[tex]\huge\textbf{What should it look like when we're}\\\huge\textbf{solving for the answer?}[/tex]
[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]
[tex]\rm{= 48 + 4\times6 + 4\times10 + 4\times8}[/tex]
[tex]\rm{= 48 + 24 + 4 \times 10 + 4\times8}[/tex]
[tex]\rm{= 72 + 4\times 10 + 4\times8}[/tex]
[tex]\rm{= 72 + 40 + 4\times8}[/tex]
[tex]\rm{= 112 + 4\times8}[/tex]
[tex]\rm{= 112 + 32}[/tex]
[tex]\rm{= 144}[/tex]
[tex]\huge\textbf{What is the answer?}[/tex]
[tex]\huge\boxed{\textsf{Answer: }\boxed{\frak{144\ ft^2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Solve algebraically:
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation a.}[/tex]
[tex]\rm{2x^2 - 162 = 0}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\rm{2x^2 - 162 = 0}[/tex]
[tex]\huge\textbf{Add \boxed{\bf 162} to both sides:}[/tex]
[tex]\rm{2x^2 - 162 + 162 = 0 + 162}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{2x^2 = 0 + 162}[/tex]
[tex]\rm{2x^2 = 162}[/tex]
[tex]\huge\textbf{Divide \boxed{\bf 2} to both sides:}[/tex]
[tex]\rm{\dfrac{2x^2}{2} = \dfrac{162}{2}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x^2 = \dfrac{182}{2}}[/tex]
[tex]\rm{x^2 = 81}[/tex]
[tex]\huge\textbf{Take the square root of \boxed{\bf 81}}[/tex]
[tex]\rm{x = \pm \sqrt{81}}[/tex]
[tex]\rm{x = 9\ or\ x = -9}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{x = } \frak{9\ or } \ \textsf{x = }\frak{-9}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation b.}[/tex]
[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]
[tex]\huge\textbf{Simplify both sides of your equation:}[/tex]
[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} = -2}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf -2} to both sides:}[/tex]
[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} - (-2) = -2 - (-2)}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{- \dfrac{1}{2}x^2 + 3x - \dfrac{5}{2} = 0}[/tex]
[tex]\huge\textbf{Now, we can convert the equation to:}[/tex]
[tex]\rm{-0.5x^2 + 3x - 2.5 = 0}[/tex]
[tex]\large\text{When we changed the equation entirely, we made it easier to solve}\uparrow[/tex]
[tex]\huge\textbf{Use the quadratic formula to solve.}[/tex]
[tex]\large\textsf{The quadratic formula:}[/tex]
[tex]\mathsf{x= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
[tex]\huge\textbf{Here are your labels:}[/tex]
[tex]\text{a = }\rm{-0.5}\\\\\text{b = }\rm{ 3}\\\\\rm{c = }\rm{\ -2.5}[/tex]
[tex]\huge\textbf{Your new equation:}[/tex]
[tex]\rm{x = \dfrac{-(3) \pm \sqrt{3^2 - 4(-0.5)(-2.5)}}{2(-0.5)}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x = \dfrac{-3 \pm \sqrt{4}}{-1}}[/tex]
[tex]\rm{x = 1\ or \ x = 5}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\textsf{x = }\frak{1}\ \textsf{or x = }\frak{5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex][tex]a)\ x_1=-9,\ x_2=9\\\\b)\ x_1=1,\ x_2=5[/tex]
Step-by-step explanation:Given equations:
[tex]a)\ 2x^2 - 162 = 0\\\\b) -\dfrac{1}{2}(x-3)^2=-2[/tex]
A) 2x² - 162 = 0
Step 1: Divide both sides by 2.
[tex]\\\implies \dfrac{2x^2 - 162}{2} = \dfrac{0}{2}\\\\\implies x^2-81=0\\\\\implies x^2=81[/tex]Step 2: Take the square root of both sides (using both the positive and negative roots).
[tex]\\\implies \sqrt{x^2}=\sqrt{81}\\\\\implies x=\pm\ 9[/tex]
Step 3: Separate into two cases.
[tex]\implies x_1 = -9,\ x_2 =-9[/tex]
----------------------------------------------------------------------------------------------------------------
B) -1/2(x - 3)² = -2
Step 1: Multiply both sides by -2.
[tex]\\\implies -2\left(-\dfrac{1}{2}(x-3)^2\right)=-2(-2)\\\\\implies (x-3)^2=4[/tex]
Step 2: Take the square root of both sides (using both the positive and negative roots).
[tex]\\\implies\sqrt{(x-3)^2}=\sqrt{4}\\\\\implies x-3=\pm\ 2[/tex]
Step 3: Separate into two cases and solve each one.[tex]1)\ x-3=-2\implies x=-2+3\implies \boxed{x=1}\\\\2)\ x-3=2\implies x=2+3\implies \boxed{x=5}[/tex]
You have one type of chocolate that sells for $1.50/lb and another type of chocolate that sells for $6.50/lb. You would like to have mix the $1.50/lb type with 10 lbs of the $6.50/lb type to make a chocolate mixture that sells for $2.50/lb. How much of the $1.50/lb type will you need to obtain the desired mixture
14 of the $1.50/lb type will you need to obtain the desired mixture.
According to the statement
Chocolate A that sells for $1.50/lb
Chocolate B that sells for $6.50/lb
Then in equation form the quantity of mixture will
A + B = X
then
$1.50A + $6.50(10) = X
1.50A + 65 = X -(1)
after solving the equation the value of a and b will become
A = 14.
So, 14 of the $1.50/lb type will you need to obtain the desired mixture.
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The points (1, 5) and (0, –2) fall on a particular line. What is its equation in slope-intercept form?
The equation of the line in slope intercept form is y = 7x - 2
How to find the equation of a line?The equation of the line can be solved with the following equation.
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = -2 - 5 / 0 - 1 = -7 / -1
m = 7
Hence, using (1, 5)
y = 7x + b
5 = 7(1) + b
5 - 7 = b
b = -2
Therefore,
y = 7x - 2
Hence, the equation of the line in slope intercept form is y = 7x - 2
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Geometry: Write a formal proof, ASAP!!!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex] \sf \: \angle1 \cong \angle3[/tex][tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \: \angle1 \cong \angle2[/tex]
( by corresponding angle pair )
[tex]\qquad❖ \: \sf \: \angle2 \cong \angle3[/tex]
( given in the question )
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \angle1 \cong \angle3[/tex]
Ben has 3/4 pounds of cherries and ate 2/3 of the cherries. How many pounds of cherries does Ben eat?
Answer:
1/2 pounds
Step-by-step explanation:
3/4 * 2/3 = 1/2 pounds
Using that income equation, after how many years will the income be $300? Round your answer correct UP TO TWO (2) decimal digits.
The number of years based on the equation is 24 years.
How to illustrate the information?The information is incomplete. An overview will be given. Let the income equation be represented as I = 60 + 10x where x represents the years taken.
Therefore i = 60 + 10x
60 + 10x = 300
10x = 300 - 60
10x = 240
x = 240/10
x = 24
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The probability that a football game will go into overtime is 18%. What is the probability that two of three football games will go to into overtime
The probability that two of three football games will go to into overtime is 0.08
How to determine the probability that two of three football games will go to into overtime?From the question, we have the following parameters about the probability
Sample size, n = 3
Proportion that goes to overtime, p = 18%
Number that goes into overtime, x = 2
The probability that two of three football games will go to into overtime is calculated using the following binomial probability
P(x) = nCx * p^x * (1 - p)^(n -x)
Substitute the known values in the above equation
P(2) = 3C2 * (18%)^2 * (1 - 18%)^(3 -2)
Express 18% as decimal
P(2) = 3C2 * (0.18)^2 * (1 - 0.18)^(3 -2)
Evaluate the difference
P(2) = 3C2 * (0.18)^2 * (0.82)^1
Evaluate the combination expression
P(2) = 3 * (0.18)^2 * (0.82)^1
Evaluate the exponent
P(2) = 3 * 0.0324 * (0.82)
Evaluate the product
P(2) = 0.079704
Approximate
P(2) = 0.08
Hence, the probability that two of three football games will go to into overtime is 0.08
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The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°.
A) Use the Law of Cosines to find the length of the diagonal.
A) Use the Law of Sines to find the length of the shorter base.
Round your answers to the nearest hundredth.
You must show all of your work to receive credit.
The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
How to determine the lengthThe cosine rule is given as;
[tex]c = \sqrt{a^2 + b^2 - 2ab cos \alpha }[/tex]
c = length of the diagonal
a = base length = 22 feet
b = 7 feet
[tex]c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}[/tex]
[tex]c = \sqrt{533 - 308 * 0. 7660}[/tex]
[tex]c = \sqrt{533 - 235. 93}[/tex]
[tex]c = \sqrt{297. 072}[/tex]
[tex]c = 17. 24[/tex] feet
Using sine rule
[tex]\frac{a}{sin A } = \frac{c}{sin C}[/tex]
[tex]\frac{a}{sin 70} = \frac{17. 24}{sin 40}[/tex]
Cross multiply
[tex]a[/tex] × [tex]sin 60[/tex] = [tex]c[/tex] × [tex]sin 70[/tex]
[tex]a[/tex] × [tex]0. 8660[/tex] = [tex]17. 24[/tex] × [tex]0. 9397[/tex]
[tex]a = \frac{16. 20}{0. 8660}[/tex]
a = 18. 7 feet long
Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
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The write right company manufactures ballpoint pens and has been experiencing a 5% rate of defective pens. modifications are made to the manufacturing process in an attempt to improve quality, and the manager claims that the modified procedure is better, because a test of 50 pens shows that only one is defective. a. assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective. b. assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective. c. what probability value should be used for determining whether the modified process results in a defect rate that is less than 5%? d. what do you conclude about the effectiveness of the modified production process?
a. The probability that exactly one is defective is 0.2025
b. The probability that none will be defective is 0.0769
c. The probability rate that should be used is 2%
d. The modified production process is better.
The question has to do with binomial probability.
What is binomial probability?Binomial probability is probability in which the event can only have two values or is binary.
Given the binomial probability formula,
P(X = x) = ⁿCₓpˣ(1 - p)ⁿ ⁻ ˣ
where
p = probability of defective = 5% = 0.05 and n = 50a. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective.For the probability that exactly one is defective, x = 1
So, P(x = 1) = ⁵⁰C₁p¹(1 - p)⁵⁰ ⁻ ¹
= ⁵⁰C₁p(1 - p)⁴⁹
= ⁵⁰C₁(0.05)(1 - 0.05)⁴⁹
= ⁵⁰C₁(0.05)(0.95)⁴⁹
= 50(0.05)(0.95)⁴⁹
= 50(0.05)(0.081)
= 0.2025
So, the probability that exactly one is defective is 0.2025
b. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective.For the probability that exactly one is defective, x = 0
So, P(x = 0) = ⁵⁰C₀p⁰(1 - p)⁵⁰ ⁻ ⁰
= ⁵⁰C₀(1 - p)⁵⁰
= ⁵⁰C₀(1 - 0.05)⁵⁰
= ⁵⁰C₀(0.95)⁵⁰
= 1 × (0.95)⁵⁰
= 0.0769
So, the probability that none will be defective is 0.0769
c. What probability value should be used for determining whether the modified process results in a defect rate that is less than 5%?
Since the modified result results in a defective rate of one out of 50 pens.
The probability rate that should be used is p = number of defective pens/total number of pens = 1/50
= 1/50 × 100 %
= 2%
The probability rate that should be used is 2%
d. What do you conclude about the effectiveness of the modified production?Since the defective rate of the modified production process is 2% which is less than that of the previous production process which is 5%, the modified production process is better.
So, the modified production process is better.
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Quincy uses the quadratic formula to solve for the values of x in a quadratic equation. He finds the solution, in simplest radical form, to be x
Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:
"Zero, because the discriminant is negative".
A quadratic equation is a polynomial of degree 2, in a single variable x.
The standard form of a quadratic equation is ax² + bx + c = 0.
The quadratic formula is used to find the solution(s)/root(s) of this equation.
The quadratic formula is:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
In this formula, [tex]b^2-4ac[/tex] is called the discriminant (D).
The solution(s)/root(s) of the equation, depends on this discriminant value as follows:
When D > 0, the roots of the equation are real and distinct.When D = 0, the roots of the equation are real and equal.When D < 0, then no real roots exist.In the question, we are given that the simplest form of Quincy's equation in the radical form was,
[tex]x = \frac{-3 \pm \sqrt{-19} }{2}[/tex].
Comparing this to the quadratic formula,
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
we get the discriminant (D) = -19.
Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:
"Zero, because the discriminant is negative".
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For complete question, refer to the attachment.
A psychologist treats 16 patients and records the number of sessions required to complete a behavioral therapy treatment for each patient. she computes ss = 800. assuming the 16 patients constitute all patients under her care (so the population of her patients), what is the standard deviation for these data?
Hence, the standard deviation for these data is 7.1 sessions
In statistics, the standard deviation is a measure of the volatility or variance of a set of values. [1] A low standard deviation indicates that the values tend to be close to the mean of the set (also known as the mean), and a high standard deviation indicates that the values are more widely distributed. indicate.
Standard deviation can be abbreviated as SD, and in mathematical texts and equations, it is most commonly represented by the Greek lower σ (sigma) for population standard deviation or the Latin letter s for sample standard deviation. It is a target.
The standard deviation of a random variable, sample, population, dataset, or probability distribution is the square root of its variance. It's algebraically simple, but it's actually less robust than mean absolute deviation. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.
Expression
\ sigma = {\ sqrt {\ frac {\ sum (x_ {i}-{\ mu}) ^ {2}} {N}}}
\ sigma = Population standard deviation
N = size mother Population
x_i = Arbitrary value from population
\ mu = Population mean
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