After solving, the value of Test statistic z is 1.449.
In the given question,
A sample of 1700 computer chips revealed that 36% of the chips fail in the first 1000 hours of their use.
The company's promotional literature states that 39% of the chips fail in the first 1000 hours of their use.
Then we have to find the value of z statistic.
Hypothesized proportion (p) = 36%=0.36
Sample proportion (p') = 39% = 0.39
Sample size (n) = 1700
Hence,
Test statistic z
z= (0.76-0.78)/√(0.78* 0.22/900)
z= (-0.02)/√(0.78* 0.000244)
z= -0.02/√0.00019032
z= -0.02/0.0138
z = -1.449
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If a 16-foot utility pole is connected to a cable
that is attached to the ground 12 feet from the
base of the pole, find then length of the cable?
Answer:20 ft
Step-by-step explanation:
Using Pythagoras' Theorem:
[tex]h^{2} = a^{2} +b^{2} \\h^{2} = 16^{2} +12^{2} \\h^{2} = 256+144h^{2} = 400\\\\[/tex]
Now you want to get h alone. To do that you need to get rid of the squared by finding the square root of 400.
[tex]h=\sqrt{400}\\h=20[/tex]
Need help, please!
Is a^+b^6 = (a²+b²)(a^4-a²b^2+b^4) an identity? Explain or show your reasoning.
Expression a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴) is an identity, by left-hand term and right-hand term property.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)
To prove that the given expression is an identity,
Solve left-hand term,
Substitute a² = x, b² = y
a⁶ + b⁶
= x³ + y³
Use formula x³ + y³ = (x + y)(x² - x y + y²)
= (x + y)(x² - x y + y²)
Again substitute x = a², y = b², expression will be,
= (a² + b²)(a⁴ - a²b² + b⁴)
Hence, a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)
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Is 700% of 6 less than 10,greater than 10 but less than 100,or greater than 100?
Greater than 100. 700% of 6 is 42.
a right triangle's height is 5 times the length of its base. if the area of the triangle is 160, what is its height?
If a right triangle's height is 5 times the length of its base and the area of the triangle is 160, then the height of the triangle is 40 units
A right triangle's height is 5 times the length of its base
Consider the length of the base as b and the height as h
h = 5b
The area of the triangle = 160 square units
The area of the triangle = 1/2 × b × h
Where b is the base of the triangle
h is the height of the triangle
Substitute the values in the equation
1/2 × b × h = 160
1/2 × b × 5b = 160
1/2 ×5b^2 = 160
5b^2 = 320
b^2 = 320/5
b^2 = 64
b = [tex]\sqrt{64}[/tex]
b = 8 units
Then the height of the triangle h = 5b
= 5 × 8
= 40 units
Therefore, the height of the triangle is 40 units
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21 out of 300 equals what percent
Answer:
7%
Step-by-step explanation:
When trying to figure out percentages, we can try to use a proportional relationship. Percent means out of a hundred, and since we don't know the percentage on top, we can mark it as ?.
21/300 = ?/100
To figure this out quickly, we can try figuring out how many times we need to multiply or divide to get to the next number. Between 21 and ?, we can't do anything because we are unsure of what ? is.
Between 300 and 100, we can notice that to get to 100, we must divide by 3. 300/3 = 100
This means that the first ratio is three times the amount of the second ratio, which means that the second ratio is 1/3 of the first.
We can multiply 21 by 1/3 (or divide by 3), which will get us to 7.
7/100 = 0.07 = 7%
the regression equation netincome = 2,277 + .0307 revenue was estimated from a sample of 100 leading world companies (variables are in millions of dollars). (a-1) calculate the residual for the x, y pair ($41,078, $8,301).
From a sample of 100 leading world companies we can estimate the residual value is 4,762.9054 .
It is given that,
Regression equation net income = 2277+0.0307
From a sample of 100 leading world companies we can estimate the revenue.
(a-1)
for the (x,y) pair, x = $41,078 and y = $8,301 or it is represented as ($41,078 , $8,301)
then the above (x,y) pair's residual value is e = y - ÿ
ÿ = 2277+0.307x
= 2277+0.0307(41078)
= 2277+1261.0946
= 3538.0946
Thus, e = y - ÿ
so, e = 8301 - 3538.0946
= 4762.9054
Hence, the residual value = 4,762.9054
To calculate the correlations between a dependent variable and one or more independent variables, a statistical technique grouping together several statistical techniques known as regression analysis is utilized. Revenue is the entire amount of money received from the sale of goods or services related to a company's main operations. Revenue, also known as gross sales, is often referred to as the "top line" because it appears at the top of the income statement. The residual value, also known as salvage value, is the estimated value of a fixed asset at the end of its useful life or lease term.
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PLS ACTUALLY ANSWER BOTH REASONS !!!!! 100 PTS CHOICES ARE THE SAME FOR BOTH
The blanks in this two-column proof should be completed (filled) as follows:
Statements Reasons_______________
ΔADB ≅ ΔCDB HL.
AD ≅ CD CPCTC.
What is the Right Triangles Similarity Theorem?In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.
What is CPCTC?In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent i.e AD ≅ CD.
Additionally, HL is an acronym for hypotenuse leg and it states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.
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Answer:
ΔADB ≅ ΔCDB HL.
AD ≅ CD CPCTC.
Step-by-step explanation:
or what the guy said on top :D
let n be a positive integer and suppose n distinct lines are drawn in the plane. no two of these lines are parallel, and no three of these lines intersect at a common point. prove that these lines divide the plane into n 0 c n 1 c n 2 regions.
There are 0 lines, 1 regions, and no line junctions. There are always k+1k+1 regions and kk intersections added whenever a line is added and crosses k other lines.
Another perspective is that k+1k+1 areas are added for each line and k intersections added (the number of added lines and intersections).Consequently, the total number of regions is 1 plus the sum of the number of lines and junctions.The number of intersections is 1 + the number of lines. There are (n2) (n2) crossovers with nn lines (if no two lines are parallel and no three lines are coincident). Therefore, there are (n2) +n+1=n(n1)/2+n+1=n2+n+2/2 areas instead of (n2) +n+1=n(n1)/2+n+1=n2+n+2/2).
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In triangle def, m∠d = (2x 19)°, m∠e = (3x 24)°, and m∠f = 87°. determine the degree measure of the exterior angle to ∠d. 54° 39° 141° 126°
Each corner of a triangle can form an exterior angle of the triangle by extending one side of the triangle. As we can see in above picture, where 'w' is exterior angle of angle 'z'.
The measure of the exterior angle to ∠d is 126°. So, the correct option is option (D).
We have given that,
A ∆DEF such that m∠d = (2x + 19)°,
m∠e = (3x + 24)°, and m∠f = 87°.
we have to find out the degree measure of the exterior angle to ∠d.
As we know that sum of angles of triangle is equal to 180° .
so, m∠d + m∠e + m∠f = 180°
=> (3x + 24)° + (2x + 19)° + 87° = 180°
=> (5x + 24 + 19 + 87)° = 180°
=> 5x + 130° = 180°
=> 5x = 50°
=> x = 10°
plug this value in angle d , angle e we get ,
m∠d = (3 ×10 + 24 )° = 54°
We can see that adding the angle measurement d and the exterior angle measurement gives d = 180 degrees. This is because they are a pair of adjacent angles and both lie on a straight line.
measure of Exterior angle of ∠d + measure of ∠d = 180°
Measure of exterior angle of ∠d
= 180° - m∠d
= 180° - 54° = 126°
Hence, the measure of exterior angle of d is 126°.
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Write an equation for the nth term of the arithmetic seqeuence. Then find a10. 12,1,112,2,.
An equation for the nth term of the arithmetic sequence: an = n - 6.
ad 10th term a10 = 4.
Define the term arithmetic sequence?A sequence of a form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.A common difference of the sequence is d, and the number an is the first term.The formula for the nth term of the
an = a + (n -1)d
In which,
a = initial termd = common differencen = total number of termsThe arithmetic sequence is given as-
−5,−4,−3,−2, ...
Then, the equation will be
d = a2 - a1
d = -4 - (-5) = 1
an = a + (n -1)d
an = -5 + n - 1
Put n = 10 in the equation.
a10 = 10 - 6
a10 = 4
Thus, the 10th term of the sequence is 4.
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The correct question is-
Write an equation for the nth term of the arithmetic sequence. Then find a10.
−5,−4,−3,−2, ...
Without graphing or plugging in any values, enter a point that lies on y – 5 = 2(x + 9).
For the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that, the equation of the line is
y – 5 = 2(x + 9)
Compare the equation with the standard equation as
y-y₁=m(x-x₁)
y – 5 = 2(x + 9).
y-5=2(x-(-9)
Where x₁ and y₁ are the points on which the line lies.
Thus, for the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).
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The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 59.1. O b. 7.688. O C. 7.018. O d. 49.25.
The point estimate of the population standard deviation is Select one is 5.4558.
Given data
9,13,15,15,21,24
We have to find first mean
Here n=6
[tex]$\begin{aligned} \text { mean } \bar{x} & =\frac{\sum x_i}{n} \\ & =\frac{9+13+15+15+21+24}{6} \\ & =\frac{97}{6} \\ & =16.166\end{aligned}$[/tex]
[tex]$\therefore$[/tex] Standard deviation
[tex]S=\sqrt{\frac{\sum\left(x_i-x\right)^2}{n-1}}$$[/tex]
S= root (9-16.(66)^2+(13-16.166)^2+(15-16.166)^2+(15-16.166)^2+(21-16.166)^2+(25- 16.166)^2/(6-1)
[tex]\begin{aligned}& =\sqrt{\frac{148.833336}{5}} \\& =\sqrt{29.7666} \\& =5.4558\end{aligned}[/tex]
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Answer:
Step-by-step explanation:
b) 7.688 The point estimate of the population standard deviation is 7.688. The point estimate of a population parameter is the estimate of the population parameter based on a single sample. In this case, the point estimate of the population standard deviation is the sample standard deviation, which is a measure of the spread or variability of the sample data. To calculate the sample standard deviation, we need to first calculate the sample mean, which is the average of the values in the sample. In this case, the sample mean is (9 + 13 + 15 + 15 + 21 + 24)/6 = 14.5. We can then use this value to calculate the sample standard deviation, which is √(((9-14.5)² + (13-14.5)² + (15-14.5)² + (15-14.5)² + (21-14.5)² + (24-14.5)²)/6) = 7.688. This is the point estimate of the population standard deviation. The other answer choices are not the sample standard deviation.
please
help I will give brainly
The distance AC to be covered for the given triangle will be 429.94 meters.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
As per the given triangle,
By cosine law,
Cos∠ABC = (220² + 430² - AC²)/(2 × 220 × 430)
Cos∠ABC = (233300 - AC²)/189200
Cos(180° - 75°) = (233300 - AC²)/189200
(233300 - AC²) = -48968.56
AC² = 184331.4367
AC = 429.94 meter
Hence "The distance AC to be covered for the given triangle will be 429.94 meters".
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I need help with a linear equation.
The slope (-8) of the linear equation that is represented by the table, is the amount Austin pays each week, which is $8.
What is the Slope of a Linear Equation?A linear equation which is given as y = mx + b, has a slope value which represents the change in y over a change in x and is given by the value of m in the linear equation.
If a table is said to represent a linear equation, the slope of the linear equation, which can also be called the unit rate, can be found by using two pairs of values from the table to calculate the change in y over the change in x.
Given that the table above represents a linear equation where L is dependent on the value of t, it means that slope of the linear equation represents the amount Austin paid back each week.
Find the slope using two points, (2, 24) and (4, 8):
Slope (m) = (24 - 8) / (2 - 4)
m = 16/-2
m = -8
Therefore, this means that Austin pays $8 every week.
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help w this, dont guess
does someone mind helping me with this question? Thank you!
Answer:
50,000
Step-by-step explanation:
1,750 x 2 = 3,500
25,000 x 2 = 50,000
PLS HELP!!! I really need help!
Use substitution to solve the system.
5x + 4y = 9
-2x + y = -14
Answer:
x=9/5 − 4y/5
x = 7 + y/2
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
louisa walks from her school 40 feet south and then walks 100 feet east. what is the shortest distsnce louisa is from her school? round to the nearest tenth
The shortest distance Louisa is from her school is 107.7 feet
How to determine the shortest distance from her school?From the question, we have the following parameters that can be used in our computation:
East = 100 feet
South = 40 feet
The shortest distance from her school is calculated using the following theorem
Shortest distance = √(East² + South²)
Substitute the known values
Shortest distance = √(100² + 40²)
Evaluate
Shortest distance = 107.7
Hence, the shortest distance = 107.7 feet
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Drag the tiles to the correct boxes to complete the pairs.
The correct boxes to the complete pairs are,
12 - 1/2r → (-8 - r) + (2r - 4)
r - 13/6 → (7r - 3/2) - (2/3 + 6r)
13r + 20 → (6r + 7) + (13 + 7r)
-12 + r → (-8 - r) + (2r - 4)
What is simplified expression?
Writing a similar expression devoid of similar terms is what is meant by the expression "simplify." In other words, we will rewrite the expression using the fewest number of terms.
Consider, the given expressions
(1) (6r + 7) + (13 + 7r)
Simplifying this,
6r + 7 + 13 + 7r
13r + 20
(2) (13 - 3/2r) - (1 - r)
Simplifying this,
13 - 3/2r - 1 + r
12 - 1/2r
(3) (-8 - r) + (2r - 4)
Simplifying this,
-8 - r + 2r - 4
-12 + r
(4) (7r - 3/2) - (2/3 + 6r)
Simplifying this,
7r - 3/2 - 2/3 - 6r
r - 13/6
Hence, the correct boxes to the complete pairs are,
12 - 1/2r → (-8 - r) + (2r - 4)
r - 13/6 → (7r - 3/2) - (2/3 + 6r)
13r + 20 → (6r + 7) + (13 + 7r)
-12 + r → (-8 - r) + (2r - 4)
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Complete question:
Complete question is attached below,
The figure is made up of a cone and a cylinder.
To the nearest whole number, what is the volume of this figure?
Use 3.14 to approximate π . Round only your final answer to the nearest whole number.
Enter your answer in the box.
The volume of the composite shape is 38mm³(nearest whole number)
What is a composite solid?A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes.
The volume of a the composite solid above = volume of cone + volume of cylinder
volume of cone = 1/3πr²h
=1/3×3.14×2²×3
= 12.56mm³
volume of the cylinder = πr²h
= 3.14×2²×2
= 25.12mm³
therefore the volume of the shape = 12.56+25.12
= 37.68mm³
= 38mm³( nearest whole number)
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urgent help needed the question is written in the image below plss
#1= 36
#2=81
#3= 32
#4=125
let x and y be i.i.d. unif(0, 1). (a) compute the covariance of x y and x −y. (b)arex y andx−y independent?
⇒ Yes X+Y and X-Y are independent
What is covariance?
Covariance is a measure of the combined variability of two random variables used in probability theory and statistics. The covariance is positive if the greater values of one variable primarily match the greater values of the other variable, and the same is true for the lesser values.
Define U=X+Y, V=X−Y
Then, [tex]x=\frac{(U+V)}{2}[/tex], and
[tex]Y=\frac{(U-V)}{2}[/tex]
Find the Jacobian J for the transformation.
Then, fU,V(u,v)= fX(x=(u+v)/2) fY(y=(u−v)/2)|J|
You will find that fU,V(u,v) factors into a function of u alone and a function of v alone. Thus, by the Factorization thm, U and V are independent.
b) Yes X+Y and X-Y are independent
a) Since , X+Y and X-Y are independent,
COV(X+Y , X-Y) = 0 Answer
Cov(X+Y , X-Y) = 0
b)
Yes these are independent
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Factor each polynomial
Answer:
(x + 7)(x² - 8)
Step-by-step explanation:
x³ + 7x² - 8x - 56 =
let's put the total multiplier x² out of brackets
x²(x + 7) - 8x - 56 =
let's put the total multiplier -8 out of brackets
x²(x + 7) - 8(x + 7) =
let's put the total multiplier (x + 7) out of brackets
(x + 7)(x² - 8)
Calculate the social security and Medicare deductions for the following employee assume a tax rate of 6.2% on $128,400 for social security and 1.45% for Medicare. Logan has a cumulative earnings before this pay period was $128,300 , and pay amount this period was$3,000. What is the social security and what was the medicare
The social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots
Main body:
Cumulative Earnings before this pay period = $128,300
pay amount this period = $3000
tax rate of 6.2% on social security = 6.2%
effective earning = 128300 = 3000
= 125300
social security deduction = 6.2 % of 125300
⇒ 6.2 *125300 /100
⇒$7768
Medicare deductions = 1.45%
⇒ 1.45*125300/100
⇒$1816
Hence , the social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
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in order to calculate the correlation between two variables related to the same sample what do you need to calculate first?
In order to calculate the correlation between two variables related to the same sample you need to calculate first the mean of each variable.
Before determining the correlation, the covariance of the two variables in the issue must always be computed. The standard deviation of each variable is then needed. The correlation analysis is calculated by dividing the covariance even by combination of a standard deviations of two or more variables.
A correlation is a statistical measurement of the two-variable connection. The measure works best with parameters that have a linear connection with one another.
The degree of the relationship between two variables is examined using correlation. To get the correlation between two variables, divided the covariance value by the standard deviation of both variables. Correlation analysis for two variables in the same sample should be performed. If you run a survey with two factors, a responder should be able to answer both variables at a glance. Furthermore, other participants' replies to the parameter might be evaluated for a correlation test.
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mary lee's natural food store sells a combination of teas. the most popular is a mixture of a tea that sells for per pound with one that sells for per pound. if she needs of tea that will sell for per pound, how many pounds of each tea should she use?
She may thus combine 21 pounds of tea priced at $3 and 14 pounds of tea priced at $2 to create tea that costs $2.6 per pound.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Here,
Let 3x be the pounds of tea for $3 and 2x be the pounds of tea for $2.
Total required pounds=35
3x+2x=35
x=35/5
x=7
So, She can add 21 pounds of tea for $3 and 14 pounds of tea for $2 to make the tea that is $2.6 per pound.
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12 is 30% of what number?
Answer: 3.6
Step-by-step explanation:
Step 1: 30/100 = x/12
Step 2: Multiply 12x30 and then divide it by 100
The diameter, d, of the circle below is 77 cm.
What is the circumference of the circle?
Give your answer to 1 d.p.
77 cm
circumference = nd
Answer:
C ≈ 241.9 cm
Step-by-step explanation:
the circumference (C) of the circle is calculated as
C = πd ( d is the diameter )
here d = 77 , then
C = π × 77 ≈ 241.9 cm ( to 1 dec. point )
Solve using substitution.
y = –7x − 8
y = 2x + 10
expected counts 153 94.5 63 49.5 45 45 enter the test statistic - round to 4 decimal places. test statistic
On solving the provided question, we got that - 0.000005178 as the P-value,the null hypothesis is a common statistical theory that contends that no statistical relationship
How do you define a null hypothesis?Using a single observed variable to compare two sets of observed data and measured phenomena, the null hypothesis is a common statistical theory that contends that no statistical relationship and significance exists.
h0; no change in beverage preferences
h1: alterations in drink preferences
alpha = 0.05
We find the test statistics' solution.
The attachment underwent the chsquare test.
Chi-square: (O-E)2/E
Chi square is 32.30188.
[tex]number of degrees of freedom = n-1 = 6-1 = 5[/tex]
I determined the p value using the chi distribution tool in Excel.
CHIDIST(3.20188, 5) =
0.000005178 as the P-value
We reject the null hypothesis since the pvalue is less than 0.05 and come to the conclusion that there is enough evidence to support the shift in drink preferences.
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