The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³) is equal to w = -1.
As given in the question,
Given equation is equal to :
7 ( w + 7 )³ = 7(6³)
Divide both the side of the equation by 7 we get,
⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7
⇒( w + 7 )³ = (6³)
Take cube root both the side of the equation we get,
⇒∛( w + 7 )³ = ∛(6³)
⇒ w + 7 = 6
Now subtract 7 from both the side of the equation we get,
⇒w + 7 - 7 = 6 - 7
⇒ w = -1
Therefore, the value of the variable 'w' for the given equation is equal to w = -1.
The complete question is:
Solve this equation:
7 ( w + 7 )³ = 7(6³)
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3. Carissa is considering job offers from two companies. Company A offered her a starting salary of $45,000 with a $2100 raise at the end of each year. Company B offered her a starting salary of $45,000 with a 4.2% raise at the end of each year. Let f(t) represent Carissa's salary at Company At years after accepting a position at Company A, and let g(t) represent Carissa's salary at Company B t years after accepting a position at Company B. a. Find a function formula for f. b. Find a function formula for g. C. If Carissa was expecting to work for 5 years before going back to school, which company do you think she should work for? Use your functions to justify your answer. I d. If Carissa was expecting to work for 10 years before going back to school, which company do you think she should work for? Use your functions to justify your answer.
Let f(t) be 51000+ (2100)t which represent Chelsea's salary at Company A and g(t) be 45000(1.041)t which Chelsea salary at Company B.
Chelsea's offer from company A includes a raise of $2100 annually and a starting salary of $45,000.
Since the increase is constant, the salary of Chelsea from Company A is a linear function, as can be seen here.
f(t) is salary of chelsea from company A after t years.
f(t) = 45000+ (2100)t
The offer made to Chelsea by company B includes a starting salary of $45,000 and an annual raise of 4.1%.
we can see here that raise is exponential, so raise is:
(1+4.1/100) = (1+0.041) = (1.041) per year.
Consequently, the salary of Chelsea from Company B is a function that is exponential.
g(t) is salary of chelsea from company B after t years.
g(t) = 45000(1.041)t
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suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. the time t is measured in seconds and the units for r(t) are measured in tonnes (metric tons) per second. note that r(t) is increasing over the interval [0, 6]. t 0 1 2 3 4 5 6 r(t) 2 10 18 32 44 54 60 (a) give upper and lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds. (use six equal subintervals.)
The lower estimate and upper estimate of the erupted materials of total q(6) quantity after 6 seconds is equal to 160 metric tons and 218 metric tons respectively.
As given in the question,
Reading of the rate is represented by r(t) in metric tons
Time interval in seconds:
t : 0 1 2 3 4 5 6
r(t) : 2 10 18 32 44 54 60
Lower estimate for the q(6) quantity of the erupted material after 6 seconds.
= r(0)(1) + r(1)(1) + r(2)(1) + r(3)(1)+ r(4)(1) + r(5)(1)
= 2 + 10 + 18 + 32 + 44 + 54
= 160
Upper estimate for the q(6) quantity of the erupted material after 6 seconds.
= r(1)(1) + r(2)(1) + r(3)(1)+ r(4)(1) + r(5)(1) + r(6)(1)
= 10 + 18 + 32 + 44 + 54 + 60
= 218
Therefore, the lower estimate and upper estimate of the total q(6) quantity after 6 seconds is equal to 160 metric tons and 218 metric tons respectively.
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Is it true n ⊥ p? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
No, the lines are not perpendicular because Line m has a slope of 2/3 and line n has a slope of 3/5.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
For two lines to be perpendicular if the slopes are reciprocal of each other.
line m: 2/3
line n: 3/5
Therefore,
n ⊥ p is False.
The slopes are not negative reciprocal of each other. so the lines are not perpendicular.
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2. A gas in a flexible container with volume 8L has a temperature of 400 K. If the temperature of the gas changes to 200 K, what is the expected new volume of the gas?
A. 2 L
B. 4 L
C. 16 k
D. 32 L
The volume of the gas becomes 4L. Option B is correct.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
From the ideal gas equation, we know that,
Volume is directly proportional to the temperature,
So,
V₁ / V₂ = T₁ / T₂
Where,
V₁ and T₁ are the initial pressure and temperature,
V₂ and T₂ are the final pressure and temperature.
Substitute the values,
8 / V₂ = 400 / 200
V₂ = 4
Thus, the volume of the gas becomes 4L. Option B is correct.
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Calculate the area, in square units, bounded by f(x) = 3x^3-3x^2-x+8 and g(x) = 2x^3 - 10x^2 + 29x + 8 over the interval [1, 5].
The area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8
over the interval [1, 5] is 164 square units.
What is meant by a function?Exactly one element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The domain and codomain of the function are, respectively, the sets X and Y as a whole.
The first presentation of the idea of function that is known about was developed by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. Originally, functions were used to depict the desired relationship between two varying values. For example, time affects the position of a planet. Up to the 19th century, the functions that were taken into consideration were differentiable.
Given,
f(x)=3x³-3x²-x+8
g(x) = 2x³- 10x² + 29x + 8
And the interval is [1, 5].
By using area formula,
A=[tex]\int\limits^a_b {f(x)-g(x)} \, dx[/tex]
A=[tex]\int\limits^a_b[/tex](Upper function-Lower function)dx
A=[tex]\int\limits^3_1[/tex][g(x)-f(x)]dx+[tex]\int\limits^5_3[/tex][f(x)-g(x)]dx
A=[tex]\int\limits^3_1[/tex](-x³-7x²+30x)dx+[tex]\int\limits^5_3[/tex](x³+7x²-30x)dx
A= (118/3)+(374/3)
A=164 square units.
Therefore, the area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8
over the interval [1, 5] is 164 square units.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answer: b. radius of the cone = 5; height of the cone = 12
Step-by-step explanation:
The volume of the cylinder is [tex]\pi (5^2)(4)=100\pi[/tex].
The only option that makes the same volume is option b. In this case, the volume is [tex]\frac{\pi}{3}(5^2)(12)=100\pi[/tex].
-7 - 4/4 I need this evaluated and j don’t see that in the thing
Answer:
-7 - 4/4
= -7 - 1
= -8
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Answer:
-8
Step-by-step explanation:
-7 - 4/4= -7 - 1= -8
a nail is measured with a ruler and its length is reported as 5.46 cm. select all the statements that are correct about the certainty and uncertainty represented in this recorded measurement.
If the nail is measured with a ruler and its length is 5.46 cm , then the correct statements are :
(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ;
(b) The uncertainty is in the final digit of the measurement .
The Uncertainty of a number helps to estimates in comparison of experimental numbers .
it is given that , the reported length of the ruler is = 5.46 cm ;
we know that ,
the uncertainty In any number , is present in last digit only ,
the place value of the last digit in 5.46 is 0.01 .
So , uncertainty can be expressed by reporting measurement as 5.46 ± 0.1 cm
Therefore , the correct statements about the certainty and uncertainty are (a) and (b) .
The given question is incomplete , the complete question is
A nail is measured with a ruler and its length is reports as 5.46 cm.
Select ALL the statements that are correct about the certainty and uncertainty represented in this recorded measurement.
(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ,
(b) The uncertainty is in the final digit of the measurement ,
(c) All three digits shown in the measurement are known with certainty ,
(d) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.01 cm .
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Show that the set of numbers in the interval [0,1] having decimal expansions using only odd digits is closed. Describe this set by a Cantor set type construction.
T be the set of all points x in [0,1] by a Cantor set type construction is x=∑∞n=1 qn/4n
for some sequence of qns with each qn∈{1,3}.
What is Cantor set type construction?
The Cantor set is a collection of points situated on a single line segment that possesses a variety of odd characteristics.
By deleting the center third of a line segment and then repeating the process with the remaining shorter segments, the Cantor ternary set, the most popular construction, is created. The ternary construction was only briefly described by Cantor as an illustration of a more basic concept—that of a perfect set that isn't dense anywhere.
According to the given question:
The proportion (i.e., measure) of the unit interval that is left can be determined by subtracting the entire length as the Cantor set is defined as the set of points that are not excluded.
T be the set of all points x in [0,1] by a Cantor set type construction is x=∑∞n=1 qn/4n
for some sequence of qns with each qn∈{1,3}.
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Pls help its due today!!! 50 points!!!
Answer:
Step-by-step explanation:
Part 1: true
(-4, -1) and (0, 2)
m = 2+1/0+4
m = 3/4
(0, -3) and (4, 0)
m = 0+3/4+0
m = 3/4
Part 2: true
It intercepts at (0, -3)
Part 3:
I can't really see what slope it says but if it says -3/5, then its true, otherwise it's false.
(5, -1) and (0, 2)
m = 2+1/0-5
m = 3/-5
m = -3/5
Part 4: false
Graph A would have 2 and Graph C would have different intersecting points.
Suppose that $800 was budgeted for the month. Determine the exact amount for each category
The exact amounts for each category are given as follows:
Landline: $120.Water: $104.Electric: $200.Gas: $136.Sanitation: $80.Cell phone: $160.How to obtain the exact amounts?The exact amounts for each category are obtained applying the proportion relative to the percentage of each category, that is, multiplying the decimal equivalent of the percentage by the total amount of $800.
Hence the amounts are given as follows:
Landline: 0.15 x 800 = $120.Water: 0.13 x 800 = $104.Electric: 0.25 x 800 = $200.Gas: 0.17 x 800 = $136.Sanitation: 0.1 x 800 = $80.Cell Phone: 0.2 x 800 = $160.Missing InformationThe pie chart with the categories and their percentages is given by the image shown at the end of the answer.
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Determine which integer in the solution set will make the equation true
Answer:
2
Step-by-step explanation:
First, we must add 14 to both sides to put the variable and coefficient alone.
4s - 14 = -6
+14 +14
4s = 8
s = 2
(30 points) The fixed costs of manufacturing basketballs in a factory are $1,400.00 per day. The variable costs are $5.25 per basketball. Which of the following
expressions can be used to model the cost of manufacturing b-basketballs in 1 day?
O $1,405.25b
o $5.25b-$1,400.00
O $1,400.00b+$5.25
O $1,400.00-$5.25b
The correct expression to model the cost of manufacturing b basketballs in 1 day is:
O $5.25b-$1,400.00
The fixed costs of manufacturing the basketballs are $1,400.00 per day, and the variable costs are $5.25 per basketball. To find the total cost of manufacturing b basketballs in 1 day, you need to add the fixed costs and the variable costs for each basketball.
The variable costs for b basketballs would be $5.25 * b. To find the total cost, you need to subtract the fixed costs of $1,400.00 from this amount. This can be represented by the expression $5.25b - $1,400.00.
The other expressions do not correctly represent the cost of manufacturing b basketballs in 1 day because they do not correctly account for both the fixed costs and the variable costs.
Find the volume of the composite solid (STEP BY STEP PLEASE) 15 POINTS
Answer: 226.19
Step-by-step explanation:
Using the formula for a cyclinder{ V=πr2h} and inputing the values given in the diagram, (the radius and height given) you get 28.27.
Then adding the cone's volume (V=πr2h/3) and inputing that values in the diagram (the radius and height) you get 197.92.
Adding those values you got from the cyclinder and cone together, you get the volume of the composite solid.
find the value of x. (4x-101)° (2x+3)
The value of x in . (4x-101)° = (2x+3) is 52°.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
The value of x. (4x-101)° = (2x+3)
Collect the like terms
4x - 2x = 3 + 101
2x = 104
Divide
x = 104 / 2
x = 52°
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Complete question
Find the value of x. (4x-101)° = (2x+3)
Who is the pattern made from sticks how many sticks would be in pattern number 6 in triangles 6 is the first and it adds 4 to make two
The number of sticks in pattern 6 is; 26
The nth term of the sequence formed is; aₙ = 4n + 2
How to find the arithmetic sequence?From the attached image, we see that;
Number of sticks in pattern 1 is 6
Number of sticks in pattern 2 is 10
Number of sticks in pattern 3 is 14
Thus, the sequence will be;
6, 10, 14, ...
This is an AP because the difference is 4.
The formula for the nth term of an AP is;
aₙ = a + (n - 1)d
where;
a is first term
n is position of term
d is common difference
In our sequence, first term; a = 6
Common difference; d = 10 - 6 = 4
Thus, the equation for the nth term is;
aₙ = a + (n - 1)d
aₙ = 6 + (n - 1)4
aₙ = 6 + 4n - 4
aₙ = 4n + 2
Now, substitute n = 6 in the above equation to find the number of sticks in pattern 6. This gives;
a₆ = 4(6) + 2
a₆ = 26
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The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p).^1(a) What is the meaning of the derivative f^1(8)? What are its units?
The derivative f'(8) gives the rate of change of the quantity (in pounds) of coffee sold as we increase the price (in dollars).
The units of the derivative are always output units from original function input units from original function . For the original function, the output is pounds of coffee sold, and the input is the price in dollars per pound.
Thus the units for f′(8) are pounds dollars/pound.(b) Is f′(8) positive or negative? Explain. We interpret the rate given by the derivative as the input increases, so the price per pound is increasing. From the law of supply and demand, as the price increases, the quantity sold decreases. Thus we expect
f′(8) to be negative.
The answers to both subparts are shown:
(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.
(B) The unit of f'(5) is pounds/dollar.
What is derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument.
Calculus's core tool is the derivative.
We may find the slope of a function at any point by using its derivative. We can find numerous derivatives by adhering to certain rules.
For instance: A constant value, such as 3, always has a slope of 0.
(A) Meaning of derivative of: f'(5)
We have: Q = f(p) ...(1)
Differentiating Q in relation to p results in:
qQ/dp = f'(p) ...(2)
The rate of change of the price per pound in relation to the volume of coffee sold is implied by equation (2).
If p = 5, we get:
qQ/dp = f'(5) ...(3)
The rate at which the price per pound changes in relation to the amount of coffee sold at $5 per pound is implied by equation (3).
(B) Unit of f'(5):
Equation (3)'s result that qQ/dp = f'(5) suggests that f'(5) units are pounds/dollar.
Therefore, the answers to both subparts are shown:
(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.
(B) The unit of f'(5) is pounds/dollar.
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Correct question:
The quantity (in pounds) of gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p). (a) What is the meaning of the derivative f '(5)? The rate of change of the price per pound with respect to the quantity of coffee sold. The supply of coffee needed to be sold to charge $5 per pound. The rate of change of the quantity of coffee sold with respect to the price per pound when the price is $5 per pound. The rate of change of the price per pound with respect to the quantity of coffee sold when the price is $5 per pound. The price of the coffee as a function of the supply. What are the units of f '(5)? dollars dollars/pound pounds/(dollars/pound) pounds dollars/(pound/pound) pounds/dollar
592 x 43 in standard algorithm
Answer:
25456
Step-by-step explanation:
592 over 43
592
x 43
multiply 3 by 2, 9 and 5. 3 by 2 is 6. 3 by 9 is 27. 3 by 5 is 15.
add a zero at the second row then,
multiply 4 by 2, 9, 5. 4 by 2 is 8. 4 by 9 is 36. 4 by 5 is 20.
if you aligned them properly, when you add them you should get 25456
I'll try to include a picture of my work, hopefully you can see it**
The t distribution is a family of similar probability distributions, with each
individual distribution depending on a parameter known as the
Group of answer choices
degrees of freedom
sample size
standard deviation
population mean
The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.
How are the degrees of freedom determined?
When calculating degrees of freedom, one is subtracted from the total number of items in the data sample. Degrees of freedom are frequently addressed in relation to different types of statistical hypothesis testing, like a chi-square.The number of independent bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. It is determined by subtracting the number of constraints from the sample size.Finding essential cutoff values for inferential statistical tests requires consideration of the degree of freedom. Degrees of freedom often (but not always) relate to sample size depending on the sort of study you conduct.Hence, the t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.
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HELP PLEASE the question and answer choices are on the picture, please help it’s an emergency
Answer:
Its the 3rd one
Step-by-step explanation:
Find the value of x in the figure
Please show all your work.
Answer:
x = 7/3.
Step-by-step explanation:
DE is parallel to BC and AD= DB and AD = EC.
So, AD/DB = (x+1)/(4x-6)
(x + 1)/(4x - 6) = 1
x + 1 = 4x - 6
1 + 6 = 4x - x
3x = 7
x = 7/3.
The integer 5 makes which of the following equation false
Answer:
(a) 3m +4 = 6m
Step-by-step explanation:
You want to know which of the equations is false when the value of the variable is 5.
3m +4 = 6m3(5) +4 = 19 ≠ 6(5) . . . . . the given equation is false for m=5
-5(t -7) = 10-5(5 -7) = -5(-2) = 10 . . . . true
17 = 4x -317 = 4(5) -3 = 20 -3 . . . . true
t +9 = 145 +9 = 14 . . . . true
what is the width of the frame?
For each of the values of GPD, use the regression equation to predict the carbon dioxide emission amount. Type either a numerical value or the word no. Do not round the answer. Units are in parentheses, so do not convert your answer 2.6 (trillions of dollars) (millions of metric tons) 4.0 (trillions of dollars) (millions of metric tons) 7.1 (trillions of dollars) (millions of metric tons
For each of the values of GPD, use the regression equation to predict the carbon dioxide emission amount is 1300.715.
What is carbon dioxide ?
Our atmosphere contains carbon dioxide, an odorless and colorless gas. According to its chemical composition, CO2, it is made up of one carbon atom joined to two oxygen atoms. It is a waste product created both by burning fossil fuels and by human bodies.
Given regression eq.
[tex]$$\hat{y}=166.92+115.725$$[/tex]
* Given [tex]$x=2.6$[/tex]
[tex]$$\begin{aligned}& \hat{y}=166.9(2.6)+115.725 \\& \hat{y}=549.665\end{aligned}$$[/tex]
* Given [tex]$x=4.0$[/tex]
[tex]$$\begin{aligned}& \hat{y}=166.9(4.0)+115.725 \\& \hat{y}=783.325\end{aligned}$$[/tex]
* Given [tex]$x=7.1$[/tex]
[tex]$$\hat{y}=166.9(7.1)+115.725$$[/tex]
[tex]\hat{y}=1300.715[/tex]
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6 3 points F L(2x-48) 32 W Using the diagram above find the value of x and use it to find the measures of all the missing angles. X = type your answer..... m/FOW= m/FLW= m/OLW= = type your answer... type your answer... type your answer.....
The value of x is 80
The measure of angle FOW, m ∠FOW, is 80°
The measure of angle FLW, m ∠FLW, is 112°
The measure of angle OLW, m ∠OLW, is = 68°
Calculating the measure of anglesFrom the question, we are to determine the measure of the missing angles
From the given diagram, we can write that
(2x - 48)° = x° + 32°
Solve for x
(2x - 48)° = x° + 32°
2x° - 48° = x° + 32°
Subtract x° from both sides of the equation
2x° - x° - 48° = x° - x° + 32°
x° - 48° = 32°
Add 48° to both sides of the equation
x° - 48° + 48° = 32° + 48°
x° = 32° + 48°
x° = 80°
Therefore,
x = 80
Calculating the m ∠FOW
m ∠FOW = x°
m ∠FOW = 80°
Calculating the m ∠FLW
m ∠FLW = (2x - 48)°
m ∠FLW = (2(80) - 48)°
m ∠FLW = (160 - 48)°
m ∠FLW = 112°
Calculating the m ∠OLW
m ∠OLW + m ∠FOW + m ∠OWL = 180° (Sum of angles in a triangle)
m ∠OLW + 80° + 32° = 180°
m ∠OLW + 112° = 180°
m ∠OLW = 180° - 112°
m ∠OLW = 68°
Hence, the measure of m ∠OLW is 68°
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If i have 2 apples and i get 69 times that, than i give three-ninths of it to a friend, how much would i have left?
Answer:
92 apples remaining
Step-by-step explanation:
2 * 69 = 138 apples
138 * (3/9) =
138 * (1/3) =
138 * 1/3 =
138/3 = 46 apples
138 - 46 = 92 apples remaining
Answer:
you have 2 apples
then you got it 69 times= 2×69 = 138
then you give 3 ninths to a friend
138/9 = 15.33
you gave it 3 one-ninths = 3× 15.33 = 46
so must be left with 138-46 = 92
Prove that a polynomial function f of odd degree has at least one real root. Hint: it may help to consider first the case of a cubic f(x)=a0+a1x+a2x^2+a3x^3.
the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.
Let f(x) = a0 + a1x + a2x2 + a3x3 be a polynomial function of odd degree 3.
We know that the degree of a polynomial is the highest power of the variable in the equation. Since the degree of f(x) is 3, then a3 ≠ 0.
Now, consider the Discriminant of the polynomial, which is defined as the expression below:
Discriminant = b2 - 4ac
In this case, b2 = a2^2, c = a0 and a = a3, thus the Discriminant is:
Discriminant = a2^2 - 4a0a3
Since a3 ≠ 0 (as mentioned before), the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.
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in a recent poll of 1,000 homeowners in the united states, one in eight homeowners reports having a home equity loan that he or she is currently paying off. using a confidence coefficient of 0.99, construct the confidence interval for the proportion of all homeowners in the united states that hold a home equity loan.
Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.)
Confidence interval to
For the proportion of all hometowners in the united states that hold a home equity loan, confidence interval is (0.0992, 0.1508).
We have given that in a recent poll of 1000 homeowners in the United states, one in eight homeowners reports havinf a home equity loan that he or she is curently paying off.
If one in eight reports having a home equity loan then for 1000 hometowners = 1000/8 = 125.
Sample proportion p = 125/1000 = 0.125
given that confidence coefficient = 0.99
α = 1 - confidence coefficient = 1 - 0.99
α = 0.01
z₀.₀₁ / 2 = 2.58
Therefore the interval estimate for the proportion of all homeowners in the United states that hold a home equity
= p ± z₀.₀₁/2 √p(1-p)/n
= 0.125 ± 2.58 √0.125(0.875)/1000
= 0.125 ± 2.58 √0.0001
= 0.125 ± 0.0258
= (0.125 - 0.0258,0.125 + 0.0258)
= (0.0992, 0.1508)
Hence (0.0992, 0.1508) is the confidence interval.
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The measures of the acute angles in the isosceles trapezoid are one-half times the measures of the obtuse angles. Write and solve a system of equations to find the measures of all the angles.
Answer:
[tex]\textsf{System of equations: \quad }\begin{cases}x=\dfrac{1}{2}y\\\\2x+2y=360\end{cases}[/tex]
[tex]\begin{aligned} \textsf{Solutions}: \quad x &= 120^{\circ}\\y &= 60^{\circ}\end{aligned}[/tex]
Step-by-step explanation:
An obtuse angle is greater then 90° and less than 180°.
An acute angle is less than 90°.
Therefore, from inspection of the given diagram:
x = obtuse angley = acute angleIf the measures of the acute angles are one-half times the measures of the obtuse angles:
[tex]\implies x=\dfrac{1}{2}y[/tex]
Angles in a quadrilateral sum to 360°.
[tex]\implies 2x+2y=360[/tex]
Therefore, the system of equations is:
[tex]\begin{cases}x=\dfrac{1}{2}y\\\\2x+2y=360\end{cases}[/tex]
Substitute the first equation into the second equation and solve for y:
[tex]\implies 2\left(\dfrac{1}{2}y\right)+2y=360[/tex]
[tex]\implies y+2y=360[/tex]
[tex]\implies 3y=360[/tex]
[tex]\implies \dfrac{3y}{3}=\dfrac{360}{3}[/tex]
[tex]\implies y=120[/tex]
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x=\dfrac{1}{2} \cdot 120[/tex]
[tex]\implies x=60[/tex]
Graph line segment BC with endpoints B(8 and
C(-4,5) and label the points.
Steps for solving:
Draw and label an x and y axis (make sure you include arrows).
Plot the given points.
Label the given points.
The graph of the Line Segment BC with the endpoints B(8,9) and C(-4,5) is shown below.
In the question ,
it is given that ,
the end points of the line segment is B(8,9) and C(-4,5) .
we have to graph the line segment BC.
first we mark the point on the coordinate plane , with point B and point C .
after that we join the points .
and the equation of the line segment is
(y - 5) = (9-5/8+4)*(x + 4)
(y - 5) = (1/3)*(x + 4)
3y - 15 = x + 4
x - 3y + 19 = 0
Therefore, the graph of the line segment BC is shown below.
The given question is incomplete , the complete question is
Graph line segment BC with endpoints B(8,9) and C(-4,5) and label the points.
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