Expected frequencies must be equal for all groups is correct option.
Expected frequency of all groups in chi square test should not be equal initially to perform the test.To help establish whether observed results are consistent with expected outcomes and to rule out the possibility that observations are the result of chance, a chi-square test is utilized. When data are being evaluated from a random sample and the variable in issue is a categorical variable, a chi-square test is applicable.Chi-square distributions are helpful for testing hypotheses because of how closely they resemble the conventional normal distribution. Many significant statistical tests and theories revolve around the standard normal distribution, which is a normal distribution with a mean of zero and a variance of one.To know more about frequency check the below link:
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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.
is it possible to use the law of cosines to solve for one angle in a triangle?
Yes, it is possible to use the law of cosines to solve for one angle in a triangle.
The law of cosines states that in any triangle, the square of the length of any side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) minus twice the product of those sides and the cosine of the angle between them (C):
c^2 = a^2 + b^2 - 2ab * cos(C)
If you know the lengths of all three sides of a triangle (a, b, and c), you can use the law of cosines to solve for the cosine of one of the angles (C). Once you have the cosine of the angle, you can use the inverse cosine function (also known as the arccosine) to find the measure of the angle in degrees.
For example, if you know the lengths of sides a and b and the measure of angle C in a triangle, you can use the law of cosines to find the length of side c:
c = sqrt(a^2 + b^2 - 2ab * cos(C))
Alternatively, if you know the lengths of sides a and c and the measure of angle B in a triangle, you can use the law of cosines to find the length of side b:
b = sqrt(c^2 - a^2 - 2ac * cos(B))
In both cases, once you have found the value of one of the sides, you can use the law of sines to find the measure of the remaining angle in the triangle.
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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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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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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a die is rolled until the first time t that a six turns up, what is the probability distribution for t
The probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.
What is a probability distribution?
A probability distribution is a function that describes the probabilities of different outcomes in a random event or experiment. It is used to represent the likelihood of different outcomes occurring in a given situation.
In the case of rolling a die until the first time that a six turns up, the probability distribution for t (the number of rolls it takes to get a six) would describe the probability of getting a six on each roll.
The probability of getting a six on the first roll is 1/6, since there is a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the second roll is 1/6, since there is still a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the third roll is also 1/6, and so on.
The probability distribution for t in this case can be represented by the following table:
t Probability
1 1/6
2 1/6
3 1/6
4 1/6
5 1/6
... ...
This probability distribution indicates that the probability of getting a six on the first roll is 1/6, the probability of getting a six on the second roll is 1/6, and so on.
Hence, the probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.
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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
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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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:
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.
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].
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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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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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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what is the width of the frame?
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)
96% of Americans report eating a diet that includes meat, 3.5% of Americans claim to be exclusively vegetarian, and 0.5% claim to be strictly vegan. Of a random sample of undergraduates in the University of Virginia dining hall (n = 175), 156 students report eating a diet that includes meat, 11 report being exclusively vegetarian, and 8 are strictly vegan.
5. State the test you would use to determine if the observed and expected frequencies of diets are consistent. List the conditions required for this test and verify that they are satisfied.
6. How many students would you expect to eat meat, be exclusively vegetarian, and be a strict vegan?
7. Calculate the chi-square statistic, the degrees of freedom associated with it, and the p-value.
8. Based on the p-value calculated in Question 7, what is the conclusion of the hypothesis test at α = 0.05? Interpret your conclusion in context of the question.
A study about the diet of undergraduate students,
5) Chi-square statistic test , would use to determine if the observed and expected frequencies of diets are consistent. With null hypothesis as the observed and expected frequencies of diets are consistent.
6) The excepted students to eat
meat = 165
exclusively vegetarian= 6
strict vegetarian= 1
7) Chi-square statistic value is 62.755 and degree of freedom are 2 . The critical value for Chi-square statistic is 0.00001
8) P-value< 0.05, so reject the null hypothesis.
Therefore there is no sufficient evidence to support that the observed and expected frequencies of diets are consistent.
A random sample of undergraduates in the University of Virginia dining hall.
Sample size , n = 175
Three categories are given as shown in above table with percentage of report eating a diet.
Report also consists observed values about the number of students diet including the three different categories
5) The Chi-square test would use to determine the required result. Consider Null and alternative hypothesis as :
H₀ : the observed and expected frequencies of diets are consistent
Hₐ : the observed and expected frequencies of diets are not consistent
χ² =∑(Oᵢ - Eᵢ)²/Eᵢ
where, χ² --> chi-square cofficient or value
Oᵢ --> observed values which are provided
Eᵢ --> excepted values
Excepted values , Eᵢ = n× p
here we assume that,
These categories are independentindividuals are selected randomly6) The number of students would you expect to eat meat = 168
The number of students would you expect to eat exclusively vegetarian
= 6.125 ~ 6
The number of students would you expect to eat strict vegetarian = 0.875 ~ 1
7) Degree of freedom,df = k - 1 = 2, where k denotes total number of categories here
Chi-square statistic, χ² = ∑(Oᵢ - Eᵢ)²/E
χ² = 62.755
Using chi-square table, the critical chi-square value for χ² = 62.755 and degree of freedom 2 is 0.00001 ..
8) Significance level, alpha = 0.05
As we see that p-value = 0.00001< alpha = 0.05
So, we reject the null hypothesis.
Thus, there is no sufficient evidence to support null hypothesis.
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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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-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
for an closed cylinder with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 6 cm3
The dimensions giving the minimum surface area are r = 0.98 cm approx. and h = 1.998 cm .
What is surface area?
The surface area of a solid object could be a live of the full area that the surface of the article occupies.
Main body:
The surface area of the closed cylinder is given by,
S = 2πr²+2πrh
And volume is given by,
V = πr²h
Where, R is radius and h is height of cylinder.
Volume is given to be 6 cm³.
V = πr²h = 6
h = 6/πr²
Inserting this value of h in Surface area equation, we get,
S = 2πr²+ 2πr ( 6/πr²)
S = 2πr² + 12 /r
Now differentiating wrt x to find minimum, inserting ds/dr = 0 , we get,
4πr = 12/r²
r = (3/π)¹/³
r = 0.98 cm approx.
h = 6/π *(0.98)²
h = 6/3.017
h = 1.998 cm
Hence ,the dimensions giving the minimum surface area are r = 0.98 cm approx. and h = 1.998 cm .
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A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm) , and the foot length, in cm , for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown.
The figure presents a scatterplot in a coordinate plane. The horizontal axis is labeled Foot Length, in centimeters, and the numbers 18 through 34, in increments of 2, are indicated. The vertical axis is labeled Height, in centimeters, and the numbers 150 through 190, in increments of 10, are indicated. There are 65 data points in the scatterplot, and a trend line is given as follows. Note that all values are approximate. The data points begin in the lower left part of the plane at the point with coordinates 19 comma 160. The data points trend upward and to the right and end with the coordinates 33 comma 190. The least-squares regression line begins at the point 18 comma 153, and slants upward and to the right at a constant rate to end at the point 35 comma 197.
Term Coef (SE) Coef T -Value P -Value
Constant 105.08 6.00 17.51 0.000
Foot length 2.599 0.238 10.92 0.000
S=5.90181 R–sq=65.42%
(a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm .
(b) The standard deviation of the residuals is s=5.9 . Interpret the value in context.
Unit 2 Progress Check: FRQ
Aubree Flores
As per the least-squares regression,
a) The residual for the high school senior with a foot length of 20cm and a height of 160cm is 2.94
b) As per the given standard deviation, the value of the context 5.9
The term standard deviation in math is defined as a measure of how dispersed the data is in relation to the mean.
Here we have given that the random sample of 65 high school seniors was selected from all high school seniors at a certain high school.
And we need to find following.
While we looking into the given question, as per the least-squares regression line, here the estimated height for a high school senior with a foot length of 20 cm is calculated as,
=> y = 2.599x + 105.08
Now, we have to apply the value of x as 20, then we get,
=> y = 2.599(20) + 105.08
=> y = 157.06
Therefore, the residual is calculated as,
=> 160 − 157.06 = 2.94
b) As per the given standard deviation, here the differences between each data point and its corresponding estimate varies with a standard deviation of 5.9 cm.
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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
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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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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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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Ajay and deepak can do an allocated work in 15 days and 10days respectively. They stated the work together but Deepak left after sometimes and ajay finished the remaining work in 5 days. After how many days (from the start)did Deepak leave
Answer:
Deepak have taken 5 days leave from the start of the work.
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]
(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.
Given the function:
f(x) = (3x+7)
What is the output of the function when the input is x = 9?
A 9
B 15
C 17
D 21
Answer isn't one of your options, it is 34.
Step-by-step explanation:1. Write the function.[tex]f(9) = (3(9)+7)[/tex]
3. Calculate.[tex]f(9) = (27+7)\\ \\f(9) = 34[/tex]
4. Conclude.[tex]f(9) = 34[/tex].