Answer:
The correct option is d
[tex]f(1) = -5[/tex]
[tex]f(2) = 11[/tex]
The correct option is d
The correct option is c
the correct option is b
Step-by-step explanation:
The given equation is
[tex]f(x) = x^4 + x -7 =0[/tex]
The give interval is [tex](1,2)[/tex]
Now differentiating the equation
[tex]f'(x) = 4x^3 +7 > 0[/tex]
Therefore the equation is positive at the given interval
Now at x= 1
[tex]f(1) = (1)^4 + 1 -7 =-5[/tex]
Now at x= 2
[tex]f(2) = (2)^4 + 2 -7 =11[/tex]
Now at the interval (1,2)
[tex]f(1) < 0 < f(2)[/tex]
i.e
[tex]-5 < 0 < 11[/tex]
this tell us that there is a value z within 1,2 and
f(z) = 0
Which implies that there is a root within (1,2) according to the intermediate value theorem
In a sample of 800 adults, 214 think that most celebrities are good role models. Two us adults are selected from this sample without replacement. find the probability that both adults think most celebrities are good role models
Answer:
11449/160000
Step-by-step explanation:
The probability of selecting a single adult that thinks most celebrities are good role models is 214/800 = 107/400
The probability that both do is
(107/400)^2 =. 11449/160000
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
HELP PLEASE
Answer:
y=2/3x+1
Step-by-step explanation:
The slope is 2/3 and the y-intercept is 1.
the volume of a cuboid is 24cm² if the base is 6cm by 2cm find the height of the cuboid
Answer:
2cm
Step-by-step explanation:
h=v/(l)w
h=24/(6)2
h=24/12
h=2cm or 2cm²
How can I make the red segment less steep than the blue segment , and more steep than the green segment ?
A researcher classifies firefighters according to whether their gloves fit well or poorly and by gender. They want to know if there is a difference in the proportion of poorly fitted gloves and gender. At alpha = 0.01, use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly
Gloves fit well
Total
Answer:
Step-by-step explanation:
Hello!
The objective is to test if the proportion of "X: gloves fitness, categorized: Fit poorly and Fit well" is the same for two populations of interest, "male firefighters" and "female firefighters"
To do this you have to conduct a Chi-Square test of Homogeneity.
In the null hypothesis you have to state that the proportion of the categories of the variable are the same for all the populations of interest.
Be
M: the firefighter is male
F: the firefighter is female
Y: represents the category that the gloves "fit poorly"
W: represents the category that the gloves "fit well"
The null hypothesis will be:
H₀: P(Y|M)=P(Y|F)=P(Y)
P(W|M)=P(W|F)=P(W)
H₁: At least one of the statements in the null hypothesis is false.
α: 0.01
To calculate the statistic under the null hypothesis you have to calculate the expected frequencies first:
[tex]E_{ij}= O_{.j}*\frac{O_{i.}}{n}[/tex]
O.j= total of the j-column
Oi.= total of the i-row
n= total of observations
[tex]E_{11}= 547*\frac{152}{586} = 141.88[/tex]
[tex]E_{12}=39*\frac{152}{586}= 10.12[/tex]
[tex]E_{21}= 547*\frac{434}{586} = 405.12[/tex]
[tex]E_{22}= 39*\frac{434}{586} = 28.88[/tex]
[tex]X^2= sum \frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~~~X^2_{(r-1)(c-1)}[/tex]
r= number of rows (in this case 2)
c=number of columns (in this case 2)
[tex]X^2_{H_0}= \frac{(132-141.88)^2}{141.88} +\frac{(20-10.12)^2}{10.12} +\frac{(415-405.12)^2}{405.12} +\frac{(19-28.88)^2}{28.88} = 13.95[/tex]
Using the critical value approach, you have to remember that this test is always one-tailed to the right, meaning that you'll have only one critical value from which the rejection region is defined:
[tex]X^2_{(r-1)(c-1);1-\alpha }= X^2_{1;0.99}= 6.635[/tex]
The decision rule is then:
If [tex]X^2_{H_0}[/tex] ≥ 6.635, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 6.635, do not reject the null hypothesis.
The calculated value is greater than the critical value, the decision is to reject the null hypothesis.
So at a 1% level you can conclude that this test is significant. This means that the proportions of gloves fitness, categorized in "Fit poorly" and "Fit well" are different for the male and female firefighters populations.
I hope this helps!
Answer:
The Chi - Square Test Statistics is 13.98
p-value = 0.0002
CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.
Thus; there is a difference in the population proportion of glove fitness for the two genders.
Step-by-step explanation:
From the information given ; the structure of the table can be well represented as follows;
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly
Gloves fit well
Total
The objective of this question is to use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.
We call represent the hypothesis as follows:
The null hypothesis: [tex]H_o:[/tex] states that there is no difference in the population proportion of glove fitness for the two genders.
The alternative hypothesis: [tex]H_a[/tex] states that there is difference in the population proportion of glove fitness for the two genders.
The expected frequency of a particular cell can be calculated by multiplying the sum of the rows and columns together, then dividing it by the Total sum
For row 1 column 1 (gloves fit poorly (male) ; we have:
[tex]= \dfrac{547*152}{586} =141.884\\[/tex]
For row 2 column 1 (gloves fit well(male) ; we have:
[tex]= \dfrac{547*434}{586} =405.116[/tex]
For row 1 column 2 (gloves fit poorly (female)) ; we have:
[tex]= \dfrac{39*152}{586} =10.116[/tex]
For row 2 column 2 ( gloves fit well ( female ) ; we have:
[tex]= \dfrac{39*434}{586} =28.884[/tex]
Thus; we can have the complete table to now be:
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly 141.884 10.116 152
Gloves fit well 405.116 28.884 434
Total 547 39 586
The Chi - Square Test Statistics can be calculated via the formula:
[tex]X^2 = \dfrac{\sum (f_o-f_e)^2}{f_e}[/tex]
where;
[tex]f_o[/tex] = observed data frequency
[tex]f_e[/tex] = expected data frequency
∴
The Chi - Square Test Statistics is as follows:
[tex]=\dfrac{(131-141.884)^2}{141.884} + \dfrac{(20-10.116)^2}{10.116}+ \dfrac{(415-405.116)^2}{405.116}+ \dfrac{(39-28.884)^2}{28.884}[/tex]
= 0.68+9.6+0.2+3.5
= 13.98
We are given the level of significance ∝ to be = 0.01
numbers of rows = 2; number of column = 2
Thus; the degree of freedom = (2-1)(2-1) = 1×1 = 1
Using the Excel Function : [ = CHISQ.DIST.RT²(X²,df)]
p-value = 0.0002
CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.
Thus; there is a difference in the population proportion of glove fitness for the two genders.
Chris Evans drives 300 miles per week in his Honda Civic that gets 22 miles per gallon of gas. He
is considering buying a new fuel-efficient car for $20,000 (after trade-in of your Honda Civic)
that gets 50 miles per gallon. Insurance prerniums for the new car and old care are $900 and
$500 per year respectively. If he decides to keep his car, he will need to spend $1200 on repairs
per year. Assume gas costs $3.50 per gallon over a 5-year period,
a, what is the cost of the old car?
b. what is the cost of the new car?
Answer:
old car $20,909new car: $29,960Step-by-step explanation:
At 300 miles per week, Chris drives 300×52 = 15,600 miles per year. His gas cost can be figured as ...
(5 years)×(miles per year)÷(miles/gallon)×($ per gallon) = $273,000/(miles per gallon)
__
a) old car cost = repair cost + gas cost + insurance cost
= 5($1200) + $273,000/22 + 5($500) ≈ $20,909 . . . over 5 years
__
b) new car cost = purchase cost + gas cost + insurance cost
= $20,000 + $273,000/50 +5($900) = $29,960 . . . over 5 years
Find the value of x for which the figure below is a parallelogram
Answer:
x = 2
Step-by-step explanation:
Well the diagonals bisect each other.
4x = 8
x = 2
Answer:
x = 2
Step-by-step explanation:
5x = 3x+4
2x = 4
x = 2
The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x)
= 9x - 2. Which expression represents the profit, (k-h(x), of producing soccer balls?
Answer:
4x - 8
Step-by-step explanation:
k - H(x)
(9x -2) - (5x + 6)
4x -8
Find the length of side x in simplest radical form with a rational denominator
Answer:
[tex] x = 7 \sqrt{3} [/tex]
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{7}{x} \\ \\ \therefore \: \frac{1}{ \sqrt{3} } = \frac{7}{x} \\ \\ x = 7 \sqrt{3} \\ [/tex]
In a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.
Answer:
The length of the side opposite the 60 degree angle 'c' = 4
Step-by-step explanation:
Step(i):-
Given data ∠A = 90° , ∠B = 60° and ∠C = 30°
Given data the length of the side opposite the 30 degree angle is 8
let 'a' = 8
step(ii):-
By using sine rule formula in properties of triangle
[tex]\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]
[tex]\frac{a}{Sin A} = \frac{c}{Sin C}[/tex]
[tex]\frac{8}{Sin 90} = \frac{c}{Sin 30}[/tex]
cross multiplication , we get
[tex]\frac{8 X sin 30}{Sin 90} = c[/tex]
we know that trigonometry formulas
sin 30° = [tex]\frac{1}{2}[/tex] and sin 90°= 1
C = 8 X 1/2 = 4
conclusion:-
The length of the side opposite the 60 degree angle 'c' = 4
A report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized. Assume that you plan to test the claim that p1=p2. Find the test statistic for the hypothesis test. (Let the houses with the dogs be the first population.)
Answer:
The test statistic for the hypothesis test is -1.202.
Step-by-step explanation:
We are given that a report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized.
Let [tex]p_1[/tex] = population proportion of households with pet dogs who were burglarized.
[tex]p_2[/tex] = population proportion of households without pet dogs who were burglarized.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex] {means that both population proportions are equal}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex] {means that both population proportions are not equal}
The test statistics that would be used here Two-sample z-test for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of households with pet dogs who were burglarized = [tex]\frac{10}{129}[/tex] = 0.08
[tex]\hat p_2[/tex] = sample proportion of households without pet dogs who were burglarized = [tex]\frac{23}{197}[/tex] = 0.12
[tex]n_1[/tex] = sample of households with pet dogs = 129
[tex]n_2[/tex] = sample of households without pet dogs = 197
So, the test statistics = [tex]\frac{(0.08-0.12)-(0)}{\sqrt{\frac{0.08(1-0.08)}{129}+\frac{0.12(1-0.12)}{197} } }[/tex]
= -1.202
The value of z test statistics is -1.202.
A spinner with 6 colors is spun and a number cube is tossed determine the number of outcomes
Answer:
36
Step-by-step explanation:
since there are six outcomes for the spinner and six outcomes for the cube,
6 x 6 = 36
Which transformations could be performed to show that
AABC is similar to AA"B"C"?
10
8
B
4
VX
2
A
-10 -3 -6 -4 -21 14
B"
4
8 10
X
O a reflection over the x-axis, then a dilation by a scale
factor of 3
O a reflection over the x-axis, then a dilation by a scale
factor of
O a 180° rotation about the origin, then a dilation by a
scale factor of 3
O a 180° rotation about the origin, then a dilation by a
scale factor of
6
8
-10
Save and Exit
Next
Submit
Mark this and return
Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
What is mean by Transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Given that;
Triangle ABC is similar to A"B"C".
Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)
Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
Learn more on transformation at:
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Which equation is part of solving the system by substitution? 4(y + 11)2 – 3y2 = 8 4(11 – y)2 – 3y2 = 8 4(y – 11)2 – 3y2 = 8 4(–11y)2 – 3y2 = 8
Answer: B
Step-by-step explanation:
A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation
Answer:
(x, y) → (4/5 x, 4/5 y)
Question:
The answer choices to determine the rule that represent the dilation were not given. Let's consider the following question:
A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?
A) (x, y) → (0.5 − x, 0.5 − y)
B) (x, y) → (x − 7, y − 7)
C) (x, y) → ( 5/4 x, 5/4 y)
D) (x, y) → (4/5 x, 4/5 y)
Step-by-step explanation:
To determine the rule that could represent the dilation, we would multiply each coordinate by a dilation factor (a constant) to create a dilation. Since the dilation would be used to create a smaller polygon, the constant multiplied with the coordinates of x and y would be less than 1.
Let's check the options out.
In option (A), the coordinates is subtracted from the constant (0.5).
In option (B), the constant (7) is subtracted from the coordinates.
In option (C), the coordinates are multiplied by constant (5/4).
But 5/4 = 1.25. This is greater than 1.
In option (D), the coordinates are multiplied by constant (4/5).
4/5 = 0.8
The constant multiplied with the coordinates of x and y is less than 1 in option (D) = (x, y) → (4/5 x, 4/5 y)
4/5 = 0.8
0.8 is less than 1
a condition for two vectors to be equal is that?
Answer:
Vector is equal to vector b. For two vectors to be equal, they must have both the magnitude and the directions equal.
Step-by-step explanation:
Indicate in standard form equation of the line passing through the given 
Answer:
x - 3y= -14
Step-by-step explanation:
Slope is rise over run
m = (6-5)/(4-1) = 1/3
we write in slope-intercept form:
y = 1/3x + b
solve for b by plugging in either point
i'm going to plug in H
5 = 1/3 + b
b = 14/3
we get our equation
y = 1/3x + 14/3
now re-write it in standard form
-1/3x + y = 14/3
make it pretty
x - 3y = -14
A box lunch costs b. A bag of chips is $2 extra. Choose the expression to show the cost of 12 lunches with chips and 10 lunches without?
Answer:
22b+24
Step-by-step explanation:
If a box lunch costs b and a bag of chips is $2 extra then we would have:
box lunch = b dollars
box lunch with bag of chips = b + 2 dollars
Now, we need to find the expression for the cost of 12 lunches with chips and 10 lunches without chips, this would be:
12 lunches with chips = 12 (b + 2)
10 lunches without chips = 10b
Let's sum up and simplify these two expressions:
[tex]12(b+2)+10b\\12b+24+10b\\22b+24[/tex]
Thus, the cost of 12 lunches with chips and 10 lunches without chips is 22b+24
Triangle ABC is a right triangle whose right angle is ZABC.
Find the measure of ZEBF.
ZABC and DBF are vertical angles, so they have the same
measure. Because IZABC is 90°, the sum of m2. DBE and
m2 EBF must also be 90°
Solve for x in this equation.
x + (x - 12) = 90
2x - 12 = 90
2x = 102
X51
m2 EBF = 51°
1.What is m
2.What is m
3.Explain how to find m
Answer: m is 13
m is 6
you find m by calculating!
Step-by-step explanation:
Which of the following numbers are in setA? Check all that apply.
A = {x | x is a positive, odd integer less than 7}
0
1
2
5
3
Answer:
1, 3, 5.
Step-by-step explanation:
The members of the set are {1, 3, 5}.
Note 0 is an even integer so is not included in the set.
Also 0 is neither negative or positive.
Ronald needs a morning breakfast drink that will give him at least 390 calories. Orange juice has 130 calories in 8oz. How many ounces does he need to drink to reach his calorie goal?
Answer:
24 ounces of orange juice
Step-by-step explanation:
Given-
Calories needed=390 calories
Calories in 8oz juice=130 calorie
Therefore ounces of juice=(390/130)8
=3 x 8
=24 ounces
If Ronald needs a morning breakfast drink that will give him atleast 390 calories. Orange juice has 130 calories in 8oz. Then 24 ounces does he need to drink to reach his calorie goal.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Ronald needs a morning breakfast drink that will give him at least 390 calories.
Orange juice has 130 calories in 8oz.
We need to find how many ounces does he need to drink to reach his calorie goal
Calories needed=390 calories
Calories in 8oz juice=130 calorie
Three hundred ninety divided by one hundred thirty times of eight.
Therefore ounces of juice=(390/130)8
Three hundred ninety divided by one hundred thirty is three.
=3 x 8
Three times of eight is twenty four.
=24 ounces
Hence 24 ounces of orange juice does he need to drink to reach his calorie goal.
To learn more on Equation:
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Use the following information for questions 34-36: Deanna is the principal at a Midwestern middle school and wants to know the average IQ of all female, seventh grade students. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Based on the interval you calculated in question 34, does it seem plausible that the true average IQ score for all seventh-grade female students at this school is 113
Answer:
Since, 113 is on the confidence interval obtained (97.502, 114.098), so, we can suggest that is plausible that the true average IQ score for all seventh-grade female students at this school is 113.
Step-by-step explanation:
The question isn't complete, the missing part asked us to obtain a 99.5% confidence interval for the true average IQ score
Finding the confidence interval using the sample data provided, we can answer the question of plausibility.
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 105.8
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 31 - 1 = 30
Significance level for 99.5% confidence interval
(100% - 99.5%)/2 = 0.25% = 0.0025
t (0.0025, 30) = 3.03 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 15
n = sample size = 30
σₓ = (15/√30) = 2.739
99.5% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 105.8 ± (3.03 × 2.739)
CI = 105.8 ± 8.298
99.5% CI = (97.502, 111.387)
99.5% Confidence interval = (97.502, 114.098)
Since, 113 is on the confidence interval obtained, so, we can suggest that is plausible that the true average IQ score for all seventh-grade female students at this school is 113.
Hope this Helps!!!
Answer for (12x+5)x-7x+2
Answer:
(12x2-2x+2)
Step-by-step explanation:
(12x)(x)+(5)(x)+-7x+2
12x2+5x+-7x+2
(12x2)+(5x+-7x)+(2)
12x2+-2x+2
Tyson’s puppy weighed 8 pounds 3 ounces last year.
In one year the puppy gained 2 pounds 4 ounces.
How much does Tyson’s puppy weigh now in ounces?
Last year- 8 lbs 3 ounces
Add 2 lbs and 4 ounces
Which is 10 lbs 7 ounces
10 lbs in onces is 160 ounces
Then you add the other 7 ounces so the final answer is 167 ounces
Tyson’s puppy weighs 167 ounces!
Good luck please mark me as braniliest!!!!!!
The following data represent the number of flash drives sold per day at a localcomputer shop and their prices.Price Units Sold34 336 432 635 530 938 240 1a. Develop the estimated regression equation that could be used to predict thequantity sold given the price. Interpret the slope.b. Did the estimated regression equation provide a good fit? Explain.c. Compute the sample correlation coefficient between the price and the number offlash drives sold. Use a= 0.01 to test the relationship between price and units sold.d. How many units can be sold per day if the price of flash drive is set to $28.
Answer:
a)3145 x 0.01 = 31.45 3145- 31.45 = 3113.55
Compute the sample correlation 3113.55 -? we find the least square pressing at least 15x on the calculator then minus this from 3113.55 to find a better fit and minimum regression.
We add the differences of units then divide by distribution as seen below.
b) unsure.
c) = (see below) just test each number shown unit sold per day / price then x can show the differences in each number from day 1 to day 2.
d) = 16 sold.
Step-by-step explanation:
a) We count the units up and deduct from it from the equation p is recognized as units sold. R1 is cost R2 is total days.
b) The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X = 0).
c) r 2= decimal ; the regression equation has accounted for percentage of the total sum of squares. You cna do this one.
d) = 16 sold at $28 each. - Why ? We using 7 day data and prove a how many units can be sold p/d if the price of flash drive is set to $28 each per unit.
Day 1 = 34 / 28 = 1 = 1.21428571429 = 1 no difference day prior.
Day 2 = 336 / 28 = 12 = 12 = difference day prior is 11
Day 3 = 432 / 28 = 15 = 15.4285714286 = 15 difference day prior is 3
Day 4 = 635 / 28 = 23 = 22.6785714286 = 23 difference day prior is 8
Day 5 = 530 / 28 = 19 = 18.9285714286 = 19 difference day prior is minus - 4
Day 6 = 938 / 28 = 34 = 33.5 = 34 difference day prior is 15
Day 7 = 240 / 28 = 9 = 8.57142857143 = 9 difference day prior is minus -25
Total days 7 = Total revenue / price = average units sold
Average units sold total = 1+ 12+15 +23 +19+34+9 = 113 rounded.
Average units sold total = 1.21428571429 + 12 + 15.4285714286
+ 22.6785714286
+18.9285714286
+ 33.5
+ 8.57142857143 = 112.321428572 units sold weekly when priced at $28
To answer D we divide this by 7 to show;
112.321428572/ 7 = 16.0459183674
Daily units sold = 16
How do u solve this?
Answer:
0
Step-by-step explanation:
Tuesday : -1/2
Wednesday + 3/4
Thursday : -3/8
Add them together
-1/2 + 3/4- 3/8
Get a common denominator
-4/8 + 6/8 - 3/8
-1/8
The closest integer value to -1/8 is 0
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Base area = 9 × 13
= 117 square feet
Now
Volume of pyramid = (1/3)(A)(H)
= (1/3)(117)(30)
= 117 × 10
= 1170 cubic feet
Assume that random guesses are made for nine multiple choice questions on an SAT test, so that there are nequals9 trials, each with probability of success (correct) given by pequals0.55. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4.
Answer:
[tex]P(X=0)=(9C0)(0.55)^9 (1-0.55)^{9-0}=0.000757[/tex]
[tex]P(X=1)=(9C1)(0.55)^9 (1-0.55)^{9-1}=0.0083[/tex]
[tex]P(X=2)=(9C2)(0.55)^9 (1-0.55)^{9-2}=0.0407[/tex]
[tex]P(X=3)=(9C3)(0.55)^9 (1-0.55)^{9-3}=0.1160[/tex]
And adding we got:
[tex] P(X < 4) = 0.000757 +0.0083+0.0407 +0.1160= 0.2626[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of correct answers", on this case we now that:
[tex]X \sim Binom(n=9, p=0.55)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X < 4) =P(X=0) +P(X=1) +P(X=2) +P(X=3) [/tex]
And we can find the individual probabilities:
[tex]P(X=0)=(9C0)(0.55)^9 (1-0.55)^{9-0}=0.000757[/tex]
[tex]P(X=1)=(9C1)(0.55)^9 (1-0.55)^{9-1}=0.0083[/tex]
[tex]P(X=2)=(9C2)(0.55)^9 (1-0.55)^{9-2}=0.0407[/tex]
[tex]P(X=3)=(9C3)(0.55)^9 (1-0.55)^{9-3}=0.1160[/tex]
And adding we got:
[tex] P(X < 4) = 0.000757 +0.0083+0.0407 +0.1160= 0.2626[/tex]
Which inequality is represented by this graph
The right answer is of option D.
[tex]x \geqslant 4[/tex]
In the given graph, X is greater than 4 and X equals to 4.
Hope it helps.....
Good luck on your assignment
(a) Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.
(b) Based on the information given in the section on algebraic properties of power series, for which values of x can you guarantee that the new series converges.
(If you have a CAS, you can easily find several more nonzero terms in the power series expansions of the functions.)
(e^x)/(cos(x))
Answer:
a) [tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]
b) See Below for proper explanation
Step-by-step explanation:
a) The objective here is to Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.
The function is [tex]e^x + 3 \ cos \ x[/tex]
The expansion is of [tex]e^x[/tex] is [tex]e^x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ...[/tex]
The expansion of cos x is [tex]cos \ x = 1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...[/tex]
Therefore; [tex]e^x + 3 \ cos \ x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ... 3[1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...][/tex]
[tex]e^x + 3 \ cos \ x = 4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} + \dfrac{x^3}{3!}+ ...[/tex]
Thus, the first three terms of the above series are:
[tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]
b)
The series for [tex]e^x + 3 \ cos \ x[/tex] is [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!} + 3 \sum \limits^{\infty}_{x=0} ( -1 )^x \dfrac{x^{2x}}{(2n)!}[/tex]
let consider the series; [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!}[/tex]
[tex]|\frac{a_x+1}{a_x}| = | \frac{x^{n+1}}{(n+1)!} * \frac{n!}{x^x}| = |\frac{x}{(n+1)}| \to 0 \ as \ n \to \infty[/tex]
Thus it converges for all value of x
Let also consider the series [tex]\sum \limits^{\infty}_{x=0}(-1)^x\dfrac{x^{2n}}{(2n)!}[/tex]
It also converges for all values of x