Answer:
A. We are 92% confident that the population mean height of college football players is between 63.2 and 65.9 inches.
Step-by-step explanation:
Confidence interval:
x% confidence
Of a sample
Between a and b.
Interpretation: We are x% sure(or there is a x% probability/chance) that the population mean is between a and b.
In this question:
92% confidence interval for the average height of football players is (63.2, 65.9).
Interpretation: We are 92% sure that the true average height of all college football players, that is, the population mean, is in this interval.
The correct answer is:
A. We are 92% confident that the population mean height of college football players is between 63.2 and 65.9 inches.
Which of the following indicates the subtraction property of equality when solving the equation 86 – 2 (9x + 4) = 12x + 18 A) 2(9x + 4) = 86 – 12x – 18 B) x = 2 C) –2(9x + 4) = 12x + 18 – 86 D) 86 – 18x – 8 = 12x + 18
Answer:
D) 86 – 18x – 8 = 12x + 18
X = 2
Step-by-step explanation:
86 – 2 (9x + 4) = 12x + 18
This question has a straight forward answer...
It's just to open up the bracket and ensure that the negative sign before the bracket multiply the values in the bracket exactly.
So opening up the bracket gives us this as the answer
86 - 18x -8 = 12x +18
86-18-8 = 12x+ 18x
60 = 30x
X = 2
1/3 times the difference of a number and five is -2/3 which equation best shows this
Answer:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Step-by-step explanation:
Let the number be x
Difference of a number & 5 : x-5
1/3 time the difference of a number & 5: 1/3 (x-5)
Equation:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Solution:
[tex]x-5=\frac{-2}{3}*\frac{3}{1}\\\\x-5=-2\\\\x=-2+5\\x=3[/tex]
PLEASE HELP ME! Simplify the expression 3 4 (1440) + 295.25 + (-33.50) to determine how much money the theater brought in.
Answer:
1341.75
Step-by-step explanation:
I did the math :)
The guy above me is correct
Please answer this correctly without making mistakes
Answer: Anything above 2
Step-by-step explanation:
Answer: 3,4,5,6,7,8,9 (Any of these digits work)
Step-by-step explanation:
We want to find a digit that makes the number greater than 3260.2. There are many digits that can fit in there.
3318.7≥3260.2
Here, we plugged in a 3. that makes this sentence true because 3318.7 is greater than or equal to 3260.2. Since 3 works, we know that any digit greater than 3 would fit.
Determine whether the parallelogram is a rhombus, rectangle, square, or none. Explain.
Q(1, 3), R(3, 4), S(5, 3), T(3, 2)
Select one:
A. QRST is a rhombus that is not a square because its diagonals are perpendicular but not congruent.
B. QRST is a rectangle that is not a square because its diagonals are congruent but not perpendicular.
C. QRST is a square because its diagonals are both perpendicular and congruent.
D. QRST is none of these because its diagonals are neither congruent nor perpendicular.
Answer:
Step-by-step explanation:
The diagonals of the given parallelogram are QS and RT. We would first determine if its diagonals are congruent.
QS = √(1 - 5)² + (3 - 3)² = 16
RT = √(3 - 3)² + (4 - 2)² = 4
Since QS ≠ RT, it means that they are not congruent and this means that the parallelogram is not a rectangle.
Let us check if the diagonals are perpendicular.
Slope of QS = (3 - 3)/(5 - 1) = 0/4
Slope of RT = (2 - 4)/(3 - 3) = - 2/0
The slopes are not opposite reciprocals. It means that the diagonals are not perpendicular. Therefore, the correct option is
D. QRST is none of these because its diagonals are neither congruent nor perpendicular.
Write the Maclaurin series for f(x) = x^7e^x5. (2 points) a) the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial b) the summation from n equals 0 to infinity of the quotient of x to the 12th power and the quantity n plus 5 factorial c) the summation from n equals 0 to infinity of the quotient of x to the quantity 5 times n plus 7 power and n factorial d) the product of x raised to the 5 times n power and the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial
Recall that
[tex]e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]
Then
[tex]e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n}}{n!}[/tex]
and
[tex]x^7e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n+7}}{n!}[/tex]
I NEED HELP ASAP PLEASE! :)
Answer:
option 1
Step-by-step explanation:
[tex]r=\sqrt{(5\sqrt{2})^{2}+(-5\sqrt{2})^{2} } \\\\=\sqrt{25*2+25*2}\\\\ =\sqrt{50+50}\\\\=\sqrt{100}\\\\=10[/tex]
[tex]x=tan^{-1}(\frac{-5\sqrt{2}}{5\sqrt{2}})\\\\x=tan^{-1} (-1)\\x=\frac{7\pi}{4}[/tex]
[tex]re^{ix}=10e^{i\frac{7\pi}{4}}[/tex]
Point M is in the interior of angle AOB, the ray OC is a bisector of this angle. Prove that the measure of angle MOC is equal to one-half the difference of the measure of angles AOM and BOM
Answer:
Step-by-step explanation:
Given: point M,
m<AOB,
OC the bisector of m<AOB
Thus,
m<AOC = m<BOC (bisector property of OC)
m<MOC = m<BOM (congruence property)
m<AOM - m<BOM = m<AOC = m<BOC
m<BOC = m<MOC = [tex]\frac{m<AOC}{2}[/tex] (angle property)
Therefore,
m<AOM > m<BOM (point M location property)
m<MOC = [tex]\frac{m<AOM - m<BOM}{2}[/tex]
A committee of 4 people is chosen from 7 women and 7 men. How many different committees are possible that consist of 2 women and 2 men?
Answer: 441
Step-by-step explanation:
2 men from 7 will be the members of committee that makes 7*6/2=21 outputs
2 women from 7 will be the members of committee that makes 7*6/2=21 outputs as well.
Total number of outputs is 21*21=441
The number of ways different committees are possible that consist of 2 women and 2 men is 441.
What is binomial?Two terms joined by a plus or minus sign make up a mathematical expression are termed as binomial.
What is the binomial coefficient?The positive integers that appear as coefficients in the binomial theorem are known as binomial coefficients in mathematics. A binomial coefficient is typically written and indexed by the two integers n ≥ k ≥ 0.
There are the binomial coefficient "7 choose 2", i.e. [tex]\frac{7!}{2!5!}=21[/tex] ways to choose 2 people from a set of 7 people.
So, there are 21 ways to choose 2 men and 21 ways to choose 2 women. This means that there is [tex]21^2 = 441[/tex] ways to choose both 2 men and 2 women.
Learn more about application of binomial coefficient from given link.
https://brainly.com/question/14216809
#SPJ2
A farmer owns 30 acres of land on which he wishes to grow corn and barely. The cost per acre for seedcorn is $30, and the cost per acre for barely seed is $20. The farmer can invest a maximum of $600 in seed for the two crops. During the cultivation process, the farmer needs to spray fertilizers and insecticides specific to each crop. This costs $10 per acre for corn and $15 per acre for barely. He can invest only $400 in this process.
A) Write the two inequalities that are deciding factors for the number of acres of each crop the farmer will plant, based on the amount of money the farmer will spend on planting and cultivating the two crops.
B) replace the inequality signs in the two any qualities with equal signs. For a graft representing the two equations that influence the farmers choice of how much of each crop to grow.
C) should the lines be dilated or solid? Give reasons for both lines. What area should be shaded?
Help please
ok hola bro graicas por los punto qui :
A pair of surfers collected data on the self-reported numbers of days surfed in a month for 30 longboard surfers and 30 shortboard surfers. Complete parts a and b below.
Longboard: 2, 7, 16, 13, 10, 18, 7, 8, 15, 15, 19, 17, 3, 10, 11, 16, 24 5, 20, 6, 9, 11, 8, 21, 22, 18, 14, 12, 16, 24
Shortboard: 17, 16, 7, 5, 13, 8, 7, 6, 15, 8, 8, 16, 10, 23, 24, 10, 20, 16, 16, 24, 23, 14, 6, 12, 10, 7, 12, 25, 13, 22
a) Compare the typical number of days surfing for these two groups.
The median for the longboards was________ days, and the median for the shortboards was_______ days, showing that those with________ typically surfed more days in this month
b) Compare the interquartile ranges.
The interquartile range for the longboards was________ days, and the interquartile range for the shortboards was_______ days, showing more variation in the days surfed this month for the________
Answer:
(a)The median for the longboards was 13.5 days, and the median for the shortboards was 13 days, showing that those with longboards typically surfed more days in this month.
(b)The interquartile range for the longboards was 10 days, and the interquartile range for the shortboards was 10.5 days, showing more variation in the days surfed this month for the shortboards.
Step-by-step explanation:
Longboard:
2, 7, 16, 13, 10, 18, 7, 8, 15, 15, 19, 17, 3, 10, 11, 16, 24 5, 20, 6, 9, 11, 8, 21, 22, 18, 14, 12, 16, 24
Sorting in ascending order, we have:
[tex]2, 3, 5, 6, 7, 7, \boxed{8, 8}, 9, 10, 10, 11, 11, 12, \boxed{13, 14,} 15,15, 16, 16, 16, 17, \boxed{18, 18}, 19, 20, 21, 22, 24 , 24[/tex]
Median [tex]=\dfrac{13+14}{2}=13.5[/tex]
[tex]Q_1=\dfrac{8+8}{2}=8 \\Q_3=\dfrac{18+18}{2}=18\\$Interquartile range, Q_3-Q_1=18-8=10[/tex]
Shortboard
17, 16, 7, 5, 13, 8, 7, 6, 15, 8, 8, 16, 10, 23, 24, 10, 20, 16, 16, 24, 23, 14, 6, 12, 10, 7, 12, 25, 13, 22
Sorting in ascending order, we have:
[tex]5, 6, 6, 7, 7, 7, \boxed{8, 8,} 8, 10, 10, 10, 12, 12, \boxed{13, 13} 14, 15, 16, 16, 16, 16, \boxed{17, 20,} 22, 23, 23, 24, 24, 25[/tex]
Median [tex]=\dfrac{13+13}{2}=13[/tex]
[tex]Q_1=\dfrac{8+8}{2}=8 \\Q_3=\dfrac{17+20}{2}=18.5\\$Interquartile range, Q_3-Q_1=18.5-8=10.5[/tex]
Therefore:
(a)The median for the longboards was 13.5 days, and the median for the shortboards was 13 days, showing that those with longboards typically surfed more days in this month.
(b)The interquartile range for the longboards was 10 days, and the interquartile range for the shortboards was 10.5 days, showing more variation in the days surfed this month for the shortboards.
Choose the name of this figure.
A.
line
B.
angle
c.
line segment
D.
ray
Answer:
we dont see aa figure
Step-by-step explanation:
a water storage tank is in the shape of a hemisphere. If the radius is 29ft, approximate the volume of the tank in cubic feet
Answer:
The answer is 51080.2 cubic feetStep-by-step explanation:
Volume of a hemisphere is given by
[tex]V = \frac{2}{3} \pi {r}^{3} [/tex]
where r is the radius of the hemisphere
From the question
r = 29 ft
Substitute the value of r into the formula
That's
[tex]V = \frac{2}{3} \pi \times {29}^{3} [/tex]
[tex]V = \frac{48778}{3} \pi[/tex]
We have the final answer as
V = 51080.2 cubic feetHope this helps you
Let f(x)= |x| and g(x) = x+2. What are the domain and range of (fog)(x)?
If [tex]f(x)=\mid x\mid[/tex] and [tex]g(x)=x+2[/tex] then [tex]f(g(x))=\mid x+2\mid[/tex].
The domain is [tex]x\in(-\infty, +\infty)=\mathbb{R}[/tex].
The range is [tex]y\in[2,+\infty)[/tex].
Hope this helps.
Answer:
D) domain: all real numbersrange: y>0Step-by-step explanation:
with range there is a horizontal line under the > sign, just as a side note:D
BRANLIEST?
Consider the following hypothesis test.H0:μ1−μ2=0 Ha:μ1−μ2≠0The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1=80n2=70 x¯¯¯1=104x¯¯¯2=106 σ1=8.4σ2=7.6a. What is the value of the test statistic?b. What is the p-value?c. With α=.05,α=.05, what is your hypothesis testing conclusion?
Answer:
a) [tex]z =\frac{104-106}{\sqrt{\frac{8.4^2}{80} +\frac{7.6^2}{70}}}= -1.53[/tex]
b) [tex]p_v =2*P(z<-1.53)=0.126[/tex]
c) Since the p value is higher than the significance level provided we have enogh evidence to FAIL to reject the null hypothesis and we can't conclude that the true means are different at 5% of significance
Step-by-step explanation:
Information given
[tex]\bar X_{1}= 104[/tex] represent the mean for 1
[tex]\bar X_{2}= 106[/tex] represent the mean for 2
[tex]\sigma_{1}= 8.4[/tex] represent the population standard deviation for 1
[tex]\sigma_{2}= 7.6[/tex] represent the population standard deviation for 2
[tex]n_{1}=80[/tex] sample size for the group 1
[tex]n_{2}=70[/tex] sample size for the group 2
z would represent the statistic
Hypothesis to test
We want to check if the two means for this case are equal or not, the system of hypothesis would be:
H0:[tex]\mu_{1}=\mu_{2}[/tex]
H1:[tex]\mu_{1} \neq \mu_{2}[/tex]
The statistic would be given by:
[tex]z =\frac{\bar X_1-\bar X_2}{\sqrt{\frac{\sigma^2_1^2}{n_1} +\frac{\sigma^2_2^2}{n_2}}}= [/tex](1)
Part a
Replacing we got:
[tex]z =\frac{104-106}{\sqrt{\frac{8.4^2}{80} +\frac{7.6^2}{70}}}= -1.53[/tex]
Part b
The p value would be given by this probability:
[tex]p_v =2*P(z<-1.53)=0.126[/tex]
Part c
Since the p value is higher than the significance level provided we have enogh evidence to FAIL to reject the null hypothesis and we can't conclude that the true means are different at 5% of significance
A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.
a) 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. c) 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144d) We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.
Answer:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
Step-by-step explanation:
Confidence interval:
Confidence level of x%
We build from a sample.
Between a and b.
Intepretation: We are x% sure that the population mean is between a and b.
In this question:
90%
45 CEO's
Between ($139,048, $154,144).
So
We are 90% sure that the mean salary of all CEO's falls within this interval.
The correct answer is:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below: As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below:f(x)=-14 cos(720(t-10))+14
Using the equation, determine the following. Show your work for part marks.
a) What is the diameter of the bike wheel?
b) How long does it take the tire to rotate 3 times?
c) What is the minimum height of the nail? Does this height make sense? Why?
Step-by-step explanation:
a) The diameter of the wheel is the distance between the minimum and maximum. In other words, it's double the amplitude.
d = 2 × 14 = 28.
b) The period of the wave is:
720 = 2π / T
T = π/360
So the time for 3 revolution is:
3T = π/120
3T = 0.026 seconds
c) The minimum here is when cosine = 1.
h(t) = -14(1) + 14
h(t) = 0
This makes sense, since the minimum height is when the nail is at the bottom of the wheel, or at the ground.
Find the approximations T10, M10, and S10 for π 7 sin x dx. 0 (Round your answers to six decimal places.)
Answer:
Step-by-step explanation:
Well, since it was not given the interval let's use the interval [0,5] with n=10
So now, for the Trapezoidal Rule to approximate the area enclosed by the Integral of: [tex]f(x)=7\pi \sin(x)[/tex]
[tex]T_{10}=\frac{b-a}{2n}[f(a)+2f(x_1)+ ....2f(x_{n-1})+f(b)][/tex] Plugging in:
[tex]T_{10}=\frac{5-0}{2*10}[f(0)+2f(\frac{1}{2})+2f(1)+2f(\frac{3}{2})+2f(2)+2f(5/2)+2f(3)+2f(7/2)+2f(4)+2f(9/2) +f(5)][/tex]
[tex]T_{10}=\frac{1}{4}[0+21.086+37+43.87+39.99+26.322+6.20-15.43-33.285-42.99-21.087][/tex]
[tex]T_{10}\approx 15.419[/tex]
Now the same area according to Simpson rule:
[tex]S_{10}=\frac{b-a}{3n}[f(a)+4f(x_{1})+2f(x_{2})+4f(x_{3} )+2f(x_{4})+4f(x_{5})+2f(x_{6})+4f(x_{7})+2f(x_{8})+4f(x_{9})+f(b)]\\S_{10}=\frac{5}{3*10}[0+74.01+43.87+79.98+26.322+12.413-15.43-66.571-42.99-21.08]\approx 15.085[/tex]
[tex]S_{10}\approx 15.0585[/tex]
Charles's law states that at constant pressure, the volume of a fixed amount of gas varies directly with its temperature measured in Kelvins. A gas has a volume of 250 ml at 300°K. a.) Write an equation for the relationship between volume and temperature. b.) What is the volume if the temperature increases at 420°K?
Answer:
equation is pv=nRT
p, n, R are constants
so, v is directly proportional to Temperature
v1/v2=T1/T2
250/v2=300/420
v2=350
SOMEBODY HELP
Jill bought 7 books more than Sam. If Sam and Jill together have 25 books, find the
number of books Sam has.
Answer:
Jill bought 16 books and Sam bought 9 books
Step-by-step explanation:
Let the number of books that Jill bought be j.
Let the number of books that Sam bought be s.
Jill bought 7 more books than Sam:
j = 7 + s
They bought 25 books altogether:
j + s = 25
Put j = 7 + s into the second equation:
7 + s + s = 25
7 + 2s = 25
2s = 25 - 7 = 18
s = 18/2 = 9 books
Therefore:
j = 7 + s = 7 + 9
s = 16 books
Jill bought 16 books and Sam bought 9 books.
If sin t=0.29 and sin w = 0.43, both t and w are positive, and the angles determined by t and w are in quadrant 2, then which of the following statements is true? Explain your selection
a. t>w
b. w>t
c. cannot be determined
Answer:
a. t>w
Step-by-step explanation:
Sin t= 0.29
t = sin^-1(0.29)
t= 16.86°
Sin w= 0.43
W = sin^-1(0.43)
W= 25.47°
Angles in the second quadrant are positive in sine and they are generally determined by subtracting the initial value from 180°
For t= 180°-16.86°
t = 163.14°
For w = 180°-25.47°
W= 154.53°
163.14°>154.53°
t>w
The rectangle has an area of 60 square feet. Find its dimensions (in ft). (x + 4) feet smaller value ___________________ ft larger value ____________________ ft
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The rectangle has an area of 60 square feet. Find its dimensions (in ft) if the length of the rectangle is 4 ft more than its widh.
smaller value ___________________ ft
larger value ____________________ ft
Answer:
Smaller value = 6 ft
Larger value = 10 ft
Step-by-step explanation:
Recall that the area of a rectangle is given by
[tex]Area = W \times L[/tex]
Where W is the width and L is the length of the rectangle.
It is given that the rectangle has an area of 60 square feet.
[tex]Area = 60 \: ft^2 \\\\60 = W \times L \\\\[/tex]
It is also given that the length of the rectangle is 4 ft more than its width
[tex]L = W + 4[/tex]
Substitute [tex]L = W + 4[/tex] into the above equation
[tex]60 = W \times (W + 4) \\\\60 = W^2 + 4W \\\\W^2 + 4W - 60 = 0 \\\\[/tex]
So we are left with a quadratic equation.
We may solve the quadratic equation using the factorization method
[tex]W^2 + 10W - 6W - 60 \\\\W(W + 10) – 6(W + 10) \\\\(W + 10) (W - 6) = 0 \\\\[/tex]
So,
[tex](W + 10) = 0 \\\\W = -10 \\\\[/tex]
Since width cannot be negative, discard the negative value of W
[tex](W - 6) = 0 \\\\W = 6 \: ft \\\\[/tex]
The length of the rectangle is
[tex]L = W + 4 \\\\L = 6 + 4 \\\\L = 10 \: ft \\\\[/tex]
Therefore, the dimensions of the rectangle are
Smaller value = 6 ft
Larger value = 10 ft
Verification:
[tex]Area = W \times L \\\\Area = 6 \times 10 \\\\Area = 60 \: ft^2 \\\\[/tex]
Hence verified.
Pls hurry least to greatest
Answer:
First choice
Step-by-step explanation:
Start by arranging the exponents of 10 in ascending order.
9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7 * 10^3
The exponents are in ascending order, -8, -6, 3, 3
Since the last two exponents are equal, we must compare the numbers that multiply the powers of 10. They are 2.5 and 7. Since 2.5 < 7, ascending order is 2.5, 7. That means the line above is in ascending order.
Answer: First choice
Please answer this correctly
Answer:
8/25
Step-by-step explanation:
The probability of picking a number less than 9 is 4/5.
The probability of picking an even number is 2/5.
[tex]4/5 \times 2/5[/tex]
[tex]=8/25[/tex]
In a large school, it was found that 69% of students are taking a math class, 70% of student are taking an English class, and 50% of students are taking both.
A. True
B. False
Answer:
P(Math or English) = 0.89
Step-by-step explanation: This solution will only be applicable if finding the probability that a randomly selected student is taking a math class or an English class.
Lets study the meaning of or , and on probability. The use of the word or means that you are calculating the probability
that either event A or event B happened
Both events do not have to happen
The use of the word and, means that both event A and B have to happened
The addition rules are: # P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they
have at least one outcome in common)
The union is written as A ∪ B or “A or B”.
The Both is written as A ∩ B or “A and B”
Lets solve the question
The probability of taking Math class 69%
The probability of taking English class 70%
The probability of taking both classes is 50%
P(Math) = 69% = 0.69
P(English) = 70% = 0.70
P(Math and English) = 50% = 0.50
To find P(Math or English) use the rule of non-mutually exclusive
P(A or B) = P(A) + P(B) - P(A and B)
P(Math or English) = P(Math) + P(English) - P(Math and English)
Lets substitute the values of P(Math) , P(English) , P(Math and English)
in the rule P(Math or English) = 0.69 + 0.70 - 0.50 = 0.89
P(Math or English) = 0.89
P(Math or English) = 0.89
This solution will only be applicable if we are to find the probability that a randomly selected student is taking a math class or an English class.
In a jar of coins, 18 out of the 40 coins are dimes. Express the fraction of the coins
that are dimes in three different ways below: (a) as a fraction, (b) as a decimal, and (c) as a percent.
Use long division to determine the decimal.
(a) as a fraction
(b) as a decimal
(c) as a percent
Answer:
Percent: 20%
Fraction: 1/5
Decimal: 0.20
Step-by-step explanation:
8:40*100 =
( 8*100):40 =
800:40 = 20%
Percent to fraction:
20%=20/100
= 0.2
=0.2×10/10
=2/10
=1/5
Percent to decimal:
20/100 = 0.20
What are the angle measurements of angles 1 &4 for #1 & measurements of angles 1-3 on #2?
Answer:
1. To find m∠1, we can notice that ∠1 and 46° are complementary, meaning they add up to 90° This means that m∠1 = 90 - 46 = 44°. We can do the same for ∠4. In this case, ∠4 = 90 - 23 = 67°.
2. To find m∠1, we can use the exterior angle formula which means that the measure of an exterior angle is equal to the sum of both of its remote interior angles. This means that ∠1 = 52 + 62 = 114°. To find ∠2 we can do 180 - 52 - 62 = 66° because the sum of all angles in a triangle is 180°. Since ∠2 and ∠3 are vertical angles, ∠3 = ∠2 = 66°.
Solve the equation. Round the solution to the nearest tenth . Enter the solution set of the equation . 2P o =P 0 (1.053)^ t
Answer: t= 13.4
Step-by-step explanation:
The given equation is [tex]2P_0=P_0(1.053)^t[/tex]
To solve this equation for 't', we first divide both sides by [tex]P_0[/tex], we get
[tex]2=(1.053)^t[/tex]
Taking log on both the sides, we get
[tex]\log 2= \log(1.053)^t[/tex]
Since [tex]\log a^b=b\log a[/tex]
Then,
[tex]\log 2= t\log1.053\\\\\Rightarrow0.30103=t(0.02243)\\\\\Rightarrow t=\dfrac{0.30103}{0.02243}\\\\\Rightarrow t=13.4208649131\approx13.4[/tex]
Hence, the value of t is 13.4.
Please answer this correctly without making mistakes
Answer:
A digit that makes this sentence true is 4.
Step-by-step explanation:
Since the first digit in the number to the left is 3, you simply have to find a digit greater than 3. Here are the possibilities:
4
5
6
7
8
and
9
Out of any of these you can choose, I chose 4.
9514 1404 393
Answer:
3, or any greater digit
Step-by-step explanation:
Suppose the digit is 'd'. Then the value on the right is ...
69.436 +100d
Subtracting the value on the left, we want the difference greater than 0.
69.436 +100d - 352.934 > 0
100d -293.498 > 0 . . . . simplify
100d > 293.498 . . . . . . . add 293.498
d > 2.93498 . . . . . . . . . . divide by 100
That is d is any single digit greater than 2.9. Those digits are ...
d ∈ {3, 4, 5, 6, 7, 8, 9}
Any digit 3 or greater makes the sentence true.
A sample of 17 patients in a hospital had these hemoglobin readings 112 120 98 55 71 35 99 142 64 150 150 55 100 132 20 70 93 find a 95% confidence interval for the hemoglobin reading for all the patienta in the hospital
Answer:
The 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
The data provided is:
S = {112, 120, 98, 55, 71, 35, 99, 142, 64, 150, 150, 55, 100, 132, 20, 70, 93}
Compute the sample mean and sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{17}\times[112+120+98+...+93]=92.1176\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 25041.7647}=39.56[/tex]
The critical value of t for 95% confidence level and n - 1 = 16 degrees of freedom is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 16}=2.120[/tex]
*Use a t-table.
Compute the 95% confidence interval for the hemoglobin reading for all the patients in the hospital as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=92.1176\pm 2.120\times\frac{39.56}{\sqrt{17}}\\\\=92.1176\pm 20.3408\\\\=(71.7768, 112.4584)\\\\\approx (72, 112)[/tex]
Thus, the 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).