Step-by-step explanation:
cot x / (1 + csc x)
Multiply by conjugate:
cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)
Distribute the denominator:
cot x (1 − csc x) / (1 − csc²x)
Use Pythagorean identity:
cot x (1 − csc x) / (-cot²x)
Divide:
(csc x − 1) / cot x
In the Cash Now lottery game there are 8 finalists who submitted entry tickets on time. From these 8 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousand dollars, and the third prize is ten thousand dollars. Determine the total number of different ways in which the winners can be drawn. (Assume that the tickets are not replaced after they are drawn.)
Answer:
The number of ways is [tex]\left n} \atop {}} \right. P_r = 336[/tex]
Step-by-step explanation:
From the question we are told that
The number of tickets are [tex]n = 8[/tex]
The number of finalist are [tex]r =3[/tex]
Generally the number of way by which this winners can be drawn and arrange in the order of [tex]1^{st} , \ 2nd , \ 3rd[/tex] is mathematically represented as
[tex]\left n} \atop {}} \right. P_r = \frac{n\ !}{(n-r) !}[/tex]
substituting values
[tex]\left n} \atop {}} \right. P_r = \frac{ 8!}{(8-3) !}[/tex]
[tex]\left n} \atop {}} \right. P_r = \frac{ 8* 7*6*5*4*3*2*1}{ 5*4*3*2*1}[/tex]
[tex]\left n} \atop {}} \right. P_r = 336[/tex]
(21x-3)+21=23x+6 solve
Answer:
False
Step-by-step explanation:
You Cnat solve it
Answer:
you cannot solve it
Step-by-step explanation:
false
Salaries of 42 college graduates who took a statistics course in college have a mean, , of . Assuming a standard deviation, , of $, construct a % confidence interval for estimating the population mean .
Answer:
The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
Step-by-step explanation:
The complete question is:
Salaries of 42 college graduates who took a statistics course in college have a mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard deviation, σ of $10,016 construct a 99% confidence interval for estimating the population mean μ.
Solution:
The (1 - α)% confidence interval for estimating the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
The critical value of z for 99% confidence interval is:
[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]
Compute the 99% confidence interval for estimating the population mean μ as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]
Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
Which of the following is not a characteristic of the F distribution? Multiple Choice It is always right-skewed. It describes the ratio of two variances. It is a family based on two sets of degrees of freedom. It is negative when s12 is smaller than s22.
Answer:
It is negative when s12 is smaller than s22.
Step-by-step explanation:
The F distribution has the following properties.
1) It is always right-skewed. but as the degrees of freedom v1 and v2 become large F distribution approaches normal distribution.
2) It describes the ratio of two variances.
3) It is a family based on two sets of degrees of freedom.
4) It is negative when s12 is smaller than s22. This is not true sometimes as the F distribution does not depend on the population variance but on the two parameters v1 and v2.
A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to Minitab with the following results:
Analysis of Variance
Source df SS MS F P
Factor 3 28.17 9.39 5.37 0.010
Error 15 26.26 1.75
Total 18 54.43
A) Reject H0 if F >
B) For the 0.05 level of significance, is there a difference in the mean difference in the mean number of months before a raise was anted among the four CPA firms?
Answer:
A) Reject H0 if F > 5.417
B) we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms
Step-by-step explanation:
A) From the table, we can see that we have df1 = 3 and df2 = 15. And we are given a significance level of α = 0.01
We are also given f-value of 1.75
Thus,from the f-distribution table attached at significance level of α = 0.01 and df1 = 3 and df2 = 15, we have;
F-critical = 5.417
Normally, we reject H0 if F > 5.417
But in this case, F is 1.75 < 5.417 and so we conclude that we do not reject H0 at the 0.01 level of significance
B) for 0.05 level of significance, df1 = 3 and df2 = 15, from the 2nd table attached, we have;
F-critical = 3.2874
Again the f-value is less than this critical one.
Thus, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms
The cost of a daily rental car is as follows: The initial fee is $39.99 for the car, and it costs $0.20 per mile. If Julie's final bill was $100.00 before taxes, how many miles did she drive?
Answer:
300.05 miles
Step-by-step explanation:
initial fee= $39.99
final bill = $ 100
cost =$ 0.20 per mile
remaining amount = $ 60.01
solution,
she drive = remaining amount / cost
=60.01/0.20
=300.05 miles
Answer:
500 miles
Step-by-step explanation:
Let us use cross multiplication to find the unknown amount.
Given:
1) Cost for 1 mile=$0.20
2)Cost for x miles=$100
Solution:
No of miles Cost
1) 1 $0.20
2)x $100
By cross multiplying,
100 x 1= 0.20x
x=100/0.20
x=500 miles
Thank you!
The mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days. Suppose that the rain pattern is Normally distributed. what is the probability of raining if the number of days are more than 23?
Answer:
The probability of raining if the number of days is more than 23 is 0.0668.
Step-by-step explanation:
We are given that the mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days.
Let X = Number of days of observing rain in a particular city.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean number of days = 20 days
[tex]\sigma[/tex] = standard deviation = 2 days
So, X ~ Normal([tex]\mu=20, \sigma^{2} = 2^{2}[/tex])
Now, the probability of raining if the number of days is more than 23 is given by = P(X > 23 days)
P(X > 23 days) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{23-20}{2}[/tex] ) = P(Z > 1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)
= 1 - 0.9332 = 0.0668
The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.
Please help. I’ll mark you as brainliest if correct!
Answer:
9 3 -7 -13
4 -4 11 8
0 9 2 -4
Step-by-step explanation:
9 3 -7 -13
4 -4 11 8
0 9 2 -4
Answer: 9 3 -7 -13
4 -4 11 8
0 9 2 -4
Step-by-step explanation:
You are studying for your final exam of the semester up to this point you received 3 exam scores of 61% 62% and 86% to receive a grade of c and the class you must have an average exam score between 70% and 79% for all four exams including the final find the widest range of scores that you can get on the final exam in order to receive a grade of C for the class 63 to 100% 71 to 100% 68 to 97
There will be a total of 4 test scores including the final exam. To get a 70, the 4 tests need to equal 4 x 70 = 280 points , to be 79, they have to equal 4 x 79 = 316 points.
The 3 already done = 61 + 62 + 86 = 209 points.
The final exam needs to be between :
280 -209 = 71
316 -209 = 107. The answer would be between 71 and 100%
Foram prescritos 500mg de dipirona para uma criança com febre.Na unidade tem disponivel ampola de 1g/2ml.Quantos g vão ser administrados no paciente
De acordo com a disponibilidade da unidade, há apenas a seguinte dosagem: 1g/2mL - ou seja, uma grama de dipirona a cada 2mL
O enunciado está meio mal formulado, pois é dito que foram prescritos 500mg de dipirona e é essa quantidade de farmaco que a criança tem que tomar. Deseja-se saber quantos mL deverao ser administrados.
Fazendo a classica regra de 3, podemos chegar no volume desejado:
(atentar que 500mg = 0,5g)
g mL
1 --------- 2
0,5 --------- X
1 . X = 0,5 . 2
X = 1mLFind the point(s) on the ellipse x = 3 cost, y = sin t, 0 less than or equal to t less than or equal to 2pi closest to the point(4/3,0) (Hint: Minimize the square of the distance as a function of t.) The point(s) on the ellipse closest to the given point is(are) . (Type ordered pairs. Use a comma to separate answers as needed.)
Answer and Step-by-step explanation:
The computation of points on the ellipse is shown below:-
Distance between any point on the ellipse
[tex](3 cos t, sin t) and (\frac{4}{3},0) is\\\\ d = \sqrt{(3 cos\ t - \frac{4}{3}^2) } + (sin\ t - 0)^2\\\\ d^2 = (3 cos\ t - \frac{4}{3})^2 + sin^2 t[/tex]
To minimize
[tex]d^2, set\ f' (t) = 0\\\\2(3cos\ t - \frac{x=4}{3} ).3(-sin\ t) + 2sin\ t\ cos\ t = 0\\\\ 8 sin\ t - 16 sin\ t\ cos\ t = 0\\\\ 8 sin\ t (1 - 2 cos\ t) = 0\\\\ sin\ t = 0, cos\ t = \frac{1}{2} \\\\ t= 0, \ 0, \pi,2\pi,\frac{\pi}{3} , \frac{5\pi}{3}[/tex]
Now we create a table by applying the critical points which are shown below:
t [tex]d^{2} = (3\ cos t - \frac{4}{3})^{2} + sin^{2}t[/tex]
0 [tex]\frac{25}{9}[/tex]
[tex]\pi[/tex] [tex]\frac{169}{9}[/tex]
[tex]2\pi[/tex] [tex]\frac{25}{9}[/tex]
[tex]\frac{\pi}{3}[/tex] [tex]\frac{7}{9}[/tex]
[tex]\frac{5\pi}{3}[/tex] [tex]\frac{7}{9}[/tex]
When t = [tex]\frac{\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{\sqrt{3} }{2})[/tex]
When t = [tex]\frac{5\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{-\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{-\sqrt{3} }{2})[/tex]
Factor quadratic plz 15x^2-4x-4=
Answer:
x = 2/3 or x = -2/5
Step-by-step explanation:
15x^2 - 4x - 4 = ?
factor the left side of the expression and set factors equal to zero:
(3x-2)(5x+2)=0
3x - 2 =0 or 5x + 2 =0
3x =2 or 5x = -2
x = 2/3 or x = -2/5
Use Lagrange multipliers to minimize the function subject to the following two constraints. Assume that x, y, and z are nonnegative. Question 18 options: a) 192 b) 384 c) 576 d) 128 e) 64
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option C is the correct option
Step-by-step explanation:
From the question we are told that
The equation is [tex]f (x, y , z ) = x^2 +y^2 + z^2[/tex]
The constraint is [tex]P(x, y , z) = x + y + z - 24 = 0[/tex]
Now using Lagrange multipliers we have that
[tex]\lambda = \frac{ \delta f }{ \delta x } = 2 x[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta y } = y[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta z } = 2 z[/tex]
=> [tex]x = \frac{ \lambda }{2}[/tex]
[tex]y = \frac{ \lambda }{2}[/tex]
[tex]z = \frac{ \lambda }{2}[/tex]
From the constraint we have
[tex]\frac{\lambda }{2} + \frac{\lambda }{2} + \frac{\lambda }{2} = 24[/tex]
=> [tex]\frac{3 \lambda }{2} = 24[/tex]
=> [tex]\lambda = 16[/tex]
substituting for x, y, z
=> x = 8
=> y = 8
=> z = 8
Hence
[tex]f (8, 8 , 8 ) = 8^2 +8^2 + 8^2[/tex]
[tex]f (8, 8 , 8 ) = 192[/tex]
PLEASE HELP ASAP RN!!!!!!
Answer:
3sqrt(2)
Step-by-step explanation:
sqrt(32) - sqrt(2)
rewriting sqrt(32)
sqrt(16*2) - sqrt(2)
sqrt(16) * sqrt(2) - sqrt(2)
4 sqrt(2) - sqrt(2)
3sqrt(2)
Allison bought jelly beans to share with her friends. She bought pounds of blueberry jelly beans and pounds of lemon jelly beans. If she gave pounds of jelly beans away to her friends, how many pounds of jelly beans does Allison have left?
Answer: [tex]1\dfrac{11}{12}\text{ pounds}[/tex]
Step-by-step explanation:
The complete question is provided in the attachment.
Given, Amount blueberry jelly beans= [tex]1\dfrac{1}{4}[/tex] pounds
[tex]=\dfrac{5}{4}[/tex] pounds.
Amount lemon jelly beans = [tex]2\dfrac{1}{3}[/tex]pounds
[tex]=\dfrac{7}{2}[/tex] pounds
Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans
[tex]=(\dfrac{5}{4}+\dfrac{7}{3})[/tex] pounds
[tex]=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}[/tex]
Amount of jelly beans she gave away = [tex]1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}[/tex]
Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away
=[tex]\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}[/tex]
She has left [tex]1\dfrac{11}{12}\text{ pounds}[/tex] of jelly beans.
A sport jacket is on sale for 35% off, if the originsl price is $140, what is the sale price?
Answer:
$91
Step-by-step explanation:
If a jacket is on sale for 35% off, that means that the price of the jacket is [tex]100-35=65[/tex]% of its original price.
We can find 65% of 140 by making 65% into a decimal - 0.65, then multiply it by 140.
[tex]140\cdot0.65=91[/tex]
Hope this helped!
Answer:
$91.00
Step-by-step explanation:
The jacket is on sale for 35%. Usually, you pay for 100% of the jacket's price. Since it is on sale, we can subtract 35% from 100%.
100%-35%=65%
With the sale, you only pay for 65% of the price.
Now, we can multiply 65% and 140.
65% * 140
Convert 65% to a decimal. Divide 65 by 100 or move the decimal place 2 spots to the left.
65/100=0.65
65.0 --> 6.5 --> 0.65
0.65 * 140
Multiply
91
$91
The sale price for the sports jacket is $91.00
A child weighing 22.5 kg has an IV order for Vancomycin Calculate the q8h per dose dosage if the label states that
the total daily intravenous dosage is 40 mg/kg of body weight.
Answer:
q8h dosage = 112.5mg
Step-by-step explanation:
Given
Child Weight = 22.5 kg
Daily Intravenous Dosage = 40mg/kg
Type of Dose = q8h
Required
Calculate the q8h per dose
We start by calculating the total daily dosage in mg
This is calculated by multiplying the child weight by the intravenous dosage
Daily Dosage = 22.5kg * 40mg/kg
Daily Dosage = 900mg
This implies that the body weight requires 900 mg daily
Next is to calculate the q8h dosage
q8h means every 8 hours.
q8h dosage = 900mg/8
q8h dosage = 112.5mg
Which statements about the dilation are true? Check all that apply. Triangle X prime Y prime Z prime. Point X prime is 2 units from the center of dilation C and point Z prime is 3 units from the center of dilation. Triangle X Y Z. Point X is 5 units from point C and point Z is 7.5 units from point C. The center of dilation is point C. It is a reduction. It is an enlargement. The scale factor is 2.5. The scale factor is Two-fifths.
Answer:
I only know two right answers.
A: The center of dilation is point C.
C: It is an enlargement.
E: The scale factor is 2/5.
Step-by-step explanation:
These two answers are correct because When you look in the center you see a C.
You tell if it is a reduction because the pre image is small but the image is big.
The center of dilation is point C.
It is an enlargement.
The scale factor is 2/5
The correct options are D, F, H.
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
Given:
The transformation of the figure is dilation.
The figure is given in the attached image.
From the diagram:
The center of dilation is point C.
It is an enlargement.
The scale factor is 2/5
Therefore, all the correct statements are given above.
To learn more about the dilation in geometry;
https://brainly.com/question/10713409
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The value of 3 in 783.97
Answer:
place value of 3 in 783.97 is 3
Step-by-step explanation:
Answer:
Units
Step-by-step explanation:
The units start counting from 3 because after the point that is the 9 start counting tenth
Let X denote the day she gets enrolled in her first class and let Y denote the day she gets enrolled in both the classes. What is the distribution of X
Answer:
X is uniformly distributed.
Step-by-step explanation:
Uniform Distribution:
This is the type of distribution where all outcome of a certain event have equal likeliness of occurrence.
Example of Uniform Distribution is - tossing a coin. The probability of getting a head is the same as the probability of getting a tail. The have equal likeliness of occurrence.
will rate7 you brainliest
Answer:
[tex]\Large \boxed{\sf \bf \ \ \dfrac{x^2-x-6}{x^2-3x+2} \ \ }[/tex]
Step-by-step explanation:
Hello, first of all, we will check if we can factorise the polynomials.
[tex]\boxed{x^2+6x+8}\\\\\text{The sum of the zeroes is -6=(-4)+(-2) and the product 8=(-4)*(-2), so}\\\\x^2+6x+8=x^2+2x+4x+8=x(x+2)+4(x+2)=(x+2)(x+4)[/tex]
[tex]\boxed{x^2+3x-10}\\\\\text{The sum of the zeroes is -3=(-5)+(+2) and the product -10=(-5)*(+2), so}\\\\x^2+3x-10=x^2+5x-2x-10=x(x+5)-2(x+5)=(x+5)(x-2)[/tex]
[tex]\boxed{x^2+2x-15}\\\\\text{The sum of the zeroes is -2=(-5)+(+3) and the product -15=(-5)*(+3), so}\\\\x^2+2x-15=x^2-3x+5x-15=x(x-3)+5(x-3)=(x+5)(x-3)[/tex]
[tex]\boxed{x^2+3x-4}\\\\\text{The sum of the zeroes is -3=(-4)+(+1) and the product -4=(-4)*(+1), so}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=(x+4)(x-1)[/tex]
Now, let's compute the product.
[tex]\dfrac{x^2+6x+8}{x^2+3x-10}\cdot \dfrac{x^2+2x-15}{x^2+3x-4}\\\\\\=\dfrac{(x+2)(x+4)}{(x+5)(x-2)}\cdot \dfrac{(x+5)(x-3)}{(x+4)(x-1)}\\\\\\\text{We can simplify}\\\\=\dfrac{(x+2)}{(x-2)}\cdot \dfrac{(x-3)}{(x-1)}\\\\\\=\large \boxed{\dfrac{x^2-x-6}{x^2-3x+2}}[/tex]
So the correct answer is the first one.
Thank you.
Lines a and b are parallel. If the slope of line a is , what is the slope of line b?
A.
-
B.
4
C.
D.
-4
Answer:
C. 1/4
Step-by-step explanation:
Parallel lines always have the same slope.
Answer:
C. 1/4
Step-by-step explanation:
Parallel lines have the same slope. If line b is parallel to line a, and line a has slope 1/4, then line b has slope 1/4.
The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100, and the standard deviation is 2. You wish to test H0: μ = 100 versus H1: μ ≠ 100 with a sample of n = 9 specimens.
A. If the acceptance region is defined as 98.5 le x- 101.5, find the type I error probability alpha.
B. Find beta for the case where the true mean heat evolved is 103.
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?
Answer:
A.the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]
B. β = 0.0122
C. β = 0.0000
Step-by-step explanation:
Given that:
Mean = 100
standard deviation = 2
sample size = 9
The null and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o: \mu = 100}[/tex]
[tex]\mathtt{H_1: \mu \neq 100}[/tex]
A. If the acceptance region is defined as [tex]98.5 < \overline x > 101.5[/tex] , find the type I error probability [tex]\alpha[/tex] .
Assuming the critical region lies within [tex]\overline x < 98.5[/tex] or [tex]\overline x > 101.5[/tex], for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is [tex]\mu = 100[/tex]
∴
[tex]\mathtt{\alpha = P( type \ 1 \ error ) = P( reject \ H_o)}[/tex]
[tex]\mathtt{\alpha = P( \overline x < 98.5 ) + P( \overline x > 101.5 )}[/tex]
when [tex]\mu = 100[/tex]
[tex]\mathtt{\alpha = P \begin {pmatrix} \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline 98.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} + \begin {pmatrix}P(\dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{101.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} }[/tex]
[tex]\mathtt{\alpha = P ( Z < \dfrac{-1.5}{\dfrac{2}{3}} ) + P(Z > \dfrac{1.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\alpha = P ( Z <-2.25 ) + P(Z > 2.25) }[/tex]
[tex]\mathtt{\alpha = P ( Z <-2.25 ) +( 1- P(Z < 2.25) })[/tex]
From the standard normal distribution tables
[tex]\mathtt{\alpha = 0.0122+( 1- 0.9878) })[/tex]
[tex]\mathtt{\alpha = 0.0122+( 0.0122) })[/tex]
[tex]\mathbf{\alpha = 0.0244 }[/tex]
Thus, the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]
B. Find beta for the case where the true mean heat evolved is 103.
The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis [tex]\mathtt{H_o}[/tex]
Thus;
β = P( type II error) - P( fail to reject [tex]\mathtt{H_o}[/tex] )
∴
[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]
Given that [tex]\mu = 103[/tex]
[tex]\mathtt{\beta = P( \dfrac{98.5 -103}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-103}{\dfrac{2}{\sqrt{9}}}) }[/tex]
[tex]\mathtt{\beta = P( \dfrac{-4.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-1.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\beta = P(-6.75 \leq Z \leq -2.25) }[/tex]
[tex]\mathtt{\beta = P(z< -2.25) - P(z < -6.75 )}[/tex]
From standard normal distribution table
β = 0.0122 - 0.0000
β = 0.0122
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?
[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]
Given that [tex]\mu = 105[/tex]
[tex]\mathtt{\beta = P( \dfrac{98.5 -105}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-105}{\dfrac{2}{\sqrt{9}}}) }[/tex]
[tex]\mathtt{\beta = P( \dfrac{-6.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-3.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\beta = P(-9.75 \leq Z \leq -5.25) }[/tex]
[tex]\mathtt{\beta = P(z< -5.25) - P(z < -9.75 )}[/tex]
From standard normal distribution table
β = 0.0000 - 0.0000
β = 0.0000
The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.
Which expression is equivalent to 73 ⋅ 7−5? 72 77 1 over 7 to the 2nd power 1 over 7 to the 7th power
Answer:
1/7^2
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
__
Then your expression simplifies to ...
[tex]7^3\cdot 7^{-5}=7^{3-5}=7^{-2}=\boxed{\dfrac{1}{7^2}}[/tex]
Answer:
The answer is 1/7^2
Step-by-step explanation:
I took the test lol
If a recipe which makes 8 servings calls for 2 cups of sugar, how many cups of sugar will it take to make 18 servings?
Answer:
4.5
Step-by-step explanation:
2/8=x/18
Answer:
4.5 cups
Step-by-step explanation:
first you set up the problem like servings/cups. This would look like 8/2. Then you add the 18 servings and make it a cross multiplication problem. The expression would look like 8/2=18/x. You cross multiply and get 8x=36. Divide by 8 and get x=4.5 cups.
Time
(minutes)
Water
(gallons)
1
16.50
1.5
24.75
2
33
find the constant of proportionality for the second and third row
Answer:
16.50
Step-by-step explanation:
Constant of proportionality = no of gallons of water per 1 minute.
In the first row, we have 16.50 gallons of water per 1 minute.
In the 2nd row, we have 24.75 gallons of water in 1.5 minutes. In 1 minute, we will have 24.75 ÷ 1.5 = 16.50 gallons
In the 3rd row, we have 33 gallons in 2 minutes. In 1 minute, we will have 33 ÷ 2 = 16.50 gallons.
We can see that there seems to be the same constant of proportionality for the 2nd and 3rd row, which is 16.50.
Thus, a relationship between gallons of water (w) and time (t), considering the constant, 16.50, can be written as: [tex] w = 16.50t [/tex]
This means the constant of proportionality, 16.50, is same for all rows.
A professional soccer player kicked a ball across the field. The ball’s height, in meters, is modeled by the function graphed below. What's the average rate of change between the point when the ball reached its maximum height and the point where it hit the ground?
Answer:
Hey there!
You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.
Let me know if this helps :)
Answer:
–3 meters per second
Step-by-step explanation:
Evaluate integral _C x ds, where C is
a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)
b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)
Answer:
a. [tex]\mathbf{36 \sqrt{5}}[/tex]
b. [tex]\mathbf{ \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]
Step-by-step explanation:
Evaluate integral _C x ds where C is
a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)
i . e
[tex]\int \limits _c \ x \ ds[/tex]
where;
x = t , y = t/2
the derivative of x with respect to t is:
[tex]\dfrac{dx}{dt}= 1[/tex]
the derivative of y with respect to t is:
[tex]\dfrac{dy}{dt}= \dfrac{1}{2}[/tex]
and t varies from 0 to 12.
we all know that:
[tex]ds=\sqrt{ (\dfrac{dx}{dt})^2 + ( \dfrac{dy}{dt} )^2}} \ \ dt[/tex]
∴
[tex]\int \limits _c \ x \ ds = \int \limits ^{12}_{t=0} \ t \ \sqrt{1+(\dfrac{1}{2})^2} \ dt[/tex]
[tex]= \int \limits ^{12}_{0} \ \dfrac{\sqrt{5}}{2}(\dfrac{t^2}{2}) \ dt[/tex]
[tex]= \dfrac{\sqrt{5}}{2} \ \ [\dfrac{t^2}{2}]^{12}_0[/tex]
[tex]= \dfrac{\sqrt{5}}{4}\times 144[/tex]
= [tex]\mathbf{36 \sqrt{5}}[/tex]
b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)
Given that:
x = t ; y = 3t²
the derivative of x with respect to t is:
[tex]\dfrac{dx}{dt}= 1[/tex]
the derivative of y with respect to t is:
[tex]\dfrac{dy}{dt} = 6t[/tex]
[tex]ds = \sqrt{1+36 \ t^2} \ dt[/tex]
Hence; the integral _C x ds is:
[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]
Let consider u to be equal to 1 + 36t²
1 + 36t² = u
Then, the differential of t with respect to u is :
76 tdt = du
[tex]tdt = \dfrac{du}{76}[/tex]
The upper limit of the integral is = 1 + 36× 2² = 1 + 36×4= 145
Thus;
[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]
[tex]\mathtt{= \int \limits ^{145}_{0} \sqrt{u} \ \dfrac{1}{72} \ du}[/tex]
[tex]= \dfrac{1}{72} \times \dfrac{2}{3} \begin {pmatrix} u^{3/2} \end {pmatrix} ^{145}_{1}[/tex]
[tex]\mathtt{= \dfrac{2}{216} [ 145 \sqrt{145} - 1]}[/tex]
[tex]\mathbf{= \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]
Solve for x:
x/-6 ≥ -20?
Answer: x ≤ 120
Step-by-step explanation: To get x by itself in this inequality, since it's being divided by -6, we must multiply both sides by -6, just like we would if we were solving an equation, but here is the trick you have to watch out for with inequalities.
When you multiply or divide both sides of an inequality by a
negative, you must switch the direction of the inequality sign.
So our second step in this problem reads x ≤ 120.
Please give this idea your full attention.
Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when multiplying or dividing both sides of an inequality by a negative.
Answer:
x ≤ 120
I hope this helps!
5x+4(-x-2)=-5x+2(x-1)+12
Answer:
x=9/2
Step-by-step explanation:
Let's solve your equation step-by-step.
5x+4(−x−2)=−5x+2(x−1)+12
Step 1: Simplify both sides of the equation.
5x+4(−x−2)=−5x+2(x−1)+12
5x+(4)(−x)+(4)(−2)=−5x+(2)(x)+(2)(−1)+12 (Distribute)
5x+−4x+−8=−5x+2x+−2+12
(5x+−4x)+(−8)=(−5x+2x)+(−2+12) (Combine Like Terms)
x+−8=−3x+10
x−8=−3x+10
Step 2: Add 3x to both sides.
x−8+3x=−3x+10+3x
4x−8=10
Step 3: Add 8 to both sides.
4x−8+8=10+8
4x=18
Step 4: Divide both sides by 4.
4x/4=18/4
x=9/2
