Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use
α = 0.05
and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
n1 = 16
n2 = 10
x1 = 6.82
x2 = 6.28
s1 = 0.65
s2 = 0.75
(a)
State the null and alternative hypotheses.
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 > 0
Ha:
μ1 − μ2 ≤ 0
H0:
μ1 − μ2 ≠ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 > 0
H0:
μ1 − μ2 = 0
Ha:
μ1 − μ2 ≠ 0
(b)
Compute the value of the test statistic. (Round your answer to three decimal places.)
(c)
What is the p-value? (Round your answer to four decimal places.)
p-value =
(d)
What is your conclusion?
Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Do not reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. Do not Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Answers
Answer:
A) Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Test statistic = t = 1.878
C) p-value is 0.038823.
D) Reject the Null hypothesis H0
Step-by-step explanation:
We are given;
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
A) The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Formula yo determine the test statistic is;
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
Plugging in the relevant values, we have;
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
C) The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Plugging in the relevant values, we have;
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value;
From online p-value calculator from t-score and DF which i attached, we have the p-value as;
The p-value is 0.038823.
D) The p-value result is significant at p < 0.05
Thus, we reject the Null hypothesis H0
A) Null hypothesis: μ1 − μ2 ≤ 0
B) Test statistic = t = 1.878
C) The p-value is 0.038823.
D) Reject the Null hypothesis H0.
HypothesisWhat all information we have ?
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
Part A)
The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
Part B)
The formula to determine the test statistic is :
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
The formula to determine the test statistic is t = 1.878.
Part C)
The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value is 0.038823.
Part D)
The p-value result is significant at p < 0.05 is :
Thus, we reject the Null hypothesis H0.
Learn more about "Hypothesis":
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Related Questions
Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c. sin(B) = sin(A) sin(B) = cos(90 – B) cos(B) = sin(180 – B) cos(B) = cos(A)
Answers
Answer:
sin(B) = cos(90 – B)
Step-by-step explanation:
Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.
sin(B) = sin(A)
sin(B) = cos(90 – B)
cos(B) = sin(180 – B)
cos(B) = cos(A)
Assuming the angles are in degrees, the second relation is always true.
By definition of sine,
sin(B) = AC/AB
cos(90-B) = cos (A) = AC/AB
therefore the second relation is true, for arbitrary values of B.
Answer:
sin(B) = cos(90 – B)
Step-by-step explanation:
Which relationship in the triangle must be true?
Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.
Name the major arc and find its measure.
Answers
Answer:
ADB = Major Arc
arc measure = 310
Step-by-step explanation:
major arc measure = 360 - 50 = 310
Write the fraction in simplest form. (3/6) x (7/10)
Answers
7/20
Explanation:
In order to do this, you must first simplify all the equations to the simplest forms. Do this by simplifying 3/6 to 1/2. We know this because 3 is half of 6, therefore it would reduce down to 1/2. 7/10 is already simplified; we know this because 7 is a prime number and can’t do down any further
Now, multiply the two fractions buy multiplying the numerators and denominations together. In other words, 1 x 7 is 7 so your numerator is 7, and 2 x 10 is 20 so your denominator is 20.
Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided. Lower bound equals 0.345, upper boundequals0.895, nequals1000
Answers
Answer:
For this case we have the following confidence interval given:
[tex] 0.345 \leq p \leq 0.895 [/tex]
And for this case we want to find the estimated proportion like this:
[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]
And the margin of error for this case would be given by:
[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]
Step-by-step explanation:
For this case we have the following confidence interval given:
[tex] 0.345 \leq p \leq 0.895 [/tex]
And for this case we want to find the estimated proportion like this:
[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]
And the margin of error for this case would be given by:
[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]
Which best describes the structure outlined in the bridge.
Answers
Answer:D
Step-by-step explanation:
Express it in slope-intercept form.
Answers
In 4 days, the price of a share of stock rose 3/4 of a point. On a average, what was the change in stock each day?
Answers
Answer:
0.15 or 15%
Step-by-step explanation:
If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.
To calculate how much the price went up each day on average, we will create exponential equation.
x = price of the stock
y = average daily change
[tex]x*y^{4} =1.75x[/tex] divide by x
[tex]y^{4} = 1.75[/tex]
We will calculate it using logarithms.
y = 1.15016, rounded to 1.15
We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%
how are the values of the eights related in 880
Answers
Answer:
8 is in the hundreds place as well as in the tens place.
Step-by-step explanation:
We use the base 10 system. 880 would represent eight hundred and eighty. So our 0 would be the ones place, 8 in the tens place, and 8 also in the hundreds place.
A model for consumers' response to advertising is given by the equation N(a)=2600 + 470ln (a) Where N(a) is the number of units sold, a is the amount spent on advertising, in thousands of dollars, & a≥1.
Required:
a. How many units were sold after spending $1,000 on advertising?
b. Find N′(a).
c. Find the maximum value, if it exists.
d. Find lim a→[infinity] N′(a).
Answers
Answer:
a. [tex]N(1)=2600[/tex]
b. [tex]N'(a) = 470/a[/tex]
c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)
d. lim a→[infinity] N′(a) = 0
Step-by-step explanation:
a.
the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:
[tex]N(1)=2600 + 470ln(1)[/tex]
[tex]N(1)=2600 + 470*0[/tex]
[tex]N(1)=2600[/tex]
b.
To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:
[tex]N'(a) = 2600' + (470ln(a))'[/tex]
[tex]N'(a) = 0 + 470*(1/a)[/tex]
[tex]N'(a) = 470/a[/tex]
c.
The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).
The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.
d.
When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.
by which number -7 /25 should be divided to get -1/15?
Answers
Answer:
21/5
Step-by-step explanation:
if a/b = c, then b=a/c
in other words:
divide -7/25 by -1/15 to get the answer
It also helps to use the fact that a/b / c/d = a/b * d/c
-7/25 / -1/15 = -7/25 * -15/1
= 105 / 25
= 21 / 5
Answer:
[tex]4 \frac{1}{5} [/tex]
Step-by-step explanation:
[tex] \frac{ - 7}{25} \div x = \frac{ - 1}{15} [/tex]
[tex]x = \frac{ - 7}{25} \div \frac{ - 1}{15} [/tex]
[tex] = \frac{7}{25} \times \frac{15}{1} [/tex]
[tex] = \frac{21}{5} = 4 \frac{1}{5} [/tex]
A child is playing games with empty soda cups. There are three sizes: small, medium, and large. After some experimentation
she discovered she was able to measure out 160 ounces in the following ways:
1) 2 small, 2 medium, 4 large
2) 2 small, 6 medium, 1 large
3) 5 small, 1 medium, 3 large
Determine the size of the cups.
Answers
Answer:
S is the volume of the small cup, M the volume of the medium cup and L the volume of the large cup:
2*S + 2*M + 4*L = 160oz
2*S + 6*M + 1*L = 160oz
5*S + 1*M + 3*L = 160oz.
First, we must isolate one of the variables, for this we can use the first two equations and get:
2*S + 2*M + 4*L = 160oz = 2*S + 6*M + 1*L
We can cancel 2*S in both sides:
2*M + 4*L = 6*M + 1*L
now each side must have only one variable:
4*L - 1*L = 6*M - 2*M
3*L = 4*M
L = (4/3)*M.
now we can replace it in the equations and get :
2*S + 2*M + 4*(4/3)*M = 160oz
2*S + 6*M + (4/3)*M = 160oz
5*S + 1*M + 4M = 160oz.
simplifing them we have:
2*S + (22/3)*M + = 160oz
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
(the first and second equation are equal because we used those to get the relation of M and L, so we now have only two equations):
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
We can take the second equation and simplify it:
S + M = 160oz/5 = 32oz
S = 32oz - M
Now we can replace it in the first equation and solve it for M
2*S + (22/3)*M = 2*(32oz - M) + (22/3)*M = 160oz
62oz - 2*M + (22/3)*M = 160oz
-(6/3)*M + (22/3)*M = 98oz
(18/3)*M = 98oz
M = (3/18)*98oz = 16.33 oz
Then:
L = (4/3)*M =(4/3)*16.33oz = 21.78 oz
and:
S = 32oz - M = 32oz - 16.33oz = 15.67oz
what are the multiples of 5,6,8,9?
Answers
the multiples of 6 at
6,12,18,24,30,36,42,48,55,60
the multiples of 8 are
8,16,24,32,40,48,56,64,72,80
the multiples of 9 are
9,18,27,36,45,54,63,72,81
Determine whether the sequence converges or diverges. If it converges, find the limit. an = 9 + 14n2 n + 15n2 Step 1 To find lim n → [infinity] 9 + 14n2 n + 15n2 , divide the numerator and denominator by the highest power of n that occurs in the fraction. This is n .
Answers
Answer:
The sequence ConvergesStep-by-step explanation:
Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]
To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;
[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]
As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;
[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]
Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]
Since the limit of the sequence gave a finite number , the sequence converges.
Note that the only case when the sequence diverges id when the limit of the sequence is infinite
1. A fruitseller bought 200 apples for Rs 300.40 of them were rotten and thrown away.
She sold the rest at Rs 2.25 each. Find its gain or loss percent.
253
A Book of Mathematics-8
Answers
Answer:
ok I am tellin6 to you
Step-by-step explanation:
ok I will tell to you
Please answer this correctly
Answers
Answer:
Option 2
Step-by-step explanation:
The average temperature in January is -1 degrees celsius. Last year, it was 1 degrees celsius higher than the average.
-1 + 1 = 0
Answer:
The second answer.
Step-by-step explanation:
The average temp. is -1C.
'was 1C warmer' = +1
-1+1=0
A poll found that 5% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 11 teenagers sleeping in each tent. Assume that these 11 teenagers are independent of each other. (Round your answers to four decimal places.)
a) Calculate the probability that at least one of them suffers from arachnophobia. - 0.4312
b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666
c) Calculate the probability that at most 1 of them suffers from arachnophobia? What is C?
Answers
Answer:
a) Calculate the probability that at least one of them suffers from arachnophobia.
x = number of students suffering from arachnophobia
= P(x ≥ 1)
= 1 - P(x = 0)
= 1 - [0.05⁰ x (1 - 0.05)¹¹⁻⁰ ]
= 1 - (0.95)¹¹
= 0.4311999 = 0.4312
b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666
= P(x = 2)
= (¹¹₂) x (0.05)² x (0.95)⁹
where ¹¹₂ = 11! / (2!9!) = (11 x 10) / (2 x 1) = 55
= 55 x 0.0025 x 0.630249409 = 0.086659293 = 0.0867
c) Calculate the probability that at most 1 of them suffers from arachnophobia?
P(x ≤ 1)
= P(x = 0) + P(x = 1)
= [(¹¹₀) x 0.05⁰ x 0.95¹¹] + [(¹¹₁) x 0.05¹ x 0.95¹⁰]
= (1 x 1 x 0.5688) + (11 x 0.05 x 0.598736939) = 0.5688 + 0.3293 = 0.8981
In the diagram below, if AD= 100 and AC = 34, find CD.
A 59
B 76
C 45
D 66
Answers
Answer:
D. 66
Step-by-step explanation:
Well if AD is 100 and AC is 34 that leaves CD so we can just subtraction 34 from 100 and get 66.
Answer:
D. 66
Step-by-step explanation:
AD = 100
AC = 34
The whole line is 100. A part of the line is 34. The other part will be 66.
100 - 34 = 66
Two fair dies are rolled. What is the conditional probability thatat least one lands on 6 given that the dies land on different numbers?
Answers
Answer:
33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
All outcoms of the dices:
Format(Dice A, Dice B)
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
36 in all
Total outcomes:
In this question, we want all with no repetition.
There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.
Desired outcomes:
One landing on six:
(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).
10 desired outcomes.
Probability:
10/30 = 0.3333
33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers
co
Which graph represents the inequality?
-2
1-1
-12
1
1 2
NE
1
Y>-
2
2
А
++
1 -1
-12
ou
-2
od
1
NIE
1
B
1 2
2
2
---
Oto
-2
-1
1 2
-12
-
NIE
NI
12
D
-2
1 - 1
1
0
1
1 2
NIS
2
NI
Answers
Answer:
A
Step-by-step explanation:
Given the equality y > -½, it means the values of y is greater than -½.
The values of y would range from 0 upwards. I.e. 0, ½, 1, 1½, 2. . .
Thus, when graphed on a number line, the circle that appears like "o" would start from -½, and the "o" would not be full or shaded to indicate that -½ is not included in the values of y, which are greater than -½. Since the values of y are greater than -½ the direction of the arrow that indicates values of y would point towards our far right, to indicate the values included as y.
Therefore, the graph that indicates the inequality y > ½ is A
Answer:
A
Step-by-step explanation:
What is the value of this expression when n approaches infinity?
Answers
Answer:
C. Approaches 35
Step-by-step explanation:
If we graph the expression, we see that we have an asymptote at y = 35.
Question 1
You can ride a taxi and pay a flat rate of $25 to go anywhere in the city, or you can pay a
base rate of $15 and $1 per mile. For which trip would it make more sense to pay the base
rate and 1$ per mile?
15 mile trip
9 mile trip
25 mile trip
O 12 mile trip
Answers
Answer:
9 mile trip
Step-by-step explanation:
$15 + $15 = $30
$15 + $9 = $24
$15 + $25 = $40
$15 + $12 = $27
$30 > $25
$24 < $25
$40 > $25
$27 > $25
A quadrilateral has three angles that measure 80°, 110°, and 75°. Which is the measure of the fourth angle? A. 50° B. 90° C. 95° D. 125°
Answers
Answer: 95 degrees.
Step-by-step explanation:
A quadrilateral has a total combined angle measure of 360 degrees. If you do 360-(80+110+75) it would equal 95.
Answer:
95°Option C is the correct option
Solution,
The sum of the angles in the quadrilateral is 360°
Let the forth angle be X
X + 80° + 110° + 75° = 360°
Calculate the sum:
X + 265° = 360°
Subtract 265° on both sides
X + 265° - 265° = 360° - 265°
Calculate the difference
X = 95°
Hope this helps...
Good luck on your assignment...
Is the area of this shape approximately 57 6 cm ? If not, give the correct area.
O True
O False
Answers
Answer: True
Step-by-step explanation: Taking the triangle from the left and moving it to the right creates a rectangle. From there just do 12.8×4.5.
Pls help see (pic posted)
Answers
Answer:
AB=8.4 inchesAC=13.05 inchesSolution,
[tex] \frac{ab}{bc} = tan \: 40 \\ ab = bc \times tan \: 40 \\ ab = 10 \times 0.84 \\ ab = 8.4 \: inches \: [/tex]
[tex] \frac{bc}{ac} = cos \: 40 \\ \frac{bc}{cos \: 40} = ac \\ ac = \frac{10}{cos \: 40} \\ ac = 13.05 \: inches[/tex]
Hope this helps...
Good luck on your assignment..
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 39 in. by 21 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume.
Answers
Answer:
Length=29.8 inches
Width=11.8 inches
Height=4.6 inches
Volume=1,617.54 cubic inches
Step-by-step explanation:
Let the side of congruent square cut =x inches
So the length of the rectangular box=(39-2x)
width = (21-2x)
height = x
The volume V=Length*Width*Height
= (39-2x)*(21-2x)*x
dV/dx= (39-2x)(21-4x)-2x(17-2x)=0
Simplify the equation above
819-156x-42x+8x^2-34x+4x^2=0
We have,
12x^2 -232 +819=0
Solve the quadratic equation using formula
a=12
b= -232
c=819
x= -b +or- √b^2-4ac/2a
= -(-232) +- √(-232)^2 - (4)(12)(819) / (2)(12)
= 232 +or- √53824 - 39312 / 24
= 232 +or- √14512 / 24
= 232 +or- 4√907 / 24
x= 232 / 24 + 4√907 / 24
=14.6861
Or
x=232 / 24 - 4√907 / 24
=4.64726
x=4.6 inches
Length=(39-2x)
={39-2(4.6)}
= 29.8 inches
Width=(21-2x)
={21-2(4.6)}
= 11.8 inches
Height=x= 4.6 inches
Volume=(39-2x)*(21-2x)*x
={39-2(4.6)}*{21-2(4.6)*4.6
=(39-9.2)*(21-9.2)*4.6
=29.8*11.8*4.6
=1,617.544
Approximately 1,617.54
Volume=1,617.54 cubic inches
Select the correct answer from each drop down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
Answers
Answer:
the slope of A'B' = 3
A'B' passes through point O
Step-by-step explanation:
A dilation with scale factor 3 gives the effect of stretching the line AB three times longer. As dilation does not change the direction of the line, the slope will stay the same. If point O lies on AB and is the center of dilation, then the point O must also lie on A'B'
The required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Given that,
To Select the correct answer from each drop-down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
The scale factor is defined as the ratio of modified change in length to the original length.
Here, is o is the center of the line AB and slope of line AB is 3 than the line dilated with scale factor 3 A1B1 has also a scale factor of 3 because Position of dilation is center 0 thus dilation did not get any orientation.
And the center of dilation is O so line A1B1 passes through O.
Thus, the required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
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What multiplication expression is equal to 3/5÷1/4 out of 3/5×1/4 or 5/3×1/4 or 3/5×1/4 or 3/5×4/1
Answers
Answer:
it would be 3/5*4/1
Step-by-step explanation:
To divide you multiply the first number by the reciprocal of the second number. Check and you'll see that the answer is the same. Hope this helps!
Answer:
The answer is 3/5 x 4/1
Step-by-step explanation:
How do you write 0.00609 in scientific notation? ____× 10^_____
Answers
Answer:
6.09 * 10 ^-3
Step-by-step explanation:
We want one non zero digit to the left of the decimal
Move the decimal 3 places to the right
6.09
The exponent is 3 and it is negative since we move to the right
6.09 * 10 ^-3
Answer:
6.09(10⁻³)
Step-by-step explanation:
Step 1: Put number into proper scientific decimal form
6.09
Step 2: Figure out how many decimals places it moves
Since it moves to the left 3, our exponent would be -3
A kite 100 ft above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? rad/s g
Answers
Answer:
0.015 radians per second.
Step-by-step explanation:
They tell us that at the moment the speed would be 6 ft / s, that is, dx / dt = 6 and those who ask us is dθ / dt.
Which we can calculate in the following way:
θ = arc sin 100/200 = pi / 6
Then we have the following equation of the attached image:
x / 100 = cot θ
we derive and we are left:
(1/100) * dx / dt = - (csc ^ 2) * θ * dθ / dt
dθ / dt = 0.01 * dx / dt / (- csc ^ 2 θ)
dθ / dt = 0.01 * 6 / (- csc ^ 2 pi / 6)
dθ / dt = 0.06 / (-2) ^ 2
dθ / dt = -0.015
So there is a decreasing at 0.015 radians per second.
The horizontal distance and the height of the kite are illustration of rates.
The angle is decreasing at a rate of 0.24 radian per second
The given parameters are:
[tex]\mathbf{Height =y= 100ft}[/tex]
[tex]\mathbf{Speed =\frac{dx}{dt}= 6fts^{-1}}[/tex]
[tex]\mathbf{Length = 200}[/tex]
See attachment for illustration
Calculate the angle using the following sine ratio
[tex]\mathbf{sin(\theta) = \frac{100}{200}}[/tex]
[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]
The horizontal displacement (x) is calculated using the following tangent ratio:
[tex]\mathbf{tan(\theta) = \frac{100}{x}}[/tex]
Take inverse of both sides
[tex]\mathbf{cot(\theta) = \frac{x}{100}}[/tex]
[tex]\mathbf{cot(\theta) = \frac{1}{100}x}[/tex]
Differentiate both sides with respect to time (t)
[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dx}{dt}}[/tex]
Substitute known values
[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 6}[/tex]
[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]
Recall that:
[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]
Take inverse of both sides
[tex]\mathbf{csc(\theta) = 2}[/tex]
Square both sides
[tex]\mathbf{csc^2(\theta) = 4}[/tex]
Substitute [tex]\mathbf{csc^2(\theta) = 4}[/tex] in [tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]
[tex]\mathbf{-4 \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]
Divide both sides by -4
[tex]\mathbf{\frac{d\theta}{dt} = -\frac{24}{100}}[/tex]
[tex]\mathbf{\frac{d\theta}{dt} = -0.24}[/tex]
Hence, the angle is decreasing at a rate of 0.24 radian per second
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Find the percent of increase. Original Price: $135 Retail Price: $162
Answers
20%
Here's a tip: Always start percentage calculating with dividing the current number by 10.