Answer:
2 hours.
Step-by-step explanation:
From the question given above, the following data were obtained:
Speed of motorboat (sₘ) = 8 mph
Speed of cabin cruiser (s꜀) = 16 mph
From the question given, we were told that the cabin cruiser started his journey 2 hours later after the motorboat has left.
Let t be the time for the cabin cruiser.
Thus, the time for the motorboat will be (2 + t)
Also, if the cabin cruiser and the motorboat must be along side each other, then their distance must be the same.
With the above information, we can obtain the time taken for the cabin cruiser and the motorboat to be along side each other. This can be obtained as follow:
Speed of motorboat (sₘ) = 8 mph
Time for motorboat (tₘ) = t + 2
Speed of cabin cruiser (s꜀) = 16 mph
Time for cabin cruiser (t꜀) = t
Distance of motorboat = distance of cabin cruiser
Recall:
Distance = speed × time
Therefore,
sₘ × tₘ = s꜀ × t꜀
8 × (t + 2) = 16 × t
Clear bracket
8t + 16 = 16t
Collect like terms
16 = 16t – 8t
16 = 8t
Divide both side by 8
t = 16 / 8
t = 2 hours
Thus, it will take 2 hours for the cabin cruiser and the motorboat to be along side each other.
What is the slope of the line 4x + 2y = 8?
А 2
b -2
c 1/2
d -1/2
Answer:
x = -1/2y+2
Step-by-step explanation:
4x+2y=8
Step 1: Add -2y to both sides.
4x+2y+−2y=8+−2y
4x=−2y+8
Step 2: Divide both sides by 4.
4x/4 = -2y+8/4
x = -1/2y+2
Hope this helps!
Lincoln is seeking a loan with a simple interest rate of 8% per year. If he wants to borrow $5000, then how much will he be charged in interest for 24 months? $8,000 $9,600 $1,250 $800
Answer:
Lincoln will be charged $9,600.
Step-by-step explanation:
To find the answer we will first turn 8% into a decimal. 8 ÷ 100 = 0.08. Now multiply 0.08 by $5,000 and we get $400. then multiply $400 by 24 and we get $9,600. Therefore, $9,600 is our answer.
help me please!!!!
The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
A. 7 m
B. 14 m
C. 24.5 m
D. 49
Answer:
= p× r²
= 3,14×7×7
= 21,98×7
= 153,86
[tex]153.86 \div 3.14 = 7[/tex]
the peremeter of a square is 16 inches what is the lenth of each side
Answer:If the figure is a square with a perimeter of 16 inches, then each side of the square is 4 inchest in length.
Step-by-step explanation:
Answer:
The length of each side is 4 inches.
Step-by-step explanation:
Since the shape is a square, all sides are equal so you do 16÷4 since there are 4 sides to get your answer of 4 inches.
Enter the measure of YVZ in degrees
Answer:
(3x+5)+(2x) = 90
5x + 5 = 90
5x = 85
x = 17
YVZ = 3×17 +5
=56°
Leslie is installing blue carpet that will cover the entire floor of a room.
What is the area, in square feet, of the room Leslie will cover with blue
carpet?
I need it step by step please
Answer:
392 ft²
Step-by-step explanation:
The composite figure can be divided into a rectangle, 2 triangles and a square
Area of rectangle = Length * width
Area of rectangle = 21 feets * 14 feets = 294 feet²
Area of triangle = 0.5 * base * height
Area of triangle = 0.5 * 7 * 7 = 24.5
AREA of square = a² = 7² = 49 feets²
Total area :
294 feets + (2 * 24.5) feets² + 49 feets²
294 + 49 + 49 = 392 ft²
1. A waste management service attempts to design routes so that each of their trucks pick-up on average four tons of garbage or less. A garbage collector believes, however, that he averages picking up more than four tons of garbage per day and decides to perform a hypothesis test. If the hypothesis test is performed at a 5% significance level and the resulting p-value is 0.04. Your conclusion should be:
2. It has been determined with 95% confidence that the proportion of on-line students at NYU who live in Brooklyn is between 0.73 and 0.77. Determine the sample proportion of on-line NYU students who live in Brooklyn.
3. Assume a normal distribution and use a hypothesis test to test the given claim.
According to city reports, it was found that the mean age of the prison population in the city was 26 years. Marc wants to test the claim that the mean age of the prison population in his city is less than 26 years. He obtains a random sample of 25 prisoners, and finds a mean age of 24.4 years and a standard deviation of 9.2 years. At a significance level of 0.05, what should his conclusion be?
Answer:
1.-Then we p-value indicates that we are in the rejection region we reject H₀
We support the claim of the garbage collector the average picking up more than 4 tn of garbage
2.- p = 75 %
3.-3.-t(s) is in the rejection region we accept H₀ we have not evidence to support Marc´s claim
Step-by-step explanation:
1.- If p-value is 0,04 and significance level α = 5 % or α = 0,05 then p-value < α
Test hypothesis should be ( x the average of garbage)
Null hypothesis H₀ x = 4 Tn
Alternative Hypothesis Hₐ x > 4 Tn
Then alternative hypothesis suggests a one tail-test to the right and
p-value < 0,05
Then we p-value indicates that we are in the rejection region we reject H₀
We support the claim of the garbage collector the average picking up more than 4 tn of garbage
2.- As we are dealing with a normal distribution the CI 95 % is symmetrical with respect to the mean, therefore the proportion of student living in Brooklyn is:
(0,73 + 0,77) /2
p = 0,75 p = 75 %
Test hypothesis:
Null Hypothesis H₀ μ = 26
Alternative Hypothesis Hₐ μ < 26
Alternative hypothesis tells us the test is a one-tail test to the left
Sample size n = 25
Sample mean μ = 24,4
Sample Standard deviation = 9,2
We assume normal distribution, and as n < 30 we use t-student table
with 24 degree of freedom
Significance level is 0,05 and df = 24 we find t (c) in t- student table
t(c) = 1,7109 test to the left t(c) = -1,7109
To calculate t(s)
t(s) = ( 24,4 - 26 ) / 9,2 / √25
t(s) = - 1,6 * 5 / 9,2
t(s) = - 0,87
Comparing t(s) and t(c) we have
t(s) > t(c)
t(s) is in the rejection region we accept H₀ we have not evidence to support Marc´s claim
What is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=x^3, the x-axis, and the vertical line x=2 is revolved about the x-axis?
Show work.
A
[tex]4[/tex]
B
[tex] \frac{128}{7} [/tex]
C
[tex]4\pi[/tex]
D
[tex] \frac{128\pi}{7} [/tex]
Answer:
The first thing we need to do is to find the area bounded by:
y = x^3
y = 0
between:
x = 0 and x = 2
This is the integral of the given function between x = 0 and x = 2, written as:
[tex]\int\limits^2_0 {x^3} \, dx = \frac{2^4}{4} - \frac{0^4}{4} = 2^2 = 4[/tex]
This means that the area of the bounded region is 4 square units.
Now, if we do a full rotation around the x-axis, the volume generated will be equal to the area that we obtained times 2*pi units.
The volume is:
V = (4 square units)*(2*pi units) = 8*pi cubic units.
(Notice that no option coincides with this, there may be a mistake in the options)
If ∠1 and ∠2 are vertical angles and m∠2 = 108°, find m∠1.
Answer:
angle 1 = 108°
Step-by-step explanation:
because angle 1 and angle 2 are vertical angles and vertical angles are equal.
Question 3 (Fill-In-The-Blank Worth 3 points) (04.04) Point R is at (2, 1.2) and Point T is at (2, 2.5) on a coordinate grid. The distance between the two points is such as 8.2.) (Input numbers and decimal point only, Answer for Blank 1:
9514 1404 393
Answer:
1.3
Step-by-step explanation:
The two points are on the same vertical line, so the distance between them is the distance between their y-coordinates:
2.5 -1.2 = 1.3
The distance between the two points is 1.3 units.
mong 500 marriage license applications chosen at random in a givenyear, there were 48 in which the woman was at least one year older than the man, and among400 marriage license applications chosen at random six years later, there were 68 in which thewoman was at least one year older than the man. Construct a 99% confidence interval for thedifference between the corresponding true proportions of marriage license applications in whichthe woman was at least one year older than the man. Interpret the CI in the context of theproblem.
Answer:
CI 99% = ( 0,022 ; 0,126 )
Step-by-step explanation:
First sample
n₁ = 500
x₁ = 48
p₁ = x₁ / n₁ = 48 / 500 p₁ = 0,096 p₁ = 9,6 %
Second sample
n₂ = 400
x₂ = 68
p₂ = x₂ / n₂ = 68 / 400 p₂ = 0,17 p₂ = 17 %
CI = 99 % significance level α = 1 % α = 0,01
z(c) for α = 0,01 is from z- table z(c) = 2,325
CI = ( p₂ - p₁ ) ± z(c) *√ p*q* ( 1/n₁ + 1 / n₂ )
Where
p₂ - p₁ = 0,17 - 0,096 = 0,074
p = ( x₁ + x₂ ) / n₁ + n₂
p = ( 48 + 68 ) /( 500 + 400)
p = 116/ 900 p = 0,1288 and q = 1 - p q = 0,8712
z(c) *√ p*q* ( 1/n₁ + 1 / n₂ ) = 2,325 * √ 0,1288*0,8712 ( 1 / 500 + 1/ 400)
2,235 * 0,02247
z(c) *√ p*q* ( 1/n₁ + 1 / n₂ ) = 0,052
Then
CI 99 % = 0,074 ± 0,052
CI 99% = ( 0,022 ; 0,126 )
The difference between the groups shows that the proportion in the second group was bigger than in the first group.
The CI in the context of the problem is CI 99% = ( 0,022 ; 0,126 )
What will be the Solution of This problem?
Given first sample is
n₁ = 500
x₁ = 48
[tex]P_{1} =\dfrac{X_{1} }{n_{1} }[/tex] [tex]P_{1} =\dfrac{48}{500}[/tex]
p₁ = 0,096 p₁ = 9,6 %
Given second sample
n₂ = 400
x₂ = 68
[tex]P_{2} =\dfrac{X_{2} }{n_{2} }[/tex] [tex]P_{2} =\dfrac{68}{400}[/tex]
p₂ = 0,17 p₂ = 17 %
Since given CI = 99 % so significance level α = 1 % α = 0,01
From Z-Table z(c) for α= 0,01 is = 2,325
CI = [tex](P_{2} -P_{1}[/tex] ± [tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex]
Where
p₂ - p₁ = 0,17 - 0,096 = 0,074
[tex]P= \dfrac{X_{1} +X_{2} }{n_{1}+n_{2} }[/tex]
[tex]P=\dfrac{48+68}{500+400}[/tex]
[tex]P=\dfrac{116}{900}[/tex]
p = 0,1288 and q = 1 - p q = 0,8712
[tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex] [tex]2325\times\sqrt[2]{0.1288\times 0.8712} (\dfrac{1}{500_{} } +\dfrac{1}{400_{} } )[/tex]
[tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )=0.052[/tex]
Then
CI 99 % = 0,074 ± 0,052
CI 99% = ( 0,022 ; 0,126 )
Hence the difference between the groups shows that the proportion in the second group was bigger than in the first group.
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Where is the blue point on the number 0 0 4 4 − 4 −4 ?
Answer:
The answer should be -12
Which type of sequence is shown? 5, 10, 15, 20, 25, . . .
geometric
both arithmetic and geometric
arithmetic
neither arithmetic nor geometric
Answer:
Arithmetic Sequence
Step-by-step explanation:
In Arithmetic sequence each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k.
AP Statistics Quiz 10.2
1.
Mrs. Toguchi wants to determine if politicians tend to have higher salaries, on average, than first
responders (specifically emergency medical technicians, EMTs). Independent random samples from each
of these two professions were selected and their salaries were recorded. The data are summarized below.
a) the distribution of salary in each group is skewed right. The use of two-sample t procedures is still justified why?
b) construct and interpret a 99% confidence interval for the difference in the true mean salaries for politicians and EMTs
Answer:
Hello some data related to your question is missing attached below is the missing data
a) we will reject the null hypothesis hence it can be determined that the salary of politicians is greater than that of EMTs through the use of two-sample t procedures. since ( to > critical value )
b) ( 3.819 , 8.5226 )
Step-by-step explanation:
Applying the Given data:
The test hypothesis :
H0 : μ1 = μ2
Ha : μ1 > 2
A) since ( to > critical value ) we will reject the null hypothesis hence it can be determined that the salary of politicians is greater than that of EMTs through the use of two-sample t procedures
B ) construct and interpret
next calculate the SP value
[tex]S^{2} _{p}[/tex] = [tex]\frac{( n1 - 1 )S^{2} _{1} + ( n_{2}- 1 )S^{2} _{2} }{n1 + n2 - 2}[/tex]
where: S1 = 7524 , n1 = 50 , n2 = 100 , S2 = 5551 ( input values into equation above )
∴ [tex]S^{2} _{p}[/tex] = 39354491.3716
hence : [tex]S_{p}[/tex] = 6273.32
next calculate the value of test statistic
to = ( X1 - X2 - Δo ) / Sp [tex]\sqrt{\frac{1}{n1} + \frac{1}{n2} }[/tex]
where: X1 = 61234 , X2 = 54529 , Sp = 6273.32 , n1 = 50 , n2 = 100 ( input values into equation above )
to = 6705 / 1086.5702 = 6.1708
Df ( degree of freedom ) = n1 + n2 - 2 = 148
critical value at ∝ = 0.01 = ± 2.3518 ( using excel function : T.INV(0.01,148) )
hence the confidence Interval
= ( 6.1708 ± 2.3518 )
= ( 3.819 , 8.5226 )
For the table of Mrs. Toguchi the t test for two sample is not justified and the confidence interval for this two values is (6.1708, ±2.3518).
What is random sample?Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.
Mrs. Toguchi wants to determine if politicians tend to have higher salaries, on average, than first responders (specifically emergency medical technicians, EMTs).
Independent random samples from each of these two professions were selected and their salaries were recorded. The data are summarized below.
Politicians EMT's
Mean $61,234 $54,529
Standard deviation $7524 $5551
n 50 100
a) The distribution of salary in each group is skewed right. The use of two-sample t procedures is still justified-The hypothesis for the test,
[tex]H_0:\mu_1=\mu_2\\H_a:\mu_1 > 2[/tex]
No it is not justifies, as the null hypothesis is rejected.
b) construct and interpret a 99% confidence interval for the difference in the true mean salaries for politicians and EMTsThe pooled estimate of a common population standard deviation can be given as,
[tex]S_p=\sqrt{\dfrac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}}[/tex]
Put the values in the above formula from the table, we get,
[tex]S_p=\sqrt{\dfrac{(50-1)(7524)^2+(100-1)(5551)^2}{50+100-2}}\\S_p=6273.32[/tex]
Use the formula of test statistics for equal variance as,
[tex]t=\dfrac{\overline y_1-\overline y_2-0}{s_p\sqrt{\dfrac{1}{n_1}+\dfrac{1}{n_2}}}[/tex]
Put the values from the table as,
[tex]t=\dfrac{61234-54529-0}{(6263.32)\sqrt{\dfrac{1}{50}+\dfrac{1}{100}}}\\t=6.1708[/tex]
The degree of freedom can be given as,
[tex]DF=100+50-2\\DF=148[/tex]
The critical value for 99 percent interval (0.01) is ±2.3518.
Hence, the confidence interval for this two values is (6.1708, ±2.3518).
Thus, for the table of Mrs. Toguchi the t test for two sample is not justified and the confidence interval for this two values is (6.1708, ±2.3518).
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For every 16 mango trees in the orchard, there are 8 coconut trees. If there are 1320 trees. How many trees of each kind are there?
SHOW PROCESS PO pa help po need ko po ngayon:(
I BRAINLIEST ko po yung tamang sagot :(
Answer:
let's say coconut trees is X is there from mango trees will be 2X
Step-by-step explanation:
2x+x=1320
3x=1320
divide both sides by three
3x/3=1320/3
x=440(coconut)
2x=880(mango)
Help me out pls, i’m new to this whole hypotenuse thing
Answer:
x = 6.5
Step-by-step explanation:
Reference angle = 54°
Length of Side opposite to 54° = x
Hypotenuse = 8 cm
Recall: SOHCAHTOA.
Apply SOH:
Sin 54 = Opp/Hyp
Sin 54 = x/8
x = 8*sin 54
x = 6.47213595 ≈ 6.5 cm (nearest tenth)
Plsssss help it is khan academy!!!
Given the triangle below, what is m angle A, rounded to nearest tenth.
Answer:
D.82.8°
Step-by-step explanation:
Hope it helps
Have a great day
Which set of numbers is in DESCENDING order?
* 1 point
WILL GIVE BRANLIEST
55, -8, -2, -282
55, -2, -8, -282
-282, -8, -2, 55
-282, 55, -8, -2
what is the value of x?
4 * (3.4+2)-(56 divided by 7)= 13.6, please give an explanation to this problem!!
Answer:
[tex]=13.6[/tex]
Step-by-step explanation:
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]=4\left(3.4+2\right)-\frac{56}{7}[/tex]
[tex]=21.6-8[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:21.6-8=13.6[/tex]
[tex]=13.6[/tex]
18 out of 20 to percentage
Answer:
90%
Step-by-step explanation:
Need help!! algebra!!!
Part A: The area of a square is (4a2 − 20a + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (9a2 − 16b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Part A
we have to solve the associated equation
4a^2 - 20a + 25 = 0
first of all we have to find the delta/4
Δ/4 = (b/2)^2 - ac where a is the term that multiply a^2, b is the term that multiply a and c is the therm without the variable
Δ/4 = (-10)^2 -100 = 100-100 = 0
the delta is equal to 0 that is mean that the equation has two coincident solutions, that can be find thanks to this formula
a1,a2 = -b/2/a = 10/4 = 5/2
now we can factorize the trinomial in this way:
4(a-5/2)(a-5/2)
4[(2a-5)/2][(2a-5)/2]
(2a-5)(2a-5)
the side of the square is 2a-5
Part B
the area of the rectangle is expressed as difference by two squares, so it can be rewritten as
(3a+4b)(3a-4b)
so the dimension of the rectangle are
3a+4b and 3a-4b
PLSS HELPPPPPPPPPPPP
Answer:
c Melindas account will have about 5.40 more than olivia's account
Step-by-step explanation:
The average of an electrician's hourly wage and a plumber's hourly wage is $33. One day a contractor hires an electrician for 7hr of work and the plumber for 4hr of work and pays a total of $396 in wages. Find the hourly wage for the electrician and for the plumber.
Answer:
Electrician = 44
Plumber = 22
Step-by-step explanation:
Let :
Electrician Hourly wage = x
Plumber's hourly wage = y
Average = 33
(x + y ) /2 = 33
x + y = 66 - - - - (1)
7x + 4y = 396 - - - (2)
From (1)
x = 66 - y
Put x = 66 - y in (2)
7(66-y) + 4y = 396
462 - 7y + 4y = 396
-3y = - 66
y = 22
x = 66 - 22
x = 44
Electrician = 44
Plumber = 22
Find the slope of the line.
Please Help
Which graph represents the solution set of the system y ≤ x2 – 1 and x > y2 – 6?
The fourth option is indeed correct on Edge 2021.
The graph that represents the system of nonlinear inequalities is graph (a)
The nonlinear inequalities are given as:
[tex]y \le x^2 - 1[/tex]
[tex]x > y^2 - 6[/tex]
Rewrite the above nonlinear inequalities as:
[tex]y - x^2 \le - 1[/tex]
[tex]x -y^2 > -6[/tex]
[tex]y - x^2 \le - 1[/tex] means that the inequality has a solid line, and the outside part is shaded
[tex]x -y^2 > -6[/tex] means that the inequality has a dotted line, and the inner part is shaded
So, the graph that represents the system of nonlinear inequalities is graph (a)
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find the volume of this cylinder. geometry help
Answer:
Volume=3418.1 ft²
Step-by-step explanation:
Volume:π r² h
r=8 ft
h=17ft
π×8²×17
=3418.052 ft³
=3418.1 ft³
hope it helps...
6=24(x+1)^2 what is the answer simplified
Answer:
hi can i fu k u
Step-by-step explanation:
The answer is:
-0.5, -1.5
A trader buys 30 shirts for #x each. He sells
them all for #y each. What is his profit