Megan’s plant grew at a faster rate, Growing at a rate of 3 inches per week.
What is the slope?The y-rate axis of change with respect to the x-axis is known as the slope.
y = mx + b, where slope = m and y-intercept = b, is the slope-intercept form equation of a line.
We are aware that a slope's graph or rate of change will be steeper the higher its absolute value.
Given, Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
From the given options, Megan's plant which is growing at a rate of 3 inches per week has a faster growth rate.
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A worker in the automobile industry works an average of 43.7 hours per week. Assume the distribution is normal with a standard deviation of 1.6 hours.
(i) What is the probability that a randomly selected automobile worker works less than 40 hours per week?
(ii) If 15 automobile workers are randomly selected, what is the probability that the sample mean of working time is more than 45 hours per week?
Answer:
The solution is:
(1) 0.0104
(2) 0.0008
Step-by-step explanation:
Given:
Mean,
[tex]\mu = 43.7[/tex]
Standard deviation,
[tex]\sigma = 1.6[/tex]
(1)
⇒ [tex]P(X<40) = P(\frac{x-\mu}{\sigma}<\frac{40-43.7}{1.6} )[/tex]
[tex]=P(z< - 2.3125)[/tex]
[tex]=P(z<-2.31)[/tex]
[tex]=0.0104[/tex]
(2)
As we know,
n = 15
⇒ [tex]P(\bar X > 45)= P(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } } >\frac{45-43.7}{\frac{1.6}{\sqrt{15} } } )[/tex]
[tex]=P(z> 3.15)[/tex]
[tex]=1-P(z<3.15)[/tex]
[tex]=1-0.9992[/tex]
[tex]=0.0008[/tex]
A ray of light passing from air through an equilateral glass prism undergoes minimum
deviation, when the angle of incidence is 3/4th of the angle of prism. If the speed of light
in air is 3x10^8m/s, calculate the speed of light in the prism?
Answer: 45° and speed of light in prism 2×10⁸m/s
Step-by-step explanation:
The minimum deviation of the equilateral glass prism will form 60° angle.
So angle of incidence = 3/4×60
= 3 ×15
= 45°
Minimum deviation = δmin
= 30
After finding the value of μ using prism law
μ = 1.41
Speed of light will be 2×10⁸m/s
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I are these orders pairs a function
х,у
0,9
2,8.
4,7
6,6
8,5
10,4
9514 1404 393
Answer:
yes
Step-by-step explanation:
No x-value is repeated, so these ordered pairs do represent a function.
Which best describes the relationship between the lines with equations 2x – 9y = 1 and x + 8y = 6?
A. perpendicular
B. neither perpendicular nor parallel
C. parallel
D. same line
9514 1404 393
Answer:
B. neither perpendicular nor parallel
Step-by-step explanation:
If the lines were perpendicular, the coefficients would be swapped and one negated. (You would have 8x -y = c, or 9x +2y = c in the system.)
If the lines were parallel, the coefficients in the two equations would only differ by a common factor. (Both equations would reduce to 2x -9y = c, or x +8y = c.)
The lines are not the same line (coefficients are different).
So, the only reasonable description is ...
neither perpendicular nor parallel
pls help! I need the answer quickly! thank you!
Answer:
C) 82/2
Step-by-step explanation:
The area of a square is calculated by multiplying a side by itself
so one side of the square is 9 in
the area of a triangle is calculated by multiplying height and base and that divided by 2
since E is the midpoint, if we draw a line show the height from there
the height would be 9
9*9/2 = 82/2
To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used
Answer:
Cluster Sampling
Step-by-step explanation:
Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.
Suppose g(x) = f( x +2) - 3. Which statement best compares the graph of g(x) with the graph of f(x)? A. The graph of g(x) is shifted 2 units left and 3 units up. B. The graph of g(x) is shifted 2 units right and 3 units down. C. The graph of g(x) is shifted 2 units left and 3 units down. D. The graph of g(x) is shifted 2 units right and 3 units up.
Given:
The function is:
[tex]g(x)=f(x+2)-3[/tex]
To find:
The statement that best compares the graph of g(x) with the graph of f(x).
Solution:
The transformation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (i)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
We have,
[tex]g(x)=f(x+2)-3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=2[/tex]
[tex]b=-3[/tex]
Therefore, the graph of g(x) is shifted 2 units left and 3 units down.
Hence, the correct option is C.
The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 45 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 45?
Do not enter the percent symbol.
ans = %
Answer:
34%
Step-by-step explanation:
Given that the distribution of daily light bulb request replacement is approximately bell shaped with ;
Mean , μ = 45 ; standard deviation, σ = 3
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
Lightbulb replacement numbering between ;
42 and 45
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(42 - 45) / 3 = -1
This lies between - 1 standard deviation a d the mean :
Hence, the approximate percentage is : 68% / 2 = 34%
Five trucks are to be transported on a ship. Each one weighs 3200 kg and comes
with 8 tyres which weigh 125 kg each. what is the total weight
Total No of trucks: 5
Weight of trucks: 3200Kg
Total weight of trucks: 3200×5
= 16000kg
Total no of tyres = 5 ×8
= 40
Weight of each tyre = 125kg
Total weight of tyres = 125 × 40
= 5000Kg
The total weight of trucks and tyres: 16000 + 5000
= 21000Kg
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FIND THE AREA OF THE SHAPE BELOW
PLEASE HELP I HAVE BEEN STUCK ON THIS FOREVERRRR!!
THANK YOU
Answer:
Is answer 22 units sqaure ?
If p=(3/4)and q=(1/2)find p-2q
Answer:
[tex]p - 2q \\ \frac{3}{4} - 2( \frac{1}{2} ) \\ = \frac{3}{4} - \frac{2}{2} \\ = \frac{3}{4} - 1 \\ = \frac{3 - 4}{4} \\ = \frac{ - 1}{4} \\ = - 0.25[/tex]
I hope I helped you^_^
Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows.
Before 13 22 65 123 56 63
After 14 21 43 84 75 72
1. The article included the statement "A paired t-test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs." Carry out such a test. (Note: The relevant normal probability plot shows a substantial linear pattern.)
a. State and test the appropriate hypotheses. (Use α = 0.05.)
b. Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t = _____
p-value = _____
c. State the conclusion in the problem context.
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
B. Reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
C. Fail to reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
D. Reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
2. If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in the number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)
Answer:
Test statistic = 0.63
Pvalue = 0.555
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
Step-by-step explanation:
Given :
Before 13 22 65 123 56 63
After_ 14 21 43 84 75 72
To perform a paired t test :
H0 : μd = 0
H1 : μd ≠ 0
We obtain the difference between the two dependent sample readings ;
Difference, d = -1, 1, 22, 39, -19, -9
The mean of difference, Xd = Σd/ n = 33/6 = 5.5
The standard deviation, Sd = 21.296 (calculator).
The test statistic :
T = Xd ÷ (Sd/√n) ; where n = 6
T = 5.5 ÷ (21.296/√6)
T = 5.5 ÷ 8.6940555
T = 0.6326
The Pvalue : Using a Pvalue calculator ;
df = n - 1 = 6 - 1 = 5
Pvalue(0.6326, 5) = 0.5548
Decision region :
Reject H0 ; If Pvalue < α; α = 0.05
Since 0.5548 > 0.05 ; we fail to reject the Null and conclude that the data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
An adult can lose or gain two pounds of water ina course of a day. Assume that the changes in water weight isuniformly distributed between minus two and plus two pounds in aday. What is the standard deviation of your weight over a day?
Answer:
The standard deviation of your weight over a day is of 1.1547 pounds.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b, and the standard deviation is:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
Assume that the changes in water weight is uniformly distributed between minus two and plus two pounds in a day.
This means that [tex]a = -2, b = 2[/tex]
What is the standard deviation of your weight over a day?
[tex]S = \sqrt{\frac{(2 - (-2))^2}{12}} = \sqrt{\frac{4^2}{12}} = \sqrt{\frac{16}{12}} = 1.1547[/tex]
The standard deviation of your weight over a day is of 1.1547 pounds.
Find the first six terms of the sequence.
a1=- 6, an= 4 • an-1
Answer:
I think it's 3
Step-by-step explanation:
because an=4 and the question is
an-1
=4-1
=3
Which exponential expression is equivalent to (4x^2 y^3)^2
Answer:
[tex] 16 {x}^{4} {y}^{6} [/tex]
Step-by-step explanation:
[tex](4 {x}^{2} {y}^{3} {)}^{2} [/tex]
➡️ [tex] {4}^{2} \times ( {x}^{2} {)}^{2} \times ( {y}^{3} {)}^{2} [/tex]
➡️ [tex] = 16 {x}^{4} {y}^{6} [/tex] ✅
If the volume of the expanding cube is increasing at the rate 24 cm3 / min , how fast is its surface area increasing when the surface area is 216 cm2 ?
Answer:
16 cm^2/min
Step-by-step explanation:
dV/dt=24
V=a^3, differentiate with respect to t
dV/dt=3a^2*da/dt, a^2*da/dt=8
S=6a^2, 216=6a^2. a=6. da/dt=(8/36)
dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min
A ladder leans against the side of the a house. The ladder is 19 feet long and forms an angle of elevation of 75 degree when leaned against the house. How far away from the house is the ladder? Round your answer to the nearest tenth.
Answer: 18.35259
Hope it helps!
equation that passes 1,3 and slope of 2 in point slope form
Answer:
y-3 = 2(x-1)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-3 = 2(x-1)
Answer:
3=2x+1
Step-by-step explanation:
Use the equation y=mx+b
where y is the y component, x is the variable and b is the x intercept
If f(x) = 4x + 3 and g(x) = 22 – 3, then f(g(4)) = ???
Answer:
f(g(4))=79
Step-by-step explanation:
given:
f(x) = 4x + 3
g(x) = 22 – 3
g(x) = 19
the x in parentheses represents x's value. if it is just x then example f(x)=3x would be 3x. if f(x) was f(2)=3x, then x would be 2 and f(2)=3x would be 3*2=6
f(g(4))
first solve g(4)
g(x) = 19
g(4)=19 because there are no x
then substitute
f(g(4))
f(19)
f(19) = 4x + 3
all x become 19
f(19) = 4(19) + 3
=76+3
=79
hope this helps.
find the supplement of 158 degrees and 17 minutes
Answer:
supplement of 158 degree
x+158=180
x=180-158
x=22 degree.
Step-by-step explanation:
Please help me with this question
Find the difference between each number:
-11 to -3 is +8
-3 to 5 is +8
The difference is 8
Use the following formula:
Bn = b1 + d(b -1)
Answer: bn = -11 + 8( b-1)
A triangle is rotated 90° about the origin. Which rule describes the transformation?
(x, y) (-x, -y)
O(x,y) (-y, x)
(x, y) (-), -x)
(x,y) →ly, -x)
Answer:
(x,y) -> (-y,x), second option.
Step-by-step explanation:
Rotation of 90 degrees about the origin:
The rule for a rotation of a point (x,y) 90 degrees about the origin is given by:
(x,y) -> (-y,x)
This is that the question asks, and so, this is the answer, which is the second option.
giving brainliest! :)
Answer:
239=5
478=10
956=20
Step-by-step explanation:
Gianna's car can travel 478 mi with 10 gallons of gas
so, 47.8 mi with 1 gallon
by dividing 239 by 47.8 miles/gallon we get the answer 5 miles.
if we multiply 20 gallons by 47.8 mi/gallon #e get the answer 956 miles.
easy weasy
Write the sum using summation notation, assuming the suggested pattern continues. 6, -18, 54, -162, +… Is this sequence arithmetic or geometric? Explain your answer.
Answer:
Hello,
This sequence is geometric with a ratio of -3
the first term is 6
Step-by-step explanation:
[tex]u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\[/tex]
serie does not converge.
Devy likes to learn! Could someone please tell me how to answer this question?
If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?
On a coordinate plane, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).
On a coordinate plane, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).
On a coordinate plane, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).
On a coordinate plane, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).
Answer:
B
Step-by-step explanation:
Recall that if two functions, f and g, are inverses, then by definition:
[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]
Hence, the graph of f(g(x)) should be simply y = x.
Therefore, our answer is B, as both coordinates are equivalent for all three points.
Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? Use a level of significance of 0.05. Table shows the results of the survey. Has there been a change in the distribution of voter preferences since the earthquake?
Peter Alan Sui
Before 1838 418 1475
After 1420 329 1140
What is the chi-square test-statistic for this data?
χ2=_____.
Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = 6/5x-1
Step-by-step explanation:
We have two points so we can find the slope
(-5,-7) and (5,5)
The slope is
m = ( y2-y1)/(x2-x1)
= ( 5- -7)/( 5 - -5)
= (5+7)/(5+5)
= 12/10
= 6/5
The slope intercept form of a line is
y = mx+b
y = 6/5x+b
Using the point (5,5)
5 = 6/5(5)+b
5=6+b
b=-1
y = 6/5x-1
Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^3- x2 - 4x-6?
A. F(x) - (x - 3)(x + 1 + I)(x+1- I)
B. F(x) = (x - 3)(x+1+I)(x-1-I)
C. F(x) = (x+3)(x + 1)(x - 1)
D. F(x) - (x+3)(x+1+I)(x +1-I )
The completely factored form for the given algebraic expression is f(x) = (x-3)(x+1+i)(x+1-i).
What is a completely factored polynomial?A completely factored polynomial is a polynomial that can no longer be further simplified. A completely factored polynomial can be expressed as a root of its own equation.
Given that:
f(x) = x³ - x² - 4x - 6
To express this as a factored polynomial using the rational:
f(x) = (x-3)(x²+2x+2)
f(x) = (x-3)(x+1+i)(x+1-i)
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Dia is 10 years old. How many years have to add with twice of her age to get 24?
Answer:
4
Step-by-step explanation:
twice her age:
10*2 = 20
24-20 = 4
Answer:
4 i believe that's the answer
1) A 22-ft ladder is leaning against a building. If the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.)
2)How high does the ladder reach on the building? (Round your answer to the nearest whole number.)
Answer:
21.9 ft
Step-by-step explanation:
Answer:
Part A)
About 74.2°.
Part B)
About 21 feet.
Step-by-step explanation:
A 22 feet ladder is leaning against a building, where the base of the ladder is six feet from the base of the building.
This is shown in the diagram below (not to scale).
Part A)
We want to determine the angle of elevation of the ladder. That is, we want to find the value of θ.
Since we know the values adjacent to θ and the hypotenuse, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent is 6 and the hypotenuse is 22. Thus:
[tex]\displaystyle \cos \theta = \frac{6}{22} = \frac{3}{11}[/tex]
Take the inverse cosine of both sides:
[tex]\displaystyle \theta = \cos^{-1}\frac{3}{11}[/tex]
Use a calculator. Hence:
[tex]\displaystyle \theta = 74.1733...\approx 74.2^\circ[/tex]
The angle of elevation is approximately 74.2°
Part B)
We want to find how high up the ladder reaches on the building. In other words, we want to find x.
Since x is opposite to θ and we know the adjacent side, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
The opposite side is x and the adjacent side is 6. The angle θ is cos⁻¹(3/11) (we use the exact form to prevent rounding errors). Thus:
[tex]\displaystyle \tan \left(\cos^{-1}\frac{3}{11}\right) = \frac{x}{6}[/tex]
Solve for x:
[tex]\displaystyle x = 6 \tan \left(\cos^{-1}\frac{3}{11}\right)[/tex]
Use a calculator. Hence:
[tex]x = 21.1660... \approx 21\text{ feet}[/tex]
The ladder reaches about 21 feet up the building.
