Answer: 25 years
Step-by-step explanation:
t = I / Pr
t = 5700 / ( 3800 × 0.06 ) = 25
t = 25 years
Why do interest rates on loans tend to be higher in a strong economy than in a weak one?
A study was conducted to explore the effects of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 got only water (control). Treatment 2 got 1g of ethanol per kg of body weight, and treatment 3 got 2g/kg. The amount of REM sleep in a 24hr period was recorded, in minutes: Treatment 1: 63, 54, 69, 50, 72 Treatment 2: 45, 60, 40, 56 Treatment 3: 31, 40, 45, 25, 23, 28
A) Graph the data. Why did you choose the graph that you did and what does it tell you?B) Create an ANOVA table for the data using the formulas provided in class. C) Evaluate the ANOVA assumptions graphically. Was ANOVA appropriate here?D) Based on the ANOVA table, make a conclusion in the context of the problem.E) Create 95% CIs for all pairwise comparisons of means using the Tukey method.
Answer: Find answer in the attachment
Step-by-step explanation:
Su Jean is driving from phoenix to houston. A distance of 1185 miles. After driving for 4 hours she calculates that she has driven 237 miles. What portion of the distance does she have left to drive?
Answer:
4/5
Step-by-step explanation:
237/1185 = .2 = 1/5
meaning there's 4/5 left
Decide whether the pair of ratios form a proportion 15/12=4.5/3.6
Answer: Yes they form a proportion. The given equation is a true equation.
==========================================
Explanation:
The idea is that if we have
a/b = c/d
then that it is the same as
a*d = b*c
This is known as cross multiplication. We'll use this rule to get
15/12 = 4.5/3.6
15*3.6 = 12*4.5
54 = 54
We got the same value on both sides, meaning that the last equation is true. Consequently, it means the first equation is true as well (all three equations are true).
--------
You could also use your calculator to see that
15/12 = 1.25
4.5/3.6 = 1.25
showing that 15/12 = 4.5/3.6 is a true equation and the ratios form a proportion.
Answer:
15/12=4.5/3.6 = True
Step-by-step explanation:
Simplify the following: Left-hand
15/12
Hint: | Reduce 15/12 to lowest terms. Start by finding the GCD of 15 and 12.
The gcd of 15 and 12 is 3, so 15/12 = (3×5)/(3×4) = 3/3×5/4 = 5/4:
Answer: 5/4
______________________________
Approximate the following:
4.5/3.6
Hint: | Express 4.5/3.6 in decimal form.
4.5/3.6 = 1.25:
Answer: 1.25 = 5/4
A house m by m is surrounded by a walkway m wide. 27 9 1.8 a) Find the area of the region covered by the house and the walkway. b) Find the area of the walkway.
Answer:
A. 385.56 square meters.
B. 142.56 square meters.
Step-by-step explanation:
A house 27m by 9m is surrounded by a walkway 1.8m wide.
a) Find the area of the region covered by the house and the walkway.
b) Find the area of the walkway.
Let
Length of the house=l=27m
Width of the house=w=9m
Wideness of the walkway=x=1.8m
Area of the region covered by the house and the walkway
=( L + 2*x) * (w + 2*x)
= (27+2*1.8)*(9+2*1.8)
=(27+3.6)*(9+3.6)
=(30.6)*(12.6)
=385.56 square meters.
b) Area of the walkway
= (L + 2*x)*(w + 2*x) - l*w
= (27+2*1.8)*(9+2*1.8) - 27*9
=(27+3.6)*(9+3.6) - 243
=(30.6)*(12.6) - 243
=385.56 - 243
=142.56 square meters.
75% of this
number is 13.5
Answer:
10.125
Step-by-step explanation:
Hello!
To find this we first have to convert the percentage to a decimal
We do this by moving the decimal point two times left
75.0% = 0.75
Now we multiply this by the number
13.5 * 0.75 = 10.125
The answer is 10.125
Hope this helps!
Which point slope form equations could be produced with the points (3,2) and (4,6)
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of a line given two points first find the slope of the line and use the formula
y - y1 = m( x - x1) to find the Equation of the line using any of the points given
Slope of the line using points
(3,2) and (4,6) is
[tex]m = \frac{6 - 2}{4 - 3} = \frac{4}{1} = 4[/tex]
So the equation of the line using point
( 3 , 2 ) and slope 4 is
y - 2 = 4( x - 3)Hope this helps you
The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. Suppose there is not information about the proportion of students who might choose the option. What size sample should the department head take if he wants to be 95% confident that the estimate is within 0.10 of the true proportion
Answer:
96
Step-by-step explanation:
From the given information:
At 95% Confidence interval level,Level of significance [tex]\alpha[/tex] 0.05, the value of Z from the standard normal tables = 1.96
Margin of Error = 0.10
Let assume that the estimated proportion = 0.5
therefore; the sample size n can be determined by using the formula: [tex]n =(\dfrac{Z}{E})^2 \times p\times (1-p)[/tex]
[tex]n =(\dfrac{1.96}{0.1})^2 \times 0.5\times (1-0.5)[/tex]
[tex]n =(19.6)^2 \times 0.5\times (0.5)[/tex]
n = 96.04
n [tex]\approx[/tex] 96
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.) ∫4x2 lnx dx ; u= lnx , dv=4x 2dx
Take
[tex]u=\ln x\implies\mathrm du=\dfrac{\mathrm dx}x[/tex]
[tex]\mathrm dv=4x^2\,\mathrm dx\implies v=\dfrac43x^3[/tex]
Then
[tex]\displaystyle\int4x^2\ln x\,\mathrm dx=\frac43x^3\ln x-\frac43\int x^2\,\mathrm dx=\frac43x^3\ln x-\frac49x^3+C[/tex]
[tex]=\boxed{\dfrac49x^3(3\ln x-1)+C}[/tex]
The required integration is,
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C
The given integral is,
∫4x² lnx dx
Using integration by parts, choose u and dv.
In this case, we choose u = lnx and dv = 4x²dx.
Using the formula for integration by parts, we have:
∫ u dv = uv - ∫ v du
Substituting the values of u and dv, we get:
∫4x² lnx dx = (lnx) (∫ 4x² dx) - ∫ [(d/dx)lnx] (∫4x² dx) dx
Simplifying the first term using the power rule of integration, we get:
∫ 4x² dx = (4/3)x³ + C₁
For the second term, we need to evaluate (d/dx)lnx,
Which is simply 1/x. Substituting this value, we get:
∫ [(d/dx)lnx] (∫4x² dx) dx = ∫ [(1/x) ((4/3)x³ + C₁)] dx
Simplifying this expression, we get:
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - ∫ [(4/3)x³/x] dx
Using the power rule of integration again, we get:
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C
Where C is the constant of integration.
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Factor 13ab3 + 39a2b5.
[tex]13ab^3+39a^2b^5\\\\\boxed{\boxed{\boxed{13ab^3(1+3ab^2)}}}\\\\[/tex]
Brazil number one.
Answer:
there's no answer for that equation
Find the sum of the infinite geometric series -27, -9, -3, … The ratio is /3 and u1 is -27
===================================================
Work Shown:
a = -27 = first term
r = 1/3 = common ratio, note how this is between -1 and 1
We start with -27 and multiply by 1/3 each time to get the next term
S = infinite sum
S = a/(1-r), which only works because -1 < r < 1 is true
S = -27/(1-1/3)
S = -27/(2/3)
S = (-27/1) divided by (2/3)
S = (-27/1) times (3/2)
S = (-27*3)/(1*2)
S = -81/2
As you generate and add up the terms of the sequence, the infinite sum slowly starts to approach -81/2 = -40.5; we'll never actually achieve this sum exactly. Think of it as approaching an asymptote.
Hi people if someone gives me a hint please. Show algebraically that the product of two consecutive numbers is always even l wrote n (n+1) is always an even number But doesnt recognise it as 100% right thanks for any help
Step-by-step explanation:
Consider the following rules.
even + odd = odd
even - odd = odd
even × odd = even
even ÷ odd = even (if divisible)
Now for the two consectives terms...
One will surely be even and the other, odd.
So using the rule
Their product will always be odd
Hope it helps....
BRAINLIEST PRETTY PLEASE!!
which rate can you set 7 miles over 1 hour equal to in order to find the distance traveled in 49 hours at 7 miles per hour
Answer:
Step-by-step explanation:
time = 49 hours
speed = 7 miles/hour
speed = distance / time
∴ distance = speed × time
= 7 × 49
= 343 miles
Given that the sum of squares for error is 60 and the sum of squares for regression is 140, then the coefficient of determination is:
Answer:
0.7Step-by-step explanation:
The coefficient of determination which is also known as the R² value is expressed as shown;
[tex]R^{2} = \frac{sum\ of \ squares \ of \ regression}{sum\ of \ squares \ of total}[/tex]
Sum of square of total (SST)= sum of square of error (SSE )+ sum of square of regression (SSR)
Given SSE = 60 and SSR = 140
SST = 60 + 140
SST = 200
Since R² = SSR/SST
R² = 140/200
R² = 0.7
Hence, the coefficient of determination is 0.7. Note that the coefficient of determination always lies between 0 and 1.
The coefficient of determination of the dataset is 0.7
The given parameters are:
[tex]SSE = 60[/tex] --- sum of squared error
[tex]SSR = 140[/tex] --- sum of squared regression
Start by calculating the sum of squared total (SST)
This is calculated using
[tex]SST =SSE + SSR[/tex]
So, we have:
[tex]SST =60 +140[/tex]
[tex]SST =200[/tex]
The coefficient of determination (R^2) is then calculated using
[tex]R^2 = \frac{SSR}{SST}[/tex]
So, we have:
[tex]R^2 = \frac{140}{200}[/tex]
Divide
[tex]R^2 = 0.7[/tex]
Hence, the coefficient of determination is 0.7
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According to a survey, typical American spends 154.8 minutes per day watching TV. A survey of 50 Internet users results in a mean time watching TV per day of 128.7 minutes, with a standard deviation of 46.5 minutes. Which appropriate test we should use to determine if Internet users spend less time watching TV
Answer:
Z > ± 1.645
z= 3.968
Step-by-step explanation:
We formulate the null and alternate hypotheses as
H0 =μ2 ≥ μ1 Ha: μ2 <μ1 one sided
Let α= 0.05
Since the sample sizes are large therefore the test statistic used under H0 is
The critical region for α= 0.05 for a one tailed test Z > ± 1.645
Z = (x`2- x`1) /s/ √n
Z= 154.8-128.746.5/√50
z= 26.1/6.577
z= 3.968
Since the calculated value of z lies in the critical region we reject H0 that internet users spend more time or equal time.
For an experiment with 3 groups of 10 participants in each group. Fcrit for alpha 0.05=_________
a. 3.35
b. 2.35
c. 5
d. 12
Answer:
a. 3.35
Step-by-step explanation:
Given that :
an experiment with 3 groups consist of 10 participant in each group.
This implies that:
number of group k = 3
number of participants n = 10
N = nk
N = 10 × 3 = 30
The degree of freedom within can be calculate as:
dfw = N - k
dfw = 30 - 3
dfw = 27
The degree of freedom for the critical value
dfc = n- 1
dfc = 3 - 1
dfc = 2
At the level of significance ∝ = 0.05
The F critical value from the standard normal F table
i.e
[tex]F_{critical { (2, 27)}=[/tex] 3.35
A box is 30 inches wide, 16 inches long, and 14 inches high. To the nearest cubic inch, what is the volume of the box?
Answer:
6720 in ^3
Step-by-step explanation:
Volume = length * width * height
= 30*16*14
=6720 in ^3
Which polynomial is prime? x2 + 9 x2 – 25 3x2 – 27 2x2 – 8
This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).
Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.
Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.
Answer:
A
Step-by-step explanation:
because it has a + sign
Given a dataset with the following properties:
mean = 50
median = 40
standard deviation = 5
What is the shape of the distribution?
Answer:
The distribution is positively skewed.
Step-by-step explanation:
A measure of skewness is defined in such a way that the measure should always be zero when the distribution is symmetric and measure should be a pure number i.e independent of origin and units of measurement.
The shape of the distribution can be found by finding the coefficient of skewness.
The coefficient of skewness can be found by
Sk= 3(Mean-Median)/ Standard Deviation
Sk= 3( 50-40)5= 30/5=6
The shape will be positively skewed.
In a positively skewed distribution the mean > median > mode. It has a long right tail.
Using the skewness formula, it is found that the distribution is right-skewed.
------------------
The skewness of a data-set with mean M, median [tex]M_e[/tex] and standard deviation s is given by:[tex]S = \frac{3(M - M_e)}{s}[/tex]
If |S| < 0.5, the distribution is said to be symmetric.If S <-0.5, the distribution is left-skewed.If S > 0.5, the distribution is right-skewed.------------------
Mean of 50, thus, [tex]M = 50[/tex]Median of 40, thus [tex]M_e = 40[/tex]Standard deviation of 5, thus, [tex]s = 5[/tex]The coefficient is:
[tex]S = \frac{3(M - M_e)}{s} = \frac{3(50 - 40)}{5} = \frac{30}{5} = 6[/tex]
Thus, the distribution is right-skewed.
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[tex]f(x) = sqr root x+3 ; g(x) = 8x - 7[/tex]
Find (f(g(x))
[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]
Need a little help thanks :D
Answer:
71°
Step-by-step explanation:
Consider triangle BDH. x is the external angle that is remote to internal angles B and D, so is equal to their sum:
x° = 41° +30°
x° = 71°
A population of values has a normal distribution with μ= 106.9 and σ=14.5
You intend to draw a random sample of size n=20
What is the probability that a single randomly selected value is less than 109.8?
P(X < 109.8)
How do you the probability that a sample of size n= 20 is randomly selected with a mean less than 109.8?
P(M < 109.8)
Also, I have to round the answer to the 4th decimal place. How do I do that?
Step-by-step explanation:
Find the z-score.
z = (x − μ) / σ
z = (109.8 − 106.9) / 14.5
z = 0.2
Use a chart or calculator to find the probability.
P(Z < 0.2) = 0.5793
Find the mean and standard deviation of the sampling distribution.
μ = 106.9
σ = 14.5 / √20 = 3.242
Find the z-score.
z = (x − μ) / σ
z = (109.8 − 106.9) / 3.242
z = 0.894
Use a calculator to find the probability.
P(Z < 0.894) = 0.8145
What is the value of the mean from the following set of data: 12,10, 11, 8, 6, 5, 3, 7, 9. Round to the nearest hundredth.
Answer:
7.88 or 7.9
Step-by-step explanation:
To find the mean, we need to do:
=> (12 + 10 + 11 + 8 + 6 + 5 + 3 + 7 + 9) / 9
=> 71/9
=> 7.88 or 7.9
I divided the sum of all numbers by 9 because we added 9 numbers.
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
ii. How far west is Musah’s final point from the centre?
iii. How far north is Musah’s final point from the centre?
iv. Describe how you would guide a JHS student to find the bearing and distance of
Musah’s final point from the centre.
Answer:
ii. 75 steps
iii. 75 steps
iv. 106 steps, and [tex]315^{0}[/tex]
Step-by-step explanation:
Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.
ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;
bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]
To determine distance AB,
[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex] + [tex]/25/^{2}[/tex]
= 25000 + 625
= 3125
AB = [tex]\sqrt{3125}[/tex]
= 55.90
AB ≅ 56 steps
Thus, AC = 50 steps + 56 steps
= 106 steps
From ΔACD,
Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]
⇒ x = 106 × Sin [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance west from centre to final point is 75 steps
iii. From the secon attachment, Musah's distance north, y, can be determined by;
Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]
⇒ y = 106 × Cos [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance north from centre to final point is 75 steps.
iv. Musah's distance from centre to final point is AC = AB + BC
= 50 steps + 56 steps
= 106 steps
From ΔACD,
Tan θ = [tex]\frac{75}{75}[/tex]
= 1.0
θ = [tex]Tan^{-1}[/tex] 1.0
= [tex]45^{0}[/tex]
Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]
= [tex]315^{0}[/tex]
I dont understand how to do this
Answer:
Put 25 in the box.
Step-by-step explanation:
Apply the exponent rule: (ax)^n = a^n × x^n
So we have:
(5x)^2 = 5^2 × x^2
= 25x^2
Best Regards!
Karl needs a total of $30 to buy a bike. He has $12. He can earn $6 an hour
babysitting. Which equation can be used to find the number of hours, h, Karl has to
babysit to have the money he needs?
30 - 6h + 12 = 0
6+ n = 12
6 + 12 h = 30
6 h + 12 = 30
Answer:
6h + 12 = 30
Step-by-step explanation:
Hence, the equation obtained for number of hours worked is given as 12 + 6h = 30.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
The total money required is given as $30.
Suppose the number of hours for babysitting be h.
Then, the money earned by doing it is $6h.
And, the total money with Karl is 12 + 6h.
As per the question, the following equations can be written as,
12 + 6h = 30
Hence, the equation for finding the number of hours is given as 12 + 6h = 30.
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in this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answer:
2.7 in²
Step-by-step explanation:
Area of ∆BAC : ∆Area of EDF = BC² : EF² (based on the area of similar triangles theorem)
Thus:
[tex] 6 in^2 : x in^2 = (3 in)^2 : (2 in)^2 [/tex]
[tex]\frac{6}{x} = \frac{3^2}{2^2}[/tex]
[tex]\frac{6}{x} = 2.25[/tex]
[tex]\frac{6}{x}*x = 2.25*x[/tex]
[tex]6 = 2.25x[/tex]
[tex]\frac{6}{2.25} = \frac{2.25x}{2.25}[/tex]
[tex]2.67 = x[/tex]
Area of ∆EDF = 2.7 in²
Determine whether each equation has one solution, no solution or infinitely many solutions. 4x + 10 = 2(2x + 5) 4x - 5 = 4x + 10 4x - 5 = -5
Answer:
see below
Step-by-step explanation:
4x + 10 = 2(2x + 5)
Distribute
4x+10 = 4x+10
Since the left side is identical to the right side, there are infinite solutions
4x - 5 = 4x + 10
Subtract 4x from each side
-5 = 10
This is never true, so there are no solutions
4x-5 = -5
Add 5 to each side
4x = 0
x=0
There is one solutions
If all angles are 90 degrees, and the crystal has a square base with a height that is larger than one of the square sides, what type of unit cell is it
Answer:
Tetragonal unit cell.
Step-by-step explanation:
A unit cell is the smallest part of a material which is formed by a well arranged lattice points. Some common types are; face centered, body center, tetragonal, cubic etc
Tetragonal unit cell has a square top and base, with rectangular sides. The internal angles are [tex]90^{0}[/tex] each, and consists of molecules, atoms, or ions (lattice points) arranged at each corners of the unit cell.
The crystal as described in the given question is a tetragonal unit cell.
Subtract 2x^2 -9x - 7 from 8x^2 -5x + 9.
Answer:
-6x² -4x -16
Step-by-step explanation:
be watchful of signs to avoid making errors