Answer:
f(8) = 216
Step-by-step explanation:
f(x) = (2x - 10)³
So f(8) = (2(8) - 10)³
==> f(8) = (16 - 10)³
==> f(8) = (6)³
==> f(8) = 216
How do you evaluate ln(1/0.32)?
The value of natural logarithm, ln(1/0.32) where base "e" or e =2.7182 is 1.13943..
What is Logarithm function ?Logarithm, an exponent or power that must be raised to obtain a particular number. Expressed mathematically, x is the logarithm of n in base a, where x = logₐ n.
Ln where bx = n is called the natural logarithm. Also called the base e logarithm. where e is an irrational number approximately equal to 2.718281828459... The natural logarithm (ln) is represented as ln(x).Common Logarithms: Base 10Basic Rules:
log(a) + log(b) = log(ab)log(a) - log(b) = log(a/b)Wehave given that,
ln(1/0.32) here , a = 1 , b = 0.32
using formula, ln(1/0.32) = ln(1) - ln(0.32)
Now, from logarithm table , log(1) = 0
log(0.32)= ln(0.32) = - 1.13943
ln(1/0.32) = ln(1) - ln(0.32) = 0-(- 1.13943)
=> ln(1/0.32) = 1.13943
Hence, the value of ln(1/0.32) is 1.13943.
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a rectangular enclosure at a zoo is 35 feet long by 18 feet wide. the zoo doubles the area of the enclosure by adding the same distance to the length and width. what are the new dimensions of the enclosure?
The new dimensions of the enclosure is length is 45 feet and the new width is 28 feet
What is Area of Rectangle?
Area of rectangle is length times of breadth.
Given that rectangular enclosure at the zoo is 35 feet long by 18 feet wide. It means length is 35 feet and width is 18 feet.
Area of Rectangle=Length × Width
=35×18
=630
The zoo wants to double the area of the enclosure by adding the same distance x to the length and width.
(35+x)×(18+x)= 2(630)
630+35x+18x+x²=1260
x²+53x+630-1260=0
x²+53x-630
Now use the quadratic formula we get
x=10.
The new length is 35+10=45
The new width is 18+10=28.
Hence the new length is 45 and the new width is 28 feet after doubling of the area of enclosure.
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find the total interest for a principal of $125,000 at a rate of 7.5% for 5 years paid monthly
Answer:
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 7.5/100
r = 0.075 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 125,000.00(1 + 0.075/12)(12)(5)
A = 125,000.00(1 + 0.00625)(60)
A = $181,661.80
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $125,000.00 at a rate of 7.5% per year compounded 12 times per year over 5 years is $181,661.80.
The table defines the observed data values and the corresponding predicted values, based on a line of fit.
Observed Predicted
9 8.81
10 10.41
13 10.41
13 13.61
15 13.61
25 24.81
26 26.41
30 29.61
How many negative residuals does the data set have? How many positive residuals does the data set have?
6 negative residuals and 2 positive residuals
5 negative residuals and 3 positive residuals
3 negative residuals and 5 positive residuals
2 negative residuals and 6 positive residuals
The correct statement regarding the sign of the residuals in the table is given as follows:
3 negative residuals and 5 positive residuals.
What are residuals?For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:
Residual = Observed - Predicted.
Hence the residuals are classified as either positive or negative as follows:
Positive residual: the observed measure is greater than the predicted measure.Negative residual: the predicted measure is greater than the observed measure.Thus the residuals in this problem are classified follows:
9 8.81 -> positive.10 10.41 -> negative. 13 10.41 -> positive.13 13.61 -> negative. 15 13.61 -> positive.25 24.81 -> positive.26 26.41 -> negative.30 29.61 -> positive.Hence the third statement is correct.
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5x4x5x3+56
help ma pls why they got such long multipictacion in -8th garde
[tex]\fbox{356}[/tex]
[tex](5\times4\times5\times3)+56[/tex]
[tex]5\times4=20\\5\times3=15\\20\times15=300[/tex]
[tex]300+56=356[/tex]
Answer: 356
Step-by-step explanation:
-start by grouping numbers into smaller portions (ex. the 5x5)
-5x5=25
-4x3=12
-Now we have 25x12.
-10x25=250, now add two more 25's
-250+50=300 or 25x12=300
-Add 56 to get 356
Which of the following is not a test of congruence of triangle a SAS B SAA C SSS D AAA?
the results of a mathematics placement exam at two different campuses of mercy college follow: campus sample size sample mean population standard deviation 1 330 33 8 2 310 31 7 the college wants to test the hypothesis that the mean score on campus 1 is higher than on campus 2. if we test the null hypothesis at the 5% level of significance, what is the decision?
If we test the null hypothesis at the 5% level of significance, then the decision is (c)reject null hypothesis and conclude the means are different .
In the question ,
it is given that ,
the results of a mathematics placement exam for two different campuses of college ,
we have to test the hypothesis that the mean score on campus 1 is higher than on campus 2 .
sample size (n₁) is = 330
the sample size (n₂) is = 310
the sample mean (μ₁) = 33
the sample mean (μ₂) = 31
the standard deviation , σ₁ = 8
the standard deviation , σ₂ = 7
the test statistic test z can be calculated using the formula ,
z = (μ₁ - μ₂)/√(σ₁²/n₁ + σ₂²/n₂)
Substituting the values of the sample size , sample mean and standard deviation ,
we get ,
z = (33 - 31)/√(8²/330 + 7²/310)
Simplifying further ,
we get ,
Z = 3.37
the test is for the null hypothesis at the 5% level of significance .
that means ,
Z₀.₉₅ = 1.645 ;
So , the p value = P(Z > 3.37)
= 1 - P(Z < 3.37)
= 1 - 0.9996
= 0.0004
since the p-value is (0.0004) < the level of significance (0.05) .
we can reject the null hypothesis .
There is significant evidence to conclude that the mean score on campus 1 is higher than campus 2 .
Therefore , the correct option is (c) .
The given question is incomplete the complete question is
The results of a mathematics placement exam at two different campuses of mercy college follow: ( the table is given below)
The college wants to test the hypothesis that the mean score on campus 1 is higher than on campus 2. if we test the null hypothesis at the 5% level of significance, what is the decision ?
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a farmer wishes to enclose a rectangular area of 80,000 square feet and divide it into three pens with fencing parallel to one of the sides of the rectangle. what is the minimum amount of fence that he can use?
The minimum amount of fence that he can use is 1600 ft.
Given ;
Area of rectangular = 80,000 sq. ft
i.e. xy = 80,000
Total fencing needed ,
x + y + x + y + 2y = 2x + 4y
To minimize 2x + 4y, constrained to xy = 80,000
i.e. xy = 80,000
⇒ y = 80,000/x
⇒ so, s = 2x + 4 (80,000/x) to be minimized
⇒ To minimum value at ds/dx = 0
i.e. s = 2x + 4 (80,000/x)
= 2x + (3,20,00/x)
⇒ Now, ds/dx = 0 = 2 + (3,20,000) - [tex]\frac{1}{x^{2} }[/tex]
⇒ [tex]\frac{320000}{x^{2} } = 2[/tex]
⇒ [tex]x^{2} = 160000[/tex]
⇒ x = 400
∴ x = 400 ft
y = 80,000/400 = 200
∴ y = 200 ft
Total frencing is
⇒ 2x + 4y = 2 × 400 + 4 × 200
= 800 + 800
= 1600 ft
∴ The minimum amount of fence that he can use is 1600 ft.
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