sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875
sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992
62. A chemist mixes 15 liters of 40 percent acid solution and 25 liters of 20 percent acid solution.
What percent of the mixture is acid?
40% of 15 L = 6 L of acid
20% of 25 L = 5 L of acid
This means the mixture contains a total of 11 L of acid, and with a total volume of 15 L + 25 L = 40 L, that means the mixture is at a concentration of
(11 L acid) / (40 L solution) = 0.275 = 27.5%
How long will it take the same crew to clear the entire plot of 2 1/2 acres?
Answer:
It will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
Step-by-step explanation:
Given that a crew clears brush from 1/3 acre of land in 2 days, to determine how long will it take the same crew to clear the entire plot of 2 1/2 acres, the following calculation must be performed:
1/3 = 0.333
1/2 = 0.5
0.333 = 2
2.5 = X
2.5 x 2 / 0.333 = X
15 = X
Therefore, it will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
Exercise
a. I choose the correct option from Contain Questions
i Which of the following is a group set ?
(b) A happy person in the Village
(c) Simple Ex in the book (d) school age student
(Weekly
Answer:
happy person in the village
A field book is a private notepad used by a surveyor to transcribe notes and is not considered a legal document True False
Answer:
False
Step-by-step explanation:
A field book is a private notepad used by a surveyor to record measurements and notes.
Basically, the size of a field book is 200 millimeters × 120 millimeters (20 centimeters × 12 centimeters) and it's typically opened lengthwise. There are two (2) main types of field book and these includes;
I. Double-line field book.
II. Single-line field book.
As a general rule, it's best that all findings, entries (notes) and observations are recorded or made into a field book after each and every measurement have been taken by a surveyor.
In conclusion, a field book is considered to be a legal document used by surveyors to keep records of accomplished field work or work done in the field. Thus, it's not a private notepad used by a surveyor to transcribe notes.
Answer:
False
Step-by-step explanation:
A field book is a private notepad used by a surveyor to transcribe notes and is not considered a legal document is False.
Which rations are equivalent to 30:20? check all that apply
Answer:
3:2, 6;4 hope this helps
Answer:
C, D
Step-by-step explanation:
If you multiply both numbers of a ratio by the same number, you get an equivalent ratio.
A. Divide both numbers by 10
40:30 = 4:3 No
B. 10:0 No
C. Multiply both numbers by 10
3:2 = 30:20 Yes
D. Multiply both numbers by 5
6:4 = 30:20 Yes
suppose △abc≅△xyz. what is the corresponding congruent part for each segment or angle?
Answer:
Step-by-step explanation:
what are the missing numbers ?
what is the equation of the directx for the following parabola -8(x-5)=(y+1)^2
Answer:
x=7
Step-by-step explanation:
The directrix of a parabola is the vertical line found by subtracting
p from the x-coordinate h
of the vertex if the parabola opens left or right.
x=h-p
Substitute the known values of
p and h
into the formula and simplify.
x=7
Find the area of the figure
Please help :)
9514 1404 393
Answer:
66.5 cm²
Step-by-step explanation:
A horizontal line at the "knee" on the right will divide the figure into a 4 cm by 2 cm rectangle, and a trapezoid with bases 4 cm and 9 cm, and height 11-2 = 9 cm. Then the total area of the figure is ...
A = LW + 1/2(b1 +b2)h
A = (4 cm)(2 cm) + (1/2)(4 cm +9 cm)(9 cm) = 8 cm² +58.5 cm²
A = 66.5 cm² . . . . area of the figure
What fraction of the total number of students are boys?
Step-by-step explanation:
total number of students are :4x 3 = 12
Fraction that's boys are : 3÷12
Find the values of x for which the denominator is equal to zero for y=x^2/x^2+1 .
Answer:
Step-by-step explanation:
I assume that you mean y = x²/(x²+1), not y = x²/x²+1.
x²+1 = 0
x² = -1
x = ±√(-1) = ±i
deleted: deleted by user
how much water consumed by Aguilar family as shown in the meter reading
Answer:
?????????????????
Step-by-step explanation:
????????
answer please don't skip plz answer
What is the value of x^2
-2xy+y^2
if x-y = 4 ?
please answer
Answer:
16
Step-by-step explanation:
[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]
[tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]
The value of x^2-2xy+y^2
will be 16 .
Explanation is in the attachment .
hope it is helpful to you ☺️
Given: x + 2 < -5.
Choose the solution set.
{x | x R, x < -3}
{x | x R, x < 3}
{x | x R, x < -7}
{x | x R, x < 7}
Answer:
C
Step-by-step explanation:
x + 2 < -5
x < - 5 - 2
x < - 7
Answer:
{x| x R, x<-7}
Step-by-step explanation:
=> x+2<-5
=> x<-5-2
=> x<-7
Create your own proportion problems?
Answer:
See Explanation
Step-by-step explanation:
Required
Proportion problems
An example is:
y is directly proportional to x such that: y=4 when x = 2;
Derive the equation
For direct proportions, we have:
[tex]y\ \alpha\ x[/tex]
This gives:
[tex]y = kx[/tex]
Make k the subject
[tex]k = y/x[/tex]
So:
[tex]k = 4/2 =2[/tex]
So, the equation is:
[tex]y = kx[/tex]
[tex]y = 2x[/tex]
Assume the above question is for inverse proportion
The variation will be:
[tex]y\ \alpha\ \frac{1}{x}[/tex]
This gives:
[tex]y\ = \frac{k}{x}[/tex]
Make k the subject
[tex]k =x*y[/tex]
[tex]k =2* 4 = 8[/tex]
So, the equation is:
[tex]y\ = \frac{k}{x}[/tex]
[tex]y = \frac{8}{x}[/tex]
determine lcm and HCF of 24 and 26 using prime factors
Answer:
WHAT IS THE FACTOR?
Step-by-step explanation:
Solve the system by substitution.
y + 4 = x
10x + 2y = 16
Answer:
(2, -2)Step-by-step explanation:
Given system:
y + 4 = x 10x + 2y = 16Substitute x into the second equation:
10(y + 4) + 2y = 1610y + 40 + 2y = 1612y = -24y = -2Find x:
x = -2 + 4x = 2Answer:
x = 2 and y = -2
Step-by-step explanation:
Given system :-
y + 4 = x
10x + 2y = 16
Solve the system by substitution:-
Let,
y + 4 = x ...(1)
10x + 2y = 16 ...(2)
Solve for y;
Substitute y + 4 as x in the eq.(2)
10( y + 4 ) + 2y = 16
Distribute 10.10y + 40 + 2y = 16
Combine like terms.12y + 40 = 16
Move constant to the right-hand side and change their sign.12y = 16 - 40
Subtract 16 from -40.12y = -24
Divide both side by 12.12y / 12 = -24/12
Hence, y = -2
Solve for x.
Substitute the value of y in eq.(1)-2 + 4 = x
Add -2 and 4.Hence, 2 = x
if x can be divide by 7 and 9 without leaving a remainder, it can also divided by which number without leaving a remainder
Answer:
all counting numbers except one
To determine the organic material in a dried lake bed, the percent carbon by mass is measured at two different locations. To compare the means of the two different locations, it must first be determined whether the standard deviations of the two locations are different. For each location, calculate the standard deviation and report it with two significant figures.
Answer:
[tex]\sigma_1 = 0.08[/tex] --- Location 1
[tex]\sigma_2 = 0.34[/tex] --- Location 2
Step-by-step explanation:
Given
See attachment for the given data
Required
The standard deviation of each location
For location 1
First, calculate the mean
[tex]\bar x_1 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_1 =\frac{30.40+30.20+30.30+30.40+30.30}{5}[/tex]
[tex]\bar x_1 =\frac{151.60}{5}[/tex]
[tex]\bar x_1 =30.32[/tex]
The standard deviation is calculated as:
[tex]\sigma_1 = \sqrt{\frac{\sum(x - \bar x_1)^2}{n-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{(30.40 - 30.32)^2+(30.20 - 30.32)^2+(30.30 - 30.32)^2+(30.40 - 30.32)^2+(30.30 - 30.32)^2}{5-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{0.028}{4}}[/tex]
[tex]\sigma_1 = \sqrt{0.007}[/tex]
[tex]\sigma_1 = 0.08[/tex]
For location 2
First, calculate the mean
[tex]\bar x_2 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_2 =\frac{30.10+30.90+30.20+30.70+30.30}{5}[/tex]
[tex]\bar x_2 =\frac{152.2}{5}[/tex]
[tex]\bar x_2 =30.44[/tex]
The standard deviation is calculated as:
[tex]\sigma_2 = \sqrt{\frac{\sum(x - \bar x_2)^2}{n-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{(30.10-30.44)^2+(30.90-30.44)^2+(30.20-30.44)^2+(30.70-30.44)^2+(30.30-30.44)^2}{5-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{0.472}{4}}[/tex]
[tex]\sigma_2 = \sqrt{0.118}[/tex]
[tex]\sigma_2 = 0.34[/tex]
State the final conclusion in simple nontechnical terms.
Original claim: The proportion of male golfers is less than 0.6.
Initial conclusion: Fail to reject the null hypothesis.
Which of the following is the correct conclusion?
A. There is suffficient evidence to support the claim that the proportion of male golfers is less than 0.6.
B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.
Answer:
B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.
Step-by-step explanation:
The proportion of male golfers is less than 0.6.
At the null hypothesis, we test if the proportion is of at least 0.6, that is:
[tex]H_0: p \geq 0.6[/tex]
At the alternative hypothesis, we test if the proportion is of less than 0.6, that is:
[tex]H_1: p < 0.6[/tex]
Fail to reject the null hypothesis.
This means that there is not sufficient evidence to conclude that the proportion is less than 0.6, and thus the correct answer is given by option B.
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated samplingg distribution.
The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.5 years and a standard deviation of 2.1 years. Random samples of size 17 are drawn from the population and the mean of each sample is determined.
a. 1.33 years, 2.1 years
b. 5.5 years, 0.12 years
c. 5.5 years, 0.51 years
d. 1.33 years, 0.51 years
Answer:
c. 5.5 years, 0.51 years
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Mean of 5.5 years and a standard deviation of 2.1 years.
This means that, for the population, [tex]\mu = 5.5, \sigma = 2.1[/tex]
Random samples of size 17.
This means that [tex]n = 17[/tex]
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.
The mean is the same as the mean for the population, that is, 5.5 years.
The standard deviation is:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{17}} = 0.51[/tex]
This means that the correct answer is given by option c.
On Monday, Ray had $153.75 in his bank account. On Tuesday, he withdrew $71.00 from his account. After depositing #292.50 on Wednesday, how much money did Ray have in his account
Answer:
$375.25
Step-by-step explanation:
[tex]===========================================[/tex]
Withdrew- taking out money (-)
Deposit- putting in money (+)
[tex]===========================================[/tex]
Ray started off with 153.75. He withdraws (-) 71.
[tex]153.75-71=82.75[/tex]
Then he deposits (+) 292.5.
[tex]82.75+292.5=375.25[/tex]
That's your answer!
I hope this helps ❤
Which statement is false?
A. Every irrational number is also real.
B. Every integer is also a rational number.
• C. Every rational number is also an integer.
D. No rational number is irrational.
Answer:
A. false B. true C. false D. true
Whope you all like this answer
37. Two numbers are such that their
difference, their sum and their
product are in the ratio 1:7: 24.
Find the product of the
number.
Answer:
8 and 6
Step-by-step explanation:
Two numbers are such that their difference, their sum, and their product are to
each other as 1:7:24. Their product must equal what number?
:
Two numbers a & b
Let x = the multiplier
:
a - b = 1x
a + b = 7x
a * b = 24x
:
Add the 1st two equations
a - b = x
a + b = 7x
2a = 8x
a = 4x
or
x = .25a
:
a * b = 24x
Replace 24x; a = 4x therefore:
a * b = 6a
b = 6
;
Using the 1st equation
a - b = 1x
Replace b with 6 and x with .25a
a - 6 = .25a
a - .25a = 6
.75a = 6
a =
a = 8
:
Find the multiplier
a - b = x
8 - 6 = 2
:
Check this
a - b = 2 (1*2)
a + b = 14; (7*2)
a * b = 48: (24*2)
:
The numbers are 8 and 6; their products = 48
Gemma recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 16 miles per hour faster than on her way home. If Gemma spent a total of 1 hour bicycle, find the two rates.
first speed --- x mph
return speed -- x+16 mph
6/x + 6/(x+16) = 1
times each term by x(x+16)
6(x+16) + 6x = x(x+16)
x^2 + 4x - 96 = 0
(x-8)(x+12) = 0
x = 8 or x is a negative
her first speed was 8 mph
her return speed was 24 mph
check:
6/8 + 6/24 = 1 , that's good!
A radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now. What will be the amount of the material right after 20 years
Answer:
x = 960.4
Step-by-step explanation:
980 = 1000[tex]e^{kt}[/tex]
.98 = [tex]e^{10 k}[/tex]
ln(.98) = 10k ln(e)
k = ln(.98)/10
k=-0.00202
~~~~~~~~~~~~~~
x = 1000[tex]e^{20 *-.00202}[/tex]
x = 960.4
The amount of the material right after 20 years will be x = 960.4.
What is an exponential expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."
Given that radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now.
The amount of the material will be calculated as,
980 = 1000
[tex]0.98 = e^{10k}[/tex]
ln(.98) = 10k ln(e)
k = ln(.98)/10
k=-0.00202
The value after 20 years will be,
[tex]x = 1000e^{20\times 0.00202}[/tex]
x = 960.4
Therefore, the amount of the material right after 20 years will be x = 960.4.
To know more about an exponential expression follow
https://brainly.com/question/2456547
#SPJ5
Tell whether the following two triangles can be
proven congruent through SAS.
A.Yes, the two triangles are congruent
because two sides and their included
angle are congruent in both triangles.
B.No, the two triangles don't have
corresponding sides marked congruent.
C. Yes, the two triangles are congruent because they’re both right triangles.
D.No, the two triangles can only be proven congruent through SSA.
Answer:
B. No, the two triangles don't have
corresponding sides marked congruent.
Jun 29, 8:51:41 AM
Find the volume of a pyramid with a square base, where the perimeter of the base is
10.7 ft and the height of the pyramid is 9.8 ft. Round your answer to the nearest
tenth of a cubic foot.
9514 1404 393
Answer:
23.4 ft³
Step-by-step explanation:
In terms of the perimeter of the square base, the volume of a pyramid can be found using the formula ...
V = (1/48)P²h . . . . . where P is the base perimeter and h is the height
V = (1/48)(10.7 ft)²(9.8 ft) ≈ 23.4 ft³
_____
Additional comment
The relevant formulas usually used are ...
P = 4s . . . . perimeter of a square with side length s
A = s² . . . . area of a square with side length s
V = (1/3)Bh . . . . . volume of a pyramid with base area B and height h
Solving the perimeter equation for s, and using that result in the other formulas, we get ...
s = P/4
B = (P/4)² = P²/16
V = 1/3(P²/16)h = (1/48)P²h . . . . the formula used above
Using this result saves the effort of computing the intermediate values of side length and base area.
f(x) = 1
g(x) = x - 4
Can you evaluate (g•f)(0)? Explain why or why not?
Answer:
This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]
Step-by-step explanation:
We are given the following functions:
[tex]f(x) = 1[/tex]
[tex]g(x) = x - 4[/tex]
Can you evaluate (g•f)(0)?
This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]
Answer:
To evaluate the composition, you need to find the value of function f first. But, f(0) is 1 over 0, and division by 0 is undefined. Therefore, you cannot find the value of the composition.
You must evaluate the function f first.
Division by 0 is undefined.
The composition cannot be evaluated.
PLEASE HELP MATH⚠️⚠️⚠️⚠️⚠️
Convert this into algerbraic expression:
The difference of a number cubed and the same number
Step-by-step explanation
n^3-n.
Hope this will help you :) <3
