Answer:
b. 300x1 + 125x2 < = 4,000
Step-by-step explanation:
Maximum of 4,000 hours
This means that the the total amount of labor has to be of at most 4,000, that is:
[tex]T \leq 4000[/tex]
300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor
The total amount of labor is:
[tex]T = 300x1 + 125x2[/tex]
Uniting the two equations:
[tex]T \leq 4000[/tex]
[tex]300x1 + 125x2 \leq 4000[/tex]
And thus the correct answer is given by option b.
write your answer in simplest radical form
Answer:
[tex]s=6\sqrt{3}[/tex]
Step-by-step explanation:
In any 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.
In the given diagram, the hypotenuse is marked as 12 miles. Therefore, the side opposite to the 30 degree angle must be [tex]12 \div 2=6[/tex] miles. The final leg, [tex]s[/tex], must then represent the [tex]x\sqrt{3}[/tex] part of our ratio, hence [tex]\implies \boxed{6\sqrt{3}}[/tex]
find the missing segment below brainly
Let missing side be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{6}{4}=\dfrac{x}{20-x}[/tex]
[tex]\\ \sf\longmapsto 6(20-x)=4x[/tex]
[tex]\\ \sf\longmapsto 120-6x=4x[/tex]
[tex]\\ \sf\longmapsto 120=6x+4x[/tex]
[tex]\\ \sf\longmapsto 120=10x[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{120}{10}[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
Find the length of the third side. If necessary, round to the nearest tenth.
6
8
PLS HELP
Answer:
a = 5.3
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
where a and b are the legs and c is the hypotenuse
a^2 + 6^2 = 8^2
a^2 +36 = 64
a^2 = 64-32
a^2 =28
Taking the square root of each side
sqrt(a^2) = sqrt(28)
a=5.29150
To the nearest tenth
a = 5.3
The length of the third side of the right triangle is; 5.3
What is the length of the third side of the triangle?The triangle given is a right triangle and hence, the length of the third side can be evaluated by using the Pythagoras theorem as follows;
a² = 8² -6²
a² = 64- 36
a² = 28
a = √28
a = 5.3
Read more on Pythagoras theorem;
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Explain how to multiply
the following
binomials
(2x - y)(2x + y).
Step-by-step explanation:
you can just use the punnet square method to multiply it
Use FOIL; first, outer, inner, last. Multiply the first terms in each binomial, the outer terms of each binomial, the inner terms of each binomial, and the last terms of each binomial. In this case, you multiply 2x*2x, 2x*y, -y*2x, and -y*y.
Use the drop-down menu to create true statements,
If the graph of an inverse passes the
, you know that the inverse is
a function,
The composition of a function and its inverse is
always
DONE
DOWE
The range values of an inverse are the
values of the original function,
The graph of an inverse is the reflection of the
graph of the function over the line
DONE
DOWE
Answer:
A) Vertical test
B) y=x
C) x
D) domain
If the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.
What is Inverse Function?Inverse functions are functions which can be reversed in to another function.
Then the function is said to be the inverse of the second function.
The test which is used to know whether an inverse is a function or not is Vertical line Test.
So, if the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.
Composition of a function and it's inverse is always x.
Let y = f(x) be a function. Then x = f⁻¹ (y)
(f⁻¹of)(x) = f⁻¹ (f(x)) = f⁻¹ (y) = x
The graph of an inverse is the reflection of the graph of the function over the line y = x.
The range values of the inverse function are the domain values of the original function.
Hence the blank terms are found.
Learn more about Inverse of Functions here :
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Help please:)) 2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,
a. What would be the optimal dimensions (radius and height) to minimize surface area?
b. What would the surface area be?
C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
Answer:
a. The radius r = 5.42 cm and the height h = 10.84 cm
b. 553.73 cm²
c. i. Beauty ii. Design
Step-by-step explanation:
a. What would be the optimal dimensions (radius and height) to minimize surface area?
The volume of the standard container is a cylinder and its volume is V = πr²h where r = radius of container and h = height of container.
Since V = 1000 cm³,
1000 cm³ = πr²h (1)
Now, the surface area of a cylinder is A = 2πr² + 2πrh where r and h are the radius and height of the cylinder.
From (1), h = 1000/πr².
Substituting h into A, we have
A = 2πr² + 2πrh
A = 2πr² + 2πr(1000/πr²)
A = 2πr² + 2000/r
To maximize A, we differentiate A with respect to r and equate to zero to find the value of r at which A is maximum.
So, dA/dr = d[2πr² + 2000/r]/dr
dA/dr = d[2πr²]/dr + d[2000/r]/dr
dA/dr = 4πr - 2000/r²
Equating the equation to zero, we have
4πr - 2000/r² = 0
4πr = 2000/r²
r³ = 2000/4π
r = ∛(1000/2π)
r = 10(1/∛(2π))
r = 10(1/∛(6.283))
r = 10/1.8453
r = 5.42 cm
To determine if this value of r gives a minimum for A, we differentiate dA/dr with respect to r.
So, d(dA/dr)/dr = d²A/dr²
= d[4πr - 2000/r²]/dr
= d[4πr]/dr - d[2000/r²]/dr
= 4π + 4000/r³
Substituting r³ = 2000/4π into the equation, we have
d²A/dr² = 4π + 4000/r³ = 4π + 4000/(2000/4π) = 4π + 2 × 4π = 4π + 8π = 12π > 0
Since d²A/dr² = 12π > 0, then r = 5.42 cm gives a minimum for A.
Since h = 1000/πr²
h = 1000/π(5.42)²
h = 1000/92.288
h = 10.84 cm
So, the radius r = 5.42 cm and the height h = 10.84 cm
b. What would the surface area be?
Since the surface area, A = 2πr² + 2πrh
Substituting the values of r and h into A, we have
A = 2πr² + 2πrh
A = 2πr(r + h)
A = 2π5.42(5.42 + 10.84)
A = 10.84π(16.26)
A = 176.2584π
A = 553.73 cm²
c. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
i. Beauty
ii. Design
PLEASE HELPPPPPPPPPP
Answer:
167/346 or 0.483
Step-by-step explanation:
From the question given above, the following data were obtained:
Number of Tails (T) = 167
Number of Heads (H) = 179
Probability of tail, P(T) =?
Next, we shall determine total outcome. This can be obtained as follow:
Number of Tails (T) = 167
Number of Heads (H) = 179
Total outcome (S) =?
S = T + H
S = 167 + 179
Total outcome (S) = 346
Finally, we shall determine the probability of tails. This can be obtained as follow:
Number of Tails (T) = 167
Total outcome (S) = 346
Probability of tail, P(T) =?
P(T) = T / S
P(T) = 167 / 346
P(T) = 0.483
Thus, the probability of tails is 167/346 or 0.483
Let θ be an angle in quadrant IV such that sinθ = -2/5 .
Find the exact values of secθ and tanθ.
If θ lies in the fourth quadrant, then sin(θ) < 0 and cos(θ) > 0. So we have from the Pythagorean identity,
sin²(θ) + cos²(θ) = 1 ==> cos(θ) = +√(1 - sin²(θ)) = √21/5
Then
sec(θ) = 1/cos(θ) = 5/√21
and
tan(θ) = sin(θ)/cos(θ) = (-2/5)/(√21/5) = -2/√21
Phân loại theo kiểu bố trí (cấu trúc) của mẫu sổ kế toán không gồm sổ nào trong các sổ dưới đây
Answer:
I I want everything in English
Step-by-step explanation:
it is difficult to read other languages write it in English please
2√3x+1 - √4x+5 =3
show your steps please
Answer:
x = 5
Step-by-step explanation:
I'm assuming that 3x +1 & 4x + 5 are all underneath the square root
2 √3x + 1 - √4x + 5 = 3
2 √3x + 1 = 3 + √4x + 5
4 (3x+1) = 9 + 6 √4x + 5 + 4x + 5
12x + 4 = 14 + 6√4x + 5 + 4x
-6 √4x + 5 = 14 + 4x - 12x - 4
-6 √4x + 5 = 10 - 8x
3 √4x + 5 = -5 + 4x (divided both sides by - 2)
9 (4x +5) = 16x^2 - 40x + 25
36x + 45 = 16x^2 - 40x + 25
36x + 45 - 16x^2 + 40x - 25 = 0
76x + 20 - 16x^2 = 0
-16x^2 + 76x + 20 = 0
4x^2 - 19x -5 = 0 (dividied by -4)
4x^2 + x - 20x -5 = 0
x (4x + 1) -5 (4x +1) = 0
(4x +1) (x-5) = 0
Possible answers:
4x + 1 = 0
x - 5 = 0
x = -1/4
x =5
Now we will check which one satisfies the equation
2√3x+1 - √4x+5
Substitue 5 for x and we get 3
Thus we know that 5 is the correct answer
Answered by Gauthmath
Let f(x) = e ^3x/5x − 2. Find f'(0).
Answer:
Step-by-step explanation:
Our friend asking what the actual function is has a point. I completed this under the assumption that what we have is:
[tex]f(x)=\frac{e^{3x}}{5x-2}[/tex] and used the quotient rule to find the derivative, as follows:
[tex]f'(x)=\frac{e^{3x}(5)-[(5x-2)(3e^{3x})]}{(5x-2)^2}[/tex] and simplifying a bit:
[tex]f'(x)=\frac{5e^{3x}-[15xe^{3x}-6e^{3x}]}{(5x-2)^2}[/tex]and a bit more to:
[tex]f'(x)=\frac{5e^{3x}-15xe^{3x}+6e^{3x}}{(5x-2)^2}[/tex] and combining like terms:
[tex]f'(x)=\frac{11e^{3x}-15xe^{3x}}{(5x-2)^2}[/tex] and factor out the GFC in the numerator to get:
[tex]f'(x)=\frac{e^{3x}(11-15x)}{(5x-2)^2}[/tex] That's the derivative simplified. If we want f'(0), we sub in 0's for the x's in there and get the value of the derivative at x = 0:
[tex]f'(0)=\frac{e^0(11-15(0))}{(5(0)-2)^2}[/tex] which simplifies to
[tex]f'(0)=\frac{11}{4}[/tex] which translates to
The slope of the function is 11/4 at the point (0, -1/2)
Which of the following statements are true?
Answer:
last one
Step-by-step explanation:
they both whole
Which graph shows a set of ordered pairs that represent a function?
Answer:
Graph C.
*See attachment below
Step-by-step explanation:
A graph that shows a set of ordered pairs representing a function would have each x-value being plotted against only one y-value. That is, every x-value must have exactly one y-value. Every x-value must not have more than 1 y-value being plotted against it.
The graph that shows this is the graph in option as shown in the attachment below.
The lengths of pregnancies in a small rural village are normally distributed with a mean of 264.1 days and a standard deviation of 12.9 days. In what range would you expect to find the middle 95% of most pregnancies
Answer:
The range of the 95% data (X) = 238.3 days < X < 289.9 days
Step-by-step explanation:
Given;
mean of the normal distribution, m = 264.1 days
standard deviation, d = 12.9 days
between two standard deviation below and above the mean is 96% of all the data.
two standard deviation below the mean = m - 2d
= 264.1 - 2(12.9)
= 238.3 days
two standard deviation above the mean = m + 2d
= 264.1 + 2(12.9)
= 289.9 days
The middle of the 95% of most pregnancies would be found in the following range;
238.3 days < X < 289.9 days
Question 5(Multiple Choice Worth 2 points)
(02.05)
Determine the vertex of the function f(x) = −4(x − 3)2 + 6.
(6, −3)
(6, 3)
(3, 6)
(−3, 6)
Answer:
(3, 6)
Step-by-step explanation:
The vertex form of a quadratic is y = a(x-h)^2 + k
where (h, k) is the point of the vertex. So the answer is (3,6)
Which expression is equivalent to 5y^-3?
Answer:
5/y^3
Step-by-step explanation:
which expression is equivalent to 5y^-3
for example a^-1 = 1/a
5y^-3 = 5/y^3
Please help explanation need it
Step-by-step explanation:
jejejebe. s shs sjs sibskkw
A superhero can fly from New York to Los Angeles in 30 minutes. The distance from New York to Los Angeles is approximately 2,450 miles.
How many miles per hour is the superhero flying?
Work Shown:
30 min = 30/60 = 0.5 hours
distance = rate*time
rate = distance/time
rate = (2450 miles)/(0.5 hours)
rate = (2450/0.5) mph
rate = 4900 mph
For the sake of comparison, a typical commercial passenger jet can reach max speeds of about 600 mph.
1 Construct the following triangles. You will need a ruler and a protractor.
a) Triangle ABC, where AB = 5 cm,
Answer:
abcdefghijklmnopqrstuvwxy and z
Step-by-step explanation:
I operate a small convenience store. Typically, I get about 10 customers per hour. If the mean time before I get my 25th customer is 2.5 hours, what is the standard deviation associated with the time until I see my 25th customer
Answer:
The standard deviation associated with the time until I see my 25th customer is of 2.5 hours.
Step-by-step explanation:
In this problem, we have the mean time between x successes, which characterizes the exponential distribution.
As in this question context, the important thing to note is that for the exponential distribution, the mean and the standard deviation are the same.
Mean time before I get my 25th customer is 2.5 hours, what is the standard deviation associated with the time until I see my 25th customer?
They are the same in the exponential distribution, so 2.5 hours.
Find the equation of the circle, if (4, -2)
and (2, 1) are the extremities of the
diameter.
Answer:
(x-3)^2+(y+1/2)^2=3.25
Step-by-step explanation:
The radius of the circle would be the midpoint of diameter. Radius is (3,-1/2) and the length would be 1.8.
Làm ơm giúp tôi giải bài tập kinh tế vi mô này với
Step-by-step explanation:
i don't know this language
A number increased by a% and decreased by 80% is 400. What is the number?
Answer:
[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]
updated response , given that you confirmed the question....
if the percent is the variable a% then ....
[tex]x*(\frac{a+100}{100}) = 2000[/tex]
[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]
I think that there is missing information here ....
you can make any number work here the result of the number being increased by the percent has to be 2000...
so if if the number is 1000 then the percent would be 100%
if you make the number 1500 then the percent would be 33 1/3 %
Step-by-step explanation:
The number is [tex]\frac{2000}{(1+\frac{a}{100})}[/tex]
What will be the new number when the original number is increased by a% and decreased by 80%?Let us assume that the number be x.
When the number x is increased by a% the new number will be,
[tex]x(1+\frac{a}{100})[/tex]
Now, this number is decreased by 80%. So, the new number will be,
[tex]x(1+\frac{a}{100})*(1-\frac{80}{100} )\\=x(1+\frac{a}{100})*(1-0.8 )\\=x(1+\frac{a}{100})*0.20[/tex]
By the given condition,
When x increased by a% and decreased by 80% it becomes 400
Therefore, we can write
[tex]x(1+\frac{a}{100})*0.20=400[/tex]
[tex]x(1+\frac{a}{100})=\frac{400}{0.20}[/tex]
[tex]x(1+\frac{a}{100})=2000[/tex]
[tex]x=\frac{2000}{(1+\frac{a}{100})}[/tex]
So, the number will be [tex]\frac{2000}{(1+\frac{a}{100})}[/tex].
Learn more about the percentage change of a number please follow: https://brainly.com/question/26527346
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what is the mean in 0.33, 0.33, 0.54, 0.46, 0.30, 0.77, 0.42, 0.44, 0.60, 0.32, 0.47, 0.64, 0.61, 0.69, 0.41, 0.39, 0.66, 0.60, 0.61, 0.70
Answer:
0.5145
Step-by-step explanation:
Mean is also known as average. It is expressed as:
Mean = Sum of data/Sample size
Sum of data = 0.33+0.33+0.54+0.46+0.30+0.77+0.42+0.44+0.60+0.32+0.47+0.64+0.61+0.69+0.41+0.39+0.66+0.60+0.61+0.70
Sum of data = 10.29
Sample size = 20
Mean = 10.29/20
Mean = 0.5145
Hence the mean of the data is 0.5145
Find the measure of each angle in the problem. RE contains point P.
Answer:
∠3z = 108 degrees
∠2z = 72 degrees
Step-by-step explanation:
First, we need to create an equation.
3z + 2z = 180
5z = 180
Divide both sides by 5:
z = 36
Now, substitute z for five for both angles.
3 x 36 = 108 degrees
2 x 36 = 72 degrees
Hope this helps!
If there is something wrong, please let me know.
a/(b+ce^x) dx = ? Please solve this
Answer:
1/ab en (c/be^-x+c)
Step-by-step explanation:
Sure is a harsh question! Here's my Explanation
b+ce^x = t
ce^x an = dt
e^xan = dt/c
an = dt/ce^x = dt/c(t-b/c) = at/(t-b)
en = t-b/c
A/b+ce^x dx = a/t dt/t-b
a ∫1/t (t-b) dt = 1/a∫ (1/(t-b) - 1/t) dt
= 1/ab [∫1/(t-b) dt + ∫-1/t dt]
= 1/ab [en (t-b) - en(t)]
= 1/ab en ((t-b)/t)
t = b + ce^x
= 1/ab en (b+ce^x -b/b+ce^x)
=1/ab en (ce^x/b+ce^x)
= 1/ab en (c/be^-x+c)
The 47th Annual PDK/Gallup Poll of the Public’s Attitudes toward the Public Schools, conducted in May 2015, sampled 4,500 adult Americans and found that 64% feel there is too much emphasis on standardized testing in the public schools in their community.
Using the quick method, the estimated margin of error for conclusions having 95% confidence about the entire adult population of adult Americans is ___%?
Answer:
1.3809%
Step-by-step explanation:
Given ;
Sample size, n = 4500
Phat = 64% = 0.64
The margin of error :
Zcritical * √[Phat(1 - Phat) / n]
At 95% confidence level:
Zcritical at 95% = 1.96
Margin of Error :
1.96 * √[0.64(0.36) / 4500]
1.96 * 0.0071554
= 0.0138099
= 0.0138099 * 100%
= 1.3809%
Is (5, 4) a solution to the equation y = x − 1?
yes or no
The cost of three pants and four shirts is $68.45 if a pant costs $6.85 more than a shirt find the cost of a pant and a shirt estimate to the nearest whole number.
Answer:
3 pants are $20.55
4 shirts are $47.9
Step-by-step explanation:
a pant is $6.85 × 3= $20.55
68.45 - 20.55 = $47.9
$47.9 ÷ 4 = $11.98 a shirt
On January 2, 2008, the American Idol website (www .americanidol) conducted an online poll that asked respondents which contestant they liked best among six former contestants. To become part of the sample, respondents simply clicked on a response. Of the 941,434 responses to this poll, 55% voted for Clay Aiken. We can conclude that _________________________________ .
a. the sample is too small.
b. a fraction of the millions of people who watched the TV show to draw any conclusion.
c. most Americans prefer Clay Aiken out of those former contestants.
d. the poll uses voluntary response, so the results tell us little about the population of all adults.
Answer:
Online Poll
We can conclude that
c. most Americans prefer Clay Aiken out of those former contestants.
Step-by-step explanation:
Sample responses received from the poll = 941,434
Proportion of voters for Clay Aiken = 55%
Computed proportion of voters for the other 5 contestants = 45% (100% - 55%)
This gives an average of 7.5% (45%/5) for the other 5 contestants.
Therefore, the conclusion is that "most Americans prefer Clay Aiken out of those former contestants" in the American Idol contest.
