Answer:
A. 32 ft
Step-by-step explanation:
Pythagoras for right-angled triangles (as that is what this is here - the floor from the base of the ladder to the wall, the wall up to where the ladder ends, and the ladder itself as the Hypotenuse).
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90 degree angle).
so, we know,
c = 40 ft
a = 24 ft
we are looking for B
=>
40² = 24² + b²
1600 = 576 + b²
1024 = b²
b = 32 ft
Anne invested $1000 in an account with a 3% annual interest rate. She made no deposits or
withdrawals on the account for 2 years. If interest was compounded annually, which equation
represents the balance in the account after the 2 years?
Can some one help me is that correct ?
Answer:
i think it is..
Step-by-step explanation:
Answer:
First one would be y=2x (the cost of each ticket is 2 and x is the number of tickets that you are buying)
The second one is y=x+10 (each ticket is one and 10 is the one time set up fee)
A rectangular storage container with an open top is to have a volume of 14 cubic meters. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 8 dollars per square meter. Find the cost of materials for the cheapest such container.
Answer:
C(min) = 277.95 $
Container dimensions:
x = 2.822 m
y = 1.411 m
h = 3.52 m
Step-by-step explanation:
Let´s call x and y the sides of the rectangular base.
The surface area for a rectangular container is:
S = Area of the base (A₁) + 2 * area of a lateral side x (A₂) + 2 * area lateral y (A₃)
Area of the base is :
A₁ = x*y we assume, according to problem statement that
x = 2*y y = x/2
A₁ = x²/2
Area lateral on side x
A₂ = x*h ( h is the height of the box )
Area lateral on side y
A₃ = y*h ( h is the height of the box )
s = x²/2 + 2*x*h + 2*y*h
Cost = Cost of the base + cost of area lateral on x + cost of area lateral on y
C = 10*x²/2 + 8* 2*x*h + 8*2*y*h
C as function of x is:
The volume of the box is:
V(b) = 14 m³ = (x²/2)*h 28 = x²h h = 28/x²
C(x) = 10*x²/2 + 16*x*28/x² + 16*(x/2)*28/x²
C(x) = 5*x² + 448/x + 224/x
Taking derivatives on both sides of the equation we get:
C´(x) = 10*x - 448/x² - 224/x²
C´(x) = 0 10x - 448/x² - 224/x² = 0 ( 10*x³ - 448 - 224 )/x² = 0
10*x³ - 448 - 224 = 0 10*x³ = 224
x³ =22.4
x = ∛ 22.4
x = 2.822 m
y = x/2 = 1.411 m
h = 28/x² = 28 /7.96
h = 3.52 m
To find out if the container of such dimension is the cheapest container we look to the second derivative of C
C´´(x) = 10 + 224*2*x/x⁴
C´´(x) = 10 + 448/x³ is positive then C has a minimum for x = 2.82
And the cost of the container is:
C = 10*(x²/2) + 16*x*h + 16*y*h
C = 39.82 + 158.75 + 79.38
C = 277.95 $
A box of golf balls contains 10 balls. Each golf ball has a diameter of 3.6 centimeters. What is the total
volume of golf balls in 3 boxes?
about 1465.74 cm
c. about 1221.45 cm
b. about 732.87 cm
d. about 81.43 cm
Answer:
C
Step-by-step explanation:
Can you help me with this question
Answer:
Below in bold.
Step-by-step explanation:
We see from the diagram that:
SY = SK + KY
So, substituting the given values:-
36 - x = 13x - 5 + 2x + 9
-x - 13x - 2x = - 5 + 9 - 36
-16x = -32
x = 32/16 = 2.
So SK = 13(2) - 5 = 21.
KY = 2(2) + 9 = 13.
SY = 36 - 2 = 34.
21 + 13 = 34 so this is a check that our calculation is correct.
The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When
the length is 12 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm/s)? Write an equation for A in terms of l and w.
Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
[tex]A=w\ell[/tex]
Where w is the width and l is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to t, where w and l are both functions of t:
[tex]\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell][/tex]
By the Product Rule:
[tex]\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w[/tex]
Since we know that dl/dt = 6 and that dw/dt = 5:
[tex]\displaystyle \frac{dA}{dt}=5\ell + 6w[/tex]
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
[tex]\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}[/tex]
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
What number must you add to complete the square? x^2+26x=11
Answer:
[tex] {x}^{2} + 26x = 11 \\ x = 0.4 \: and \: - 26.4[/tex]
how did you find the standard deviation?
Answer:
Step-by-step explanation:
It's the square root of the variance
The variance is just the second moment minus the first moment squared
explain what it means for a function to be O(1)
Answer:
a function that converges to 0. '' This means that there is some input size past which the function is always between -0.1 and 0.1; there is some input size past which the function is always between -0.01 and 0.01; and so on.
To estimate the benefits of an SAT prep course, a random sample of 10 students enrolled in the course is selected.
For each of these students, their entrance score on the exam taken at the beginning of the course is recorded. Their
exit score on the exam they take at the end of the course is recorded as well. The table displays the scores.
Answer: 57%
Step-by-step explanation:
how do I use the following cosine equation to get the Sinusoid Max & Min Times (x values), and Sinusoid Max and Min Values (y values) in order graph a Tidal Wave Chart?
y = 11.412 cos ((5π / 31)(x-3:12)) +174.91
9514 1404 393
Answer:
maximum: (x, y) = (12.4n+3.2, 186.322)minimum: (x, y) = (12.4n+9.4, 163.498)Step-by-step explanation:
You know that cos(α) is a maximum at α=0, 2π, 4π, and all even multiples of π. You know cos(α) is a minimum for α=π, 3π, 5π, and all odd multiples of π.
You can find your value of x at which y will be a maximum by setting the argument of the cosine function equal to zero (and/or 2nπ). If we use α=2nπ, then we have ...
α = (5π/31)(x -3.2) = 2nπ
(x -3.2) = (31/5)(2n) = 12.4n
Tidal maxima will occur at ...
x = 12.4n +3.2 . . . . . for integer values of n
Without bothering to go through the solution for α being odd multiples of π, we can see from this that the period is 12.4 hours. We know the tidal minimum will be half a period later, or 6.2 hours later than this.
Tidal minima will occur at ...
x = 12.4n +9.4 . . . . for integers n
__
Of course, cos(α) has extremes of ±1, so your tidal maximum will be ...
y = 11.412 +174.91 = 186.322
and your tidal minimum will be ...
y = -11.412 +174.91 = 163.498
what is the volume of the triangular prism 13 m x 6 m x 5 m
Answer:
U R ANSWER
Step-by-step explanation:
177.26657
Answer:
[tex]V=195m^2[/tex]
Step-by-step explanation:
Volume formula of a triangular prism is [tex]V=\frac{1}{2} (b)(h)(l)[/tex]
[tex]V=\frac{1}{2}(13)(6)(5)[/tex]
[tex]V=\frac{1}{2} (390)[/tex]
[tex]V=195[/tex]
Hope this helps
The picture has the question
Find the missing value of x. Show your work.
Answer:
68 degrees
Step-by-step explanation:
Since the angle is a right angle, it is 90 degrees, to figure out the measurement of a section if it, simply subtract the known angle 22, from 90 to get an answer of 68.
if f(×) = [tex] \frac{1}{ \sqrt{x - 1} } [/tex]
then find [tex] \frac{f(x) - f(2)}{x - 2} [/tex]
9514 1404 393
Answer:
(1 -x +√(x -1))/(x² -3x +2)
Step-by-step explanation:
Fill in the given function definition and simplify.
[tex]\dfrac{f(x)-f(2)}{x-2}=\dfrac{\dfrac{1}{\sqrt{x-1}}-\dfrac{1}{\sqrt{2-1}}}{x-2}=\dfrac{1-\sqrt{x-1}}{(x-2)\sqrt{x-1}}\\\\=\dfrac{\sqrt{x-1}-x+1}{(x-2)(x-1)}=\boxed{\dfrac{\sqrt{x-1}-x+1}{x^2-3x+2}}[/tex]
A company is interested in testing sample sets of 20 Widgets to see how they withstand a heat test. Widgets fail the heat test when they develop cracks in their top paint coating. Suppose historically that 10% of the Widgets develop paint cracks. a. Does this problem represent the application of a Continuous or Discrete Distribution
Answer:
Discrete Distribution.
Step-by-step explanation:
For each widget, there are only two possible outcomes. Either they develop paint cracks, or they do not. The probability of a widget developing paint cracks is independent of any other widgets, which means that the binomial probability distribution, which is a discrete distribution, is used to solve this question. Thus the answer is a Discrete Distribution.
if f(y)=y^6/6lny-y^6/36, find f'(y)
It looks like you have
[tex]f(y)=\dfrac{y^6}{6\ln(y)}-\dfrac{y^6}{36}[/tex]
Differentating gives
[tex]f'(y)=\dfrac{6y^5\times6\ln(y)-6y^6\times\frac1y}{(6\ln(y))^2}-\dfrac{6y^5}{36}= -\dfrac{y^5\left(\ln^2(y)-6\ln(y)+1\right)}{6\ln^2(y)}[/tex]
Nichol walks at a constant pace of 1.2 m/s and takes 15 minutes to get to school.
Sakura walks at 1.4 m/s and takes 20 minutes to get to school.
What is the difference between the distances they walked?
Answer:
The difference between the distances they walked is 600 meters.
Step-by-step explanation:
Let's calculate the distance traveled by Nichol and Sakura with the following equation:
[tex] d = v*t [/tex]
Where:
v: is the speed
t: is the time
The distance traveled by Nichol is:
[tex] d_{n} = 1.2 m/s*15min*\frac{60 s}{1 min} = 1080 m [/tex]
And the distance traveled by Sakura is:
[tex] d_{s} = 1.4 m/s*20 min*\frac{60 s}{1 min} = 1680 m [/tex]
Hence, the difference between the distances they walked is:
[tex] d_{t} = d_{s} - d_{n} = 1680 m - 1080 m = 600 m [/tex]
Sakura traveled 600 meters more than Nichol.
Therefore, the difference between the distances they walked is 600 meters.
I hope it helps you!
Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounces.
(a)What is the standard deviation of the average fill volume of 22 bags?
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
Answer:
a) 0.0171 fluid ounces.
b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces
c) The mean should be of 6.153 fluid ounces.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
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.
Standard deviation of 0.08 fluid ounces.
This means that [tex]\sigma = 0.08[/tex]
(a)What is the standard deviation of the average fill volume of 22 bags?
This is s when n = 22. So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{0.08}{\sqrt{22}}[/tex]
[tex]s = 0.0171[/tex]
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]
[tex]Z = -12.3[/tex]
[tex]Z = -12.3[/tex] has a p-value of 0.
0% probability that the average fill volume of 22 bags is below 5.95 ounces.
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]
[tex]6.1 - \mu = -3.09*0.0171[/tex]
[tex]\mu = 6.153[/tex]
The mean should be of 6.153 fluid ounces.
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST
1/3(-15 divide 1/2) 1/4 what does it equal
Answer:
-2.5 or - 2 1/2
Step-by-step explanation:
Writing out the expression Mathematically ;
1/3(-15÷1/2)1/4
Using PEMDAS :
Solving the bracket first
(-15 ÷ 1/2) = (-15 * 2/1) = - 30
We have :
1/3(-30)1/4 = - 10 * 1/4 = - 10 / 4 = - 2.5
-2.5 = - 2 1/2
tracy has 63 colors pens and jacob has 46 colors pens how many more colors pens does tracy have than jacob
Given:
Number of color pens Tracy have = 63
Number of color pens Jacob have = 46
To find:
How many more colors pens does Tracy have than Jacob?
Solution:
We need to find the difference between the number of color pens Tracy have and the number of color pens Jacob have.
[tex]Difference=63-46[/tex]
[tex]Difference=17[/tex]
Therefore, Tracy have 17 more color pens than Jacob.
Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x
How many classes would Gina need to take for the total cost to be the same at both dance studios?
Answer:
Gina would need to take 10 classes.
Step-by-step explanation:
Cost of x classes at dance studio:
[tex]y_d(x) = 15x[/tex]
Cost of x classes at toe tappers:
[tex]y_t(x) = 25 + 12.5x[/tex]
How many classes would Gina need to take for the total cost to be the same at both dance studios?
This is x for which:
[tex]y_d(x) = y_t(x)[/tex]
So
[tex]15x = 25 + 12.5x[/tex]
[tex]2.5x = 25[/tex]
[tex]x = \frac{25}{2.5}[/tex]
[tex]x = 10[/tex]
Gina would need to take 10 classes.
Answer:
10 just took it on edge
4x - 3(2x - y) if x = and y = 4.
Help me pls
Answer:
[tex]=0[/tex]
Step-by-step explanation:
Given:
[tex]4x-3(2x-y)[/tex]
Let's substitute for y
[tex]4x-3(2x-4)=0[/tex]
Let's distribute the parenthesis
[tex]4x-6x+12=0[/tex]
Combine like terms
[tex]-2x+12=0[/tex]
Subtract 12 from both sides
[tex]-2x=-12[/tex]
divide both sides by -2
[tex]x=6[/tex]
Now let's insert 6 for the [tex]x[/tex] and 4 for the [tex]y\\[/tex]
[tex]24-3(12-4)=[/tex]
[tex]24-3(8)=[/tex]
[tex]24-24=0[/tex]
Hope this helps
Answer: The x = -1
Step-by-step explanation: I just looked it up on line.
Can someone please answer this
A formula is given as J = 10V/11 + 143
make V the subject of the formula
answer asap please.
Answer:
11j - 1573/10
Step-by-step explanation:
J = 10v /11 +143
collect terms
J - 143 =10v /11
11 (J -143) = 10v
Divide both sides by 10
11(J - 143)/10 = v
v = 11J - 1573/10
Hope this helps!
What is the expected price of a calculator in the year 2000 if it costs $13 in 2015
Answer:
$10.90
Step-by-step explanation:
I don't know why but it wants me to talk when I dont need to
32 1/3% of animals at an animal shelter are dogs. About what fraction of the animals are dogs
Answer:
about 8/25
Step-by-step explanation:
32.3% = 32/100 = 16/50 = 8/25
rounded percentage down.
put over 100
reduce fraction
At a local concert, the cost for 3 adults and 2 children was $32.00. The cost for 8 adults and 5 children
was $84.00. Find how much it costs for an individual adult and how much it costs for an individual
child.
Adult ticket price = $
Child ticket price = $
Answer:
Hence the cost of adult tickets is $8
and the cost of child ticket is $4
Step-by-step explanation:
Given data
Let the cost per adult be x
and the cost per child be y
So
3x+2y= 32------------1
8x+5y= 84------------2
Now solving 1 and 2 simultaneously, we have
3x+2y= 32------------1X 5
8x+5y= 84------------2 X 2
15x+ 10y= 160
16x+ 10y= 168
-x+0)=-8
-x= -8
x= 8
Put x= 8 in 1 to find y
3*8+2y= 32
24+2y= 32
2y= 32-24
2y= 8
y= 4
30 points ~ Thirty-eight kids are riding the bus. Half of the kids are girls. How many boys are on the bus?
Answer:
19 boys
Step-by-step explanation:
38 kids on the bus
1/2 are girls, that means 1/2 are boys
1/2 * 38 = 19
There are 19 girls and 19 boys