A 13-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 8 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 12 feet from the wall?
Answer:
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
Step-by-step explanation:
From the question we are told that:
Slant height [tex]h=13ft[/tex]
Velocity [tex]v=\frac{dx}{dt}=8[/tex]
Distance [tex]d=12ft[/tex]
Generally the equation for area is mathematically given by
[tex]A=0.5*x*sqrt(169 - x^2)[/tex]
Differentiating
[tex]\frac{da}{dx}=\frac{169-2 x^2}{(2 sqrt(169-x^2))}[/tex]
Multiplying through by dx/dt
[tex]\frac{da}{dx}*\frac{dx}{dt}=\frac{169-2 x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-2x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-(2*12^{2})}{2*\sqrt{(169-12^{2})}}*8[/tex]
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
A credit card advertises an annual interest rate of 23%.
What is the equivalent monthly interest rate?
Given:
A credit card advertises an annual interest rate of 23%.
To find:
The equivalent monthly interest rate.
Solution:
We know that,
1 year = 12 months
It is given that, the credit card advertises an annual interest rate of 23%. So, the equivalent monthly interest rate is:
[tex]\dfrac{23\%}{12}=1\dfrac{11}{12}\%[/tex]
[tex]\dfrac{23\%}{12}\approx 1.9167\%[/tex]
Therefore, the equivalent monthly interest rate is [tex]1\dfrac{11}{12}\%[/tex] and the approximate equivalent monthly interest rate is 1.9167%.
If 12th term of an ap is -13 and sum of 1st four term is 24. What is the sum of first 20 terms
Answer:
-200
Step-by-step explanation:
ATQ, a+11d=-13 and a+a+d+a+2d+a+3d=24, 4a+6d=24. Solving this, we get a=9 and d=-2. Sum of the first 20 terms is 10*(18+(19)*(-2))=-200
I need help ASAP please help me solve this math question
Answer:
b appears to be correct
Step-by-step explanation:
I need help on this plzzz I and not the best at math
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex]f(x) = \left[\begin{array}{cc}-1&x<-1\\0&-1\le x \le -1\\1&x>1\end{array}\right[/tex]
Required
The graph of the step function
Before plotting the graph, it should be noted that:
[tex]\le[/tex] and [tex]\ge[/tex] use closed circle at its end
[tex]<[/tex] and [tex]>[/tex] use open circle at its end
So, we have:
[tex]f(x) = -1,\ \ \ \ x < -1[/tex]
The line stops at -1 with an open circle
[tex]f(x) = 0,\ \ \ \ -1 \le x \le 1[/tex]
The line starts at - 1 and stops at -1 with a closed circle at both ends
[tex]f(x) = 1,\ \ \ \ x > 1[/tex]
The line starts at 1 with an open circle
The options are not complete, so I will plot the graph myself.
See attachment for graph
An auto transport truck holds cars. A car dealer plans to bring in new cars in June and July. If an auto transport truck is filled for each delivery, except for the last one, how many full truckloads are needed and how many cars will be in the last truck?
Answer:
95 truckloads
Last truck = 10 cars
Step-by-step explanation:
Capacity of auto truck = 12 cars
Total number of cars to be brought in = 1150
The number of truckloads required :
Total number of cars to be brought in / capacity of auto truck
Number of truckloads = 1150 / 12 = 95.83333
This means that the number of full truckloads required will be, the whole number = 95
The last truck won't be full and will contain :
1150 - (95 * 12)
1150 - 1140
= 10 cars
What is the remainder when x2+ 3 is divided by x - 1?
Answer:
Step-by-step explan
6v(2v + 3) 2) 7(−5v − 8)
Answer:
6v(2v+3)2)7（-5v-8）
6v+2v-5v+3+2-8
3v-3
I need help please if you know help me with this, thanks
Answer:
B
note: in most cases (6x-3)[tex]\sqrt{2 }[/tex] would be the way people simplify this
Step-by-step explanation:
Answer:
Option B, 6x√2 - 3√2
Step-by-step explanation:
5x√2 - 3√2 + x√2
= x√2(5+1) - 3√2
= 6x√2 - 3√2
Answered by GAUTHMATH
A company pays a bonus to four employees A, B, C, and D. A gets four times as much as B. B gets 50% of the amount paid to C. C and D get the same amount. If the total bonus is ¢1,800.00, set all necessary equations to ascertain the share of each employees.
Answer:
A = 800, B = 200, C = 400 Andy D = 400
Step-by-step explanation:
Length of a line segment with endpoints (3,-2) and (-3,4).
Answer:
6squareroot2
Step-by-step explanation:
that's the answer I think
HELP ME PLEASE I NEED HELP
Answer:
1. 3-5
2. 5-3
3. 3-5
4. 5-3
Step-by-step explanation:
This is simple! Just get rid of the parenthesis for each of the expressions shown.
3 + (-5)
the plus sign is next to the negative which is in the parenthesis. Negative times positive is equal to negative. The expression then becomes
3 - 5
Now do the same for the rest!
For things like 3 and 4, you can just flip it like 3-5 and 5-3 because it will all equal the same :]
Hope this helps !!
-Ketifa
Which expression is equivalent to (b^n)m?
Step-by-step explanation:
By the law of exponent :
(a^n)^m=a^n×m
Option C
b^n×m is the correct answer...
hope it helps
In what quadrant would the triangle be if rotated 90 degrees
I strongly believe the answer is 2, if it isnt that it must be 3.
"Rotated around the origin", as the question actually says, puts it in Quadrant-II (2).
But the way you put the question, just saying the triangle is rotated 90°, leaves it right where it is, in Quadrant-I, with vertex-H on the bottom.
Suppose you work for a political organization and you are interested in hearing how the residents of New York State feel about a particular issue. You are asked to create a sample of at least 10000 residents using a CLUSTER methodolgy. Explain how you could create this sample of New York State residents?
Since the state is broken up into counties, and each county subdivided into precincts, this provides a natural way to form cluster samples.
If the precinct populations are too large, then you can further subdivide based on household or building residence. In other words, you can randomly select a building and consider that a separate cluster. All residents of that building would be part of the cluster.
In cluster sampling, the idea is that whichever clusters you select, you survey every person who resides in that cluster. So naturally you need to be careful not to go overboard.
I need helpppp please I don’t understand this question at alll
Answer:
17000
Step-by-step explanation:
17^1 * 10^3
17 * 10*10*10
17*1000
17000
the answer is 17,000
the exponent shows how many times you multiply the number by itself
here is an image for an explanation
hope I helped ❤
There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of exactly 1 red?
please need ASAP
Answer:
3 out of 12 chance i believe.
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
We'll need to use casework, since the problem stipulates there needs to be exactly one red drawn. Because we're drawing two marbles, we can either draw a red one first or a red one second. With casework, we'll add the probability a red marble is drawn the first draw and the probability a red marble is drawn the second draw.
There are [tex]4+3+5=12[/tex] marbles total. The probability of drawing a red marble is equal to the number of red marbles (3) divided by the total number of marbles (12). Therefore, the probability of getting a marble on the first draw is [tex]3/12=1/4[/tex]. Since the marble is replaced, there are still 12 marbles, 4 blue, 3 red, and 5 green, for the second draw. We want to add the probability a red marble is drawn the first draw to the probability a red marble is drawn the second draw. Therefore, for the second draw, let's find the chances of not choosing a red marble. There is a [tex]9/12[/tex] chance that the marble chosen is not red. Therefore, the probably of this case happening is [tex]\frac{1}{4}\cdot \frac{9}{12}=\frac{9}{48}[/tex].
This case has the exact same probability as the other case, where a non-red marble is chosen the first draw and the red marble is now chosen the second draw ([tex]9/12[/tex] chance to choose a non-red marble and [tex]1/4[/tex] chance to choose a red marble).
Add these cases up:
[tex]\frac{9}{48}+\frac{9}{48}=\frac{18}{48}=\boxed{\frac{3}{8}}[/tex]
A building security code has 2 numeric
digits, O through 9, followed by 2 letters.
What is the probability that the first digit
is 9 and the last letter is A?
Answer:
Step-by-step explanation:
First number is 1/10
Last letter is 1/26
The second digit is 1/9
The first letter is 1/25
1/10 * 1/26 * 1/9 * 1/25
0.00001709
This assumes no duplication is allowed,
If there are duplications
then 1/10 * 1/10 * 1/26 * 1/26
0.000014782
Can someone help me out plz
Volume = πr²h
Radius = 3yd
Height = 12yd
Take π = 22/7
Volume = 22/7×3×3×12
= 2376/7
= 339.4285714yd³
Rounding off to nearest tenth
= 339.43yd³
Answered by Gauthmath must click thanks and mark brainliest
Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16.
Use the 68-95-99.7
Rule to find the percentage of people with IQs between 84 and 116.
Answer:
Approximately 68% of people have IQs between 84 and 116.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 100, standard deviation of 16.
Percentage of people with IQs between 84 and 116.
84 = 100 - 16
116 = 100 + 16
So within 1 standard deviation of the mean, which, by the Empirical Rule, is approximately 68%.
The difference of a number and its opposite is 28. Find
the number.
Step-by-step explanation:
Lets break this word problem down:
"The difference" means we're going to be finding x - y ("difference" means we're finding how much one value "differs" from the other)
"a number and it's opposite" so we're doing x - y, where y = -x. So already, we can re-write this as x - (-x) or x + x
"is 28" so x + x = 28 ("is" always means "equals")
"Find the number" so we're finding x.
x - (-x) = 28 (I went back a step so I could write everything out more plainly)
simplify
x + x = 28
add
2x = 28
divide both sides by 2 to get x on its own
x = 14
Answer:
14
Find the area AND perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
a=40+8pi, p=4pi+4(sqrt of 29)
Step-by-step explanation:
rsm geometry class 122?
The baker bought the buttercream icing from Crave Cupcakes. Calculate how many containers of icing the baker needs to buy in order to ice a wedding cake. Each container of icing contains 16 ounces of icing. If it takes 56 ounces of icing to cover 678 square inches of cake, calculate the total cost for the icing before tax if each 16 ounce(2 cup) container of icing costs $10.
Answer:
$40.
Step-by-step explanation:
You need 4 16oz containers of icing to fully cover the cake. As each container costs $10, and you need 4 containers, the total cost of icing to cover the wedding cake, before tax, is $40.
CUSTOMERS AT A STORE
The bar graph above shows the number of customers who shopped at a store Monday through Thursday of
one week. If the number of customers on Friday was a one-fifth increase over the number of customers on
Thursday, how many customers shopped at the store on Friday?
O 480
O 500
O 525
O 600
Answer:
480
Step-by-step explanation:
We are looking for the total number of customers in the store on Friday using a chart and a fractional increase.
On Thursday there were 400 customers, so we need to find the amount of the increase.
1/5 of 400 =80
Increase Thursday's amount, 400, by the amount of the increase, 80, to find the number of customers on Friday.
400+80 = 480
Friday has 480
Answer:
480
Step-by-step explanation:
400 + 1/5(400) = 400 + 80 = 480
The scatterplot shows the average miles per gallon versus the age, in years, of a car.
A graph titled Fuel efficiency has age (years) on the x-axis, and miles per gallon on the y-axis. Points are at (1, 25), (2, 32), (3, 26), (4, 23), (5, 19), (6, 16), (7, 17), (8, 14), (9, 13), (10, 10).
If age was on the vertical axis and miles per gallon on the horizontal axis, how would the correlation change? Select all statements that would apply to the new correlation coefficient.
The sign would be the opposite.
The sign would remain the same.
It would have the same value.
It would become closer to 0.
It would become closer to 1.
(2 and 3) B,C
Answer:
The sign would remain the same.
It would have the same value.
ED2021
Answer: b&c
The sign would remain the same.
It would have the same value.
P (6,0) under the translation (x-6, y-1)
Answer:
(0,-1)
Step-by-step explanation:
(6-6,0-1)
or, (0,-1)
What does union mean in a statistics problem?
Step-by-step explanation:
The union of two sets is the set of elements that belong to one or both sets.
Symbolically, the union of X and Y is denoted by X ∪ Y. As an example, suppose set A = {1, 2, 3} and set B = {1, 3, 5}.
Then, the union of sets A and B would be {1, 2, 3, 5}.
About 6% of the population of a large country is math phobic. If two people are randomly selected, what is the probability both are math phobic?
Answer:
0.0036
Step-by-step explanation:
Given that :
Proportion of population that are math phobic = 6% = 6/100 = 0.06
P(math phobic) = 0.06
If two selections are made ; probability that both are math phobic ;
P1 = selection 1 = 0.06
P2 = selection 2 = 0.06
Probability that both are math phobic :
P1 * P2 = (0.06 * 0.06) = 0.0036
Which of the following equations is modeled by the graph?
A)
a = 50t
B)
a = 5t
C)
a = 50 + t
D)
a = 10t
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
Answer: 24 feet
Step-by-step explanation: i just guessed it on pluto and got it right. please leave a like if it worked
The length of another axis for the given ellipse will be around 25.6125 feet so none of the options will be correct.
What is an ellipse?a regular oval form produced when a cone is cut by an oblique plane that does not intersect the base, or when a point moves in a plane so that the sum of its distances from two other points remains constant.
In another word, an ellipse is a curve that becomes by a point moving in such a way that the sum of its distances from two fixed points is a closed planar curve produced.
General equation of an ellipse
(x 2 / a 2 )+ (y2 / b 2 )= 1
Given that
the plot of land is 40 feet across one axis
so 2a = 40 feet
a = 20 feet
The foci are 16 feet from the center so
c = 16
Now we know that
c = √(b² - a²)
c² = b² - a²
16² = b² - 20²
b = 25.6125
So, the length of the minor axis will be around 25.6125 feet.
To learn more about ellipse,
https://brainly.com/question/14281133
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