Answer:
The length of the ladder is 7.21 feet
Step-by-step explanation:
Let
y = Height of the wall
x = Distance between the wall and the ladder (bottom)
L = Length of the ladder
So, the given parameters are:
[tex]\frac{dy}{dt} = -2ft/s[/tex]
When [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]
The ladder, the wall and the ground forms a right-angled triangle where the hypotenuse is the length of the ladder; So:
[tex]L^2 = x^2 + y^2[/tex]
Differentiate with respect to time
[tex]2L\frac{dL}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
The length of the ladder does not change with time. So:
[tex]2L*0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
[tex]0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
Rewrite as:
[tex]2x\frac{dx}{dt} =- 2y\frac{dy}{dt}[/tex]
Divide both sides by 2
[tex]x\frac{dx}{dt} =- y\frac{dy}{dt}[/tex]
Recall that:
[tex]\frac{dy}{dt} = -2ft/s[/tex] and [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]
So:
[tex]4 * 3 = -y * -2[/tex]
[tex]12 = 2y[/tex]
[tex]6 = y[/tex]
[tex]y = 6[/tex]
Substitute [tex]y = 6[/tex] and [tex]x =4[/tex] in: [tex]L^2 = x^2 + y^2[/tex]
[tex]L^2 =4^2 + 6^2[/tex]
[tex]L^2 =52[/tex]
[tex]L = \sqrt{52[/tex]
[tex]L = 7.21ft[/tex]
4x10^3 times what number is equal to 16x10^5
Answer:
4 × 10²
Step-by-step explanation:
16 x 10^5 ÷ 4 x 10³ = 4 × 10²
4 * 10² is the number when multiplied to 4 * 10³ gives 16 * 10⁵
What is division exponent theorem ?To divide exponents (or powers) with the same base, subtract the exponents.
Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.
The given expression is
4 * 10³ multplies with ____ = 16 * 10⁵
We have to solve this ,
Let the number be x
4 * 10³ multplies with __x__ = 16 * 10⁵
x = (16 * 10⁵ )/(4 * 10³)
x= ( 4² * 10⁵ )/(4 * 10³)
Therefore the numerator and denominator has the same base so
[tex]\rm 4^{2-1} \times 10^{5-3}\\\\\\4^{1} \times 10^{2}\\\\\\4\times 10^{2}[/tex]is the number that when multiplied to 4 * 10³ gives 16 * 10⁵
To know more about Exponent Theorem
https://brainly.com/question/6532227
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Kai can wrap 42 gifts in 3 hours. Answer the following questions, assuming that Kai can continue wrapping gifts at that same rate. How many gifts can Kai wrap in 24 hours? _______________ How many hours would it take him to wrap 126 gifts? _______________ How many gifts does Kai wrap per hour? _______________
Answer:
1. 336
2. 9
3. 14
Step-by-step explanation:
He wraps 42 gifts/3hours
24 hours is 8 "3 hours"
42 hours per 3 gifts * 8 "3 hours" = 336 gifts
126 gifts is 3 "42 gifts"
3 hours per 42 gifts * 3 "42 gifts" = 9 hours
He wraps 42 gifts/3hours
divide these values by 3 and you get 14 gifts/one hour
14 gifts every one hour
Select ALL the correct answers.
A pitcher for a professional baseball team allows runs in the first nine games he starts this season. Let A be the set of the number of
runs allowed by the pitcher in his first nine starts.
A = {1, 4, 2, 2, 3, 1, 1, 2, 1}
In the tenth game he starts, he allows 9 runs. Let B represent the set of the number of runs allowed in all ten games he has started.
Select the true statements.
The median of Bis 1 run more than the median of A.
The interquartile range of B is greater than the interquartile range of A.
The interquartile range of A is 1 less than the interquartile range of B.
The median of A is the same as the median of B.
Including the runs allowed in the tenth game does not cause the spread of the data to
change
Answer:
The median of A is the same as the median of B.
The interquartile range of B is greater than the interquartile range of A.
Step-by-step explanation:
Given that:
A = number of runs allowed in first 9 games
A = {1, 4, 2, 2, 3, 1, 1, 2, 1}
Rearranging A : 1, 1, 1, 1, 2, 2, 2, 3, 4
Median A = 1/2(n + 1) th term
Median A = 1/2(10) = 5th term = 2
Q1 of A = 1/4(10) = 2.5th term = (1 + 1)/ 2 = 1
Q3 of A = 3/4(10) = 7.5th term = (2+3)/2 = 2.5
Interquartile range = Q3 - Q1 = 2.5 - 1 = 1.5
Number of runs allowed in 10th game = 9
B = {1, 4, 2, 2, 3, 1, 1, 2, 1, 9}
Rearranging B = 1, 1, 1, 1, 2, 2, 2, 3, 4, 9
Median A = 1/2(n + 1) th term
Median A = 1/2(11) = 5.5th term = (2+2)/2 = 2
Q1 of A = 1/4(11) = 2.75th tetm = (1 + 1)/ 2 = 1
Q3 of A = 3/4(11) = 8.25th term = (3+4)/2 = 3.5
Interquartile range = Q3 - Q1 = 3.5 - 1 = 2.5
Median A = 2 ; median B = 2
IQR B = 2.5 ; IQR A = 1.5 ; IQR B > IQR A
a college employs 15 stewards. what is the average monthly wage of the stewards if the college pays 226.20 naira in wages each months
true or false: a well-designed sample survey, the sample percentage is very likely to equal the population percentage. explain.
Answer:
false
Step-by-step explanation:
There's going to be some variabilty between the sample and population percentages, cus the sample only contains part of of the population. Even if it is a well designed survey, it doesn't affect this, because no matter how good the sample is, there will always be variability between the two (unless the sample includes the whole population). I hope this helps :)
5th grade math. Correct answer will be marked brainliest
Answer:
3,5
Step-by-step explanation:
Will give brainlest, find the area
A wooden wagon wheel has 12 equally spaced spokes radiating from the central hub.
Answer: 12 INCHES
Step-by-step explanation:
Solve 7k ÷ 3 = 21.
The solution is k=?
Answer:
k=9
..............................
Please help me it’s a Friday and my cousin birthday tomorrow and if I don’t finish I can’t go. (NO LINKS) need explanation. (EXPLAIN) and no lying.
Answer:
D. 0-69
Step-by-step explanation:
I'm not quite 100% sure but I believe it is D. This is because the spread means the range, and the range is the lowest value to between the highest value so it makes sense that the spread is 0-69
apologize of its wrong
1. Observa el siguiente conjunto de enteros (-1,0, 1)
A. ¿Cuál de las propiedades de los números reales son verdaderas
para el conjunto?
Answer:
no hablo espanol papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas
Step-by-step explanation:
The following figure is made of a square and a rectangle.
4 cm
4 cm
7
10 cm
What is the perimeter of the figure?
cm
PLS HELP AND ANSWER QUICK PLZ
Answer:
∠CDE = 76
Explanation:
1) Find ∠CED
- 180 - 116 = 64
2) Find y
- 4y + 7y + 6 + 64 = 180
- 11y + 70 = 180
- 11y = 110
- y = 10
3) Substitute 10 for y
- 7y + 6
- 7(10) + 6
- 70 + 6
= 76
Need help 15 points pls help me
5 1/2 feet is the base of window.
Answer:
area of parllelogram =base×height
25 2/3=base×4 2/3
77/3=base×14/3
77/3×3/14=base
base=77/14=11/2=5 1/2feet
PLEASE HELP I WILL MARK YOU BRAINIEST!!
Select all the expressions that equal 4-12.
Find slope of (2,3) and (-5,6).
Answer:
Slope is 3/-7
Step-by-step explanation:
[tex]slope = \frac{6 - 3}{ - 5 - 2} = \frac{3}{ - 7} [/tex]
please help me on this question. I forgot how to do it
Answer:
141
Step-by-step explanation:
Area of triangle = 24
Area of Trapezoid= 117
117+24
141
Please answer I’ll give Brainly
Answer:
62.5%
Step-by-step explanation:
There are a total of 8 people on the data plot.
5 of them got 15 questions or more correct, meaning 5/8 people got 15 or more questions correct.
5/8 = 5 ÷ 8
5 ÷ 8 = 0.625
0.625 = 62.5%
2 ( x - 10) + 1 = 60
Answer:
x = 39.5
Step-by-step explanation:
2(x-10) = 59
x - 10 = 29.5
x = 39.5
Answer:
x=39.5 or 79/2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
A company offers a flood insurance policy that costs a homeowner $200 per year, and the company will make a payout of $100,000 to the homeowner if they have a flood in that year. The company set this price based on the probability of a flood in the area being 0.001. The table below displays the probability distribution of X=X= the company's profit from one of these policies.
No flood Flood
X=profit $200 -$99,800
P(X) 0.999 0.001
Given that μX=$100, calculate σX.
You may round your answer to the nearest dollar.
Answer:
σX = 3161
Step-by-step explanation:
The standard deviation is the square root of the multiplication of each probability multiplied by the squared difference between the values and the mean.
In this question:
[tex]\sigma X = \sqrt{0.999*(200-100)^2 + 0.001*(-99800-100)^2} = 3160.7[/tex]
Rounding to the nearest dollar, σX = 3161
Thomas lives more than 0.55 km and less than 0.75 km from his school.
Thomas lives from his school?
A. 0.06 km
B 0.50 km
c. 0.60 km
D. 1.30 km
What is the difference between 75 and 55
Answer:
C 0.60km
I hope this answer helps if you have any questions just ask
Please help worth 10 points
Answer:
JK, NK
Step-by-step explanation:
both start at a point and extend through an arrow
The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)
Answer:
A sample of 2017 people should be taken.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Suppose a 95% confidence level:
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Preliminary estimate of the proportion who smoke of .30.
This means that [tex]\pi = 0.3[/tex]
a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)
This is n for which M = 0.02. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.3*0.7}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96\sqrt{0.3*0.7}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.02}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.02})^2[/tex]
[tex]n = 2016.84[/tex]
To the nearest whole number, 2017.
A sample of 2017 people should be taken.
Lin went hiking on five different weekends. The table shows the
elevation changes in feet for each of her five hikes. Fill in the
missing numbers
Initial Elevation
Elevation Change Final Elevation
hike
768
1
-96
672
hike
2
82
20
hike
62
3
- 100
hike
354
4
129
hike
-20
-40
-60
5
Explain what each of the numbers-20, -40, and -60 tells you about
hike 5. What does it mean for the numbers to be negative in this
situation?
Answer:
Hike 1 : 768, -96, 672
Hike 2: -62, 82, 20
Hike 3: 62, -100, -38
Hike 4: 354, -225, 129
Hike 5: -20, -40, -60
The -20 is at what surface level Lin began Hike 5 at. From there, they continued to go in this situation lower by - 40, and arrive at the surface region of -60.
Negative numbers in the present circumstance mean under 0. (Underneath surface region)
What is the area of a rectangle with a length of 7 feet and a width of 3 ¾ feet?
Answer:
105/4 ft^2
Step-by-step explanation:
Multiply length and width: 7*15/4 = 105/4 ft^2
Trapezoid ABCD has an area of 525 cm squared. If height AB = 21 cm and BC = 37 cm, what is the measure of AD?
Answer:
AD = 13
Step-by-step explanation:
Area of trapezoid ABCD
[tex] = \frac{1}{2} (AB + AD) \times AB \\ \\ 525= \frac{1}{2} (37+ AD) \times21\\ \\ 525 \times 2= (37+ AD) \times21 \\ \\ 1050 = 21 \times 37 + 21AD \\ \\ 1050 = 777+ 21AD \\ \\ 21AD = 1050 - 777 \\ \\ 21AD = 273 \\ \\ AD = \frac{273}{21} \\ \\ AD = 13[/tex]
3.5.1 Why do banks charge transaction fees?
question is above in the picture
Answer:
Known
Step-by-step explanation:
I hope this helps :)
Answer:
Known. The other answers are absurd.
Step-by-step explanation:
In geometry, often times you must have at least one angle to problem solve and find the rest. So having a known angle to build off of is important. Vertical Angles and Supplementary Angles are examples of things that require a known angle to find the rest. Why?
Say you only know one angle and the other is congruent to that angle, but across from it...Due to the theory of vertical angles, you now know the other side has to be the same/congruent. For supplementary angles, say you're dealing with a shape like the one I've attached. Once you have a or b, you can determine c. You have to know at least one of those angles to determine it's other unknown angles.
How to find the volume of the cube?
Answer:
its 125
Step-by-step explanation:
5x5x5
Answer:
Volume = [tex]length * width * height.[/tex]
Step-by-step explanation:
[tex]V=a^{3}[/tex] that is the formula
So the volume of this cube is 125 cm