The distance from the bottom of the ladder be from the bottom of the building is 13.3feet
Application of pythagoras theoremThe theorem states that the square of the hypotenuse is equal to the square of the other two sides
Given the following
Hypotenuse = 24 feet
Opposite side = height = 20ft
Required
Base of the ladder
Use the theorem
24^2 = 20^2 + b^2
b^2 = 576 - 400
b^2 = 176
b = 13.3feet
Hence the distance from the bottom of the ladder be from the bottom of the building is 13.3feet
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Which statement is false? A. A number is even if and only if it is divisible by 2. B. 3x=15 if and only if x=5. C. Two points are collinear if and only if they lie on the same line. D. Two angle form a linear pair if and only if they are adjacent
Answer:
option Ais false
Step-by-step explanation:
this is because even number can be divisible by 2 and its multiples as well which are larger than 2 as well.
Which function is the inverse of f(x) = 2x + 3?
Answer:
f^-1(x)=1/2x-3/2
Step-by-step explanation:
f(x)=2x+3
y=2x+3
x=2y+3
2y+3=x
2y=x-3
y=1/2x-3/2
substitute f^-1(x) for y
f^-1(x)=1/2x-3/2
The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the average size of their advertised 13-inch pizzas. She takes a random sample of 37 pizzas and records their mean and standard deviation as 13.50 inches and 1.90 inches, respectively. She subsequently computes the 95% confidence interval of the mean size of all pizzas as [12.89, 14.11]. However, she finds this interval to be too broad to implement quality control and decides to reestimate the mean based on a bigger sample. Using the standard deviation estimate of 1.90 from her earlier analysis, how large a sample must she take if she wants the margin of error to be under 0.5 inch
Answer:
She must take a sample of 56.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation estimate of 1.90
This means that [tex]\sigma = 1.9[/tex]
Wow large a sample must she take if she wants the margin of error to be under 0.5 inch?
This is n for which M = 0.5. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.5 = 1.96\frac{1.9}{\sqrt{n}}[/tex]
[tex]0.5\sqrt{n} = 1.96*1.9[/tex]
[tex]\sqrt{n} = \frac{1.96*1.9}{0.5}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*1.9}{0.5})^2[/tex]
[tex]n = 55.5[/tex]
Rounding up:
She must take a sample of 56.
PLEASE HELP ME!! The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long
is the ladder?
the ladder is 10 ft long.
a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36 + 64 = c^2
sqrt of 100 = sqrt of c^2
10ft = C
I’ll give brainliest if you answer this correctly
Answer:
B y = (-7/4)x - 7
Step-by-step explanation:
Slope intercept form is
y = mx + b
Where m is the slope and b is the y-intercept
m = rise/run
m = ∆y/∆x
m = (y₂ - y₁) / (x₂ - x₁)
m = (-7 - 0) / (0 - -4)
m = -7/4
From the graph the y-intercept
b = -7
-------------------------
y = (-7/4)x - 7
A circle is centered at $O$ and has an area of $48 \pi.$ Let $Q$ and $R$ be points on the circle, and let $P$ be the circumcenter of triangle $QRO.$ If $P$ is contained in triangle $QRO,$ and triangle $PQR$ is equilateral, then find the area of triangle $PQR.$
Answer:
Area of Triangle QRP = 3[tex]\sqrt{3}[/tex]
Step-by-step explanation:
According to Question , We have a circle With Centre 'O' & Area 48[tex]\pi[/tex] .
Area Of Circle = 48[tex]\pi[/tex]
[tex]\pi[/tex][tex]r^{2}[/tex] = 48[tex]\pi[/tex]
r = [tex]\sqrt{48}[/tex]
Now We Have Two Points Given On Circle Q & R , P Is Circumcentre Of Triangle QRO .
Thus A Circle Can Also Be Formed with Centre P . ( See attachment For Diagram )
Now The Diameter of Circle With Centre P = Radius Of Circle with Centre O
so Radius Of Circle With Centre P([tex]r_{2}[/tex]) = [tex]\frac{\sqrt{48}}{2}[/tex]
Now We Have To Find Area Of Equilateral Triangle .
A = [tex]\frac{\sqrt{3}}{4} r_{2} ^{2}[/tex]
A= [tex]\frac{\sqrt{3} }{4} * \frac{\sqrt{48} }{2}*\frac{\sqrt{48} }{2}[/tex]
The Area Of PQR is = 3[tex]\sqrt{3}[/tex]
For Diagram , Please Find In Attachment
In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculate the 95% confidence interval for the proportion of students who get coaching on the SAT .
Answer:
The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).
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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
427 had paid for coaching courses and the remaining 2733 had not.
This means that [tex]n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147[/tex]
The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).
giải phương trình Bermolli : y' +[tex]\frac{y}{x}[/tex] =x[tex]y^{2}[/tex]
Answer:
y(x) = -1/(x^2 + c_1 x)
Step-by-step explanation:
Solve Bernoulli's equation ( dy(x))/( dx) + y(x)/x = x y(x)^2:
Divide both sides by -y(x)^2:
-(( dy(x))/( dx))/y(x)^2 - 1/(x y(x)) = -x
Let v(x) = 1/y(x), which gives ( dv(x))/( dx) = -(( dy(x))/( dx))/y(x)^2:
( dv(x))/( dx) - v(x)/x = -x
Let μ(x) = e^( integral-1/x dx) = 1/x.
Multiply both sides by μ(x):
(( dv(x))/( dx))/x - v(x)/x^2 = -1
Substitute -1/x^2 = d/( dx)(1/x):
(( dv(x))/( dx))/x + d/( dx)(1/x) v(x) = -1
Apply the reverse product rule f ( dg)/( dx) + g ( df)/( dx) = d/( dx)(f g) to the left-hand side:
d/( dx)(v(x)/x) = -1
Integrate both sides with respect to x:
integral d/( dx)(v(x)/x) dx = integral-1 dx
Evaluate the integrals:
v(x)/x = -x + c_1, where c_1 is an arbitrary constant.
Divide both sides by μ(x) = 1/x:
v(x) = x (-x + c_1)
Solve for y(x):
y(x) = 1/v(x) = -1/(x^2 - c_1 x)
Simplify the arbitrary constants:
Answer: y(x) = -1/(x^2 + c_1 x)
Which of the following verifies that AABC is similar to ADEF?
A. AA postulate
B. SAS theorem
C. Similarity cannot be determined.
D. SSS theorem
Answer:
B. SAS Theorem
Step-by-step explanation:
SAS means that there are 2 corresponding sides with an angle in between. This condition is satisfied in this case because AC corresponds to DF (18/2 = 9), angle c and angle f are congruent, and BC corresponds to EF
By ''SAS theorem'' triangle ABC is similar to DEF.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
To find the theorem which can be used to verify triangle ABC is similar to DEF.
Now,, By figure,
There are one angle are common.
And, Ratio of two sides are equal.
Hence, By ''SAS theorem'' triangle ABC is similar to DEF.
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Use commutative, then distributive. And explain how the properties were helpful in simplifying the expression.
ONLY ANSWER IF YOU KNOW THE ANSWER. SHOW ALL WORK
Answer:
8
Step-by-step explanation:
1 3/5=8/5
45*8/5*1/9=360/5*1/9=72*1/9=72/9=8
Surface area of rectangular prism length 6 in., width 5 in., height 12 in.
The surface area is 324
Answer:
The surface area of this rectangular prism is 324 [tex]inches^{2}[/tex].
Step-by-step explanation:
The formula for surface area of a rectangular prism is this :
A = 2(wl + hl + hw)
l = 6, w = 5, h = 12.
Now knowing these values, we can solve for A.
A = 2(wl + hl + hw) = 2(5 · 6 + 12 · 6 + 12 · 5) = 324
The surface area of this rectangular prism is 324 [tex]inches^{2}[/tex].
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n a linear regression model, the variable (or variables) used for predicting or explaining values of the response variable are known as
Answer:
Independent variable or explanatory variables.
Step-by-step explanation:
this variable is referred to as the independent variable.
A linear regression equation is of the form
Y = B0 + B1X1 + u
Y is the depndent variable
X1 is the independent variable
With u as the error term.
The independent variable is used to explain changes in Y, which is the dependent variable. The independent or explanatory variable has a direct effect on the dependent variable. This means that as X1 changes, Y would also change in response to the changes in the independent variable.
2logb - 3logb = log8b - log4b
Answer:
b=1/2
Step-by-step explanation:
2logb - 3logb = log8b - log4b
log[tex]b^{2}[/tex] - log[tex]b^{3}[/tex] = log8b - log4b
log([tex]\frac{1}{b}[/tex]) = log(2)
∴1/b = 2
∴b = 1/2
Define logic and explain how it is used in math.
Answer:
Logic is the study of how to critically think about propositions or statements that are either true or false.
Logic is very useful in the world of mathematics. Mathematicians use logic all the time to prove theorems and other mathematical facts. Everything we know about math right now is based off of these logical proofs. Without these, we wouldn't have our formulas, like the wonderful quadratic formula or the very useful Pythagorean Theorem.
Using logic in math is about mixing the specific language used in logic with the specific symbols used in math.
Step-by-step explanation:
I need help on this practice question
Answer:
6ft
Step-by-step explanation:
first you need to properly provide your work
A 6-sided die is rolled twice. Determine
the probability of the rolling any
number more than 2.
Answer:
4/6 x 4/6 = 16/24
Step-by-step explanation:
Therefore, the answer is 2/3 because there are 6 sides and you need to roll more than 2 which is 4 sides.
A jar contains 7 poker chips: 3 blue, 3 red and 1 white. You randomly select two chips from the jar. What is the probability that your selection includes the white chip? Round your answer to two decimal places.
Answer:
The probability that you will have a white chip is 0.309
Step-by-step explanation:
You on the first try have a 1/7 or 14.285% chance the second one has a 1/6 or a 16.666% you then add them together and you have a 30.9% chance
The Probability of selecting white chips is [tex]0.0286[/tex].
Let,
Number of blue chips [tex]=3[/tex] Number of red chips [tex]=3[/tex]Number of white chips [tex]=1[/tex]Number of chips drawn [tex]=2[/tex]Total chips [tex]=7[/tex]The probability of the poker chips is,
[tex]\ n(A)=3\\\\n(B)=3\\\\n(C)=1[/tex]
Lets find the the probability of selecting white clip:
"Probability [tex]=[/tex] Number of outcomes/ Total outcomes"
Randomly select two chips from the jar,
The probability of the first chip taken being white is,
[tex]P(C)=\frac{n(c)}{n(s)} \\\\P(C)=\frac{1}{7}[/tex]
If the first chip is not white then the probability of the second chip being white is,
[tex]P(no\ white)=\frac{1}{6}[/tex]
Since, (of the 6/7 times that the first was not white) is,[tex]\frac{1}{6} * \frac{1}{7} = \frac{1}{7}[/tex]
Total probability is the sum of the two probability is,
[tex]P=\frac{1}{7} +\frac{1}{7} \\\\P=\frac{2}{7}=0.286[/tex]
Hence,
The Probability of selecting white chips is [tex]0.0286[/tex].
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Based on the percentage of total daily calories in the number of calories needed how many biscuits and packages of pemmican and packages of butter and cocoa just one person need each day
(5600 calories per person)
pls help me my test us due tmr
Answer:
28 biscuits
18 packages of pemmicans
4 packages of butter and cocoa
Step-by-step explanation:
We are given percentage of total daily calories for each item.
Since total number of calories per person each day is 5600,then;
Number of calories from biscuit daily = 40% × 5600 = 2240 calories
Since there are 80 calories per biscuits, then number of biscuits = 2240/80 = 28 biscuits
Number of calories from pemmican daily = 45% × 5600 = 2520 calories
Since there are 140 calories per package, then number of packages of pemmican = 2520/140 = 18 packages of pemmicans
Number of calories from butter and cocoa daily = 15% × 5600 = 840
Since there are 210 calories per package, then number of packages = 840/210 = 4 packages of butter and cocoa
A right triangular prism has a height of 26 cm and base edges of 10 cm, 24 cm, and 26 cm. What is the lateral area of the prism?
Answer:
1,560 cm²
Step-by-step explanation:
LA = (10+24+26) × 26
= 60×26
= 1,560
There are 18 white
socks and 27 black
socks in a drawer.
Write the ratio of white
socks to black socks.
Answer: 18:27 I believe
Step-by-step explanation: There are 18 white socks and 27 black socks therfore the answer is 18:27
Can someone help me with this please!
Answer:
Maybe 24 ft.......................????
Answer:
24 feet.
Step-by-step explanation:
We can solve this with a proportion.
[tex]\frac{Height}{Shadow}=\frac{Height}{Shadow}\\\frac{Height}{12}=\frac{2}{1}\\Height=\frac{2}{1}(12)\\Height = 24[/tex]
Therefore, the height of the sailboat is 24 feet.
If (10,3) and (6,31) are two
anchor points on a trend line,
then find the equation of the
line.
Answer:Step-by-step explanation:
would it be (5.6)
Answer:
Step-by-step explanation:
Three numbers have a mean of 12 and a mode of 9. What are the three numbers?
Answer:
The three numbers are : 9, 9 and 18
Step-by-step explanation:
Since the mean is 12 the sum of the three numbers must be 36. This is because:
(let the three numbers be x y and z)
(x+y+z)/3=12
(x+y+z)=12*3
(x+y+z)=36
And since the mode is 9 two of the numbers must be 9.
So to find the third number;
9+9+z=36
z=36-18
z=18
Suppose that you have two different algorithms for solving a problem of size n. The first algorithm uses exactly n(log n) operations and the second algorithm uses exactly n 3/2 operations. As n grows, determine which algorithm uses fewer operations?
Answer:
Algorithm 1 uses:
n*log(n) operations.
While algorithm 2 uses:
n^(3/2) operations.
We want to see, as n grows, which algorithm uses fewer operations.
So we would want to first solve:
n*log(n) = n^(3/2)
This will give us the exact value of n such that the number of operations is the same in both algorithms.
dividing both sides by n we get:
log(n) = n^(3/2)/n = n^(3/2 - 1) = n^(1/2)
where we can use:
log(n) = ln(n)/ln(10)
ln(n) = ln(10)*n^(1/2)
This equation actually has no solutions.
This happens because the right side is always larger than the left side.
Then, the same thing happens for our two initial equations:
n^(3/2) is always larger than n*log(n), as you can see in the graph below, where n^(3/2) is represented with the orange graph:
So we can conclude that the fist algorithm uses less operations as n grows.
is this table a function? PLEASE HELPPP
Answer:
It is a function.
Step-by-step explanation:
I would suggest use the website Desmos.
65.874,326.59,13.555,7.959 round to the following numbers to 1 decimal place
Answer:
a)65.9
b)326.6
c)13.6
d)8.0
Step-by-step explanation:
Answer: 65.87
Step-by-step explanation: Identify which place value you are rounding to. The smaller the place value, the more accurate the final result will be.
Look to the next smallest place value, the digit to the right of the place value you're rounding to. For example, if you want to round to the nearest ten you'd look at the ones place.
What is the midpoint of the segment shown below?
(-2,4) (6,-4)
A. (3, 0)
B. (1, 0)
C. (4, 0)
D. (2, 0)
a p e x :(
Answer:
answer is option D
Step-by-step explanation:
(-2 , 4) = (x1 , y1)
(6 , -4) = (x2 , y2)
midpoint = (x1 + x2/2 , y1 + y2/2)
=(-2 +6/2 , 4+(-4)/2)
=(4/2 , 0/2)
=(2 , 0)
What value of x is in the solution set of 8x -
- 6 > 12 + 2x?
Answer:
x>2 (x=any number greater than 2)
Step-by-step explanation:
8x-6>12+2x
-2x -2x
6x-6>12
+6 +6
6x>12
/6 /6
x>2
:) ur welcome
what is the slope of the line passing through the points A(-2,-3) and B(6,4) ?
Answer:
Slope is the change in y over the change in x. Just subtract and simplify the fraction.
Step-by-step explanation:
(-3 - 4)
______
(-2 - 6)
Find all solutions to the equation. Show steps!
sin^(2)x + sin x = 0
Step-by-step explanation:
sin^(2)x + sin x = 0
sin x(sin x +1)= 0
sin x = 0 or sin x = -1
so, x = 0°, 180°, 270°
{0°, 180°, 270°}