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)
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).
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.
Find all real values of a such that the given matrix is not invertible.
A= [0 9 a]
[a 1 7]
[0 a 1]
Answer:
The answer is "0,3,-3".
Step-by-step explanation:
Let the matrix is not invertible.
then |A|=0
[tex]\left|\begin{array}{ccc}0&9&a\\a&1&7\\0&a&1\end{array}\right|=0[/tex]
[tex]-a[9-a^2]=0\\\\a=0\\\\a=\pm 3\\\\a=0, 3,-3\\[/tex]
A health food store was charging $5.40 for a small salad but raised the price 8%. The new price after the increase is $5.83.
Enter an expression to show how the new price was calculated.
Answer:
[tex]\frac{8}{100}[/tex]×5.40
Step-by-step explanation:
If you know how to solve this, Please answer it. Thank You
Please show your work and the steps.
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
Answer:
11
Step-by-step explanation:
(2(-5)+13) + (-4+12)
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)
PLEASE HELP IM GONNA FAIL
Answer:
16 in.
Step-by-step explanation:
formula to find area of a triangle
A=1/2bh
A=1/2(8)(4)
A=1/2(32)
A=16
hope this helps:)
Jamie says the value of the expression 1.43 x (19/37) is close to 0.75. Does Jamie's estimate seem reasonable? Explain. *
Answer:
Jamie's estimate is correct, since the result is 2.1% less than the estimated number.
Step-by-step explanation:
Given that Jamie says the value of the expression 1.43 x (19/37) is close to 0.75, to determine if Jamie's estimate seems reasonable the following calculation must be performed:
1.43 x (19/37) = X
1.43 x 0.513 = X
0.7343 = X
0.75 = 100
0.7343 = X
0.7343 x 100 / 0.75 = X
97.9 = X
Therefore, Jamie's estimate is correct, since the result is 2.1% less than the estimated number.
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)
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
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
Ty
7
What is the slope of a line that is perpendicular to the line
shown on the graph?
6
5
O-2
4
3+
2
2
0 -
0 2 / 2
o
1
O 2
1
2 3
4 5 6 7 X
7 6 5 4 3 2 - 21.
-2-
--3-
6
Answer:
-1/2
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
The solution is, -1/2 is the slope of a line that is perpendicular to the line
shown on the graph.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
we have to,
find the slope of the line shown using
the formula, m = y1- y2 / x1- x2
from the given graph we get,
Let
P1(0,1)
P2(1,3)
now we get,
replacing
m = 2/1
= 2
so, here, m1 = 2
two lines are perpendicular when
m1 * m2 = -1
as, we know that,
Perpendicular lines have negative reciprocal slopes.
so, we get ,
m2 = -1/2
Hence, The solution is, -1/2 is the slope of a line that is perpendicular to the line
shown on the graph.
To learn more on slope click:
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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.
last week Pizza Hut sold 36 pizzas,64 pepperoni pizzas and 20 veggie pizzas based on the data which number is closest to the probability that the next customer will order a cheese pizza
Answer:
13 pizzas maybe
Step-by-step explanation:
The probability that a male professional golfer makes a hole-in-one is 1/2780. Suppose 36 professional male golfers play the sixth hole during a round of golf. Let the random variable X be the number of golfers in the group of 36 who make a hole-in-one. Calculate the probability that exactly four of the 36 golfers make a hole-in-one on the sixth hole – as actually happened during the 1989 U.S. Open
Answer:
The right solution is "[tex]9.7\times 10^{-10}[/tex]".
Step-by-step explanation:
According to the question,
The probability that male professional golfer makes hole in one will be:
[tex]P=\frac{1}{2780}[/tex]
Number of players,
n = 36
and,
[tex]q=1-P=\frac{2779}{2780}[/tex]
By using the Binomial theorem, we get
⇒ [tex]P(x=r) = \binom{n}{r} p^r q^{n-r}[/tex]
Bu substituting the values, we get
[tex]=\binom{36}{4} (\frac{1}{2780} )^4 (\frac{2779}{2780} )^{32}[/tex]
[tex]=9.74929\times 10^{-10}[/tex]
or,
[tex]=9.7\times 10^{-10}[/tex]
Help please . Help . Thank you
Answer:
Total weight = 111.6 lbs
Step-by-step explanation:
Given the following data;
Length = 1 feet
Width = 9.5 feet
Height = 13.5 feet
Mass of contents = 0.87 pounds per cubic foot
To find the weight of the contents in the container;
First of all, we would determine the volume of the rectangular prism;
Volume = length * width * height
Volume = 1 * 9.5 * 13.5
Volume = 128.25 cubic feet
Next, we find the overall weight;
Total weight = volume * mass of contents
Total weight = 128.25 * 0.87
Total weight = 111.6 lbs
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.
Learn more about the triangle visit;
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A square has a side length of 3x3y5. What is the area of the square?
Answer:
9x^3 y^5
Step-by-step explanation:
Since the formula to finding area is (L*W = A), we first have to find the width.
Width: 3x^3 y^5 times 2 = 6x^3 y^5
Then we add them. So, 3x^3 y^5 + 6x^3 y^5 = 9x^3 y^5
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
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
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].
Hope this helps, please mark brainliest. Have a great day!
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.
The expression 2(l + w) is used to calculate the perimeter of a rectangle, where l is length and w is width. If the length is Fraction 2 over 3 unit and the width is Fraction 1 over 3 unit, what is the perimeter of the rectangle in units?
Answer:
Perimeter = 1 unit
Step-by-step explanation:
[tex]length \ is \ a \ fraction \ 2 \ over \ 3 = \frac{2}{3}\\\\Width \ is \ a \ fraction \ 1 \ over \ 3 = \frac{1}{3}\\\\Perimeter = 2 ( l + w)\\[/tex]
[tex]= 2 \times (\frac{2}{3} + \frac{1}{3}) \\\\=2 \times (\frac{3}{3})\\\\= 1 unit[/tex]
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
A kite is staked to the ground and blowing in the wind. It currently has a
string let out to a length of 89 meters. It has an altitude of 68 feet. To the
nearest tenth of a degree, find the angle of elevation.
Answer:
50 °
Step-by-step explanation:
that is the procedure above
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 thx with steps
Answer:
440cm³
.45
1.49538 ft
43.6
Step-by-step explanation:
1.
Start by finding the area of the base
.5*(a+b)*h
.5*(8+14)*4= 44
Then just multiply this by distance between the ends
44*10=440
2.)
To get from 2.7 to 9 we muiltply by 9/2.7= 3.33333333
which means that
3.333333333x=1.5
x=.45
3.)
Height:shadow
6.5:1.8
5.4:x
To get from 6.5 to 5.4 we multiply it by (5.4/6.5) or .8307
which means to get from 1.8 to x we muiltply 1.8*.8307= 1.49538
4.)
Same kind of deal as the last one
to get from 13 to 27 we mulitply by (27/13) or 2.076923 which means to get from 21 to x we multuply 21*2.076923=43.6
Here is the answer for the volume of the trapezoidal prism.
We make two rectangular prisms out of the shape, or a rectangular prism and two triangles.
For this case, I'll just do the two prisms.
Here is the formula for volume we'll be using.
V = lwh (shape's volume = length × width × height), or
V = bh (shape's volume = base area × height)
A reference of the rectangular prism can be identified because the length of the horizontal crest is marked at 8 centimeters.
Following V = lwh, we already have the length we need.
The width of the reference prism that doesn't include the diagonal triangular prisms is 10 centimeters.
l = 8 cm
w = 10 cm
And as indicated by the line inside,
h = 4 cm
We'll label this first volume calculation V[tex]_{1}[/tex].
V[tex]_{1}[/tex] = 8 cm × 10 cm × 4 cm
Now for the second volume.
Since two congruent right triangular prisms can come together to equal a second rectangular prism whose volume is two times their original shapes, we can use the same formula
V = lwh
And in order to determine what values are needed, we
subtract the length of the trapezoid's base from the rectangular prism's.And that's it. No adjustments are made in the width or height. Those measurements are equal to the reference rectangular prism (center prism).
14 cm - 8 cm = 6 cm
l = 6 cm
w = 10 cm
h = 4 cm
This part of the enumeration will be V[tex]_{2}[/tex].
V[tex]_{2}[/tex] = 6 cm × 10 cm × 4 cm
V[tex]_{1}[/tex] + V[tex]_{2}[/tex] = V[tex]_{t}[/tex], or the actual volume of the trapezoidal prism.
(8 cm × 10 cm × 4 cm) + (6 cm × 10 cm × 4 cm) = 320 cm + 240 cm = 560 cm.
You round to 2 decimal places, so V[tex]_{t}[/tex] = 560.00 cm.
2. x = 0.45[tex]\frac{2.7}{x} = \frac{9.0}{1.5}[/tex]
Let's look at the right side.
9.0, or 9, divided by 1.5 equals 6.
Now your equation looks like
[tex]\frac{2.7}{x} = 6[/tex]
You want to get the variable x by itself so that there aren't any real number values that stop the proportion from being simplified.
So, we multiply x on both sides.
[tex]\frac{2.7}{x}[/tex] * [tex]x[/tex] = [tex]6[/tex] * [tex]x[/tex]
On the left side of the = sign, the x on the denominator is being cancelled out.
Now it looks like
[tex]2.7 = 6[/tex] * [tex]x[/tex]
Divide 6 from both sides to cancel the 6 from the right side and get the new value of x by itself.
2.7 ÷ 6 = 0.45
0.45 is already in the hundredths, so there's no need to round up or down.
3. Height of tree = 19.5 ftAll you have to do here is find the ratios of the two figures to their shadows.
It's going to look like the [tex]2^{nd}[/tex] problem because all we're doing is finding the missing variable.
[tex]\frac{h}{s}[/tex] will represent the height-shadow ratio.
For a 6.5-foot human to cast a 1.8-foot shadow,
[tex]\frac{h}{s}_1 = \frac{6.5}{1.8}[/tex]
6.5 ft ÷ 1.8 ft ≅ 3.611
All we have to do now is find a tree height that divides by its shadow, 5.4, to get roughly 3.611.
We can solve that by multiplying 3.611 with the shadow's height.
3.611 * 5.4 = 19.5
The tree is 19.5 feet tall.
4. x = 43.6
These two triangles aren't congruent, but similar.
Like the last two problems, finding the ratio between the sides is key to solving the problems.
This time, the ratios of the two given sides for each triangle will let us solve the side-side-side (SSS) rule, if we take it a step further and use the Pythagorean Theorem. For now, just solve the target of the problem.
[tex]\frac{27}{13} = \frac{x}{21}[/tex]
27 ÷ 13 = 2.077
[tex]2.077 = \frac{x}{21}[/tex]
[tex]2.077[/tex] * 21 = [tex]\frac{x}{21}[/tex] * 21
Cancel the 21s from the denominator and factor on the right side.
43.617 = x
x = 43.6 because you round to one decimal.