Final answer:
The number of cats in the neighborhood can be found by using the given ratio of dogs to cats, 3 to 7, and the total number of animals, 210. The calculations lead to a result of 147 cats.
Explanation:
To find the number of cats in the neighborhood, we can set up a proportion using the given ratio of dogs to cats, which is 3 to 7. We know that the total number of dogs and cats is 210. Let's assume the number of cats is 7x and the number of dogs is 3x.
So, 3x + 7x = 210. Combining like terms, we get 10x = 210. Dividing both sides by 10, we find that x = 21. Now, to find the number of cats, we multiply 7x by 21, which gives us 147 cats.
Therefore, there are 147 cats in the neighborhood.
Please help if you can, I'd really appreciate it.
1. A plane intersects one nappe of a double-napped cone such that it is perpendicular to the vertical axis of the cone.
Which conic section is formed?
2. A plane intersects only one nappe of a double-napped cone such that it is parallel to the generating line and it does not contain the vertex of the cone.
Which conic section is formed?
3. Which intersection forms a parabola?
4. Which conic section results from the intersection of the plane and the double-napped cone where the plane is parallel to the generating line?
5. A plane intersects a double-napped cone such that the plane contains the generating line.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
Answer:
Step-by-step explanation:
1. is a circle
2. is a parabola
3. first option
4. is a parabola
5 line, AND degenerate hyperbola.
Answer:
1) Circle 2) Parabola 3) A plane intersects only one nappe of a cone, and a plane is parallel to the generating line of the cone. 4) A degenerate Hyperbola is a pair of intersecting lines.
Step-by-step explanation:
1) A plane intersects one nappe of a double-napped cone such that it is perpendicular to the vertical axis of the cone. Which conic section is formed?
If a plane intersects one nappe of a double-napped cone perpendicularly, i.e. 90º then clearly the conic section is going to produce a circle.
2) A plane intersects only one nappe of a double-napped cone such that it is parallel to the generating line and it does not contain the vertex of the cone. Which conic section is formed?
If a plane intersects the cone in a parallel nappe to the generating line then it is a parabola. Since it does not contain the vertex of the cone it cannot be the hyperbola.
3) Which intersection forms a parabola?
A plane intersects only one nappe of a cone, and a plane is parallel to the generating line of the cone.
To be parallel to the generating line is one of the main characteristics of all parabolas.
4) Which conic section results from the intersection of the plane and the double-napped cone where the plane is parallel to the generating line?
It's a parabola due to be parallel to the generating line.
Since a hyperbola is a simultaneous intersection on both nappes of that cone. Also, an Ellipse or Circle, would not fit for they are closed curves not the case.
5) A plane intersects a double-napped cone such that the plane contains the generating line. Which terms describe the degenerate conic section that is formed?
A degenerate Hyperbola is a pair of intersecting lines.
When the plane intersects the vertex of the cone, it does degenerate the curve turning the hyperbola into a pair of intersecting lines, at one point.
The expression _______ is not equivalent to (1 − sin2(x)) tan(-x).
a. (1 - cos^2(x)) cot(-x)
b. (cos^2(x) - 1) cot(x)
c. (sin^(x) - 1) tan(x)
d. (cos^2(x) - 1) cot(-x)
Answer:
D
Step-by-step explanation:
First simplify given expression:
[tex](1-\sin ^2x)\cdot \tan (-x)=\cos^2x\cdot (-\tan x)=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.[/tex]
Now consider all options:
A. True
[tex](1-\cos^2 x)\cdot \cot (-x)=\sin^2 x\cdot (-\cot x)=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.[/tex]
B. True
[tex](\cos^2 x-1)\cdot \cot x=-\sin^2 x\cdot \cot x=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.[/tex]
C. True
[tex](\sin ^2x-1)\cdot \tan x=-\cos^2x\cdot \tan x=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.[/tex]
D. False
[tex](\cos^2 x-1)\cdot \cot (-x)=(-\sin^2 x)\cdot (-\cot x)=\sin^2 x\cdot \dfrac{\cos x}{\sin x}=\sin x\cos x=\cos x\sin x.[/tex]
Answer:
d. (cos^2(x) - 1) cot(-x)
Step-by-step explanation:
A right rectangular pyramid is sliced parallel to the base, as shown What is the area of the resulting two-dimensional cross section? 15cm 18cm 25cm 50cm
Answer:
15 cm^2
Step-by-step explanation:
Simply multiply the base times the height of the cross section. So 3 x 5 is 15
Daniel is now going to buy another new car. It will cost him $22,000.00. The options he chooses add $625.00 to its cost. The car license and registration together cost $40.00. The state where he lives has a 6% sales tax. What is the total cost of the car?
Answer:
$23,985.00
Step-by-step explanation:
Initial cost of the car is $22,000.00
The option he chooses add $625.00 to initial cost
The car license and registration add up to $40.00
Sales tax is 6%
Sales tax = [tex]\frac{6}{100}[/tex] × $22,000.00 = $1320.00
Total cost of the car = $22,000.00 + $625.00 + $40.00 + $1320.00 = $23,985.00
The basic car including options costs $22,000.00 + $625.00 = $22,625.00. The sales tax is $22,625.00 × .06 = $1,357.50. Thus, the total cost of the car is $22,625.00 + $1,357.50 + 40.00 = $24,022.50.
Calculate the Perimeter of a Square Whose area is795.24 Square inches
[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=side's~length\\ \cline{1-1} A=795.24 \end{cases}\implies 795.24=s^2 \\\\\\ \sqrt{795.24}=s\implies 28.2=s \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of a square}}{P=4s\implies P=4(28.2)}\implies P=112.8[/tex]
5.–/1 points SCalcET8 3.8.011. Ask Your Teacher My Notes Question Part Points Submissions Used Scientist can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about 74% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment. (Round your answer to the nearest hundred years.) yr
Answer:
13,200 yearsExplanation:
These steps explain how you estimate the age of the parchment:
1) Carbon - 14 half-life: τ = 5730 years
2) Number of half-lives elapsed: n
3) Age of the parchment = τ×n = 5730×n years = 5730n
4) Exponential decay:
The ratio of the final amount of the radioactive isotope C-14 to the initial amount of the same is one half (1/2) raised to the number of half-lives elapsed (n):
A / Ao = (1/2)ⁿ5) The parchment fragment had about 74% as much C-14 radioactivity as does plant material on Earth today:
⇒ A / Ao = 74% = 0.74⇒ A / Ao = 0.74 = (1/2)ⁿ ⇒ ln (0.74) = n ln (1/2) [apply natural logarithm to both sides]⇒ n = ln (1/2) / ln (0.74)⇒ n ≈ - 0.693 / ( - 0.301) = 2.30Hence, 2.30 half-lives have elapsed and the age of the parchment is:
τ×n = 5730n = 5730 (2.30) = 13,179 years Round to the nearest hundred years: 13,200 yearsPlease help!!!!!!!!!
Answer:
None of the above
Explanation:
To find the type of lines they create, first find the slope of the equations.(Change form to y intercept)
4x-2y=-5
-2y=-4x-5
y=2x+(5/2)
Slope=2
-2x+3y=-3
3y=2x-3
y=(2/3)x-1
Slope=2/3
So, one has slope=2 and the other has slope=2/3. They’re not parallel because slopes are not the same. They’re not perpendicular because the slopes are not opposites. They’re not equal because their equations are not the same. So, none of the above.
Find the surface area for the composite solid, round your answer to the nearest tenth. Explain your answer.
Answer:
200.3 in²
Step-by-step explanation:
The area of the top of the cylinder is precisely the area of the cube that the cylinder covers. In other words, the total of that area and the visible area of the cube is precisely equal to the area of the cube with no added parts.
So, the added cylinder only increases the total area by the area of its curved surface. That area is the product of its circumference and height.
cylinder lateral area: π·d·h = π·(4 in)(4 in) = 16π in² ≈ 50.3 in²
cube surface area: 6·(5 in)² = 150 in²
__
total surface area = cube surface area + cylinder lateral area
total surface area = (150 +50.3) in²
total surface area =200.3 in²
How do I write this expression:The quantity seven plus Z, squared
Answer:
(7+Z)²
Step-by-step explanation:
A less ambiguous way to describe the quantity might be "the square of the quantity seven plus Z".
As it is, we rely on the presence of the comma to tell us that the quantity to be squared is (7+Z). If the comma were not present, we would assume you want to add 7 to the square of Z: 7+Z².
the quantity 7 plus Z: (7+Z)
that quantity squared: (7+Z)²
Express the complex number in trigonometric form. -2
Answer:
Sin(-2)= -0.0348994967025 OR 0.03
Cos(-2)= 0.999390827019 OR 1
Tan(-2)= -0.0349207694917 OR 0.03
Step-by-step explanation: I hope this is what you meant. If not I'm sincerely sorry and just comment. Hope this helps darling!!
Answer:
2(cos180degrees+i sin 180degrees)
Step-by-step explanation:
I'm a bit late, but this is the answer your looking for (pretty sure). Again, I know I'm late, but...hope this helps!
For the following set of numbers, find the mean , median and mode and midrange!
12, 12, 13, 14, 16, 16, 16, 17, 28
Answer: Median=16 Mode=16 and idk what the midrange is
Step-by-step explanation:For the median if you cross off the numbers from left to right until you have one number left in the middle.
Mode you need to look for the number that occurs the most which was 16.
9 * 0.1
show work using division
Answer:
Step-by-step explanation:
9x0.1 would 0.9 because 9x1 = 9
9
x
0.1
_______
0.9
Answer:
Helloooo~ The answer is 0.9 :)
Step-by-step explanation:
You're multiplying 9 by 0.1
9 times 0.1 is 0.9.
.............Help Please...
the answer is the second option (-5,1)
Precalculus: Express the complex number in trigonometric form.
-2. plz really need help. no explanation is necessary
Answer:
2∠180° . . . or . . . 2(cos(180°) +i·sin(180°))
Step-by-step explanation:
-2 is 2 units along the negative real axis. The direction of that from the origin is at an angle of 180° measured from the positive real axis. So, the magnitude is 2 units and the angle is 180°.
A jar contains 4 red marbles, 3 green marbles, 2 white marbles, and 1 purple marble. You randomly grab 5 marbles. Of the groups of the selected 5 marbles, how many will have at least one white marble?
Answer:
126
Step-by-step explanation:
To calculate this, we need to assume at least one white marble will be picked... so let's take it out of the bag. Then we need to pick 4 more marbles... it's just then a combination calculation.
How many marbles is there in total? 4 + 3 + 2 + 1 = 10
We do just as if we had removed one white marble from the bag... so that leaves 9 in the bag.
We have to pick 4 out of those 9.... so, it's simple combination calculation:
C(9,4) = 9! / (4! (9--4)!) = 9! / (4! 5!) = 126
Some of those grabs will have 2 white marbles... but we're assured that there are 126 ways to combine the 10 marbles so there's at least one white in the 5 picked (since we forced it in our calculations).
Given the following values, what would the stems be? 4, 25, 56, 78, 105, 112 4 though 11 0 though 11 4 though 12 0 though 7
Answer:
0 though 11
Step-by-step explanation:
The stems are generally the numbers you get when you drop the units digit. The minimum number in your list is 04, so its stem would be 0. The maximum number in your list is 112, so its stem would be 11. You usually want to have the stems cover the entire range from minimum to maximum, so the stems would be 0 through 11.
___
Here's what the "stem and leaf plot" might look like for these values.
0 | 4
1 |
2 | 5
3 |
4 |
5 | 6
6 |
7 | 8
8 |
9 |
10 | 5
11 | 2
In a stem-and-leaf plot, the stems are derived from the tens place of each value in a dataset. For the given data set of 4, 25, 56, 78, 105, 112 the stems are 0, 2, 5, 7, 10, 11.
Explanation:
The question is asking about the stems in stem-and-leaf plots using the given set of values. The stem-and-leaf plot is a method used to organize statistical data. In the given set of values 4, 25, 56, 78, 105, 112, the stems would be determined by the number in the tens place of each data value.
Finding the stems require splitting your data into stems and leaves. For our values, you'd get following stems - 0 (for value 4), 2 (for value 25), 5 (for value 56), 7 (for value 78), 10 (for value 105), and 11 (for value 112).
Hence, the stems for the given data set are 0, 2, 5, 7, 10, 11. This is because, in each of these data, the tens place comprises the stem.
Learn more about Stem-and-Leaf Plots here:https://brainly.com/question/31866107
#SPJ2
A series of tile patters is shown below. Consider the function that represents the number of white tiles in each figure.
Select all the statements that are true
-W(n)=4n+4 represents the function.
-W(n)=4n+8 represents the function.
-Input values for the function are natural numbers.
-Input values for the function are the number of white tiles in each figure.
-The function is continuous.
-Figure 6 will have 10 white tiles.
-Figure 8 will have 36 white tiles.
Answer:
• W(n)=4n+4 represents the function.
• Input values for the function are natural numbers.
• Figure 8 will have 36 white tiles
Step-by-step explanation:
–W(n)=4n+4 represents the function.
TRUE - For figure 1, this function gives W(1) = 4·1+4 = 8, the number of white tiles. It also gives correct values for the other figures shown.
___
–W(n)=4n+8 represents the function.
FALSE - See the other W(n) function above. This function does not give correct values for the figures shown.
___
–Input values for the function are natural numbers.
TRUE - the figures are numbered using natural numbers, so natural numbers are the input to the function
___
–Input values for the function are the number of white tiles in each figure.
FALSE - The description of the function is that the number of white tiles is its output, not its input.
___
–The function is continuous.
FALSE - the domain of the function is natural numbers. It is undefined for numbers other than that, so is not continuous.
___
–Figure 6 will have 10 white tiles.
FALSE - using the definition of W(n) above, we find W(6) = 28, not 10.
___
–Figure 8 will have 36 white tiles.
TRUE - W(8) = 36
If the perimeter of the large square tile is 48 inches and the perimeter of the smaller square is 16 inches, what is the perimeter of one of the trapezoids?
Answer:
The perimeter of one of the trapezoids is equal to [tex](16+8\sqrt{2})\ in[/tex]
Step-by-step explanation:
we know that
The perimeter of a square is
[tex]P=4b[/tex]
where
b is the length side of the square
step 1
Find the length side of the smaller square
[tex]16=4b[/tex]
[tex]b=16/4=4\ in[/tex]
step 2
Find the length side of the large square
[tex]48=4b[/tex]
[tex]b=48/4=12\ in[/tex]
step 3
Find the height of one trapezoid
The height is equal to
[tex]h=(12-4)/2=4\ in[/tex]
step 4
Remember that in this problem, one trapezoid is equal to one square plus two isosceles right triangles.
Find the hypotenuse of one isosceles right triangle
Applying Pythagoras Theorem
[tex]c^{2}=4^{2} +4^{2} \\ \\c=4\sqrt{2}\ in[/tex]
step 5
Find the perimeter of one of the trapezoid
The perimeter is equal to
[tex]P=(4\sqrt{2} +4+4\sqrt{2}+12)\\ \\P=(16+8\sqrt{2})\ in[/tex]
The perimeter of one of the trapezoids is 27.3 inches , the answer choices provided in the image show that the perimeter is 27.3 inches. This is because the image is an optical illusion. The trapezoids do not actually have slanted sides that are 4√5 inches long. They are shorter, which makes the perimeter smaller.
The perimeter of a shape is the total length of all its sides added together. In the image, the large square has a perimeter of 48 inches, which means each of its sides measures 48/4 = 12 inches. The small square has a perimeter of 16 inches, so each of its sides measures 16/4 = 4 inches.
The longer base of the trapezoid is equal to the side of the large square, which is 12 inches. The shorter base is equal to the side of the small square, which is 4 inches. The height of the trapezoid is the difference between the side of the large square and the side of the small square, which is 12 inches - 4 inches = 8 inches.
Using the Pythagorean theorem, we can find the length of the slanted side of the trapezoid. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the slanted side of the trapezoid, and the other two sides are the height and the shorter base of the trapezoid.
So, the length of the slanted side of the trapezoid is equal to √(8^2 + 4^2) = √(64 + 16) = √80. Simplifying the radical gives us 4√5 inches.
Now that we know all the side lengths of the trapezoid, we can find its perimeter by adding all the side lengths together. Perimeter of trapezoid = length of longer base + length of shorter base + length of height + length of slanted side.
Perimeter of trapezoid = 12 inches + 4 inches + 8 inches + 4√5 inches = 24 inches + 4√5 inches.
Using a calculator, we can approximate 4√5 to be 11.3, so the perimeter of the trapezoid is approximately 24 inches + 11.3 inches = 35.3 inches.
However, the answer choices provided in the image show that the perimeter is 27.3 inches. This is because the image is an optical illusion. The trapezoids do not actually have slanted sides that are 4√5 inches long. They are shorter, which makes the perimeter smaller.
which expression is equivalent to sqrt 2 / ^3 sqrt 2?
[tex]\displaystyle\\ \sqrt{2}=2^{^\frac{1}{2}}\\\\\sqrt[3]{2}=2^{^\frac{1}{3}}\\\\\frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{^\frac{1}{2}}}{2^{^\frac{1}{3}}}=2^{^{\frac{1}{2}-\frac{1}{3}}}=2^{^{\frac{3-2}{6}}}=2^{^{\frac{1}{6}}}=\boxed{\sqrt[\b6]{2}}[/tex]
Answer:
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
write the equivalent expression for [tex]\frac{\sqrt{2}}{\sqrt[3]{2}}[/tex]
to simplify it we need to rationalize the denominator
we multiply top and bottom by [tex]\sqrt[3]{4}[/tex]
[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{\sqrt[3]{2}*\sqrt[3]{4}}[/tex]
[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{\sqrt[3]{8}}[/tex]
[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{2}[/tex]
square root can be written as 1/2 and then cube root can be written as 1/3
[tex]\sqrt[3]{4} =2^\frac{2}{3}[/tex]
[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{2}[/tex]
[tex]\frac{2^\frac{1}{2}*2^\frac{2}{3}}{2}[/tex]
Now add the fractions [tex]\frac{1}{2} + \frac{2}{3} =\frac{3}{6} + \frac{4}{6}=\frac{7}{6}[/tex]
[tex]\frac{2^\frac{7}{6}}{2}[/tex]
[tex]\frac{\sqrt[6]{2^7}}{2}[/tex]
[tex]\frac{2\sqrt[6]{2}}{2}[/tex]
cancel out 2 at the top and bottom
[tex]\sqrt[6]{2}[/tex]
Compare and contrast the solution of |2x + 8| > 6 and the solution of |2x + 8| < 6.
A.
The solution of |2x + 8| > 6 includes all values that are less than –2 or greater than –14.
The solution of |2x + 8| < 6 includes all values that are greater than –2 and less than –14.
B.
The solution of |2x + 8| > 6 includes all values that are less than –7 or greater than –1.
The solution of |2x + 8| < 6 includes all values that are greater than –7 and less than –1.
C.
The solution of |2x + 8| > 6 includes all values that are less than –1 or greater than –7.
The solution of |2x + 8| < 6 includes all values that are greater than –1 and less than –7.
D.
The solution of |2x + 8| > 6 includes all values that are less than –14 or greater than –2.
The solution of |2x + 8| < 6 includes all values that are greater than –14 and less than –2.
Answer:
B.
The solution of |2x + 8| > 6 includes all values that are less than –7 or greater than –1.
The solution of |2x + 8| < 6 includes all values that are greater than –7 and less than –1.
__
Step-by-step explanation:
You can find the solution by "unfolding" the absolute value, then dividing by 2 and subtracting 4:
-6 > 2x +8 > 6 . . . . . read this as -6 is less than 2x+8 or 2x+8 is greater than 6
-3 > x +4 > 3 . . . . . . .divide by 2
-7 > x > -1 . . . . . . . . . solution to the first inequality: x is less than -7 or greater than -1.
___
The solution to the other inequality is identical, except the direction of the comparison is reversed. It is read differently, because the segments overlap, rather than being disjoint.
-7 < x < -1 . . . . . . . . solution to the second inequality: x is greater than -7 and less than -1.
__
These descriptions match choice B.
On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. What is the probability that Erin will have a heart attack and the test predicts it?
Answer: There is probability of 46.9% that Erin will have a heart attack and the test predicts it.
Step-by-step explanation:
Since we have given that
Probability that her family had a risk of heart attack P(A)= 70%
Probability that the reliability of the stress test P(B)= 67%
Since events A and B are independent events.
so, we can apply the rule of independent events :
We need to find the probability that Erin will have a heart attack and the test predicts it .
[tex]P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.70\times 0.67\\\\P(A\cap B)=0.469\\\\P(A\cap B)=0.469\times 100\%\\\\P(A\cap B)=46.9\%[/tex]
Hence, there is probability of 46.9% that Erin will have a heart attack and the test predicts it.
The probability that Erin will have a heart attack and the test predicts it is 46.9%.
Explanation:To find the probability that Erin will have a heart attack and the test predicts it, we need to multiply the probability of Erin having a heart attack (the family risk of 70%) with the reliability of the stress test (67%).
Probability of having a heart attack = 70% = 0.70
Reliability of the stress test = 67% = 0.67
Probability of Erin having a heart attack and the test predicting it = 0.70 * 0.67 = 0.469 (or 46.9%)
it takes 1 worker 15 hours to paint a room. it takes 3 workers 5 hours to paint the same room. martin wrote the function y = -5x + 20 to model the number of hours requires for x workers to paint the room. did he choose the correct kind of equation to model the situation? if so, did he write the correct equation? if not, what equation should he have written?
PLEASE HELP MUCH APPRECIATED
Answer:
• the equation kind is incorrect
• the equation is incorrect
• the equation should be: y = 15/x
Step-by-step explanation:
We observe that the data tells us the time is inversely proportional to the number of workers, and that the product of time and workers is 15 worker·hours. The form for inverse proportionality is ...
y = k/x
or
xy = k
Our observation tells us k = 15 (worker·hours), so our model equation is ...
y = 15/x . . . . . where x is the number of workers, and y is the hours to paint the room
Find the distance between the pair of points with the given coordinates. (-5,8) and (2,-5)
Answer: 14.76
Step-by-step explanation:
You need to use this formula for calculate the distance betweeen two points:
[tex]d=\sqrt{(x_2-x_1)^ 2+(y_2-y_1)^2}[/tex]
Given the points (-5,8) and (2,-5), you only has to substitute the coordinates of these points into the formula [tex]d=\sqrt{(x_2-x_1)^ 2+(y_2-y_1)^2}[/tex].
Therefore, you get that the distance between these two points is the following:
[tex]d=\sqrt{(2-(-5))^ 2+(-5-8)^2}\\\\d=\sqrt{218}\\\\d=14.76[/tex]
ANSWER
[tex]\sqrt{218} [/tex]
EXPLANATION
We want find the distance between the pair of points with the given coordinates. (-5,8) and (2,-5)
We use the distance formula given by;
[tex]d = \sqrt{(x_2-x_1) ^{2} + {(y_2-y_1)}^{2} } [/tex]
[tex]d = \sqrt{(2- - 5) ^{2} + {( - 5-8)}^{2} } [/tex]
[tex]d = \sqrt{(7) ^{2} + {( - 13)}^{2} } [/tex]
[tex]d = \sqrt{49+ 169 } [/tex]
[tex] = \sqrt{218} [/tex]
Help me with Thursday ASAP please
Answer:
a + 3
Step-by-step explanation:
Kim's age is always three more than Tom's age.
Where does the graph of
y = x^2 - x - 20 cross the x-axis?
(-5,0) and (4,0)
(4,0) and (5,0)
(2,0) and (-10,0)
(5,0) and (-4,0)
Answer:
D
Step-by-step explanation:
"Cross the x-axis" means that y =0
0=x²-x-20
(x-5)(x+4)=0
x=5, x= - 4
Points (5,0) and (-4,0)
The standard deviation of a sample taken from population A is 17.6 for a sample of 25.
The standard deviation of a sample taken from population B is 21.2 for a sample of 30.
The standard deviation of the sample mean differences is _____. Round your answer to the nearest hundredth.
Answer:
The standard deviation of the sample mean differences is _5.23_
Step-by-step explanation:
We have a sample of a population A and a sample of a population B.
For the sample of population A, the standard deviation [tex]\sigma_A[/tex] is
[tex]\sigma_A = 17.6[/tex]
The sample size [tex]n_A[/tex] is:
[tex]n_A = 25[/tex].
For the sample of population B, the standard deviation [tex]\sigma_B[/tex] is
[tex]\sigma_B = 21.2[/tex]
The sample size [tex]n_B[/tex] is:
[tex]n_B = 30[/tex].
Then the standard deviation for the difference of means has the following form:
[tex]\sigma=\sqrt{\frac{\sigma_A^2}{n_A}+\frac{\sigma_B^2}{n_B}}[/tex]
Finally
[tex]\sigma=\sqrt{\frac{17.6^2}{25}+\frac{21.2^2}{30}}\\\\\sigma= 5.23[/tex]
Answer:
5.23
Step-by-step explanation:
Find the radius of the circle circumscribed around an equilateral triangle, if the radius of the circle inscribed into this triangle is 10 cm.
Answer:
20 cm
Step-by-step explanation:
Let a cm be the length of the side of equilateral triangle.
Use formula for the radius of inscribed circle into the equailteral triangle:
[tex]r_{inscribed}=\dfrac{a\sqrt{3}}{6}[/tex]
Hence,
[tex]\dfrac{a\sqrt{3}}{6}=10\Rightarrow a=\dfrac{60}{\sqrt{3}}[/tex]
Now, use formula for the circumscribed circle's radius:
[tex]R_{circumscribed}=\dfrac{a\sqrt{3}}{3}[/tex]
Therefore,
[tex]R_{circumscribed}=\dfrac{\frac{60}{\sqrt{3}}\cdot \sqrt{3}}{3}=20\ cm[/tex]
Answer:
20 cmStep-by-step explanation:
Look at the picture.
The formula of a radius of a circle circumscribed around an equaliteral triangle:
[tex]R=\dfrac{2}{3}\cdot\dfrac{a\sqrt3}{2}[/tex]
The formula od a radius of a circle inscribed into an equaliteral triangle:
[tex]r=\dfrac{1}{3}\cdot\dfrac{a\sqrt3}{2}[/tex]
As you can see in the formulas above, the radius of the circumscribed circle is twice the radius of the inscribed circle.
Therefore
[tex]R=2r[/tex]
Given:
[tex]r=10\ cm[/tex]
therefore
[tex]R=2(10\ cm)=20\ cm[/tex]
Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1, -1).
Answer:
y = 2x +1
Step-by-step explanation:
The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:
y = 2x + b
-1 = 2(-1) +b . . . substitute for x and y
2 -1 = b . . . . . . add 2
1 = b
So the equation for the parallel line is ...
y = 2x + 1
simply the expression
-|-13|=
Answer:
-13
Step-by-step explanation:
The absolute value of -13 is 13 so if you put a negative sign in front of it, it will make the 13 negative.
Answer:
-13
Step-by-step explanation:
it's absolute value, the absolute value of -13 is 13. Then you have to use the other negative.
:))
Look at the graph below: First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ −1? Part A Part B Part C Part D
Answer:
Part B shaded below first line and above second line.
Step-by-step explanation:
The first inequality corresponds to the second line (-3 = -4+1, for example) The ≥ symbol in that inequality tells you it will be satisfied by y values above those on the line.
The second inequality corresponds to the first line (-4+3 = -1, for example) The ≤ symbol in that inequality tells you it will be satisfied by y values below those on the line.
Hence the solution set is those values shaded below the first line and above the second line — matching Part B.