Answer:
B
Step-by-step explanation:
Not much to say but that i the definition. You sing the midpoint of each side, make a perpendicular line and see where the three perpendicular bisectors intersect.
A is the incenter, C sounds like the Orthocenter and D sounds like the centroid.
Aside from being able to tell from the parts of the words, you just kinda have to memorize these.
find the slope of the line perpendicular to given line
Answer:
perpendicular slope = - 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] + 5 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+165x+69
Answer:
The rocket hits the gorund after approximately 10.71 seconds.
Step-by-step explanation:
The height of the rocket y in feet x seconds after launch is given by the equation:
[tex]y=-16x^2+165x+69[/tex]
And we want to find the time in which the rocket will hit the ground.
When it hits the ground, its height above ground will be 0. Hence, we can let y = 0 and solve for x:
[tex]0=-16x^2+165x+69[/tex]
We can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = -16, b = 165, and c = 69.
Substitute:
[tex]\displaystyle x=\frac{-165\pm\sqrt{(165)^2-4(-16)(69)}}{2(-16)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{-165\pm\sqrt{31641}}{-32}=\frac{165\pm\sqrt{31641}}{32}[/tex]
Hence, our solutions are:
[tex]\displaystyle x_1=\frac{165+\sqrt{31641}}{32}\approx 10.71\text{ or } x_2=\frac{165-\sqrt{31641}}{32}\approx-0.40[/tex]
Since time cannot be negative, we can ignore the first answer.
So, the rocket hits the gorund after approximately 10.71 seconds.
Answer:
10.71
Step-by-step explanation:
the person below was correct!
£100 is deposited in a bank paying 2.25% simple interest per annum. How much interest will have been paid after 5 years?
Answer:
£11.25
Step-by-step explanation:
The formula to calculate simple interest is given as:
Simple Interest = Principal × Rate × Time
Principal = Amount deposited in the bank = £100
Interest rate = 2.25%
Time in years = 5 years
Hence,
Simple Interest = £100 × 2.25% × 5
= £11.25
Therefore, the interest that will have been paid after 5 years is £11.25
Let z be inversely proportional to the cube root of y. When y =.064, z =3
a) Find the constant of proportionality k.
b) Find the value of z when y = 0.125.
Given:
z be inversely proportional to the cube root of y.
When y =0.064, then z =3.
To find:
a) The constant of proportionality k.
b) The value of z when y = 0.125.
Solution:
a) It is given that, z be inversely proportional to the cube root of y.
[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]
[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, z=3 when y=0.064. Putting these values in (i), we get
[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]
[tex]3=k\dfrac{1}{0.4}[/tex]
[tex]3\times 0.4=k[/tex]
[tex]1.2=k[/tex]
Therefore, the constant of proportionality is [tex]k=1.2[/tex].
b) From part (a), we have [tex]k=1.2[/tex].
Substituting [tex]k=1.2[/tex] in (i), we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]
We need to find the value of z when y = 0.125. Putting y=0.125, we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]
[tex]z=\dfrac{1.2}{0.5}[/tex]
[tex]z=2.4[/tex]
Therefore, the value of z when y = 0.125 is 2.4.
Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n}[/tex]
or
[tex]n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For the given case, it is given that:
[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]
Let the constant of proportionality be k, then we have:
[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]
It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:
[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]
Thus, the constant of proportionality k is 1.2. And the relation between z and y is:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]
Putting value y = 0.0125, we get:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]
Thus, for the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4Learn more about proportionality here:
https://brainly.com/question/13082482
Use the Distributive Property to expand
the expression:
2 (y + 5x - 3)
Use the chart to multiply the binomial by the trinomial.
The expression (y + 3)(y squared minus 3 y + 9) is shown above a blank table with 3 columns and 2 rows.
What is the product?
y3 + 27
y3 – 27
y3 – 6y2 + 27
y3 + 6y2 + 27
Answer:
A. y^3 + 27
Step-by-step explanation:
Ed22
Answer: A. y3+27
Step-by-step explanation:
Find a parabola with equation y=ax^2+bx+c that has a slope 10 at x=1, slope -26 at x=-1, and passes through the point (2,29)
9514 1404 393
Answer:
y = 9x^2 -8x +9
Step-by-step explanation:
The given equation has derivative ...
y' = 2ax +b
The requirements on slope give rise to two equations:
2a(1) +b = 10
2a(-1) +b = -26
Adding these equations together gives ...
2b = -16 ⇒ b = -8
Then we have ...
2a -8 = 10
a = (10 +8)/2 = 9
__
The given point lets us find the constant term c.
y = 9x^2 -8x +c
c = y -(9x -8)x = 29 -(9(2) -8)(2) = 29 -20 = 9
The equation of the parabola is ...
y = 9x^2 -8x +9
Select the equation that is parallel to: y = -4x + 5
A. y = 4x - 5
B. y = 1/4x - 5
C. y = -1/4x - 5
D. y = -4x - 5
Answer:
D.
[tex]y = - 4x - 5[/tex]
Step-by-step explanation:
This is because the slopes are the same
The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116.
Answer:
10 and 42
Step-by-step explanation:
The difficulty with word problems is translating them into math.
Let's do that
---------------------
The sum of a number and two times a smaller number is 62.
let's call the bigger number b, and the smaller number s
b + 2s = 62
Three times the bigger number exceeds the smaller number by 116
3b = s + 116
-----------------------
Now manipulate one of the equations to isolate the variable
3b = s + 116
Subtract 116 from both sides
3b - 116 = s
substitute for s = 3b - 116 in
b + 2s = 62
b + 2(3b - 116) = 62
Distribute
b + 6b - 232 = 62
combine like terms
7b = 294
Divide both sides by 7
b = 42
to find s plug in b = 42 into
b + 2s = 62
42 + 2s = 62
subtract 42 from both side
2s = 20
divide both sides by 2
s = 10
Footlocker was selling Jordans. They bought the Jordan from Nike for $35. They bought 200 pairs of shoes. They sold the Jordans in their stores to the customers for $180. They sold out on the first day. How much did they make/Collect? What was their total expenses? What was their profit?
Answer:
I don't know what to say to someone who is a high school diploma Android to the other side of the kingdom of the crystal skull and bones
y-(-4) =m(x-(-5)) solve for m
Answer:
m = [tex]\frac{y+4}{x+5}[/tex]
Step-by-step explanation:
y-(-4) = m(x-(-5))
Simplify, distribute the negative sign outside of the parenthesis, remember negative times negative equals positive
y + 4 = m (x + 5)
Inverse operations, divide the equation by the value inside of the parenthesis
[tex]\frac{y+4}{x+5}[/tex] = m
Answer:
m=y+4x/x+5 your welcome !!
How many solutions exist for the given equation?
3(x – 2) = 22 – x
Answer:
One solution
Step-by-step explanation:
3(x – 2) = 22 – x
Distribute
3x - 6 = 22 -x
Add x to each side
3x-6+x = 22-x+x
4x -6 =22
Add 6 to each side
4x-6+6 = 22+6
4x = 28
Divide by 4
4x/4 = 28/4
x = 7
Answer:
One solution
Step-by-step explanation:
Solve for x to determine how many solutions it has
3(x - 22) = 22 - x
Distribute the 3
3x - 66 = 22 - x
Add x to both sides
4x - 66 = 22
Add 66 to both sides
4x = 88
Divide both sides by 4
x = 22
The equation has only one solution, the solution being 22
Simplify the expression. 4^0
be careful i think this is a trick question
Answer:
1
Step-by-step explanation:
4^0
Any number raised to the 0 power is 1.
Answer:
1
Step-by-step explanation:
Anything raised to 0 is 1.
What is the measure of KPN?
Answer:
angle KPN=95 degree
Step-by-step explanation:
angle KPN = angle JPO (because they are vertically opposite angles)
Now,
angle JPO+angle LOP=180 degree(being co interior angles)
angle JPO + 85 =180
angle JPO =180-85
angle JPO =95
since angle JPO is equal to KPN ,angle KPN is 95 degree
From a stick 2y metres long, I cut a piece of length 4y centimetres. What fraction of the original stick remains?
Answer: [tex]\dfrac{49}{50}[/tex]
Step-by-step explanation:
Given
Length of the stick is [tex]2y\ m[/tex]
A piece of [tex]4y\ cm[/tex] is cut
We know, 1 m=100 cm
So, [tex]2y\ m[/tex] in cm is [tex]200y\ cm[/tex]
Remaining length after cut is
[tex]\Rightarrow 200y-4y=196y[/tex]
Fraction of length that is left after the cut is
[tex]\Rightarrow \dfrac{196y}{200y}\\\\\Rightarrow \dfrac{49}{50}[/tex]
Thus, [tex]\frac{49}{50}[/tex] fraction of original stick remains after cut
Hello please help asap, thanks!
Answer:
Last image.
Step-by-step explanation:
So, we know that the orginal graph is of [tex]\sqrt[7]{x}[/tex]
We need to find the graph of [tex]-\sqrt[7]{x}-8[/tex]
First off, we see a negative in front of the root.
This means that all the values will be flipped across the x axis.
This removes the first two answer graphs, for they are of the postive root.
Next, we have a -8 following the root.
So, when another number is inside of the root(example: [tex]\sqrt[7]{x-6}[/tex]) You are going to add 6 to the x axis, basically shifting everything to the right(postive). If it was a postive 6 inside the root, we would move it left(negative)
This is not what is being done in our graph, I just wanted to explain this for future graphing.
Now, when a number is outside the root, such as the one above, then it shifts the y axis. In this case we have a -8 outside the root. This means that the graph will be shifted down(negative) by 8.
This eliminates the 3rd graph image, leaving the last graph answer shown below.
Hope this helps!
Ethan is installing a new tile backsplash in his kitchen. The tile he likes costs $3.50 per square foot. The area he is tiling is 36.5 square feet. How much will Ethan pay for the tile for his backsplash?
Answer:
$127.75
Step-by-step explanation:
Multiply the cost by the area to find the total cost
The amount of ice cream dispensed from a machine at an ice cream shop is normally
distributed. If the machine is used 800 times in a day, how many times did the
machine dispense an amount that falls within three standard deviations from the
mean amount?
A 798
B 760
C 544
D 267
The difference of two trinomials is x square - 10x+2. If one of the trinomials is 3x squared -11x-4, then which expression could be the other trinomial?
Answer:
4x²+21x-2
(OR)
2x²-x-6
Step-by-step explanation:
According to the Question,
Given, The difference Between two trinomials is x²-10x+2 & If one of the trinomials is 3x²-11x-4.
Let, Two Trinomials are P(x) = A & Q(x) = 3x²-11x-4
Then, P(x) - Q(x) = x²-10x+2
Put Value, We get
A - (3x²-11x-4) = x²-10x+2
A = x²-10x+2 + (3x²-11x-4)
A = x²-10x+2 + 3x²-11x-4
A = 4x²+21x-2
(OR)
If we Let, Two Trinomials are Q(x) = A & P(x) = 3x²-11x-4
Then, P(x) - Q(x) = x²-10x+2
Put Value, We get
(3x²-11x-4) - A = x²-10x+2
A = 3x²-11x-4 - (x²-10x+2)
A = 3x²-11x-4 - x²+10x-2
A = 2x²-x-6
3/4x × 12/11 ÷ 3x/22
Answer:
242/48
Step-by-step explanation:
Pedro y su socia Karina vendieron 520 calendarios en el mes de Diciembre. Pedro vendió 120 calendarios más que su socia. ¿Cuántos calendarios vendió cada uno?
Answer:
Pedro vendió = 320 calendarios
Katrina vendió = 200 calendarios
Step-by-step explanation:
Dejemos que el número de calendarios
Pedro vendió = x
Katrina vendió = y
Pedro y su compañera Karina vendieron 520 calendarios en diciembre.
x + y = 520 .... Ecuación 1
Pedro vendió 120 calendarios más que su socio.
x = y + 120
Sustituimos y + 120 por x
y + 120 + y = 520
2 años = 520 - 120
2 años = 400
y = 400/2
y = 200 calendarios
Resolviendo para x
x = y + 120
x = 200 + 120
x = 320 calendarios
Por lo tanto,
Pedro vendió = 320 calendarios
Katrina vendió = 200 calendarios
evaluate 3ac - a + 2b, if a=2, b=1 and c=4 pls help me thk u
The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs. Click on the datafile logo to reference the data. City Daily Living Cost ($) City Daily Living Cost ($) Bangkok 242.87 Mexico City 212.00 Bogota 260.93 Milan 284.08 Cairo 194.19 Mumbai 139.16 Dublin 260.76 Paris 436.72 Frankfurt 355.36 Rio de Janeiro 240.87 Hong Kong 346.32 Seoul 310.41 Johannesburg 165.37 Tel Aviv 223.73 Lima 250.08 Toronto 181.25 London 326.76 Warsaw 238.20 Madrid 283.56 Washington, D.C. 250.61 a. Compute the sample mean (to 2 decimals). b. Compute the sample standard deviation (to 2 decimals). c. Compute a confidence interval for the population standard deviation (to 2 decimals).
Answer:
[tex]\bar x = 260.1615[/tex]
[tex]\sigma = 70.69[/tex]
The confidence interval of standard deviation is: [tex]53.76[/tex] to [tex]103.25[/tex]
Step-by-step explanation:
Given
[tex]n =20[/tex]
See attachment for the formatted data
Solving (a): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}[/tex]
[tex]\bar x = \frac{5203.23}{20}[/tex]
[tex]\bar x = 260.1615[/tex]
[tex]\bar x = 260.16[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
[tex]\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}[/tex][tex]\sigma = \sqrt{\frac{94938.80}{19}}[/tex]
[tex]\sigma = \sqrt{4996.78}[/tex]
[tex]\sigma = 70.69[/tex] --- approximated
Solving (c): 95% confidence interval of standard deviation
We have:
[tex]c =0.95[/tex]
So:
[tex]\alpha = 1 -c[/tex]
[tex]\alpha = 1 -0.95[/tex]
[tex]\alpha = 0.05[/tex]
Calculate the degree of freedom (df)
[tex]df = n -1[/tex]
[tex]df = 20 -1[/tex]
[tex]df = 19[/tex]
Determine the critical value at row [tex]df = 19[/tex] and columns [tex]\frac{\alpha}{2}[/tex] and [tex]1 -\frac{\alpha}{2}[/tex]
So, we have:
[tex]X^2_{0.025} = 32.852[/tex] ---- at [tex]\frac{\alpha}{2}[/tex]
[tex]X^2_{0.975} = 8.907[/tex] --- at [tex]1 -\frac{\alpha}{2}[/tex]
So, the confidence interval of the standard deviation is:
[tex]\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }[/tex] to [tex]\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }[/tex]
[tex]70.69 * \sqrt{\frac{20 - 1}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{20 - 1}{8.907}[/tex]
[tex]70.69 * \sqrt{\frac{19}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{19}{8.907}[/tex]
[tex]53.76[/tex] to [tex]103.25[/tex]
Simplify the expression. 7(-2-7k) +4 Show all work below
(yo please help me im failing math and I have 1 day left of school. ;-;)
==================================================
Work Shown:
7(-2-7k) + 4
7(-2) + 7(-7k) + 4
-14 - 49k + 4
-49k + (-14+4)
-49k - 10
In the second step, I distributed the outer 7 to each term inside. From there, I grouped and combined like terms, which were the -14 and 4.
How many fifths are there in 6
Answer: 30
Step-by-step explanation:
there are 5 fifths in 1 hinting the name fifths
So that means there are 30 fifths in 6
A jar contains five red marbles and three green marbles. A
marble is drawn at random and not replaced. A second marble is
then drawn from the jar.
find the probability that both marbles are the same color
Answer:
I figured out that the probability that both marbles are red is 20/56 and the probability that both are green is 6/56. Then I added them together to get 26/56.
Hope this answer is right !
help please need to get this in today will mark brainlist
Answer:
acute
Step-by-step explanation:
it is acute because it is less than 90 degrees
a study is planned to compare the proportion of men who dislike anchovies with the proportion of women who dislike anchovies. the study seeks to determine if the proportions of men and women who dislike anchovies are different. a sample of 41 men was taken and the p^ estimate for the true proportion of men who dislike anchovies was determined to be 0.67. a sample of 56 women was also taken and the p^ estimate for the true proportion of women who dislike anchovies was determined to be 0.84. are the requirements satisfied to perform this hypothesis test
Answer:
d. No because n·(1 - [tex]\hat p[/tex]) = 8.96 is less than 10
Step-by-step explanation:
Question options;
a. Yes because the sample sizes of both groups are greater than 5
b. Yes, because in both cases n·[tex]\hat p[/tex] > 10
c. Yes, because we know that the population is evenly distributed
d. No, because the n·(1 - [tex]\hat p[/tex]) is less than 10
Explanation;
The given data are;
The number of men in the sample of men, n₁ = 41
The proportion of men who dislike anchovies, [tex]\hat p_1[/tex] = 0.67
The number of women in the sample of women, n₂ = 56
The proportion of men who dislike anchovies, [tex]\hat p_2[/tex] = 0.84
The assumptions for an analysis of the difference between means using a T-test are;
1) The data should be from a random sample of the population
2) The variables should be approximately normal (n·[tex]\hat p[/tex] ≥ 10, and n·(1 - [tex]\hat p[/tex]) ≥ 10)
3) The scale of the data is a continuous ordinance scale
4) The sample size should be large
5) The sample standard deviations should be approximately equal
From the requirement for normality, we have;
For the sample of men, n₁·[tex]\hat p[/tex]₁ = 41 × 0.67 = 24.47 > 10
n₁·(1 - [tex]\hat p[/tex]₁) = 41 × (1 - 0.67) = 13.53 > 10
For the sample of women, n₂·[tex]\hat p[/tex]₂ = 56 × 0.84 = 47.04 > 10
n₂·(1 - [tex]\hat p[/tex]₂) = 56 × (1 - 0.84) = 8.96 < 10
Therefore, the for n₂·(1 - [tex]\hat p[/tex]₂), the sample does not meet the requirement for normality
The correct option is d. No because n₂·(1 - [tex]\hat p[/tex]₂) = 8.96 is less than 10
how do you ifnd circumfranceof citlve
Answer:
The formula of the circumference of the circle
[tex]C =\pi D[/tex]
Step-by-step explanation:
To find the circumference of the circle follow the given steps.
1. Take a thread.
2. Fix one end of the thread at one point of the circle.
3. Move the thread along the length of the circle.
4. You reach the same fix end.
5. Measure the length of the thread.
6. It is the circumference of the circle.
The formula of the circumference of the circle
[tex]C =\pi D[/tex]
where D is the diameter of the circle.
There are 5 red, 4 blue, and 3 green marbles in a bag. What are the odds of randomly pulling a blue marble out of the bag and then randomly pulling a green marble out of the bag? The blue marble is NOT replaced.
A - 7/2
B - 12/24
C - 1/12
D - 1/11
