Answer:
Circle Equation : x² + y² = 21
Step-by-step explanation:
So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.
The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,
( √5 )² + ( 4 )² = r²,
5 + 16 = r²,
r = √21
In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -
( x - 0 )² + ( y - 0 )² = (√21 )²
Circle Equation : x² + y² = 21
How many 2cm×2cm cubes can be packed in a box 1m long,20cm wide and 4cm deep.
Answer:
1000
Step-by-step explanation:
I guess, something went wrong with the text up there.
I assume it should say 2cm×2cm×2cm cubes. right ? because a cube has 3 dimensions, not just 2.
otherwise an infinitely large number of "just squares" would fit into the box ...
so, the box is
1m×20cm×4cm = 100cm×20cm×4cm = 8000 cm³
a single cube would be
2cm×2cm×2cm = 8 cm³
therefore,
8000 / 8 = 1000 cubes can be packed into that box, since the dimensions of the box in relation to the dimensions of the cubes do not force to have some empty left over space. the box can be packed tightly.
Draw the image of ABC under dilation whose center is P and scale factor is 4.
Answer:
Step-by-step explanation:
Let the point P is origin (0, 0), segment AB lies on the x-axis and segment PC on the y-axis,
Coordinates of A, B and C will be (1, 0), (2, 0) and (0, 2).
When triangle ABC is dilated by a scale factor 4 about the origin,
Rule for dilation;
(x, y) → (4x, 4y)
New coordinates of the points A, B and C will be,
A(1, 0) → A'(4, 0)
B(-2, 0) → B'(-8, 0)
C(0, 2) → C'(0, 8)
By plotting points A', B' and C' we can get the dilated image A'B'C'.
Dilation involves changing the size of a shape.
Assume point P is the center of origin, then we have the following coordinates of ABC
[tex]A = (1,0)[/tex]
[tex]B = (-2,0)[/tex]
[tex]C = (0,2)[/tex]
The scale factor (k) is given as:
[tex]k= 4[/tex]
So, the dilation rule is represented as:
[tex](x,y) \to (4 \times (x,y)[/tex]
Using the above dilation rule, the following coordinates represent the image of triangle ABC
[tex]A' = (4,0)[/tex]
[tex]B' = (-8,0)[/tex]
[tex]C = (0,8)[/tex]
See attachment for the image of the dilation.
Read more about dilation at:
https://brainly.com/question/8532602
The volume of a rectangular prism is the products it’s dimensions. If the dimensions of a rectangle prism are approximately 1.08 feet,5.25 feet, and 3.3 feet ,what is the approximate volume of the cube?Express your answer using an approximate level of accuracy.
Answer:
To find the volume of this cube, you would have to multiply 1.08 by 5.25 by 3.3 feet. If you did this, you would get: 18.711 feet^3. This is the volume of the rectangular prism.
Hope this helped!
PLEASE HELP ME!!! The students in Suzanne's school are painting a rectangular mural outside the building that will be 15 feet by 45 feet. To prepare they are create a scale drawing that represents 20% of the given dimensions. What is the length and width of the scale drawing?
Answer:
length of scale drawing = 9 feet
width of scale drawing = 3 feet
Step-by-step explanation:
Actual dimension 15 feet by 45 feet.
length = 45 feet
width = 15 feet
Dimension on drawing is 20% of actual dimension.
20% = 20/100
Thus,
20% of 15 feet = 20/100 * 15 feet = 3 feet
20% of 45 feet = 20/100 * 45 feet = 9 feet
Thus, length of scale drawing = 9 feet
width of scale drawing = 3 feet
Travis has a budget of $300 that he can spend on perennial flowers and at least 6 annual flowers. Perennial flowers are 18 dollars per plant and annual flowers are 15 dollars per plant. Let x be the amount spent on perennial flowers, and let y be the amount spent on annual flowers. What system of inequalities describes this situation?
Answer:
18x + 15y ≤ 300x ≥ 0; y ≥ 6Step-by-step explanation:
Variables are defined in the problem statement.
18x +15y ≤ 300 . . . . total budget
y ≥ 6 . . . . . . . . . . . . minimum number of annuals
x ≥ 0 . . . . . number of perennials cannot be negative
This system of inequalities describes the situation.
A certain dataset of systolic blood pressure measurements has a mean of 80 and a standard deviation of 3. Assuming the distribution is bell-shaped and we randomly select a measurement:
a) What percentage of measurements are between 71 and 89?
b) What is the probability a person's blood systolic pressure measures more than 89?
c) What is the probability a person's blood systolic pressure being at most 75?
d) We should expect 15% of patients have a blood pressure below what measurement?
e) Would it be unusual for 3 patients to have a mean blood pressure measurement of more than 84? Explain.
Answer:
Explained below.
Step-by-step explanation:
Let X = systolic blood pressure measurements.
It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].
(a)
Compute the percentage of measurements that are between 71 and 89 as follows:
[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]
[tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of measurements that are between 71 and 89 is 99.73%.
(b)
Compute the probability that a person's blood systolic pressure measures more than 89 as follows:
[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.
(c)
Compute the probability that a person's blood systolic pressure being at most 75 as follows:
Apply continuity correction:
[tex]P(X\leq 75)=P(X<75-0.5)[/tex]
[tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]
Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.
(d)
Let x be the blood pressure required.
Then,
P (X < x) = 0.15
⇒ P (Z < z) = 0.15
⇒ z = -1.04
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]
Thus, the 15% of patients are expected to have a blood pressure below 76.9.
(e)
A z-score more than 2 or less than -2 are considered as unusual.
Compute the z score for [tex]\bar x[/tex] as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]
The z-score for the mean blood pressure measurement of 3 patients is more than 2.
Thus, it would be unusual.
Please help!!! On my hw
Answer:
c(X)=R(X)
125x+18000=215x
18000=215x-125x
18000=90x (divede both sides by 90)
X=200
20 POINTS ANSWER QUICK
Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)? left 13 units, down 2 units right 13 units, down 2 units left 13 units, up 2 units right 13 units, up 2 units
Answer:
Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function
g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)?
left 13 units, down 2 units
right 13 units, down 2 units
left 13 units, up 2 units
right 13 units, up 2 units
The table shows the probability distribution of student ages in a high school
with 1500 students. What is the expected value for the age of a randomly
chosen student?
Age
13
14
15
16
17
18
Probability 0.01 0.23 0.26 0.28 0.20 0.02
Answer:
Exoected age is 15.49 years
Step-by-step explanation:
Expected age
= E(x)
= sum (p(i)*i)
= 13*0.01+14*0.23+15*0.26+16*0.28+17*0.20+18*0.02
= 15.49
let p and p+2 be prime numbers (i.e they are twin primes) with p>3. Show that 6|(p+1)
from the well known theorem that, primes are multiple of 6 ±1 ( eg 5,7,11,13,17,19...)
and one of them has [tex]-1[/tex] and other has $+1$ from the multiple of 6
let , $p=6n-1$, so $p+2=6n+1$
$\implies p+1=6n$
$\therefore 6|(p+1)$
QED
(a + b + c) power of 10 - abc
Tip
A=1
B=2
C= -3
[tex]\\ \rm\longmapsto (a+b+c)^{10}-abc[/tex]
[tex]\\ \rm\longmapsto (1+2-3)^{10}-(1)(2)(-3)[/tex]
[tex]\\ \rm\longmapsto (3-3)^{10}+6[/tex]
[tex]\\ \rm\longmapsto 0^{10}+3[/tex]
[tex]\\ \rm\longmapsto 0+3[/tex]
[tex]\\ \rm\longmapsto 3[/tex]
(a+b+c)^10-abc
= (1+2-3)^10-(1×2×-3)
= 0- (-6)
=6 answer.....
Part of the population of 6,750 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 3 of them are infected. How many elk are likely to be infected?
Answer:
405
Step-by-step explanation:
We can use a ratio to solve
3 infected x infected
------------------ = ----------------
50 sampled 6750 population
Using cross products
3*6750 = 50x
Divide each side by 50
3*6750/50 = x
405
Answer:
Around 405 elk should be infected with the parasite.
Step-by-step explanation:
6,750/50=135
135 * 3 = 405
hope this helps :)
In a study of 24 criminals convicted of antitrust offenses, the average age was 60 years, with a standard deviation of 7.4 years. Construct a 95% confidence interval on the true mean age. (Give your answers correct to one decimal place.)___ to____ years
Answer: 56.9 years to 63.1 years.
Step-by-step explanation:
Confidence interval for population mean (when population standard deviation is unknown):
[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].
Given: n= 24
degree of freedom = n- 1= 23
[tex]\overline{x}[/tex]= 60 years
s= 7.4 years
[tex]\alpha=0.05[/tex]
Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:
[tex]t_{\alpha/2}=2.0687[/tex]
A 95% confidence interval on the true mean age:
[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]
Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.
Is u=−12 a solution of 8u−1=6u?
Answer:
No, -12 is not a solution.
Step-by-step explanation:
8u-1=6u
8(-12)-1=6(-12)
-96-1=-72
-97=-72
Untrue, to it’s not a solution
Let a >= b.
show that gcd(a,b) = gcd(a-b, b)
let [tex] \gcd(a,b)= G[/tex] , $a\ge b$
$\therefore a=G\cdot m$ and $b=G\cdot n$
$a-b=Gm-Gn=G(m-n)$
Now, $\gcd(a-b,b)$ clearly is, $G$
What is the perimeter of half of a circle with a diameter of 14 inches?
Answer:
35.991
Step-by-step explanation:
HELP ASAP ROCKY!!! will get branliest.
Answer:
work pictured and shown
Answer:
Last one
Step-by-step explanation:
● [ ( 3^2 × 5^0) / 4 ]^2
5^0 is 1 since any number that has a null power is equal to 1.
●[ (3^2 ×1 ) / 4 ]^2
● (9/4)^2
● 81 / 16
Suppose a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207]. The population standard deviation used for the analysis is known to be $14,900.
Required:
a. What is the point estimate of the mean salary for all college graduates in this town?
b. Determine the sample size used for the analysis.
Answer: a. $40,800 b. 36
Step-by-step explanation:
Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].
[tex]\sigma= \$14,900[/tex]
a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.
Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]
= 40,800
hence, the point estimate of the mean salary for all college graduates in this town = $40,800
b. Since lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.
Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]
Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.
z-value for 99% confidence level = 2.576
So,
[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]
The sample size used for the analysis =36
a game is played with a fishpond containing 100 fish; 90 white, 9 red, and 1 blue. a contestant randomly catches a fish and receives payments as follows: $0.30 for white, $1.00 for red, and $10.00 for blue. If it cists $0.60 to play this game, how much (on average) does a contestant win on each play
Answer:
loses 14 cents
- $0.14
Step-by-step explanation:
90% $0.30 $(0.30) $(0.27)
9% $1.00 $0.40 $0.04
1% $10.00 $9.40 $0.09
$(0.14)
A pole that is 3 m tall casts a shadow that is 1.23 m long. At the same time, a nearby building casts a shadow that is 42.75 m long. How tall is the building? round your answer to the nearest meter.
Answer:
Hello,
Just using the theorem of Thalès,
Step-by-step explanation:
Let say h the hight of the building
[tex]\dfrac{h}{3} =\dfrac{42.75}{1.23}\\\\h=104.268296...\approx{104(m)}[/tex]
How??????????????????????
Answer:
y=-1/3x+7
Step-by-step explanation:
y=mx+c
m=-1/3, c=7
y=-1/3x+7
We have seen how to convert specified odds from a "fair bet" into the gamblerâs belief about the likelihood of an event happening. The following are related.a. Torik gives 5:3 odds that someone will walk in late for class tomorrow. What probability does lie assign for this event? b. Mikko believes there is a 60% chance that at least five students from this class will be at the next basketball game. If he were to set up odds, what would they be? c. Change the 60% to 75%. Now would would be the odds?
use the spinner to find the probability
Answer:
P(multiple of 5) = 0.1667
Step-by-step explanation:
The multiples of 5 on the spinner are 5 and 10. This means out of 12 numbers, only 2 multiples of 5. Therefore, there is a 2/12 chance to get a multiple of 5.
[tex]\frac{2}{12}=\frac{1}{6}=0.1667[/tex]
Therefore, P(multiple of 5) = 0.1667.
Mary states, "If the diagonals of a parallelogramare congruent, then the
parallelogram is a rectangle." Decide if her statement is wue or false.
A. True
B. False
Answer:
True
Step-by-step explanation:
A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,
AD ≅ BC (opposite side property)
AB ≅ CD (opposite side property)
<ABC = <BCD = <CDA = <DAC = [tex]90^{0}[/tex] (right angle property)
Thus,
<ABC + <BCD + <CDA + <DAC = [tex]360^{0}[/tex]
AC ⊥ BD (diagonals are perpendicular to each other)
AC ≅ BD (congruent property of diagonals)
Therefore, the parallelogram is a rectangle.
An 8×8×8 cm cube was painted red, and then broken up into small cubes with side lengths of 1 cm. How many small cubes have none of their faces painted red?
Answer:
216
Step-by-step explanation:
If you just paint the surface of the cube, then the inside of the cube would not have any of their faces painted red.
Just looking at the cube from a side view, you would realize that there would be a smaller cube, 6 x 6 x 6 (not 7 since you have to account for both the top side and the bottom side), and so that is the answer, 6 ^ 3, which is 216.
Answer:
216
Step-by-step explanation:
8 * 8 * 8 = 512
8 * 8 = 64
Each face is 64 cubes, overlapping at the edges, with 6 faces total.
16 + 12 = 28 for each overlapping cube on each side
64 * 6 = 384
384 - 2(28) = 328
Top & Bottom dealt with, overlap from them is 56 units total, 14 units on top and bottom of each face..
64 - 14 = 50
50 * 2 = 100
Front & Back dealt with.
328 - 100 = 228
64 - 28 = 36
36 * 2 = 72
228 - 72 = 156
...
OR
6^3 = 216
The expression $16x^2-106x-105$ can be written as $(8x + a)(2x + b),$ where $a$ and $b$ are integers. What is $a + 2b$?
Answer:
-23
Step-by-step explanation:
16x² - 106x - 105
factoring X
14 x -120 = -1680
14 - 120 = -106
16x² + 14x - 120x - 105
(16x² + 14x) -(120x - 105)
factor out 2 and -15 to get the same expression (8x + 7)
2x(8x + 7) - 15(8x + 7)
(8x + 7)(2x - 15)
a = 7
b = -15
a + 2b
7 + (-15 x 2)
7 + (-30)
= -23
A box is 30 inches wide, 16 inches long, and 14 inches high. To the nearest cubic inch, what is the volume of the box?
Answer:
6720 in ^3
Step-by-step explanation:
Volume = length * width * height
= 30*16*14
=6720 in ^3
2067 Supp Q.No. 2a Find the sum of all the natural numbers between 1 and 100 which are divisible by 5. Ans: 1050
5
Answer:
1050
Step-by-step explanation:
Natural Numbers are positive whole numbers. They aren't negative, decimals, fractions. We can just divide 5 into 100 to find how many natural numbers go up to 100 and just add them but that is just to much.
There is a easier method.
E.g: Natural Numbers that are divisible by a Nth Number. is the same as adding the Nth Numbers to a multiple of that Nth Term. For example, let say we need to find numbers divisible by 2. We know that 4 is divisible by 2 because 4/2=2. We can add the Nth numbers which is 2 to 4. 4+2=6. And 6 is divisible by 2 because 6/2=3. We can call this a arithmetic series. A series which has a pattern of adding a common difference
Back to the problem, we can use the sum of arithmetic series formula,
[tex]y = x( \frac{z {}^{1} + {z}^{n} }{2} )[/tex]
Where x is the number of terms in our sequence. Z1 is the fist term of our series. ZN is our last term. And y is the sum of all of the terms
The first term is 5, the numbers of terms being added is 20 because 100/5=20. The last term is 100.
[tex]y = 20( \frac{5 + 100}{2} )[/tex]
[tex]y = 20( \frac{105}{2} )[/tex]
[tex]y = 1050[/tex]
Lena is comparing offers from two banks on checking accounts that include debit cards. Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions. Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
Suppose Lena makes 35 transactions in a given month.
How much would she pay at each bank for the given month?
Bank A
Bank B
For the given month, which bank is cheaper and by how much?
Bank A. is cheaper than Bank B by $
or
Bank B is cheaper than Bank A by $
Answer:
Bank A spending= $20
Bank B spending= $22.5
Bank A is cheaper with $2.5
Step-by-step explanation:
Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions.
Sheade 35 transactions.
Total charges from bank A
= $20 monthly
Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
She made 35 transactions.
Total charges on bank B= $5 + (0.5)35
Total charges on bank B= $5+17.5
Total charges on bank B= $22.5
Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
The portfolio beta is [tex]\alpha = 1.354[/tex]
Step-by-step explanation:
From the question we are told that
The first investment is [tex]i_1 = \$ 25,000[/tex]
The first beta is [tex]k = 0.8[/tex]
The second investment is [tex]i_2 = \$ 40,000[/tex]
The second beta is [tex]w = 1.7[/tex]
Generally the portfolio beta is mathematically represented as
[tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]
substituting values
[tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]
[tex]\alpha = 1.354[/tex]