Answer:
[tex]BC = \sqrt{(-3+8)^2 +(1+2)^2} = \sqrt{34}\\\\AB =\sqrt{(-3-2)^2+(1-a)^2} = \sqrt{25+(1-a)^2} \\\\AC = \sqrt{(2+8)^2+(a+2)^2} = \sqrt{100+(a+2)^2} \\\\AB^2 + AC^2 = BC^2\\\\ (\sqrt{25+(1-a)^2})^2+ (\sqrt{100+(a+2)^2})^2= (\sqrt{34})^2 \\\\25+(1-a)^2+100+(a+2)^2=34\\\\125+1+a^2-2a+a^2+4+2a=34\\\\130+2a^2 =34\\\\2a^2+96=0\\\\a^2+48=0\\\\a = \sqrt{-48}[/tex]
Can the surface area of a sphere and the volume of a sphere be the same numerical value if the units are measured relative to the same unit of length?
A. Yes; the radius would need to be the unit radius, 1.
B. Yes; the radius would need to be 3.
C. No, the surface area would always be greater than the volume.
D. No, the volume would always be greater than the surface area.
Answer:
Volume = surface area
[tex]\frac{4}{3}\pi r^3 = 4\pi r^2\\\\\frac{r}{3} = 1\\r = 3[/tex]
option B
Choose all of the points that are solutions to 3x + 2y = 12.
A. (0.6)
B. (1,6)
C. (2,3)
D. (3,2)
E. (4,0)
F. (4,1)
G. (4,6)
Ans - A, C, E
Hope it helps You
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Thank You
The correct points to the equation. are (0,6) , C. (2,3) , E. (4,0) a
What is an Equation ?An equation, statement of equality between two expressions consisting of variables and/or numbers.
3x + 2y = 12
To determine the points that are solutions to this equation
we have to apply substitution method
1. 3 * (0) + 2*6 = 12 Correct
2. 3 + 12 = 12 Incorrect
3. 6 + 6 = 12 Correct
4. 9+4 = 12 Incorrect
5. 12 + 0 = 12 Correct
6. 12 + 2 = 12 Incorrect
7. 12 + 12 = 12 Incorrect
Therefore A. (0,6) , C. (2,3) , E. (4,0) are the correct points to the equation.
To know more about equation
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What is the area??? 12m 6m 3m
Answer:
1320m
hope this helps
have a good day :)
have a good day :)
Step-by-step explanation:
I need help with this question and no links or I will report you
TERM 2: WEEK 8
CLASSWORK 1
1.
Solve the simultaneous equations using elimination method
4x - 3y = 1
x + 3y = 19c
a.
9514 1404 393
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
We notice that the coefficients of y are opposites, so we can eliminate y by adding the two equations together.
(4x -3y) +(x +3y) = (1) +(19)
5x = 20 . . . . . . simplify
x = 4 . . . . . . . . .divide by 5
Substituting into the second equation gives ...
4 +3y = 19
3y = 15 . . . . . . . subtract 4
y = 5 . . . . . . . . . divide by 3
The solution is (x, y) = (4, 5).
The curriculum director in a large 3 points school district wants to determine the difference between the proportion of high school juniors who are enrolled in AP classes and the proportion of high school seniors who are enrolled in AP classes. She randomly selects 75 seniors and 70 juniors. Twenty-six of the seniors are enrolled in AP classes and 15 of the juniors are enrolled in AP classes. A 90 percent confidence interval for the difference between the proportion of seniors and juniors who are enrolled in AP classes is calculated. Which statement is not true?
A) The critical value used is 1.645.
B) The standard error of the difference is 0.074
C) The 90% interval was constructed using a method that results in intervals which capture the true difference in the proportion of seniors who are enrolled in AP classes and the proportion of juniors who are enrolled in AP classes 90% of the time.
D) She can be 90% confident that the true difference between the proportion of seniors who are enrolled in AP classes and the proportion of juniors who are enrolled in AP classes is between 0.0112 and 0.2535 students.
E) There is a 90% chance that the true difference between the proportion of seniors who are enrolled in AP classes and the proportion of juniors who are enrolled in AP classes is between 0.0112 and 0.2535
Answer:
C) The 90% interval was constructed using a method that results in intervals which capture the true difference in the proportion of seniors who are enrolled in AP classes and the proportion of juniors who are enrolled in AP classes 90% of the time.
Step-by-step explanation:
x% confidence interval -> Options c, d and e:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
This means that options d and e are correct, while option c is not true.
Option a -> Critical Value:
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
This means that option A is true.
Estimate of the standard error:
Before building the estimate, we should take a look at the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
26 of 75 seniors:
This means that:
[tex]p_s = \frac{26}{75} = 0.3467, s_s = \sqrt{\frac{0.3467*0.6533}{75}} = 0.055[/tex]
15 of 70 juniors:
This means that:
[tex]p_j = \frac{15}{70} = 0.2143, s_j = \sqrt{\frac{0.2143*0.7857}{70}} = 0.049[/tex]
Estimate of the standard error:
[tex]s = \sqrt{s_s^2 + s_j^2} = \sqrt{0.055^2 + 0.049^2} = 0.074[/tex]
Thus option b is correct.
62% of what number is 84
Answer:
135.48
Step-by-step explanation:
g00gl3
Answer:
135.5
Step-by-step explanation:
0.62 = 62% and 135.5 times 0.62 is 84.01
HELP ME!!! 4- 5/8 =?
Answer:
27/8
Step-by-step explanation:
1.) 4-5/8
Convert element to fraction
2.) 4 x 8/8-5/8
3.) 4 x 8-5/8
4.) 27/8
If the square of a positive integer is added to four times to integer the result is 117 find the integer.
Answer:
x = -2 ± 452i
Step-by-step explanation:
x² + 4x = 117
x² + 4x - 117 = 0
if you solve this quadratic by using the quadratic formula you get:
x = -2 ± 452i
452i is an imaginary number that equals [tex]\sqrt{-452}[/tex]
write in algebraic expression the difference between a number m and the product of m and n. If you can help it would mean a lot
Answer:
m - mn
Step-by-step explanation:
The two numbers are denoted by m and n respectively.
From the question, we can deduce the following points;
- the difference between m and another variable (mn).
- product or multiplication of m and n.
Translating the word problem into an algebraic expression, we have;
m - (m*n)
m - mn
Using no other digits except 2 and 5 write down, if possible, a three-digit multiple of 6
Answer:
225
Step-by-step explanation:
Some other numbers that would work are:
255, 525, 555
Answer:
252, 522, 222, and 552
Step-by-step explanation:
For a number to be divisible by 6, it needs to be divisible by both 2 and 3. For a number to be divisible by 2, it needs to end in an even number, and the only even number we can use is 2.
So far our number is _ _ 2.
For a number to be divisible by three, its digits have to add up to a multiple of three. As of now we need to fill in the hundreds and tens place, and there are 4 combinations to check: 2, 5; 5, 2; 2, 2; and 5, 5.
Case #1: 2, 5
We are checking to see if the number 252 is divisible by six.
2 + 5 + 2 = 9
Since the numbers add up to a multiple of 3, 252 is divisible by 6.
Case #2: 5, 2
We are checking to see if the number 522 is divisible by six.
5 + 2 + 2 = 9
Since the numbers add up to a multiple of 3, 522 is divisible by 6.
Case #3: 2, 2
We are checking to see if the number 222 is divisible by six.
2 + 2 + 2 = 6
Since the numbers add up to a multiple of 3, 222 is divisible by 6.
Case #4: 5, 5
We are checking to see if the number 552 is divisible by six.
5 + 5 + 2 = 12
Since the numbers add up to a multiple of 3, 552 is divisible by 6.
What is the y-intercept in the equation y = 3x + 4 ?
Answer:
4 is the y-intercept
Step-by-step explanation:
Here's a photo the explains the equation
Answer:
[tex]The ~y-intercept ~is~ (0,4)[/tex]
------------------------
hope it helps...
have a great day!!
Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units:
Rooms 1 2 3 4 5
Owned 0.003 0.002 0.023 0.105 0.218
Rented 0.008 0.027 0.287 0.362 0.165
Rooms 6 7 8 9 10
Owned 0.225 0.198 0.149 0.053 0.024
Rented 0.095 0.033 0.013 0.003 0.004
Required:
a. Express "the unit has 7 or more rooms" in terms of X. x≥7. What is the probability of this event?
b. Express the event {X > 7} in words.
c. What important fact about discrete random variables does comparing your answers to (a) and (b) illustrate?
Answer:
Part a:
"The unit has 7 or more rooms" in terms of X is given by the unit which has 7, 8, 9 or 10 rooms.
P{ X≥7}= 0.424
Part b:
The event {X > 7} in words is that the unit has more than 7 rooms. .
Part C:
A continuous random variable is given by intervals of numbers
A discrete random variable is the variable that is obtained by counting.
Step-by-step explanation:
Part a:
"The unit has 7 or more rooms" in terms of X is given by
{ X≥7} = {x=7} + {x=8} + {x=9} + {x=10}
the unit which has 7, 8, 9 or 10 rooms.
The probability of this event is given by
P{ X≥7} =P {x=7} + P {x=8} + P {x=9} + P {x=10}
P{ X≥7} = 0.198 + 0.149+ 0.053 + 0.024
P{ X≥7}= 0.424
Part b:
The event {X > 7} in words is that the unit has more than 7 rooms. This does not include the unit having 7 rooms.
Part C:
A continuous random variable takes all the values in the given interval as in part a.The random variable X takes the values between 7 and 10 inclusive of 7.
A discrete random variable is the variable that is obtained by counting as in part b. The variable X takes the values of the units with 8 , 9 or 10 rooms.
Use an exponential inequality to determine the number of years, t, after which the area covered by purple loosestrife will
exceed 850 acres.
Type the correct answer in the box. Use numerals instead of words.
The area covered by purple loosestrife will be greater than 850 acres for t > ___ years.
Answer: t>3
Step-by-step explanation:
PLATO
Answer:
t > 5
Step-by-step explanation:
The estimated difference of 3209 and 1893, when rounded off to the nearest ten is
o(a) 1300
(b) 1310
(c) 1320
0 (d) 1000
Answer:
[tex] = (3209) - (1893) \\ = 1.32 \times {10}^{3} \\ = 1320[/tex]
[tex] \small{ \star{ \underline{ \blue{becker}}}}[/tex]
Answer:
1320
Step-by-step explanation:
round off
3209 ≈ 3210
1893 ≈ 1890
estimated difference = 3210 - 1890 = 1320
expand:X(3x-1)
please quickly
Answer:
[tex]x(3x - 1) \\ = {3x}^{2} - x[/tex]
Answer:
[tex]x(3x-1) = {3x}^{2} - x[/tex]
Pls help me with this
Answer:
f(X)=2x is the correct answer
What is the area of AABC?
B
2
X2
O
2
A
6
O A 26
B 13
OC 226
D
26
Answer:
[tex]Area = 13[/tex]
Step-by-step explanation:
Given
[tex]A = (4,0)[/tex] -- [tex]x1,y1[/tex]
[tex]B =(5,5)[/tex] -- [tex]x2,y2[/tex]
[tex]C =(0,6)[/tex] -- [tex]x3,y3[/tex]
Required
Area of ABC
This is calculated as:
[tex]Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|[/tex]
This gives:
[tex]Area = \frac{1}{2}|4 * 5 - 5 *0 +5*6 - 0*5 + 0*0 - 4*6|[/tex]
Using a calculator, we have:
[tex]Area = \frac{1}{2}|26|[/tex]
Remove absolute bracket
[tex]Area = \frac{1}{2}*26[/tex]
[tex]Area = 13[/tex]
A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 5 minutes?
(Type an integer or decimal rounded to one decimal place as needed.)
Answer: 7.5 gallons
Step-by-step explanation:
1. You divide 15 by two
9 - x < - 11
Show steps please
Answer: x > 20
Step-by-step explanation:
9 - x < - 11
In this scenario, we've to collect like terms in order to.wolve for x. This will be:
9 - x < - 11
- x < - 11 - 9
- x < - 20
Divide both side by -1
-x/-1 < -20/-1
When we divide by a coefficient with minus sign, the sign changes too from less than to greater than
-x/-1 < -20/-1
x > 20
Please help which is the greatest one!
Answer:
the Answer is 2^5
Step-by-step explanation:
Answer:
2^5
Step-by-step explanation:
5^2 = 25
2^5 = 32
3^3 = 27
1^10 = 1
Hope that this helps!
Get brainly if right !!
John and Jack divided their math homework. John solved twice
as many problems as Jack, plus one more problem. How many
problems did each boy solve if there are 28 assigned problems?
Answer:
Jack=9, John= 19
Step-by-step explanation:
28/3=9 1/3, counting as nine, as thats what got the right answer in my homework.
9 *2) +1= 19, no idea why the plus one, thats just what showed up
J1=19
J2=9
The graph of the invertible function h is shown on the grid below. What is the value of h -1(-4)
Answer: ℎ + 4
Step-by-step explanation:
h − 1 (−4)
ℎ + 4
Answer:
The answer is h^-1(-4)= -2
Step-by-step explanation:
This answer was pulled from Khan Academy.
How to solve 4x - 5 = 2x + 19?
Answer:
x = 12
Step-by-step explanation:
4x - 5 = 2x + 19
First subtract the 2x from 4x.
2x - 5 = + 19
Then add the 5 to the 19.
2x = 24
Divide 24 by 2 in order to get x by itself.
x = 12
I need help with this algebra question can someone help me?!
Answer:
consider a right angle triangle. ∠A = 90° , ∠B = [tex]\theta[/tex]
[tex]Sin\theta = \frac{6}{7} => AC = 6, BC = 7 \\\\BC^2 = AB^2 + AC^2 \\\\49 = 36 + AB^2 \\\\AB = \sqrt{13} \\\\Tan \theta = \frac{opposite}{adjacent } = \frac{6}{\sqrt{13} }[/tex]
Events A and B are mutually exclusive. Find the missing probability.
P(B) = 7/20 P(A or B) = 7/10 P(A) = ?
A) 3/5 B) 7/20 C)4/5 D) 1/5
Answer:
B, 7/20
Step-by-step explanation:
If two events are mutually exclusive that means that there is no intersection
so in the union formula: AUB=A+B-A∩B
A∩B=0
we can write P(a)=x
7/10=7/20+x+0
7/10-7/20=x
x=7/20
Find the sum of each of the following polynomials.
a) [tex]x^3+5x^2+2, 3x^2-4x+7[/tex]
b) [tex]2x + 5x^3-2x^2+7, 9+4x-5x^2-2x^3[/tex]
c) [tex]5x^3+2x^2+4, 2x^2+7x-5, 7-5x^2 +3x-4x^3[/tex]
d) [tex]2x^4-3x^2+4x^3-5, 9x^2-7x^3-2x^4, 7-x+3x^4[/tex]
Answer:
[tex](a)\ Sum = x^3+8x^2-4x+9[/tex]
[tex](b)\ Sum =3x^3-7x^2+6x +16[/tex]
[tex](c)\ Sum = x^3-x^2+10x+6[/tex]
[tex](d)\ Sum = 3x^4 -3x^3+ 6x^2-x+2[/tex]
Step-by-step explanation:
Required
Sum of the polynomials
[tex](a)\ x^3+5x^2+2, 3x^2-4x+7[/tex]
[tex]Sum = x^3+5x^2+2+3x^2-4x+7[/tex]
Collect like terms
[tex]Sum = x^3+5x^2+3x^2-4x+2+7[/tex]
[tex]Sum = x^3+8x^2-4x+9[/tex]
[tex](b)\ 2x + 5x^3-2x^2+7, 9+4x-5x^2-2x^3[/tex]
[tex]Sum =2x + 5x^3-2x^2+7+ 9+4x-5x^2-2x^3[/tex]
Collect like terms
[tex]Sum =5x^3-2x^3-2x^2-5x^2+4x+2x +7+ 9[/tex]
[tex]Sum =3x^3-7x^2+6x +16[/tex]
[tex](c)\ 5x^3+2x^2+4, 2x^2+7x-5, 7-5x^2 +3x-4x^3[/tex]
[tex]Sum = 5x^3+2x^2+4+ 2x^2+7x-5+ 7-5x^2 +3x-4x^3[/tex]
Collect like terms
[tex]Sum = 5x^3-4x^3+2x^2+ 2x^2-5x^2+7x+3x-5+ 7 +4[/tex]
[tex]Sum = x^3-x^2+10x+6[/tex]
[tex](d)\ 2x^4-3x^2+4x^3-5, 9x^2-7x^3-2x^4, 7-x+3x^4[/tex]
[tex]Sum = 2x^4-3x^2+4x^3-5+ 9x^2-7x^3-2x^4+ 7-x+3x^4[/tex]
Collect like terms
[tex]Sum = 2x^4-2x^4+3x^4 +4x^3 -7x^3-3x^2+ 9x^2-x-5+ 7[/tex]
[tex]Sum = 3x^4 -3x^3+ 6x^2-x+2[/tex]
sebuah kubus memiliki volume 1.331 cm³ panjang rusuk kubus adalah
Menjawab:
1.1 cm
Penjelasan langkah demi langkah:
Volume kubus, V = a³
Dimana a = panjang sisi kubus
Untuk V = 1.331 cm³
Panjang sisi 'a' adalah:
V = a³
1,331 = a³
Ambil akar pangkat tiga dari kedua sisi
(1,331) ⅓ = a
a = 1,1 cm
In 2017, you are starting to plan for retirement. You decide to deposit
$2.000 into a mutual fund that compounds quarterly and earns 4.2% annual interest.
Find the balance in 2027.
Answer:
10,369.04
Step-by-step explanation:
Sorry if i'm wrong i got a little confused with this
Look at the graph below. Identify the slope to create the equation.
Answer:
y +x and the answer will be xy