Question: Perform the following computation with radicals. Simplify the answer. √6 • √8
Answer:
[tex] 4\sqrt{3} [/tex]
Step-by-step explanation:
Given, √6 • √8, to perform the computation, we would simply evaluate the radicals and try as much as possible to leave the answer in the simplest form in radicals.
Thus,
[tex] \sqrt{6}*\sqrt{8} = \sqrt{6*8} [/tex]
[tex] = \sqrt{48} [/tex]
[tex] = \sqrt{16*3} = \sqrt{16}*\sqrt{3}[/tex]
[tex] = 4\sqrt{3} [/tex]
Caleb made 6 quarts of trail mix for his camping trip. Each week,he ate 4 pints of the trail mix. How many weeks did Caleb have trail mix?
Sry if this is too much
Answer:
3 weeks
Step-by-step explanation:
6 quarts = 12 pints
12 divided by 3 = 4
Step-by-step explanation:
1 quart = 2 pints
6 quarts = 2 x 6 = 12 pints
12 ÷ 4 = 3
He can have 3 weeks
] You are scheduled to receive $20,000 in two years. When you receive it, you will invest it for six more years at 8.4 percent per year. How much will you have in eight years?
Answer:
32449.3
Step-by-step explanation:
use the formula A = P(1+r / 100)^t
20000 × (1+ (8.4 / 100))^6
=32449.3
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. , The mean, , is nothing. (Round to the nearest tenth as needed.)
Complete Question
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. , The mean, , is nothing. (Round to the nearest tenth as needed.)
p = 0.6 n = 18
Answer:
The mean [tex]\mu = 10.5[/tex]
The standard deviation [tex]\sigma = 2.08[/tex]
The variance [tex]var = 4.32[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is [tex]p = 0.6[/tex]
The sample size is [tex]n = 18[/tex]
Generally given that the distribution is binomial, then the probability of failure is mathematically represented as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.6[/tex]
[tex]q =0.4[/tex]
Generally the mean is mathematically evaluated as
[tex]\mu = np[/tex]
substituting values
[tex]\mu = 18 * 0.6[/tex]
[tex]\mu = 10.5[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{npq}[/tex]
substituting values
[tex]\sigma = \sqrt{18 * 0.6 * 0.4}[/tex]
[tex]\sigma = 2.08[/tex]
The variance is evaluated as
[tex]var = \sigma^2[/tex]
substituting value
[tex]var = 2.08^2[/tex]
[tex]var = 4.32[/tex]
f(x)=1/3x+7 find inverse
Answer:
Step-by-step explanation:
Can someone please help me with this question?
Answer:
B
Step-by-step explanation:
11q + 5 ≤ 49
Subtract 5 from each side
11q + 5-5 ≤ 49-5
11q ≤44
Divide each side by 11
q ≤44/11
q≤4
There is a close circle at 4 because of the equals sign and the lines goes to the left
Answer:
B
Step 1:
To solve this, we need to isolate the variable q. To do so, we will subtract 5 from both sides of the inequality.
[tex]11q+5(-5)\leq 49(-5)\\11q\leq 44[/tex]
Step 2:
We divide both sides by 11 to get our q.
[tex]\frac{11q}{11}\leq \frac{44}{11} \\q\leq 4[/tex]
q ≤ 4
Step 3:
To find the correct graph, we need to know that a close circle means a ≤ or ≥ and an open one means a < or >. Here, we are using a ≤ so C and D are not our answers. Also remember that if the "arrow" is pointing left (<), then the arrow on the graph should be facing the left side. If the arrow is facing the right side, then that means we are using > or ≥. Here, we are using ≤ (left), so that means the arrow on the graph should be on a 4, facing left, with a closed circle.
Our answer is B.
a
A solid metal cone of base radius a cm and height 2a cm is melted and solid
spheres of radius are made without wastage. How many such spheres can be
made?
volume of a cone
.
.
.
volume of sphere
.
.
number of spheres that can be made......
.
.
hence a hemisphere can be formed
Convert the decimal 0.984 to a fraction.
984/100
984/1000
984/99
984/999
Answer:
[tex]\boxed{\frac{984}{1000}}[/tex]
Step-by-step explanation:
Hey there!
Well .984 is 984 over 1000 so .984 as a fraction is 984/1000.
We can check this by doing 984 / 1000 which is .984.
Hope this helps :)
Juan starts a bacteria culture and records the number of bacteria in the Petri dish for the first couple of hours.
Hours Bacteria
0
160
1
320
2
640
If the pattern continues, how many bacteria can he expect to find after 17 h?
Enter your answer in the box.
9514 1404 393
Answer:
20,971,520
Step-by-step explanation:
The population is doubling every hour, so after 17 hours it will be the initial population (160) multiplied by 2^17 = 131,072.
After 17 hours, he can expect to find 160×131072 = 20,971,520 bacteria.
Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB, find the location of point B.
The required coordinates of point B are (-3, 7) where point M is the midpoint of AB.
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB
We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AB.
Let the coordinates of B would be (x, y)
Substituting the coordinates of points A into the midpoint formula gives us :
-1 = (x+1)/2 ; 6 = (y+5)/2
-2 = x +1 ; 12 = y + 5
x = -3; y = 7
Therefore, the required coordinates of point B are (-3, 7).
Learn more about the midpoint here :
brainly.com/question/5127660
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Two friends compete with each other and five other, equally good, violinists for first and second chair in an orchestra, in a blind competition What is the probability that the two friends end up as first and second chair together?
Answer: 0.0476
Step-by-step explanation:
Given : Two friends and 5 other people compete with each other for first and second chair in an orchestra.
Total people in this competition= 2+5=7
By permutation , Number of ways to arrange 7 people= 7!
Also, number of ways for two friends end up as first and second chair together= 2 × 5! [ 2 ways to arrange friends on first and second chair and 5! ways to arrange others]
I.e. Required probability = [tex]\dfrac{2\times5!}{7!}[/tex]
[tex]=\dfrac{2!\times5!}{7\times6\times5!}\\\\=\dfrac{1}{7\times3}\\\\=\dfrac{1}{21}\\\\=0.0476[/tex]
Hence, the probability that the two friends end up as first and second chair together = 0.0476
Find 2
x
y у
30°
4√3
OA. 4/2
OB.22
0.8
D.4
Answer:
8
Step-by-step explanation:
The given is a special right triangle with angle measures
90-60-30 and side lengths represented by
2a-a[tex]\sqrt{3}[/tex]-a
x is the side length that sees angle measure 90 degrees so it's represented by 2a
and 4[tex]\sqrt{3}[/tex] is the side length that sees angle measure that sees 60 degrees so the value of a is 4
therefore x = 2*4 = 8
If the statement is true, type true in the space provided. If it is false, replace the underlined
word(s) with the word(s) that will make the statement true.
* The associative (associative is underlined) property is used on the following expression: 2 + 3 = 3 + 2.
In a triangle ABC two points D,E are taken on BC so that angle BAD=angle DAE=angleCAE. Determine AE if AB=5,BC=10 angle BAC=90. PLEASE HELP I NEED HELP WITHIN TEN MINS PLEASE
Answer:
AE = 7.5
Step-by-step explanation:
Since <BAC = [tex]90^{0}[/tex], then;
<BAD = <DAE = <CAE = [tex]30^{0}[/tex] (complementary angles)
From ΔABC, applying the Pythagoras theorem to determine the length of side AC;
[tex]/BC/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/AB/^{2}[/tex]
[tex]/10/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/5/^{2}[/tex]
100 = [tex]/AC/^{2}[/tex] + 25
[tex]/AC/^{2}[/tex] = 100 - 25
[tex]/AC/^{2}[/tex] = 75
AC = [tex]\sqrt{75}[/tex]
Applying trigonometric function to ΔCAE,
Cos [tex]30^{0}[/tex] = [tex]\frac{AE}{\sqrt{75} }[/tex]
AE = [tex]\sqrt{75}[/tex] × Cos [tex]30^{0}[/tex]
= 7.5
Therefore, AE = 7.5
12. 12 ounces is roughly the same as
O A. 340 grams.
B. 356 grams.
O C. 400 grams.
O D. 120 grams.
Mark for review (Will be highlighted on the movin
Answer:
A. 340 grams
Step-by-step explanation:
My brain
Smoking by Race for Males Aged 18-24
Smoker Nonsmoker Row Total
(S) (N)
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
Calculate the probabilities given below (Round your answers to 4 decimal places.):
i. P(S) 0.3200
ii. P(W) 0.8500
iii. P(S | W) 0.2720
iv. P(S | B) 0.0300
v. P(S and W) 0.9062
vi. P(N and B) 0.1765
Answer:
(i) 0.32 (ii) 0.85
(iii) 0.3412 (iv) 0.20
(v) 0.29 (vi) 0.12
Step-by-step explanation:
The data provided is as follows:
Race Smoker (S) Nonsmoker (N) Row Total
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
(i)
Compute the value of P (S) as follows:
[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]
P (S) = 0.32.
(ii)
Compute the value of P (W) as follows:
[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]
P (W) = 0.85.
(iii)
Compute the value of P (S|W) as follows:
[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]
P (S|W) = 0.3412.
(iv)
Compute the value of P (S|B) as follows:
[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]
P (S|W) = 0.20.
(v)
Compute the value of P (S∩W) as follows:
[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]
P (S∩W) = 0.29.
(vi)
Compute the value of P (N∩B) as follows:
[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]
P (S∩W) = 0.12.
PLS HELP ASAP:Find all the missing elements:
Answer:
b ≈ 9.5, c ≈ 14.7
Step-by-step explanation:
Using the Sine rule in Δ ABC, that is
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values
[tex]\frac{7}{sin23}[/tex] = [tex]\frac{b}{sin32}[/tex] ( cross- multiply )
b × sin23° = 7 × sin32° ( divide both sides by sin23° )
b = [tex]\frac{7sin32}{sin23}[/tex] ≈ 9.5 ( to the nearest tenth )
Also
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
[tex]\frac{7}{sin23}[/tex] = [tex]\frac{c}{sin125}[/tex] ( cross- multiply )
c × sin23° = 7 × sin125° ( divide both sides by sin23° )
c = [tex]\frac{7sin125}{sin23}[/tex] ≈ 14.7 ( to the nearest tenth )
please help solving.
Answer:
right machine first, then left.6 into left machine, then rightStep-by-step explanation:
a) Putting 6 into the first (left) machine will give an output of ...
y = √(6 -5) = √1 = 1
Putting 1 into the second (right) machine will give an output of ...
y = 1² -6 = -5
This answers the second question, but not the first question.
__
If we put 6 into the right machine first, we get an output of ...
y = 6² -6 = 30
Putting 30 into the left machine, we get an output of ...
y = √(30 -5) = √25 = 5 . . . . . the desired output.
The input must go into the right machine first, then its output goes into the left machine to get a final output of 5 from an input of 6.
__
b) The left machine cannot produce negative outputs, so achieving an output of -5 with the arrangement used in part A is not possible. (green curves in the attached graph)
However, as we have shown above, inputting 6 to the left machine first, following that by processing with the right machine, can produce an output of -5. (purple curve in the attached graph)
For this problem, use the tables and charts shown in this section. (Use picture provided)
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
0 $0.00
$5.00
$10.00
$300
Answer:
0
Step-by-step explanation:
0 because there is a $100 duty free exemption.
answer:
For this problem, use the tables and charts shown in this section.
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
$0.00 !
$5.00
$10.00
$300
What is the value of x for the given equation?
4 – 2(x + 7) = 3(x + 5)
X=
Answer:
-5
Step-by-step explanation:
What is the area of the trapezoid shown below?
2
15
12
help fast please!!!
Answer:
78 units2
Step-by-step explanation:
The Area of the triangle is 54 units2
The rectangle on the side has an area of 24 units2.
Add them together, and you get 78.
I hope this helps!
pls ❤ and give brainliest pls
Math 120 - 01 Summer 2021
Consuelo Butler
08/07
Homework: Practice
Exam 3
Question 1, 12.1.13
HW Score: 10%, 3 of 30 points
Score: 1 of 1
A professor had students keep track of their social interactions for a week. The
number of social interactions over the week is shown in the following grouped
frequency distribution. How many students had at least 60 social interactions for
the week?
12
Number of Social
Interactions
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
Frequency
9
14
11
15
16
8
7
3
1
1
Step-by-step explanation:
Consuelo Butler
08/07
Homework: Practice
Exam 3
Question 1, 12.1.13
HW Score: 10%, 3 of 30 points
Score: 1 of 1
A professor had students keep track of their social interactions for a week. The
number of social interactions over the week is shown in the following grouped
frequency distribution. How many students had at least 60 social interactions for
the week?
12
Number of Social
Interactions
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
Frequency
9
14
11
15
16
8
7
By calculating the greater than cumulative frequency using the given frequency table, 12 students had at least 60 social interactions for the week.
What is greater than cumulative frequency?The greater than cumulative frequency is also known as the more than type cumulative frequency. Here, the greater than cumulative frequency distribution is obtained by determining the cumulative total frequencies starting from the highest class to the lowest class.
Class interval Frequency Cumulative frequency
30-34 9 85
35-39 14 76
40-44 11 62
45-49 15 51
50-54 16 36
55-59 8 20
60-64 7 12
65-69 3 5
70-74 1 2
75-79 1 1
[We read the cumulative frequencies with respect to the corresponding lower class limits. For example, 85 students had 'more than 30' social interactions, 76 students had 'more than 35 social interactions and so on.]
By reading the greater than cumulative frequency, we find that 12 students had at least 60 social interactions for the week.
Learn more about greater than cumulative frequency here
https://brainly.com/question/5102661
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Suppose ACT Science scores are normally distributed with a mean of 20.8 and a standard deviation of 5.2. A university plans to send letters of recognition to students whose scores are in the top 12%. What is the minimum score required for a letter of recognition? Round your answer to the nearest tenth, if necessary.
Answer:
Hello,
Answer 26.9
Step-by-step explanation:
[tex]z=\dfrac{x-m}{\sigma} \\m=20.8\\\sigma=5.2\\\\p(z>?)\geq 0.12\ \longrightarrow 1-p(z\leq ?)=(1-0.12))\\\\Using\ table\ of\ normal\ reduce\ with\ 4 \decimals : ?=1.175\\\\x=1.175*5.2+20.8=26.91\approx{26.9}[/tex]
A probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12}. Let event E={3,4,5,6,7,8}. Assume each outcome is equally likely. List the outcomes in Ec. Find P(Ec).The outcomes of Ec are {_____}P(Ec)=
Answer:
This list of all the outcome of [tex]E^c[/tex] is [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]
[tex]P(E^c ) = 0.5[/tex]
Step-by-step explanation:
From the question we are told that
The sample sample space is [tex]S = \{ 1,2,3,4,5,6,7,8,9,10,11,12 \}[/tex]
The number of elements in the sample space is [tex]n = 12[/tex]
The event is [tex]E = \{ 3,4,5,6,7,8 \}[/tex]
The number of outcomes in the Event is [tex]n_e = 6[/tex]
The objective in to obtain [tex]P(E^c)[/tex]
Now [tex]E^c[/tex] is the compliment of E and number of elements in [tex]E^c[/tex] ican be mathematically evaluated as
[tex]nE^c = n - n_e[/tex]
substituting values
[tex]E^c = 12-6[/tex]
[tex]E^c = 6[/tex]
This list of all the outcomes of [tex]E^c[/tex] is
[tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]
Generally [tex]P(E^c )[/tex] which is the probability of [tex]E^c[/tex] is mathematically evaluated as
[tex]P(E^c ) = \frac{nE^c}{n}[/tex]
substituting values
[tex]P(E^c ) = \frac{6}{12}[/tex]
[tex]P(E^c ) = 0.5[/tex]
If you’re good at statistics please help
Answer:
Step-by-step explanation:
probabilty distribution= interval of x/total area of the distribution
OR P(x)= frequency of x/total frequency(N)*the interval of x(w)
x f probabilty f/N*w
16 10 0.2
17 16 0.32
18 20 0.4
19 4 0.08
w is the width of the bar( interval) 17-16=1
N=10+16+20+4=50
( only need to draw histogram)
Reduce to Standard form : (a) -21/91 (b) 32/(-256)
Answer:
a) -3/13
b) -1/8
Step-by-step explanation:
a) - (21 / 7) / (91 / 7) = 3/13
b) (32 / 32 ) / - (256 / 32) = -1/8
Use technology to solve the following problem: A certain car model has a mean gas mileage of 30 miles per gallon (mpg) with a standard deviation A pizza delivery company buys 42 of these cars. What is the probability that the average mileage of the fleet is greater than
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, let me solve a question that is exactly like this one.
A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability that the average mileage of the fleet is greater than 33.5 mpg?
Answer:
Given that the mean (μ) is 34 miles per gallon (mpg) with a standard deviation (σ) 5 mpg. The sample (n) is 43.
The z score is used in statistics to determine by how much the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\for\ a \ sample\ size:\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For the average mileage of the fleet is greater than 33.5 mpg (x > 33.5):
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\z=\frac{33.5-34}{5/\sqrt{43} } =-0.66[/tex]
From the normal distribution table, The probability that the average mileage of the fleet is greater than 33.5 mpg = P(x > 33.5) = P(z > -0.66) = 1 - P(z < -0.66) = 1 - 0.2546 = 0.7454 = 74.54%
The average age of a college is 21.8 years. The average age of students of college is 24.2 years and average age of lecturers of college is 20.6 years. Find the ratio of the number of students to that of lecturers?
Answer:
22,2
Step-by-step explanation:
average also known as mean
so you find it by adding all the numbers together and dividing them by how many there are
so 21,8 + 24,2 + 20.6 = 66,6 divided by 3 equals 22,2
Can I have help with 43 and 44 I need to see how to do them thanks.
Answer:
see explanation
Step-by-step explanation:
(43)
3[tex]x^{5}[/tex] - 75x³ ← factor out 3x³ from each term
= 3x³(x² - 25) ← this is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
x² - 25 = x² - 5² = (x - 5)(x + 5)
Thus
3[tex]x^{5}[/tex] - 75x³ = 3x³(x - 5)(x + 5)
(44)
81c² + 72c + 16 ← is a perfect square of the form
(ac + b)² = a²c² + 2abc + b²
Compare coefficients of like terms
a² = 81 ⇒ a = [tex]\sqrt{81}[/tex] = 9
b² = 16 ⇒ b = [tex]\sqrt{16}[/tex] = 4
and 2ab = 2 × 9 × 4 = 72
Thus
81c² + 72c + 16 = (9c + 4)²
1. 3x^5 -75x³
=3x³(x²-25)
=3x³(x²-5²)
=3x³(x-5)(x+5)
2. 81c²+72c+16
=81c²+36c+36c+16
=9c(9c+4)+4(9c+4)
=(9c+4)(9c+4)
=(9c+4)²
What is the value of n in the equation shown?
Captionless Image
Answer:
bzbdvdbdyrhevgdhs sdd
Step-by-step explanation:
ushebdvrudvd very
zhrjdvfjvrhfbrjrbr
hhrbdbdbfbfhfhthr
rhdjdbbffbdbbdve
whats the perimeter of a squre with a side measurement of 6 in.?
Answer:
The Perimeter is 24 inches
Step-by-step explanation:
Perimeter is all the sides of something added up. All sides on a square are equal so each side is 6 inches
6+6+6+6=24