Six math books, four physics books and three chemistry books are arranged on a shelf.
How many arrangements are possible if all books of the same subject are grouped together?
Answer:
622,080
Step-by-step explanation:
The total number of subjects is 3
= 3×2×1
= 6
Six maths book
= 6×5×4×3×2×1
= 720
Four physics book
= 4×3×2×1
= 24
Three chemistry book
= 3×2×1
= 6
6×720×24×6
= 622,080
Hence if the books are grouped together 622,080 arrangement is possible
Which table represents a linear function?
Answer:
the the 3rd one Is the one
Find the area of the triangle with the given
Answer:
616.2442
area to the nearest whole number=616
Step-by-step explanation:
using formula 1/2absinx
where a =44,b=29 ,x=105
1/2x44x29xsin105
44x29=1276
1276÷2=638
638 x sin 105
the sin of 105 is 0.9659
if u are using a four figure table where u can't find 105 under sin of angle
u simply subtract 105 from 180=75
638 x 0.9659 =616.2442
approx.616
What is the volume of the following rectangular prism?
Answer:
44/3
Step-by-step explanation:
V=L*W*H
WH=22/3
V=2*(22/3)
A contributor for the local newspaper is writing an article for the weekly fitness section. To prepare for the story, she conducts a study to compare the exercise habits of people who exercise in the morning to the exercise habits of people who work out in the afternoon or evening. She selects three different health centers from which to draw her samples. The 57 people she sampled who work out in the morning have a mean of 5.2 hours of exercise each week. The 70 people surveyed who exercise in the afternoon or evening have a mean of 4.5 hours of exercise each week. Assume that the weekly exercise times have a population standard deviation of 0.6 hours for people who exercise in the morning and 0.4 hours for people who exercise in the afternoon or evening. Let Population 1 be people who exercise in the morning and Population 2 be people who exercise in the afternoon or evening.
Step 1 of 2: Construct a 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers. Round the endpoints of the interval to one decimal place, if necessary.
Answer:
The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).
Step-by-step explanation:
Before building the confidence intervals, we need to understand 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.
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.
In the morning:
Sample of 57, mean of 5.2, standard deviation of 0.6, so:
[tex]\mu_1 = 5.2[/tex]
[tex]s_1 = \frac{0.6}{\sqrt{57}} = 0.0795[/tex]
In the afternoon/evening:
Sample of 70, mean of 4.5, standard deviation of 0.4, so:
[tex]\mu_2 = 4.5[/tex]
[tex]s_2 = \frac{0.2}{\sqrt{70}} = 0.0239[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 5.2 - 4.5 = 0.7[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0795^2 + 0.0239^2} = 0.083[/tex]
Confidence interval:
The confidence interval is:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower bound of the interval is:
[tex]\mu - zs = 0.7 - 1.96*0.083 = 0.5[/tex]
The upper bound of the interval is:
[tex]\mu + zs = 0.7 + 1.96*0.083 = 0.9[/tex]
The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).
Find the local linear approximation L(x) of the function f(x) = 5−x^2 at x = 2.
Use this to estimate f(2.1).
Answer:
L(x)=-4x+9
L(2.1)=0.6
Step-by-step explanation:
It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.
Theb use this to estimate f(2.1).
To find slope of tangent line, we must differentiate and then plug in 2 for x.
f'(x)=0-2x by constant and power rule.
f'(x)=-2x
So the slope of the tangent line is -2(2)=-4.
A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.
f(2)=5-(2)^2
f(2)=5-4
f(2)=1
So let's rephrase the question a little.
What's the equation for a line with slope -4 and goes through point (2,1).
Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.
Plug in our information: y-1=-4(x-2).
Distribute: y-1=-4x+8
Add 1 on both sides: y=-4x+9
Let's call this equation L(x), an expression to approximate value for f near x=2.
L(x)=-4x+9
Now the appropriation at x=2.1:
L(2.1)=-4(2.1)+9
L(2.1)=-8.4+9
L(2.1)=0.6
If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.
3. Find the minimum number of students needed to guarantee that five of them belong to the same class (Freshman, Sophomore, Junior, Senior)
Answer:
100
Step-by-step explanation:
well you can put 5 students in each class guaranteed 5 times over so it would make sense because 5 for each class 9th-12th 5 times over again and again will eventually give you the answer of 100 5•20
If we take 5 students are in each class.
Then let minimum number of students be x
ATQ
1/20()x = 5
x = 5 × 20
x = 100
Answer: 100 people
Must click thanks and mark brainliest
A bag of M&M's has 6 red, 5 green, 4 blue, and 8 yellow M&M's. What is the probability of randomly picking: (give answer as a reduced fraction) 1) a yellow? w 2) a blue or green? 3) an orange?
Answer:
P( yellow) = 8/23
P( blue or green) = 9/23
P(orange) = 0
Step-by-step explanation:
6 red, 5 green, 4 blue, and 8 yellow M&M's = 23 total
P( yellow) = yellow / total = 8/23
P( blue or green) = (blue+green) / total = (5+4)/23 = 9/23
P(orange) = orange/ total = 0/23
Answer:
there are 23 m&m's.
Step-by-step explanation:
Probability of getting red is 6/23
Probability of getting green is 5/23
Probability of getting blue is 4/23
Probability of getting yellow is 8/23
Orange = red + yellow = 6+8/23
Probability of getting Orange = 14/23
i need help ON THIS PLS
Answer:
No, because the ratio of pay to hours is not the same for each pair of value.
(b) Express the prime number 43 as the difference of two squares? 43 =
Which of the following graphs represents the line that passes through (–2, –3) and has a slope of 2/3?
Answer:
Step-by-step explanation:
From quadrilateral ABCD is a quadrilateral with area of 48 square units, find the length of AC.
A. 48/5
B. 24
C. 24/5
D. 48
Step-by-step explanation:
I do hope that you understand through the steps in the attachment, if not kindly reach out!
write your answer in simplest radical form
Answer:
[tex]s=6\sqrt{3}[/tex]
Step-by-step explanation:
In any 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.
In the given diagram, the hypotenuse is marked as 12 miles. Therefore, the side opposite to the 30 degree angle must be [tex]12 \div 2=6[/tex] miles. The final leg, [tex]s[/tex], must then represent the [tex]x\sqrt{3}[/tex] part of our ratio, hence [tex]\implies \boxed{6\sqrt{3}}[/tex]
Select the statement that best justifies the conclusion based on the given information.
a. Definition of bisector.
b. Definition of midpoint.
c. If two lines intersect, then their intersection is exactly one point.
d. Through any two different points, exactly one line exists.
9514 1404 393
Answer:
a. Definition of bisector.
Step-by-step explanation:
Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.
The conclusion is justified by the definition of a bisector.
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. Area of larger triangle = 165 ft^2 Thank you!!
9514 1404 393
Answer:
73 ft²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)
smaller area = 73 1/3 ft² ≈ 73 ft²
Answer:
Area of the smaller triangle = 73 square feet
Step-by-step explanation:
Area of the larger triangle = 165 square feet
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]
[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]
Height = 22 ft
Since, both the triangles are similar.
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
Let the height of smaller triangle = h ft
Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]
h = [tex]\frac{22\times 10}{15}[/tex]
h = 14.67 ft
Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]
= 73.33
≈ 73 square feet
write your answer in simplest radical form
Answer:
a = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos60° = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
a = 4[tex]\sqrt{3}[/tex]
Solve x2 + 8x + 22 = 0 by completing the square.
Question 20 options:
A)
x = –4 + i√ 6 , x = –4 – i√ 6
B)
x = –4 + √ 14 , x = –4 – √ 14
C)
x = –4 + i√ 14 , x = –4 – i√ 14
D)
x = –4 + √ 6 , x = –4 – √ 6
Answer:
A)
Step-by-step explanation:
the solution of a squared equation is
x = (-b ± sqrt(b² - 4ac)) / (2a)
in our case
a = 1
b = 8
c = 22
x = (-8 ± sqrt(64 - 88))/2 = (-8 ± sqrt(-24))/2 =
= (-8 ± sqrt(4×-6))/2 = (-8 ± 2×sqrt(-6))/2 =
= -4 ± sqrt(-6) = -4 ± i×sqrt(6)
3. (02.01)
Solve for x:
wim
(x – 4) = 2x. (1 point)
2
-2
-8
-4
What are the solutions of this quadratic equation?
4x2 + 3 = 4x + 2
Answer:
A. x = 1/2
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringStandard Form: ax² + bx + c = 0Solving quadraticsStep-by-step explanation:
Step 1: Define
Identify
4x² + 3 = 4x + 2
Step 2: Solve for x
[Equality Property] Rewrite in standard form: 4x² - 4x + 1 = 0Factor: (2x - 1)² = 0Solve: x = 1/2A boat has a rip-hole in the bottom while 20 miles away from the shore. The water comes in at a rate of 1.5 tons every minute, and the boat would sink after 70 tons of water came in. How fast must the boat go in order to reach the shore before sinking?
Answer:
t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks
S = V * t
V = S / t = 20 mi * 5280 ft/mi / 2800 sec = 37.7 ft/sec
Since 88 ft/sec = 60 mph
the speed is 60 * 37.7 / 88 = 25.7 mph
What is the length of AC?
a. 3ft
b. 4ft
c. 18ft
d. 12ft
plz hurry
d. 12ft
Answer:
Solution given:
∆ABC is similar to∆MBN
since their corresponding side are proportional.
so
AB/MB=AC/MN
[since AM=BM=4ft
AB=AM+BM=4+4=8ft]
8/4=AC/6
doing crisscrossed multiplication
2*6=AC
AC=12ft
1
What is the perimeter of a rectangle
whose length is 5 feet and whose width
is 3.5 feet?
O 8.5 ft.
O 16.5 ft.
O 17 ft.
O 17.5 ft.
Answer:
17ft
Step-by-step explanation:
5*2 + 3.5*2=17
PLEASE HELP FAST!! WILL GIVE FIRST PERSON THAT RESPONDS A HIGH RATING AND POINTS!
Answer:
Step-by-step explanation:
3
For a standard normal distribution, find:
P(z > c) = 0.058
Find c.
Answer:
1.572
Step-by-step explanation:
For a standard normal distribution,
P(z > c) = 0.058
To obtain C ; we find the Zscore corresponding to the proportion given, which is to the right of the distribution ;
Using technology or table,
Zscore equivalent to P(Z > c) = 0.058 is 1.572
Hence, c = 1.572
17 Geometry question: Use an algebraic equation to find the measurement of each angle that is represented in terms of X
Answer:
2x + 30° = 40°
4x + 30° = 50°
Step-by-step explanation:
2x + 30° and 4x + 30° are complementary angles.
Complementary angles sum up to give 90°.
Therefore,
2x + 30° + 4x + 30° = 90°
Add like terms
6x + 60 = 90
6x = 90 - 60
6x = 30
6x/6 = 30/6
x = 5
✔️2x + 30°
Plug in the value of x
2(5) + 30
10 + 30
= 40°
✔️4x + 30°
4(5) + 30°
20 + 30
= 50°
Joel and Matt must together save at least $50.00 to buy a special present for their mother.
Joel saves twice as much as Matt. Which inequality best represents the situation if x
represents the amount of money that Matt saves?
Answer:
Option (2)
Step-by-step explanation:
Let the savings of Joel = $y
And the savings of Matt = $x
They jointly save at least $50 to buy a special present.
Therefore, equation for this condition will be,
x + y ≥ 50 --------(1)
Joel saves twice as much as Matt.
Equation for this condition will be,
y = 2x ------ (2)
By substituting the value of 'y' in the equation,
x + 2x ≥ 50
Therefore, Option (2) will be the answer.
A simple random sample of 400 individuals provides 112 Yes responses. (a) What is the point estimate of the proportion of the population that would provide Yes responses
Answer:
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
Step-by-step explanation:
Point estimate of the proportion of the population that would provide Yes
The sample proportion of yes responses.
In the sample:
112 yes responses in the sample of 400, so:
[tex]p = \frac{112}{400} = 0.28[/tex]
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
a. 1.5
b. 2.3
c. 2.4
d. 1.9
Answer:
2.3
Step-by-step explanation:
.5 - .3 = .2
.8 - .5 = .3
1.2 - .8 = .4
1.7 - 1.2 = .5
We should add .6 next
1.7+.6 = 2.3
What is the common ratio for this geometric sequence?
27, 9, 3, 1, ...
Answer:
1/3
Step-by-step explanation:
common ratio is
9÷27=1/3
3÷9=1/3
1÷3=1/3
therefore common ratio is 1/3
Answer: 1/3
Step-by-step explanation:
Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.
A)15.8 inches
B) 17.8 inches
C)16.2 inches
D)14.8 inches
Answer:
B
Step-by-step explanation:
Use pythagorean theorem
4^2+5^2=AC^2, AC= 6.4
7^2+9^2=CB^2, CB=11.4
