Answer:
Complementary angle 1st = 66.3°
Complementary angle 2nd = 23.7°
Step-by-step explanation:
Assume;
Complementary angle 1st = a
Complementary angle 2nd = a - 42.6°
Sum of complementary angles = 90°
So,
a + a - 42.6 = 90
a = 66.3
Complementary angle 1st = 66.3°
Complementary angle 2nd = 23.7°
Suppose you asked 100 commuters how much they spend each year and obtained a mean of $167 spent on transportation and a standard deviation of $40. Using the 2 SE rule of thumb, calculate a 95% confidence interval for the mean and select the values that come closest to those that would fill the spaces in the following interpretation: we can be 95% confident that the mean amount of money spent on transportation lies between _____ and _____ .
Answer:
The correct answer is "$159 and $175".
Step-by-step explanation:
The give values are:
Mean,
= $167
Standard deviation,
[tex]\sigma[/tex] = $40
Number of commuters,
n = 100
Now,
⇒ [tex]SE=\frac{\sigma}{\sqrt{n} }[/tex]
On putting the given values, we get
⇒ [tex]=\frac{40}{\sqrt{100} }[/tex]
⇒ [tex]=\frac{40}{10}[/tex]
⇒ [tex]=4[/tex]
By using the 2 SE rule of thumb, we get
= [tex]$(167 - 2\times 4)[/tex]
= [tex]167-8[/tex]
= [tex]159[/tex] ($)
Or,
= [tex](167 + 2\times 4)[/tex]
= [tex]167+8[/tex]
= [tex]175[/tex] ($)
i.e,
$159 and $175
Example 1
(a) Consider the pulse rates of two patients in a hospital for ten different days:
Patient A: 17 16 70 69 70
75 78 70 71
69
Patient B: 59
92
60
80 71
65
50
88
95 70
Find the mean pulse rate for each patient and the corresponding range.
Answer:
1a. Mean pulse rate for A = 60.5
1b. Range for A = 62
2a. Mean pulse rate for B = 73
2b. Range for B = 45
Step-by-step explanation:
1a. Determination of the mean pulse for patient A.
Data => 17, 16, 70, 69, 70, 75, 78, 70, 71, 69
Mean =?
The mean pulse rate for patient A can be obtained as follow:
Summation of data = 17 + 16 + 70 + 69 + 70 + 75 + 78 + 70 + 71 + 69
Summation of data = 605
Number of data = 10
Mean = summation of data / number of data
Mean = 605 / 10
Mean pulse rate for A = 60.5
1b. Determination of the range for patient A
Data => 17, 16, 70, 69, 70, 75, 78, 70, 71, 69
Range =?
Range = Highest – Lowest
Highest = 78
Lowest = 16
Range = Highest – Lowest
Range = 78 – 16
Range for A = 62
2a. Determination of the mean pulse for patient A.
Data => 59, 92, 60, 80, 71, 65, 50, 88, 95, 70
Mean =?
The mean pulse rate for patient B can be obtained as follow:
Summation of data = 59 + 92 + 60 + 80 + 71 + 65 + 50 + 88 + 95 + 70
Summation of data = 730
Number of data = 10
Mean = summation of data / number of data
Mean = 730 / 10
Mean pulse rate for B = 73
2b. Determination of the mean pulse for patient B.
Data => 59, 92, 60, 80, 71, 65, 50, 88, 95, 70
Range =?
Range = Highest – Lowest
Highest = 95
Lowest = 50
Range = Highest – Lowest
Range = 95 – 50
Range for B = 45
Find the equation of the line with slope =8 and passing through (3,21) write your equation in the form y=Mx+b
Answer: y = 8x -3
Step-by-step explanation:
we know the slope already which is 8.
so the equation is: y = 8x + b
subsutite the x and y to get the value of b
21 = 8(3) + b
21 = 24 + b
b = -3
So the equation is: y = 8x -3
The equation with the given condition is y=8x-3.
Given that, the slope of an equation (m)=8 which is passing through (3, 21).
We need to find an equation for the given condition.
What is slope intercept form?The slope-intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis). The equation of the line is the equation that is satisfied by each point that lies on that line.
Now, put m=8 and the coordinates (3, 21) in y=mx+b and simplify.
That is, 21=8×3+b
⇒21=24+b
⇒b=-3
So, the equation is y=8x-3
Therefore, the equation with the given condition is y=8x-3.
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What is the effective interest rate on an account that earns 5.5% compounded monthly?
Answer:
.46%
Step-by-step explanation:
.055/12= .00458= .46%
Please help! Marking brainliest if correct.
Answer:
110 degrees
Step-by-step explanation:
Because these angles are vertical, 5x+15=8x-42. thus, 15=3x-42, 3x=57, and x=19. 5x+15=5(19) +15=110. So, m<CDE=110 degrees.
Answer:
110°
Step-by-step explanation:
Since CDE and FDG are vertical, they are congruent, so:
5x + 15 = 8x - 42
Solve the equation for x
57 = 3x
19 = x
Then solve for one of the angles (I chose CDE but FDG would also work)
5(19)+15
95 + 15
110
If the projections of vector à on x, y and z axis are 2,1,2 units respectively, find the angle at which vector à is inclined to the z-axis
If 4a-3 = 2a then 12a=?
Answer:
18
Step-by-step explanation:
4a-3=2a
2a=3
a=1.5
12a=1.5*12
12a=18
Natalie bought a three pack of erasers $1.47. At the same rate how much would a 10 pack of erasers cost?
Answer:
The price for a 10 pack of erasers would cost $4.09
Step-by-step explanation:
1.47 ÷ 3 = 0.49
0.49 × 10 = 4.9
Answer:
$4.9
Step-by-step explanation:
[ Unitary method]
3 pack of erasers = $1.47
1 pack = $1.47 / 3 = $ 0.49
10 pack = $ 0.49 x 10 = $4.9
(I hope im right!)
help please “SHOW YOUR WORK!”
Answer:
384π cm³ ≈ 1206.37 cm³
Step-by-step explanation:
Insert the values the problem gives to us.
V = π(12)²(8)/3
⇒ π(144)(8)/3
⇒ 384π ≈ 1206.37
Two gym classes are participating in Field Day. One class has 24 students and the other has 27 students. The gym teachers want to divide the students in each class into the largest possible equal groups, with no students left over. If all the groups have the same number of students, how many students are in each group?
HELP
Answer:
one class 25 and the other 26
Step-by-step explanation:
That's because if there is 24 students in each class then 3 students will be left in which the other class will take two and the other 1 student
Answer:
Step-by-step explanation:
Class 1: 24 students
Class 2: 27 students
24+27=51
51 divided by 2 = 25.5
25.5 students are in each group
The ratio of boys to girls Ms. Garcia’s class is 4:5.
a. If there are 12 boys in the class, how many girls are there?
Answer:
15 girls
4x3=12 so u multiply 3 on both sides and 5 x 3=15
The diagram shows a right-angled triangle.
hcm
7 cm
38°
What is the value of h?
Give your answer correct to 1 decimal place.
The measure of value of h from the trigonometric relations is h = 11.4 cm
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔABC
Now , the value of sides of the right triangle ABC is
AB = 7 cm
AC = h cm
The angle ∠ACB = 38°
Now , from the trigonometric relations , we know
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin θ = 7 / h
sin 38° = 7 / h
Multiply by h on both sides of the equation , we get
h ( sin 38° ) = 7
Divide by sin 38° on both sides , we get
h = 7 / sin 38°
Substitute the value of sin 38° = 0.6157
h = 7 / 0.6157
h = 11.369 cm
Rounding the value to 1 decimal place , we get
The value of h = 11.4 cm
Hence , The measure of value of h is h = 11.4 cm
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Scrieți multipli lui 7 mai mari decât 10 și mai mici decât 20
The answer is here:
7 . 2 = 14, 10 >14 > 507 . 3 = 21, 10 > 21 > 50
7 . 4 = 28, 10 > 28 > 50
7 . 5 = 35, 10 > 35 > 50
7 . 6 = 42, 10 > 42 > 50
Hope This Helps! Have A GREAT Day!
(5⁴)²??????
A:5⁶
B:5⁸
C:20²
D:25⁸
Answer:c 20
Step-by-step explanation:
help me plz due today
Answer:
4x , 2y , 5
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation:
The terms are
4x, 2y, 5
Hope that helps
HELP ASAP WILL MARK BRAINLIEST
Estimate the difference by rounding each mixed number to the nearest half or whole number.
6 9/10 - 2 2/9
Answer:
4 1/2
Step-by-step explanation:
exact
6 9/10=6 81/90
2 2/9=2 20/90
6 81/90-2 20/90=4 61/90
rounds to 4 1/2
Rahul visited Taj Mahal. He found that the fountains near
the entry gate are sprinkling in circles. If the area covered
by the sprinkler of two circles is in the ratio 25:36. Find the
ratio of their circumference.
Answer:
5:6.
Step-by-step explanation:
The areas are 2 dimensional and the circumference is one dimensional.
So the ratio of the circumferences is √25:√36
= 5:6.
A triangular pyramid has a right triangle for its base. The perpendicular sides of the triangle are 10 inches and 18 inches long. Compute the volume of the triangular pyramid if the height is 14 inches.
A. 252 in 3
B. 420 in 3
C. 2520 in 3
D. 1260 in 3
Answer:
90 cubic inches
Step-by-step explanation:
The formula for a triangular pyramid is 1/3AH. A is the area of the base. H is the height of the pyramid. So to find the area of a right triangle, you would use the formula (a x b)/2. So (10 x18)/2 is 90 inches^2. Now you can fill in the first formula. 1/3(90 x 14), which equals 420 inches^3.
V = 1/3 · area of base · height
V = 1/3 · 18 · 15
V = 6 · 15
V = 90
I hope you find this helpful (if correct.)
Write inequalities to represent the situations below.
Ryan exercises no less than 35 minutes per day. Use t to represent Ryan's amount of exercise (in minutes per day).
( ≤ < > ≥ )
Answer:
T<45
Step-by-step explanation:
More than is a greater than symbol
Inequalities help us to compare two unequal expressions. The inequality that can be used to represent the time for which Ryan exercise is t≥35.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Given Ryan exercises no less than 35 minutes per day. The inequality that can be used to represent the time for which Ryan exercise is t≥35.
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Which expression is equivalent to 12x - 20 - 5(x
Answer:
7x-5 combine like terms order off operations hope this helped
Step-by-step explanation:
Answer:
Step-by-step explanation:
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Solve X³=64. im trying to finsh my class
Answer:
C
Step-by-step explanation:
multiply the number 3 times
A 1536
B 512
C 64!!!D Dum answer choice
Answer:
x = 4
Step-by-step explanation:
We have the equation x^3 = 64 and are asked to solve for x.
To solve, we need to isolate x.
x^3 = 64
Cube root both sides by 3 to get x alone :
[tex](x^3)^3 = \sqrt[3]{64}[/tex]
[tex]x = \sqrt[3]{64}[/tex]
Solve for the cube root of 64 :
[tex]\sqrt[3]{64} = 4[/tex]
[tex]x = 4[/tex]
A show started at 6:30 p.m. and ended at 8:35 p.m. about how long was the show?
Answer:
2 hours and 5 minutes
Step-by-step explanation:
6:30 --> 8:30 is two hours
plus 5 minutes
Hello and it would be very helpful if you know these answers!
1. 15 decreased by the product of a number x and 4.
2. Your uncle is 2 years older than 3 times your age.
Answer:
1) 15-4x
2) 3x+2
Step-by-step explanation:
1) product of x and 4 is 4x then subtract that from 15
2) use x as your age in this situation so your age times 3 is 3x and since he's 2 years older than that u add 2 more
write 5/17 has a mixed number
Answer:
Since 5/17 is a proper fraction, it cannot be written as a mixed number.
Step-by-step explanation:
Cannot be written as a mixed number.
3. Simplify 3 x g x 5 x h
Answer:
3 into g into 5 into h
in this we will group the term 3 and 5 together and then the g and h
so the answer will be 3 into 5 into g into h = 15gh
The expression 3 × g × 5 × h is in the simplified form of 15gh.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
The expression is given below.
⇒ 3 × g × 5 × h
Simplify the expression, then we have
⇒ 3 × g × 5 × h
⇒ 15gh
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Express 9 as a ratio of 27
Answer:
9/27 or 9 to 27
Step-by-step explanation:
a number reduced by the difference between 14 and 6 equals -6. Find the number.
Answer:
2
Step-by-step explanation:
?-(14-6)=-6
?-8=-6
2-8=-6
2x-7y=14
Solve for x
help plz I will give you BRAINLYST I don't know if I spelled that right lol but plz and I will give you a follow plz help me
If s = 1 over 2 unit and A = 16s2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)
Answer:
The value of A, in square units is:
1
Step-by-step explanation:
Answer:
6o0
Step-by-step explanation:
help! (Math and area!!)
Answer:
1.) Triangle is 1/2 x b x h (Which is option C)
2.) Rhombus is ½ × d1 × d2. (Which is option A)
3.) Trapezoid is ½(b 1+b 2)h or (b1 + b2)h/2 (Which is option B)
4.) Parallelogram is base x height (Which is option D)
Step-by-step explanation: