Answer:
[tex]\frac{2+\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Using the product to sum formula
sinxcosy = [tex]\frac{1}{2}[/tex] [ sin(x + y) + sin(x - y) ] , then
2sinxcosy = sin(x + y) + sin(x - y)
Given
2sin75°cos15° ← with x = 75 and y = 15 , then
= sin(75 + 15) + sin(75 - 15)
= sin90° + sin60°
= 1 + [tex]\frac{\sqrt{3} }{2}[/tex]
= [tex]\frac{2+\sqrt{3} }{2}[/tex]
The mean per capita income is 21,604 dollars per annum with a standard deviation of 727 dollars per annum. What is the probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected?
Answer:
0.72321
Step-by-step explanation:
Given that :
Mean = 21604
Standard deviation (s) = 727
Sample size (n) = 193
P(x < 21635) :
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s/√n
Z = (21635 - 21604) / 727/√193
Z = 31 / 52.330605
Z = 0.5923875
P(Z < 0.5924) = 0.72321 (Z probability calculator)
p(Z < 0) = 0.5 ( Z probability calculator)
A large random sample of adults aged 40 to 50 living in San Francisco, California, was polled about how likely they are to purchase an electric vehicle sometime in the next year. To which population can the results of the poll safely be generalized
Answer:
Adults living in San Francisco, California
Step-by-step explanation:
The population is the large group from which the sample is selected or chosen. In the question given the sample is drawn from the adult population of San Francisco who are aged 40 to 50 to find out whether they can buy
an electric vehicle sometime in the next year.
The population it can be generalized to is adults living in San Francisco, California.
A population is defined as the group of all the individual members or objects having some common interest or characteristics.
The individual members are called the sampling units or simply units.
Answer:
adults only who live in San Francisco
A store offers a 14% discount on a DVD. If the cost is discounted by $4.90, what is the original cost of the DVD?
Answer:
35
Step-by-step explanation:
Let's call the original price X
14% of x is equal to $4.90 to calculate 100% of the price we multiply 100 with 4.9 then divide it with 14
4.9 × 100 ÷ 14 = 35
which table represents a linear function?
Answer:
Step-by-step explanation:
Only the first table represents a linear function. In order to be in linear function, the graph of the function must be a straight line.
Construct a triangle ABC, right angled at B and the sides BC = 4cm and AC = 5cm. Measure side AB.
Answer:
3
Step-by-step explanation:
I don't know how to solve this.
Answer:
y^5
Step-by-step explanation:
you subtract the exponents
P. Antonio is ordering 5 identical sandwiches and a bag of chips. The bag of chips costs $1.25, and the entire order costs $38.75. What is the price of one sandwich
Answer:
$7.50
Step-by-step explanation:
Let the price of one sandwich = x
Hence,
The total cost = Cost of 5 identical sandwiches + 1 bag of chips
The bag of chips costs $1.25, and the entire order costs $38.75.
Hence:
$38.75 = 5x + $1.25
5x = $38.75 - $1.25
5x = $37.50
x = $37.50/5
x = $7.50
Therefore, the price of one sandwich is $7.50
Complete the proof. Someone please help me answer this!
Answer:
Step-by-step explanation:
Supplementary angles are two or more angles that add up to give the measure of angle on a straight line (i.e [tex]180^{o}[/tex]).
It can be deduced from the given question that;
1. <1 and <2 are supplementary, also <1 and <3 are supplementary. Reason: as given in the question.
2. Given statements: m<1 + m<2 = [tex]180^{o}[/tex], and m<1 + m<3 = [tex]180^{o}[/tex]. The reason is the definition of supplementary angles.
3. Statement: m<2 = m<3. The reason is a transitive property.
4. Statement: m<1 + m<2 = m<1 + m<3. The reason is subtraction property of equality.
5.Given statement: <2 ≅ <3. The reason is that definition of congruent angles.
Therefore, <2 ≅ <3.
Bobby, Rachel, and Sherry are going to have a water battle.
- Bobby fills his bucket at a rate of 3/4 gallon in 2 minutes.
- Rachel can fill her bucket at 1/5 gallon in 1/2 minute.
- Sherry can fill 3/8 gallon in 3/4 minute.
Order from fastest to slowest.
Answer:
The order is
Sherry >> Rachel>>Bobby
Step-by-step explanation:
Step one:
We want to find the smallest unit rate
given data
1. Bobby fills his bucket at a rate of 3/4 gallon in 2 minutes.
unit rate
=3/4/2
=3/4*1/2
=3/8
=0.375 gallons per minute
2. Rachel can fill her bucket at 1/5 gallon in 1/2 minute.
unit rate
=1/5/1/2
=1/5*2/1
=2/5
=0.4 gallons per minute
3. Sherry can fill 3/8 gallon in 3/4 minute.
unit rate
=3/8/3/4
=3/8*4/3
=12/24
=0.5 gallons per minute
What is the base area of Box 3?
Answer:
[tex]1x^{2}+4x[/tex]
Step-by-step explanation:
Usually, you'd not include the "1" before x, but Edge has no brains and can't comprehend it not being there for some reason.
So 1 and 4.
The answer to the next question on the same page as the one I just answered:
What is the volume of Box 3?
B. x^4 + 4x^3 + x^2 + 4x
Answer:
1 & 4
Step-by-step explanation:
i did the question
Difference between x=2 and x>2 in terms of their solutions
Answer:
When x = 2, there's a solid answer, if x > 2, it's an inequality
Step-by-step explanation:
Can anybody help with this ( hope this is better)
Which of these situations is not a situation of proportionality? Immersive reader A person's age and height The cost of filling up with gasoline and the number of liters purchased The number of working days and the salary The number of movie tickets purchased and the total bill
Answer:
A person's age and height
Step-by-step explanation:
Required
Select which do not represent proportionality
Proportionality exists when a unit rate can be calculated.
For instance:
- If 2 litres of gas is $2, then the unit rate is $1 per litre
- If an employee is paid $100 for 5 days, then the unit rate is $20 daily
- If 5 movie tickets cost $50, then the unit rate is $10 per movie
The above scenario are used to describe options (2 - 4) because they can be expressed in unit rates.
However, this is not the same for age and height because age is not a function of height and height is not a function of age. In other words, they can not be expressed in proportions.
So, option (a) is not a situation of proportionality.
The ratio of bOYS to giris
that went to camp Ozarks
this summer was 4:5. If
there were 32 boys that
went to the camp, how
many girls were there?
Answer:
There were a total of 40 girls there
Step-by-step explanation:
32 divided by 4 is 8
So multiply 8 x 5 to get 40
What is 6% sales tax on a $12
pair of mittens?
(show your work)
Answer:
$0.72
Step-by-step explanation:
In order to solve this question we need to know that 1% is one hundredth of something. Another important thing you need to understand is that when we are trying to find n% of y we multiply just need to multiply "y" by [tex](\frac{n}{100} )[/tex]. In our case we have to find 6% of 12, in other word they are asking as the following "What is $12 times [tex](\frac{6}{100} )[/tex]?". So in order to find the answer we do the following..............
[tex]12 (\frac{6}{100} ) = \frac{(12)(6)}{100} = \frac{72}{100} = 0.72[/tex]
How do you factor 9-6x+x^2
Answer:
Step-by-step explanation:
rewrite 9-6x+[tex]x^{2}[/tex] as [tex]x^{2}[/tex]-6x+9. (this step isn't necessary, but it's easier when the bigger term is in front)
There's two ways: using the quadratic formula, or just doing it in your head (for simple ones)
For the simple way:
think about what numbers not only multiply to equal c (represented by 9 in this case) but also add to equal -6 (represents b in this problem). There are two numbers for this problem that work: -3 and -3. So you would write the factored form as (x-3)(x-3)
Quadratic formula:
The formula is [tex]\frac{-b}{2a}[/tex] ±[tex]\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
This formula works for equations in the form of a[tex]x^{2}[/tex]+bx+c.
Substitute in the values to get:
[tex]\frac{6}{2} +\frac{\sqrt{-6^{2} -4(1)(9)} }{2}[/tex]
simplify:
3±[tex]\frac{\sqrt{36-36} }{2}[/tex]
3±[tex]\frac{0}{2}[/tex]
the answer is 3, which is the x-intercept. Write that as (x-3)(x-3)
Select all of the factions that are equivalent to -2/3
Answer:
-4/6, -8/12, -16/24, etc. look at the picture.
Step-by-step explanation:
Brainliest Please!!! Also, Tip: show the multiple choice options.
Answer:
4/6
Step-by-step explanation:
Use the graph of function g to answer the following questions
What is the value of g(1)
The value of g(1) is 2 because the graph represents the greatest integer function, the answer is 2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The graph of the greatest integer function is shown in the picture:
From the graph:
g(1) = 2
g(2) = 4
g(3) = 4
g(4) = 4
g(5) = 4
And so on
Thus, the value of g(1) is 2 because the graph represents the greatest integer function, the answer is 2.
Learn more about the function here:
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Combine and simplify these radicals.
18.20
Answer:
[tex]4\sqrt{10}[/tex]
Step-by-step explanation:
Through (6,-2), slope = 1/3
Write the equation in slope-intercept form.
Answer:
y=1/3x+4
Step-by-step explanation:
Slope = 1/3
y=1/3x-b
Through (6,-2)
-2=1/3(6)-b
-2=2-b
-4=-b
b=4
y=1/3x+4
Hope this helps!
which ordered pair is a solution of the eqaution
2x-y=9?
Answer:
(5,1)
Step-by-step explanation:
2x-y=9
(5,1)
There are many ordered pairs you could choose. For instance if x=0, then y=9. So you have the pair (0,9). If y=0, then 2x=9, so x=4.5. So you have the pair (4.5,0). You can keep making pairs by plugging in different values!
A student buys a guitar that is on sale for 15% off the regular price of $200. He also must pay an 8% sales tax. What is his total cost for the guitar?
ASNWER CHOICES
$176.80
$178.00
$183.60
$186.00
Answer:
option c
Step-by-step explanation:
a guitar 15% off means that the cost is now 85%
[tex]100percent---200dollars\\85percent---x\:dollars\\\\x=\frac{200*85}{100}\\\\x=2*85\\\\x=170[/tex]
now the 8% of 170 is
[tex]100\:percent---170\:dollars\\\\8\:percent---x\:dollars[/tex]
[tex]x=\frac{8*170}{100}\\\\x=\frac{8*17}{10}\\\\x=13.6[/tex]
so the total cost is
170+13.6
183.6
family built a house that has lenght and widht in 5:4, how long and wide is the house if it's 160m2 big?
Answer:
length = 14.14 m and width=width 11.32 m
Step-by-step explanation:
length be L and width be w
L:w = 5:4
L/w = 5/4
Let L =5k and w=4k
since A= lengthxwidth
A=5k x 4k
so, 160 = 20 k2
k 2 = 8
k = 2.828
since L = 5k in above, L= 5x2.828= 14.14
and since w=4k in above, w=4x2.828 = 11.32
This is my Guess. ..
Answer:
I hope it will help u
Step-by-step explanation:
As given that
L:W=5:4
L/W=5/4
L=(5/4)Whence we also know that
Area of rectangle= L*WAs given A=160m2
putt the value of A and L=(5/4)W in above equation ,
hence 160 = (5/4)W * W
W^2 = 160*4/5
W^2 = 32*4
W^2=128
taking square root
W= +_ 11.3
but length can't be negative so we take positive value of W
W=11.3 mNow for L putt in above equation,L=5/4 * 11.3 = 14.12 mCribe how making a list can help you solve a math problem. Write a problem that could be solved by making a list.
Answer:
Step-by-step explanation:
All that making a list does is creates a visible step by step instruction manual on what needs to be done in order to solve the math problem that needs to be solved. Lists are extremely helpful and can be used in every single math problem, for example....
15x - 25 = 275
Get rid of -25 by adding 25 on both sidesDivide 15 on both sides to isolate xCelebrate on solving the problemSee making a list isolates the problem into an easy to read instruction manual.
James sold 450 tickets for the community play. Tickets for children cost $2, and tickets for adults cost $5. James sold $1,800 worth of tickets.
How many tickets for adults did James sell?
PLEASE HELP!!!!!
Answer:
Adults = 300
Step-by-step explanation:
Andy has $150 in a savings account that earns a simple interest rate of 5%. How much will be in Andy’s savings account after 3 years?
Answer
$172.5
U find one percent of a 150 then times that by 15
Cherries are on sale for $16 for 4 pounds. Jordyn pays $88.00 for cherries to make a cobbler. How many pounds of cherries doses she buy?
Hi! Ok so my little sister needs help with math but I have no idea what to do.
"A recipe makes 6 2/3 cups of pancake batter. If you use 5/6 of a cup of batter for one pancake, how many pancakes can you make?"
I know the answer is 8, but what are the units?
Answer:
Cups are the unit
Step-by-step explanation:
If you were using cups so 8 pancakes you use 5/6 of a cup per pancake
(a unit is just what you use to measure something, so cups, liters, or even cm or meters)
PLEASE ILL GIVE 40 POINTS!!! How do the magnetic and electrical components of electromagnetic waves travel in relation to each other?
at right angles
toward each other
in a circular motion
parallel to each other
Answer:
im pretty sure it's right angles
Step-by-step explanation:
Answer:
they travel at right angles to each other in a bundle of light energy called a photon.. (probably, not sure)
A rectangle is 15 feet long and 9 feet wide. Find its area.
Step-by-step explanation:
Since area = length(width) = l(w)
We need to multiply 15 and 9.
15(9) = 135
Therefore, the area of the rectangle is 135 ft
Area of the rectangle is 135 feet square
What is Rectangle?A rectangle is a quadrilateral with four right angles.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface
Given,
Length of the rectangle = 15 feet
Width of the rectangle = 9 feet
Area of the rectangle = Length × Width
=15×9
=135 feet square
Hence, the area of the Rectangle is 135 feet square
Learn more about Rectangle and Area here
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