Answer:
7
Step-by-step explanation:
\underline{\text{Solution Method 2:}}
Solution Method 2:
Use original formula
a^2=b^2+c^2-2bc\cos A
a
2
=b
2
+c
2
−2bccosA
From reference sheet.
\text{Since we are finding }\angle M\text{,}
Since we are finding ∠M,
\text{plug in }2.3\text{ for side }a:
plug in 2.3 for side a:
Opposit the angle we want
2.3^2 = 6.6^2+8.7^2-2(6.6)(8.7)\cos M
2.3
2
=6.6
2
+8.7
2
−2(6.6)(8.7)cosM
Plug in values. Side "a" is opposite the wanted angle.
5.29 = 43.56+75.69-114.84\cos M
5.29=43.56+75.69−114.84cosM
Square sides.
5.29 =
5.29=
\,\,\color{white}{-} 119.25-114.84\cos M
−119.25−114.84cosM
Add.
-119.25=
−119.25=
\,\,-119.25
−119.25
-113.96=
−113.96=
\,\,-114.84\cos M
−114.84cosM
\frac{-113.96}{-114.84}=\cos M
−114.84
−113.96
=cosM
Divide to solve for cos(A).
M= \cos^{-1}(\frac{-113.96}{-114.84})\approx7.098\approx 7^{\circ}
M=cos
−1
(
−114.84
−113.96
)≈7.098≈7
∘
The angle according to the given data about the triangle will be equal to 7°.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol ∠.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the given information in the question,
The length of the sides is given as:
l = 8.7 cm
m = 2.3 cm
n = 6.6 cm
Use the formula given below to find the angle,
a² = b² + c² - 2bc cos A
The formula modified to the information will be,
m² = n² + l² - 2nl cos M
2.3² = 6.6² + 8.7² - 2(6.6)(8.7)cos M
5.29 = 43.56 + 75.69 - 114.84 cos M
-119.25 + 5.29 = -114.84 cos M
cos M = 113.96/117.84
M = cos⁻¹ 0.992
M = 7.09 ≈ 7°.
To know more about an angle:
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#SPJ2
(x +y)^5
Complete the polynomial operation
Answer:
Please check the explanation!
Step-by-step explanation:
Given the polynomial
[tex]\left(x+y\right)^5[/tex]
[tex]\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
[tex]a=x,\:\:b=y[/tex]
[tex]=\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i[/tex]
so expanding summation
[tex]=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5[/tex]
solving
[tex]\frac{5!}{0!\left(5-0\right)!}x^5y^0[/tex]
[tex]=1\cdot \frac{5!}{0!\left(5-0\right)!}x^5[/tex]
[tex]=1\cdot \:1\cdot \:x^5[/tex]
[tex]=x^5[/tex]
also solving
[tex]=\frac{5!}{1!\left(5-1\right)!}x^4y[/tex]
[tex]=\frac{5}{1!}x^4y[/tex]
[tex]=\frac{5}{1!}x^4y[/tex]
[tex]=\frac{5x^4y}{1}[/tex]
[tex]=\frac{5x^4y}{1}[/tex]
[tex]=5x^4y[/tex]
similarly, the result of the remaining terms can be solved such as
[tex]\frac{5!}{2!\left(5-2\right)!}x^3y^2=10x^3y^2[/tex]
[tex]\frac{5!}{3!\left(5-3\right)!}x^2y^3=10x^2y^3[/tex]
[tex]\frac{5!}{4!\left(5-4\right)!}x^1y^4=5xy^4[/tex]
[tex]\frac{5!}{5!\left(5-5\right)!}x^0y^5=y^5[/tex]
so substituting all the solved results in the expression
[tex]=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5[/tex]
[tex]=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Therefore,
[tex]\left(x\:+y\right)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Jade practices tennis for 3.5 hours. Hayley only spends 0.75 hour practicing
tennis. How much more time does Jade spend practicing tennis than Hayley?
Answer:
2.75 hours
Step-by-step explanation:
3.5-0.75 which is 2.75.
So 2.75 hours.
Hope this helps :D
POINTS AND POINTS AND POINTS. ANSWER ONLY IF U TOOK THE TEST ON K12 AND POST PICTURE OF CORRECT ANSWERS.
The coordinates of the vertices of quadrilateral ABCD are A(−1, −1), B(−3, 3), C(1, 5), and D(5, 2). Drag and drop the choices into each box to correctly complete the sentences. The slope of AB⎯⎯⎯⎯⎯ is Response area, the slope of BC⎯⎯⎯⎯⎯ is Response area, the slope of CD⎯⎯⎯⎯⎯⎯ is Response area, and the slope of AD⎯⎯⎯⎯⎯ is Response area. Quadrilateral ABCD is Response area because Response area.
Answer:
AB=-2
BC=1\2
CD=-3\4
AD=1\2
Step-by-step explanation:
The slope of AB is - 2,
Slope of BC is
Slope of CD is
Slope of AD is ,
ABCD is trapezoid because one pair of opposite sides is parallel.
Answer:
slope of AB: -2
slope of BC: 1/2
slope of CD: -3/4
slope of AD: 1/2
Quadrilateral ABCD is a trapezoid because there is one pair of parallel sides.
Step-by-step explanation:
I solved for the slopes using slope formula. Also, I determined that the quadrilateral was a trapezoid since there was at least one pair of parallel sides. I'm sorry that I don't have a k12 account, but I hope this helps.
Find the area of a compound shape
Can you please explain
Answer:
Bruh the answer is there so uh yea
Step-by-step explanation:bruh sorry for being a little rude.
{17}{15}={10}{2x-2} x =
Answer: 12.85
Step-by-step explanation: If you start off by multiplying them then. You'd get 225=20x-2. So from there you subtract the 2, to isolate the 20x. Then divide bother sides by 20 to get 12.85.
Answer:
The answer is 5.4
Step-by-step explanation:
{17}{15}={10}{2x-2} x =92/17
92/17 rounded to the nearest tenth is 5.4117...
5.4
im late to answer this question but to help people in the future with this same question... here you go x)
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.6 years with a standard deviation of 0.9 years. If a sampling distribution is created using samples of the ages at which 49 children begin reading. What would be the mean of the sampling distribution?
Answer:
The value is [tex]\mu_{x} = 5.6 \ years[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 5.6 \ years[/tex]
The standard deviation is [tex]\sigma = 0.9 \ years[/tex]
The sample size is n = 49
Generally given that the sample size is large enough, the sampling distribution created using the samples of the ages at which 49 children begin reading is equal to the population mean
i.e
[tex]\mu_{x} = \mu[/tex]
=> [tex]\mu_{x} = 5.6 \ years[/tex]
(Ill give brainliest)
Solve 9,396 ÷ 18 = __________ Using partial quotients.
Draw it out
Answer:
522
Step-by-step explanation:
Which equation represents a line that passes through the two points in the
table?
Answer:
C
Step-by-step explanation:
use the points to find the slope (y-y1/x-x1) 3-5/3-6 = 2/3
the answers are all in point slope form so the slope is 2/3 and the point represented is 3,3
Answer: It’s A. Just did it
Step-by-step explanation:
Help a brotha out........
Answer:
it's flipped I guess ♀️
Answer:
6/12 = 1/2
12/6 = 2
you get different answers when the numerator & denominator are flipped
Let be a continuous random variable that follows a normal distribution with a mean of and a standard deviation of . Find the value of so that the area under the normal curve to the right of is . Round your answer to two decimal places.
Complete Question
Let x be a continuous random variable that follows a normal distribution with a mean of 550 and a standard deviation of 75.
a
Find the value of x so that the area under the normal curve to the left of x is .0250.
b
Find the value of x so that the area under the normal curve to the right ot x is .9345.
Answer:
a
[tex]x = 403[/tex]
b
[tex]x = 436.75[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 550[/tex]
The standard deviation is [tex]\sigma = 75[/tex]
Generally the value of x so that the area under the normal curve to the left of x is 0.0250 is mathematically represented as
[tex]P( X < x) = P( \frac{x - \mu }{ \sigma} < \frac{x - 550 }{75 } ) = 0.0250[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P( X < x) = P( Z < z ) = 0.0250[/tex]
Generally the critical value of 0.0250 to the left is
[tex]z = -1.96[/tex]
=> [tex]\frac{x- 550 }{75} = -1.96[/tex]
=> [tex]x = [-1.96 * 75 ]+ 550[/tex]
=> [tex]x = 403[/tex]
Generally the value of x so that the area under the normal curve to the right of x is 0.9345 is mathematically represented as
[tex]P( X < x) = P( \frac{x - \mu }{ \sigma} < \frac{x - 550 }{75 } ) = 0.9345[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P( X < x) = P( Z < z ) = 0.9345[/tex]
Generally the critical value of 0.9345 to the right is
[tex]z = -1.51[/tex]
=> [tex]\frac{x- 550 }{75} = -1.51[/tex]
=> [tex]x = [-1.51 * 75 ]+ 550[/tex]
=> [tex]x = 436.75[/tex]
Deonna is arranging pictures of her trip to Jamaica into a photo album. Twenty percent of her photos are just of her. If Deonna took 200 photos, then how many photos are there of just her in the picture?
Answer:
I think it is 10% but I may be wrong hope this kinda helped
Step-by-step explanation:
Find the equation of a line that has a slope of -3/7 and goes through the point (49,-17)
___ x 2 = 30
12 divided by ___ = 4
Just a practice :)
15 x 2 = 30
12 ÷ 3 = 4
Have a wonderful day!
- Audrey :)
Carter's trampoline has a diameter of 10 ft. Its circumference is twice as great as the circumference of Reed's trampoline. What is the circumference of Reed's trampoline.
Answer:
no
Step-by-step explanation:
nsjdjfhfjskskdknxiwiwfbrbbewiisaksndbbfeueiaooand
A basketball team played 15 games and won 80% of them. If the team expects to play 30 games in all, how many more games must it win to finish the season with a 90% winning percentage?
A. 12
B. 14
C. 15
D. 27
Answer: C
Step-by-step explanation:
multiply 15 x 2
(03.01) Match the two numbers with their least common multiple (LCM). Match Term Definition 8 and 4 A) 24 8 and 6 B) 8 8 and 10 c) 40 Previous Question Question 1 (Not Answered)
Answer:
LCM of 8 and 4 = [tex]8[/tex]
LCM of 8 and 6 [tex]=24[/tex]
LCM of 8 and 10 = [tex]40[/tex]
Step-by-step explanation:
Least common multiple (LCM) of numbers is their smallest common multiple.
First find prime factorization of [tex]4,6,8,10[/tex]
[tex]4=2^2\\6=2(3)\\8=2^3\\10=2(5)[/tex]
LCM of 8 and 4 = [tex]2^3=8[/tex]
LCM of 8 and 6 [tex]=2^3(3)=8(3)=24[/tex]
LCM of 8 and 10 = [tex]2^3(5)=8(5)=40[/tex]
Ricky walked a total of 4 3/4
miles on the school track. He stopped every 1/4
mile to rest.
Rick stopped
times to rest. Round your answer to the nearest whole number, if necessary.
Answer:
19
Step-by-step explanation:
Is he stop every 1/4 mile you get 19
There are 4 1/4 miles in every mile. 4x4(Equation of total 1/4th's in 4 miles) is 16. Add 3 more 1/4th's to get 19
Hope this helps!
Total number of rest is 19 times
Fraction based problem:Given that;
Distance walked by Ricky = 4³/₄ miles = 19 / 4 miles
rest on every mile = 1/4 miles
Find:
Total number of rest
Computation:
Total number of rest = Distance walked by Ricky ÷ Rest on every mile
Total number of rest = [19 / 4] ÷ [1 / 4]
Total number of rest = 19 times
Find out more information about 'Distance'.
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a tank containing 50 liter of water develops a leak and loss water at a constant rate. after 20 minutes it contains 40 liter. after a further 30 minutes the tank is 5% of its full capacity. determine the tanks capacity
Answer:
The tank's capacity is 500 liters
Step-by-step explanation:
Proportions
The tank initially contains 50 liters of water. The tank's capacity is more than that, as we'll show later.
We know after 20 minutes of leaking from the tank, 40 liters still remain. This means 10 liters have leaked in 20 minutes. The loss of water occurs at a constant rate or 10/20=0.5 liters per minute.
After 30 more minutes, the tank has lost 0.5*30 = 15 more liters of water and now has 40 - 15 = 25 liters remaining.
We are told those 25 liters correspond to 5% of the tank's full capacity. Thus, the full capacity of the tank is:
[tex]\displaystyle \frac{25 }{ (5 / 100)} = 500~liters[/tex]
The tank's capacity is 500 liters
The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially. How many grams of the substance are left after 300 years?
Answer:
There are 2,000 grams left after 300 years.
Step-by-step explanation:
Giving the following information:
The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially.
First, we need to calculate the reduction of the substance each year:
Yearly reduction= 8,000/400= 20 grams per year
Now, for 300 years:
300 year reduction= 20*300= 6,000
There are 2,000 grams left after 300 years.
just a tad bit more points :)
Answer:
Thx have a great day :)
Step-by-step explanation:
yoink.
Thank you very much, kind sir/ma'am.
Have a nice day.
The incubation time for Rhode Island Red chicks is normally distributed with a mean of 21 days and a standard deviation of approximately 1 day. If 1000 eggs are being incubated, how many chicks do we expect will hatch?
a. In 19 to 23 days?
b. In 22 days or more?
c. In 21 days or fewer?
d. In 18 to 21 days?
e. In 19 days or fewer?
f. In 19 to 24 days?
g. In 18 to 24 days?
h. In 18 days or more?
Answer:
a - c
Step-by-step explanation:
if standard is 21 days then in incubator will hatch faster or at the same time but with high percentage of hatching a chick (btw hi from rhodes)
HELP PLZ
i need help with this math side i just need b,c,d a =4x+2y=16
Answer:
Please check the explanatio.
Step-by-step explanation:
Solving Part b)
We know that the slope-intercept form of the equation line is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
Given the equation
[tex]4x+2y=16[/tex]
Re-writing the equation in the slope-intercept form
[tex]4x+2y=16[/tex]
[tex]y=-2x+8[/tex]
Here, m=-2 and b=8
Thus, the equation in the slope-intercept form will be:
[tex]y=-2x+8[/tex]
Solving Part c)
As you sold two pounds of cheddar cheese.
i.e. y=2
substituting y=2 in the slope-intercept form of the line equation
[tex]y=-2x+8[/tex]
[tex]2=-2x+8[/tex]
Subtract 8 from both sides
[tex]-2x+8-8=2-8[/tex]
[tex]-2x=-6[/tex]
Divide both sides by -2
[tex]\frac{-2x}{-2}=\frac{-6}{-2}[/tex]
[tex]x=3[/tex]
You sold 3 pounds of swiss cheese.
Solving Part d)
[tex]y=-2x+8[/tex]
putting x=2.5 in the equation
[tex]y=-2x+8[/tex]
[tex]2=-2\left(2.5\right)+8[/tex]
[tex]2=3[/tex]
The sides are not equal
FALSE
Thus, x=2.5 does not make any sense in the context of the problem.
Helpppppppppppppppppppppppppp
The difference between two same side interior angles of two parallel lines is 35 degrees. Find the measures of these two angles.
Answer: 2x+43
Step-by-step explanation:
Answer:
107.5 degrees and 72.5 degrees (Don't forget the degrees symbol)
Please mark me Brainliest if I'm right :D
The grades on a midterm were Normally distributed with a mean of 120 and a standard deviation of 17. The passing score was 111 or higher.
Use the z-table to answer the question.
What percent of students passed the midterm?
70% IS THE ANSWER
Answer:
70% is the correct answer
Step-by-step explanation:
Answer:
70% is correct
At an amusement park, 25 riders ride the race cars every 30 minutes and 20 riders ride the spinning swings every 20 minutes. Which ride will have more riders each hour and how many more? Use the drop-down menus to answer the problem. The Choose... will have Choose... more riders each hour.
Answer:
The spinning swings will have 10 more riders each hour.
Step-by-step explanation:
1. If 25 riders ride the race car every 30 mins, that would mean each hour 50 riders ride the race car.
2. If 20 riders ride the spinning swings every 20 mins, that would mean each hour 60 riders ride the spinning swings.
Lets say 4 hours have passed. We could say 25 × 8. I don't know if this would make sense but there would be 8 30 mins in 4 hours. If you multiply 25 × 8 you would get 200 riders riding the race cars in 4 hours.
Lets do the same thing with the spinning swings. There are 12 20 mins in 4 hours. So we could do could do 20 × 12. That would equal 240 riders riding the spinning swings in 4 hours.
So if the race cars got 200 riders in 4 hours, each hours they will have 50 riders. And If the spinning swings got 240 riders in 4 hours, each hour they got 60 riders. So that would mean the spinning swings got more riders each hour. They also got 10 more riders each hour. Hopefully I didn't confused you.
Natalie drove 12.25 hour for a total of 686 miles. How fast did she drive in miles per hour?
Answer:
step 1= 12.25*60=735minutes
step 2=686/735=0.933333kilometer.
step 3=0.9333333*60=56kilometers.
1 point
Find the slope of each line that passes through the points (4.0) and (7.9),
Answer:
[tex]m=3[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (4, 0)
Point (7, 9)
Step 2: Find slope m
Substitute: [tex]m=\frac{9-0}{7-4}[/tex]Subtract: [tex]m=\frac{9}{3}[/tex]Divide: [tex]m=3[/tex]When is subtraction always the first operation done in an expression?
Answer:
When it is in parentheses.
Step-by-step explanation:
In PEMDAS, first is always parentheses, no matter what operation.
If it is subtraction, do that first.
hope this helped!
Answer:
the 3rd one
Step-by-step explanation:
this is only true when it is in perenthisis because when you do PEDMAS you go in that order. P (perenthisis) beng first. so TECHNECLY perenthisis is first, but the first actual MATH PROBLEM being done is subtraction.
You and your friend skate at the same rate. You complete 6 laps in 5 minutes. How long does your friend take to complete 18 laps?
Answer:
15 minutes
Step-by-step explanation:
Answer:
69
Step-by-step explanation:
haha 69= funny number