Answer:
¼(√6 + √2)
Step-by-step explanation:
We want to find cos (π/12) in surd form.
Now, cos (π/12) can be expressed as;
cos [(π/4) - (π/6)]
Now, from trig derivations we know that;
Cos (A - B) = CosACosB + sinAsinB
Thus;
cos [(π/4) - (π/6)] = cos(π/4)Cos(π/6) + sin(π/4)sin(π/6)
Now, in surd form;
cos(π/4) = sin(π/4) = (√2)/2
Cos(π/6) = (√3)/2
sin(π/6) = 1/2
Thus, Plugging in relevant values to get;
cos(π/4)Cos(π/6) + sin(π/4)sin(π/6) = ((√2)/2 × (√3)/2) + ((√2)/2 × 1/2)
This gives;
((√6)/4) + ((√2)/4) = ¼(√6 + √2)
4 (n-4) + 14
n = 5 btw
Answer:
=18
Step-by-step explanation:
5-4=1
1x4=4
4+14=18
hope it helped
9(2+2p) show distributive property
Answer:
9(2+2p)
9 x2 + 9 x 2p
18 +18p
Do
5 cm
5 cm
20 cm
form a triangle
Answer:
Step-by-step explanation:
No. If two sides are 5cm the third side must be less than 2(5)=10cm
Answer: No, a triangle cannot be formed with these side lengths.
=========================================================
Explanation:
Recall that the triangle inequality theorem says that for a triangle to be possible, the sum of any two sides must be larger than the third side.
With these given side lengths, we can see that 5+5 = 10 is not larger than 20, so a triangle is not possible here. I recommend you try it out with 3 slips of paper of these lengths. You should find that the two 5 cm sides are too short to be able to connect to the 20 cm side properly.
Kristin wants to buy a pair of jeans that cost $35 and are on sale
20% off. She is also buying two T-shirts at a full price of $9.99 each.
She must pay 6.5% sales tax. How much will she pay for the clothes
Answer:
$51.10
Step-by-step explanation:
First, find 20% of $35, then add the sale price of the jeans and the two t-shirts. Take the total and find the sales tax and add that onto the cost.
100 - 20 = 80 If you multiply the jeans by 80% it gives you the price for the jeans saving you from having to subtract the discount from the original price.
35 * 0.80 = $28.00 jeans 28.00 47.98
9.99 + 3.12
+ 9.99 $51.10
47.98
X 0.065
$3.12
The following table shows a proportional relationship between j and m.
write an equation to describe the relation between j and m
Answer:
m=3/4 j or m = .75j
Step-by-step explanation:
i need help with this down below
Answer:
hi the answer is elven twelths or 11/12
Step-by-step explanation:
first you multiply 1/8 x 2/3 which is 1/12 +5/6= 11/ 12. because you cant simplify it anymore
hope this help
What is the area of a parallelogram with a height of 8 feet and a base of 12.5 feet?
41 ft 2
96.5 ft 2
50 ft 2
100 ft 2
Answer:
Option D- 100 ft 2
Step-by-step explanation:
Area = h x b
= 12.5 x 8 = 100 ft 2
I hope im right!!!
Can anyone locate the coordinates for every letter in the graph?
Answer:
A = 2,3
B = -4,-1
C = 3,0
D = -5,4
E = 1,-6
F = 0,-4
what is y=− 2/9 x+2 written in standard form?
Answer:
2x+9y=18
Step-by-step explanation:
Distribute the denominator
y=-2/9x+2
9y=-2x+2
9y+2x=2
im sorry if this is wrong
Pleaseeee help meeeeeeeee
Answer:
A. m = -6
Step-by-step explanation:
find the value of w and then x. round side lengths to the nearest tenth and angle measures to the nearest degree
Answer:
w = 7.7 units; x = 44°
Step-by-step explanation:
20 points!!!Please help HURRY!!!
Answer:
Definitely not!
Step-by-step explanation:
It was reflected across the x axis, resized and moved in x and y directions, but since the shape ABCD is symmetrical across the y axis, a reflection across y axis won’t change anything!
Lara draws some triangle models with the measurements she wants to use to construct them. Which of these
triangle constructions would NOT be possible?
a triangle with side measurements of 3, 4, and 6 inches
a triangle with side measurements of 2, 3, and 5 inches
a triangle with side measurements of 3, 3, and 4 inches
a triangle with side measurements of 5, 5, and 5 inches.
Answer:
a triangle with side measurements of 5, 5, and 5 inches
Step-by-step explanation:
I took the test.
Construction of triangle with side measurement 2 inch, 3 inch, 5 inch is not possible.
What is triangle equality theorem?This theorem simply states that the sum of two sides of a triangle must be greater than the third side. If this is true for all three combinations, then you will have a valid triangle.
If triangle has the sides, a , b and c then
a + b > c
b + c > a
a + c > b
Given length of the sides,
a) Triangle made with sides having length 3 inch, 4 inch, 6 inch.
3 + 4 > 6 ; 4 + 6 > 3 ; 3 + 6 > 4
= 7 > 6 ; 10 > 3 ; 9 > 4
Triangle inequality theorem is satisfied, hence triangle construction is possible
b) Triangle made with sides having length 2 inch, 3 inch, 5 inch.
2 + 3 > 5 ; 3 + 5 > 2 ; 2 + 5 > 3
= 5 = 5 ; 8 > 3 ; 7 > 3
Triangle inequality theorem is not satisfied, hence triangle construction is not possible
a) Triangle made with sides having length 3 inch, 3 inch, 4 inch.
3 + 3 > 4 ; 3 + 4 > 3 ; 3 + 4 > 3
= 6 > 4 ; 7 > 3 ; 7 > 3
Triangle inequality theorem is satisfied, hence triangle construction is possible
a) Triangle made with sides having length 5 inch, 5 inch, 5 inch.
5 + 5 > 5 ; 5 + 5 > 5 ; 5 + 5 > 5
= 10 > 5 ; 10 > 5 ; 10 > 5
Triangle inequality theorem is satisfied, hence triangle construction is possible.
Hence, Triangle with side measurements of 2 inch , 3 inch , and 5 inch is not possible to construct.
Learn more about triangle inequality theorem here:
https://brainly.com/question/30066983
#SPJ6
Two weeks ago price was $220 now it's $325. What is the percent increase? What is percent increase if there is an additional $50 baggage fee with the new ticket price?
Answer:
68.18%
Step-by-step explanation:
325+50=375
375-220=155
155÷220×100%
≈68.18%
Which expression is equivalent to −14x+12?
−14(x+2)
14(−x+12)
14(−x+2)
−14(−x+12)
Step-by-step explanation:
[tex] = - 14x + 12[/tex]
[tex] = - 2 \times 7x + ( - 2) \times 6[/tex]
[tex] = - 2(7x - 6)[/tex]
No Option Solution.
the area of a square plot is 1600m². the side of the plot is
Answer:
2800m2
12345667888888
Answer:
400m squared
Step-by-step explanation:
so a square has 4 EVEN sides.. 16 divide 4 is 4 just add the zeros..
Mhanifa please help me with this! I need it done ASAP! I will mark brainliest
Answer:
[tex]1) \to \: B \\ 2) \to A[/tex]
Answer:
The third one
Step-by-step explanation:
a sporting goods manufacturer requires 2/5yd of fabrick to a pair of soccer shorts how many shorts can be made from 4yd of fabric
Answer:
10 pair of soccer shorts.
Step-by-step explanation:
Let the unknown be x.
Translating the word problem into an algebraic equation, we have;
2/5 yard = 1 pair of short
4 yard = x pair of short
Cross-multiplying, we have;
2x/5 = 4
Multiplying both sides by 5, we have;
2x = 20
x = 20/2
x = 10 pair of soccer shorts.
The mean diameter of the rim of Honda tires is 16 inches. Assume that the standard deviation of diameter of the rims is 0.3 inches. For quality control purposes, the diameter of the rims of 9 tires is measured every hour. The manager applies the rule that if the mean of diameter of a rim is greater or equal to 16.25, and lesser or equal to 15.75, the manufacturing should be stopped. If the diameter is between 15.75 and 16.25, the manufacturing process is not to be disturbed. a. Calculate the probability of stopping the manufacturing when the sample mean is 16 inches. b. Calculate the probability of stopping the manufacturing in case the mean is shifted to 16.05 inches. c. Calculate the probability of not disturbing the manufacturing if mean shifts to 16.25 inches.
Answer:
a. 0.0124 = 1.24% probability of stopping the manufacturing when the sample mean is 16 inches.
b. 0.0241 = 2.41% probability of stopping the manufacturing in case the mean is shifted to 16.05 inches.
c. 0.5 = 50% probability of not disturbing the manufacturing if mean shifts to 16.25 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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].
Assume that the standard deviation of diameter of the rims is 0.3 inches. Samples of 9.
This means that [tex]\sigma = 0.3, n = 9, s = \frac{0.3}{\sqrt{9}} = 0.1[/tex]
a. Calculate the probability of stopping the manufacturing when the sample mean is 16 inches.
Here we have [tex]\mu = 16[/tex]
Higher than 16.25:
This is 1 subtracted by the pvalue of Z when X = 16.25. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{16.25 - 16}{0.1}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
Lower than 15.75:
This is the pvalue of Z when X = 15.75. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15.75 - 16}{0.1}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
Probability of stopping:
2*0.0062 = 0.0124
0.0124 = 1.24% probability of stopping the manufacturing when the sample mean is 16 inches.
b. Calculate the probability of stopping the manufacturing in case the mean is shifted to 16.05 inches.
Here we have [tex]\mu = 16.05[/tex]
Higher than 16.25:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{16.25 - 16.05}{0.1}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
Lower than 15.75:
This is the pvalue of Z when X = 15.75. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15.75 - 16.05}{0.1}[/tex]
[tex]Z = -3[/tex]
[tex]Z = -3[/tex] has a pvalue of 0.0013
Probability of stopping:
0.0228 + 0.0013 = 0.0241
0.0241 = 2.41% probability of stopping the manufacturing in case the mean is shifted to 16.05 inches.
c. Calculate the probability of not disturbing the manufacturing if mean shifts to 16.25 inches.
Between 16.25 and 15.75 with [tex]\mu = 16.25[/tex]. This is the pvalue of Z when X = 16.25 subtracted by the pvalue of Z when X = 15.75.
X = 16.25
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{16.25 - 16.25}{0.1}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
X = 15.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15.75 - 16.25}{0.1}[/tex]
[tex]Z = -5[/tex]
[tex]Z = -5[/tex] has a pvalue of 0
0.5 - 0 = 0.5
0.5 = 50% probability of not disturbing the manufacturing if mean shifts to 16.25 inches.
Pls help me with math ASAP
Answer:
y = 5/2x - 5
Step-by-step explanation:
y-int = -5
slope = 5/2
rise/run
alright my friend i've gotta go but i think you can solve these on your own.
just use the number that's on the Y vertical line to find y-int
and then use 2 points and count up to find the rise and then count across to fine thet run.
use the formula y=mx+b
good luck my friend <3
Answer:
Step-by-step explanation:
(0,-5) (4,5)
(5+5)/(4-0)= 10/4 = 5/2
y + 5 = 5/2(x - 0)
y + 5 = 5/2x - 0
y = 5/2x - 5
Meliyah is an administrative assistant. She earns a weekly salary of $412.00. She applied and was hired for an administrative specialist position. Meliyah’s annual salary in her new position will be $24,388.00. How much will Meliyah’s weekly salary be in her new position?
Answer:
[tex]Weekly\ Salary = \$469[/tex]
Step-by-step explanation:
Given
[tex]Current = \$412.00[/tex] --- weekly
[tex]NEw = \$24.388.00[/tex] --- annually
Required
Determine her new weekly salary
To do this, we simply divide her salary by 52 (the number of weeks).
So, we have:
[tex]Weekly\ Salary = \frac{\$24,388.00}{52}[/tex]
[tex]Weekly\ Salary = \$469[/tex]
Her weekly salary is $469
can someone help me?
Answer:
21
Step-by-step explanation:
Determine the center of the circle whose equation is (x – 5)2 + (y + 7) = 14
Answer:58 approximately c
Step-by-step explanation:
a stadium with 80 rows has 20 seats in the first rows,30 in the second,and so on.how many total seats are in the stadium
Sydney needs $450 to buy a TV for her room.she already saved $50. She earns $20 an hour at her job.set up and solve an equation to find how many hours she needs to work to buy the TV.
Select all that apply.
Which graphed lines represent direct variation functions?
line a
line 6
linec
lined
Answer:
C and D
Step-by-step explanation:
If a square has a side of (3x+5), what is its perimeter?”
O
a.6x + 10
b.3x + 15
c.123 + 5
d.123 + 20
Answer:
Step-by-step explanation:
The perimeter of a square is four times a side. We are told a side equals 3x+5 so
P=4S
P=4(3x+5)
P=12x+20
if right answer good review
Answer:
Top left: a is negative and p is positive
Step-by-step explanation:
The formula y = ax + p is referring to the formula y = mx + b where m is the slope and b is the y-intercept.
Since the line is going down, the slope is negative-- a is negative.
Since the line crosses the y-axis above the origin, the y-intercept is positive-- p is positive.
Answer:
a is negative and p is positive
Step-by-step explanation:
The equation y = ax + p is written in slope-intercept form, where a is the slope and p is the y-intercept.
When a slope is negative, the line goes down the further right it goes.
The line on the graph lowers as it moves right, which means that the slope(a) is negative.
The line intercepts the y-axis above the origin, which means that it must be positive.
Fossils show that
insects were much larger around 300 million
years ago than they are today. The table at
the right shows some of the wing lengths
found in fossils. How much longer was the
wing length of the dragonfly than the wing
length of the fly?
Answer:
The wing of the dragonfly was 9.65 cm longer than that of the fly, 102% larger in percentage terms.
Step-by-step explanation:
Since the length of the wing of the old dragonfly was 19.5 cm, while the length of the wing of a common fly is 9.85 cm, to determine how long the dragonfly's wing was compared to that of the fly, the following must be done calculations:
19.5 - 9.85 = X
9.65 = X
Thus, the wing of the dragonfly was 9.65 cm longer than that of the fly. In turn, in terms of percentages, the result is the following:
9.65 = 100
19.5 = X
19.5 x 100 / 9.65 = X
1950 / 9.65 = X
202 = X
Thus, in percentage terms, the dragonfly's wing was 102% larger than that of the current fly.
need help with this triangle problem
Its an acute triangle by angles.
Its a NONE by sides.