Help ASAP!! A triangle has side lengths of 11in, 15in, and 20in. Find the angle measures of the triangle. Round decimal answers to the nearest tenth. Someone help pls.
Answers
Answer:
<A = 47.7°
<B = 99.4°
<C = 32.9
Step-by-step explanation:
When given the measurements of all three sides, you can calculate the angles using the Cosine Law.
c² = a² + b² - 2ab cos C
(based on Pythagorean Theorem)
If we say: a = 15
b = 20
c = 11
11² = 15² + 20² - 2(15)(20) cos C
121 = 625 - 2(15)(20) cos C
121 = 625 - 600 cos C
⁻504 = ⁻600 cos C
cos⁻¹ (504 ÷ 600) = C
< C = 32.9°
a² = b² + c² - 2bc cos A
15² = 20² + 11² - 2(20)(11) cos A
225 = 521 - 2(20)(11) cos A
225 = 521 - 440 cos A
⁻296 = ⁻440 cos A
cos⁻¹ (296 ÷ 440) = A
<A = 47.7°
Then, since we know the sum of all three angles of a triangle equals 180°:
180° - 32.9° - 47.7° = 99.4°
<B = 99.4°
Related Questions
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x^2+10x+7.5 where x is the number of feet away from the sprinkler head (along the ground) the spray is.
The irrigation system is positioned____ feet above the ground to start.
The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.
The spray reaches all the way to the ground at about_____ feet away
Answers
9514 1404 393
Answer:
7.5 ft32.5 ft, 5 ft10.7 ftStep-by-step explanation:
a) The starting height is h(0) = 7.5 feet, the constant in the quadratic function.
The irrigation system is positioned 7.5 feet above the ground
__
b) The axis of symmetry for quadratic ax^2 +bx +c is x = -b/(2a). For this quadratic, that is x=-10/(2(-1)) = 5. This is the horizontal distance to the point of maximum height. The maximum height is ...
h(5) = (-5 +10)(5) +7.5 = 32.5 . . . feet
The spray reaches a maximum height of 32.5 feet at a horizontal distance of 5 feet from the sprinkler head.
__
c) The maximum distance will be √32.5 + 5 ≈ 10.7 ft.
The spray reaches the ground at about 10.7 feet away.
Answer:
7.5
32.5
5
maximum
10.7
Step-by-step explanation:
A family eats out at a restaurant and the total for their meals is $73.89. They also pay sales tax of 5.8% and leave a tip for their server. If the family leaves a total of $93, which of the following might be a description of the service they received?
a.
They left a 10% tip, so the service was probably below average.
b.
They left a 15% tip, so the service was probably average.
c.
They left a 20% tip, so the service was probably above average.
d.
They left a 25% tip, so the service was probably outstanding.
Answers
$73.89 • 5.8% = 4.29
73.89 + 4.29 = 78.18
78.18 • 20% = 15.636 so 15.64
78.18 + 15.64 = 93.82
Hope it helps
The answer is They left a 20% tip, so the service was probably above average.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
First step is to the amount of the sales tax.
If 100% is $73.89,
5.8% will be x (tax):
100% : $73.89 = 5.8% : x.
x = $73.89 * 5.8% : 100%.
x = $4.28.
Now, we have the price for meals, sales tax, and the total amount of money left, so we can calculate how much the tip is:
$93.00 - $73.89 - $4.28 = $14.83.
So, the tip is $14.83.
Let represent it as percent.
If $73.89 is 100%, $14.83 will be x.
$73.89 : 100% = $14.83 : x.
x = $14.83 * 100% : $73.89.
x = 20%.
So, they left a 20% tip, so the service was probably above average.
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If u get a negative answer for exponents is it correct?
Answers
9514 1404 393
Answer:
maybe
Step-by-step explanation:
It can be. It depends on the problem.
__
The rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
Clearly, for division problems if the denominator exponent is larger, the difference 'b-c' will be negative.
__
You recall that an exponent is the way we show repeated multiplication.
x·x·x = x³
In division, like factors cancel, so ...
[tex]\dfrac{x\cdot x\cdot x}{x\cdot x}=\dfrac{x^3}{x^2}=\dfrac{x}{1}\cdot\dfrac{x\cdot x}{x\cdot x}=x^{3-2}=x^1=x[/tex]
Now, consider the same problem "upside down."
[tex]\dfrac{x\cdot x}{x\cdot x\cdot x}=\dfrac{x^2}{x^3}=\dfrac{1}{x}\cdot\dfrac{x\cdot x}{x\cdot x}=x^{2-3}=x^{-1}=\dfrac{1}{x}[/tex]
EXERCISE 3 Date:......... A shop sells a pencil at ¢500.00 and pen at 42,000.00. (a) If Afua bought 8 pencils and 5 pens, how much did she pay altogether for them? (b) The price of a pencil is increased by 20% and a pen by 10%. Find how much she will pay for 10 pencils and 8 pens.
Answers
Answer:
ok so its is 5 dollars for a pencil and 420 dollars for a pen(dang)
a40+2100=2140
now
b6 pencil 462 pen
60+3696=3756
Hope This Helps!!!
(a) Afua paid ¢44,500.00 for 8 pencils and 5 pens.
(b) Afua will pay ¢71,400.00 for 10 pencils and 8 pens after the price increase.
(a) To find how much Afua paid altogether for 8 pencils and 5 pens, we need to calculate the total cost for each item and then add them together.
Given:
Cost of a pencil, [tex]Pencil_{cost}[/tex] = ¢500.00
Cost of a pen, [tex]Pen_{cost}[/tex] = ¢42,000.00
Number of pencils bought, [tex]n_{pencils}[/tex] = 8
Number of pens bought, [tex]n_{pens}[/tex] = 5
Total cost of pencils,
[tex]Total_{pencil}_{cost} = Pencil_{cost} * n_{pencils}[/tex]
= ¢500.00 × 8
= ¢4,000.00
Total cost of pens,
[tex]Total_{pen}_{cost} = Pen_{cost} * n_{pens}[/tex]
= ¢42,000.00 × 5
= ¢210,000.00
Altogether, [tex]Total_{cost} = Total_{pencil}_{cost} + Total_{pen}_{cost}[/tex]
= ¢4,000.00 + ¢210,000.00
= ¢214,000.00.
Therefore, Afua paid ¢214,000.00 for 8 pencils and 5 pens.
(b) Now, let's calculate the new total cost after the price increase.
The price of a pencil increased by 20%, which means the new pencil cost is:
[tex]New_{pencil}_{cost}[/tex] = [tex]Pencil_{cost}[/tex]+ (20% × [tex]Pencil_{cost}[/tex])
= ¢500.00 + (0.20 × ¢500.00)
= ¢500.00 + ¢100.00
= ¢600.00
Similarly, the price of a pen increased by 10%, which means the new pen cost is:
[tex]New_{pen}_{cost}[/tex] = [tex]Pen_{cost}[/tex] + (10% × [tex]Pen_{cost}[/tex])
= ¢42,000.00 + (0.10 × ¢42,000.00)
= ¢42,000.00 + ¢4,200.00
= ¢46,200.00
Now, we can find the total cost for 10 pencils and 8 pens with the increased prices:
Number of pencils to be bought, [tex]n_{pencils}_{new}[/tex] = 10
Number of pens to be bought, [tex]n_{pens}_{new}[/tex] = 8
Total cost of pencils with new prices,
[tex]Total_{pencil}_{cost}_{new}[/tex] =[tex]New_{pencil}_{cost}[/tex] × [tex]n_{pencils}_{new}[/tex]
= ¢600.00 × 10
= ¢6,000.00
Total cost of pens with new prices,
[tex]Total_{pen}_{cost}_{new}[/tex] = [tex]New_{pen}_{cost}[/tex] × [tex]n_{pens}_{new}[/tex]
= ¢46,200.00 × 8
= ¢369,600.00
Altogether, [tex]New_{total}_{cost}[/tex] = [tex]Total_{pencil}_{cost}_{new}[/tex] + [tex]Total_{pen}_{cost}_{new}[/tex]
= ¢6,000.00 + ¢369,600.00
= ¢375,600.00
Therefore, Afua will pay ¢375,600.00 for 10 pencils and 8 pens with the increased prices.
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An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the same rate of speed?
Answers
Answer:
262.5 miles
Step-by-step explanation:
Correct me if I am wrong
URGENT GIVING BRAINLIEST
Answers
A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Treasury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%. Write and graph the system of equations of linear inequalities that describes the possible amounts of each investment.
Answers
Answer:
See Explanation
Step-by-step explanation:
According to the Question,
Given that, A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Treasury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%.
Therefore,
Let, x be the amount of money invested in Treasury bills
y be the amount invested in corporate bonds
Thus, the system of equations of linear inequalities is
x + y ≤ 50000
x ≥ 35000
0 ≤ y ≤ 10000
For, the graph of the system of equations of linear inequalities describes the possible amounts of each investment.
(Please find in the attachment)
If P(E)=0.55, P(E or F)=0.65, and P(E and F)=0.20, find P(F).
P(F)=
(Simplify your answe
Answers
Answer:
.3
Step-by-step explanation:
let x= P(f)
.65= .55+x-.2
P(F)=.3
Can someone help and explain this to me ,much appreciated thankyouuu
Answers
Answer:
A. 2x + 1
Step-by-step explanation:
f(x) = 2x + 7
g(x) = x - 3
To find f(g(x)), substitute x = x - 3 into f(x) = 2x + 7
Thus:
f(g(x)) = 2(x - 3) + 7
f(g(x)) = 2x - 6 + 7
Add like terms
f(g(x)) = 2x + 1
Convert 1.5% to decimal and a fraction. Show and explain your method.
Answers
Answer:
0.015
Step-by-step explanation:
1.5% = means 1.5 per 100 or simply 1.5/100.if you divide 1.5 by 100 you will get 0.015
A license plate consists of a letter, followed by three numbers, followed by another
letter. Due to possible confusion, the letters I and O are not used. Repetition is not
allowed.
How many different license plates are possible?
Answers
This is one single number that's slightly smaller than 400 thousand.
======================================================
Explanation:
There are 26 letters in the english alphabet. We don't use letters i or o, so we have 26-2 = 24 choices for that first slot.
Then we have 10 choices for the second slot because there are 10 single digits 0 (zero) through 9.
After making the selection for the second slot, we have 10-1 = 9 choices left for the third slot. The fourth slot has 10-2 = 8 digits to pick from. The subtraction occurs because we cannot reuse the digits.
Finally, the last slot will be a letter. We have 24-1 = 23 letters left to pick from.
Overall, we have 24*10*9*8*23 = 397,440 different license plates possible.
--------------------
Extra info (optional section)
You may be wondering "why do we multiply those values?". Well consider a simple example of having only 2 slots instead of 5.
Let's say the first slot is a letter A to Z, excluding letters i and o. The second slot will be the digit from 0 through 9.
If you make a table with 24 rows and 10 columns, then you'll have 24*10 = 240 cells overall. Notice the multiplication here. The 24 rows represent each letter, and the 10 columns are the digit numeric digits.
Each inner cell is a different two character license plate. For example A5 is one such plate. This idea can be extended to have 5 characters.
HELP PLEASE!!!!!!!!!!!!!!!
Answers
3 maybe is a correct ans thxxxxxx
Answer:
i think possible the last one...
I'm not sure but i hope you get it correct!
The expression x−y equals 0.7 if x and y have certain values. Evaluate the following expressions with the same values of x and y. What is 1/x-y.
PLEASE HELP FAST I NEED THIS DONE IN 30 MINUTES!!!
Answers
Answer:
10/7 or 1.428571429
Step-by-step explanation:
We know that x-y=0.7
So, now we have the equation 1÷0.7 or 1÷7/10
Meaning, we can multiply by the reciprocal,
And make this equation into 1×10/7= 10/7
ANSWER ASAPPPP PLS
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6
Answers
Answer:
I'm going to help you figure this out because I am actually on the same assignment. If you do not understand what it is asking, it is not asking you to break down the function notation, it is simply asking you to substitute (X) with 2,3,4,5,and 6 and then to solve it on each line
The following figure appears in a math workbook. Students are asked to reflect the polygon across the line, then rotate it 90 degrees clockwise . Which figure shows the result of the two transformations?
Answers
Answer:
C
Step-by-step explanation:
tracing paper is your friend
probability that an individual has 20-20 vision is 0.16. In a class of 90 students, what is the mean and standard deviation of the number with 20-20 vision in the class? Round to the nearest thousandth.
A.
The mean is 90. The standard deviation is 1.1.
B.
The mean is 14.4. The standard deviation is 3.478.
C.
The mean is 90. The standard deviation is 1.2.
D.
The mean is 1.44
Answers
When f(x) = 4 , what is the value of ?
A. 0
B. 2
C. 3
D. 4
Answers
The annual demand for a product is 16,400 units. The weekly demand is 315 units with a standard deviation of 90 units. The cost to place an order is $31.00, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.20 per unit.
a. Find the reorder point necessary to provide a 95 percent service probability.
b. Suppose the production manager is asked to reduce the safety stock of this item by 55 percent. If she does so, what will the new service probability be?
Answers
Answer:
a) The reorder point necessary to provide a 95 percent service probability is 1557 units.
b) The Z value of 0.74 corresponds to 77% service probability.
Step-by-step explanation:
Average weekly demand (d) = 315 units
The standard deviation of weekly demand (\sigmad) = 90 units
Lead time (L) = 4 weeks
At 95% service level value of Z = 1.65
Reorder point = d x L + safety stock
[tex]= d \times L + (Z \times \sigma d \times \sqrt L)\\\\= 315 x 4 + (1.65 x 90 x \sqrt 4)\\\\= 1260 +(1.65 x 90 x 2)\\\\= 1260 + 297\\\\= 1557 units[/tex]
b) Earlier the safety stock was 297 units(calculated in part a)
Now the safety stock is reduced to 55%.so,55% of 297 = 163.35 units
So the new safety stock = 297 - 163.35 = 133.65
[tex]Safety stock = Z \times \sigma d \times \sqrt L\\133.65 = Z x 90 x 2\\133.65 = 180Z\\ Z = 133.65/180\\Z = 0.74[/tex]
The Z value of 0.74 corresponds to 77% service probability.
Simplify:
-5x+6y-9y+4x
Answers
Answer:
-x-3y
Step-by-step explanation:
-5x+6y-9y+4x
-5x+4x+6y-9y
-x-3y
What are the coordinates of vertex F" of ΔF"G"H"?
Answers
Which of the following best describes the histogram?
The histogram is evenly distributed.
The histogram is symmetrical.
The left side of the histogram has a cluster.
The left side of the histogram is the mirror image of the right side.
Answers
Answer:
The left side of the histogram has a cluster.
Step-by-step explanation:
The others don't make since.
It's not evenly distributed,
it's not symmetrical, and
it is definitely not a mirror image of the right side.
Answer:
A
Step-by-step explanation:
PLEASE HELP ME! I am so confused
Answers
Answer:
x = 5.5
Step-by-step explanation:
Based on the Mid-segment theorem of a triangle, we would have the following:
EF = 2(AB)
AB = 7
EF = 2x + 3
Plug in the values
2x + 3 = 2(7)
Solve for x
2x + 3 = 14
Subtract 3 from each side
2x + 3 - 3 = 14 - 3
2x = 11
2x/2 = 11/2
x = 5.5
To determine the organic material in a dried lake bed, the percent carbon by mass is measured at two different locations. To compare the means of the two different locations, it must first be determined whether the standard deviations of the two locations are different. For each location, calculate the standard deviation and report it with two significant figures.
Answers
Answer:
[tex]\sigma_1 = 0.08[/tex] --- Location 1
[tex]\sigma_2 = 0.34[/tex] --- Location 2
Step-by-step explanation:
Given
See attachment for the given data
Required
The standard deviation of each location
For location 1
First, calculate the mean
[tex]\bar x_1 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_1 =\frac{30.40+30.20+30.30+30.40+30.30}{5}[/tex]
[tex]\bar x_1 =\frac{151.60}{5}[/tex]
[tex]\bar x_1 =30.32[/tex]
The standard deviation is calculated as:
[tex]\sigma_1 = \sqrt{\frac{\sum(x - \bar x_1)^2}{n-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{(30.40 - 30.32)^2+(30.20 - 30.32)^2+(30.30 - 30.32)^2+(30.40 - 30.32)^2+(30.30 - 30.32)^2}{5-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{0.028}{4}}[/tex]
[tex]\sigma_1 = \sqrt{0.007}[/tex]
[tex]\sigma_1 = 0.08[/tex]
For location 2
First, calculate the mean
[tex]\bar x_2 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_2 =\frac{30.10+30.90+30.20+30.70+30.30}{5}[/tex]
[tex]\bar x_2 =\frac{152.2}{5}[/tex]
[tex]\bar x_2 =30.44[/tex]
The standard deviation is calculated as:
[tex]\sigma_2 = \sqrt{\frac{\sum(x - \bar x_2)^2}{n-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{(30.10-30.44)^2+(30.90-30.44)^2+(30.20-30.44)^2+(30.70-30.44)^2+(30.30-30.44)^2}{5-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{0.472}{4}}[/tex]
[tex]\sigma_2 = \sqrt{0.118}[/tex]
[tex]\sigma_2 = 0.34[/tex]
A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 3.
Answers
Answer:
0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.
Step-by-step explanation:
We have the mean during an interval, so the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive.
This means that [tex]\mu = 3.3[/tex]
Find the probability that in a randomly selected office hour, the number of student arrivals is 3.
This is P(X = 3). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-3.3}*3.3^{3}}{(3)!} = 0.2209[/tex]
0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.
Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.
Answers
Answer:
[tex]\bar x = 107.11[/tex]
[tex]\sigma_x = 31.07[/tex]
Step-by-step explanation:
See comment for complete question
Given
[tex]x: 97\ 178\ 129\ 90\ 75\ 94\ 116\ 100\ 85[/tex]
Solving (a): The sample mean
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{97+ 178+ 129+ 90+ 75+ 94+ 116+ 100+ 85}{9}[/tex]
[tex]\bar x = \frac{964}{9}[/tex]
[tex]\bar x = 107.11[/tex]
Solving (b): The sample standard deviation
This is calculated as:
[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{(97 - 107.11)^2 +.............+ (85- 107.11)^2 }{9-1}}[/tex]
[tex]\sigma_x = \sqrt{\frac{7720.8889}{8}}[/tex]
[tex]\sigma_x = \sqrt{965.1111125}[/tex]
[tex]\sigma_x = 31.07[/tex]
What is the equation of the line graphed below?
5
- 5
5
(3,-1)
1
-5
O A. y=-3x
1
O B. y = -
O c. y =
C. 5
-X
What is the equation of the line graphed below
Answers
y= mx+ c
m is -1/3
"If a = − 9 and b = − 6, show that (a−b) ≠ (b−a)."
Answers
Answer:
Step-by-step explanation:
LHS a - b = -9 - (-6) = -9 +6 = -3
RHS b-a = -6 - (- 9) = -6 +9 = 3
as LHS not equal to RHS
a-b not equal to b-a
Thus proven
Solve x2 + 4x + 3 = 0 by completing the square.
options:
–6, –1
–3, –1
1, 3
–6, –2
Answers
Answer:
-3,-1
Step-by-step explanation:
x²+4x+3=0
x²+4x=-3
x²+4x+(2)²=-3+(2)²
(x+2)²=-3+4
(x+2)²=1
Take square root of both sides
x+2=±1
x=-2±1
x=-1 or-3
X^2 +4x +3=0
Factorization:
(x+3=0)(x+1)=0
Solution based on top factorization:
X+3=0. X1= -3
X+1=0. X2= -1
Multiply and show work
Answers
Answer:
-15m^10 -38m8+57m^6+98m^4-30m^2
Answer:
jere is your answer i hope it will help u
Select the two values of x that are roots of this equation 2x^2+5x-3=0
Answers
Answer:
A and D are the answer.
Step-by-step explanation:
We can factor this by grouping
[tex]2 {x}^{2} + 5x - 3[/tex]
[tex]2 {x}^{2} + 6x - x - 3[/tex]
[tex]2x(x + 3) -1 (x + 3)[/tex]
The roots are
[tex](x + 3) = 0[/tex]
and
[tex]2x - 1 = 0[/tex]
Let solve for zero in each roots.
[tex]x = - 3[/tex]
[tex]2x = 1[/tex]
[tex]x = \frac{1}{2} [/tex]
