part 5. Use the laws of sines. Please show work. Round to the nearest tenth.
Answer: 17) 41.0° 18) 60.8° 19) 36.0° 20) 19.7°
Step-by-step explanation:
Law of Cosines: a² = b² + c² - 2bc · cos A
b² = a² + c² - 2ac · cos B
c² = a² + b² - 2ab · cos C
17) a = 29, b = 13, c = 21, C = ???
c² = a² + b² - 2ab · cos C
21² = 29² + 13² - 2(29)(13) · cos C
441 = 841 + 169 - 754 cos C
441 = 1010 - 754 cos C
-569 = -754 cos C
[tex]\dfrac{569}{754}=\cos C\\\\\cos^{-1}\bigg(\dfrac{569}{754}\bigg)=C[/tex]
41.0° = C
18) a = 29.3, b = 25.7, c = 16.8, B = ???
b² = a² + c² - 2ac · cos B
25.7² = 29.3² + 16.8² - 2(29.3)(16.8) · cos B
660.49 = 858.49 + 282.24 - 984.48 cos B
660.49 = 1140.73 - 984.48 cos B
-480.24 = -984.48 cos B
[tex]\dfrac{480.24}{984.48}=\cos B\\\\\cos^{-1}\bigg(\dfrac{480.24}{984.48}\bigg)=B[/tex]
60.8° = B
19) a = 12, b = 19, c = 11, A = ???
a² = b² + c² - 2bc · cos A
12² = 19² + 11² - 2(19)(11) · cos A
144 = 361 + 121 - 418 cos A
144 = 482 - 418 cos A
-338 = -418 cos A
[tex]\dfrac{338}{418}=\cos A\\\\\cos^{-1}\bigg(\dfrac{338}{418}\bigg)=A[/tex]
36.0° = A
20) a = 10, b = 9, c = 18, A = ???
a² = b² + c² - 2bc · cos A
100² = 9² + 18² - 2(9)(18) · cos A
100 = 81 + 324 - 324 cos A
100 = 405 - 324 cos A
-305 = -324 cos A
[tex]\dfrac{305}{324}=\cos A\\\\\cos^{-1}\bigg(\dfrac{305}{324}\bigg)=A[/tex]
19.7° = A
Answer:
7) 41.0° 18) 60.8° 19) 36.0° 20) 19.7°
Step-by-step explanation:
Customers at a certain pharmacy spend an average of $54.40, with a standard deviation of $13.50.What are the largest and smallest amounts spent by the middle 50% of these customers?
Answer:
Largest is [tex]x_2 = \$ 63.506[/tex]
Smallest is [tex]x_1 = \$ 45.29[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = \$ 54.40[/tex]
The standard deviation is [tex]\sigma = \$ 13.50[/tex]
The largest and the smallest amount spent by 50% of the costumer is mathematically represented as
[tex]P(x_1 < X < x_2) = P(\frac{ x_1 -\mu}{\sigma } < \frac{X - \mu }{ \sigma } < \frac{ x_2 -\mu}{\sigma } ) = 0.50[/tex]
=> [tex]P(x_1 < X < x_2 ) = P(\frac{x_1 - 54.40}{ 13.50} < X < \frac{x_2 - 54.40}{ 13.50} ) = 0.50[/tex]
Given that this is normally distributed we have that
[tex]P(X <- \frac{x_1 - 54.40}{ 13.50} ) = 0.25[/tex]
and
[tex]P(X < \frac{x_2 - 54.40}{ 13.50} ) = 0.25[/tex]
From the normal distribution curve that z-score having a probability of 0.25 is
0.6745
So
[tex]\frac{x_1 - 54.40}{ 13.50} = -0.6745[/tex]
=> [tex]x_1 = \$ 45.29[/tex]
and
[tex]\frac{x_2 - 54.40}{ 13.50} = 0.6745[/tex]
=> [tex]x_2 = \$ 63.506[/tex]
Suppose we flip a fair coin n times. We say that the sequence is balanced when there are equal number of heads and tails. For example, if we flip the coin 10 times and the results are HT HHT HT T HH, then this sequence balanced 2 times, i.e. at position 2 and position 8 (after the second and eighth flips). In terms of n, what is the expected number of times the sequence is balanced within n flips?
Answer:
Step-by-step explanation:
Given:
fair coin is flipped n times
sequence is balanced when there are equal number of heads and tails
To find:
In terms of n, what is the expected number of times the sequence is balanced within n flips
Solution:
Let C(n,r) be the binomial co-efficient. The sample space has [tex]2^{n}[/tex]
Suppose that n is even because there are equal number of heads and tails and the number of heads and tails is not equal when n is odd.
As the result can be either head or tail so the probability of getting head is 1/2. So the number of these sequences with n/2 head is C(n,n/2) since we choose n/2 out of n to be assigned heads.
As every string sequence is equal chance of occurring so the probability is
C(n,n/2) / [tex]2^{n}[/tex]
Soccer ball specifications require a diameter of 8.65 inches with an allowable margin of error of 0.05 inch.
Use this information to complete these statements.
The equation that can be used to find d, the diameter of a new soccer ball, is
| ____ | = ____
The minimum possible diameter of a soccer ball is ____,
and the maximum possible diameter is ____
Answer:
Equation for new diameter: |d' - 8.65| ≤ 0.05
Minimum possible diameter = 8.60 inches
Maximum possible diameter = 8.70 inches
Step-by-step explanation:
We are told that:
Ball specifications require a diameter (d) = 8.65 inches.
Allowable margin of error = 0.05 inch
Now, since we have a value for the allowable margin of error, it means that the absolute value equation to determine the possible value or the new diameter (d') would be;
|d' - 8.65| ≤ 0.05
Minimum possible diameter = 8.65 - 0.05 = 8.60 inches
Maximum possible diameter = 8.65 + 0.05 = 8.70 inches
What is the lenght of the unknown log in the right triangle?
25 m
b
20 m
O 5 m
5 m
O 745 m
15 m
Calculate the a50 term of the geometric sequence with a28 = 3 and r = -1
Answer:
3
Step-by-step explanation:
multiplying by -1 only changes the number if you're multiplying an odd amount of times, but this time you're going from 28 to 50, so it's even, so the number stays the same.
Find the volume of the solid shown or described. If necessary round to the nearest tenth. What is the volume of the shed?
Answer:
Volume of shed = 38 m³
Step-by-step explanation:
Given:
Length = 5 m
Width = 2 m
Height of wall = 3 m
Height of triangular shed = 1.6 m
Find:
Volume of shed
Computation:
Volume of shed = Volume of walls + Volume of triangular shed
Volume of shed = [lbh] + [1/2][Base area]h
Volume of shed = [(5)(2)(3)] + [1/2][(5)(2)]1.6
Volume of shed = [30] + [8]
Volume of shed = 38 m³
When writing a repeating decimal as a fraction, does the number of repeating decimal digits you use matter? Explain.
Answer:
No
Step-by-step explanation:
If you have a repeating decimal it doesn't matter who many decimal digits there are. Most repeating decimals I have encountered end up converting into a fraction that has a denominator of 9.
Hope This Helps :)
Answer:
It depends
Step-by-step explanation:
It depends on what the repeating decimal is. For instance if the decimal is a repeating 8 then you only have to use one digit. If, however, it is something like .673673673 going on forever you just need however many until it loops again. In this case you would need three, because that is how long the loop is.
A recipe for 24 cookies calls for 6 tablespoons of sugar. Which of the amounts below would be a correct ratio of cookies to sugar if you were to use the recipe?
Answer:
1:4
Step-by-step explanation:
0.25 tablespoons of sugar will be used per cookie
Answer:
4 cookies per tablespoon of sugar
Step-by-step explanation:
24 cookies divided by 6 tablespoons of sugar equal 4 cookies per tablespoon of sugar
If 50 percent of the families in a certain city subscribe to the morning newspaper, 65 percent of the families subscribe to the afternoon newspaper, and 85 percent of the families subscribe to at least one of the two newspapers. What percentage of the families subscribe to both newspapers?
Answer: 30%
Step-by-step explanation:
Given, Percent of families subscribe to the morning newspaper = 50%
Percent of families subscribe to the afternoon newspaper = 65%
Percent of families subscribe to at least one of the two newspapers. = 85%
Now, percentage of the families subscribe to both newspapers = % for morning newspaper + % for afternoon newspaper - % for at least one of the two newspapers
= (50+65 - 85) %
= 30 %
Hence, the percentage of the families subscribe to both newspapers = 30%
Simplify the given expression below: (3 + 4i) + (5 − 2i) (2 points)
Answer:
your answer will be 8+2i
Answer:
8 + 2i.
Step-by-step explanation:
(3 + 4i) + (5 - 2i
= 3 + 5 + 4i - 2i
= 8 + 2i.
please helppppppppp meeeeee
Answer:
2 1/4
Before Simplifying:
9/4
After Simplifying:
2 1/4
Answer: the exact form is 9/4 decimal form is 2.25 and the mixed number form is 2 and 1/4.
Step-by-step explanation:
so take 9/10 and turn 4/10 into 10/10 and the when you divied use KFC and you turn your division sign into a multiplication sign then you just multiply 9/10 and 10/10 and you get 90/40
Then you just take the zero's off and you have 9/4 which equals 2 and 1/4
2 and 1/4 is your answer.
Mr. Adams plans to have a swimming pool built in his backyard. He would like to have
a rectangular section and a square section for the design of his pool
Swimming Pool
- square foot
What is the total area of the swimming pool in square feet?
OF) 105 square units
OG) 26 square units
OH) 80 square units
OJ) 56 square units
Answer
56
Step-by-step explanation:
i do it on usa test prep
Jessica buys ground beef in a 10 pound tube at the store. She spends $19.90 on ground beef. Identify the unit of measure for this problem.
Answer: $1.99
Step-by-step explanation:
PART A: Cost Of Item/ Number of units of measure
Part B: 10 Pound Tube.
Part C: $19.90 / 10 Lb Tube = $1.99
The Unit cost for the ground beef is $1,99
If h(x) = -2x+5/4, find h(x) = 3/4
Answer:
x = 1/4
Step-by-step explanation:
We are given the function as h(x) = - 2x + 5/4. If we have to determine h(x) = 3/4 given this function, let's substitute this value into our function and solve for 'x.' This will be our solution -
3/4 = - 2x + 5/4,
If we subtract 5/4 from either side : - 2x = - 1/2
Now divide either side by - 2 : x = 1/4
Therefore our solution is x = 1/4
Answer:
[tex]x=\frac{1}{4}[/tex]
Step-by-step explanation:
So we have the function:
[tex]h(x)=-2x+\frac{5}{4}[/tex]
And we want to find h(x)=3/4.
So, we want to find the value of x such that h(x) equates to 3/4.
So, substitute 3/4 for h(x):
[tex]\frac{3}{4}=-2x+\frac{5}{4}[/tex]
First, subtract both sides by 5/4. The right will cancel.
[tex]\frac{3}{4}-\frac{5}{4}=-2x+\frac{5}{4}-\frac{5}{4}[/tex]
Subtract on the left:
[tex]-\frac{2}{4}=-2x[/tex]
Reduce on the left:
[tex]-\frac{1}{2}=-2x[/tex]
Now, multiply both sides by -1/2. The right will again cancel:
[tex]-\frac{1}{2}(-\frac{1}{2})=-\frac{1}{2}(-2x)[/tex]
Multiply on the left:
[tex]x=\frac{1}{4}[/tex]
So, for h(x) to be 3/4, the value of x is 1/4.
And we're done!
1. Estimate 6,963 - 3,098. Round each number first.
A about 5,000
B about 4,000
C about 2,000
D about 3,000
Answer:
the answer is 3,765
so the estimate is 4,000
B. About 4,000
At Davidson's Bike Rentals, it costs $22 to rent a bike for 6 hours. How many dollars does it cost per hour of bike use? dollarsperhour
Answer:
$3.66
Step-by-step explanation:
22÷6=3.66666666667 or 3.66
please answer thank you!!
Answer:
C
Step-by-step explanation:
Distribute
-6x + 20 = 15
C
just distribute
hope it helps
-5x² – 2x+10 - x² + 7x +5
Answer:
-6x² + 5x + 15
Step-by-step explanation:
Combine like terms. Like terms are terms with the same amount of variables.
Reorder based on descending powers:
-5x² - x² + 7x - 2x + 10 + 5
(-5x² - x²) + (7x - 2x) + (10 + 5)
(-6x²) + (5x) + (15)
-6x² + 5x + 15 is your answer.
~
One-fourth of a number is five-eighths. Find the number.
Answer:
5/32
Step-by-step explanation:
Since 5/8 x 1/4 = 5/32, that is the answer.
Key Note: When you get this type of question, multiply the second umber by the first.
If there are 90 calories in Three-fourths cup of yogurt, how many calories are in 3 cups of yogurt? 30 calories 202 calories 270 calories 360 calories
Answer:
360 calories
Step-by-step explanation:
you divide 3 by 3/4ths and you get 4. You then multiply 90 by 4 and the solution is 360 calories.
Answer:
360
Step-by-step explanation:
AB = 5x -9; BC= -2x + 12
Answer:
X=-3
Step-by-step explanation:
5x - 9
-2x + 12
(+) (-)
7x = -21
X= -3
plz mark ice bear as Brainliest
2. A laser printer prints 200 pages in 4
minutes. How many pages does it print in 25
minutes?
А
1000
800
2
1250
1050
Answer: I think the answer is 1250.
Step-by-step explanation:
I did 200 divided by 4 which is 50. I then multiplied 50 * 25 and got 1250.
Determine the input that would give an output value of 2/3.
Answer:1/6 is the answer
Step-by-step explanation: I have done this befor.
Answer: x = 19
Step-by-step explanation:
Value of 3 in 6300 is what times the value of 3 in 530
Answer:
Value of 3 in 6300 is 10 times the value of 3 in 530
Step-by-step explanation:
3 in 6300=hundreds place
3 in 530=tens place
Therefore 10 times
3w – 15
Factoring out the GCF
The factored form of 3w - 15, after factoring out the Greatest Common Factor, is 3(w - 5).
To factor out the greatest common factor (GCF) from the expression 3w - 15, we first need to determine the GCF of the two terms.
In this case, the GCF of 3w and 15 is 3. Both terms are divisible by 3.
To factor out the GCF, we divide each term by the GCF:
3w/3 - 15/3
Simplifying further, we have:
w - 5
Therefore, the factored form of 3w - 15, after factoring out the GCF, is 3(w - 5).
Factoring out the GCF is a process that involves identifying the highest common factor of all the terms in an expression and dividing each term by that factor. This helps simplify the expression and can make it easier to work with or further factorize if needed.
In this case, the GCF was 3, so we divided both terms by 3 to factor it out, resulting in the simplified expression w - 5.
To learn more about the greatest common factor;
https://brainly.com/question/11221202
#SPJ6
The complete question:
Find out the factored form of the following expression,
3w – 15
Factoring out the GCF
Demonstrate your knowledge of probability here. If you were to spin the spinner and roll the die below….. What is the P(green or 5)?
Answer:
P= any number or color
Step-by-step explanation:
because there is all sorts of cobinations.
But the most possible one is
Red for the spinner and any number for the die.
possible answers.
red:1
Red:2
Red:3
Red:4
Red:5
Red:6
Brainly please
A soup recipe calls for 6 chopped onions. You want to make of the recipe. How many onions will you need?
Answer:
6?
Step-by-step explanation:
??????????????????????????????????????????Is confoosed
Is easy?
Answer:
six
Step-by-step explanation:
bc if u need 6 chopped onions it still means 6 onions just u chop them
Which algebraic rule for a rotation describes the change in coordinates: G(5, -1) to G' (-5, 1)?
Answer:
Rotate 180 degrees around (0,0) or flip y axis and then x axis
If someone rode for 2 hours at 3 miles per hour, how far would they go?
Answer:
Six miles
Step-by-step explanation:
You multiply the two by the three (2x3) and get six (6)