SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given sides
\(\begin{gathered} a=7.3in \\ b=13.2in \\ c=15.8in \end{gathered}\)STEP 2: Write the formula to calculate the missing angles
To get the missing angles, we use the cosine laws and sine laws stated below:
\(\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ b^2=a^2+c^2-2ac\cos B \\ c^2=a^2+b^2-2ab\cos C \\ \\ Sine\text{ law:} \\ \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{sinC}{c} \end{gathered}\)STEP 3: Use the cosine law to find the angle A
\(\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ Making\text{ sin A the subject of the formula, we have:} \\ -2bc\cos A=a^2-b^2-c^2 \\ \sin A=\frac{a^2-b^2-c^2}{-2bc} \\ \\ By\text{ substitution,} \\ \cos A=\frac{7.3^2-13.2^2-15.8^2}{-2(13.2\times15.8^)} \\ \cos A=\frac{-370.59}{-417.12}=0.888449367 \\ A=\cos^{-1}0.888449367 \\ A=27.3209628 \\ A\approx27.3^{\circ} \end{gathered}\)Angle A = 27.3 degrees
STEP 4: Find Angle B
Using sine rule, we have:
\(\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ By\text{ substitution,} \\ \frac{\sin27.3}{7.3}=\frac{\sin B}{13.2} \\ By\text{ cross multiplication,} \\ sinB\times7.3=sin27.3\times13.2 \\ sinB=\frac{\sin27.3\times13.2}{7.3} \\ \sin B=0.82933892 \\ B=\sin^{-1}0.82933892 \\ B=56.0308892 \\ B=56.1^{\circ} \end{gathered}\)STEP 5: Calculate the Angle C
Recall that the sum of angles in a triangle is 180 degrees, therefore,
\(\begin{gathered} A+B+C=180^{\circ} \\ By\text{ substitution,} \\ 27.3^{\circ}+56.1^{\circ}+C=180^{\circ} \\ C=180^{\circ}-27.3^{\circ}-56.1^{\circ} \\ C=180^{\circ}-83.4=96.6^{\circ} \end{gathered}\)Hence, the angles are:
\(A=27.3^{\circ},B=56.1^{\circ},C=96.6^{\circ}\)OPTION A
Help pleaseeeeeee!!!!!!
Answer:
1. 3x7
2. 4A
3. 2M
4. 4X
5. 7D (left) 7x4 (right)
6. 2Y (left) 3Y (right)
Step-by-step explanation:
very simple for me, just take the variable or number on the left or right and multiply by the number on the top or bottom. And for problems with 2 variables do 2X or 2Y whatever the variable may be. Hope this helped
What is the range of the function f(x)=2x^3−3x for the domain {−1, 1, 2}?
The range of the function is {1,-1,10} for function f(x)=2x³−3x .
What is a function?A relation is a function if it has only One y-value for each x-value.
In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.
The given function is f(x)=2x³−3x
The domain is {-1,1,2}
Now f(-1)=2(-1)³-3(-1)
=-2+3=1
f(1)=2(1)³-3(1)=2-3=-1
f(2)=2(2)³-3(2)=16-6=10
Hence, the range of the function is {1,-1,10} for f(x)=2x³−3x .
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I am stuck on this step.
You will earn at least $1 million per day for a period of 43.8 weeks.
How to obtain the earnings?The quadratic function in this problem is defined as follows:
f(x) = -0.06x² + 3.75x - 4.87.
The variables of the function are given as follows:
x is the number of weeks after launch.f(x) is the number of people playing the game, in millions.You charge $0.04 per user each day, hence the number of users that you need to earn $1 million per day is given as follows:
0.04n = 1
n = 1/0.04
n = 25 million users.
Hence the quadratic equation that we have to solve to find if you ever earn $1 million a day is of:
-0.06x² + 3.75x - 4.87 = 25
0.06x² - 3.75x + 29.87 = 0.
Which has the coefficients given as follows:
a = 0.06, b = -3.75, c = 29.87.
Using a quadratic equation calculator, the solutions are given as follows:
x = 9.3 weeks.x = 53.1 weeks.These are real values, meaning that you will earn at least $1 million per day for a period.
This is a concave down quadratic function, hence the period that you will earn at least $1 million per day is given by the subtraction of the roots, as follows:
53.1 - 9.3 = 43.8 weeks.
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find the area of a rectangle with a length of 10 inches and a width of 4 inches
Answer:
40 in²---------------------
Formula for area of a rectangle with dimensions l and w is:
A = lwSubstitute 10 for l and 4 for w:
A = 10*4A = 40 in²If the water park is open fo 9 hours each day, how many passengers can go on the ride
Answer: I would say about 63
Step-by-step explanation:
Well I know this because if the water park is opened everyday for 9 hours you can simply do 9*? Which gives you the answer of 63(like for example 7 days equals a week) but since I’m lazy to multiply it every time to a year I just did a week)
2 + 2 = ?
I'm so confused, HELP!!!
fun fact: ΜΟΜ in Greek means LOL apparently
Answer:
4
Step-by-step explanation:
Answer:
22 dude everybody knows that cmon....
Step-by-step explanation:
Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x)= 1= ² + 4
X-4
To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:
\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)
To simplify this expression, we can expand the square:
\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)
Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)
Next, let's find g(f(x)). We substitute f(x) into the function g(x):
\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)
Hence, g(f(x)) simplifies to 1/x^2.
In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.
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Which is NOT a line of symmetry?
1
2
3
4
Help please what is this answer
Answer: there is nothing
Step-by-step explanation: there is nothing to see so if there is no photo nobody can help you. Sorry
Use formulas to find the greatest four consecutive
numbers whose sum is less than 1,000.
Answer:
The greatest four consecutive numbers whose sum is less than 1,000 are 248, 249, 250, and 251.
Step-by-step explanation:
Let x be the smallest integer. Then:
x + x + 1 + x + 2 + x + 3 < 1,000
4x + 6 < 1,000
2x + 3 < 500
2x < 497
x < 248.5, so x = 248
So we have the integers 248, 249, 250, and 251.
I need to find side x in its simplest radical form using the special right triangles method
Answer:
\sqrt{6}
Explanation:
From the given diagram,
Hypotenuse sde = x
Opposite side = \sqrt{3}
Using the SOH CAH TOA identity
Sintheta = opposite/hypotenuse
Sin 45 = \sqrt{3}/x
x = \sqrt{3}/sin45
\(\begin{gathered} x\text{ =}\frac{\sqrt[]{3}}{\sin 45} \\ x\text{ = }\frac{\sqrt[]{3}}{\frac{1}{\sqrt[]{2}}} \\ x\text{ = }\sqrt[]{3^{}}\cdot\sqrt[]{2} \\ x\text{ =}\sqrt[]{6} \end{gathered}\)Hence the value of x is \sqrt{6}
2.1. Provide a general rule to describe the relationship between the dates of spread and number of people infected infected.
The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.
However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.
This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.
As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.
It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.
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A rectangle has a length of 38 meters less than 8 times its width. If the area of the rectangle is 4050 square meters, find the length of the rectangle.
Let
width be x Length=8x-38Area=4050m^2We know
\(\boxed{\sf Area =Length\times Width}\)
\(\\ \sf\longmapsto x(8x-38)=4050\)
\(\\ \sf\longmapsto 8x^2-38x=4050\)
\(\\ \sf\longmapsto 8x^2-38x-4050=0\)
By solving\(\\ \sf\longmapsto x=\dfrac{81}{4}\:or\:x=25\)
Take x as 25\(\\ \sf\longmapsto Length=8x-38=8(25)-38=200-38=162m\)
Royce kept track of the inches of snowfall in his town over a 15-day period. Royce’s data is given below. 1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3 Which box plot shows this data set?
Answer:
The correct option - Figure A
Step-by-step explanation:
The exact question is as follows :
Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.
1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3
To find - Which box plot shows this data set?
Solution -
Given the data is -
1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3
Firstly,
Arrange the data from smallest to largest
0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7
Now,
Find the median
Median is the middle value - i.e. (15 + 1)/2 = 8th value
So, we get Median = 2
Now,
Find the Quartile -
The first quartile is the median of the data points to the left of the median.
i.e. Median of 0, 0, 0, 0, 0, 1, 1
so, we get
Q1 = 0
The third quartile is the median of the data points to the right of the median.
i.e. Median of 2, 2, 2, 3, 3, 5, 7
so, we get
Q3 = 3
Now,
Compute the min and the max
Minimum value = 0
Maximum value - 7
So,
five number summary is -
0, 0, 2, 3, 7
And we draw the box as follows -
So,
The correct option - Figure A
How many pounds of butterfat are in one gallon of whole milk that weighs approximately 8.6 lb. And contains about 4% butterfat
Answer:
Below
Step-by-step explanation:
8.6 lb x 4 % fat = 8.6 x .04 = .344 lb fat
Write these numbers from least to greatest.
0.8
0.9
7/8
5/6
Answer:
0.8 5/6 7/8 0.9
Step-by-step explanation:
5/6 is 0. 83
7/8 is 0.875
Answer: 0.9,0.8,7/8 , 5/6
Find the value of x, y, and z in the parallelogram below.
(-y-10)⁰
(-4x-1)⁰
75°
(4z-3)°
The values of x, y, and z of the parallelogram are -19°, -115° and 27°
What is a parallelogram?A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. The Sum of adjacent angles of a parallelogram is equal to 180 degrees.
for a parallelogram opposite angles are equal
-4x -1 = 75
-4x = 76
x = 76/-4
x = -19°
sum of adjacent angles are supplementary
(-y-10) + 75 = 180
-y + 65 = 180
-y = 180 - 65
-y = 115
y = -115°
Also
4z - 3 + 75 = 180
4z + 72 = 180
4z = 180 - 72
4z = 108
z = 108/4
z = 27°
In conclusion, the values of x = -19, y = -115, z = 27
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Find x to the nearest tenth
Answer: 0.20
Step-by-step explanation:
A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
\(f(x) = \lambda e^{-\lambda x}\)
And the cumulative distribution function (CDF) is,
\(CDF = 1 - e^{-\lambda x}\)
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
The price of an airline ticket was $320, and it is now $400. What is the percent increase in the price of the ticket?
================================================
Work Shown:
A = old price = 320
B = new price = 400
C = percent change
C = [ (B-A)/A ] * 100%
C = [ (400-320)/320 ] * 100%
C = (80/320)*100%
C = 0.25*100%
C = 25%
The positive C value indicates a percent increase.
--------------------------------
A slightly alternative method:
A = old price = 320
B = new price = 400
C = change in price
C = B-A
C = 400-320
C = 80 is the price increase
D = percent change
D = (C/A)*100%
D = (80/320)*100%
D = 0.25*100%
D = 25%
We get the same result as before.
I NEED HELP PLS HURRY
1. Write each expression with a single exponent:
a. (10^7)²
b. (10^9)³
c. (10^6)³
d. (10^2)³
e. (10³)²
f. (10^5)^7
Answer:
We use the rule,
\((a^b)^c = a^{bc}\)
a. (10^7)²
\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)
10^14
b. (10^9)³
\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)
10^27
c. (10^6)³
\(10^{(6)(3)}= 10^{18}\)
10^18
d. (10^2)³
\(10^{(2)(3)} = 10^{6}\)
10^6
e. (10³)²
\(10^{(3)(2)}=10^{6}\)
10^6
f. (10^5)^7
\(10^{(5)(7)} = 10^{35}\)
10^35
Step-by-step explanation:
Bottles of sparkling water usually cost $1.69 each. This week they are on sale for 4 for $5. You bought one last week and one this week. Did you pay more or less for the bottle this week?
Answer: You payed less this week because if you divide 5 divided by 4 you get $1.25 for a bottle and last week you payed $1.69 so overall you saved money this week than last week
Step-by-step explanation: Read Above
Answer: You paid $0.44 less for the bottle this week than last week.
Step-by-step explanation: You paid $0.44 less for the bottle this week than last week.
In order to know if you paid more or less than you did the week before for the water, you need to find the unit cost this week.
This week you could buy 4 bottle for $5 which means that the effective cost of one bottle is:
= Cost / Number of bottle
= 5 / 4
= $1.25 per bottle
Last week you paid $1.69 for the bottle but this week you paid $1.25.
Difference is:
= 1.69 - 1.25
= $0.44
In conclusion, you paid $0.44 less for the bottle this week than the last week.
©C a r n e g ie L e a r n in g 6.1 Picture Algebra • 3093. The members of a small town’s local arts council are selling raffle tickets. The art council decides that the top three raffle ticket sellers will share a portion of the profits. The second-place seller will receive twice as much as the third-place seller. The first-place seller will receive $20 more than second-place seller. How much will each of the top three sellers receive if the profit portion they will share is $200?
Answer:
1st - $92
2nd - $72
3ed - $36
Step-by-step explanation:
save 20 dollars for first place, because they are going to get that no matter what.
200 - 20 = 180
we'll need to divide 180 into 5 parts, one for 3ed place, two each for 1st and second.
180 / 5 = 36
3ed place gets $36
2nd gets twice that, $72
1st gets the same as 2nd +$20, so $92
to check our answer, add up all their profit and make sure it's 200 even.
Round $5.760,000,000,000 to the nearest hundred billion
Answer:
5,800,000,000,000
hope this helps
have a good day :)
Step-by-step explanation:
This may be hard to put together, but I need help with an angle equation. I'm looking for example equations and how to do these types of equations. *please note that this equation is completely random and probably ends with an ugly number. it's just an example of a type of problem*
Example: (2x - 4) x=7 so (2x (x=7) - 4) =18
Jack, Evan and Molly share somo money in the ratio 5:9:6 In total, Jack and Molly receive $77 Work out the amount of money that Evan receives.
Answer:
$63
Step-by-step explanation:
Find out the total amount of units that Jack and Molly have.
5 + 6 = 11
11 units = $77
Find out 1 unit to be able to find out how much Evan receives.
1 unit = $77 ÷ 11 = 7
Evan has 9 units, so find out how much money is 9 units.
9 units = 7 x 9 = $63
The function p(x) is an odd degree polynomial with a negative leading coefficient.
If q(x)=x^3+5x^2-9x-45, which statement is true?
A. As x approaches negative infinity, p(x) approaches positive infinity and q(x) approaches negative infinity.
B. As x approaches negative infinity, p(x) and q(x) approach positive infinity.
C. As x approaches negative infinity, p(x) and q(x) approach negative infinity.
D. As x approaches negative infinity, p(x) approaches negative infinity and q(x) approaches positive infinity.
Which is bigger 6.8" or 6.52"
Answer:
6.8 is bigger than 6.52
53 POINTS!!!!!!!!!!!!!
respuesta de x+y+3=0