In Exercises 19-22, two triangles can be formed using the given meas- urements. Solve both triangles. 14. 19. A = 64°, a = 16,. 20. B 38°,. 21. C 68°,.
Answers
Two triangles can be formed using the given measurements,
19. Triangle 1: A = 64°, B ≈ 53.07°, C ≈ 62.93°, a = 16, b ≈ 14.83, c ≈ 16.64
Triangle 2: A = 64°, B ≈ 126.93°, C ≈ 9.07°, a = 16, b ≈ 80.17, c ≈ 8.98
20. Triangle 1: A ≈ 52°, B = 38°, C ≈ 94°, a ≈ 22.57, b = b, c ≈ 34.60
Triangle 2: A ≈ 128°, B = 38°, C ≈ 14°, a ≈ 22.57, b = b, c ≈ 16.66
19. We are given angle A and the side opposite to it, a. We can use the law of sines to find the other sides and angles of the triangle:
a/sin(A) = b/sin(B) = c/sin(C)
b/sin(B) = a/sin(A)
b = a × sin(B)/sin(A)
b = 16 × sin(64°)/sin(180°-64°-90°)
b ≈ 14.83
c/sin(C) = a/sin(A)
c = a × sin(C)/sin(A)
c = 16 × sin(68°)/sin(64°)
c ≈ 16.64
Therefore, the two triangles are:
Triangle 1: A = 64°, B ≈ 53.07°, C ≈ 62.93°, a = 16, b ≈ 14.83, c ≈ 16.64
Triangle 2: A = 64°, B ≈ 126.93°, C ≈ 9.07°, a = 16, b ≈ 80.17, c ≈ 8.98
20. We are given angle B. Let the length of the side opposite to B be b. We can use the fact that the angles in a triangle add up to 180° to find angle A, and then use the law of sines to find the remaining sides and angles:
A = 180° - 90° - 38°
A = 52°
a/sin(A) = b/sin(B) = c/sin(C)
a/sin(52°) = b/sin(38°)
c/sin(C) = b/sin(38°)
c = b*sin(C)/sin(38°)
The angles in a triangle add up to 180°, so we have:
C = 180° - A - B
C ≈ 94°
Substituting the values of A, B, and C in the above equations, we get:
a ≈ 22.57
b = b
c ≈ 34.60
Therefore, the two triangles are:
Triangle 1: A ≈ 52°, B = 38°, C ≈ 94°, a ≈ 22.57, b = b, c ≈ 34.60
Triangle 2: A ≈ 128°, B = 38°, C ≈ 14°, a ≈ 22.57, b = b, c ≈ 16.66
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The question is -
In Exercises 19-22, two triangles can be formed using the given measurements.
Solve both triangles.
19. A = 64°, a = 16,
20. B 38°
Related Questions
Hahn received $10 for his birthday with a promise of $15 more each month. Write a function that describes Hahn's new wealth. How much money does Hahn have after 5 months?
Answers
Answer:
95$
Step-by-step explanation: 15x5=85 + 10 =95
Answer:
$85
Step-by-step explanation:
15 multiplied by 5 will give how much he earns each month
15*5=75
Then add the ten he got for his birthday
75+10=85
Hahn will have $85 after 5 months.
Hope this helps!
Find f(-3)
I Need help asp!!
Answers
Hope this helps
The formula below gives the area of a semi-circle, A, with a radius of r.
Solve the formula for the radius
Answers
The area of a semicircle with respect to radius is √2A/π sq. units.
What is a semicircle?A semicircle is half of a circle. It is a 2D shape formed when a circle is cut into two equal parts. We can create two semi-circles from any circle.
The area of a semicircle = π × radius² / 2
So, the area with respect to radius will be =
A = π × radius² / 2
2A = π × radius²
2A / π = radius²
Radius = √2A/π
Hence, the area of a semicircle with respect to radius is √2A/π sq. units.
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Can you please check my answer? Your final expression should be Simplified. Distribute 2(x+3) + (x+4)
Answers
Using the distributive property we have that multiplying by some terms grouped in parenthesis is the same as multiplying each term.
On one hand:
2(x+3) = 2 · x + 2 · 3
= 2x + 6
On the other:
(x+4) = x + 4
Then
2(x+3) + (x+4) = 2x + 6 + x + 4
Combining like termsWe combine like terms in the expression
2x + 6 + x + 4
terms with x: 2x and x
numbers: 6 and 4
adding them we have that:
terms with x: 2x + x = 3x
numbers: 6 + 4 = 10
Then
2x + 6 + x + 4
= 3x + 10
Answer: 2(x+3) + (x+4) = 3x + 10
statistical power is a measure of the ability to reject the null hypothesis when:
Answers
Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.
A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.
Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.
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help please !! this is algebra just in case !
Answers
Answer: The answer to this equation is 50.
Step-by-step explanation:
Evaluate the equation like this using PEMDAS.
2 x (1 + 4) ^2
2 x ( 5 ) ^ 2
2 x 25
50
Therefore, the answer to this equation is 50.
Hope this helps!
Add the following military times:
0645 + 0745 =
Answers
Answer:
2316
Step-by-step explanation:
use a calculator
Answer:
0645+0745= 1390 but there are not 90 mins in an hour so you roll over 60 over those min to get 1430
2:30
explanation:
The table below shows numerical summaries for the length of dogs' tails in inches (measured from hip bone to tail
tip) for several breeds of dogs.
Which of the following statements is true?
This is a skewed-left distribution, because the mean is less than the median.
O This is a skewed-right distribution, because the mean is less than the median.
This is a skewed-left distribution, because the mean is greater than the median.
This is a skewed-right distribution, because the mean is greater than the median.
Because the mean is the same as the median, this distribution is roughly symmetric.
Answers
The correct option regarding the skewness of the distribution is given by:
This is a skewed-left distribution, because the mean is less than the median.
Given the mean and the median of a distribution, how we classify it's skewness?If the mean is greater than the median, the distribution is right-skewed, also called positively skewed. Otherwise, if the median is greater than the mean, the distribution is left-skewed, also called negatively skewed.
In this problem, we have that:
The mean is of 10.4.The median is of 13.4.The median is greater than the mean, hence the correct option is given by:
This is a skewed-left distribution, because the mean is less than the median.
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A 55.9-kg hiker ascends a 46.6-meter high hill at a constant speed of 1.0 m/s. If it takes 373 s to climb the hill, then determine the power delivered by the hiker.
Answers
Step 1
State formula for Power
\(\begin{gathered} \text{Power =}\frac{work}{\Delta time} \\ \text{But work = Force(F)}\times Dis\tan ce(S)\text{ for rectilinear motion} \\ \end{gathered}\)Hence,
\(\begin{gathered} \text{Power}=\frac{F\times S}{\Delta Time(t)} \\ \text{Also Force(F) for rectilinear motion}=\text{Mass(M)}\times acceleration(a) \\ \text{Hence,} \\ \text{Power}=\text{ }\frac{M\times a\times S}{\Delta t} \end{gathered}\)Step 2
Determine the power delivered by the hiker.
\(\begin{gathered} \text{Power}=\frac{M\times a\times S}{\Delta t} \\ M=\text{mass = 55.9kg} \\ a=\text{ rectilinear acc}eleration\text{ = 1.0m/s} \\ S=\text{distance}=46.6m \\ \Delta t=373s \end{gathered}\)\(\begin{gathered} \text{Power}=\frac{55.9\times1.0\times46.6}{373} \\ \end{gathered}\)\(\begin{gathered} \text{Power}=6.983753351 \\ \text{Power }\approx\text{ 6.984 Joules(J)/Seconds(s) or Watts(w) to 3 decimal places} \\ \end{gathered}\)Hence the power delivered by the hiker to 3 decimal places is approximately 6.984 J/s or watts
Word problem: A High School had a musical in which students ($5 tickets) and adults ($7 tickets) attended. If a total of 47 tickets were sold and they made a total of $269. How many student tickets were sold and how many adult tickets were sold?
Answers
Answer:
30 of them were students
17 were adults
Step-by-step explanation:
bunny and rabbit problems
if they were all adults
7 x 47 = 329
329 - 269 = 60
60/ (7-5) = 30
30 of them were students
17 were adults
POINT Is the graph of s(x) = -6x + 8x2 + 5x + 3 concave up or down at the point with x-coordinate -1? Select the correct answer below: O Concave down O Concave up
Answers
The graph of s(x) = -6x + \(8x^2\) + 5x + 3 is concave up at the point with x-coordinate -1. Let us consider the second derivative.
To determine the concavity of a function at a specific point, we need to analyze the second derivative of the function. If the second derivative is positive, the graph is concave up, and if it is negative, the graph is concave down.
Given s(x) = -6x + \(8x^2\) + 5x + 3, let's find the second derivative:
s'(x) = -6 + 16x + 5
s''(x) = 16
The second derivative is a constant, 16, which is positive. Since it is always positive, the graph of s(x) is concave up for all values of x. Therefore, at the point with x-coordinate -1, the graph is also concave up.
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What is the
slope of the line that passes through the points (8, -4) and (6, 2)?
Write your answer in simplest form
Answers
Answer:
y=-3x+20
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-(-4))/(6-8)
m=(2+4)/-2
m=6/-2
m=-3
y-y1=m(x-x1)
y-(-4)=-3(x-8)
y+4=-3(x-8)
y=-3x+24-4
y=-3x+20
The breaking strengths of a random sample of 20 bundles of wool fibers have a sample mean 436.5 and a sample standard deviation 11.9. (a) Construct 90%, 95%, and 99% confidence intervals for the average breaking strength of the wool fibers. (b) Compare the widths of the three confidence intervals. At which level of confidence do you have the widest interval
Answers
(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].
(b) The 99% confidence interval has the widest interval.
(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:
Confidence interval = sample mean ± (critical value * standard error)
The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.
Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.
Plugging in the values, we can calculate the confidence intervals:
90% confidence interval:
Lower bound = 436.5 - (1.645 * (11.9 / √20))
Upper bound = 436.5 + (1.645 * (11.9 / √20))
95% confidence interval:
Lower bound = 436.5 - (1.96 * (11.9 / √20))
Upper bound = 436.5 + (1.96 * (11.9 / √20))
99% confidence interval:
Lower bound = 436.5 - (2.576 * (11.9 / √20))
Upper bound = 436.5 + (2.576 * (11.9 / √20))
(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.
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A and B are two events. Let P(A) = 0.65, P (B) = 0.17, P(A|B) = 0.65 and P(B|4) = 0.17 Which statement is true?
1. A and B are not independent because P(A|B) + P(A) and P(B|4) + P(B).
2. A and B are not independent because P (A|B) + P(B) and P(B|4) + P(A)
3. A and B are independent because P (A|B) = P(A) and P(BIA) = P(B).
4. A and B are independent because P (A|B) = P(B) and P(B|A) = P(A).
Answers
Answer:
the statement that is true is: A and B are not independent because P(AIB) + P(B) is not equal to P(BIA) + P(A)
Step-by-step explanation:
ur welcome
Hey, I need help what is 12+3s+9s+2=?
Answers
Answer:
Below
Step-by-step explanation:
12 + 3s + 9s + 2 =
(3s+9s) + (12+2) =
12s + 14 ( or 2 (6s+7) )
The U.S. Department of Education reported that for the past seven years:4,0335,6426,4077,7538,71911,15411,121people received bachelor's degrees in JournalismWhat is the arithmetic mean annual number receiving this degree
Answers
The arithmetic mean annual number of people receiving a bachelor's degree in Journalism is about 7,833.
To find the arithmetic mean annual number of people receiving a bachelor's degree in Journalism over the past seven years, we need to calculate the average of the given data set.
The data set representing the number of people receiving bachelor's degrees in Journalism for each of the seven years is:
4,033
5,642
6,407
7,753
8,719
11,154
11,121
To find the mean, we sum up all the values and divide by the total number of years (in this case, seven).
Mean = (4,033 + 5,642 + 6,407 + 7,753 + 8,719 + 11,154 + 11,121) / 7
= 54,829 / 7
≈ 7,832.714
Rounding to the nearest whole number, the arithmetic mean annual number of people receiving a bachelor's degree in Journalism over the past seven years is approximately 7,833.
Therefore, the arithmetic mean annual number of people receiving a bachelor's degree in Journalism is about 7,833.
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Find the surface area of an open-top box with length 9cm width 8cm and height 7m = cm2
Answers
The surface area of the open-top box is 23872 cm².
In the question, we are asked to find the surface area of an open-top box with a length of 9cm, a width of 8cm, and a height of 7m.
The length is given to be, l = 9 cm.
The width is given to be, w = 8 cm.
The height s given to be, h = 7 m = 700 cm.
The box is in the shape of a cuboid.
The surface area of a cuboid is calculated using the formula, A = 2(lw + wh + hl).
But, the given box has an open top. Thus, one surface involving the length and width, that is, with an area of lw is missing.
Thus, the surface area of the open-top box can be calculated as:
A = 2(lw + wh + hl) - lw,
or, A = lw + 2h(w + l).
Substituting the values now, we get:
A = 9*8 + 2*700/(9 + 8),
or, A = 72 + 1400*17,
or, A = 72 + 23800,
or, A = 23872 cm².
Thus, the surface area of the open-top box is 23872 cm².
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What is the example of obtuse angle?.
Answers
An example of an obtuse angle is 135°.
What is an angle?When two straight lines or rays intersect at a shared terminal, an angle is generated.
An angle whose measure is more than 90° but less than 180° is said to be an obtuse angle.
Therefore, an example of an obtuse angle is 135°.
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What is the distance number between two numbers 3/4 , 1/8?
Answers
Answer:
Answers are 7/8 and -5/8.
the students government wants to sell magazines subscription to make a profit of at least 3000.They make 1.25 per m magazine sold. only expense were for advertisement of 100 in the school and 150 in the community. write a linear inequality that models this problem situation.
Answers
Let's use the variable 'm' to represent the number of magazines sold.
If they make 1.25 per magazine sold, the total revenue is the product of the unitary value of one magazine by the number of magazines sold:
\(R=1.25m\)The costs are the values of 100 and 150, so we have:
\(C=100+150\)Finally, the profit they want to have is at least 3000, so:
\(P\ge3000\)If the profit is calculated by the revenue minus the cost, we have that:
\(\begin{gathered} P=R-C \\ R-C\ge3000 \\ 1.25m-100-150\ge3000 \end{gathered}\)I need help plzz thank you
Answers
Answer:
She's wrong because she didn't distribute correctly. She was supposed to multiply 4 and 12, which makes 48.
The proper answer should be 4x+48
6.
5. The florist has 90 roses to arrange. After 5 vase
arrangements, there are 50 roses left. How
many total vase arrangements will be needed to
have only 10 roses left?
Answers
Answer:
1 vase arrangement when 10 roses are left
Step-by-step explanation:
1. so 50 divided by 5 is 10.
That means every arrangement is 10 roses.
2. it asks us to find how many vase arrangement will be needed to have only 10 roses left. We already know that we only need 1 arrangement, because we already found that out in step 1.
Large cheese pizzas cost $5 each and large pepperoni pizzas cost $6 each. The expression 5c+6p models the total cost of large cheese pizzas (c) and large pepperoni pizzas (p). What does each part of the expression represent in the context of the situation? Drag the correct description to each part of the expression.
Answers
Answer: 5c represents the cost of 'c' large cheese pizzas and 6p represents the cost of 'p' large pepperoni pizzas.
Step-by-step explanation:
Given: Large cheese pizzas cost $5 each and large pepperoni pizzas cost $6 each.
The expression 5c+6p models the total cost of large cheese pizzas.
here c represents Number of large cheese pizzas and p represents number of large pepperoni pizzas such that
5c represents the cost of 'c' large cheese pizzas and 6p represents the cost of 'p' large pepperoni pizzas.
[Total cost = Cost of each item x Number of items ]
explain how to graph the circle by hand on the coordinate plane (3 points)
Answers
First find the center, then graph all the points that are at a distance of R units from that center.
How to graph a circle by hand?A circle of radius R is the set of all points that are at a distance R from a given point (the center of the circle).
So to graph it, we need to know these two things, radius and center.
Once we do, first we graph the center on the coordinate plane.
Once we find the center, we can find all the poiints that are at a distance of R units from our center, so we need to graph these. Once we do, we will have the graph of our circle on the coordinate plane.
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Which point is in the graphed solution set of this system o
4x - 3y 12
6x + 3y > 5
Answers
Answer:
i dont know
The cost of petrol rises by 2 cents a liter. last week a man bought 20 liters at the old price. This week he bought 10 liters at the new price. Altogether, the petrol costs $9.20. What was the old price for 1 liter? 34 POINTS I MARK BRAINLIEST!
Answers
Answer:
We suppose that a is the old price in cents
the total cost of 9.20 $ equals 920 cents
so we have 20 liters bought with the old price (a) and 10 liters with the new price (a + 2). This is translated into this equation where a is the old price therefore our quest to be answered
20 xa + 10 x (a + 2) = 920 (cents)
20 xa + 10 xa + 20 = 920
30 xa + 20 = 920
30 xa = 920 - 20
30 xa = 900
a = 900: 30
a = 30 (cents)
therefore the old price for 1 liter of petrol is 30 cents
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
if using the method of completing the square to solve the quadratic equation x^2+17x+3=0x 2 +17x+3=0, which number would have to be added to "complete the square"?
Answers
Answer:
Step-by-step explanation:
answer:289/4
x² + 17x + 12 = 0
x² + 17x = -12
Take half of the second coefficient, square it, then add the result to both sides.
(17/2)² = 289/4
x² + 17x + 289/4 = -12 + 289/4
(x + 17/2)² = 241/4
Answer:
i think it might be 72.5
also theres an app called air math it could possibly help with questions you have
Step-by-step explanation:
.
please help me now!! 40% of an hour in hours and minutes.
Answers
Answer:
i cant see it
Step-by-step explanation:
?
question 1(multiple choice worth 1 points) (4.02 mc) a standard showerhead in marty's house dispenses 7 gallons of water per minute. marty changed this showerhead to an energy-saving one. the equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y
Answers
The amount of water that would be saved by the energy saving shower is 32 gallons. Option C
A linear equation is what?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
We can be able to attest that we have that the previous number of gallons that would be dispersed in the first instance is;
7 gal/min * 8 mins
= 56 gallons
In the other case we use the equation for the energy saving shower;
y = 3(8)
= 24 gallons
We would now save;
56 gallons - 24 gallons
= 32 gallons of water
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Missing parts;
A standard shower head in Marty's house dispenses 7 gallons of water per minute. Marty changed this shower head to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new shower head.
y = 3x
How much water does Marty save each day with the change in shower heads if he uses the shower for 8 minutes each day?
A. 4 gallons
B . 12 gallons
C . 32 gallons
D . 53 gallons
Look at the image shown.
H-H
What does this image represent?
a
Linear molecule with one domain
Linear molecule with two domains
Tetrahedral molecule with four domains
Trigonal planar molecule with three domains
Answers
Answer: salamibrain
Step-by-step explanation: hey guys it's salamibrain
The image has been consisted of the linear molecule with two domains. Thus, option B is correct.
The given image has been the structure of the carbon dioxide. There has been the two oxygen atoms that has been linked with the central carbon atom.
The molecules have been consisted of equal number of valence electrons, thus the structure has been causing lesser extent of the distortion. The symmetrical structure has been consisted with the linear symmetry.
Thus, the image has been consisted of the linear molecule with two domains. Thus, option B is correct.
(I did not make this answer so all credit goes to the one who made it)