Answer:
Given: A = 72°, a = 34, b = 21
Calculated: B = 35.97°, C = 72.03°, c = 34.00
Step-by-step explanation:
[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} [/tex]
[tex] \dfrac{\sin 72^\circ}{34} = \dfrac{\sin B}{21} [/tex]
[tex] \sin B = \dfrac{21\sin 72^\circ}{34} [/tex]
[tex] \sin B = 0.5874 [/tex]
[tex] B = \sin^{-1} 0.5874 [/tex]
[tex] B = 35.97^\circ [/tex]
C = 180° - 72° - 35.97°
C = 72.03°
[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin 72^\circ}{34} = \dfrac{\sin 72.03^\circ}{c} [/tex]
[tex]c = \dfrac{\sin 72.03^\circ \times 34}{\sin 72^\circ}[/tex]
[tex] c = 34.00 [/tex]
Given: A = 72°, a = 34, b = 21
Calculated: B = 35.97°, C = 72.03°, c = 34.00
Answer:
[tex]B\approx35.97^\circ\\C\approx72.03^\circ\\c\approx34[/tex]
Step-by-step explanation:
Law of Sines
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
Given information
[tex]A=72^\circ\\a=34\\b=21[/tex]
Check if solutions exist
As [tex]A=72^\circ < 90^\circ[/tex] and that [tex]a > b\rightarrow 34 > 21[/tex], then there exists only one possible triangle by the Ambiguous Case
Solve the triangle
[tex]\frac{sin(72^\circ)}{34}=\frac{sin(B)}{21}\\ \\ 21sin(72^\circ)=34sin(B)\\\\\frac{21sin(72^\circ)}{34}=sin(B)\\ \\B=sin^{-1}(\frac{21sin(72^\circ)}{34})\\ \\B=35.97394255^\circ\approx35.97^\circ[/tex]
[tex]A+B+C=180^\circ\\\\72^\circ+35.97394255^\circ+C=180^\circ\\\\107.97394255^\circ+C=180^\circ\\\\C=72.02605745^\circ\approx72.03^\circ[/tex]
[tex]\frac{sin(72^\circ)}{34}=\frac{sin(72.02605745^\circ)}{c}\\\\c*sin(72^\circ)=34sin(72.02605745^\circ)\\\\c=\frac{34sin(72.02605745^\circ)}{sin(72^\circ)}\\ \\c=34.00502065\approx34[/tex]
Scarlett brought a pack of candies for 25 students. She plans to distribute 4 candies to each of her classmates. If five of them were absent, how many candies did each get?
Answer:
5 candies
Step-by-step explanation:
25×4=100
100/20=5
What is the name of the shape graphed by the function theta= pi/3
O A. Spiral
O B. Line
O C. Circle
O D. Lemniscate
Answer:
B. Line
Step-by-step explanation:
It is a line passing through the origin and rising to the right. The angle between the line and the x axis = pi/3 radians.
What are the values of the new mean and standard
deviation of the students' reading times?
A group of 19 students registered for a speed-reading
class at a local community college. On the first day of
class, students were timed as they read a passage
from a novel. The mean time of all the students was
189 minutes with a standard deviation of 21 minutes.
Six months later, the students were timed again as they
read a passage of similar length and readability level.
Each student in the course lost exactly 10 minutes on
their reading times.
O mean = 179 minutes and standard deviation = 11
minutes
O mean = 179 minutes and standard deviation = 21
minutes
O mean = 179 minutes and standard deviation = 31
minutes
O mean = 189 minutes and standard deviation = 11
minutes
O mean = 189 minutes and standard deviation = 21
minutes
Answer:
Second answer, O mean = 179 and standard deviation = 21 minutes.
Step-by-step explanation:
The mean will decrease but the standard deviation(average difference) between the data points will remain the same.
give the location of Berlin as an ordered pair X, Y
The coordinates are based on two factors: the x coordinate and the y-coordinate.
The x coordinate is the position of the coordinate horizontally.
The y coordinate is the position of the coordinate vertically.
Berlin is at x-coordinate of 7 and y-coordinate of 8.
Thus the whole coordinate for Berlin is (7,8).
Hope that helped!
IF you have 2 dogs and one cat how many dogs do you own?
Answer:
2 dogs
Step-by-step explanation:
because... JUST BECAUSe
PLS HELP need it quick (The other guy tried giving me a virus)
Answer:
I'm not sure if it's the point at which they meet. I need to see how many marks it hold before I can answer
Simplify the following expression. 3x4 +2x3 - 5x2 + 4x2 +6x-2x - 3x4 + 7 x - 3x3
**I want to mention that please use asterisk (*) symbol for multiplication as multiplication symbol x and variable x look the exact same
Your question is
3*4+2*3-5*2+4*2+6x-2x-3*4+7x-3*3
First calculate each term getting
=12+6-10+8+6x-2x-12+7x-9
Now combine like term which means adding all of the constant together and all of the term containing variable x together
=11x-5
Therefore 11x-5 is the answer to the expression.
A real estate agent believes that the values of houses in the neighborhood she works in have increased from last year. To test this claim, she selects random houses in this neighborhood and compares their estimated market values in the current year to their estimated market values in the previous year. Suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market value of the previous year from the market value of the current year. Assume that the values are normally distributed. What type of test is this hypothesis test?
Answer:
alternative hypothesis test
Explanation:
Remember, the alternative hypothesis test usually suggests that there is a chance of variation (difference) in the data observed.
Hence, since we are told the "real estate agent believes that the values of houses in the neighborhood she works in have increased (the chance of variation) from last year," and that "each difference is calculated by subtracting the market value of the previous year from the market value of the current year," we can reach the conclusion that this is an example of an alternative hypothesis test.
Domain range the above is
A function
Not a function
in the triangle below what is the length of the opposite the 30 anngle
Answer:
Please attach the picture so we find the answer...
Step-by-step explanation:
Hope it Helps!!!!
How to solve 0=X+1/x-2
Answer:
x = -1
Step-by-step explanation:
[tex]0= \frac{x+1}{x-2}\\[/tex]
Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x−2.
0 = x + 1
Swap sides so that all variable terms are on the left hand side.
x + 1 = 0
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
x = -1
Help help help ASAP
Answer:
The answer is C
Step-by-step explanation:
A trend line should attempt to be in the middle of the data points not above them. If it does not do as staed above, it is NOT a correct trend line.
Have an amazing day!
PLEASE RATE!!
50 numbers are written in a row. Every number starting with the third equals the sum of all the preceding numbers. What will you get if you divide the 23rd number by the 15th?
Assume the first two numbers are A and A
The row will be
A, A, 2A, 4A, 8A
For the nth number in the list it can be represented in the way number=[tex]A*(2)^{n-2}[/tex] for any n≥3
Using this formula the answer of the question can be obtained with division of the 23th and 15th term
[tex]\frac{A*(2)^{23-2}}{A*(2)^{15-2}}[/tex]
Simplify
=[tex]\frac{A*(2)^{21}}{A*(2)^{13}}[/tex]
=[tex]\frac{2^{21}}{2^{13}}[/tex]
=[tex]2^{21-13}[/tex]
=[tex]2^8[/tex]
=256
Done!
Please help 20 points please helpppp I don’t understand
Answer:
I think that its 58 degrees
Answer:
Angle CED=58°
Step-by-step explanation:
Angle CED=180-122 (adj angles on a str line)
=58°
Please solve this don’t say you can’t see it if you see it answer please only if you know the answer
Answer:
5) 3 units
6) 9 units
7) 15.5
8) 67
She visits 12 patients in 6 hours. At the same rate, how many patients will she visit in 9 hours?
Answer:
18 patients
Step-by-step explanation:
12/6=2
2x9=18
match the figures with thier name =D--------------C
Multiply $81$ by the sum of $2$ and $3$.
Answer:
405$
Step-by-step explanation:
81(2 + 3)
81(5)
405
Have a great day!!
Please rate and mark brainliest!!
Answer:
2 + 3 is 5= 81 * 5 = 405
Step-by-step explanation:
What is the codomain of a function
Answer:
Step-by-step explanation:
The set of all possible output values of a function. (Or in other words the set of values that the output values lie in.)
There are 5,000 fish in the pond and the population is increasing by 3.1% each year. How many fish will there be in 1 year?
Answer:
5,155 Fish
Step-by-step explanation:
Multiply 5,000 by 3.1%. After doing so, you should get 155. Add this 155 to the 5000 fish and you will have 5,155 fish in the first year.
robins grandmother is 7 times older than him. in 12 years, she will be 3 times as old as him. how old is robin?
Step-by-step explanation:
the answer either maybe somebody could help
Answer:
6 year's old
Step-by-step explanation:
Grandma is G and Robin is R
G=7R
G+12=3(R+12)
G+12=3R+36
7R+12=3R+36
7R-3R=36-12
4R=24
R=6
Robin is 6 years old
asap
Quadrilaterals LMNO and STUV are similar.
What is the value of x in inches?
In quadrilateral L M N O, the length of segment M N is two and two-tenths inches and the length of segment N O is four and one-tenth inches. In quadrilateral S T U V, the length of segment T U is unknown and represented by variable x, and the length of segment U V is twelve and three-tenths inches.
22.9 in.
6.6 in.
8.2 in.
i think its 6.6 not sure though.
27.1 in.
Answer:
6.6 inches
Step-by-step explanation:
Hey guys whats the answer agian
Answer:
toooo what?
Step-by-step explanation:
5. 8x + 4y = -5
8x + 4y = 12
Solve it algebraically
Answer:
solving for x:
8x + 4y = -5
[tex]x = \frac{ - 1}{2} y + \frac{ - 5}{8} [/tex]
and 8x + 4y = 12
[tex]x = \frac{ - 1}{2} y + \frac{3}{2} [/tex]
solving for y:
8x + 4y = -5
[tex]y = - 2x + \frac{ - 5}{4} [/tex]
and 8x + 4y = 12
[tex]y = - 2x + 3[/tex]
Sara takes 5 tests.
Her mean score is 62.
She takes another test and her mean score is now 68.
de nood ed or
video
15 ore
Work out her score in the sixth test.
bol
Sara's score in the sixth test is 98.
HOW TO CALCULATE TOTAL FROM MEAN?The mean of a set of data can be calculated by dividing the total sum by the number of data given.
According to this question, Sara is said to have a mean score of 62 in 5 tests and another mean score of 68 in 6 tests.
First total score = 62 × 5 = 310Second total score = 68 × 6 = 408Therefore, Sara's score in the sixth test can be calculated by subtracting 310 from 408 to give 98.
Learn more about mean at: https://brainly.com/question/521501
In a basket there are 7 pears and 4 oranges. What is the ratio of oranges to pears?
Question 1 options:
7:4
4:7
7:11
11:7
The answer to the question is 4:7
Identify the graphed linear equation.
Answer:
C. y = -4x + 1
Step-by-step explanation:
To find the equation for this graph in the formula of a linear equation, y = mx + b, you need 2 things:
the y-intercept, or b;slope, or mb is the y-intercept of the line, so in this case, it would be 1.
m is the slope in the form of [tex]\frac{rise}{run}[/tex], from left to right using a point on the line. If the line goes down from left to right, the slope will be negative, or if the line goes up from left to right, the slope will be positive. In this case, the line goes down 4 and right 1, so the slope is [tex]-\frac{4}{1} = -4[/tex].
Put it together, and you get this equation: y = -4x + 1
2. The table shows the mass of fibres in 100 grams of each food item below. Food Mass of fibre (grams per 100 grams) Beans Bread Soup Cornflakes Pasta 3.6 2.4 0.7 2.5 3.0 i. A small tin of beans contains 200 grams. If you are going to eat two-thirds (2/3) of this small tin of beans, how much fibres will you consume? Show your calculations. (2 marks)
Given that the amount of fiber in 100 grams of beans is 3.6 grams the amount of fiber consumed from [tex]\mathbf{\frac{2}{3}}[/tex] of the small tin is 4.8 grams.
How can the amount of fiber consumed be calculated?From the given table, we have;
Mass of fiber in 100 g of beans = 3.6 grams
Mass of beans in the small tin = 200 grams
The quantity of the beans eaten = [tex]\frac{2}{3}[/tex] of the small tin
Required:
The amount of fiber to consumed from eating [tex]\frac{2}{3}[/tex] of the small tin
Solution;
[tex]Amount \ of \ fiber \ consumed = 200 \, g \times \dfrac{3.6 \, g}{100 \, g} \times \dfrac{2}{3} = \mathbf{4.8 \, g}[/tex]
Therefore;
The amount of fiber consumed by eating [tex]\frac{2}{3}[/tex] of the small tin = 4.8 grams
Learn more about fractions here:
https://brainly.com/question/20591763
In-line skaters A study of injuries to in-line skaters used data from the National Electronic Injury Surveillance System, which collects data from a random sample of hospital emergency rooms. The researchers interviewed 161 people who came to emergency rooms with injuries from in-line skating. Wrist injuries (mostly fractures) were the most common.
The interviews found that 53 people were wearing wrist guards and 6 of these had wrist injuries. Of the 108 who did not wear wrist guards, 45 had wrist injuries. Why should we not use the large-sample confidence interval for these data?
a. Because 161 people are not enough for using the large-sample confidence interval.
b. Because the difference in sizes of the two groups is too large.
c. Because there are only 6 skaters in one group having wrist injuries.
d. Because the sample error is two large.
Using the Central Limit Theorem, it is found the correct option regarding why the large-sample confidence interval for these data.
c. Because there are only 6 skaters in one group having wrist injuries.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex], that is, as long as there are at least 10 successes and at least 10 failures in the sample.
In this problem, for the sample of people wearing wrist guards, only 6 had injuries, hence the large-sample confidence interval should not be used and option C is correct.
To learn more about the Central Limit Theorem, you can check https://brainly.com/question/24663213
A loan company charges $80 interest for a three-month loan of $550. Find the annual interest rate (APR) they are charging.
Answer:
Step-by-step explanation:
using the simple interst formula;
SI = Principal * Rtae * Time/100
Given
Principal = $550
SI = $80
Time = 3 month = 3/12 years
Required
Annual interest rate
Substitute
80 = 550 * R * 3/12*100
80 = 1650R/1200
96000 = 1650R
R = 1650/96000
R = 0.017
Rate = 0.017 * 100 = 1.7%