Answer:
[tex]\displaystyle \sin(A+B)=\frac{3008}{3233}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \cos(A)=\frac{60}{61}\text{ and } \tan(B)=\frac{45}{28}[/tex]
And that the two angles A and B are both in QI (positive acute angles).
Given this, we want to determine the value of sin(A + B).
Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, we can determine the opposite side with respect to A:
[tex]\displaystyle o=\sqrt{61^2-60^2}=\sqrt{121}=11[/tex]
Likewise, for B, tangent gives the ratio of the opposite side to the adjacent. Using this information, we can determine the hypotenuse of B:
[tex]h=\sqrt{45^2+28^2}=\sqrt{2809}=53[/tex]
In conclusion:
With respect to A, the adjacent side is 60, the opposite side is 11, and the hypotenuse is 61.
With respect to B, the adjacent side is 28, the opposite side is 45, and the hypotenuse is 53.
We can rewrite our original expression as:
[tex]\sin(A+B)=\sin(A)\cos(B)+\sin(B)\cos(A)[/tex]
And since A and B are both in QI, all trigonometric ratios will be positive.
Using the above conclusions, substitute:
[tex]\displaystyle \sin(A+B)=\left(\frac{11}{61}\right)\left(\frac{28}{53}\right)+\left(\frac{45}{53}\right)\left(\frac{60}{61}\right)[/tex]
Simplify. Hence:
[tex]\displaystyle \sin(A+B)=\frac{308+2700}{3233} = \frac{3008}{3233}[/tex]
whats 25.28 in expanded form
Please thebecks please
Answer:
1.8
Step-by-step explanation:
If we know Xin ordered 5 identical pieces of bread, this must mean that each one weighs the same
By dividing the 9 pounds with 5 (the amount of bread) we will get 1.8
So each bread is 1.8
but if u want to check the answer then we can multiply 1.8 with the 5 loaves of bread and it will result in 9
Solve for x.
8 12
24
Х
x= ? ]
Answer:
x=44
Step-by-step explanation:
LOL somebody reported my question lol anyways help what is 43/09.7
Answer: 4.432990
Step-by-step explanation:
A television selling for $940.00 is marked down by 15%. What is the price after the markdown?
Step-by-step explanation:
100%-> 940.00
100%-15%=85%
85%->940.00 ÷ 100 x 85
=799. 00
The fifth grade art class is making quilts
Answer:
trapazoid
Step-by-step explanation:
A trapezoid is a shape that belongs in the overlapped section of the
Venn diagram.
What are polygons?Regular polygons have all sides the same and that apothem bisects the side in two parts, (provable by symmetry).
Apothem for a regular polygon is a line segment that originates from the center of the regular polygon and touches the mid of one of the sides of the regular polygon.
It is perpendicular to the regular polygon's side it touches.
The fifth-grade art class is making quilts. There are some of the shapes they are putting in their quilts.
A trapezoid is a shape that belongs in the overlapped section of the
Venn diagram.
Learn more about apothem here:
https://brainly.com/question/12090932
#SPJ2
QUICK
ADD THE EXRESSIONS
(10x - 4) + ( -7 + x) = (10x +) + ( -4 + )
Answer:
(10x - 4) + ( -7 + x)
10x-4-7+x=10x-11 is your answer
The measure of an angle is 67º. What is the measure of its complementary angle?
Answer:
see explation
Step-by-step explanation:
# complementary angles are those angles which are formed when 90° is substracted from the given degree of angle.
so here,given angle is 67°
complementary angle of 67° = 90°- 67°
= 23°
please mark me as brainlist.
In the figure, the angles are formed by a transversal and two parallel lines. Which angles are congruent?
Answer:
A is your correct answer.
1, 3, 5, and 7 are equal to each other and 2, 4, 6, and 8 are equal to each other.
Step-by-step explanation:
Congruent angles are angles that have the same measure. In this example, where two parallel lines are cut by a transversal line, the angles in the same position on the top line and bottom line are congruent. For example, angle 1 and 5 are in the same position, so they have the same measure.
Also, vertical angles (opposite angles, like 5 & 7 in your example) have the same measure.
Please let me know if you have questions about this.
Please answer correctly math problemo
Answer:
2*3*4=24 (units)
l*w*h=V
brainliest plz
Step-by-step explanation:
Answer:
the answer is 24
Step-by-step explanation:
you do 3 times 4 and you get twelve and then you times it by 2
Bryan has coaught 14 of the 70 pokemon that are still currently at the park in pokemon go.what percent of pokemon does he stiñl need to catch?
Answer:
He still needs to catch 80% of the pokemon's.
Answer:80% are left.
The employees from maintenance go for coffee together every day at 9 a.m. On Monday, Hector paid $4.60 for three cartons of milk, three cups of coffee, and seven
doughnuts. On Tuesday, Guillermo paid $8.30 for four milks, nine coffees, and eight doughnuts. On Wednesday, Anna paid $4.90 for two milks, five coffees, and six
doughnuts. On Thursday, Alphonse had to pay for five milks, two coffees, and eight doughnuts. How much change did he get back from his $10 bill?
Answer:
The change will be $4.75
Step-by-step explanation:
Given data:
Monday
Total paid = 5.45
milk bought =3
coffee bought = 4
doughnuhts = 7
Tuesday
Total paid = 5.30
milk bought =4
coffee bought = 2
doughnuhts = 8
Wednesday
Total paid = 5.15
milk bought =2
coffee bought = 5
doughnuhts = 6
Thursday
Total paid = X
milk bought =5
coffee bought = 2
doughnuhts = 9
Let milk be m, Let coffee be c and Let doughnuts be d
3m + 4c + 7d = 5.45 (eqaution 1)
4m + 2c + 8d = 5.30 (equation 2)
2m + 5c + 6d = 5.15 (equation 3)
Using equation 1 and equation 2 ( to eliminate m)
3m + 4c + 7d = 5.45 (Multiply the whole equation by 4)
4m + 2c + 8d = 5.30 (Multiply the whole equation by 3)
12m + 16c +28d = 21.8
12m + 6c +24d = 15.9 (Subtracting the two equations)
0m +10c + 4d = 5.9
therefore 10c +4d = 5.9 (equation 4)
Using equation 2 and equation 3 (to eliminate m)
4m + 2c + 8d = 5.30 (Multiply the whole equation by 2)
2m + 5c + 6d = 5.15 (Multiply the whole equation by 4)
8m + 4c + 16d = 10.6
8m +20c +24d = 20.6 (Subtracting the two equations)
0m -16c -8d = -10
-16c -8d = -10 (equation 5)
Solving equation 4 and equation 5( to eliminate d)
10c +4d = 5.9 (Multiply whole equation by 8)
-16c -8d = -10 (Multiply whole equation by 4)
80c + 32d = 47.2
-64c -32d = -40 (Adding the equations)
16c =7.2
therefore c = 0.45
Substituting into equation 4
10(0.45) + 4d = 5.9
4.5 + 4d = 5.9
4d = 5.9-4.5
4d = 1.4
therefore d = 0.35
Substituting c and d into equation 1
3m + 4c + 7d = 5.45
3m + 4(0.45) + 7(0.35) = 5.45
3m + 1.8 + 2.45 = 5.45
3m = 5.45-2.45-1.8
3m = 1.2 therefore m = 0.4
Alphonse has to pay 3m + 2c + 9d
Alphonse change will be 10 - (3m + 2c + 9d) (Substituting m, c and d)
10- (3(0.4) + 2(0.45) + 9(0.35) = 10 -(1.2+0.9+3.15)
which simplifies to 10- 5.25=4.75
The change will be $4.75
11 1 point Are the two triangles are congruent by SSS, SAS, ASA, AAS or NO (not enough information given) Answer SSA : AAA NO SAS AAS SSS SASA Previous
Answer:
, its SSS ,SAS , AAS , ASA
Step-by-step explanation:
Plastic parts manufactured using an injection molding process may exhibit one or more defects, including sinks, scratches, black spots, and son on. Let x represent the number of defects on a single part, and suppose the distribution of x is as follows: x: 0 1 2 3 4 p(x): 0.79 0.09 0.05 0.04 0.03 What is the expected value, E(X), for the number of defects on a randomly selected plastic part
Answer:
The expected value for the number of defects on a randomly selected plastic part is 0.43.
Step-by-step explanation:
We have the following probability distribution:
P(X = 0) = 0.79
P(X = 1) = 0.09
P(X = 2) = 0.05
P(X = 3) = 0.04
P(X = 4) = 0.03
What is the expected value, E(X), for the number of defects on a randomly selected plastic part?
Each value multiplied by its probability. So
[tex]E(X) = 0.79*0 + 0.09*1 + 0.05*2 + 0.04*3 + 0.03*4 = 0.43[/tex]
The expected value for the number of defects on a randomly selected plastic part is 0.43.
What is the value of z?
Answer
61
Step-by-step explanation:
subtract 180-73.8-46.2
Answer:
The value of z is 26.6
Step-by-step explanation:
72.6 - 46.2=26.6
g Cell phones. Following are last year's local monthly bills, in dollars, for a random sample of 50 cell phone users. 32.88,31.09.16.13,104.2,47.65,116.96,61.97,43.74,13.52,15,37,30.09,16.93,44.67,28.08,64.68, 16.17,28.04,57.67,14.62,61.32,35.64,88.95,50.48,16.41,16.56,13.48,27.10,15.50,19.95,23.45,4 6.24,41.8,49.35,81.16,28.80,32.48,28.95,31.60,35.6,24.74,44.82,51.62,42.04,22.43,46.54,48.3 2,24.53,77.21,15.12,126.84 At the 5% significance level, do the data provide sufficient evidence to conclude that last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.37
Answer:
At 5% significant level, there is sufficient evidence to suggest that last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.37
Step-by-step explanation:
The given data are presented as follows;
32.88, 31.09, 16.13, 104.2, 47.65, 116.96, 61.97, 43.74, 13.52, 15, 37, 30.09, 16.93, 44.67, 28.08, 64.08, 16.17, 28.04, 57.67, 14.62, 61.32, 35.64, 88.95, 50.48, 16.41, 16.56, 13.48, 27.10, 15.50, 19.95, 23.45, 46.24, 41.8, 49.35, 81.16, 28.80, 32.48, 28.95, 31.60, 35.6, 24.74, 44.82, 51.62, 42.04, 22.43, 46.54, 48.32, 24.53, 77.21, 15.12, 126.84
We note that there are 51 data points, however, the points, 15 and 37 are given without decimal place values and therefore, they are taken as one data point to make 50 data points.
The given sample size = 50
The mean mean of the given data, [tex]\overline x[/tex] ≈ 41.01
The standard deviation of the given data, s ≈ 26.59
The null hypothesis, h₀; μ = 47.37
The alternative hypothesis, hₐ; μ < 47.37
The significant level, α = 5%
Therefore, we have;
The test statistics is given as follows;
[tex]t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}[/tex]
Plugging in the values gives;
[tex]t=\dfrac{41.01-47.37}{\dfrac{26.59}{\sqrt{50}}} \approx -1.69131[/tex]
The critical-t at 5% at df = n - 1 = 51 - 9 = 49 degrees of freedom and significance level, α of 5% (0.05) from a calculator = -1.676551
Given that the test statistic is larger than the critical-t, we therefore reject the null hypothesis. There is enough statistical evidence to suggest that last years mean monthly bill for cell phone users has decreased from 2001 mean to $47.37.
What is the equation of the line that passes through the point (−0.5,8) and has a slope of −5?
Answer:
Slope=-1.8, X=-0.5, y=1.9
Equation is y^2-y^1=m(x^2-x^1).
Y-1.9=-1.8(X-(-0.5))
Y-1.9=-1.8x+0.90
Add 1.9 on both sides.
Y= -1.8x+1.
I hope this helps you.
Step-by-step explanation:
Pls only give direct answers
Answer:
B
Step-by-step explanation:
A 10.0kg rock is dropped and hits the ground below at a speed of 60 m/s . Calculate the gravitational potential energy of the rock before it was dropped
Answer:
Solution:
Mass of body, m= 10kg
velocity, v= 60m/s
Now,kinetic energy on earth= potential energy at a that point [energy conservation]
so, kinetic energy= 1/2*m* v^2
= 1/2* 60(60)^2
= 30* 60*60
= 108000 joules
Which only lists multiples of 16? *
Mark only one oval.
1, 2, 4, 8, 16
16, 24, 32, 40
16, 32, 48, 64
Figure A is enlarged to create figure B. The ratio of the areas of A and B is 16:49.
One side of B is 5ft long. How long would the corresponding side on figure B be. Leave your answer as a fraction. (No image was provided, only the question itself.)
Answer: [tex]\dfrac{20}{7}[/tex]
Step-by-step explanation:
Given
The ratio of the area of the similar triangles is equal to the square of the side of the corresponding sides
Suppose the corresponding side on figure A is [tex]x[/tex]
On solving
[tex]\Rightarrow \dfrac{16}{49}=[\dfrac{x}{5}]^2\\\\\Rightarrow \dfrac{x}{5}=\sqrt{\dfrac{16}{49}}\\\\\Rightarrow \dfrac{x}{5}=\dfrac{4}{7}\\\\\Rightarrow x=\dfrac{20}{7}[/tex]
if you take 4 steps every 6 minutes, how long will 10 steps be?
Answer:
15
Step-by-step explanation:
divide 6 into 4 than what ever your answer is multi... by 10
Please help due in 5 min.
Answer:
1
Step-by-step explanation:
3×60=180
180÷45=4
4-3=1
the perimeter of a rectangle is 240 ft., If the length is 12 ft., then what is the width
Answer:
w=108
Step-by-step explanation:
Using the formula
P=2(l+w)
Solving for w
w=P /2﹣l = 240 /2﹣12 = 108
Answer:
width=20
Step-by-step explanation:
the area of a rectangle= length times width
12x=240
then you divide 12 by both sides, so the answer is 20
A small refrigerator is a cube with a side length of 19 inches.
Use the formula S = 6s2 to find the surface area of the cube.
Answer:
2166in^2
Step-by-step explanation:
S=6(19)^2=2166
4x + 10= 22 find the value of x
Answer:
x=3
Step-by-step explanation:
Problem 3.1
Jaleel wrote a book. He wants to print some copies for his
friends and family. The printing company charges a one-
time fee of $200, plus $2 for each printed book.
Is Jaleel's total cost a function of the number of books he
prints?
Answer:
C(n) = 200 + 2n
Step-by-step explanation:
Given:
Fixed cost state by printing company = $200
Variable charges per book print = $2
Find:
Cost function of number of books print
Computation:
Assume:
Number of books printed = n
Total cost of n books printed = Fixed cost state by printing company + Variable charges per book print[Number of books printed]
C(n) = 200 + 2n
Where n = number of book
C = Total cost
Jaleel's total cost as a function of the number of books he print is [tex]c = 2n + 200[/tex] (in dollars)
How to form mathematical equations from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.
If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions or equations.
For the considered case, we don't know exactly how many books will Jaleel gets printed. So we can use variable here.
Let we have:
n = number of books Jaleel gets printed.c = total cost Jaleel has to pay for printing those booksThen, as stated in the problem, for each book there is $2 price, and there is a fixed one-time charge of $200
Thus, we get total cost as:
c = Cost for n books + Fixed one-time cost.
Cost for n books = 2 + 2 + ... + 2 (n times ) (in dollars) = [tex]2n[/tex](we don't write symbols like of currency generally, and understand it from context. Also, sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)
Fixed one-time cost = $200Thus, total cost is written as:
c = Cost for n books + Fixed one-time cost.
c = 2n + 200 (in dollars)
Learn more about forming equations here:
https://brainly.com/question/11938672
Which fractions equal the whole number 3?
Answer:
9/3=3
Step-by-step explanation:
3 goes into 9 3 times
3,6,9
Find the area of the figure to the nearest hundredth.
Answer:
19.85 sq ft
Step-by-step explanation:
area of circle with diameter of 5: A = π(2.5²) = 7.85
area of triangle: A = 1/2(4)(6) = 12
Help please I’ll mark brainliest
Answer:
y=7x
Step-by-step explanation:
