Answer:
[tex]\cos(\theta - x)=\dfrac{33}{65}[/tex]
Step-by-step explanation:
Given:
[tex]\sin\theta=\dfrac{4}{5}\implies \cos \theta=\dfrac{3}{5}[/tex]
[tex]\cos x=-\dfrac{5}{13}\implies \sin x=\dfrac{12}{13}[/tex]
Using the trig identity:
[tex]\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B[/tex]
[tex]\begin{aligned}\implies \cos(\theta - x) &=\cos \theta \cos x + \sin \theta \sin x\\\\&=\dfrac{3}{5} \cdot -\dfrac{5}{13} + \dfrac{4}{5} \cdot \dfrac{12}{13}\\\\&=-\dfrac{15}{65} + \dfrac{48}{65}\\\\&=\dfrac{33}{65}\end{aligned}[/tex]
sinø=4/5
so
cosø=3/5And
cosx=-5/13
so
sinx=12/13cos(ø-x)
sinøsinx+cosøcosx(4/5)(12/13)+(3/5)(-5/13)(48/65)-(15/65)48-15/6533/65
Use the Pythagorean Theorem to find the distance between (3, 0) and (7,-6). Round
to the nearest tenth.
Answer:
14.4
Step-by-step explanation:
6^2+12^2=x^2
64+144+x^2
208=x^2
square root of 208= 14.4
x=14.4
Ronald's bill at the end of his lunch was $20.00. Using a proportion, determine the amount of his bill that he must leave for a 19% tip.
Answer:
23.80$
Step-by-step explanation:
[tex]\frac{20}{x} =\frac{100percent}{19percent}[/tex]
X = (20 × 19) ÷ 100
X =380 ÷ 100
X = 3.8$
20.00+ 3.8=
23.80
A shipping box in the shape of a rectangular prism has a volume of 15,000
cm3. The length of the box is 20 cm, and the width is 25 cm. What is the
height of the box?
A. 15 cm
B. 30 cm
C. 37.5 cm
D. 24 cm
Answer:
Option (B) 30cm.Step-by-Step explanation:
Given:
Volume of Rectangular Prism is 15,000cm³.
Length (l) ➠ 20 cm Width (w) ➠ 25 cmWe know that,
★ Volume of Rectangular Prism = whl ★
Let "h" be the height.
➛ 25 × h × 20 = 15,000
➛ h × 20 × 25 = 15,000
➛ h × 500 = 15,000
➛ h = 15,000 ÷ 500
➛ h = 30
Thus, height of the box is 30 cm.
Consider a triangle a
ABC like the one below. Suppose that A = 46°, C=79°, and b=61. (The figure is not drawn to scale.) Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
Answer:
A =24.7° ; B = 40.6° ; C =114.7°
Step-by-step explanation:
At her Fourth of July party, Marcy serves her famous grilled chicken. Her secret is to use 6 fluid ounces of lemon-garlic marinade for every pound of chicken. Marcy plans to grill 4 pounds of chicken. How many cups of marinade should she use?
cups
3 number of cups will be needed to marinade 4 pounds of chicken for grill.
What is Ounce?Ounce is the small unit of weight which is generally equal to the one by 16th of the pounds.
Here we have the data from the question:-
Marcy will use 6 fluid ounces of lemon-garlic marinade for every pound of chicken.
Marcy plans to grill 4 pounds of chicken.
So total marination required will be:-
Total marination =6x4=24 ounces
Now we know that the conversion:-
1 fluid Ounce = 0.125 Cup
24 fluid ounce =0.125 Cup
Hence 3 number of cups will be needed to marinade 4 pounds of chicken for grill.
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What is the surface area of the cylinder with height 3 km and radius 3 km? Round your answer to the nearest thousandth.
Answer:
A≈113.1km²
Step-by-step explanation:
What are the values of mode and median in the following set of numbers? 1,3,3,6,6,5,4,3,1,1,2 Mode: 1, 2, Median: 2 Mode: 1,3, Median: 3 Mode: 2,3, Median: 2 Mode: 1,3, Median: 2.5
[tex]1 \: 3 \: 3 \: 6 \: 6 \: 5 \: 4 \: 3 \: 1 \: 1 \: 2[/tex]
to find:the mode and median of the given numbers set.
solution:mode:the most frequently occurred number.
[tex]mode = 1 \: and \: 3[/tex]
median:first arrange all the numbers in either decending or ascending order, then find the number in the middle.
[tex]1 \: 1 \: 1 \: 2 \: 3 \: 3 \: 3 \: 4 \: 5 \: 6 \: 6[/tex]
[tex]median = 3[/tex]
hence, the median of the following data set is 3 and the mode is 1 and 3
Orlando is mixing nuts and cereal squares to make a party mix. Nuts sell for $7 a pound and cereal squares sell for $4 a pound. If Orlando wants to make 30 pounds of party mix at a cost of $6.50 a pound, how many pounds of nuts and how many pounds of cereal squares should he use?
Answer:
5 lbs cereal squares.
25 Ibs nuts.
Step-by-step explanation:
Let x be the weight of nuts in pounds and y be the weight of cereal squares in pounds.
Total weight of the party mix is 30 pounds.
[tex]x+y=30[/tex] ..... (1)
It is given that,
Cost of nuts = $7 per pound
Cost of cereal = $4 per pound
The cost of mix = $6.50 per pound.
[tex]7x+4y=6.50*30[/tex]
[tex]7x+4y=195[/tex] ..... (2)
Substitute the value of x in equation (2) from equation (1).
[tex]7(30-y)+4y=195[/tex]
[tex]210-7y+4y=195[/tex]
[tex]-3y=195-210[/tex]
[tex]-3y=-15[/tex]
Divide both sides by -3.
[tex]y=5[/tex]
Substitute y=5 in equation (1).
[tex]x+5=30[/tex]
Subtract both sides by 5.
[tex]x=30-5[/tex]
[tex]x=25[/tex]
Therefore, he use 25 lbs of nuts and 5 lbs cereal squares for party mix.
solve equation 3x +4/5=8
Answer:
x=2.4
Step-by-step explanation:
3x +4/5=8
3x = 8 -4/5
3x =7.2
x = 7.2/3
x=2.4
A construction company needs to remove 10 tons of dirt from a construction site. They can remove 2/5 tons of dirt each hour. How long will take to remove the dirt?
Step-by-step explanation:
You can just divide 10 by 2/5 and you get 25 or try this
Set up proportions and cross multiply 2/5 / 1 = 10/x which you can read as : if 2/5 can be done in 1 hour then 10 tons can be done in x hours cross multiplying, you get 2x/5 = 10 and x = 25
Please answer QUICK!! for brainliest!!!
Answer:
1
Step-by-step explanation:
The 2 equations have different slopes, so they have 1 solution.
A bag contains 2 gold marbles, 8 silver marbles, and 20 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $5, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss if you play this game?
Answer:
expected loss of 4/30 ≈ 0.13 dollars
Step-by-step explanation:
profit = revenue - expenses
expected profit= expected revenue - expected expenses
how i solve this is by multiplying each revenue and expense by its probability and solving from there
revenue of gold = 5
revenue of silver = 2
revenue of black = 0
this exhausts all of our revenue options
total marbles = 2+8+20 = 30
# of gold marbles = 2
probability of gold = 2/30
# of silver marbles = 8
probability of silver = 8/30
# of black marbles = 20
probability of black = 20/30
expected revenue = sum of possible revenues multiplied by their probability
= 5 * 2/30 + 2 * 8/30 + 0 * 20/30 = 10/30 + 16/30 = 26/30
cost = 1 no matter what
expected profit = expected revenue - expected expenses
= 26/30 - 1
= -4/30
= an expected loss of 4/30
4/30 ≈ 0.13
Diagonal of a square is 4 root 2. Find the length of a side of a square
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{4\sqrt{2}}\\ a=\stackrel{adjacent}{s}\\ b=\stackrel{opposite}{s}\\ \end{cases}\implies (4\sqrt{2})^2~~ = ~~s^2~~ + ~~s^2 \\\\\\ 4^2\sqrt{2^2}~~ = ~~2s^2\implies 16(2)=2s^2\implies 32=2s^2\implies \cfrac{32}{2}=s^2 \\\\\\ 16=s^2\implies \sqrt{16}=s\implies \boxed{4=s}[/tex]
.
Which line is parallel to the line that passes through the points of (2,-5) and (-4,1)
Answer:
y= -x-5
Step-by-step explanation:
m=1-(-5)/-4-2
m=-1
-1= -x
y=-x-5
The point B (3, -1) has been translated from A by the Vector (4∗3) . What are the coordinates of A?
If point B (3, -1) has been translated from A by the Vector (4, 3). Then the coordinates of A will be (12, -3)
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
Point B (3, -1) has been translated from A by the Vector (4, 3).
Then the coordinates of A will be
Point B (3, -1) x (4, 3)
Point B (3 x 4, -1 x 3)
Point B (12, -3)
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Which compound inequality has a solution set of all real numbers?
Question 5 options:
a) x > -2 or x < 1
b) x < -1 and x > 2
c) x < -1 and x > 2
d) x < -3 or x > -2
Answer:
If the number on the other side of the inequality sign is negative
Step-by-step explanation:
I just know okay
QUESTION 58
Calculate graduation rates using the following information: In 2012, 3,388 student entered the freshman class at
CMU. Of the 3,388 27.4% graduated in 4-years. The 5-year graduation rate (those that graduated in 5-years of
less) was 54.2%. The 6-year graduation rate was 60.9%.
How many students graduated in 4 years or less?
How many additional students (beyond the number of students who graduated in 4-years) graduated in their 5th
year?
How many additional students (beyond the number of students who graduated in 5-years) graduated in their 6th
year?
For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
Frankie wants to build a path from one corner of his yard to the opposite corner. His yard measures 20 ft. x 32 ft. What will be the length of his path to the nearest tenth of a foot? 21.5 ft 25.0 ft 32.6 ft 37.7 ft
Answer:
37.7 ft
Step-by-step explanation:
This is Pythagorean Theorem aka A^2+B^2=C^2
20^2+32^2=C^2
400+1024=C^2
1424=C^2 (now square root both sides)
37.7359…
Closest answer is 37.7 ft
Answer: [tex]37.7ft[/tex]
Step-by-step explanation:
[tex]a=32, b=20[/tex]
[tex]look[/tex] [tex]for~ the ~hypotenuse~ c[/tex]
[tex]a^2+b^2=c^2[/tex]
[tex]\sqrt{32^2+20^2} =37.7ft[/tex]
A standard NBA basketball has a diameter of 24.1 cm. What is the volume of a standard NBA basketball?
a.7,329 cm3
b.270 cm3
c.58,633 cm3
d.1,629 cm3
The volume of a standard NBA basketball is 7,329 cm³.
What is the volume of a sphere?The volume of a sphere is given by the formula,
V = 4/3×π×r³
Given the diameter of the ball is 24.1 cm, therefore, the radius of the ball will be 12.05cm (half the diameter of the ball). Thus, the volume of the NBA basketball will be,
V = 4/3 × π × (12.05)³
V = 7,329.084 cm³ ≈ 7,329 cm³
Hence, the volume of a standard NBA basketball is 7,329 cm³.
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Which table contains only values that satisfy the following? y = x - 1
What is the sum of 9 7/8 plus 11 2/8?
Answer:
169/8
Step-by-step explanation:
9 7/8 = 79 / 8
11 2/8 = 90 / 8
90/8 + 79/8
The denominator (8) stays the same
90+79 = 169
169/8 or 21 1/8
Part A
If Wendell creates a scale drawing using the scale 1 inch to 10 feet, what will the dimensions of the deck in the scale drawing be?
Part B
In the scale drawing, what will the length of the east side of the backyard be?
Part C
In the scale drawing, what will the length of the south side of the backyard be?
Part D
In the scale drawing, what will the length of the west side of the backyard be?
Part E
In the scale drawing, what will the length of the north side of the backyard be?
Part F
Two corners of the backyard are right angles. The third corner forms an obtuse angle measuring 127º. The fourth corner forms an acute angle measuring 53º. When transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease, or stay the same?
Part G
In the scale drawing, what is the area of the lawn (that is, the area of the whole backyard, except for the deck)?
Answer:
234
Step-by-step explanation:
What is the perimeter of the rectangle in the coordinate plane?
14 units
28 units
36 units
45 units
Answer:
45 units^2
Step-by-step explanation:
W x H = area
9 x 5 = 45 units^2
Answer:
28 units
Step-by-step explanation:
Length (l) = 9 units
Breadth (b) = 5 units
Perimeter of the rectangle will be,
→ 2(l + b)
→ 2(9 + 5)
→ 2 × 14
→ 28 units
Hence, the perimeter is 28 units.
help asap please bbbbb
Answer:432 whats the other option 4300
Step-by-step explanation:
Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,4802).
[tex]y = ab^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=14 \end{cases}\implies 14~~ = ~~ab^0\implies 14=a(1)\implies 14=a~\hfill \underline{y=14b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=4802 \end{cases}\implies 4802~~ = ~~14b^3\implies \cfrac{4802}{14}=b^3 \\\\\\ 343=b^3\implies \sqrt[3]{343}=b\implies 7=b~\hfill \underline{y=14(7)^x}[/tex]
Mr. Linares manages a construction company which is currently hiring. If today he interviewed 4 carpenters and 2 masons, what is the probability that the first applicant he saw was a carpenter?
Answer:
2/3
Explanation:
total people: 4 + 2 = 6 people
carpenters: 4 carpenters
probability = favourable outcomes/total possible outcomesprobability = 4/6 ≈ 2/3
Answer:
P (carpenter) = 2/3 or 0.67
Step-by-step explanation:
Probabilty of seeing a Carpenter first
Number of carpenters = 4Total number of applicants = 4 + 2 = 6P = No. of carpenters / Total applicants⇒ P (carpenter) = 4/6
⇒ P (carpenter) = 2/3 = 0.67
If each student needs 1/3 of a stick of clay to do an art project,and there are 4 sticks of clay, how many students can do the art project?
Answer:
12 students
Step-by-step explanation:
Because the total is 4 sticks, and each student needs 1/3 of a stick, we would have to see how many 1/3 sticks fit into 4 sticks. Because 3 of the 1/3 sticks fit into 1 stick, then 4 sticks would be 4*3=12 of the 1/3 sticks, which means 12 students can do it.
We could also just do: 4/(1/3)= 4*(3/1)=12
This is fractional division. The second value of the division process, we switch the numerator and denominator's, and the expression turns to a multiplication expression, where we can just multiply.
Heeeeelp please
An arithmetic series has ay = 3 and d= - 3. Find S20-
The first term is 3 and the common difference is negative 3. Then the sum of the first 20 terms will be negative 510.
What is a series?A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.
The first term (a₁) = 3 and the common difference (d) = -3. Then the sum of the first 20 terms will be
Sₓ = (x/2) [2a₁ + (x - 1)d]
Then we have
S₂₀ = (20/2) [2 × 3 + (20 - 1)-3]
S₂₀ = 10 [6 + (19)(-3)]
S₂₀ = 10 [6 - 57]
S₂₀ = 10 [51]
S₂₀ = -510
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What is the slope of a line through (-3, 4) and
(5, 6)?
Answer:
slope= x2- x1/y2 -y1
= 5-(-3)/6-4
8/2= 4
£6846 is shared equally between 7 people. How much does each person get?
Answer: Each person gets £978
Step-by-step explanation: £6846 divided by 7 is £978
