Answers
Work Shown:
[tex]\sin^2 \theta + \cos^2 \theta = 1\\\\\left(\frac{3}{10}\right)^2 + \cos^2 \theta = 1\\\\\frac{9}{100} + \cos^2 \theta = 1\\\\\cos^2 \theta = 1 - \frac{9}{100}\\\\\cos^2 \theta = \frac{100}{100}-\frac{9}{100}\\\\\cos^2 \theta = \frac{91}{100}\\\\\cos \theta = \sqrt{\frac{91}{100}} \ \text{ cosine positive in Q1}\\\\\cos \theta = \frac{\sqrt{91}}{\sqrt{100}}\\\\\cos \theta = \frac{\sqrt{91}}{10}\\\\[/tex]
Answer:
√91/10
Step-by-step explanation:
sin 0.3 is equal to 18(approximate value)
cos18°=0.951
which is √91/10
Related Questions
If John has pairs of red, orange, yellow, blue and green socks, how many can he wear them in over 5 days, repetition is allowed because hog is alright with wearing dirty socks. A)5! B)25 C)5^5 D)125
Answers
Answer:
Total ways = 5×5×5×5×5
Total ways = 5^5
Total ways = 3125
Therefore, the correct option is C) 5^5
Step-by-step explanation:
John has pairs of red, orange, yellow, blue and green socks.
Which means that John has 5 different colors pairs of socks.
We are asked to find out in how many ways can he wear them over 5 days.
1st Day:
On the first day John has 5 ways to choose from.
2nd Day:
On the second day John has 5×5 ways to choose from.
(Since repetition is allowed)
3rd Day:
On the third day John has 5×5×5 ways to choose from.
4th Day:
On the fourth day John has 5×5×5×5 ways to choose from.
5th Day:
On the fifth day John has 5×5×5×5×5 ways to choose from.
Total ways = 5×5×5×5×5
Total ways = 5^5
Total ways = 3125
Therefore, the correct option is C) 5^5
Write the equation of the line in point-slope form that passes through (1, -4) and has a slope of 1/4.
Answers
Answer:
y + 4 =(1/4)(x - 1)
Step-by-step explanation:
The point slope equation is y - k = m(x - h), where (h, k) is the given point and m is the given slope.
In this particular case we have y + 4 =(1/4)(x - 1)
Given the radius of a circle is 7 cm, what is the circumference?
Answers
Answer:
14π or 43.96
Step-by-step explanation:
C = 2πr and we know that r = 7 so C = 14π or 43.96.
A bag contains two red marbles, four green ones, one lavender one, four yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender
Answers
Answer:
192
Step-by-step explanation:
There are a total of 15 marbles . When the lavender is left out 14 remain.
Using combinations we find that each of the four color marbles can be chosen in the following way.
2C1*4C1*4C1*6C1= 2*4*4*6= 192
We select one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting or . (b) Compute the probability of randomly selecting or or . (c) Compute the probability of randomly selecting or .
Answers
Answer: See answer in the attached file
Step-by-step explanation:
What is the value of Sine theta in the diagram below?
Answers
Answer:
C) 24/25
Step-by-step explanation:
did the quiz and got it right
The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]
What is the trigonometric function in the first quadrant?The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.
In the first quadrant;
cos(θ) > 0, sin(θ) > 0 andtan(θ) > 0Thus, we have a positive x and y-axis.
Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)
The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]
Learn more about Trigonometric functions here:
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The surface area of a given cone is 1,885.7143 square inches. What is the slang height?
Answers
This question is not complete. This is because it lacks the appropriate diagram containing necessary information to solve this question.
Please find attached the appropriate diagram to solve for this question
Complete Question :
The surface area of a given cone is 1,885.7143 square inches. What is the slant height?
Answer:
25 inches
Step-by-step explanation:
In the diagram, we are given the following information
Height of the cone = 20 inches
Radius of the cone = 15 inches.
The formula for the slant height of a cone represented by l =
l² = r² + h²
l = √(r² + h²)
l = √(15² + 20²)
l = √(225 + 400)
l = √625
l = 25 inches
Therefore, the slant height of this cone = 25 inches
A building has eight levels above ground and one level below ground. The height of each level from floor to ceiling is feet. What is the net change in elevation going from the floor of the underground level to the ceiling of the fourth level above ground? Assume the floor at ground level is at an elevation of zero feet.
Answers
Answer:
72.5 feet
Step-by-step explanation:
The height of each level from floor to ceiling is 14 1/2 feet.
We want to find the net change in elevation going from the floor of the underground level to the ceiling of the 4th level above ground.
In other words, the change in elevation in going 5 floors up.
Each level has a height of 14 1/2 feet (29/2 feet).
Therefore, the height of the fourth level above ground from the underground level will be 5 times the height of one level:
h = 5 * 29/2 = 72.5 feet
The net change in elevation from the floor of the underground level to the 4th level above ground is:
ΔE = [tex]h_4 - h_0[/tex]
[tex]h_0 = 0 feet\\\\h_4 = 72.5 feet[/tex]
Therefore:
ΔE = 72.5 - 0 = 72.5 feet
Answer:
72.5
Step-by-step explanation:
the solution of the equation 0=4+4(m+1) is
Answers
Answer:
[tex]\boxed{m = -2}[/tex]
Step-by-step explanation:
[tex]0 = 4+4(m+1)[/tex]
Resolving Parenthesis
[tex]0 = 4+4m + 4[/tex]
[tex]0 = 4m+8[/tex]
Subtracting 8 to both sides
[tex]-8 = 4m[/tex]
[tex]4m = -8[/tex]
Dividing both sides by 4
m = -8/4
m = -2
Step-by-step explanation:
4+4m+4= 0
4m+8=0
4m=-8
m= -8/4=-2
Help, Please. File attached this time. Sorry
Answers
Answer:
27 degrees
Step-by-step explanation:
Because there is a straight line, all of the angles shown add up to 180, so if you add up all the given angles and subtract it from 180, you will get your answer.
39+86+28=153
180-153=27
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
Ingredients
•1 1/2
cups all-purpose flour.
• 31/2 teaspoons baking powder.
• 1 teaspoon salt.
1 tablespoon white sugar.
• 1 1/4 cups milk.
• 1 egg.
• 3 tablespoons butter.
1.) How much of each of the ingredients do you need to make 16 pancakes, 4 pancakes, 12pancakes? Explain which operations with fractions you used to obtain your answer.
Answers
Answer:
To make 16 pancakes, we would multiply each of the initial measurement of the ingredients by 16.
To make 4 pancakes, we would multiply each of the initial measurement of the ingredients by 4.
To make 12 pancakes, we would multiply each of the initial measurement of the ingredients by 12.
see explanation below
Step-by-step explanation:
If the ingredients to make 1 pancake is as follows:
1 1/2 cups all-purpose flour; 31/2 teaspoons baking powder; 1 teaspoon salt.
1 tablespoon white sugar.; 1 1/4 cups milk; 1 egg; and 3 tablespoons butter.
Then to make 16 pancakes, we would multiply each of the initial measurement of the ingredients by 16.
cups all-purpose flour =16× 1 1/2
= 16×3/2 = 24
teaspoons baking powder = 16 ×7/2 = 56
teaspoon salt = 1×16 = 16
tablespoon white sugar= 1×16 = 16
cups milk= 16×5/4 = 20
egg= 1×16 = 16
tablespoons butter= 3×16 = 48
Then to make 4 pancakes, we would multiply each of the initial measurement of the ingredients by 4.
cups all-purpose flour =4× 1 1/2
= 4×3/2 = 6
teaspoons baking powder = 4 ×7/2 =14
teaspoon salt = 1×4 = 4
tablespoon white sugar= 1×4 = 4
cups milk= 4×5/4 = 5
egg= 1×4 = 4
tablespoons butter= 3×4 = 12
Then to make 12 pancakes, we would multiply each of the initial measurement of the ingredients by 12.
cups all-purpose flour =12× 1 1/2
= 12×3/2 = 18
teaspoons baking powder = 12 ×7/2 =42
teaspoon salt = 1×12 = 12
tablespoon white sugar= 1×12 = 12
cups milk= 12×5/4 = 15
egg= 1×12 = 12
tablespoons butter= 3×12 = 36
The operation applied is multiplication with each fraction.
The area of each square below is 1 square unit. How can we calculate the area of the striped region? A: 7/5 x 1/2 B: 6/12 x 2/10 C: 7/5 x 2/10
Answers
Answer:
wrong thing
Step-by-step explanation:
13 arent shaded of the 20 units
7/20 are shaded, 7X1=7, 2X5=10
what equals 1+1= Why can't I see any answers help i logged off etc is it just me?
Answers
Answer:
1 + 1 = 2
Step-by-step explanation:
^
Answer:
no , it's happening to everyone , even I can't see it .
The function y=−16x2+v0x models the height of a football in feet x seconds after a player kicks it. In the equation of the function, v0 is the ball's initial velocity in feet per second. The ball hits the ground 2 seconds after the player kicks it.
What is the value of v0?
Answers
Answer:
[tex]\large \boxed{\sf \ \ v_0=32 \ \ }[/tex]
Step-by-step explanation:
Hello,
The equation is
[tex]y=f(x)=-16x^2+v_0 \cdot x[/tex]
The ball hits the ground 2 seconds after the player kicks it, it means that f(2)=0.
We need to find [tex]v_0[/tex] such that f(2)=0.
[tex]f(2)=-16\cdot 2^2+v_0 \cdot 2=-64+2v_0=0\\\\\text{*** add 64 to both sides ***}\\\\2v_0=64\\\\\text{*** divide by 2 both sides ***} \\\\v_0=\dfrac{64}{2}=32[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
v0 = 32 ft/s
Step-by-step explanation:
You work in a machine design department and need to specify the diameter of a pin that slides back and forth through a hole. The hole diameter is specified as 0.500 inch with a tolerance of 0.010 inch. The maximum pun diameter must be 0.002 inch smaller than the minimum hole diameter. If the pin diameter has a tolerance of 0.010 inch what diameter in inches should you specify for the pin?
Answers
Answer:
B. 0.478
Step-by-step explanation:
The diameter of the pin is 0.478 inches as per specification.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators.
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
The hole diameter is specified as 0.500 inches with a tolerance of 0.010 inches.
The maximum pun diameter must be 0.002 inches smaller than the minimum hole diameter.
Diameter: d = 0.500 inch
Tolerance: t = 0.010 inch
Replacing the values:
⇒ dmax = 0.500 - 0.010 - 0.002 - 0.010
Apply the subtraction operation,
⇒ dmax = 0.478 inch
Hence, the diameter of the pin is 0.478 inches as per specification.
Learn more about Arithmetic operations here:
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how many terms are in the expression 6y+3+y+4y+5
Answers
Answer:
5
Step-by-step explanation:
The 5 terms in the expression are ...
6y
3
y
4y
5
__
If like terms were combined, the expression could be reduced to one with 2 terms:
11y +8
Answer:
5 terms
Step-by-step explanation:
In an expression, a term can be a number, a variable, or a number and variable multiplied together. Terms are separated by addition or subtraction.
In the expression:
6y+3+y+4y+5
There are 5 terms. The 5 terms are:
1. 6y
2. 3
3. y
4. 4y
5. 5
We can simplify this expression by combining like terms. We can add the constants (just numbers) and the terms with variables being multiplied by numbers.
6y+3+y+4y+5
(6y+y+4y)+(3+5)
11y+(3+5)
11y+8
Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general?
42 40 39 31 22 18 15 12 11.7 10.5
____________________________________________________________________________
The Range of the sample data is $[ ] million. (Type an integer or a decimal)
The variance of the sample data is [ ]. (Round to three decimal places as needed.)
The standard deviation of the sample data is $[ ] million. (Round to three decimal places as needed)
Is the the standard deviation of the sample a good estimate of the variation of the salaries of the TV personalities in general ?
A. yes, because the standard deviation is an unbiased estimator
B. no, because the sample is not representative of the whole population.
C. no, because there is an outlier in the sample data.
D. yes, because the sample is random.
Answers
Answer:
If you do not need that actual numbers, the answer is B.
Step-by-step explanation:
In order to find a fully comprehensive study, you would need many more people than just 10, not to mention these are the top 10 people in the world.
(Brainliest would be much appreciated!)
Select the correct answer from each drop down menu.
The slope of diagonal OA is
A) 4/3
B) 3/4
C) 1
,and it’s equation is
A) 4x-y=0
B) x-3y=0
C) 4x-3y=0
Answers
Answer:
(A) [tex]\text{The slope of OA is }\dfrac{4}{3}[/tex]
(C) It’s equation is 4x-3y=0.
Step-by-step explanation:
Point O is at (0,0)
Point A is at (3,4)
[tex]\text{Slope of OA}=\dfrac{4-0}{3-0} \\m=\dfrac{4}{3}[/tex]
The equation of a straight line is in the form: y=mx+b
The y-intercept of the line OA=0
Therefore, we have:
[tex]y=\dfrac{4}{3}x+0\\3y=4x+0\\$Subtract 3y from both sides$\\4x-3y=0[/tex]
The equation of the line is: 4x-3y=0
Consider a triangle ABC like the one below. Suppose that B=36°, C= 62°, and b= 40. (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".
Answers
Answer:
A=82°
a= 67.4
c = 60.1
Step-by-step explanation:
For A
A+B+C =180°
A= 180-(B+C)
A= 180-(36+62)
A= 189-(98)
A= 82°
For a
a/sinA= b/sinB
a/sin82= 40/sin36
a= (40*sin82)/sin36
a=( 40*0.9903)/0.5878
a=67.39
Approximately = 67.4
For c
c/sinC= b/sinB
c= (sinC*b)/sinB
c= (sin62*40)/sin36
c =(0.8829*40)/0.5878
c = 60.08
Approximately = 60.1
8mi 200 yds - 2 mi 528 yds =
Answers
Answer:
5 mi 1432 yds
Step-by-step explanation:
8mi 200 yds
- 2 mi 528 yds
---------------------------
We have to borrow 1 mile and convert to yards
1 mile = 1760 yds
7mi 200+1760 yds
- 2 mi 528 yds
---------------------------
7mi 1960 yds
- 2 mi 528 yds
---------------------------
5 mi 1432 yds
Answer:
8mi 200yds - 2mi 528yds
= 5mi 1432yds
Step-by-step explanation:
1 mile = 1760 yards
8 miles = 7miles + 1 mile = 7 miles + 1760 miles = 7 miles 1760 yards
8miles 200 yards = 7miles + 1760 yards + 200 yards = 7miles + 1960 yards
then:
8mi 200 yds - 2 mi 528 yds = 7mi 1960yds - 2mi 528yds
7mi 1960yds
- 2mi 528yds
= 5mi 1432yds
HELP PLEASE! A Blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same). How many acorns is the Blue Jay going to store for the winter, and in how many trees?
Answers
Answer:
Step-by-step explanation:
Let
T = number of trees
A = number of acorns
Given:
A = 18T + 4 ...........................(1)
A = 20T -4 .........................(2)
Equate A from (1) and (2)
20T-4 = 18T+4
simplify and solve for T
20T - 18T = 4+4
2T = 8
T = 4 trees
A = 18T + 4 = 72+4 = 76 acorns, or
A = 20T - 4 = 80 - 4 = 76 acorns.
What is the relationship between angle a and angle b A) Vertical Angles B) Complementary Angles C) Supplementary Angles D) None of the above
Answers
Answer:
C. Supplementary
Step-by-step explanation:
Angle a and angle b are on the line CZA.
We can assume that line CZA is a straight line, which is equal to 180 degrees.
Since angle a and b are on the straight line together, they must add to 180 degrees. Therefore, they are supplementary angles.
So, choice C. Supplementary angles is correct.
Amber says that the data set is left-skewed because the box is farther to the left on the number line. (A) Is Amber correct? (B) Explain your reasoning.
Answers
find 10th term of a geometric sequence whose first two terms are 2 and -8. Please answer!!
Answers
Answer:
The 10th term is -524,288
Step-by-step explanation:
The general format of a geometric sequence is:
[tex]a_{n} = r*a_{n-1}[/tex]
In which r is the common ratio and [tex]a_{n+1}[/tex] is the previous term.
We can also use the following equation:
[tex]a_{n} = a_{1}*r^{n-1}[/tex]
In which [tex]a_{1}[/tex] is the first term.
The common ratio of a geometric sequence is the division of the term [tex]a_{n+1}[/tex] by the term [tex]a_{n}[/tex]
In this question:
[tex]a_{1} = 2, a_{2} = -8, r = \frac{-8}{2} = -4[/tex]
10th term:
[tex]a_{10} = 2*(-4)^{10-1} = -524288[/tex]
The 10th term is -524,288
A heptagon can be divided into how many triangles by drawing all the diagonals from one vertex
Answers
Answer:
5 triangles from the vertex
Answer:
5 triangles from the vertex
Step-by-step explanation:
Roberta sold goods costing $35,500, her expenses totaled $2,500 and her freight in totaled $750.
Her company's average stock of goods during the same period was $9,500.
The inventory turnover ratio for Roberta's company is
Answers
Answer:
Inventory turnover ratio is 3.74
explanation:
Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.
Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold
= $35,500 / $9500
= 3.74
A bag contains ten tiles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked.
What is the probability of picking a vowel?
Write your answer as a fraction in simplest form.
Answers
Answer:
1/5
Step-by-step explanation:
B, C, D, E, F, G, H, I, J, K. = 10 tiles
E and I are vowels
P ( vowel) = vowels/ total
=2/10
= 1/5
In total, we are given 10 letters.
The vowers are; A, E, I, O, and U
In the bag, we can see we have 2 vowels (E and I)
This means that 2 out of the 10 letters are vowels (2/10).
We can simplify the fraction by dividing by 2.
2÷2/10÷2
1/5
Therefore, the answer is 1/5.
Best of Luck!
The sum of a number and 9 is subtracted from 60. The result is 10. Find the number.
Answers
Answer:
Number : 41
Step-by-step explanation:
Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,
60 - (x + 9) = 10,
60 - x - 9 = 10,
51 - x = 10,
- x = 10 - 51 = - 41,
x = 41
This number will be 41
Find two numbers with difference 62 and whose product is a minimum.
Answers
Answer:
31 and -31
Step-by-step explanation:
The two numbers with a difference of 62 and whose product is a minimum are; 31 and -31
Let the two numbers be x and y.We are told that their difference is 62.
Thus; x - y = 62 ---(1)
We want their products to be minimum. Thus;f(x,y) = xy
From eq, making y the subject gives us;
y = x - 62
Thus;
f(x) = x(x - 62)
f(x) = x² - 62x
For the product to be minimum, let us find the derivative of f(x) and equate to zero. Thus;f'(x) = 2x - 62
At f'(x) = 0
2x - 62 = 0
2x = 62
x = 62/2
x = 31
Thus;
y = 31 - 62
y = -31
Read more at; https://brainly.com/question/9473957
I need help for this problem!
Answers
Answer:
[tex] a = 2.7 [/tex]
Step-by-step explanation:
Distributive property can be used to solve the equation, by multiplying [tex] \frac{2}{3} [/tex] with [tex] 6a, [/tex] and [tex] 9 [/tex]
Thus,
[tex] (\frac{2}{3}*6a) + (\frac{2}{3}*9) = 16.8 [/tex]
[tex] 2*2a + 2*3 = 16.8 [/tex]
[tex] 4a + 6 = 16.8 [/tex]
Subtract 6 from both sides.
[tex] 4a + 6 - 6 = 16.8 - 6 [/tex]
[tex] 4a = 10.8 [/tex]
Divide both sides by 4 to solve for a
[tex] \frac{4a}{4} = \frac{10.8}{4} [/tex]
[tex] a = 2.7 [/tex]