Answer:
63
Step-by-step explanation:
When dividing by a fraction, it is the same a multiplying that fraction but the reciprocal of it.
21 / 1/3 is same as 21 * 3/1
63
Answer: 63
A wooden bean 6 meters long leans against a wall and makes an angle 71 degrees with the ground. How high up the wall, to the nearest meter, does the beam reach?
Trigonometry
Answer:
The far of reaching the wall
24 71
=69.70106106ft
Step-by-step explanation:
The wooden beam reaches a height of 6 meters on the wall.
Explanation:To find the height of the beam on the wall, we can use trigonometry.
The given angle is 71 degrees and the length of the beam is 6 meters.
We can use the sine function to find the height. The formula is: height = length * sin(angle).
height = 6 * sin(71)
Using a calculator, we find that the height is approximately 5.753 meters.
Rounding to the nearest meter, the beam reaches a height of 6 meters on the wall.
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cookies are sold singly or in packages of 4 or 6. with this packaging, how many ways can you buy exactly 10 cookies?
Answer:
1. 10 singles. 2. One package of 6 and 4 singles. 3. One package of 6 and one package of 4. 4. Two packages of 4 and 2 singles 5. One package of 4 and 6 singles.
Step-by-step explanation:
There are 5 ways in which 10 cookies can be sold in singly or in packages of 4 or 6.
Given that,
cookies are sold singly or in packages of 4 or 6. with this packaging, how many ways can you buy exactly 10 cookies is to be determined.
In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Ways in which exactly 10 cookies can be sold,
= {10 cookies singly, pack of 4 cookies and 6 cookies singly, pack of 4 and pack of 6, 4 cookies singly and a pack of 6 and 2 pack of 4 and two cookies singly,}
= 5 ways
Thus, there are 5 ways in which 10 cookies can be sold in single or in packages of 4 or 6.
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What is the measure of arc HI?
Answer:
D. 62˚
Step-by-step explanation:
Identify the Domain and Range of the graph below:
PLEASE HELP I WILL GIVE BRAINLIST!
Answer:
-2.5<x<2.5
Step-by-step explanation:
Out of the 1236 employees who work for a particular company, 748 of them work in an office. One employee is selected every month to receive a free
lunch. The probability that the selected employee does not work in an office is
Answer:
458
Step-by-step explanation:
Final answer:
The probability that the selected employee does not work in an office is calculated by dividing the number of employees not working in an office (488) by the total number of employees (1236), resulting in a probability of approximately 0.395.
Explanation:
The question asks for the probability that the selected employee does not work in an office from a total of 1236 employees, where 748 work in an office. To find this, we first need to determine the number of employees who do not work in an office.
Employees not working in an office = Total employees - Employees working in an office
= 1236 - 748 = 488
Now, the probability of selecting an employee who does not work in an office is calculated by dividing the number of employees not working in an office by the total number of employees:
Probability = Number of employees not working in an office / Total number of employees
Probability = 488 / 1236
Therefore, the probability that the selected employee does not work in an office is approximately 0.395.
Mary mixes white paint and blue paint in the ratio 2:3
She makes a total of 20 litres of paint.
How much more blue paint does she need to add to the mixture so that the ratio of white paint to blue paint becomes 1:7?
Given:
Ratio of white and blue paint is 2:3
Total quantity of paint is 20 litres
To find:
Quantity of blue paint to be mixed so that the ratio of white paint to blue paint becomes 1:7
Solution:
The ratio 2:3 totals 20 that is [tex]2x+3x=20\rightarrow5x=20\rightarrow x=4[/tex]
So, the quantity of white paint in the mixture is [tex]2\times4=8[/tex] and the quantity of blue paint in the mixture is [tex]3\times4=12[/tex]
Now, to get the final ratio as 1:7, Mary should have [tex]7\times8=56 \text{ litres }[/tex] of blue paint. So, she need to add [tex]56-12=44 \text{ litres}[/tex].
Therefore, Mary has to add 44 litres of blue paint to the mixture to make the ratio as 1:7.
How do you find an outlier mathematically?
You use these formulas:
Q1 - 1.5(IQR)
Q3 + 1.5(IQR)
If any numbers fall outside the range of the solutions to the above equations, then they're an outlier.
A rectangular prism has a length of 4 1/2, a width of 4 1/2 and a height of 6. Sally has a storage container for the prism that has A volume of 143 cubic. What is the difference between the volume of the prism and the volume of the storage container
Question:
A rectangular prism has a length of 4 1/2 millimeters, a width of 4 1/2 millimeters, and a height of 6 millimeters.
Sally has a storage container for the prism that has a volume of 143 cubic millimeters.
What is the difference between the volume of the prism and the volume of the storage container?
Answer:
The difference between the volume of the prism and the volume of the storage container is 21.5 cubic millimeter
Solution:
Volume of rectangular prism is given as:
[tex]volume = length \times width \times height[/tex]
From given,
[tex]length = 4\frac{1}{2} = \frac{9}{2}\ mm\\\\width = 4\frac{1}{2} = \frac{9}{2}\ mm\\\\height = 6\ mm[/tex]
Therefore,
[tex]volume = \frac{9}{2} \times \frac{9}{2} \times 6 = 121.5\ mm^3[/tex]
Sally has a storage container for the prism that has a volume of 143 cubic millimeters
What is the difference between the volume of the prism and the volume of the storage container
Difference = 143 - 121.5 = 21.5
Thus difference between the volume of the prism and the volume of the storage container is 21.5 cubic millimeter
0.125 to the nearest thousandth
Answer:
5 SHOULD BE THE ANSWER SORRY FOR ALL CAPS
Answer:
5
Step-by-step explanation:
0 is lower than 5 so your number would stay the same
What is the range of y = –5sin(x)? all real numbers Negative 5 less-than-or-equal-to y less-than-or-equal-to 5 all real numbers Negative five-halves less-than-or-equal-to y less-than-or-equal-to five-halves all real numbers Negative 1 less-than-or-equal-to y less-than-or-equal-to 1 all real numbers Negative one-fifth less-than-or-equal-to y less-than-or-equal-to one-fifth
Answer:
The range of given function is
[tex][-5,5][/tex]
Step-by-step explanation:
We are given the function:
[tex]y = -5\sin(x)[/tex]
We have to find the range of the given function.
Range of function
Range is the collection of all possible values of y for the domain of function.Range of basic sine function is
[tex]-1\leq \sin(x) \leq 1[/tex]
Multiplying the range by -5
[tex]5\geq -5\sin(x) \geq -5[/tex]
Thus, the range of given function is
[tex]-5\leq -5\sin(x) \leq 5[/tex]
[tex]-5\leq y\leq 5[/tex]
Thus, the range of given function is
[tex][-5,5][/tex]
The attached image shows the graph for the given function.
All real numbers {y | − 5 ≤ y ≤ 5 }
Step-by-step explanation:
Can you help me please?
A lizard is jumping across the water in search of food. The equation h = -12t2 + 6t
models the lizard's height in feet above the water t seconds after he jumps. How long
after Jumping is he back on the water?
To find the time when the lizard is back on the water, set the height equation equal to zero and solve for t. The lizard is back on the water 1/2 second after jumping.
Explanation:To find the time when the lizard is back on the water, we need to set the height, h, equal to zero, and solve for t in the given equation, h = -12t^2 + 6t.
Substitute 0 for h:
0 = -12t^2 + 6t
Now we can solve for t. Rearrange the equation to quadratic form:
12t^2 - 6t = 0
Factor out a common factor of 6t:
6t(2t - 1) = 0
Set each factor equal to zero:
t = 0 or 2t - 1 = 0
If t = 0, it means the lizard is on the water at the time it jumps. Therefore, t = 0 is not the solution we're looking for. If 2t - 1 = 0, solving for t:
2t = 1
t = 1/2
Therefore, the lizard is back on the water 1/2 second after jumping.
Eric needs to order programs for the next school football game. Only 1 out of 2 people will buy a program for the game. If there will be 900 people at the game and programs come in boxes of 50, how many boxes of programs should Eric order?
Answer:
Eric should order 9 boxes of programs.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Probability of buying a program for the game = 1/2
Number of people at the game = 900
Number of programs per box = 50
2. How many boxes of programs should Eric order?
Let's calculate the answer this way:
Number of programs required for the next football game = Probability of buying a program for the game * Number of people at the game
Replacing with the values given, we have:
Number of programs required for the next football game = 1/2 * 900
Number of programs required for the next football game = 450
Now, we can calculate he number of boxes, this way:
Number of boxes of programs Eric should order = Number of programs required for the next football game /Number of programs per box
Replacing with the values given, we have:
Number of boxes of programs Eric should order = 450/50
Number of boxes of programs Eric should order = 9
What is the velocity of a wave with a frequency of 4.0 Hz and a wavelength of 0.50 m/wave?
Answer:
v=fa
Step-by-step explanation:
(4)(.5)=2
v=2
Using FOIL method. Multiply the terms. (X^2 -7)(x^2 -4)
Answer:
x^4-11x^2+28
Step-by-step explanation:
Set it upx^2(x^2-4) -7(x^2-4)
2. Multiply
x^4-4x^2-7x^2+28
3. Simplify
x^4-11x^2+28
Simplify the expression.
7(6x – 4) + 1
1. Distribute the 7 through the parentheses.
2. Combine like terms.
What is the expression in its simplest form?
42x – 28 + 7
42x – 3
42x – 28 + 1
42x – 27
Answer:
42x-27
Step-by-step explanation:
7(6x-4)+1 is your original expression. Distribute to get 42x - 28 + 1. Combine like terms and add 1 to -28, which is -27. So, 42x-27 is your answer.
The value of the expression is 9/16 and the expression in its simplest form is 42x-27
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 7(6x – 4) + 1
We need to simplify it.
In the given expression x is the variable
Plus and minus are operators of addition and subtraction.
7(6x – 4) + 1
Distribute the 7 through the parentheses.
42x-28+1
Add the like terms
42x-27
The expression in its simplest form is 42x-27
42x=27
Divide both sides by 42
x=27/42=9/16
Hence, the value of the expression is 9/16 and the expression in its simplest form is 42x-27
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what would the slope of y= -2/5x + 4 be and how can it be broken down for me to understand?
Answer:
So, the slope is the number attached to the x.
In this case the slope is -2/5.
Example: y = 5x + 3
In this case, the slope is 5 because it is the number attached to the x.
HOPE THIS HELPS :)
What is the perimeter of triangle ABC?
Answer: 24 units.
Step-by-step explanation: Count out how many units long AB is. AB goes from -3 to 3, for a length of 6 units.
Count out how long AC is. AC goes from 4 to -4, for a length of 8 units.
To find BC, use the Pythgorean theorem (a^2+b^2=c^2). 8^2 is 64, and 6^2 is 36. Add 64 and 36 to get 100. Then find the square root of 100, which is 10.
Add all the lengths. 6+8+10=24.
Which fraction is equivalent to
6
8
?
Answer:
3/4
Step-by-step explanation:
Step 1: Simplify
6/8 is same as (6/2) / (8/2)
3 / 4
Answer: 3/4
Answer:
12/16, 18/24 24/32 etc.
Step-by-step explanation:
6×2/8×2=12/16, 6×3/8×3=18/24, 6×4/8×4=24/32 and so on. If you keep multiplying the numerator and denominator of the original fractions by natural numbers, the results are equivalent fractions.
John is saving $6 a week. He has already saved $28. How many weeks will it take John to reach his goal of $100?
Answer:
12 weeks
Step-by-step explanation:
If John is aiming to save $100, with $6 a week and he has already saved $28. The leftover amount to be saved is $100 - $28 = $72
In one week → $6
2 weeks → $12
3 weeks → $18
and so on..
[tex]\frac{72}{6} = 12[/tex]
John will need 12 more weeks to save a total of $100.
Translate the phrase into an algebraic expression. The sum of 17 and twice a number
Let's make "x" the number.
So the sum of 17 and twice a number:
17 + 2 * a number
17 + 2 * x
17 + 2x
The value of algebraic expression is,
⇒ 2x + 17
Where, x is a number.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The phrase is,
'' The sum of 17 and twice a number.''
Now, Let a number = x
So, We can formulate;
The algebraic expression is,
⇒ 17 + 2 × x
⇒ 17 + 2x
⇒ 2x + 17
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Given a circle U which has a center at coordinates (1,3) and a point on its circumference at (2, 2), what is the area of the circle?
Answer:do anyone know the answer yet
Step-by-step explanation:
Braden's Sports sells golf tees in packs of 2. Meanwhile, Wayne's Gear sells them in packs of
6. If both shops sold the same number of golf tees this week, what is the smallest number of
tees each could have sold?
Answer:
6
Step-by-step explanation:
The LCM of 2 and 6 is 6. I hope this helps
15(x-3) over 5 = 3(2x-3)
What is X?
Answer:
x=0
Step-by-step explanation:
Answer: x= infinite solutions
there are infinite solutions and when graphing it shows you that they are together they are infinte solutions
Step-by-step explanation:
15(x-3)/5=3(2x-3)
15(x-3)/5=6x-9
*5 *5
15(x-3)=30x-45
15x-45=30x-45
-15x -15x
-45=15x-45+45
+45
0=15x
0/15=x
0=x
Will give brainlest
g(-5)=?
Answer:
-6
Step-by-step explanation:
g(-5) is the value of function g at x value -5
the graph shows the point (-5,-6), so g(-5)=-6
Answer:
-6
Step-by-step explanation:
The sum of two numbers is 47 and the difference is 19. What are the numbers?
Answer: The two numbers are 33 and 14
Step-by-step explanation: We shall start by first assigning letters to unknown variables. Therefore let the two numbers be called a and b. The first clue in this question states that the sum of both a and b equals 47. That means we can write the expression;
a + b = 47.
The second clue states that their difference equals 19. This also can be expressed as follows;
a - b = 19
Now we have a pair of simultaneous equations which are
a + b = 47 ———(1)
a - b = 19 ———-(2)
We shall use the substitution method. Therefore from equation (1), make a the subject of the equation.
a = 47 - b
Next we substitute for the value of a in equation (2)
a - b = 19
47 - b - b = 19
47 -2b = 19
By collecting like terms we now have 47 - 19 = 2b
28 = 2b
Divide both sides of the equation by 2
14 = b
We can now substitute for the value of b into equation (1)
a + b = 47
a + 14 = 47
Subtract 14 from both sides of the equation
a = 33.
Therefore the two numbers are 33 and 14.
The two numbers with a sum of 47 and a difference of 19 are 33 and 14. We found this by setting up two equations based on the given information and solving for the two variables.
Explanation:The sum of two numbers is 47 and the difference is 19. To find these two numbers, we can set up a system of equations and solve them. Let the numbers be x and y.
x + y = 47 (equation 1)x - y = 19 (equation 2)Adding both equations, we get 2x = 66, hence x = 33.
Substituting x in equation 1, we get 33 + y = 47, hence y = 47 - 33 = 14.
Therefore, the two numbers are 33 and 14.
Scientists put marks on 30 mooses as part of an effort to estimate the local most population greater the scientist Flew Over the area and counted a total of 210 most of which 10 remark to the nearest whole number what is the best estimate for the moose population.
A. 70
B. 630
C. 159
D. 357
Answer: It is D.
Step-by-step explanation: I have taken this quiz before!
Please give me brianliest
Answer:
Step-by-step explanation:
720
A = {1,4,5,7}
B = {1,7,9,12}
Find A ∩ B.
A) {1,4,5,7,9,12}
B) {1,7}
C) {1}
D) {7}
Answer:
B)
Step-by-step explanation:
A ∩ B means all the elements that appear in both of the groups
therefore:
1 nad 7 appear in both
the correct answer is B) 1 and 7
Answer:
pretty sure it A many people said B was wrong
Step-by-step explanation:
Missing fraction
blank + 1/16 = 3/2
Final answer:
To solve for the missing fraction in the equation blank + 1/16 = 3/2, convert 3/2 to a fraction with a denominator of 16 to give 24/16. Then, subtract 1/16 from 24/16 to get the missing fraction, which is 23/16.
Explanation:
To find the missing fraction in the equation blank + 1/16 = 3/2, we first need to express 3/2 with the same denominator as 1/16 to facilitate addition. The common denominator for 16 and 2 is 16, so we can rewrite 3/2 as 24/16 (since 3 × 8 = 24 and 2 × 8 = 16). Our equation now is blank + 1/16 = 24/16. To solve for the missing fraction (blank), we subtract 1/16 from 24/16, which gives us 23/16.
Example:
Rewrite 3/2 as 24/16
Subtract 1/16 from 24/16 to find the missing number
The missing fraction is 23/16
This method demonstrates how to find a missing fraction by creating a common denominator and then subtracting to isolate the missing number.
The line 2y - x + 5 = 0 and the curve (10 – x)^2+ (y – 5)^ 2= 10 intersect at points A and B.
Find the coordinates of A and of B.
Answer:
A(9, 2 ), B(13, 4 )
Step-by-step explanation:
Given the 2 equations
2y - x + 5 = 0 → (1)
(10 - x)² + (y - 5)² = 10 → (2)
Rearrange (1) expressing x in terms of y by adding x to both sides
x = 2y + 5 → (3)
Substitute x = 2y + 5 into (2)
(10 - (2y + 5))² + (y - 5)² = 10, that is
(10 - 2y - 5)² + (y - 5)² = 10
(5 - 2y)² + (y - 5)² = 10 ← expand the factors using FOIL
25 - 20y + 4y² + y² - 10y + 25 = 10
5y² - 30y + 50 = 10 ( subtract 10 from both sides )
5y² - 30y + 40 = 0 ( divide through by 5 )
y² - 6y + 8 = 0 ← in standard form
(y - 2)(y - 4) = 0 ← in factored form
Equate each factor to zero and solve for y
y - 2 = 0 ⇒ y = 2
y - 4 = 0 ⇒ y = 4
Substitute these values into (3) for corresponding values of x
y = 2 : x = 2(2) + 5 = 4 + 5 = 9 ⇒ (9, 2 )
y = 4 : x = 2(4) + 5 = 8 + 5 = 13 ⇒ (13, 4 )
Since we are not given the position of A or B in relation to each other then either of the points can represent A or B, that is
A(9, 2), B(13, 4)
OR
A(13, 4), B(9, 2)