find the sum
-84 + (-11)
Answer:
-84+(-11)= -95
-84 + (-11) = -84 - 11 = -95
By the commutative property, adding a negative number is the same as subtracting that number as a positive; therefore, something + (-11) = something - 11. After changing the equation from -84 + (-11) to -84 - 11, we use regular addition properties, adding the tens place and ones place to get -95.
A local animal shelter has 27 dogs and 23 cats. What percent of the
animals are dogs?
Answer:
54%
Step-by-step explanation:
total animals=27+23=50
\(dogs=\frac{27}{50} \times100=54\)
Given A = {10, 11, 12, 13}, B = {10, 12, 14, 16}, and C = {7, 8, 9, 10, 11}, find
A ∪ B
A ∩ B
A ∪ C
A ∩ C
B ∪ C
B ∩ C
The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:
A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.
A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.
A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.
A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.
B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.
B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.
Finally, performing the remaining operations:
(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.
(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.
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Write the equation of the question.
The equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.
According to the question,
We have the following information:
Slope of the line = 1/3
We know that the slope of the line is denoted by m.
y-intercept of the line = -1
We know that the y-intercept is denoted by b.
We have the following equation for the line in slope-intercept form:
y = mx+b
Putting the above values in this equation:
y = x/3-1
Hence, the equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.
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Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age. Round your answer to the nearest a needed 54, 68, 68, 54, 59, 58, 68, 57, 57
A. 59.7
B. 58.0
C. 59.0
D. 60.3
Answer:
D. 60.3
Step-by-step explanation:
Finding the mean,
M = (sum of values of data)/(number of data)
now, number of data = 9,
calculating the mean,
M = (54 + 68 + 68 + 54 + 59 + 58 + 68 + 57 + 57)/9
M = 543/9
M = 60.333
M = 60.3
What is the answer to c?
Answer:
The answer is 6.5
Step-by-step explanation:
The equation is y=3x-1. Plug in 2.5 as the value for x and solve.
3×2.5=7.5
7.5-1=6.5
why does area and perimeter change in different ways
Answer:
Step-by-step explanation:
Area and perimeter are both measurements used to describe geometric shapes, but they are fundamentally different concepts and therefore change in different ways.The perimeter of a shape is the distance around the outside of the shape. It is a measure of the total length of the boundaries or sides of the shape. Perimeter depends on the length of each side of the shape, and if one or more sides change in length, the perimeter will change accordingly. For example, if you take a square and double the length of one of its sides, the perimeter will double as well.On the other hand, the area of a shape is the measure of the surface enclosed by the shape. It is a measure of the amount of space inside the shape. The area depends on the length and width of the shape, and if one or both of these dimensions change, the area will change accordingly. For example, if you take a square and double the length of one of its sides, the area will increase by a factor of four.In summary, the perimeter of a shape depends on the length of its sides, while the area of a shape depends on its length and width. Therefore, changes to the length of a side will affect the perimeter, but not necessarily the area, while changes to the length or width will affect the area, but not necessarily the perimeter.
What type of angles are labeled and what is the value of m? Show your work.
Answer: I believe
M = 80
Step-by-step explanation:
100 - 20 = 80
A group of friends wants to go to the amusement park. They have $100 to spend on
parking and admission. Parking is $13, and tickets cost $14.50 per person, including
tax. How many people can go to the amusement park?
Answer:
3
Step-by-step explanation:
14.50 + 13.00 = 27.50
27.50 x 3 = 82.50
Answer:
6
Step-by-step explanation:
\color{red}{14.5}x+\color{blue}{13}=
14.5x+13=
\,\,\color{purple}{100}
100
-\color{blue}{13}\phantom{=}
−13=
\,\,-\color{blue}{13}
−13
Subtract 13 from both sides
\color{red}{14.5}x=
14.5x=
\,\,87
87
\frac{\color{red}{14.5}x}{\color{red}{14.5}}=
14.5
14.5x
=
\,\,\frac{87}{\color{red}{14.5}}
14.5
87
Divide both sides by 14.5
x=
x=
\,\,\boxed{6}
6
\text{6 people can go to the amusement park.}
6 people can go to the amusement park.
Can someone help me? I am stuck on this question! and tysm to the people who helped me!! <3 have a nice day!
Answer:
100/70
Step-by-step explanation:
i did 25 times 4 got 100 then did 100/70
4.Locate the opposite of point K on the number line, and label it point L.5. In the diagram above, zero represents the location of Martin Luther King Middle School Point Krelibrary, which is located to the east of the middle school. In words, create a real-world situation torepresent point L, and describe its location in relation to 0 and point K.
SOLUTION
For question 4
We want to locate the opposite of point K,
\(\text{ point K=}\frac{\text{8}}{12}\)To obtain the opposite of point k, we count from the point zero(0), backwards on the negative 8 times,
Consider the image below.
Hence the opposite of point K which is point L is
\(\text{Point L=}\frac{\text{-8}}{12}=-\frac{2}{3}\)For question 5
Since Point zero is the middle school, then
L in relation to point zero: Point L is west of the middle school with a length is 2/3 to the middle school.
\(\begin{gathered} \text{length of l from k is } \\ 2\times\frac{8}{12}=\frac{16}{12}=\frac{4}{3} \end{gathered}\)Hence
The L in relation to K: Point L is in the west of K with a length of 4/3 from K.
)The mean voltage of a battery is 15 and S.D 0.2.Find the probability that four such batteries connected in series will have combined voltage of 60.8 or more volts
The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.
In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.
The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.
The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.
Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.
First, we need to standardize the value of 60.8 using the formula:
Z = (X - μ) / σ
Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, the standardized value is:
Z = (60.8 - 60) / sqrt(0.16)
Z = 0.8 / 0.4
Z = 2
Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.
Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
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A force of 72 N is applied to an area of 610 cm2.
Calculate the pressure in N/m2.
Give your answer to the nearest integer.
Answer:
\(2 \frac{n}{ {m}^{2} } \)
Step-by-step explanation:
\( \frac{f}{a} = \frac{72}{6.1 \times 6.1} = \\ \frac{72}{37.21} = 1.93 \\ 2\)
what is one thousandth less than 0.061
Answer:
one thousandth is greater than 0.061
Step-by-step explanation:
Find the value of 36.8 divided by 2.3 show your reasoning
Answer:
the answer is 16
Step-by-step explanation:
because if you do long divison
4.1 A bag contains 6 red, 4 green, 2 yellow and 3 blue balls. In each case, give the ratio (in simplest form) of the asked number of balls in the bag.( 4 ) 4.1.1 The number of red balls to the number of green balls.
The number of red balls to the number of green balls is 3 : 2
How to determine the ratio?The distribution of the balls is given as:
6 red, 4 green, 2 yellow and 3 blue balls
The number of red balls to the number of green balls is represented as:
Ratio = Red : Green
So, we have:
Ratio = 6 : 4
Simplify
Ratio = 3 : 2
Hence, the number of red balls to the number of green balls is 3 : 2
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What is the solution to the following system of equations? 3x-2y=12 6x - 4y = 24
Answer:
D question,somewhat confusing, itsit's like simultaneous equation,but values are different
Answer:
x = 4 + 2y/3
Step-by-step explanation:
*
16. Round 234.564 to the nearest ones place
Answer:
235
Step-by-step explanation:
How do I fill out the table help me answer it but try to explain.
The diagram shows a triangle.
31° / 6x / x+16°
What is the value of x?
Step-by-step explanation:
31 + 6x + x + 16 = 180
7x + 47 = 180
7x = 180 - 47
x = 133/7
x = 19
What is 3/8 as a decimal representation and as a percent representation
Answer:
0.375 and 37.5%
Step-by-step explanation:
3/8 = 0.375
0.375*100=37.5%
The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own?
The number of Jim's model car is 48
How to determine the number of JIm's carFrom the question, we have the following parameters that can be used in our computation:
Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6
This means that
Jim : Terrence = 8 : 6
Also from the question, we have
Terrence owns 36 models cars
This means that
Terrence = 36
Substitute the known values in the above equation, so, we have the following representation
Jim : 36 = 8 : 6
Multiply by 6
Jim : 36 = 48 : 36
So, we have
Jim = 48
Hence, the number of car is 48
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Find the slope of the line. Describe how one variable changes in relation to the other. A. 2; distance increases by 2 miles per hour B. 2; distance decreases by 2 miles per hour C. 1/2; distance increases by 1 mile every 2 hours D. 1/2; distance decreases by 1 mile every 2 hours
The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.
What is a good example of a line's slope?
The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.
A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.
B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.
C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.
D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.
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At a sale this week, a suit is being sold for $244.20. This is 33% of the original price. What is the original price
Answer:
$740
Step-by-step explanation:
244.20= x(.33)
244.2/.33= x(.33)/.33
740=x
For this question “ followed by a number will mean to the power of.
I need the solution for x,y, and z with steps please
(3*5)”4*(2*3)”5*(2*5)”7= 2”x*3”y*5”z
Please and thank you
The solution for x, y, and z is x = 2, y = 2, and z = 2.
To solve the equation (35)"4(23)"5(25)"7 = 2"x3"y*5"z, let's break it down step by step:
Simplify the expressions within the parentheses using the power of operator ("^").
\((35)"4 = 15^4\\(23)"5 = 6^5\\(2\times5)"7 = 10^7\)
Apply the power rule of exponents, which states that \((a^b)^c = a^{(b\times c).\)
\(15^4 \times 6^5 \times 10^7 = (15610)^{(4+5+7)\)
Simplify the expression within the parentheses.
\((15610)^{16 }= 900^{16\)
Express both sides of the equation in terms of prime factors.
\(900 = 2^2 \times 3^2 \times 5^2\)
quate the powers of the prime factors on both sides of the equation.
\(2^2 \times 3^2 \times 5^2 = 2"x \times 3"y \times 5"z\)
From this, we can conclude that x = 2, y = 2, and z = 2.
Therefore, the solution for x, y, and z is x = 2, y = 2, and z = 2.
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4 less than the product of 8 and a number is equal to 6
A construction company will be penalized each day of delay in construction for bridge. The penalty will be $4000 for the first day and will increase by $10000 for each following day. Based on its budget, the company can afford to pay a maximum of $ 165000 toward penalty. Find the maximum number of days by which the completion of work can be delayed.
Answer:
The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.
Step-by-step explanation:
We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is
\(S_{n}\) = 165000.
Let us find the amount as arithmetic series as follows:
4000 + 5000 + 6000
The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.
We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:
\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)
The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )
Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:
Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)
⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]
⇒ 2 x 165000 = n(8000 + 1000n - 1000 )
⇒ 330000 = n(7000 + 1000n)
⇒ 330000 = 7000n + \(1000n^2\)
⇒ \(1000n^2\) + 7000n - 330000 = 0
⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0
⇒ \(n^2\) + 7n - 330 = 0
⇒ \(n^2\) + 22n - 15n - 330 = 0
⇒ n( n + 22 ) - 15 ( n + 22 ) = 0
⇒ ( n + 22 )( n - 15 ) = 0
⇒ n = -22, n = 15
We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.
Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.
Calculate the bearing of Y from X
Answer:
074°
Step-by-step explanation:
the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY
∠ NXY = 180° - 106° = 74°
the 3- figure bearing of Y from X is 074°
Please help me with this proof.
Answer:
See below
Step-by-step explanation:
For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.
Maria has a bag with 6 red marbles , 6 blue marbles , and 4 green marbles . Without looking Maria pick one marble. She does not replace it , and she picks another one. On the first pick , Maria gets a green marble. What is the probability that she gets a red marble on her second pick ?