Answer:
6.50
Step-by-step explanation:
Write down the inequality shown on the
number line below.
For the given number line the inequality equation would be -10 < x ≤ 20.
What is inequality?
In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
In the given number line, a hollow circle represents that the number is excluded and solid circle represents that the number is included in the range
and the range lies between -10 to 2.
Let's take a variable to describe the relationship,
By using inequality we can prepare the inequality equation as
-10 < x ≤ 20
Hence, for the given number line the inequality equation would be -10 < x ≤ 20.
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2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of which type of reaction?
The reaction described by 2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of oxidation - reduction reaction
What is Redox reaction?Any chemical process in which a participating chemical species' oxidation number changes is known as an oxidation-reduction reaction, often known as a redox reaction. The phrase refers to a broad range of procedures.
The equation of the reaction is written as
2H₂O + 2K → 2KOH + 2H₂
The reducing agent here is Potassium which is K it transformed from Potassium to Potassium Hydroxide. Potassium is electron donor
The oxidizing agent is water which ended up as Hydrogen molecule
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You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period. How many hours x of television must you watch in the eighth week to meet your goal?
Television Viewing
Week....... Hours Watched
1 .......................1
2 .....................1.5
3 .....................0.5
4 .......................3
5 ......................1.5
6 ........................2
7 .......................0.5
There are 2 hours of television must you watch in the eighth week to meet your goal.
What is television?
The transmission of audio and video data electronically between a source and a recipient.
The primary use of television is to transmit shows for entertainment, information, and education. Television is a system for transmitting visual images and sound that are reproduced on screens.
Given: You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period.
Suppose x is the hours of watching television in the 8th week.
Let the average of watching television per week is 1.5.
⇒
[tex]\frac{1 + 1.5 + 0.5 + 3 + 1.5 + 2 + 0.5 + x}{8} = 1.5\\ \frac{10+x}{8}=1.5 \\10+x = 12\\x = 12-10\\x = 2[/tex]
Hence, there are 2 hours of television must you watch in the eighth week to meet your goal.
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Which of the following choices correctly names the figure below?
An investor invested a total of $2900in two mutual funds. One fund earned a 8% profit while the other earned a 6% profit. If the investor's total profit was $194, how much was invested in each mutual fund?
The amount invested at 8% and 6% is 1000 and 1900 respectively.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, The person invested $2900 in two mutual funds and the total profit is $194.
Let the amount invested at 8% is x, then the amount invested at 6% is:
2900-x
Since the total profit is $194, it follows:
8% of x + 6% of (2900 - x) = 194
8x/100 + 6(2900 - x)/100 = 194
8x + 17400 - 6x = 19400
2x = 19400 - 17400
2x = 2000
x = 1000
The amount invested at 6% is:
2900 - 1000
= 1900
Hence, the amount invested at 8% and 6% is 1000 and 1900 respectively.
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the probability that a restaurant passes its health department inspection is 0.94. the owners of 58 restaurants are surveyed to see if their restaurants passed inspection.
For each binomial experiment described, find
A. the mean
B. the variance
C. the standard deviation
The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.
As given in the question,
Let success be defined by health department inspection is passed by restaurant
Probability of success rate 'p' = 0.94
Value of ' 1 - p ' = 1 - 0.94
= 0.06
Number of owners of restaurant which are surveyed 'n' = 58
For the given binomial experiments calculation of the following distributions are:
Mean 'μ' = np
= 58 × 0.94
= 54.52
Standard deviation 'σ' = √ np (1 - p)
= √ 58 × 0.94 × 0.06
= √3.2712
= 1.808
Variance 'σ²' = np( 1 - p )
= 58 × 0.94 × 0.06
= 3.2712
Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.
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Review the proof of the identity cos(π − A) = −cosA.
cos(π − A)
Step 1: = cosπcosA − sinAsinπ
Step 2: = (−1)(cosA) + (sinA)(0)
Step 3: = −1cosA + (sinA)(0)
Step 4: = −cosA + 0
Step 5: = −cosA
At which step was an error made?
step 1
step 2
step 3
step 4
In the proof of given identity, cos(π - A) = -cos A. Therefore, step 1 is error made.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
The given identity is,
cos(π - A) = -cos A.
Use formula for cos(a − b) = cosa . cosb + sina . sinb
cos(π - A) = cosπcosA + sinAsinπ
= (−1)(cosA) + (sinA)(0)
= −1.cosA + (sinA)(0)
= −cosA + 0
= −cosA
Since, in the step 1 the formula is wrongly used,
Therefore, step 1 is error made.
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write the equation in slope -intercept form. What are the slope and y intercept?
-3x-10y=7
Answer: slope -intercept form = [tex]-\frac{3}{10} x-\frac{7}{10}[/tex] the slope = [tex]-\frac{3}{10}[/tex] and the y-intecept = [tex](0,-\frac{7}{10} )[/tex]
Step-by-step explanation: I used y=mx+b and filled it in with the infomation that I already knew. Hope this helps :)
Heather works as a waitress at her family's restaurant she works every 2 hours every morning during the breakfast shift and returns to work each evening for the dinner shift in the last 4 days she worked 28 hours if Heather works the same number of hours each evening how many hours did she work during each dinner shift?
Heather worked 5 hours every evening during each dinner shift.
What is a Linear Equation?Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
Let morning shift = m
evening shift = e
Representing the word problem in an equation;
4(m + e) = 28
Diving both sides by 4
m + e = 7
but she always works 2 hours in th morning shift
2 + e = 7
e = 7 - 2
e = 5
Therefore she worked 5 hours in the evening shift for 4 days.
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a fair die is rolled four times A4 is condsider success while all.other out comes are failures what is the probability of 2 succusses?
Answer:
P(Success1) =1/6
P(Success2) =1/6
P(2Success) =1/6 × 1/6 = 1/12
Select all expressions that equal the distance between the points on the number line
| 3 | + | -2 |
| -2 + 3 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
The expressions that are equal to the distance between point A and point B would be
| 3 | + | -2 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
What is a number line?
In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
In the given number line, the distance between point A and point B is 5.
Now we have to check each option
| 3 | + | -2 | = 3 + 2 = 5
| -2 + 3 | = | 1 | = 1
| -3 - 2 | = | -5 | =5
3 - ( -2 ) = 3+ 2 = 5
| 3 - ( -2 ) | = |3 + 2| = 5
Hence, the expressions that are equal to the distance between point A and point B would be
| 3 | + | -2 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
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22. What are the values of w and x in the triangle below? Round the answers to the nearest tenth.
(1 point)
The values of x and w on the triangle are given as follows:
w = 14.4, x = 11.2.
How to obtain the values of x and w?The values of x and w are obtained applying the trigonometric ratios, as the triangle is a right triangle.
The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For the angle of 48º, we have that:
The adjacent side is w.The opposite side is of 16.Hence:
tan(48º) = 16/w
w = 16/tan(48º)
w = 14.4.
For the angle of 32º, we have that:
The adjacent side is 14.4 + x.The opposite side is of 16.Hence:
tan(32º) = 16/(14.4 + x)
tan(32º)(14.4 + x) = 16
x = (16 - 14.4tan(32º))/tan(32º)
x = 11.2.
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3x+9-7=c+10+x
-4x+9=2x+10
Consider the relation below
Is it a function?
Is the relation a one to one function?
Is the inverse of the relation below itself of function ?
7. Determine the midpoint
a) A (-4,6) B (2,-3)
The coordinates of the midpoint of line segment A (-4,6) and B (2,-3) is M (-1 , 3/2).
What is a line segment?A line segment is a measurable route between two points. Line segments can make up any polygon's sides because they have a set length.
Given:
Points A (-4,6), and B (2,-3)
Calculate the midpoint of the line segment by the formula given below,
[tex]M [(x_1 + x_2) / 2 \ \ , (y_1 + y_2)/2][/tex]
Substitute the values,
M [(-4 + 2) / 2 , (6 + (-3) / 2)]
M [(-2 / 2) , (3 / 2)]
M (-1 , 3/2)
Therefore, the coordinates of the midpoint of line segment A (-4,6) and B (2,-3) is M (-1 , 3/2).
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7. Charlie went to Juarez, Mexico, on a shopping trip.
He bought silver rings at $5 each and bracelets at $8
each. If he bought a total of 19 items and spent $131,
how many bracelets and rings did he buy?
The difference of the ages of a sister and her younger brother is 6 years. The
numerical value of the product of their ages is equal 4 times the sum of their
Find the present ages of the sister and her brother.
Answer:
bother = 6 years ; sister = 12 years
Step-by-step explanation:
s = sister
b = brother
s - b = 6
s * b = 4(s+b)
s = b + 6
b(b+6) = 4(b+6 + b)
b² + 6b = 4(2b + 6)
b² + 6b = 8b + 24
b² + 6b - 8b - 24 = 0
b² - 2b - 24 = 0
(b-6)(b+4) = 0
b = 6
b = -4 (impossible because an age can’t be negative)
s = 6 + 6
s = 12
I have a job that pays me 40 dollars an hour. However, it's far away and I pay $250
a week on gas. I have another job that's closer, but it only pays 25 dollars an hour
and I only spend 100 dollars on gas a week. What should I do? Use math to
support your answer. (Calculate this problem on a monthly basis. On both jobs, he
would work 160 hours per month.)
Answer: The first job seems better.
Step-by-step explanation:
If 1 month = 4 weeks:
40 x 40 = 1600 per week
40 x 160 = 6400 per month
250 per week on gas
250 x 4 = 1000 per month on gas
1600 - 250 = 1350
6400 - 1000 = 5400
You would earn $1350 per week on the first job, and $5400 on this job.
_____________________________________________________
25 x 160 = 4000 per month
25 x 40 = 1000 per week
100 per week on gas
100 x 4 = 400 per month on gas
1000 - 100 = 900
4000 - 400 = 3600
$900 per week on the second job, and $3600 per month on this job.
Hello,
I hope you and your family are doing well!
To compare the two jobs and determine which one is more financially advantageous, you need to calculate the total income and total expenses for each job on a monthly basis.
For the first job, the total income is 40 dollars per hour * 160 hours per month = 6400 dollars per month. The total expenses are 250 dollars per week * 4 weeks per month = 1000 dollars per month. The net income is 6400 dollars per month - 1000 dollars per month = 5400 dollars per month.
For the second job, the total income is 25 dollars per hour * 160 hours per month = 4000 dollars per month. The total expenses are 100 dollars per week * 4 weeks per month = 400 dollars per month. The net income is 4000 dollars per month - 400 dollars per month = 3600 dollars per month.
Based on these calculations, the first job is more financially advantageous because it has a higher net income. You would earn an additional 1800 dollars per month by working the first job instead of the second job.
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Happy Holidays!
determine if law of sines or law on cosines is the best choice substitute the values into the appropriate formula and solve
Answer:
Hi again, use the sine rule for length. answer: 82.42
Step-by-step explanation:
Rename 4/5 and 5/7 using the least common denominator.
7.
Which is a factored form of 8x³ + 27? (1 point)
O (2x+3)(2x+3)(2x + 3)
O (2x+3)(4x² - 6x +9)
○ (2x − 3)(4x² + 6x + 9)
O(2x-9)(4x² + 18x +81)
Answer:
B) (2x + 3)(4x² - 6x + 9)-----------------------------------
Given sum of cubes, use identity a³ + b³ = (a + b)(a² - ab + b²):
8x³ + 27 = (2x)³ + 3³ = (2x + 3)((2x)² - (2x)(3) + 3²) = (2x + 3)(4x² - 6x + 9)The matching choice is B.
Answer:
B) (2x + 3)(4x² - 6x + 9)
Step-by-step explanation:
Given expression:
[tex]8x^3+27[/tex]
Rewrite 8 as 2³ and 27 as 3³:
[tex]\implies 2^3x^3+3^3[/tex]
[tex]\textsf{Apply exponent rule} \quad a^nc^n=(ac)^n:[/tex]
[tex]\implies (2x)^3+3^3[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Sum of Cubes Formula}\\\\$a^3+b^3=(a+b)(a^2-ab+b^2)\\\end{minipage}}[/tex]
Therefore:
a = 2xb = 3Using the Sum of Cubes formula:
[tex]\begin{aligned}\implies (2x)^2+3^3&=(2x+3)((2x)^2-2x(3)+3^2)\\&=(2x+3)(4x^2-6x+9)\end{aligned}[/tex]
helpppp me please!!!
Answer:
Step-by-step explanation:
17-8=9 but if 18-7=11 then 19-8=7
A grocery store has small bags of apples for $5 each and large bags for $8 each. If you buy 15 bags and spend $93, how many of each size bag did you buy?
Answer:
There are 9 small $5 bags and 6 large $8 bags
Step-by-step explanation:
9 x 5 = 45
6 x 8 = 48
45 + 48 = 93
30. Choose all equations that are true.
48 X 1,000 = 4,800
48 x 1024,800
48 X 104
480,000
48 X 10³ = 4,800.00
48 X 10³ = 48,000
Answer: 1, 3
Step-by-step explanation:
Question 4
A seller at a farmer's market sells trays of large eggs and extra large eggs.
They sold a total of 75 trays of eggs in the past month.
•
They sold twice as many trays of large eggs as extra large eggs.
4.1. If they sold x trays of large eggs and y trays of extra large eggs, write
down two linear equations for the results above.
Answer:
They would have sold 8.2 eggs
Step-by-step explanation:
^
What Is The Order?
For The Variable Expressions
Answer:
I think it’s 4/n and 4 divided by n. Sorry if it’s wrong!
Step-by-step explanation:
if 15 and 9 are two members of a
Pythagorean triple, what is the third
member?
Answer: 12
Step-by-step explanation:
hope this helps
Im so confused on this like i think it was y=-5/3x but i dont know
Answer:
Below
Step-by-step explanation:
Slope , m, is calculated (y1-y2) / ( x1-x2) =
Using the first two points : (-5-0) / (-3 -0) = 5/3
slope = 5/3
the capacity of an elevator is either 20 children or 15 adults. if 17 children are currently in the elevator, how many adults can still get in?
Two more adults can board the elevator if there are 17 children present inside.
Explain the concept of capacity of an elevator?The point when 20 children or 15 adults can enter an elevator is considered the elevator's capacity. The number of adults who can still enter the elevator when there are 17 children inside must be determined.A linear equation can be created to resolve the aforementioned issue.The number of adults who can still enter will be determined by the linear equation solution.
let
c is equal to a child's weight.a is equal to 1 adult's weight.20c = 15a ; 5 divided by both sides
4c = 3a
Another 3 kids can enter the elevator if there are already 17 in it.
The fact that;
3c = 9/4 a
3c = 9/4 a
3c = 2.25 a
3c = 2 a (no fraction)
Thus, two more adults can board the elevator if there are 17 children present inside.
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the volume of a cube with length x is V(x)=x^3. The volume of the sphere with radius 1/2x is shown in the graph. Over the interval [1,2], which volume is increasing faster?
Answer:
The volume of the cube is increasing faster.
The volume of the cube with length : [x] is increasing faster.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the volume of a cube with length [x] is V(x) = x³. The volume of the sphere with radius (1/2)x is shown in the graph.
We have the volume of the cube with length : [x] is -
V{C} = x³
Volume of the sphere with radius : (1/2)x is
V{S} = (4/3)πr³ = (4/3)π(x/2)³ = πx³/6
V{S} = πx³/6
Refer to the graph of the function attached of both the function. It can be seen that the function of the volume of the cube with length [x] is increasing faster.
Therefore, the volume of the cube with length : [x] is increasing faster.
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