Answer:
so there are 3825 worker in total
Step-by-step explanation:
675=15%
women=85%
how much workers are 5%=675/3 =225
225=5%
how many workers is 85%= 85/5=17
85%=225x17=3825
the sum of 12 terms of an arithmetic series is 186 and the 20th term is 83. find the sum of 40 terms of the series.
The Sum of 40 terms of the Arithmetic Sequence is 3,420..
Arithmetic Series is defined as a sum of the terms of arithmetic progression or sequence.
An Arithmetic progression is a sequence of terms in which the difference between two consecutive terms is a constant number.
We have following information about series
sum of 12 terms of an arithmetic series (S₁₂) = 186
the 20th term of arithmetic sequence = 83
i.e., a₂₀ = 83
As we know that nth term of arithmetic progression is aₙ= a + (n-1)d
where , a---> first term of sequence
n ----> nth term
d -----> constant difference between two consecutive terms
put n= 20 in above formula we get,
83 = a + (20-1 )d = a+ 19d ----(1)
Now , Using the sum of n arithmetic terms formula, Sₙ = n/2 ( 2a + (n-1)d)
so, for n = 12
186 = 12/2 ( 2a + 11d ) => 2a + 11d = 31 ---(2)
Solving equations (1) and (2) we get,
27d = 135 => d = 5
putting the value of d in equation (1)
83 = a + 19×5 => a = 83 - 95 = -12
thus sequence is like as -12, -7 , -2 , ------
Sum of first 40 terms of arithmetic sequence (S₄₀) = 40/2 ( 2× (-12) + 39d ) = 20 ( -24 + 39×5)
= 20( 171) = 3,420
So, required result is 3,420..
To learn more about Arithmetic Sequence, refer:
https://brainly.com/question/10694174
#SPJ4
-7.3, 7 3/4, 7.23, -7 2/3. Order the following rational numbers from least to greatest.
The order of the rational numbers from the least to greatest is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex] .
in the question ,
it is given that the rational numbers are -7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex] .
we have to arrange the rational numbers in order from least to greatest .
For arrangement we first convert all the rational numbers in decimal form .
the decimal form of the given rational numbers are as follows .
(i) -7.3 is already given in decimal form .
(ii) [tex]7\frac{3}{4}[/tex] = (7*4+3)/4 = (28+3)/4 = 31/4 = 7.75
(iii) 7.23 is already in decimal form .
(iv) [tex]-7\frac{2}{3}[/tex] = -(7*3+2)/3 = -23/3 = -7.666
the order is -7.666 < -7.3 < 7.23 < 7.75
which is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex]
Therefore , The order of the rational numbers from the least to greatest is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex] .
The given question is incomplete , the complete question is
Order the following rational numbers from least to greatest.
-7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex] .
Learn more about Order here
https://brainly.com/question/28820570
#SPJ1
Does the relation shown in the diagram below represent a function? Explain why or why not
The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.
Given that,
In the picture we can see the domain and range.
We have to find if the domain and range is function or not.
Each of the sets of domain values has precisely one range value, according to the mapping.
Every domain value in a relation must have precisely one range value in order for it to be referred to as a function. It is not recommended to assign or map a domain value to more than one range value.
Therefore, The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.
To learn more about function visit: https://brainly.com/question/5975436
#SPJ1
A thermostat in a house regulates when the heater turns on and off. The heater turns on then
the house is 4° below the set temperature and turns off when the house is 4° above the set
temperature. The temperature is set at 68°. At 10:15am the heater turns on, and at 10:30am the
heater turns off. Write a sinusoid that models the change in temperature in the house.
The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) the change in temperature in the house.
The heater turns on when the house is 4° below the set temperature and turns off when the house is 4° above the set temperature. The temperature is set at 68°. At 10:15 am the heater turns on, and at 10:30 am the heater turns off.
Temperature fluctuations can be modeled using the sine and cosine functions throughout the day.
The equations that can be used to model these data is of the form:
At 10:30 am the heater turned off,
⇒ 4° = A cos B(x - C)
At 10:15 am the heater turned on,
⇒68° = A cos B(x - C)
where A, B, and C are constants, y is the temperature in °C and x is the time
Thus, The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) is the change in temperature in the house.
To learn more about the sinusoid models click here:
https://brainly.com/question/16839941
#SPJ1
what is the function rule in slope intercept form
Answer:
The picture is not Clear. Please provide a better view of the question.
Step-by-step explanation:
Compare and Explain: Are they equivalent?
$3 for 6 bagels; $9 for 24 bagels
Answer: No
Step-by-step explanation: You want to find the unit rate for each bagel. 6/3 is 2 dollars, so each bagel is going to cost 2 dollars. If your getting 24 bagels for 9 dollars, 24/9 is 2 2/3 dollars for each bagel. 2 ≠ 2 2/3 so therefore, they're not the same.
The sum of 3 and four times a number
Answer:
-7
Step-by-step explanation:
Whose limeade has a weaker like flavor?
well, your proportion setup is good, let's simply use that then
[tex]\stackrel{Jaylan}{\cfrac{~~ \frac{ 3}{4 } ~~}{\frac{1}{5}}}\implies \cfrac{3}{4}\cdot \cfrac{5}{1}\implies \cfrac{15}{4}\implies \cfrac{3\frac{3}{4}}{1}~\frac{water}{lime} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Wanchen}{\cfrac{~~ \frac{ 2}{3 } ~~}{\frac{1}{6}}}\implies \cfrac{2}{3}\cdot \cfrac{6}{1}\implies \cfrac{12}{3}\implies \cfrac{4}{1}~\frac{water}{lime}[/tex]
well, the one with the lesser lime flavor will be the one that put too much water in the drink, the more water the less the fruit mix, the more waterdowned the drink is, well hell who put more water per lime? well Wanchen, shame on you.
PLS HELP MEEEEEEEEEE !!!!
Answer:
Step-by-step explanation:
Ok;
1. Area is base times height.
Here shown, the base is 18cm and the height is 11cm. Don't be fooled by the 14cm for it is just the leg of a triangle not full height!!
18*11=198cm^2
2. Divide by two. We just caculated the area of the rectangle. Now we know a triangle is half of a rectangle's area so divide by 2!
198/2= 98cm^2
you have seven different video games. how many different ways can you arrange the games side by side on a shelf?
The number of different ways to arrange 7 video games is = 7!
The question requests for the number of arrangements; That means we're dealing with permutation
the number of video games is 7;
To arrange 7 games, we make use of the following permutation formula;
[tex]^{n}P_{n} = \frac{n!}{(n-n)!}[/tex]
So, we have
n=7
No. of ways we can arrange is = [tex]\frac{7!}{(7-7)!}[/tex] = 7!
To learn more about Permutations visit :
https://brainly.com/question/17134530
#SPJ4
1. Harper is going to create a graph of the equation y = -0.5x + 12. Which of the following will be true about the graph?
The graph will contain the origin.
The graph will increase from left to right.
The graph will cross the x-axis at (12, 0).
The graph will have a slope of -0.5.
The statement that would be true concerning the graph would be that the graph will have a slope of -0.5.
What is a slope?A slope is defined as the difference between a chosen point on the vertical and horizontal axis.
The slope of a straight line graph has a constant equation that is used to determine its slope. Thus;
y = mx + b
Where m = the measure of the steepness of the straight line graph.
From the equation of the graph that was given;
y = -0.5x + 12. The slope of the graph which is represented by 'm' would be -0.5.
Learn more about graph slope her:
https://brainly.com/question/28337360
#SPJ1
Highest common factor of 32 , 48 and 72
Answer:
8
Step-by-step explanation:
4*8=32
6*8=48
9*8=72
They are all multiples of 8
Answer: 8
Step-by-step explanation: You can factor out 32, 48, and 72 by using prime factorization which is listing all of the PRIME factors for each number
32: 2 x 2 x 2 x 2 x 2
48: 3 x 2 x 2 x 2 x 2
72: 3 x 3 x 2 x 2 x 2
If you look at all the prime factors, 2 appears in every number 3 times, so you do 2x2x2 to get the final answer, which is 8.
The number of computer security breaches is expected to increase at a yearly rate of 86%.
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
___ %
The equivalent monthly rate of the number of security breaches is of 5.31%, using an exponential function.
What is an exponential function?An increasing exponential function is modeled according to the rule presented by the equation as follows:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which the parameters of the exponential function are listed as follows:
A(t) is the amount after t years.A(0) is the initial amount of the function, that is, the amount of A(t) at the reference year of 0.r is the growth rate of the function, given as a decimal.In the context of this problem, considering the increase at an yearly rate of 86%, the parameter rate r is given as follows:
r = 0.86.
Hence the function is defined as follows:
[tex]A(t) = A(0)(1.86)^t[/tex]
One year is composed by 12 months, hence the monthly increase is calculated as follows:
[tex]r_m = (1.86)^{\frac{1}{12}} - 1 = 0.0531[/tex]
The monthly increase rate is of 5.31%.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
Answer:
The answer is 5.3
Jordan saved $225 and continues to save $45 each week. RayAnn saved $150 and continues to save $60 each week. Write and solve a system of equations using any method for the given situation.
Equation for Jordan:
Equation for RayAnn:
Solution:
please help me with this! I need the answer a s a p and I also the the y and x axis in the last equation please!
The equations using any method for the given situation illustrated that:
Equation for Jordan: 225 + 45w
Equation for RayAnn: 150 + 60w
How to calculate the equation?Let the number of weeks be represented by w.
Jordan saved $225 and continues to save $45 each week. The equation for this will be:
= 225 + (45 × w)
= 225 + 45w
RayAnn saved $150 and continues to save $60 each week. The equation will be:
= 150 + (60 × w)
= 150 + 60w
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
(x-1)^2/x^2-1.
what is the x intercept
The x-intercept is 1 if the function is f(x) = (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function is:
f(x) = (x-1)²/x²-1
To find the x-intercept where y = 0
or f(x) = 0
0 = (x-1)²/x²-1
x ≠ ±1
x - 1 = 0
x = 1
Thus, the x-intercept is 1 if the function is f(x) = (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
which hypothesis or hypotheses about the relation between life satisfaction and job satisfaction has received the most empirical support?
Recent research has confirmed the Spillover Hypothesis by demonstrating a favourable association between life and job happiness.
According to the spillover hypothesis, behaviour or affect in a family system might flow immediately from one place or connection to another. Transfer takes place in the same valence, which means that one subsystem's negative affect is connected to another's negative affect, or stress at work spills over and intensifies stress at home. The compensatory hypothesis offers a different perspective by arguing that transfer between family subsystems occurs in the opposite valence, leading a person to seek fulfilment in one relationship or environment in order to make up for shortages in another.
Learn more about hypothesis here
https://brainly.com/question/18173488
#SPJ4
Jace left his house at time zero and drove to the store, which is 2 blocks away, at a speed of 1 block per minute. Then he stopped and went into the store for 6 minutes. From there, he drove in the same direction at a speed of 3 blocks per minute until he got to the bank, which is 6 blocks away from the store. He stopped at the bank for 7 minutes. Then he drove home at a speed of 2 blocks every minute. Make a graph of showing the number of blocks away from home that Jace is xx minutes after he leaves his house, until he gets back home.
The total time it took Jace to out home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.
What is a graph?In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty). Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. They serve quite diverse purposes and are best suited for very different uses.So, the total number of minutes Jace takes to get back home after going out:
From Home to store = 2 minutes (1 blocks/min) + 6 minute (stop)From store to bank = 2 minutes (3 blocks/min) + 7 minutes (stop)From bank to home = 4 minutes (2 blocks/min)Total minutes:
2 + 6 + 2 + 7 + 4 = 21 min(Refer to the graph attached below)
The graph represents that Jace travels a total of 8 blocksTherefore, the total time it took Jace to out of home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.
Know more about graphs here:
https://brainly.com/question/28953186
#SPJ13
if l || m, solve for x and y
I NEED HELP ASAP
The magnitude and direction of two forces acting on an object are 70 pounds, S76°E, and 120 pounds, N80°E, respectively. Find the magnitude, to the nearest
hundredth of a pound, and the direction angle, to the nearest tenth of a degree, of the resultant force.
The magnitude is approximately
pounds.
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
The magnitude is approximately 186 pounds.
What is meant by magnitude?A mathematical object's magnitude, often known as its size, is a quality that indicates whether it is bigger or smaller than other things of the same sort. Formally speaking, an object's magnitude represents the ordered (or ranked) outcome of the class of objects it belongs to.
We have to assume that the notation starts South and then moves 76 degrees East.
The 70-pound force is going at an angle down and to the right.
The down one is negative and the right one is positive.
We have to use the vectors as the hypotenuse of a rectangle.
70 cos(76) = vertical = 16.93 down
70 sin(76) = horizontal = 67.92 right
120 cos(80) = vertical = 20.83 up
120 sin(80) = horizontal =118.17 right
We have to add up all the values vertically and horizontally, and we get
-16.93 + 20.83 =3.9 up
67.92 + 118.17= 186.09 right
Here, the magnitude is the hypotenuse.
sqrt(15.21+34629.49) =186.13 pounds.
Direction is cos⁻¹(3.9/186.13) = 88.802
Remember this is North then 88.802 degrees East
Therefore, the magnitude is approximately 186 pounds.
To know more about the magnitude, visit:
https://brainly.com/question/13918931
#SPJ13
a researcher counts the number of students who agree, disagree, or are indifferent concerning a recent school policy change. what are the degrees of freedom for this chi-square goodness-of-fit test?
The number of degrees of freedom for the chi-square goodness-of-fit test is of:
2.
How to obtain the number of degrees of freedom for a chi-square test?The number of degrees of freedom for a chi-square goodness-of-fit test is obtained according to the multiplication presented as follows;
df = (r - 1) x (c - 1).
In which the variables are listed as follows:
r is the number of rows from the table.c is the number of columns from the table.The table in this problem has three rows, given as follows:
Students who agree with the recent school policy change.Students who disagree with the recent school policy change.Students who are indifferent with the recent school policy change.The table has two columns, which are given as follows:
Student's opinions.Absolute frequencies of the student's opinions.Hence the number of degrees of freedom of the test is given as follows:
df = (3 - 1) x (2 - 1) = 2 x 1 = 2.
More can be learned about chi-square tests at https://brainly.com/question/4543358
#SPJ1
What is an
equation of the line that passes through the points (6, 0) and (3, 4)?
The equation that passes (6,0) and (3,4) is -3y=4(x-6)
What are the different forms of straight lines ?
The following information about the straight line is required if we wish to obtain the equation for it.
1. The y-intercept and slope
2. Two-point and slope
3. Two things.
4. the intersection of the x- and y-axes
the straight line that passes through (6,0) and (3,4).
The equation can be expressed in a point-slope form which is ,
y/x-6=4/-3
∵ -3y=4(x-6)
Hence,
The equation that passes (6,0) and (3,4) is -3y=4(x-6)
To learn more about equations of straight lines from the given link,
https://brainly.com/question/18831322
#SPJ1
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!
Answer:
2. 25
max = 88 feet
See the attachment photo!
1. Noah is running a portion of a marathon at a constant speed of 6 miles per hour.
Complete the table to predict how long it would take him to run different distances at that speed, and how far he would run in different time intervals.
time in hours
miles traveled at 6 miles per hour
1
6
1
2
3
1
1
3
8
1
1
2
9
4
1
2
The expected value for getting heads, on 30 coin tosses, is 15. The
expected value for rolling a 1, after 30 die rolls is 5. What is the
expected value of the sum of these events? Enter your answer in the
box.
The expected value of the sum of these events will be 2 / 3.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that the expected value for getting heads, on 30 coin tosses, is 15. The expected value for rolling a 1, after 30 die rolls is 5.
The probability of the sum will be calculated as,
P = ( 15 / 30 ) + ( 5 / 30 )
P = ( 20 / 30 )
P = 2 / 3
Therefore, the expected value of the sum of these events will be 2 / 3.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
17. If a = 3b^2 and a = 27, what is one value of b?
4.5
9
1.73
3
Answer:
b = 3
Step-by-step explanation:
Given that,
→ a = 27
Forming the equation,
→ 27 = 3b²
Now the value of b will be,
→ 27 = 3b²
→ b² = 27/3
→ b = √9
→ [ b = 3 ]
Hence, the value of b is 3.
⇒Given that a=27 in the equation [tex]a=3b^{2} \\[/tex] in the place of a plug in 27 and solve for b
[tex]27=3b^{2} \\\frac{27}{3} =\frac{3b^{2}}{3} \\b^{2} =9\\b^{2}-9=0\\(b+3)(b-3)=0\\b+3=0\\or\\b-3=0\\b=-3\\or\\b=3[/tex]
⇒Note b can also be -3 but the only option available as the answer is 3
∴ b=3 in this case.
based on the t-test assuming equal variances on the t-testequal worksheet, is the difference in mean mpg between 4 and 8 cylinder cars statistically significant?
Yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.
What is t statistic and critical value of t?
T statistic is ratio of a parameter's estimated value to its standard error when it deviates from its hypothesized value.
Critical t value is a cut-off point in t distribution
In question, the calculated t statistic is 8.1023 and critical t value one tail is 1.7139 and critical t value two tail is 2.0686. So, the value of calculated t statistic is higher than critical t value one tail or two tail. Therefore, we can reject the null hypothesis.
Thus, yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.
Learn more about t statistic here:
brainly.com/question/15236063
#SPJ4
working out the following additions
√8 + √18
[tex]\fbox{7.07...}[/tex]
First, we need the square of both numbers (8 and 18)
square of 8:
[tex]\sqrt{8}[/tex]
[tex]=2.828[/tex]
square of 18:
[tex]\sqrt{18}[/tex]
[tex]=4.242[/tex]
Now, let's add both numbers:
[tex]2.828+4.242[/tex]
[tex]=7.07[/tex]
Francisco just got his driver's license and wants to rent a car. The platinum car rental company charges $180 plus $92 per hour to rent a car. The plastic car rental company charges $250 plus $75 per hour. For what number of hours would the companies charge the same amount?
6900 hours, make a list of multiples until lcm is found
A 9-foot ladder rests against the side
of a wall. The bottom of the ladder is
2 feet from the base of the wall.
Determine the measure of the angle
between the ladder and the ground.
Round to the nearest tenth.
Answer:
about 77.2°
Step-by-step explanation:
The figure is omitted--please sketch it.
Make sure your calculator is in degree mode.
[tex] \cos( \alpha ) = \frac{2}{9} [/tex]
[tex] \alpha = {cos}^{ - 1} \frac{2}{9} = 77.2[/tex]
77.2 degrees
Trevor and Michael are hosting a banquet. They plan to spend $400, plus or minus $50, at a cost of $25 per guest. Solve |25x-400| = 50 to find the maximum and minimum number of guests. If there can be up to 7 guests at each table, what is the minimum number of tables Trevor and Michael should reserve so that every guest has a seat?
1. The maximum and the minimum number of guests that Trevor and Michael should host at the banquet are 18 and 14, respectively.
2. The minimum number of tables that Trevor and Michael will need for the banquet is 2.
How are the numbers determined?We can employ the mathematical operations of addition, multiplication, division, and subtraction to determine the numbers.
Since the budget is limited to $450 or less, we can compute the maximum and the minimum number of guests for the event, using division operation.
Total budget for the banquet = $400 ± $50
Cost per guest = $25
Maximum number of guests to expect = 18 ($450/$25)
Minimum number of guests to expect = 14 ($350/$25)
The number of guests a table can accommodate = 7
The minimum number of tables to use for the banquet = 2 (14/7)
The maximum number of tables to use = 3 (18/7)
Thus, using division operation, Trevor and Michael should expect to host between 14 and 18 guests at the banquet.
Learn more about mathematical operations at https://brainly.com/question/20628271
#SPJ1