5. In an arithmetic sequence, the fifth term is 44 and the ninth term is 80.(a) Find the common difference. (b) Find the first term. (c) Find the sum of the first 50 terms of the sequence.
Step-by-step explanation:
first you should do is that find the common difference which is 9
There are 15 men and 21 women in a club. One man and one female are to be selected at random to represent the club. How many different pairs are there?
Someone please help me with this one, thanks
There are 315 number of different pairs
How to determine the number of pairs?The given parameters are:
Men = 15
Women = 21
The number of different pairs is calculated as:
Pair = Men * Women
So,we have:
Pair = 15 * 21
Evaluate
Pair = 315
Hence, there are 315 different pairs
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HEEEEEEEELLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
6
Step-by-step explanation:
This problem centers on recognizing the relationship between fractions and repeating decimals.
Note the following:
[tex]\frac{1}{3}=0.33333333333333333333333333333333333333333333333...[/tex]
or more simply [tex]\frac{1}{3}=0.\bar{3}[/tex]
This means that [tex]2\frac{1}{3}=2.\bar{3}[/tex]
Going back to the original expression, [tex]3\frac{2}{3}+2.\bar{3}[/tex] simplifies to [tex]3\frac{2}{3}+2\frac{1}{3}[/tex]
Next, adding mixed numbers. For adding mixed numbers, whole number parts and fractional parts can be added separately (this is because of the associative and commutative properties of addition)... because
[tex]3\frac{2}{3}+2\frac{1}{3}[/tex] means the same thing as
[tex](3+\frac{2}{3})+(2+\frac{1}{3})[/tex]
Changing the order, we can write it as
[tex]3+2+\frac{2}{3}+\frac{1}{3}[/tex]
Adding the whole number parts, 3+2 is 5.
Next, adding the fraction parts:
For adding fractions, one must have a common denominator (the bottom part of the fraction must be the same). Once they are the same, the denominator just sort of "hangs out" until the end without changing, and the numerators (the tops) are added together.
Fortunately, the denominators are already the same. So, add the numerators, and the denominator will stay as a 3.
[tex]\frac{2}{3}+\frac{1}{3}[/tex]
[tex]\frac{1+2}{3}[/tex]
[tex]\frac{3}{3}[/tex]
It is important to recognize that any fraction* where the number on the top matches the number on the bottom, the fraction is equivalent to 1.
*(except if the number we're talking about is zero)
So, the fraction parts added together, are equivalent to 1, and the whole number parts added were equal to 5. Returning to our expression...
[tex]3+2+\frac{2}{3}+\frac{1}{3}[/tex]
[tex]5+\frac{3}{3}[/tex]
[tex]5+1[/tex]
[tex]6[/tex]
Please help! Evaluate the following expression:
4+ (8x √9) ÷ (2+4)
A. 6
B. 28/6
C. 8
D. 15/6
Answer:
the answer to the question is C) 8
f(x)=x²-3x-2 is shifted 4 units left. The result is g(x). What is g(x)?
A. g(x)=(x-4)² - 3(x-4)-2
B. g(x)=x²-3x+2
C. g(x) = (x+4)² - 3(x+4) - 2
D.g(x) = (x+4)² - 3x-2
Answer:
c
Step-by-step explanation:
left is in brackets and opposite sign so left is plus right is minus
Point A lies outside of plane P, how many lines can be drawn parallel to plane P that pass through point A.
The number of lines that can be drawn parallel to plane P that passes through point A is 1.
How to depict the information?From the information given, we are told that Point A lies outside of plane P. It should be noted that when a line is drawn from a point to another, it can only be one.
Therefore, the number of lines that can be drawn parallel to plane P that passes through point A is 1.
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By rounding to 1 significant figure, estimate the answers to these questions:
a)346 × 904
b) 2451 × 988
c)3204 × 7756
Answer:
a) 270000
b) 2000000
c) 24000000
Step-by-step explanation:
For a)
346 to 1 s.f is 300
904 to 1 s.f is 900
300 × 900 = 270000
For b)
2451 to 1 s.f is 2000
988 to 1 s.f is 1000
2000 × 1000 = 2000000
For c)
3204 to 1 s.f is 3000
7756 to 1 s.f is 8000
3000 × 8000 = 24000000
Hope this helped and have a good day
Practice B
Study the graph below and answer the following questions.
100
80
No. of Face Shields Sold
60
40
20
Face Shields Sold by Ms. Lopez
Monday Tuesday Wednesday
Thursday
Days
1. On what days did she sell the same number of face shields?
2. On what day's did she set more than 60 face shields?
3. How many face shields did she sell in 5 days?
4. How many more face shields did she sell on Thursday than on Friday?
What inference can you make if Ms. Lopez will sell face shield the whole week?
Friday
Answer:
Where did the writer go in holiday
The table above shows some values of the linear function F. Which of the following defines F? A) f(n) = n-3 B) f(n) = 2n-4 C) f(n) = 3n-5 D) f(n) = 4n-6
Answer:
3n - 5
Step-by-step explanation:
f(n) = 3n - 5. Works for all of them
Which of the equations have only 1 solution -5x+12=5x-5
Answer:
in the pic...
Step-by-step explanation:
Hope it Helps!!!
g(t)=2.0.4^t for t = -2
Answer:
2(0.4)^-2 = 12.5
Step-by-step explanation:
do math noob
What is the intermediate step in the form (x+a)^2=b as a result of completing the square
for the following equation? 4x^2+64x+467=15
The intermediate step in the following equation is (4x + 16)² = - 196
What is an Equation ?An Equation is the mathematical statement formed when two algebraic expressions are equated using an equal sign.
The given equation is
4x² +64x+467 = 15
4x² + 2 * 2x *16 + 256 -256 +467 = 15
(4x + 16)² +211 = 15
(4x + 16)² = - 196
Therefore the intermediate step in the following equation is
(4x + 16)² = - 196
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In a given year, a marketing firm has the following costs: $560,000 in wages and salaries paid to employees; $74,000 in rental payments for office space; and $83,000 for office supplies, advertising, and utilities. In addition, Andrew, the owner of the firm, works for the firm full time (and is not paid a salary, since he receives the firm's profits). If he did not work for the marketing firm, Andrew could earn $130,000 per year working as a marketing manager for another firm.
Accounting profit when revenue is 700,000 is $-17,000 and economic profit is $-147,000.
Accounting profit when revenue is 750,00 is $33,000 and economic profit is $-97,000
Accounting profit when revenue is 800,000 is $83,000 and economic profit is $-47,000.
Accounting profit when revenue is 850,000 is $133,000 and economic profit is $3000
What is economic and accounting profit?Accounting profit is total revenue less total explicit cost. Economic profit is accounting profit less implicit cost
Explicit cost = $560,000 + $74,000 + $83,000 =$717,000
Implicit cost = 130,000
Accounting profit when revenue is 700,000: 700,000- 717,000 = $-17,000
Economic profit = $-17,000 - $130,000 = $-147,000
Accounting profit when revenue is 750,000: 750,000- 717,000 = $33,000
Economic profit = $33,000 - $130,000 = $-97,000
Accounting profit when revenue is 800,000: 800,000 - 717,000 = $83,000
Economic profit = $83,000 - $130,000 = $-47,000
Accounting profit when revenue is 850,000: - 717,000 = $133,000
Economic profit = $133,000 - $130,000 = $3000
Here is the complete question:
For each possible amount of total revenue, fill in the accounting profit and economic profit of the marketing firm.
700,000
750,000
800,000
850,000
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2
A B
-10-9-8
5
Point A
Point B
Point C
Point D
6
ch point on the number line represents the product (-4)(-2)(-1)?
8
012
9
10
C D
5 6 7 8 9 10
59:3
We can actually deduce here that the point on the number line that represents the product (-4)(-2)(-1): -8.
What is number line?Number line is actually known to be a horizontal or vertical line that is graduated with both negative and positive numbers. A number line is known to have both negative and positive numbers.
We see here that if we multiply out the brackets, (-4)(-2)(-1) = (8)(-1) = -8.
Thus, the answer is -8.
See attached image.
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The length of the rectangle is 4 more than the width. The area of the rectangle is 45
square centimeters. Identify the length and width of this rectangle.
Answer:
You need 2 numbers whose product is 45 and whose difference is 4.
so the length is 9 and the width is 5.
Hope this helps.
It is known that 10 workers take 30 days to complete a project. They start working and the next day one quits. the next another, the third day another, and so on until the sixth day when they are left alone 5 workers. How many days will it take those 5 workers to finish the job?
Answer:
5 workers finish this work in 60 daysStep by step explanation:
The problem tells us that at the end of the day, there are only 5 workers left, which we must find how many days it takes to finish said work.
We start by finding the type of proportionality we have.
In this case, we have that the more workers there are, they will finish that work in less time, and the fewer workers there are, the longer it will take to finish the work. This is the inverse proportionality, to more less, to less more.
We have only 5 workers left.
In the first case there are 10 workers, and in the second case there are 5 workers left. We find the relationship between the workers in the second case among the workers in the first case.
Ratio = 5 workers / 10 workers = 1/2We see that the time is found by dividing the number of days in which the 10 workers finish the work, by 1/2.
As we know, dividing two fractions is the SAME as multiplying by the inverse fraction.
[tex]\rm 30 * 2/1 \: = 60 \: days[/tex]
By so
5 workers finish this work in 60 daysfind the value of a from the following 1. tan3a=cot2a
The value of a is 14.
What is Trigonometry?
The branch of mathematics concerned with specific functions of angles and their application to calculations.
Given:
tan3a=cot2a
tan 3a= tan (90- 2a)
On comparing
3a= 90- 2a
5a= 90
a= 14
Hence, the value of a is 14.
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How to rationalise 1000/3
Answer:
Step-by-step explanation:
there is no root in denominator so I think it is rationalised
The function h(x) is a transformation of the square root parent function,
f(x)=√x. What function is h(x)?
-5
5
-5-
h(x)
f(x)
K
I
5
The function h(x) is a transformation of the square root parent function,
f(x)=√x. The function is h(x) A: √x+5.
What is Transformations?Transformations come in the form;
y =√(x-h) +k,
where h is responsible for left-right movements, and k is responsible for up-down movements.
From the graph, we can see that f(x) is simply the parent square root function, √x.
To translate a function right by p units and up by q units, the function becomes
g(x) = f(x -p) +q
(p, q) = (5, 0)
To get h(x), there is a translation of 5 units to the left, which can be represented by a value of h = -5.
h(x) = f(x + 5) +0
h(x) = √(x+ 5)
Hence, The function h(x) is a transformation of the square root parent function, f(x)=√x. The function is h(x) A: √x+5.
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Can you help me graph and list the (Zeros, Maximums, Minimums, Asymptotes)
The zero of the function is at 33.69 degree , the graph is plotted and attached with the answer.
What is a Function ?A function is a law that relates a dependent variable and an independent variable with each other
It is given that
y = 2tan (x - π/2) +3
To find the zeroes of a function that function has to be equated to zero.
2tan (x - π/2) +3 = 0
2tan (x - π/2) = -3
tan (x - π/2) = -3/2
x - 90 = -56.31
x = 33.69 degree
The zero of the function is at 33.69 degree
For finding the maxima /minima
the derivative is
dy/dx = 2 sec² (x - π/2)
the point at which the slope is zero is substituted in the second derivative to find maxima/minima
d²y/dx² = 4 sec² (x - π/2) tan (x - π/2)
if the value is negative then it is a maxima and if it is positive it is a minima.
The vertical asymptote is found by finding the values that make the function undefined
x = 0+ πn
No horizontal or oblique asymptote
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A social club has 500 members.
If 62% of members are male, what percentage are female?
Answer:
[tex]\huge\boxed{\sf 38\%}[/tex]
Step-by-step explanation:
Total members = 500
Total percentage = 100%
Percentage of male members = 62%
Percentage of female members:= 100% - male members
= 100% - 62%
= 38%
[tex]\rule[225]{225}{2}[/tex]
Answer:
310 members or 38% are female
Step-by-step explanation:
100% - 62%male = 38% female
or (62 × 500) ÷ 100 = 310 females
The sum of 8 and a number is less than 15. Which of the following
inequalities expresses the solution?
The inequality which expresses the solution to the task is; x < 7.
Which inequality expresses the solution to the graph?According to the task content; The sum of 8 and a number is less than 15. Therefore, it follows that;
let
The unknown number = x
sum of 8 and a number:
8 + x
sum of 8 and a number is less than 15:
8 + x < 15
x < 15 -8
x < 7.
Ultimately, the required inequality is; x < 7.
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A _______ random variable has infinitely many values associated with measurements.
Answer:
continuous random variable
Solve the following please:
Answer:
most likely b
Step-by-step explanation:
the more than symbol tells me that it is going to move past 10.
Trigonometric ratios apply only to right triangles and not to oblique triangles.
true
false
Answer:
[tex]\fbox {True}[/tex]
Step-by-step explanation:
Trigonometric ratios apply to only right triangles, and not to oblique triangles. There various ratios of angles less than or equal to 90 degrees is taken.
Step-by-step explanation:
hope you can understand
Marcia bought a car for £34500 and sold it for £29700. what was her percentage loss?
can i have an explanation please :)
Answer:
cost of car = 34500
selling price = 29700
amount of loss = 34500 - 29700 = 4800
loss percentage = (loss amount ÷ cost price ) * 100
= 13.913 ≈ 14% loss
The jet stream is traveling nearly due south from Wyoming to Colorado at 110 knots. If the plane’s speed is 400 knots, what will be its ground speed if it travels from Wyoming to Colorado?
Considering the direction of the wind, it is found that the ground speed needs to be of 510 knots.
What is the ground speed?The ground speed, considering that the wind is flowing from Wyoming to Colorado, and the same direction as the trip, is given by:
G = Plane speed + Wind speed.
In this problem, we have that the speeds are given as follows:
Plane: 400 knots.Wind: 110 knots.Hence the ground speed is given by:
G = 400 + 110 = 510 knots.
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4. What is the slope of the line that passes through the points (2, 7) and (6, 21)? Answer may be in decimal
point. Someone please please help I would really appreciate it
Answer:
About 3.5
Step-by-step explanation:
To get slope, you essentially need to find the rise (the y values) over run (the x values). You'll most likely see the formula for slope written like this:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Thankfully, you have the values you need to solve the problem!
x1 = 2
x2 = 6
y1 = 7
y2 = 21
So plugging these numbers in, we get:
[tex] \frac{(21) - (7)}{(6) - (2)} \\ \\ \frac{14}{4} \\ \\ 3.5 [/tex]
[EDIT: I misread 6 as 5. Answer has been updated!]
A rectangular school yard has a perimeter of 294 meters. Its area is 5,162 square meters. What are the dimensions of the school yard?
The dimensions of the school yard is 58 m and 89 m.
What is rectangle ?A rectangle is a polygon with four sides , It has opposite sides parallel and equal.
It is given that
A rectangular school yard has a perimeter of 294 meters
Perimeter of a rectangle is given by
P = 2(Length +Breadth)
294 = 2( L+B)
147 = L+B
Area of a rectangle is given by
L*B = 5162
B = 5162/L
L + 5162/L =147
L² -147L +5162 = 0
L² -58L - 89L+5162 = 0
L(L-58) -89(L-58)
L = 58 , 89
The dimensions of the school yard is 58 m and 89 m.
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Mason can type 210 words in 6 minutes. find the unit rate ( words per mintute )
Answer:
Step-by-step explanation:
words type per minute =210/6
=35