Answer:
740
Step-by-step explanation:
The n th term of an arithmetic series is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 7 and a₇ = (3 × 7) + 2 = 21 + 2 = 23 , then
a₁ + 2d = 7 → (1)
a₁ + 6d = 23 → (2)
Subtract (1) from (2) term by term
4d = 16 ( divide both sides by 4 )
d = 4
Substitute d = 4 into (1)
a₁ + 2(4) = 7
a₁ + 8 = 7 ( subtract 8 from both sides )
a₁ = - 1
The sum to n terms of an arithmetic series is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , thus
[tex]S_{20}[/tex] = [tex]\frac{20}{2}[/tex] [ (2 × - 1) + (19 × 4) ]
= 10(- 2 + 76) = 10 × 74 = 740
IF Tunde, who has n eggs, has three
more than Sola, how many eggs has
Sola?
Answer:
Sola has n-3 eggs
Step-by-step explanation:
Tunde = n
Tunde has 3 more = Sola has 3 less than tunde
= Tunde - 3
= n - 3
There are 5 pencils and 8 pens. What is the ratio of pens to pencils?
Answer:
8/5
Step-by-step explanation:
The transformation (x,y) -> (y,-x) is what degree rotation for a counter-clockwise turn?
Answer:
270°
Step-by-step explanation:
For example,
(x, y) is in 1st quadrant (x- coordinate is positive, y - coordinate is positive) , then
(y, - x) is in 4th (x- coordinate is positive, y - coordinate is negative).
x and y changed places, so clockwise is 90°,
and counter-clockwise 360-90= 270°.
3/4 - 1/2n =5/8. solve for n
The solution to the equation (3/4) - (1/2)n = 5/8 is n = 1/4 as per the rule of fraction's operations.
To solve the equation (3/4) - (1/2)n = 5/8 for n, we can follow these steps:
Start by subtracting 3/4 from both sides of the equation:
(3/4) - (1/2)n - 3/4 = 5/8 - 3/4
Simplifying, we have:
(1/2)n = 5/8 - 6/8
Combine the fractions on the right-hand side:
(1/2)n = -1/8
To eliminate the fraction coefficient, multiply both sides by -2:
(-2)(-1/2)n = (-2)(-1/8)
This gives us:
n = 2/8
Simplify the right-hand side:
n = 1/4
Therefore, the solution to the equation (3/4) - (1/2)n = 5/8 is n = 1/4.
It's important to note that when solving equations involving fractions, it's crucial to perform the same operation on both sides of the equation to maintain the equality. By isolating the variable n on one side, we were able to find its value.
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Simplify the exponential express
(-1)3 =
Answer:
-1
Step-by-step explanation:
(-1) ^3
This is (-1) multiplied together 3 times
(-1) * (-1) * (-1)
-1
select the correct descriptor of the following problems: from a pack of 52 cards, two cards drawn together at random. What is the probability od both the cards being kings?
Answer:
[tex]\frac{1}{221}[/tex]
Step-by-step explanation:
We have to note that there are 4 kings in a deck of 52 cards.
This makes the probability of choosing a king the first time [tex]\frac{4}{52} = \frac{1}{13}[/tex].
We now know that we can choose another king from the deck, but it's important to note that it's not a [tex]\frac{1}{13}[/tex] chance. We now only have 51 cards in the deck, and 3 kings left. This means the probability of choosing a king now is [tex]\frac{3}{51} = \frac{1}{17}[/tex].
To find the probability of doing both these, we need to multiply the fractions.
[tex]\frac{1}{13}\cdot\frac{1}{17}=\frac{1}{221}[/tex]
Hope this helped!
What is the value of the following expression? 6p + 5 when p = 9
Answer:
I think the answer is 59
Step-by-step explanation:
6p+5
6(9)+5
54+5=59
Dylan can paint a wall in 4 hours, while Brett can paint the same wall in 3 hours. If Dylan paints the wall for 2 hours, how much time will it take for Brett to finish painting the wall
Answer:
n 1 hour Dylan can paint 1/4 of the wall, and Brett can paint 1/3 of the wall.
Therefore together they can paint 1/4+1/3 = 7/12 of wall
Therefore they can paint entire wall in 12/7 hours
Step-by-step explanation:
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Rewrite in mathematical language. Every negative integer J is less than or equal to its inverse.
Answer:
[tex]-J \leq J[/tex]
Step-by-step explanation:
Given
Negative integer J
Required
Represent as an inequality of its inverse
The question didn't state if it's additive inverse or multiplicative inverse;
Since the question has to do with negation, I'll assume it's an additive inverse
The inverse of -J is +J
To represent as an inequality (less than or equal), we have:
[tex]-J \leq +J[/tex]
Solving further, it gives
[tex]-J \leq J[/tex]
the average number of spectators at a football competition for the first five days was 3144.the attendance on the sixth day was 3990.find the average attendance for the 6 days
Answer:
3285
Step-by-step explanation:
5x3144=15720
3990
15720+3990=19710
19710/6=3285
What is the Decimal Represention of 9/11
Answer: the answer is A 0.81
which one is it ?
substitution property of equality
reflexive property of equality
transitive property of equality
symmetric property of equality
What is the probability of getting dealt a hand equal to 21?
Answer:
The odds to get a blackjack (natural) as arrangement: 128 / 2652 = . 0483 = 4.83%. 4.83% is equivalent to about 1 in 21 blackjack hands.
Decide whether is true or false.
2/11 < 5/22
=======================================
Explanation:
For now, assume the inequality is true
We can cross multiply to get
2/11 < 5/22
2*22 < 11*5
44 < 55
Since the last inequality is true (44 is smaller than 55), this means the first inequality is also true.
------------
We could use a calculator to see that
2/11 = 0.1818 approximately
5/22 = 0.2273 approximately
Since 0.1818 is smaller than 0.2273, this means 2/11 is smaller than 5/22.
In other words, 0.1818 < 0.2273 leads to 2/11 < 5/22
------------
An alternative is to multiply 2/11 by 2/2 to get 4/22
So 2/11 < 5/22 would update to 4/22 < 5/22. Both have the same denominator so we just compare the numerators. Because 4 < 5 is true, this makes 4/22 < 5/22 true, and consequently 2/11 < 5/22 true as well.
what number is between 0.40 and 0.47 as a fraction
The measures of the sides of a triangle are 20 24 and 30. Find the measures of the segments former where the bisector of the smallest angle meets the opposite side.
Answer:
One segment is 8.89 long and the other one is: 11.11 long
Step-by-step explanation:
Recall that the bisector of a triangle divides the opposite side it intersects into two segments that are proportional to the other two sides of the triangle.
In our case the bisector is generated on the angle opposite to the size 20 side (it is the smallest angle in the triangle since it is opposite to the smallest side). This bisector divides the side of length 20 into a segment of length x and a segment of length 20-x.
The proportionality indicated by the bisector theorem gives;
[tex]\frac{20-x}{x} =\frac{30}{24}[/tex]
and we can solve for "x":
[tex]\frac{20-x}{x} =\frac{30}{24}\\24\,(20-x)=30\,x\\480-24\,x=30\,x\\480=54\,x\\x=480/54\\x\approx8.89[/tex]
Then the other segment is: 20 - 8.89 = 11.11
Add 113+(−56) using the number line.
Answer:
Step-by-step explanation:
Start at 1 1/3
Add the negative number.
1 1/3 + (-5/6)
Adding a negative number means to go left on a number line.
-5/6 is equal to -2/3 plus -1/6.
Move 2/3 to the left.
1 1/3 (Start)
1 (1/3)
2/3 (2/3)
Now, move 1/6th to the left.
2/3 is equal to 4/6
4/6 - 1/6 = 3/6
So, put the point at 3/6 or 1/2.
The value of addition of 1 1/3+(−5/6) is 1/2 and plotted on a number line.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Start at 1 1/3
Add the negative number;
1 1/3 + (-5/6)
Here Adding a negative number means to go left on a number line.
-5/6 is equal to -2/3 plus -1/6.
Now Move 2/3 to the left;
1 1/3 (Start)
1 (1/3)
2/3 (2/3)
Now, move 1/6th to the left;
2/3 is equal to 4/6
4/6 - 1/6 = 3/6
Thus 1 1/3+(−5/6) = 3/6 = 1/2
The value of addition of 1 1/3+(−5/6) is 1/2 and plotted on a number line.
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Use the following function rule to find f(16.36).
f(x) = 0.77x + 8.64
Write your answer as a decimal or whole number.
f(16.36) =
Which list is in order from least to greatest?
|−9|, |4.2|, |−3.5|
|−3.5|, |−9|, |4.2|
|−3.5| , |4.2|, |−9|
|−9|, |−3.5|, |4.2|
Answer: C
Step-by-step explanation: Absolute value means all the values in the | | are positive so make them positive and you will see it’s 3.5, 4.2, and 9 in order from least to greatest.
Amir wants to create a 4-digit password for his phone.
He wants to choose 4 different numbers between 1 and 5 inclusive.
Calculate the total number of 4-digit passwords that Amir can create.
Answer:
360
Step-by-step explanation:
Given that Amir wants to create a 4-digit password for his phone.
He wants to choose 4 different numbers between 1 and 5 inclusive.
The total number of 4-digit passwords that Amir can create will be achieved by using permutation
6P4 = 6!/ ( 6 - 4)!
6P4 = (6 × 5 × 4 × 3 × 2!)/2!
6P4 = 6×5×4×3 = 360
Therefore, the total number of 4-digit passwords that Amir can create is 360 different passwords.
Which of these numbers is irrational?
Answer:
[tex] \sqrt{5} [/tex]
Step-by-step explanation:
decimal repeats without a pattern
the slope and y intercept of 3y+6x=18
Answer:
slope: -2
y-intercept: 6
Step-by-step explanation:
First, put the equation into slope intercept form.
Slope-intercept form: y = mx + b
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 6x from both sides:
3y + 6x (-6x) = 18 (-6x)
3y = -6x + 18
Next, divide 3 from both sides. Remember to divide from all terms:
(3y)/3 = (-6x + 18)/3
y = (-6x)/3 + (18)/3
y = -2x + 6
Slope-intercept form: y = -2x + 6
Again, note the slope-intercept form.
> Slope-intercept form: y = mx + b
The variables:
y = (x ,y)
m = slope
x = (x , y)
b = y-intercept
Your answers:
slope: -2
y-intercept: 6
DeMario has two ltimes and four quarters. Pratima has five dimes and two quarters. They have $2.20 altogether. Write an expression or equation that matches this situation.
Answer:
8 x2.20 = Answer
Step-by-step explanation:
Answer:
7d+6q=2.20
Step-by-step explanation:
what is (15-2)×3×2
Answer:
15−2(3−2x)=46
Step-by-step explanation:
15−2(3−2x)=46
The angle of elevation of the top of a tower from a point 100m away is 45 degrees. What is the height of the tower to the nearest metres?
===========================================
Explanation:
If you draw out the diagram, then you'll find that a 45-45-90 triangle forms. The nice thing about this type of triangle is that the two legs are always the same length. The horizontal leg is 100 meters, so the vertical leg must also be 100 meters.
Side note: this type of triangle is an isosceles right triangle.
---------
You could use the tangent rule to get the same thing
tan(angle) = opposite/adjacent
tan(45) = 100/x
1 = 100/x
1*x = 100
x = 100
In this case, the opposite leg is the vertical leg since it is furthest from the angle of elevation.
Answer:
[tex]\Huge \boxed{\mathrm{100 \ meters}}[/tex]
Step-by-step explanation:
The base of the right triangle created is 100 meters.
The angle between the base and the hypotenuse of the right triangle is 45 degrees.
We can use trigonometric functions to solve for the height of the tower.
[tex]\displaystyle \mathrm{tan(\theta) = \frac{opposite }{adjacent} }[/tex]
[tex]\displaystyle \mathrm{tan(45) }= \frac{x }{100}[/tex]
Multiplying both sides by 100.
[tex]\displaystyle \mathrm{100 \cdot tan(45) }= x[/tex]
[tex]\displaystyle \mathrm{100 }= x[/tex]
The height of the tower is 100 meters.
All of the following represent the same concept except _____. 47 take away 28 47 minus 28 47 less than 28 47 subtract 28
Answer:
C. 47 less than 28
Step-by-step explanation:
A. 47 take away 28
Equivalent to counting 47 and taking away 28
= 47 - 28
= 19
B. 47 minus 28
Simply
47 - 28
= 19
C. 47 less than 28
47 < 28
The less than sign is <
D. 47 subtract 28
= 47 - 28
= 19
Answer:47 less than 28
Step-by-step explanation:the rest are subtracting 28 from 47 , 47 less than 28 is subtracting 47 from 28.
I need help step by step Combining like terms 6 + x + 4=
Kenya is reserving a room in a hotel in France where they use euros (€). The room charge is €75. Suppose the conversion rate is €1 = $1.298. What is the cost of the room in dollars? (1 point)
If x is a rational number and y is a rational number than x + y is a rational number.
Answer:
True.
Step-by-step explanation:
The sum of two rational numbers is rational.
By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rational numbers produces another rational number.
There are 75 people in a room. Of these people, 2/5 are from Germany. If 4/9 of the people who are not from Germany are from France, how many of the people in the room are from neither Germany nor France
Answer:
25 people are not from Germany or France.
Step-by-step explanation:
1. You first want find out what is the number of people from Germany.
So you would find...
2/5 of 75
or
2/5*75= 30 people from Germany
2. Next you want to to find out the number of people from France.
So you would do the following...
75-30=45 (Subtract the number of people from Germany from 75 so you can get the total number of people from France and other countries)
4/9 of 45 to find the number of people from France.
4/9 *45= 20
3. Lastly you need to find the people who are from neither of the countries listed above.
Add 30+20= 50
Then subtract that number from 75.
75-50= 25 people who are from neither France or Germany.
Voila! This is your answer. Hope this helps! :)