Step-by-step explanation:
The first differences being [tex]2, 4, 6, 8, 10,...[/tex] means
2 is the difference between the 1st and 2nd terms4 is the difference between the 2nd and 3rd terms6 is the difference between the 3rd and 4th terms8 is the difference between the 4th and 5th terms10 is the difference between the 5th and 6th termsSo,
If
The first term of the sequence is 2.
then
The second term of the sequence is [tex]2 + 2 = 4[/tex]
The Third term of the sequence is [tex]4 + 4 = 8[/tex]
The Fourth term of the sequence is [tex]8 + 6 = 14[/tex]
The Fifth term of the sequence is [tex]14 + 8 = 22[/tex]
The Sixth term of the sequence is [tex]22 + 10 = 32[/tex]
Keywords: sequence, arithmetic sequence
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Solve X^2 - 3x - 10 = 0 by using the quadratic formula
Good evening
Answer:
x = 5 or x = -2Step-by-step explanation:
Look at the photo below for the details.
:)
Answer:
x = 5 or x = -2
Step-by-step explanation:
See the attached image for the working out.
A play was attended by 984 persons. 75% of them were adults how many adults attend
Answer:
738
Step-by-step explanation:
984 ÷ 100 = 9.84
9.84 × 75 = 738
75/100
A farm raised a total of 220
Chickens and pigs. The number of legs of the stock are 520. How many chickens and pigs are at the farm?
Answer:
180 chickens and 40 pigs
Step-by-step explanation:
We are given;
Total number of chickens and pigs as 220 Number of legs of chickens and pigs are 520We are required to determine the number of chickens and pigs in the farm;
To answer the question we need to know the following;
1 chicken has two legs 1 pig has four legsAssuming the number of chickens is x and the number of pigs is y
Then we can form two equations;
x + y = 220 ............for the total number of stock 2x + 4 y = 520 ...... for the total number of legsWe can solve the two equations simultaneously to find the number of chickens and pigs;
x + y = 220
2x + 4y = 520
Multiplying the first equation by 2, we get
2x + 2y = 440
2x + 4y = 520
Eliminating x, we get;
- 2y = -80
y = 40
Solving for x;
x = 220 - y
= 220 - 40
x = 180
Therefore, there are 180 chickens and 40 pigs at the farm
John has 12 pounds of dog food he is going to separate it into 3/4 pounds portions
Answer: 1
Step-by-step explanation:
i think u just have to divide
Yung’s taxable income is $36,558. He is filing as head of household, and he has already paid $4802 in federal taxes. What will he receive or pay after he figures his taxes for the year?
Answer:
He will pay $64
Step-by-step explanation:
Using the attached image, for the head of household earning $36,558, he's bound to pay $4,866 considering that his age bracket is in the last line of the image ($36,550-$36,600). However, since he has already paid $4,802 then he hasn't paid it all. He remains with a balance of $4,866-$4,802=$64
Therefore, he's supposed to pay additional $64
the midpoint of AB is M(2,-2). If the coordinates of A are (-2,1), what ate the coordinates of B?
Step-by-step explanation:
To go from A to M you need to go 4 to the right and 3 down. If M is the middle you'll need to do the same to get from M to B. So (2+4,-2-3)=(6,-5)
Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14?
A. 68% of the data points lie between 10 and 14.
B. 68% of the data points lie between 8 and 12.
C. 6896 of the data points lie between 10 and 18.
D. 68% of the data points lie between 10 and 16.
Answer:
Option (c) is correct.
68% of the data points lie between 10 and 18.
Step-by-step explanation:
Given : a normal distribution with a standard deviation of 4 and a mean of 14
We have to choose the sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.
Since, given 68% data.
We know mean of data lies in middle.
And standard deviation is distribute equally about the mean that is 50% of values less than the mean and 50% greater than the mean.
So, 68% of data lies
mean - standard deviation = 14 - 4 = 10
mean + standard deviation = 14 + 4 = 18
So, 68% of the data points lie between 10 and 18.
The correct sentence for a normal distribution with a standard deviation of 4 and a mean of 14, is that 68% of the data points lie between 10 and 18.
The correct answer is C.
About 68% of the data in a normal distribution lie within one standard deviation of the mean.
● 14−4=10 is one standard deviation below the mean, and
14+4=18 is one standard deviation above it.
Thus, the range of 68% of the data values is between 10 and 18. Option C, which states that "68% of the data points lie between 10 and 18," thus accurately sums up the dataset.
Bag a contains 7x counters
bag b contains 2x counters
Five counters are taken from bag a and put in bag b
To find the new number of counters in each bag, subtract 5 from bag a and add 5 to bag b.
Explanation:The subject of this question is mathematics. In this question, we are given two bags, bag a and bag b, which contain 7x and 2x counters respectively. Five counters are taken from bag a and put in bag b.
To find the new number of counters in each bag, we subtract 5 from bag a and add 5 to bag b:
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The digital price of a skateboard was $63.99. The owner of the store marked it 15% off. Calculate the discount and sale price.
Answer:54.3915
Step-by-step explanation:
Price:63.99
Off:15%
Price after 15% off:
{63.99*(100-15)}/100
={63.99*85}/100
=5439.15/100
=54.3915
find the area a polygon
What's the percent change from 52 million to 35 million?
There is 32.69% decrease.
Step-by-step explanation:
Given,
Old value = 52 million
New value = 35 million
Change = New value - Old value
Change = 35 - 52 = -17
The negative sign indicates the decrease.
Percent decrease = [tex]\frac{Change}{Old\ value}*100[/tex]
Percent decrease = [tex]\frac{17}{52}*100[/tex]
Percent decrease = [tex]\frac{1700}{52}\\[/tex]
Percent decrease = 32.69%
There is 32.69% decrease.
Keywords: percentage, division
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Which of the following terms can be combined in this expression? -13 - x/5 + 6.2y + 20.5x - 3/8y
A. -13 can be combined with 20.5.
B. 6.2y can be combined with 20.5.
C. 6.2y can be combined with -3/8y.
D. -x/5 can be combined with -3/8y.
Answer:
C. 6.2y can be combined with -3/8y.
Step-by-step explanation:
6.2y can be combined with -3/8y because both numbers have the same variable x. All of the other choices have different variable that are not like terms.
A 7-foot by 3-foot doorway is cut into the 23 by 22 foot trapezoid wall. What is the area of the wall without the door way?
Answer:
Area of the wall without the doorway = 67.5 - 21 = 46.5 [tex]feet^{2}[/tex]
Step-by-step explanation:
i) let length of smaller side of trapezoidal wall, a = 22 feet
ii) let length of longer side of trapezoidal wall, b = 23 feet
iii) height of trapezoidal wall, h = 3 feet
iv) area of trapezoidal wall = [tex](\frac{a + b}{2} )\times h[/tex] = [tex](\frac{22 + 23}{2} )\times 3[/tex] = 22.5 [tex]\times[/tex] 3 = 67.5 [tex]feet^{2}[/tex]
v) area of door = 7 [tex]\times[/tex] 3 = 21 [tex]feet^{2}[/tex]
vi) Area of the wall without the doorway = 67.5 - 21 = 46.5 [tex]feet^{2}[/tex]
The price of a desktop computer after discount was $1600 if the discount was 20% what was the original price
Answer:$2,000
Step-by-step explanation:
Solving a right triangle (ROUND TO THE NEAREST TENTH)
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180 for B
B = 180° - (90 + 40)° = 180° - 130° = 150°
--------------------------------------------------------------
sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{21}[/tex]
Multiply both sides by 21
21 × sin40° = a, thus
a ≈ 13.5 ( to the nearest tenth )
--------------------------------------------------------------
cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{b}{21}[/tex]
Multiply both sides by 21
21 × cos40° = b, thus
b ≈ 16.1 ( to the nearest tenth )
Simplify: -26a? + (-25a7)
Answer:
-26a - 25a^7
Step-by-step explanation:
On the farm, rather than use money, they exchange animals. The exchanges are as follows: 4 bunnies = 3 chickens, 5 chickens = 2 pigs, 3 pigs = 2 donkeys. How many bunnies would you have to trade for a donkey?
We have to trade 5 bunnies for a donkey.
Solution:
To calculate how many bunnies could be exchanged for a donkey, we have to multiply the exchange rates of each animal/bird.
One bunny = 3/4 chickens (0.75 chicken),
One chicken = 2/5 pigs (0.4 pigs)
One pig = 2/3 donkeys (0.67 donkeys).
On multiplying all of the above rates we get,
0.75*0.4*0.67=0.2
Since we now know a bunnies worth is 0.2 donkey
Therefore, (1/0.2=5) 5 bunnies to trade for a donkey.
prove equal chord of a circle subtends equal angle at centre
Answer:
The Proof for "Equal chord of a circle subtends equal angle at the Center".
Step-by-step explanation:
Consider a Circle with center as C,
Radius AC ,BC ,DC and EC
Chord AB = Chord CD
To Prove:
"Equal chord of a circle subtends equal angle at center".
i.e ∠ACB = ∠ECD
Proof:
In Δ ABC and Δ DEC
Chord AB ≅ Chord DE .….{Given}
AC ≅ DC …..{Radius of Same Circle}
BC ≅ EC ….{Radius of Same Circle}
Δ ABC ≅ Δ DEC ….{By Side-Side-Side Congruence Postulate}
∴∠ACB ≅ ∠ECD ...{Corresponding Parts of Congruent Triangles are Congruent or CPCTC} ....Proved
i.e Equal chord of a circle subtends equal angle at the Center.
Jenny esta en el equipo de natación por el verano y su practica es de 4 horas por dia de la semana. El horario es el mismo es el mismo cada día. El equipo nada en la mañana y otra vez por la tarde 2 horas. Si ella nada 12 horas por semana cuanto nada cada mañana
Answer:
Jenny spent 1 hour swimming in the morning.
Jenny pasó 1 hora nadando por la mañana.
Step-by-step explanation:
Translated:
Jenny is on the summer swimming team and her practice is 4 hours per day, in a week. The schedule is the same every day. The team swims in the morning and again in the afternoon 2 hours. If she swims 12 hours a week, how much does she swim every morning?
We know that she swims 4 hours per day, mornings and evenings.
We know that one specific week she swam for 12 hours total in that week.
Let as denote the number of hours swam in a day as [tex]x[/tex].
Then we can say that in that week for 12 hours total and 4 hours swimming per day, we have:
[tex]4x=12\\x=\frac{12}{4}\\x=3[/tex]hours per day swam for that week.
Now since we know for a fact that 2 hours are spend swimming in the evening then we can subtract this from the total of 3 hours as
[tex]3-2=1[/tex] hour of swimming in the morning.
So we can conclude that on the week that Jenny swam for 12 hours total, she spent 1 hour swimming in the morning and 2 hours swimming in the evening.
En Espagnol:
Entonces podemos concluir que la semana en que Jenny nadó durante 12 horas en total, pasó 1 hora nadando por la mañana y 2 horas nadando por la noche
If I worked 208 hrs out of 409 what percentage would that be?
Step-by-step explanation:
(208/409)*100%
50.85%
There were 4 car races on saturdayand 3 on Sunday. If there were 9 cars racing in each race, how many cars raced over the two days?
Final answer:
A total of 63 cars raced over the two days: 36 cars on Saturday (4 races × 9 cars) and 27 cars on Sunday (3 races × 9 cars).
Explanation:
The student is asking to calculate the total number of cars that raced over two days. There were 4 car races on Saturday and 3 on Sunday, with 9 cars racing in each race. To find the total number of cars that raced, you would multiply the number of races each day by the number of cars in each race and then add those two products together.
For Saturday: 4 races × 9 cars per race = 36 cars
For Sunday: 3 races × 9 cars per race = 27 cars
Adding the cars from Saturday to the cars from Sunday gives us the total: 36 cars + 27 cars = 63 cars.
Therefore, over the two days, a total of 63 cars raced.
can you help me with 4 and 6 only? thank you
joe divided 1.38 by .6 and what should joe's answer be?
Answer:
Step-by-step explanation:
It should be 2.3 because dividing by decimals is almost the same as dividing by normal numbers you just change the decimal point when you are done dividing.
What integer is closest to 31/7
Answer:
31/7 = 4 3/7.....3/7 is less then 1/2....so the closest integer is 4
Step-by-step explanation:
Please mark me brainlist if this helped
Round 67.6 to nearest whole number
Answer:Integer Part: 67
Fractional Part: 60
Step-by-step explanation: This is how to round 67.6 to the nearest whole number. In other words, this is how to round 67.6 to the nearest integer.
67.6 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:
Answer:67
Step-by-step explanation:
When you round 67.6 to the nearest whole number you take the 6 off and get 67
The cake store is having a 25% off sale on all of its cakes.
If the cake you want regularly costs dollar sign $9, how much would you save with the discount?
Answer:
The Discount would save $2.25 of the final purchase.
Step-by-step explanation:
If the cake originally costs $9, 25% of that would be $2.25 off the final purchase. So the discount would save $2.25
Answer:
With the discount, you are saving $2.25 on the cake that you want.
write the fraction or mixed number as a decimal
Answer:
look below
Step-by-step explanation:
To write a fraction or mixed number as a decimal, divide the numerator by the denominator. So, for example, if you had 5/2, then you'd do 5÷2, which gives you 2.5. Hope that helped!
if a pentagon has a total interior angle measure of the 540-degree ad there are 5 congruent angles find the measure of one of the interior angles
Answer:
Step-by-step explanation:
interior angle = sum of interior angles/total no. of angles
= 540/5 = 108
What is the first step to solve this equation;
11-3x=44
The first step to solve the equation 11-3x=44 is to isolate the variable x by subtracting 11 from both sides of the equation.
Explanation:To solve the equation 11-3x=44, the first step is to isolate the variable x.
To do this, we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 11 from both sides:
11 - 11 - 3x = 44 - 11-3x = 33Now we have -3x = 33 as our new equation.
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Write an equation of the line that passed through (7,10) and is perpendicular to the line y=1/2x-9
The equation of the line perpendicular to y=1/2x-9 passing through the point (7,10) is y=-2x+24.
Explanation:To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and use the negative reciprocal of that slope for our new line. The line given is y = ½x - 9, so the slope (m) is ½. The slope of the perpendicular line will be the negative reciprocal of ½, which is -2.
The next step is to use the point given, (7,10), and the slope of the perpendicular line to write the equation in point-slope form, which is y - y1 = m(x - x1). Plugging in our values we get: y - 10 = -2(x - 7).
Finally, we can rearrange this into slope-intercept form, y = mx + b, by simplifying and solving for y:
Therefore, the equation of the line perpendicular to y = ½x - 9 that passes through the point (7,10) is y = -2x + 24.