Answer:
10
Step-by-step explanation:
Let $a_n$ be the $n$th term of this sequence. We know $a_2 + a_8 = 5$, and that forces $a_5 = \dfrac 5 2$, the average of these terms.
Then $a_4a_5 = 5$ gives us $a_4 = 2$.
The common difference is $\dfrac 1 2$, and in general, $a_n = \dfrac n 2$.
Therefore the $20$th term is $\dfrac{20}{2} = \boxed{10}$.
The 20th term of the arithmetic sequence will be equal to [tex]T_{20}=10[/tex]
What is arthematic sequence?Arthematic sequence is the type of the number series in which the difference between the first and the second term is always constant in the whole series.
Let [tex]$a_n$[/tex] be the nth term of this sequence.
We know
[tex]$a_2 + a_8 = 5$[/tex], and that forces [tex]$a_5 = \dfrac 5 2$[/tex], the average of these terms.
Then [tex]$a_4a_5 = 5$[/tex] gives us [tex]a_4 = 2$.[/tex]
The common difference is [tex]\dfrac 1 2$,[/tex]and in general, [tex]$a_n = \dfrac n 2$[/tex].
Therefore the 20th term is
[tex]T_{20}=$\dfrac{20}{2} = \boxed{10}$.[/tex]
Hence the 20th term of the arithmetic sequence will be equal to [tex]T_{20}=10[/tex]
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Susan got to the school bus stop at 6:08, she waited 1 minute for the bus. What time was it when Susan’s bus came?
Answer:
6:09
Step-by-step explanation:
6:09 is one minute after 6:08
the value of a varies directly as the square of the value of b, and b=3 when a=10. Find the value of a when b=9.
Answer:
answer = 90
Step-by-step explanation:
General equation: a = k*b^2
Specifically: 10 = k*(3)^2 = 9 k
Solving for k: k = 10/9
Then a = (10/9)b^2. If b = 9, then a = (10/9)(9)^2 = 90 (answer)
There is a population of 15,500 bacteria in a colony. If the number of bacteria doubles every 234 hours, what will
che population be 936 hours from now?
bacteria
Answer:
2,48,000
Step-by-step explanation:
Initial population of bacteria = 15,500Bacteria doubles after every 234 hoursSo, after 0 (zero) hours, no of bacteria = 15,500After 234 hours, no. of bacteria = 2(15,500) = 31,000After 468 hours, no. of bacteria = 2(31,000) = 62,000 (2*234 = 468)After 702 hours, no. of bacteria = 2(62,000) = 124,000 (3*234 = 702)After 936 hours, no. of bacteria = 2(124000) = 2,48,000 (4*234 = 936)Show that if AB=DC in the figure below, then AB is parallel to CD.
AB is parallel to CD because the figure is a parallelogram and opposite sides of a parallelogram are parallel.
What are the properties of a parallelogram?Note, the figure is a parallelogram
Some properties of a parallelogram are:
The opposite sides of a parallelogram are parallel and equal.The opposite angles are equal.The consecutive angles are supplementary, that is, the sum up to 180°The two diagonals divide each other.if sides AB = DC, then AB is parallel to CD because they are opposite to each other and opposite sides of a parallelogram are parallel.
Hence, AB is parallel to CD because the figure is a parallelogram and opposite sides of a parallelogram are parallel.
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josiah is running a marathon which is 26 1/5 miles Long. At four 1/4 miles from the start, he meets his wife, who is cheering him on. 7 1/2 miles further down the marathon course, he sees some Friends from his running club volunteering at a water stop. Once he passes his friends, how many more miles does Josiah have left to run?
Once he passes his friends, The miles Josiah has left to run would be 10.95 miles.
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.
Josiah is running a marathon which is 26 1/5 miles long.
At four 1/4 miles from the start, he meets his wife, who is cheering him on.
7 1/2 miles further down the marathon course.
26 1/5 = 131/ 5
7 1/2 = 15/2
The marathon run by Josiah
= 1/4 + 15/2
= 15.25
The miles Josiah has left to run
= 131/ 5 - 15.25
= 10.95
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Use proportional thinking to answer the question. Explain how you got an answer without using pencil and paper or a calculator.
If 10% of a number is 4.3, what is
20% of the number?
Answer:
8.6
Step-by-step explanation:
If we know 10% of a number is 4.3, we can easily find 20% of the number as well.
We know 20% is 2 times 10%.
Therefore,
2 x 4.38.6You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes longer than your brother reads.
For this case we have the following notation:
y= the number of minutes that you read
x = the number of minutes that your brother read
And we have that you decide to read 30 minutes longer than your brother, so the equation would be:
y = x+30
And for the other part of the question if x =15 we got:
y = 15+30 = 45
Step-by-step explanation:Assuming this complete question: "You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes longer than your brother reads. Write an equation for the number of minutes you read, y, when your brother reads x number of minutes.
How many minutes will you read if your brother reads for 15 minutes?"
Solution to the problemFor this case we have the following notation:
y= the number of minutes that you read
x = the number of minutes that your brother read
And we have that you decide to read 30 minutes longer than your brother, so the equation would be:
y = x+30
And for the other part of the question if x =15 we got:
y = 15+30 = 45
Find the surface area of a cylinder with a height of 5 ft and a base radius of 4 ft.
Use the value 3.14 for x, and do not do any rounding.
Be sure to include the correct unit.
Answer:
A =281 ft^2
Step-by-step explanation:
A=2πrh+2πr^2
A = 2 (3.14) (4)(5) + 2 (3.14) (5)^2
A =281 ft^2
The pool company has learned that, by pricing a newly released Fun Noodle at $5, sales with reach 8000 Fun noodles per day during the summer Raising the price to $6 will cause the sales to fall to 5000 fun noodles per day
It takes3/4 cup of sugar to make a loaf of bread how much sugar would you need to make 16 loaves of bread
Too make this easier for me or others 3/4 can be represented as 0.75. 3/4 or 0.75 x 16 = 12
More depth explanation:
Multiple: 3/
4
* 16 = 3 · 16/
4 · 1
= 48/
4
= 12 · 4/
1 · 4
= 12
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(48, 4) = 4. In the following intermediate step, cancel by a common factor of 4 gives 12/
1
.
In other words - three quarters multiplied by sixteen = twelve.
the volume of a cone is 2307.9 mm^3. The height is 5 mm. What is the radius?
Answer:
21 mm
Step-by-step explanation:
Given,
Volume of cone ( V ) = 2307.9 mm³
Height ( h ) = 5 mm
To find : Radius ( r )
Formula : -
Volume of cone = πh/3 r²
Note : -
The value of π is 3.14
Volume of cone = πh/3 r²
2307.9 mm³ = 3.14 x 5/3 x r²
2307.9 = 5.23 x r²
Divide 5.23 on both sides,
r² = 2307.9 / 5.23
r² = 441
r² = 21 x 21
r² = 21²
r = 21 mm
Grace has a 1/3 cup scoop that she uses to pour sauce on pasta. She uses one full cup for each serving of pasta. Grace has 7 cups of sauce. How many servings of pasta can she make?
Answer:
7
Step-by-step explanation:
its a trick question !!
Answer:
This seems like a tricky question... i keep second guessing myself but here goes nothing....
7 servings
please read the explanation.... it always helps....
Step-by-step explanation:
Okay... so we know from the problem that each serving takes one full cup of sauce, and we also know that Grace has seven cups of sauce.... therefore we can conclude that she can make seven servings since 7/1 is 7.
Im not really sure why the question tells us that she uses a 1/3 scoop when we don't really need that when solving the question (which is why i am second guessing myself, but oh well)
i really hope this helps!!!
A circular tabletop has a circumference of 94.2 inches. What is its approximate area?
Answer:
1st choice : 706.5 square inches
Step-by-step explanation:
circumference is pi times diameter
divide 94.2 by pi to get diameter = 29.9847912785
diameter 29.9847912785 divided by 2 is
14.9923956393 which is the radius
area is pi times radius times radius again
pi times 14.9923956393 times 14.9923956393 =
706.141834613
Which of the following expanded forms represents the number words one thousand, six hundred eighty-nine?
O 1,000 + 60 + 80 + 9
O None of thse choices are correct.
O 600 + 80 + 9
O 1,000 + 600 + 80 + 9
O 1,000 + 60 + 8 + 9
Jan's electric bill is averaging $8 per day mostly due to the air conditioner. By setting the AC to a higher temperature, closing curtains to block sunlight, and using direct-blowing fans for comfort, Jan reduces the bill to $5 per day. How much did Jan reduce the electric bill for a 30-day month?
Answer:
$5×30days= $150 for the whole month
Answer: $90 saved
Step-by-step explanation:
8 - 5 = $3 dollars saved each day
Multiply daily amount saved by number of days
$3 × 30 = $90 saved
Reduce the fraction, then change to a mixed number. 20/3
[tex] \frac{20}{3} [/tex]
To find:[tex] \frac {20}{3} [/tex] as a mixed number.
Solution:First, divide the numerator by the denominator.
[tex]20 \div 3 [/tex]
[tex] = 6 \: R2[/tex]
Then, write the whole number value and use the remainder as the numerator over the denominator. As we all know the denominator won't change.
[tex]\large\boxed{\sf{= 6 \frac{2}{3}}}[/tex]
What am I supposed to do here? I will give BRAINLEST and say thank you.
Answer: It finally let me answer this. Give me brainliset if another person answers. You have to make a bar graph and then put the same info on it.
Which of the following are solutions to the inequality below? Select all that apply.
8 ≤ j j = 12 j = 5 j = 6 j =11
Answer:
j = 11
j = 12
Step-by-step explanation:
The inequality:
8 ≤ j
We will test all the options given.
-> In short, all options greater or equal to 8 will be solutions.
j = 12
8 ≤ j
8 ≤ 12 ✓
-
j = 5
8 ≤ j
8 ≤ 5 ✗
-
j = 6
8 ≤ j
8 ≤ 6 ✗
-
j =11
8 ≤ j
8 ≤ 11 ✓
A weighted (unfair) die that was purchased at a magic shop was rolled 30 times. The die landed on five dots 25 times. Based on the results, what is the margin of error for the true proportion of times this die would land on five dots? Base your margin of error on a 95% confidence level.
Using the z-distribution, it is found that the margin of error for the true proportion of times this die would land on five dots is of 0.1338.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate and the sample size are given as follows:
[tex]\pi = \frac{25}{30} = 0.8333, n = 30[/tex].
Hence the margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.8333(0.1667)}{30}}[/tex]
M = 0.1338.
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Hellppppppppppllpppp
Answer:
180 in^2
Step-by-step explanation:
S=(1/2)lP + B
B = 10x10 = 100
P = 10(4) = 40
l is 4, but you could also use the fact that each triangular side is A=(1/2)bh.
(1/2)4 x 10 = 20
20(4) = 80
add 100 + 80 = 180
Kate has a box of red nibbon and bhie ribbons The ratio of red ribbons to total ribbons is 5 14 Choose all the statements that are true about Katie's box of ribbons
(A The ratio of total ribbons to blue ribbons is
14:9
(B. The ratio of red ribbons to blue ribbons is 9:5
(C. The ratio of total ribbons to red ribbons is 14:5
(D. There must be 9 more blue ribbons than red ribbons
(E. The ratio of blue ribbons to red ribbons is 9,5
This window is designed in the shape of a right trapezoid.
Answer: 128°
Step-by-step explanation:
There are 360° in a trapezoid. Since this is a right trapezoid, two of those angles will be equal to 90°. We will set up the following equation, and solve.
360° = 90° + 90° + 52° + x°
360° = 90° + 90° + 52° + x°
360° = 232° + x°
128° = x
x = 128°
The obtuse angle has a measure of 128°.
can you help this is hard
Answer:
y=1/2x+1= A
y=-2x-4= C
x-2= E
y=-3= F
y=1/2x+3.5=B
I hope this helps
Step-by-step explanation:
Evaluate: [tex]\sqrt{100-36} + 32 - 1[/tex]
Precalculus based question.
Answer:
39
Step-by-step explanation:
[tex]\sqrt{100-36}+32-1\\\sqrt{64}+31\\8+31\\39[/tex]
Hey there!
√(100 – 36) + 32 – 1
= √(64) + 32 - 1
= 8 + 32 – 1
= 40 – 1
= 39
Therefore, the answer should be: 39
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
This is geometry and I need help
Answer:
Step-by-step explanation:
Remark
The sine of an angle involves the Hypotenuse. So the first job is to find that.
When you do Sin(H) = opposite / hypotenuse
Hypotenuse
Givens
a = √3
b = √13
c = ?
c is the hypotenuse.
Equation
c^2 = a^2 + b^2 Substitute values
Solution
c^2 = (√3)^2 + (√13)^2
c^2 = 3 + 13 Combine
c^2 = 16 Take the Square Root of Both Sides
√c^2 = √16
c = 4
Sin(H) = opposite / Hypotenuse
Opposite = √3
Hypotenuse = 4
Sin(H) = √3/4
Sin(H) = 1.7321/4
Sin(H) = 0.4330
Answer
Sin(H) = 0.43
Find the area: (I will give brainliest) +50 points.
Answer:
[tex]A_{total} = 16\ cm^2[/tex]
Step-by-step explanation:
Step 1: Determine the area of the top rectangle
We can tell that the total shape seems like two rectangles glued together. We can separate the top rectangle and determine the area of it and then determine the area of the bottom rectangle and combine them. Lets first solve the left rectangle.
[tex]A=l*w[/tex]
[tex]A_{top\ rectangle}=6\ cm * 2\ cm[/tex]
[tex]A_{top\ rectangle}=12\ cm^2[/tex]
Step 2: Determine the area of the bottom rectangle
[tex]A=l*w[/tex]
[tex]A_{bottom\ rectangle}=2\ cm * 2\ cm[/tex]
[tex]A_{bottom\ rectangle}=4\ cm^2[/tex]
Step 3: Determine the total area
[tex]A_{total}=A_{top\ rectangle}+A_{bottom\ rectangle}[/tex]
[tex]A_{total}=12\ cm^2+4\ cm^2[/tex]
[tex]A_{total} = 16\ cm^2[/tex]
Answer: [tex]A_{total} = 16\ cm^2[/tex]
Break in middle horizontally
For square (Below)
Area =Side²=2²=4cm²For rectangle
Area =LB=6(2)=12cm²Total area
12+416cm²can anyone help me identify the center and radius on these 3 pls , brainly
Answer:
See below
Step-by-step explanation:
Circle equation standard form
(x-h)^2 + ( y-k)^2 = r^2 h, k is the center
All are centered at 0,0
radii are sqrt(225) = 15 sqrt 49 = 7 and sqrt 178
Tory’s expenses of $300 in May were at least $40 less than twice her expenses in April. What is the least possible amount of her expenses in April?
Please help, I'm so confused with this. Attached is a picture
Answer:
Interquartile Range
Step-by-step explanation:
The answer is the interquartile range because there is an outlier.
The data has an extreme value, of 62, so the IQR is most appropriate for this data set. The only other time the IQR is appropriate is when the data is skewed.
You start driving north for 6 miles, turn right, and drive east for another 19 miles. At
the end of driving, what is your straight line distance from your starting point?
Round to the nearest tenth of a mile.
Answer:
mi
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M
4
G
Answer:
20 miles
Step-by-step explanation:
This is a Pythagorean Theorem Problem
1. We know that one side of the triangle is 6 miles. And we know that another side is 19 miles.
2. We use the pythagorean Theorem to solve. We get
[tex]19^2+6^2=C^2[/tex]
Where C is the distance.
Solving that we get that 20 miles is the answer.