Answer:
First three terms:
22,24,26
There are 15 terms in the sequence that are 50 or less, yet only 14 if its just less than 50.
Answers:
The first three terms are 21, 24, 29
5 terms of the sequence less than 50.
======================================================
Explanation:
Plug in n = 1 to find that n^2+20 = 1^2+20 = 1+20 = 21. The first term is 21.
Repeat for n = 2 and you should get 2^2+20 = 24 as the second term.
The third term is 29 through similar steps, but this time you use n = 3 of course.
The first three terms are 21, 24, 29
It's effectively the first three perfect squares 1, 4, 9 but we have a tens digit of 2 stuck to the left of each value.
--------------------
We want to find when n^2+20 is less than 50. We could keep plugging values of n into that expression and record if the result is less than 50 or not, then tally those occurrences. You should record 5 such occurrences.
Or we could do a bit of algebra like so
n^2+20 < 50
n^2 < 50-20
n^2 < 30
sqrt(n^2) < sqrt(30)
n < sqrt(30)
On a calculator, sqrt(30) is roughly 5.4772 which means n < 5.4772. If n is a a natural number, then the largest it can get is n = 5 to ensure n^2+20 is less than 50.
We can see that,
n^2+20 = 5^2+20 = 45 when n = 5n^2+20 = 6^2+20 = 56 when n = 6This helps show that n = 5 is the largest n to make n^2+20 < 50 a true statement. This means that there are 5 terms of the sequence less than 50.
If the cost to fill the pool is $2.55 per cubic foot, how much will it cost to fill the pool?
It will cost $
to fill the pool.
Answer:
$1346.40
Step-by-step explanation:
Find the volume of the pool first:
volume = cubiod + triangular prism
volume = (8*6*8) + (8*6*6)/2
volume = 528 cubic feet
price = price per cubic foot * cubic feet
price = $2.55 * 528 cubic feet
price = $1346.40
Finalssss!!!!
Please help ASAP!!!!!!!
Answer/Step-by-step explanation:
The figure given shows two triangles.: ∆ADB has two equal base angles while ∆BCD has three equal angles. Therefore, based on their angles, we can conclude that:
∆ADB is an isosceles triangle
∆BCD is an equilateral triangle
Before we add up he outside lengths of Quadrilateral ABCD to find the perimeter, let's recall three properties of each triangle:
Isosceles triangle:
-Has two equal base angles
-The two sides opposite the two equal base angles are also equal to each other
-the their side (base) is unequal to the other
Equilateral triangle:
-Has three equal angles
-Has three equal sides
-Each angle measures 60°
Using these properties, we can determine the outside lengths of quadrilateral ABCD:
AB = 21 (given)
AD = 17 (given)
AD = BD = 17 (equal sides of ∆ADB)
BD = 17
BD = BC = CD = 17 (properties of equilateral triangle)
BC = 17
CD = 17
✔️Perimeter of Quadrilateral ABCD = AB + BC + CD + AD = 21 + 17 + 17 + 17
Perimeter = 72 units
A rectangle has an area of 19.38 cm2. When both the length and width of the rectangle are increased by 1.50 cm, the area of the rectangle becomes 35.28 cm2. Calculate the length of the longer of the two sides of the initial rectangle.
Answer: [tex]5.7\ cm[/tex]
Step-by-step explanation:
Given
Rectangle has an area of [tex]19.38\ cm^2[/tex]
Suppose rectangle length and width are [tex]l[/tex] and [tex]w[/tex]
If each side is increased by [tex]1.50\ cm[/tex]
Area becomes [tex]A_2=35.28\ cm^2[/tex]
We can write
[tex]\Rightarrow lw=19.38\quad \ldots(i)\\\\\Rightarrow (l+1.5)(w+1.5)=35.28\\\Rightarrow lw+1.5(l+w)+1.5^2=35.28\\\text{use (i) for}\ lw\\\Rightarrow 19.38+1.5(l+w)=35.28-2.25\\\Rightarrow l+w=9.1\quad \ldots(ii)[/tex]
Substitute the value of width from (ii) in equation (i)
[tex]\Rightarrow l(9.1-l)=19.38\\\Rightarrow l^2-9.1l+19.38=0\\\\\Rightarrow l=\dfrac{9.1\pm\sqrt{(-9.1)^2-4(1)(19.38)}}{2\times 1}\\\\\Rightarrow l=\dfrac{9.1\pm\sqrt{5.29}}{2}\\\\\Rightarrow l=\dfrac{9.1\pm2.3}{2}\\\\\Rightarrow l=3.4,\ 5.7[/tex]
Width corresponding to these lengths
[tex]w=5.7,\ 3.4[/tex]
Therfore, we can write the length of the longer side is [tex]5.7\ cm[/tex]
Find the value of y in the equation. 3/y-2=8
Answer: 19/8 or 2 and 3/8
Step-by-step explanation:
Can someone help me please
Answer:
The length would be 25/5 which is 4.8
Answer:
l=8 or -3
Step-by-step explanation:
You can write this into an equation!
It will be l*(l-5)=24
Now, we can just solve.
We have to expand the equation and so on.
Subtract 65 from the product of 20 and 4.
Answer:
15 is the answer
Step-by-step explanation:
20×4=80
80-65=15
Answer:
The answer is 15
Step-by-step explanation:
(20×4)-65=15
Geometric sequences HELP ASAP!
Given:
The table for a geometric sequence.
To find:
The formula for the given sequence and the 10th term of the sequence.
Solution:
In the given geometric sequence, the first term is 1120 and the common ratio is:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{560}{1120}[/tex]
[tex]r=0.5[/tex]
The nth term of a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where a is the first term and r is the common ratio.
Putting [tex]a=1120, r=0.5[/tex], we get
[tex]a_n=1120(0.5)^{n-1}[/tex]
Therefore, the required formula for the given sequence is [tex]a_n=1120(0.5)^{n-1}[/tex].
We need to find the 10th term of the given sequence. So, substituting [tex]n=10[/tex] in the above formula.
[tex]a_{10}=1120(0.5)^{10-1}[/tex]
[tex]a_{10}=1120(0.5)^{9}[/tex]
[tex]a_{10}=1120(0.001953125)[/tex]
[tex]a_{10}=2.1875[/tex]
Therefore, the 10th term of the given sequence is 2.1875.
Find the volume of the pyramid.
4 mm
B = 15 mm2
mm3
In Δ Q R S s = 7.9 cm ∠ Q = 125 ∘ and ∠ R = 23 ∘ '. Find the length of q, to the nearest 10th of a centimeter.
Answer- 12.2
Answer:
See the attachment ⬆️⬆️
A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts? a. .0038 b. .02 c. .0004 d. .10
Turkey costs $3.38 per pound. If you buy 2.5 pounds of turkey what is the cost of the turkey?
Answer: $8.45
Step-by-step explanation:
09.03 MC) What is the domain of the following parabola? (5 points) u-shaped graph that opens down with a vertex of 2, 3 Select one: a. x ≥ 2 b. x ≤ −1 c. y ≤ 3 d. All real numbers
Answer:
The correct option is d: All real numbers.
Step-by-step explanation:
For a function f(x), the domain is the set of all the possible values of x that we can input in that function.
A general way to find the domain of a function is:
First, assume that the domain is the set of all real numbers.
Then, look at restrictions implied:
like in functions like:
f(x) = 4 if x > 3
Here the domain of the function is implied.
Third, let's find values of x that make "problems" with our function (for example, a zero in the denominator) and then remove these points from the domain.
In this case, we have a quadratic function:
y = a*x^2 + b*x + c
Here we do not have any problem (like a zero in a denominator), and we do not have any restrictions (We only know that the parabola is U shaped, so it is a function, and that its vertex is (2, 3) )
Then we can conclude that the domain of this function is the set of all real numbers.
The correct option is d: All real numbers.
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Step-by-step explanation:
perimeter o rectangle is 16
Answer:
Step-by-step explanation:
perimeter of rectangle=2(l+b)
=2(8+4)
=2*12
=24 ft
Body fat percentage of 13.4% and weighs 182 pounds. How many pounds of his weight is made up of fat? Round to the nearest tenth
Answer:
It would be 24.4 pounds.
Step-by-step explanation:
First do: 13.4 / 100 = 0.134
Then, 182 * 0.134,
to get 24.4 pounds.
What does burning fossil fuels release into the air?
When fossil fuels are burned, they release nitrogen oxides into the atmosphere, which donate to the formation of smog and acid rain. Major sources of nitrogen oxide emissions include: Cars and trucks. Coal-fired power plants.
Step-by-step explanation:
Answer:
carbon dioxide
Step-by-step explanation:
took the test
At time, t greater than or equal to 0, a particle moving in the xy plane has velocity vector given by v(t)=(t^2, 5t) What is the acceleration vector of the particle at time t=3?"
Answer:
The acceleration vector of the particle at time t=3 is (6,5).
Step-by-step explanation:
Acceleration:
The acceleration is the derivative of the velocity.
Derivative of a vector:
To derivate a vector, we derive each component.
v(t)=(t^2, 5t)
So
a(t) = v'(t) = (2t, 5).
What is the acceleration vector of the particle at time t=3?
a(3) = (2*3, 5) = (6,5)
The acceleration vector of the particle at time t=3 is (6,5).
To which rational number to which rational subset(s) does the following number belong?
15
1. Rational Numbers
II. Natural Numbers
III. Whole Numbers
IV. Integers
Answer:
15 belongs to the set of natural numbers , whole numbers , integers & rational numbers.
Step-by-step explanation:
TO FIND :-
those subsets to which 15 belongsFACTS TO KNOW BEFORE SOLVING :-
N = Set of all natural numbers
W = Set of all whole numbers
Z = Set of all integers
Q = Set of all rational numbers
It can be said that :-
N ⊂ W (∵ Whole numbers include all natural numbers along with 0)W ⊂ Z (∵ Integers include positive numbers i.e. whole numbers along with negative numbers.)Z ⊂ Q (∵ Rational numbers include all integers along with fractions.)Hence , N ⊂ W ⊂ Z ⊂ Q
SOLUTION :-
Method 1 -
{15} ⊂ N (∵ 15 is an element of set N. {15} a singleton set & it can be called as the subset of N )
⇒ {15} ⊂ N ⊂ W ⊂ Z ⊂ Q
∴ 15 belongs to the set of natural numbers , whole numbers , integers & rational numbers too.
Method 2 -
A rational number is a number which can be expressed in "p/q" form where p,q are integers & q ≠ 0. 15 can also be expressed as [tex]\frac{15}{1}[/tex]. Hence, 15 is a rational number i.e. it belongs to the set of rational numbers.Natural numbers are the countable numbers. 15 is a countable number. So , 15 is a natural number i.e. 15 belongs to the set of natural numbersWhole numbers include all natural numbers as well as zero. 15 is a natural number. So , 15 is also a whole number i.e. 15 belongs to the set of whole numbers.Integers include the negative numbers as well as whole numbers. 15 is a whole number. So , 15 is also an integer i.e. 15 belongs to the set of all integers.What is the surface area of a rectangular prism that has a height of 5 cm, a width of 10 cm, and a depth of 4 cm?
A rectangular prism with length of 10 centimeters, width of 4 centimeters, and height of 5 centimeters.
Answer:
the surface area is 220
Step-by-step explanation:
:)
What's the probability of drawing one blue marble from a bag which contains 4 red marbles, 6 green marbles, I white marble, and 3 blue
marbles?
A. 1/14
B. 3/11
c. 3/14
D. 1/7
E. 1/11
Answer:
C. 3/14
Step-by-step explanation:
Note that in a proper fraction, (part/whole) is the rule you will typically follow.
You are trying to draw 1 blue marble from a bag of:
4 red marbles
6 green marbles
1 white marble
3 blue marbles.
Note that there are 14 marbles in all, in which 3 are blue:
3 blue marbles/14 marbles in all is your chance of obtaining a blue marble.
C. 3/14
~
Answer:
Step-by-step explanation:3/14
Pleaseee help me!!!!- no links please.
Suppose Easton entered in * x * shows , So we have :
60/100 × x = 15
x = 1500/60
x = 150/6
x = 25
Thus he entered 25 shows last year.
45 = (y + 7) + 11 please help
Answer:
9/4
Step-by-step explanation:
45/(y+7)+11
y=2
45/(2+7)+11
45/9+11
45/20
9/4
If this helps please mark as brainliest
Answer:
16
Step-by-step explanation:
45 ÷ (y + 7) + 11
45 ÷ (2 + 7) + 11
45 ÷ (9) + 11
5 + 11
16
Simplify this expression (7p+3)+(5p-4)
Answer:
12p -1
Step-by-step explanation:
(7p+3)+(5p-4)
Combine like terms
7p+5p +3-4
12p -1
answer quick!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
whats the problem
Step-by-step explanation:
What additional information is needed to prove the following triangles congruent by ASA?
Answer:
angle B = angle C
Step-by-step explanation:
______________
Step-by-step explanation:
hdjsje dhd d sis s. sjxjdns
The obtuse angle between the hands of a clock at 2.30 a.m is:
A 105°
B 120°
C 135°
D 150°
E 165°
Answer:
c
Step-by-step explanation:
Which choices are equivalent to the fraction below? Check all that apply.
help?
this counts as a grade so i really need help
If the daily returns on the stock market are normally distributed with a mean of .05% and a standard deviation of 1%, the probability that the stock market would have a return of -23% or worse on one particular day (as it did on Black Monday) is approximately __________.
Answer:
The probability that the stock market would have a return of -23% or worse on one particular day (as it did on Black Monday) is approximately 0%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
If the daily returns on the stock market are normally distributed with a mean of .05% and a standard deviation of 1%
This means that [tex]\mu = 0.05, \sigma = 1[/tex]
The probability that the stock market would have a return of -23% or worse on one particular day (as it did on Black Monday) is approximately
This is the p-value of Z when X = -23. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{-23 - 0.05}{1}[/tex]
[tex]Z = -23.05[/tex]
[tex]Z = -23.05[/tex] has a p-value of approximately 0. So
The probability that the stock market would have a return of -23% or worse on one particular day (as it did on Black Monday) is approximately 0%.
pleeeaaaaasssnnsnsnsnnanannananannanamnanw
Answer:
Angle PQR = 120°
Step-by-step explanation:
The solutions of a quadratic equation are -4,9 Write a related quadratic function in factored form.
Answer:
y = (x + 4)(x - 9)
Step-by-step explanation:
x = {-4, 9}
y = (x + 4)(x - 9)