To find a1, put 1 in the given equation and evaluate.
... a1 = -3·1 +1
... a1 = -2
Each time n increases by 1, an is 3 less than the previous value. So, you can write the recursion relation as ...
... a[n] = a[n-1] - 3
Which sequence matches the recursive formula? an=2an-1+5, where a1=5. A) 5,10,15,20 B) 5,15,35,75. C)5,15,25,35. D) 5,20,35,40
The recursive formula
[tex] a_n = 2a_{n-1}+5 [/tex]
means that, to compute the next value, you have to double the previous one and then add 5.
So, we start with 5. To get the second term, we double it and add five, so we have
[tex] a_2 = 2\cdot 5+5 = 10+5 = 15 [/tex]
Next, we will double 15 and add 5:
[tex] a_3 = 2\cdot 15 + 5 = 30+5 = 35 [/tex]
So, the answer is B, because it's the only option starting with 5,15,35.
Just to check, let's compute the last step:
[tex] a_4 = 2\cdot 35 + 5 = 70+5 = 75 [/tex]
Which confirms option B
5.5 oz = __________ kg
Answer:
0.155922
Step-by-step explanation:
Answer: 0.1562 kilograms
Step-by-step explanation: To convert 5.5 ounces into kilograms, we first convert 5.5 ounces into grams using the conversion factor 1 oz = 28.4 g.
Since we are going from a larger unit "ounces" to a smaller unit "grams" we multiply 5.5 by the conversion factor which is 28.4 to get 156.2.
This means that 5.5 ounces is equal to 156.2 grams.
Next, we convert 156.2 grams into kilograms using the conversion factor
1 kilogram = 1,000 grams. Since we are going from a smaller unit "grams" to a
larger unit "kilograms" we divide 156.2 by the conversion factor which is 1,000
and we get 0.1562 kilograms.
Therefore, 5.5 ounces is equal to approximately 0.1562 kilograms.
If P(3,2) and Q(7,10) are the endpoints of the diameter of a circle, what is the area of the circle in square units?
To find the area of a circle given its diameter's endpoints, determine the diameter length, radius, and then calculate the circle's area using the radius.
Explanation:The area of a circle can be found using the distance formula between two points representing the diameter's endpoints. Given points P(3,2) and Q(7,10), the diameter length is calculated as sqrt((7-3)^2 + (10-2)^2) = sqrt(4^2 + 8^2) = sqrt(16+64) = sqrt(80).
Knowing that the radius is half the diameter, the radius, r = sqrt(80)/2 = 4*sqrt(5).
Finally, the area of the circle is A = pi*r^2 = pi*(4*sqrt(5))^2 = 80*pi square units.
Which pair of numbers is relatively prime?
A. 12 and 54
B. 9 and 21
C. 21 and 39
D. 15 and 49
Answer:
D. 15 and 49
Step-by-step explanation:
Numbers are relatively prime if the only positive integer that divides both of them is 1.
A. 12 and 54
both 12 and 54 can be divided by 3
12/3 =4 54/3 = 18
B. 9 and 21
both 9 and 21 can be divided by 3
9/3 =3 and 21/3 = 7
C. 21 and 39
both 21 and 39 can be divided by 3
21/3 =7 and 39/3 = 13
D. 15 and 49
13 is 3*5 and 49 is 7*7
This is relatively prime
simplify
[tex]( \frac{ {h}^{12} }{ {h}^{4} } ) {}^{3} [/tex]
Plz help! and explain how you got the answer
Answer:
[tex]h^{24}[/tex]
Step-by-step explanation:
[tex](\frac{h^{12}}{h^4})^3\\ (h^8)^3\\h^{24}[/tex]
When dividing two exponents (of the same bases) you subtract the exponents. When there is an exponent to an exponent, you multiply the to exponents.
[tex]\left(\dfrac{h^{12}}{h^4}\right)^3\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\left(h^{12-4}\right)^3=\left(h^8\right)^3\\\\\text{use}\ (a^n)^m=a^{n\cdot m}\\\\=h^{8\cdot3}=h^{24}\\\\Answer:\ \boxed{\left(\dfrac{h^{12}}{h^4}\right)^3=h^{24}}[/tex]
At a high school with 800 students, 80% of the students ride the school bus. if 20 students are selected randomly (without replacement) and we let x = the number of students in the sample who ride the bus, what is the probability that at least one of the students doesn't ride the bus?
Answer:
0.9885 (98.85%)
Step-by-step explanation:
Since sample is less than 10% of the population, we can use binomial distribution to approximate the probability.
So we want to calculate P( X < 20 ).
We can calculate the probability of complement event P( X = 20 ).
Use binomial formula b(x; n, p) = C( n, x ) p^(x) (1-p)^(n-x)
b( 20; 20, 0.8 )
= C( 20, 20 ) (0.8)^(20) (0.2)^0
= (0.8)^20 ≈ 0.0115
So since P( X < 20 ) = 1 - P( X = 20 ), we have
P( X < 20 ) ≈ 1 - 0.0115 = 0.9885
The required value of probability for the given sample is given as 0.9885.
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Total number of students are given as 800.
The probability of students riding the school bus is 80% = 0.8.
Then, probability of students not riding the school bus is 1 - 0.8 = 0.2.
The probability of finding at least one student out of 20 not riding the bus is given as,
1 - P(All of the students ride bus)
It can be solved using binomial distribution as follows,
⇒ 1 - ²⁰C₂₀(0.8)²⁰(0.2)⁰
⇒ 1 - 0.0115 = 0.9885
Hence, the probability that at least one of the students doesn't ride the bus is given as 0.9885.
To know more about binomial distribution click on,
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A point on the rim of a wheel moves with speed of 200 feet per second. Find the angular velocity of the point if the diameter of the wheel is 8 feet.
The angular velocity of the point is found this way:
w = v/r
w = 200/(8/2) <--the two is from 2 * Pi * r
w = 50 rad/sec.
Answer: 50 rad/sec.
fullness; live
The length of the rectangle is 7 inches, the width is w inches. If the coefficient of the width increases by 3, what could be an expression for the area of the rectangle?
Answer:
A = 10w
Step-by-step explanation:
In the area formula, the coefficient of width is length. Here, that is ...
... A = 7w
7 is the coefficient of the width. Increasing it by 3 makes it be 10, so we have ...
... A' = 10w
_____
Comment on the problem statement
The problem does not make it clear whether area stays the same as the coefficient increases. We have assumed that it does not.
Also, the coefficient of width in the area formula has units of inches. "Increases by 3" makes no sense in this context. It would make sense for it to increase by 3 inches. The result is very different if the increase is 3 microns, for example.
Which description best defines the line FG⎯⎯⎯⎯⎯ ? the set of all points that are the same distance from point F as point G the set of all points between point F and point G the set containing point F and point G the set of all points between point F and point G, including point F and point G
Answer:
the set of all points between point F and point G, including point F and point G
Step-by-step explanation:
The definition of a line segment is the set of points on a line between two given end points, including those end points. The best description is the one that matches the definition.
Answer:
the set of all points between point F and point G, including point F and point G
Step-by-step explanation:
Sandy has 18 roses, 9 daisies, and 45 tulips. She wants to arrange all the followers in bouquets. Each bouquet has the same number of flowers and same type of flower. What is the greatest number of flowers that could be in a bouquet?
Using the smallest number she has, 9 daisies..
18/9 = 2
45/9 = 5
She can make 9 bouquets with 2 roses, 1 daisy and 5 tulips in each.
That means each bouquet would have 8 total flowers.
Lane borrowed $1200 for a new drum set. She will be paying 6.5% in simple interest over the next 2 years. What is the total amount of interest she will be paying on the loan? Show Work
Answer:
Steplo-by-step explanation:loan is 1200.
The interest rate is 6.50
Pp 46.90
Cumulative payment $53.4
Total payments$1,282.93
Final answer:
Lane will pay a total of $156 in simple interest on the loan of $1200 over 2 years, calculated using the simple interest formula: I = PRT.
Explanation:
Lane borrowed $1200 at a simple interest rate of 6.5% for a period of 2 years. To calculate the total amount of interest that will be paid on the loan, we can use the simple interest formula, which is:
I = PRT
where I is the interest, P is the principal amount borrowed, R is the interest rate per year (expressed as a decimal), and T is the time in years the money is borrowed for.
First, we convert R to a decimal by dividing it by 100:
R = 6.5% / 100 = 0.065
Next, we substitute the values into the formula:
I = $1200 × 0.065 × 2
I = $1200 × 0.13
I = $156
Therefore, the total amount of interest that Lane will be paying on the loan over the next 2 years is $156.
Four Ice Skaters participate in an ice skating competition. The table shows their scores. Who has the highest score?
Natasha 75.03
Taylor 75.39
Rowena 74.98
Suki 75.3
Answer:
Your answer is Taylor
Step-by-step explanation:
Answer:
Taylor
Step-by-step explanation:
her answer is 0.09 greater then suki who is 2nd biggest
plz mark brainliest
find each side length. Round to the nearest tenth if necessary
x = 8.5
The other two sides are given in the diagram.
Step-by-step explanation:The Pythagorean theorem tells you ...
... 19² = 17² +x²
Subtracting 17², we have ...
... x² = 361 -289 = 72
Taking the square root gives x.
... x = √72 = 6√2
... x ≈ 8.5
The sides of a square are two to the power of four-ninths inches long. What is the area of the square?
two to the power of the fraction sixteen over eighty-one square inches
four to the power of the fraction sixteen over eighty-one square inches
two to the power of eight-ninths square inches
four to the power of eight-ninths square inches
Answer:
2^(8/9) in²
Step-by-step explanation:
Make use of the identity ...
... (a^b)^c = a^(bc)
Here, you have a=2, b=4/9, c=2. There is an additional factor (units of inches) inside the parentheses on the left. For that, you use the identity
... (ab)^c = a^c·b^c
In this case a = 2^(4/9), b = in, c = 2.
So, the working of your problem is ...
... Area = (side length)^2 = (2^(4/9) in)^2 = (2^(4/9))^2 in^2
... = 2^(4/9·2) in^2 = 2^(8/9) in^2
i need help on finding the orthocenter of a triangle, i got the x right, x=6 but I got the Y value wrong, it's supposed to be y=4 but i got y=8 as my answer. the question is find the coordinates of the orthocenter of Triangle ABC with vertices A(2,6), B(8,6), and C(6,2). what i did to find the Y value was find the slope of BC then use that value and the coordinates of A and substituted them into an equation y-6=1/2(x-2), i solved it and got y = 1/2x+5. i then substituted my x value that i previously found into it to find Y , y=1/2(6)+5 . i got 8 as the Y value but it's wrong, can someone tell me what i missed?
Answer:
See the attached
Step-by-step explanation:
When in doubt, draw a diagram.
The orthocenter of this acute triangle will be within its bounds. That should tell you right away that the y-coordinate of it will not be 8, but must be between 2 and 6.
The line perpendicular to BC through A must have a y-intercept greater than the y-coordinate of A, so cannot be 5. Whatever it is, the y-coordinate of the orthocenter will be less, so again, your answer fails the reasonableness test.
The perpendicular line to BC through A is ...
... y = (-1/2)(x -2) +6 = -x/2 +7 . . . . . . looks like you had a sign error in (-1/2)(-2)
The intersection of that line and x=6 is ...
... y = -6/2 +7 = 4
What common side do AEG and ADE have
Answer:
AE
Step-by-step explanation:
Pairs of letters identify line segments:
... AE, EG, AG
... AD, DE, AE
Segment AE is common to both lists.
What is the Value of x+y ? PLZ Help ASAP
Answer:
x + y = 60
Step-by-step explanation:
In the given figure, we have two lines that intersect each other at one point.
Therefore, the opposite angles are equal to each other and we can write them in the form of an equation as:
2y - 5 = 95 --- (1)
3x + 55 = 85 --- (2)
Now solving each of the equations to find the value of x and y.
For y:
2y - 5 = 95
2y = 95 + 5
2y = 100
y = 50
For x:
3x + 55 = 85
3x = 85 -55
3x = 30
x = 10
Therefore, x + y = 10 + 50 = 60.
Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race and Jenna had finished 7/12 of the race. Who had finished more of the race?
Final answer:
After converting their completion fractions to decimal form, Jose finished more of the race than Jenna after 30 minutes, with Jose at 2/3 (approximately 0.6667) and Jenna at 7/12 (approximately 0.5833).
Explanation:
Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race, and Jenna had finished 7/12 of the race. To determine who had finished more of the race, we can compare these two fractions by finding a common denominator or converting them to decimal form.
First, let's convert them to decimal form:
2/3 is approximately 0.6667
7/12 is approximately 0.5833
Comparing the decimal values, we can see that Jose's completion (0.6667) is greater than Jenna's (0.5833). Therefore, Jose had finished more of the race after 30 minutes.
I need help plz plz plz help me ASAP. And SHOW YOUR WORK
Answer:
The cost of the wristband for 8 rides is $35.
Step-by-step explanation:
The expression for the cost, C, for r rides is
C = 2.5r + 15
Since she wants to go on 8 rides, r is 8.
Substitute r with 8 in the cost equation and evaluate it.
C = 2.5r + 15
C = 2.5 * 8 + 15
C = 20 + 15
C = 35
The cost of the wristband for 8 rides is $35.
a park plants youn maple trees.a maple tree grows the rate of 1 1/2 feet per year how tall will the tree be in 20 years
Answer:
it will grow 30 ft in 20 years
Step-by-step explanation:
the height will equal the growth rate times the time
height = 1.5 ft/year * 20 year
height = 30 ft
Which value of m will create a system of parallel lines with no solution?
y = mx – 6
8x – 4y = 12
2
Step-by-step explanation:Solve the second equation for y.
... 8x -12 = 4y . . . . add 4y -12
... 2x -3 = y . . . . . . divide by the coefficient of y
The coefficient of x is 2, so a parallel line will have an x-coefficient of 2. The line ...
... y = 2x -6 . . . . . . . . m = 2
will be parallel to the given line, so will not intersect it.
Simplify 3 square root of 5 end root minus 2 square root of 7 end root plus the square root of 45 end root minus square root of 28
2 square root of 12
2 square root of 2
6 square root of 5 end root minus 4 square root of 7
6 square root of 10 end root minus 4 square root of 14
Answer:
6 square root of 5 end root minus 4 square root of 7
Step-by-step explanation:
[tex]3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}=3\sqrt{5}-2\sqrt{7}+\sqrt{3^2\cdot 5}-\sqrt{2^2\cdot 7}\\\\=(3+3)\sqrt{5}+(-2-2)\sqrt{7}=6\sqrt{5}-4\sqrt{7}[/tex]
_____
Comment on the answer form
In symbols, parentheses are preferred for grouping:
... 6√(5) -4√7
or
... 6(√5)-4√7
As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.
Answer:
Answer:
6 square root of 5 end root minus 4 square root of 7
Step-by-step explanation:
_____
Comment on the answer form
In symbols, parentheses are preferred for grouping:
... 6√(5) -4√7
or
... 6(√5)-4√7
As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.
Which equations could you use to solve the following problem? Fifty-six is 85% of what number? 56 = (0.85)w = = p = (0.85)56
Answer:
56 = (0.85)w
Step-by-step explanation:
"is" translates to "=".
"of" translates to "×".
We can let "what number" translate to "w".
Then ...
56 is 85% of what number . . . . translates to ...
56 = 0.85×w
_____
Of course, you know that 85% = 85/100 = 0.85.
A recipe calls for 1 /4 start fraction, 1, divided by, 4, end fraction cup of chocolate chips for each batch of cookies. Alonzo has 1/2 start fraction, 1, divided by, 2, end fraction cup of chocolate chips. How many batches of cookies can Alonzo make?
Answer:
2
Step-by-step explanation:
1/2 cup = 2/4 cups = 2 × 1/4 cup
Alonzo can make 2 batches that each require 1/4 cup.
Convert to rectangular form.
Answer:
-16 sqrt(3) +16i
Step-by-step explanation:
z = 2 cis (pi/6)
z^5 = 2^5 cis (5*pi/6)
z^5 = 32 cis (5pi/6)
z^5 = 32 cos (5pi/6) + 32 i sin (5pi/6)
= 32 * (-sqrt(3)/2) + 32i (1/2)
= -16 sqrt(3) +16i
Help asap I need help with these questions i have to show work too.
Answer:
1: Simplify 15/20 to 3/4
y/4=3/4
Multiply both sides by 4
y=3/4×4
Simplify 3/4×4 to 12/4
y=12/4
Simplify 12/4 to 3
y=3
2: Multiply both sides by z-3
6=8/5(z-3)
Simplify 8/5(z-3) to 8(z-3)/5
8(z-3)/5
Multiply both sides by 5
6×5=8(z-3)
Simplify 6×5 to 30
30=8(z-3)
Divide both sides by 8
30/8=z-3
Simplify 30/8 to 15/4
15/4=z-3
Add 3 to both sides
15/4+3=z
Simplify 15/4+3 to 27/4
27/4=z Switch sides z=27/4
a 18 ft tall statue standing next to a globe casts a 12 ft shadow. Of the globe casts a shadow that is 2 ft ling, then how tall is it?
3 ft
Step-by-step explanation:The statue's height is 1.5 times the length of its shadow, so we expect the same relationship for the globe.
... 1.5 × 2 ft = 3 ft
_____
Comment on the problem
As a practical matter, with the sun high enough in the sky to cast a shadow shorter than the object's height, it will be quite difficult to measure the length of the shadow of the point at the top of the globe. The shadow of other parts of the globe will interfere.
Write three different fractions that are less than 40%?
1/3, 1/4, 1/5
Step-by-step explanation:40% = 40/100 = 2/5
Any fraction with a numerator of 2 and a denominator larger than 5 will be less than 40%, for example.
So, we can choose 2/6 = 1/3, 2/8 = 1/4, and 2/10 = 1/5 as some such values.
_____
We could also choose something like 39.99% = 3999/10000, or 1% = 1/100.
Segment AN is the altitude to side BC in ΔABC. If AB = 3NC and AN = 2NC, prove that AC = BN. (Hint: Use variables in such problems. Let NC = x units and find the other lengths in terms of x.)
Answer :
The proof is as follows :
Step-by-step explanation:
Let NC = x
⇒ AB = 3x and AN = 2x
In Δ ABN, By using Pythagoras theorem,
AB² = BN² + AN²
⇒ BN² = AB² - AN²
⇒ BN² = (3x)² - (2x)²
⇒ BN² = 5x²
⇒ BN = x√5 .......................(1)
Now in ΔANC , Using Pythagoras theorem We have,
AC² = NC² + AN²
⇒ AC² = x² + (2x)²
⇒ AC² = 5x²
⇒ AC = x√5 ....................(2)
From equations (1) and (2) We get,
AC = BN , which is our required result
Answer:
BN=AC=√5 x.
The proof is explained in step-by-step explaination.
Step-by-step explanation:
Let NC=x. It is given that AB=3NC & AN=2NC
⇒ AB=3x & AN=2x
By applying Pythagoras theorem
In triangle ANC,
[tex]AC^{2}=AN^{2}+NC^{2}[/tex]
⇒ [tex]AC^{2} = (2x)^{2}+x^{2}[/tex]
⇒ [tex]AC^{2}=4x^{2}+x^{2} =5x^{2}[/tex]
⇒ [tex]AC=\sqrt{5}x[/tex] → (1)
Similarly, In triangle ABN,
[tex]AB^{2}=AN^{2}+BN^{2}[/tex]
⇒ [tex](3x)^{2}=BN^{2}+x^{2}[/tex]
⇒ [tex]9x^{2} = (BN)^{2}+4x^{2}[/tex]
⇒ [tex]BN^{2}=5x^{2}[/tex]
⇒ [tex]BN=\sqrt{5}x[/tex] → (2)
From eq (1) & (2), AC=BN
The measure of one of the angles formed by two parallel lines and a transversal is 45°. Is it possible for the measure of any of the other seven angles to be equal to 55°? Explain.
Answer: No
Step-by-step explanation:
Three of the other angles are 45°. The other four are 180° - 45°, which is not 55°. At the intersection of two lines, opposite angles are equal and adjacent angles are complementary, so two adjacent angles add to 180°. Adding a parallel line gives four more angles identical to the first four.