Answers
Given the following sequence:
[tex]\mleft\lbrace17,14,11,8,\ldots\mright\rbrace[/tex]notice that the common difference between each term is -3, therefore, we can use the explicit formula for a sequence:
[tex]\begin{gathered} a_n=a_1+(n-1)\cdot d \\ d=-3 \\ a_1=17 \\ \Rightarrow a_n=17+(n-1)(-3) \\ \Rightarrow a_n=17-3n+3=20-3n \\ a_n=20-3n \end{gathered}[/tex]we have that the explicit formula is a_n=20-3n, while the recursive formula is:
[tex]\begin{gathered} a_n=a_{n-1}+d \\ d=-3 \\ \Rightarrow a_n=a_{n-1}-3 \end{gathered}[/tex]Related Questions
When a rate is simplified so that it has a _ , it is called a unit rate
Answers
Answer:
When a rate is simplified so that it has a denominator of 1, it is called a unit rate
Step-by-step explanation:
Hope it helps!
Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.Which statements about the function are true? Select three options. Select three options.The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.
Answers
The statements about the function that are true are
The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. How to interpret the graph?The equation of the graph is given as
f(x) = (x - 1)(x + 7)
The graph of the function is added as an attachment
On the graph, we have
Vertex = (-3, -16)
This is so because the graph has a minimum point of (-3, -16)
Also, the graph crosses the x-axis at x = 1 and x = -7
This means that the graph is positive at x >1 and x >-7
Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3
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Can you help me understand how to do this please?
Answers
1/8
Explanation:The given expression is:
[tex]-\frac{1}{4}+\frac{3}{8}[/tex]Find the Least Common multiple(LCM) of the denominators
LCM of 4 and 8 = 8
After simplification, the addition expression then becomes:
[tex]\begin{gathered} \frac{-2(1)+1(3)}{8} \\ =\frac{-2+3}{8} \\ =\frac{1}{8} \end{gathered}[/tex]9. A rectangle is inscribed in a circle.
a. Calculate the area of the circle.
b. Calculate the area of the rectangle.
c. Calculate the area of the shaded region.
Answers
Answer:
a. 227 in.
b. 120 in.
c. 107 in.
Step-by-step explanation:
a. diameter is the radius 2x. divide 17 by 2 to get the radius which is 8.5 plug it in to the formula A=π(8.5)2 to get 226.98 rounded to 227
b. formula: length x width. length is 15 width is 8. 15x8 = 120
c. subtract the area of the circle & the area of the rectangle to get 107.
I really need help pls I’m in need of help
Answers
Let:
A be the number of pairs of Jeans Amina has.
I be the number of pairs of Jeans Idris has.
T be the total of pairs of Jeans.
Then,
A = 2
I = 3
Then, the equation that represents the total of pairs of jeans is:
[tex]T=A+I[/tex]Substituting the values we can find T:
[tex]\begin{gathered} T=2+3 \\ T=5 \end{gathered}[/tex]Answer:
The equation is: T = A + I.
And the solution is T = 5.
Which of the following represents the difference quotient for f of x is equal to 4 over x question mark
Answers
The difference quotient for the given function is:
[tex]-\frac{4}{x*(x + h)}[/tex]
How to get the difference quotient?For the function f(x), we define the difference quotient as:
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
In this case, the function is f(x) = 4/x, replacing that in the general difference quotient:
[tex]\frac{4/(x + h) - 4/x}{h}[/tex]
Now we can simplify this to get:
[tex]\frac{4/(x + h) - 4/x}{h} = 4*\frac{1/(x + h) - 1/x}{h} \\\\4*\frac{1/(x + h) - 1/x}{h} = 4*(\frac{1/(x + h)}{h} - \frac{1/x}{h})[/tex]
[tex]4*(\frac{1/(x + h)}{h} - \frac{1/x}{h}) = 4*(\frac{1}{(x + h)*h} - \frac{1}{x*h}) = 4*\frac{x - x - h}{x*h*(x + h)} = -\frac{4}{x*(x + h)}[/tex]
So the correct option is the last one.
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Simplify the expression -3 devided by (-2/5)
Answers
Answer:-7 1/2
Step-by-step explanation:-3 divided by -2/5. -3÷-2/5. -3×-5/2. 15/2=7.5.
1/3 * 4/5 is <, >, or =,4/5
Answers
Answer:
4/15 ___ 4/5 {nothing further can be done}.
Step-by-step explanation:
1/3 * 4/5 = 4/15
4/15 = 0.26
4/15 ≠ 4/5
Thus, nothing further can be done
Alocal aquarium found that if the price of admission was $10, the attendance was about 1000 customers per week. When the price of admission was dropped to $6,attendance increased to about 2950 per week. Write a linear equation for the attendance in terms of the price,p. (A = mp+b)
Answers
Given:
$10 price = 1000 customers per week.
$6 price = 2950 customers per week.
Let's write a linear equation for the attendance in terms of the price, p.
Apply the slope-intercept form:
y = mx + b
In this case, let's use the form:
A = mp + b
Where m is the average rate of change(slope) and b is the y-intercept.
To find the slope, m, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where:
(x1, y1) ==> (10, 1000)
(x2, y2) ==> (6, 2950)
Hence, we have:
[tex]m=\frac{2950-1000}{6-10}=\frac{1950}{-4}=-487.5[/tex]The average rate of change is -$487.5
To find the y-intercept, b, substitute either of the points for A and p, substitute -487.5 for x then evaluate.
Let's take the first point: (10, 1000)
A = mp + b
1000 = -487.5(10) + b
1000 = -4875 + b
Add 4875 to both sides:
1000 + 4875 = -4875 + 4875 + b
5875 = b
b = 5875
Therefore, the lineart equation for the attendance in terms of the price, p is:
A = -487.5p + 5875
ANSWER:
[tex]A=-487.5p+5875[/tex]The two options I selected was incorrect, what would the answer be?
Answers
The question gives us the following function:
[tex]f(x)=\frac{3x}{x-2}[/tex]The X-intercept is where the function crosses the x-axis and the Y-intercept is where the function crosses the y-axis.
X-intercept:
Since the graph must cross the x-axis to have an x-intercept, we should equate f(x) to zero.
[tex]\begin{gathered} f(x)=\frac{3x}{x-2}=0 \\ \\ 3x=0 \\ \therefore x=0\text{ is the x-intercept} \end{gathered}[/tex]Y-intercept:
Since the graph must cross the y-axis to have a y-intercept, we should equate x = 0.
[tex]\begin{gathered} f(x)=\frac{3x}{x-2} \\ \\ f(0)=\frac{3(0)}{0-2} \\ \\ f(0)=0\text{ is a y-intercept} \end{gathered}[/tex]Answer
Thus, the x and y-intercepts are: x = 0 and y = 0 respectively
5x - 29.4 + 1/2x when x equals -11/5
Answers
The answer is -83/2
Decimal Form: -41.5
Mixed Number Form: -41 1/2
Find the length of the missing hypoden as a right triangle if the two legs have lengths five and 12.
Answers
To find the hypotenuse we going to use the Pythagorean theorem
[tex]c^2=a^2+b^2[/tex]being c the hypotenuse and a and b the other two sides
Replacing
[tex]c^2=5^2+12^2[/tex]Solving
[tex]\begin{gathered} c^2=25+144 \\ c^2=169 \\ c=\sqrt{169} \\ c=13 \end{gathered}[/tex]Answer: hypotenuse = 13
Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯¯¯
M
P
.
Answers
Answer: 2.5
Step-by-step explanation:
The midpoint of the segment is the average of the coordinates.
[tex]\frac{0+5}{2}=2.5[/tex]
Find the missing sides
Answers
The missing side and angle of the similar polygons are as follows:
∠H = 90°FI = 5.4IH = 4.8BC = 7.7What are similar polygons?Similar polygons are two polygons with the same shape, but not the same size.
Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.
Therefore, polygon ABCD is similar to polygon FGHI. This means the corresponding angles are congruent and the corresponding sides are proportional.
Therefore,
∠C is corresponding angle to ∠H. This means they are both congruent.
Hence,
∠H = 90 degrees
Let's find FI,
10 / 6 = 9 / FI
cross multiply
FI = 54 / 10
FI = 5.4
Let's find IH
10 / 6 = 8 / IH
cross multiply
IH = 48 / 10
IH = 4.8
Let's find BC
10 / 6 = BC / 4.6
cross multiply
BC = 46 / 6
BC = 7.66666666667
BC = 7.7
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A 70-meter vertical tower is braced with a cable secured at the top of the tower and tied 30 meters from the base. What angle does the cable form with the ground? round measure of the angle to the nearest degree
Answers
Given: The statement in the question
To Determine: The angle the cable form with the ground
Solution
The statement can be represented using the diagram below
Using trigonometry ratio
[tex]\begin{gathered} tan\theta=\frac{70m}{30m} \\ tan\theta=2.333 \\ \theta=tan^{-1}(2.333) \\ \theta=66.8^0 \\ \theta\approx67^0 \end{gathered}[/tex]Hence, the angle the cable makes with the ground approximately to the nearest degree is 67⁰
What’s 10 17/20 simplified
Answers
[tex] = 10 \frac{17}{20} \\ = \frac{20 \times 10 + 17}{20} \\ = \frac{217}{20} [/tex]
ATTACHED IS THE SOLUTION
45. Write an inequality that represents the graph. Explain it step by step please.
Answers
Answer:
-4>x
Step-by-step explanation:
A. The graph of g(x) is the graph of f(x) compressed vertically.B. The graph of g(x) is the graph of f(x) compressed vertically andreflected over the x-axis.C. The graph of g(x) is the graph of f(x) stretched vertically.D. The graph of g(x) is the graph of f(x) stretched vertically andreflected over the x-axis.
Answers
The Solution:
Given:
Required:
to determine the best statement that compares the graph of g(x) with that of f(x).
Below is the graph of the given functions:
Thus, the graph of g(x) is the graph of f(x) compressed vertically and
reflected over the x-axis.
Answer:
[option B]
what is the remainder when 1234 is divided by 34
Answers
Answer:
10
Step-by-step explanation:
1234 / 34 = 1224
1234 - 1224 = 10
The remainder = 10
Solve this system of equations by graphing. First graph the equations, and then type the solution.y=5/2x–1y=7/2x–3
Answers
System of equations:
[tex]y=\frac{5}{2}x-1[/tex][tex]y=\frac{7}{2}x-3[/tex]Using a graphing calculator we can get the graph:
As the point in which both functions meet is (2, 4), then this is the solution.
Answer: (2, 4)
The distance between two cities on a map is 4.1 centimeters. The map uses a scale in which 1 centimeter represents 18 kilometers. What is the actual distance between these two cities in kilometers?
Answers
The actual distance between the two cities in kilometers is 73.8 kilometers.
Given:
The distance between two cities on a map = 4.1 centimeters
The Scale used by the map is, 1 centimeter is equivalent to 18 kilometers.
To find the actual distance between the two cities in kilometers,
We know, 1 centimeter = 18 kilometers.
For converting the distance in centimeters to kilometers we multiply the value in centimeters by the value of 1 centimeter i.e.18 kilometers.
So, 4.1 centimeter = (4.1 × 18) kilometers
= 73.8 kilometers
Therefore, the actual distance between the two cities calculated in kilometers is 73.8 kilometers.
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Data Collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggest that 69.8% of 18-20 year olds consumed alcoholic beverages in 2008?
(A) calculate the probability that exactly 4 out of 12 randomly sampled 18 to 20 year old consume an alcoholic drink?
(B) what is the probability that exactly 8 out of 1218 to20 year olds have not consumed an alcoholic beverage?
(C) What is the probability that at most two out of four randomly sampled 18 to 20 year old
have consume alcoholic beverage?
(D) what is the probability that at least one out of four randomly sample 18 to 20 years has consumed alcoholic beverage?
Answers
(a) The probability that exactly 4 out of 12 randomly sampled 18 to 20 year old consumes an alcoholic drink is 0.008127.
(b) The probability that exactly 8 out of 12, 18 to 20-year-olds have not consumed an alcoholic beverage is 0.231991.
(c) The probability that at most two out of four randomly sampled 18 to 20 year old have consumed alcoholic beverages is 0.35.
(d) The probability that at least one out of four randomly sample 18 to 20 years has consumed alcoholic beverages is 0.99168.
What is probability?The possibility of an event happening is defined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us.
Given that 69.8% of people of 18-20 yr old consume alcohol.
Then p=0.698
Now let X is the random variable denoting the number of people who drinks alcohol.
(a) Let the sample size, n = 12, p = 0.698
It can be seen that X follows a binomial distribution
Then,
P(X=4) = ¹²C₄p⁴(1-p)⁸
= 495 × (0.698)⁴(1-0.698)⁸
=495 × 0.2373 × 0.00006919
= 0.008127
(b) P(X=8) = ¹²C₈p⁸(1-p)⁴
= 12!/ (8!)(4!)(0.698)⁸(1-0.698)⁴
=495 × 0.05634344 × 0.0083181
= 0.231991
(c) Let sample size n=4
p= 0.698
Then,
P(X≤2) = P(X=0)+P(X=1)+P(X=2)
= ⁴C₀p⁰(1-p)⁴ + ⁴C₁p¹(1-p)³ + ⁴C₂p²(1-p)²
=1 × 1× 0.0083181 + 4× 0.698 × 0.0275 + 6× 0.4872 × 0.091204
=0.3516881
=0.35
(d)
For P(X≥1)= 1-P(X<1)
=1-P(X=0)
=1-⁴C₀ p⁰(1-p)⁴
=1-1 × 1 × 0.0083181
= 0.99168
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The height of a windmill blade above the ground (in feet) is given by the function ff where f(k)=14sin(1.1k)+24. Match the following expressions with the appropriate quantity.expressions-sin(1.1k)-1.1-24-14sin(1.1k)-k-1.1k- 14sin(1.1k)+24quantitiesspeed of the blade (in feet per second)height of the blade above ground (in radii)speed of the blade (in radians per second)height of the horizontal diameter of the fan above the ground (in radii)height of the blade above the horizontal diameter of the fan (in feet)angle measure rotated from the 3 o'clock position (in radians)height of the blade above the horizontal diameter of the fan (in radii)height of the horizontal diameter of the fan above the ground (in feet)height of the blade above ground (in feet)number of seconds elapsed since windmill started rotating
Answers
f (k ) =14 sin ( 1.1 k) + 24
The expressions with the appropriate quantity is f ( k) = - 14sin(1.1k
Your class tried to construct a tetrahedron using four smaller congruent tetrahedra. However, the result left a gap in the center, as shown in the diagram below. If the volume of each small shaded tetrahedron is 50 in.3, what is the volume of the gap? Explain how you know.
Answers
Answer:
200 in³
Explanation:
The lengths of the sides of the constructed tetrahedron are twice the length of the side of the small tetrahedron of 50 in³. It means that the scale factor for the solid is 2. So, the complete volume of the constructed tetrahedron is equal to
Vn = 2³(50 in³)
Vn = 8(50 in³)
Vn = 400 in³
However, we only use 4 small tetrahedrons, so the volume of these four solids is
4(50 in³) = 200 in³
Then, the volume of the gap is the difference between the volume of the constructed tetrahedron and the volume of the 4 small tetrahedrons
400 in³ - 200 in³ = 200 in³
So, the answer is 200 in³
15. Higher Order Thinking Jane bought three sheets
of poster board and a pack of markers. Denise
bought two packs of construction paper and a
tube of glue. Who spent more? How much more?
16. If Jane buys two more sheets of poster board, how
much does she spend all together?
DATA
Poster board
Markers
Tape
Glue
8.90
Craft Supplies
Construction paper
17.MP.2 Reasoning Julene has $25 to make posters. She buys
two packs of markers, one pack of construction paper, two tubes
of glue, and a roll of tape. How many sheets of poster board can
she buy with the money she has left? Explain your answer.
:
$1.29/sheet
$4.50/pack
$1.99/roll
$2.39/tube
$3.79/pack
Answers
Answer: Denise spent more than Jane.
Step-by-step explanation: Denise spent $9.97. We know now that Denise spent more than Jane. For the second part of the question how much more? We basically just subtract the two values. $9.97-$8.37 which is $1.60. There you go.
How do i do this question
Answers
Answer:25.12
Step-by-step explanation: To find the circumference the equation is diameter time pie. Pie=3.14
A bag of chips costs $2.42. Your total grocery bill, b, is a function of the number of bags of chips, n, you purchase. Write an equation to represent this function,
Answers
Answer:
[tex]b(n)=2.42n[/tex]Explanation:
We are told that the grocery bill b is a function of n (the number of bags of chips). This means that the grocery bill can be represented as b(n).
Furthermore, we know that each bag of chips costs 2.42, meaning n bags of chips will cost 2.42n - which is the grocery bill b(n); therefore,
[tex]b(n)=2.42n[/tex]which is the equation the gives the grocery bill (as a function of n, the number of chips bags bought).
Question 2A bag of marbles contains 8 black marbles, 4 redmarbles, 3 blue marbles, and 5 white marbles. What isthe probability of not drawing a black marble?
Answers
Probability of not drawing a black marble = (Number of marbles which are not black)/ (Total number of marbles)
Probability of not drawing a black marble = 12/ 20 (Replacing)
Probability of not drawing a black marble = 3/5 (Simplifying)
The answer is 3/5
36. Hiking You hiked 8.3 miles in Denali
National Park which is 3 miles farther than
you hiked yesterday. How far did you hike
yesterday?
Answers
Answer:
You hiked 5.3 miles yesterday
You have a jar of marbles in front of you 2 are green, 9 are yellow, 3 are white and 7 are red. What is e probability, as a decimal, of selecting a marble that is white or yellow, followed by a marble that is green?
Answers
Sample space = 21
Pr(White or Yellow) = Pr(White) + Pr(Yellow)
Pr(White) = 3/21 = 1/7
Pr(Yellow) = 9/21 = 3/7
Therefore,
Pr(White or Yellow)= 1/7 + 3/7 = 4/7