Answer:
Number of cards at week n = 10,000(0.85)^(n-1).
At week 6 Dylan has 4437 cards.
Step-by-step explanation:
At the start of week 1 he had 10,000 = 10,000(0.85)^0 cards.
So at the start of week 2 he had 10,000(0.85)^(2-1) cards.
Number of cards for week n = 10,000(0.85)^(n-1).
Number of he will have at the start of the 6th week
= 10,000(0.85)^(6-1)
= 4437 cards (answer).
The explicit rule for the number of baseball cards Dylan starts with in week n is A(n) = 10,000 * 0.85ⁿ⁻¹. In the 6th week, Dylan will start with approximately 4437 cards.
The number of baseball cards Dylan starts with in week n can be represented by an explicit rule, which is a formula that uses the starting amount of cards and a common ratio to find the amount for any given week. The starting number of cards for week n can be calculated using the geometric sequence formula: A(n) = A(1) * rⁿ⁻¹, where A(1) is the initial number of cards, r is the ratio of the remaining cards per week (85%, or 0.85), and n is the week number.
To calculate the number of cards Dylan starts with in the 6th week, we use the formula with A(1) = 10,000, r = 0.85, and n = 6:
A(6) = 10,000 * 0.85⁶⁻¹
After performing the calculations and rounding to the nearest card, Dylan will start with approximately 4437 cards in the 6th week.
Harry asked a sample of 4 people how many siblings they had. Here are their responses:
0, 0, 1, 3
The mean is x-bar = 1 sibling.
What formula gives the standard deviation?
Answer:
Formula of standard deviation = √Variance
Standard deviation = 1
Step-by-step explanation:
X-bar is the variance
Therefore, the answer would be
√X-bar
√1 = 1
!!
Answer:
C
Step-by-step explanation:
Triangle ABC contains side lengths b = 3 inches and c = 7 inches. In two or more complete sentences describe whether or not it is possible for m ∠ B = 15°.
Explanation:
A triangle can be formed for b=3 and B=15° as long as side c is between 3 and 3/sin(15°) ≈ 11.59 inches in length. The limit for side c on the high end is that it is opposite a right angle. The limit for side c on the other end is that it is opposite a linear angle.
For the given length of side c, there are two possible triangles with b=3 and B=15°. (See attached.)
_____
For the given values of b and c, the largest possible value of B is the angle that puts side c opposite a right angle: B ≤ arcsin(3/7) ≈ 25.3769°
smart people help me please
Answer:
X=5
Step-by-step explanation:
1: 90 plus 50 because there is a 90 degree angle
2: 8x=140 and then you divide by 8
3: x=5 I hope I helped you and I hope you have a wonderful day
Answer:
X=5
Step-by-step explanation:
8x+50=90
8x=40
x=5
Woodland Mound Park sells annual visitor passes for $12.50. Last year the park raised $53,500 in annual visitor pass sales. How many annual visitor passes were sold?
Answer:
4280 passes were sold
Step-by-step explanation:
The unknown we are looking for the number of passes that were sold. We don't know how MANY were sold, but we do know that the cost of ONE is 12.50. We represent the number of passes at that price per pass as
12.50x
We also know that money earned from the sale of this unknown number of passes came to 53,500. Our equation then becomes
12.50x = 53,500
Solving for x, we divide both sides by 12.50 to get that
x = 4280
Final answer:
To find the number of annual visitor passes sold at Woodland Mound Park, divide the total sales ($53,500) by the price per pass ($12.50), resulting in 4,280 passes sold.
Explanation:
The question asks how many annual visitor passes were sold at Woodland Mound Park last year if each pass costs $12.50 and the total amount raised from pass sales was $53,500. To find the number of passes sold, you'll need to divide the total sales by the price per pass. Here is the step-by-step calculation:
Identify the total revenue from sales: $53,500.Identify the price of one annual visitor pass: $12.50.Divide the total revenue by the price per pass to get the quantity sold: $53,500 / $12.50 = 4,280.Find the solution(s) to the system of equations. Select all that apply
y=x^2-1
y=2x-2
Step-by-step explanation:
y = x^2 - 1
y = 2x - 2
x^2 - 1 = 2x - 2
x^2 - 2x + 1 = 0
(x - 1)^2 = 0
x = 1
Because x = 1 the answer must be D (1, 0).
Answer:
(1,0)
Step-by-step explanation:
Replace x values and y values with the answer choices.
[tex]y=(1)^2- 1 = 0[/tex]
[tex]y= 2(1)-2=0[/tex]
Since the coordinate pair [tex](1,0)[/tex] it is safe to assume that D will be the correct answer.
Use the graph to confirm that the solution is (1,0)
The blue line intersects at (1,0), so the solution for the system of equations is (1,0)
The sum of two consecutive integers is 9. Find the numbers.
[tex]n,n+1[/tex] - two consecutive integers
[tex]n+n+1=9\\2n=8\\n=4\\n+1=5[/tex]
4 and 5
Which of the following values are in the range of the function graphed below? Check all that apply
Please help! - Will give the answer "brainliest!"
Option: D is the correct answer.
The values that lie in the range of the function which is graphed is:
D. 1
Step-by-step explanation:Range--
The range of the function is the possible values which are attained by the function.
i.e. the values of y as is obtained corresponding to different x as in the domain.
By looking at the graph of the function is defined over the interval [-2,1] and the graph passes through (0,1) and is parallel to the x-axis.
Hence, the range of the function is: 1
( Since it takes just a single value i.e. 1 over the interval [-2,1] )
A squar has a premeter of 12x+52 units which expression represents the side length of the square in units?
The square had a side length of 3x+13.
Because the perimeter is 12x+52, you have to divide that by each of the four sides.
Ammo 67 match each definition on the left with the correct term.
Priscilla graphed function g, a transformation of the quadratic parent function f(x)=1/2f(x+2)-1 which statement is correct?
A.)Priscilla made a mistake when applying the horizontal shift.
B.)Priscilla made a mistake when applying the vertical shift.
C.)Priscilla made a mistake when applying the vertical compression.
D.)Priscilla correctly graphed the transformed function .
Answer:
Step-by-step explanation:
A.)Priscilla made a mistake when applying the horizontal shift. That "x+2" indicates a horiz. shift to the LEFT, not to the right.
Answer:
Option A.
Step-by-step explanation:
Priscilla graphed function g(x), a transformation of the quadratic parent function f (x) = [tex]\frac{1}{2}[/tex] f ( x+2 ) - 1
(1) She graphed the vertical compression correctly
(2) Priscilla graphed the vertical shift of (-1) means 1 unit downwards on y-axis correctly.
(3) In the last she made a mistake because for f(x+2) the parent function should have been shifted left on x-axis by two units f (x) ⇒ f[ x- (-2)]
Therefore Option A will be the answer.
Given the following linear function identify the slope in the Y intercept of the function
Answer:
Choice #2
Step-by-step explanation:
Your linear function is in the slope-intercept form of a line, y = mx + b, where m is the value of the slope, and b is the value of the y-intercept. The number in the m position in your equation is 1/6, and thee number in the b position in your equation is 7. So the second choice is the one you want.
What must be done to each side of the equation to find the value of n?
-4n = 696
A)
add -4
B)
multiply by -4
C)
subtract -4
D)
divide by -4
Answer:
Divide both sides by -4.
Step-by-step explanation:
If you divide both sides by -4, you'll get the answer n=−174.
Please mark brainliest!
Answer:
D
Step-by-step explanation:
-4n = 696
What must be done to each side of the equation to find the value of n?
Divide both sides by -4 to find the value of n
∴ -4n/-4 = 696/-4
n = -174
Sam recorded the number of points she scored on each weekly test out of the number of points possible for the test. In which two subjects did Sam score the lowest? Choose exactly two answers that are correct. Language Arts History Science Math Sam's Test Scores Math 2225 Science 1920 Language Arts 84100 History 910
Makes no sense.
He scored the lowest in History and Science. Compare the numbers to help you prepare the obvious chart.
Sam scored the lowest in Language Arts with 84% and Math with 88%.
To determine this, We need to calculate Sam's percentage scores for each subject:
Math: [tex]\frac{25}{25}*100[/tex] = 88%Science: [tex]\frac{19}{20}*100[/tex] = 95%Language Arts: [tex]\frac{84}{100} *100[/tex] = 84%History:[tex]\frac{9}{10}*100[/tex] = 90%Based on these calculations, the two subjects where Sam scored the lowest are Language Arts (84%) and Math (88%).
complete question:
Sam recorded the number of points she scored on each weekly test out of the number of points possible for the test.In which two subjects did Sam score the lowest?Choose exactly two answers that are correct. Sam's Test Scores in Math 22/25 ,in Science 19/20 ,in Language Arts 84/100 ,in History 9/10.
Paul received a $12,000 loan from the bank the bank charges 6. 99% Do you eat interest-rate after four years how much money does Paul owe in the interest?
Answer:
$3355.20
Step-by-step explanation:
The formula for simple interest is ...
i = Prt
where P is the principal amount, r is the annual rate, and t is the number of years. Fill in the given values and do the arithmetic.
i = 12,000×0.0699×4 = 3355.20
Paul owes $3355.20 in interest.
The Substitution Property of Equality states that if m<2+m<3=m<5 and m<2=25, then _____ ____ m<5
Step-by-step explanation:
[tex]m\angle2+m\angle3=m\angle5\ and\ m\angle2=25,\ then\ 25+m\angle3=m\anlg5[/tex]
Insert 25 instead of m<2 into the equation
Answer:
25 + m∠3 = m∠5
Step-by-step explanation:
Substitution property of equality states that,
If a + b = c and b = e ⇒ a + e = c
Given,
[tex]m\angle 2 + m\angle 3 = m\angle 5[/tex] and [tex]m\angle 2 = 25[/tex]
By substituting the value of m∠2 in first equation,
[tex]25 + m\angle 3 = m\angle 5[/tex]
Hence, the missing terms is '25 + m∠3'
Help with this question, please! I don't understand!
Answer:
(1, -5); (4, 3)
Step-by-step explanation:
We generally orient maps with north at the top. This problem presumes that orientation along with a grid having units of 1 mile. "Town Center" is taken to be the origin of the grid. As is usually the case, left/right coordinates are indicated first in an ordered pair, with up/down coordinates being indicated second.
Then the warehouse location 8 miles south and 3 miles west of Town Center is considered to have coordinates of (-3, -8). Movement 3 miles north and 4 miles east is considered to be translation by (4, 3). This translation vector is the answer to the second part of the problem.
The answer to the first part of the problem is the sum of the starting position and the translation:
(-3, -8) +(4, 3) = (1, -5)
The truck's final position is (1, -5). The translation vector to get it there is (4, 3).
Find the inverse of h(x) = (2x + 6)/5
Answer:
h^-1(x) = (5x - 6)/2
Step-by-step explanation:
To find the inverse of h(x) = (2x + 6)/5, we need to solve for 'x':
y = (2x + 6)/5 ⇒ 5y = 2x + 6 ⇒ 5y - 6 = 2x ⇒ x = (5y - 6)/2
Therefore, h^-1(x) = (5x - 6)/2
Answer:
(5x-6)/2
Step-by-step explanation:
h(x) = (2x + 6)/5
y = (2x + 6)/5
To find the inverse, exchange x and y
x = (2y+6) /5
Then solve for y
Multiply each side by 5
5x = (2y+6)/5*5
5x = 2y+6
Subtract 6 from each side
5x-6 = 2y+6-6
5x-6 = 2y
Divide by 2
(5x-6)/2 = 2y/2
The inverse is
(5x-6)/2
the number of bacteria growing in an incubator culture increases with time according to b(x)=8500(3)^x where x is the time in days. After how many days will the number of bacteria in culture be 2,065,500?
Answer:
5 days
Step-by-step explanation:
Put the given number in the formula and solve for x.
2065500 = 8500·3^x
243 = 3^x . . . . . . . . . . . divide by 8500
log(243) = x·log(3) . . . take logarithms
log(243)/log(3) = x = 5 . . . . divide by the coefficient of x
After 5 days, the number of bacteria in culture will be 2,065,500.
Which of these expressions will give the unpaid balance after 6 years on a $90,000 loan with an APR of 7.2%, compounded monthly, if the monthly payment is $708.61?
A. 90,000(1+0.072)^72+708.61[1-(1+0.072)^72/0.072]
B. 90,000(1+0.006)^6+708.61[1-(1+0.006)^6/0.006]
C. 90,000(1+0.006)^72+708.61[1-(1+0.006)^72/0.006]
D. 90,000(1+0.072)^6+708.61[1-(1+0.072)^6/0.072]
Answer:
none of the expressions shown is correct
The appropriate expression is ...
90,000(1+0.006)^72+708.61[(1-(1+0.006)^72)/0.006] . . . best matches C
Step-by-step explanation:
The formula used to calculate the remaining balance is ...
A = P(1 +r)^n +p((1 -(1 +r)^n)/r) . . . . . note the parentheses on the fraction numerator
In this formula, r is the monthly interest rate: 7.2%/12 = 0.006, and n is the number of monthly payments: 6×12 = 72. Putting these values into the formula along with the loan amount (P=90,000) and the payment amount (p=708.61) gives ...
A = 90,000(1.006)^72 +708.61((1 -(1.006)^72)/0.006)
A = 74,871.52
Answer: the answer is
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hiram raises earthworms. In a square of compost 4 ft by 4 ft, he can have 1,000 earthworms. How many earthworms can he have if his square of compost has a side length that is five times longer?
A.) 20,000
B.) 25,000
C.) 100,000
D.) 5,000
Please be original!!! I am torn between B and D. THANKS!
Answer:
The answer is D: 5,000
Step-by-step explanation:
That is the easiest question to solve. Good luck!
The number of earthworms he have if his square of compost has a side length that is five times longer is 5000.
How many earthworms can he have?
The first step is to determine the number of earthworms in a compost with a side length of 1.
1000 / 4 = 250
Number of earthworms with side length five time longer : (4 x 5) x 250 = 5000
To learn more about multiplication, please check: https://brainly.com/question/13814687
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If tan x° = a divided by 4 and cos x° = 4 divided by b what is the value of sin x°? (1 point) \
Answer:
Sin x = a / b.
Step-by-step explanation:
The opposite side =a and the adjacent side = 4 (because tan x = a/4.
Cos x = 4/b so the hypotenuse = b ( because Cos = adjacent /hypotenuse.
So sin x = opposite /hypotenuse = a / b.
Answer:
sin x° = a divided by b is the answer
Step-by-step explanation:
I got 100% on the test!
PLEASE HELP
How can I find the measure of Angle A?
Answer:
∠A ≈ 58.1°
Step-by-step explanation:
Since the triangle is right use the tangent ratio to solve for ∠A
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{8.2}{5.1}[/tex], hence
A = [tex]tan^{-1}[/tex] ( [tex]\frac{8.2}{5.1}[/tex] ) ≈ 58.1°
Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y
Answer:
y = 2x + 20
Step-by-step explanation:
2 * x is the number of minutes from the math problems
20 is the number of minutes for the history homework
Answer:
y= 2x=20
Step-by-step explanation:
Julie has 5 cherry lollipops,1 lime lollipops, and 2 grape lollipops in a bag. She is going to select one lollipop, replace the lollipop in the bag, and then select a second one. What is the probability that Julie will select a cherry lollipop and then a lollipop other than grape?
a.)6/8
b.)11/16
c.)15/32
d.)10/64
Answer: [tex]\dfrac{15}{32}[/tex]
Step-by-step explanation:
Given : The number of cherry lollipop = 5
The total number of lollipop = 8
the number of lollipops other than grape =6
The probability of selecting a cherry lollipop is given by :_
[tex]\text{P(Cherry)}=\dfrac{5}{8}[/tex]
The probability of selecting a lollipop other than grape is given by :_
[tex]\text{P(Other than grape)}=\dfrac{6}{8}[/tex]
Since, there is replacement , then the events are independent of each other.
Now, the probability that Julie will select a cherry lollipop and then a lollipop other than grape is given by :-
[tex]\text{P(Cherry and other than grape)}=\dfrac{5}{8}\times\dfrac{6}{8}=\dfrac{15}{32}[/tex]
Hence, the required probability =[tex]\dfrac{15}{32}[/tex]
squared or cubed is indicated to the top right of a number - what does 3/2 stand for? Is it a number cubed? Or squared?
Answer:
Step-by-step explanation:
3/2 is a power of 1.5 or equivalently 1 1/2. This is another way to write a radical.
[tex]x^\frac{3}{2}=\sqrt[2]{x^3}[/tex]
If sinθ = 2/3 and θ is located in Quadrant II, then tan2θ = _____.
Answer:
[tex] -4 \sqrt{5} [/tex]
Step-by-step explanation:
Quadrant 2 means cosine is negative.
So [tex] \sin(\theta)=\frac{2}{3} =\frac{\text{ opp }}{\text{ hyp }} [/tex]
So the adjacent side is [tex] \sqrt{3^2-2^2}=\sqrt{9-4}=\sqrt{5} [/tex]
So [tex] \cos(\theta)=-\frac{\sqrt{5}}{3} [/tex]
Now to find [tex] \tan(2 \theta) [/tex]
[tex] \tan(2 \theta) =\frac{2\tan(\theta)}{1-\tan^2(\theta)}[/tex]
We will need [tex] \tan(\theta) [/tex] before proceeding.
[tex] \tan(\theta) =\frac{\sin(\theta)}{\cos(\theta)}=\frac{\frac{2}{3}}{\frac{-\sqrt{5}}{3}}=\frac{-2}{\sqrt{5} } [/tex]
Now plug it in and the rest is algebra.
[tex] \tan(2 \theta) =\frac{2\tan(\theta)}{1-\tan^2(\theta)} =\frac{2 (\frac{-2}{\sqrt{5}}}{1-\frac{4}{5}} [/tex]
Now the algebra, the simplifying.... We need to get rid of the compound fraction. We will multiply top and bottom by [tex] 5 \sqrt{5} [/tex]
This will give us
[tex] \frac{-4(5)}{5 \sqrt{5}-4 \sqrt{5}} [/tex]
[tex] \frac{-20}{\sqrt{5}} [/tex]
Multiply top and bottom by [tex] \sqrt{5} [/tex]
[tex] \frac{-20 \sqrt{5}}{5} [/tex]
The answer reduces to
[tex] -4 \sqrt{5} [/tex]
Final answer:
To find tan2θ when sinθ = 2/3 and θ is in Quadrant II, we use the Pythagorean identity to find cosθ and the double angle identity for tangent. After calculation, tan2θ = -4√5.
Explanation:
If sinθ = 2/3 and θ is located in Quadrant II, we first have to find cosθ and then use the double angle identity for tangent to find tan2θ. Since sinθ is positive in Quadrant II and cosθ must be negative (as the x-values are negative in Quadrant II), we can use the Pythagorean identity sin2θ + cos2θ = 1 to find cosθ. Thus, cosθ = -√(1 - sin2θ) = -√(1 - (2/3)2) = -√(1 - 4/9) = -√(5/9) = -√5/3.
The double angle identity for tangent is tan2θ = 2tanθ / (1 - tan2θ). But first, we find tanθ = sinθ/cosθ = (2/3) / (-√5/3) = -2/√5. Then, tan2θ = 2(-2/√5) / (1 - (-2/√5)2) = -4/√5 / (1 - 4/5) = -4/√5 / (1/5) = -20/√5. Simplifying further, we multiply by √5/√5 to rationalize the denominator, which gives us tan2θ = -20√5/5 = -4√5.
For the functions f(x) = x^2+ 8x + 2 and g(x) = -5+9, find (f•g)(x)and (f.g)(-1).
Answer: (f·g)(x) = -5x³ - 31x² + 62x + 18
(f·g)(-1) = -70
(fog)(x) = 25x² - 130x + 155
(fog)(-1) = 310
Step-by-step explanation:
f(x) = x² + 8x + 2 g(x) = -5x + 9
(f·g)(x) = (x² + 8x + 2)(-5x + 9)
= -5x³ + 9x²
- 40x² + 72x
- 10x + 18
= -5x³ - 31x² + 62x + 18
(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18
= -5(-1) - 31(1) - 62 + 18
= 5 - 31 - 62 + 18
= -70
****************************************************************************************
(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2
= 25x² - 90x + 81
- 40x + 72
+ 2
= 25x² - 130x + 155
(fog)(-1) = 25(-1)² - 130(-1) + 155
= 25 + 130 + 155
= 310
It wasn't clear if you wanted multiplication or composition so I solved both.
The composition (f⋅g)(x) is 50, and the product of functions (f.g)(-1) is -20.
To find the composition of the functions f(x) and g(x), denoted as (f⋅g)(x), we first need to determine g(x). Given g(x) = -5 + 9, we simply add these numbers together to get g(x) = 4. With g(x) found, we can now substitute g(x) into f(x) to find the composition. To do this, wherever there is an x in f(x), we replace it with 4.
So, (f⋅g)(x) = f(g(x)) = f(4) = 4^2 + 8(4) + 2 = 16 + 32 + 2 = 50.
Next, to find (f.g)(-1), which represents the product of the two functions evaluated at x = -1, we evaluate both f(-1) and g(-1). We already know that g(x) is constant at 4, so g(-1) = 4. Now we find f(-1):
f(-1) = (-1)^2 + 8(-1) + 2 = 1 - 8 + 2 = -5.
Thus, the product at x = -1 is:
(f.g)(-1) = f(-1) ⋅ g(-1) = (-5) ⋅ 4 = -20.
Which equation can be used to solve for the unknown number? Seven less than a number is thirteen.
n-7=13
7-n=13
n+7=13
n+13=7
Answer:
n-7=13
Step-by-step explanation:
We need to find an equation that represents the expression: "Seven less than a number is thirteen".
It means that a number minus 7 equals 13. So, the correct option is: n-7=13
Bonus: Solving for 'n' we have that n=20.
So, Seven less than 20 equals 13!!
Answer:
the anwser is: n-7=13
Step-by-step explanation:
i took the test:)
please help!
The total number of fungal spores can be found using an infinite geometric series where a1 = 11 and the common ratio is 2. Find the sum of this infinite series that will be the upper limit of the fungal spores.
465
280
The series is divergent
125
Answer:
The series is divergent
Step-by-step explanation:
An infinite geometric series with a common ratio greater than 1 does not converge to a sum. The series is divergent.
Graph the following system of linear inequalities. Identify at least two points in the solution: y < 5 - 2x | x + 5y > -7
Answer:
(1,2) and (2,-1)
Step-by-step explanation:
we have
[tex]y< 5-2x[/tex] ----> inequality A
The solution of the inequality A is the shaded area below the dashed line [tex]y=5-2x[/tex]
[tex]x+5y>-7[/tex] ----> inequality B
The solution of the inequality B is the shaded area above the dashed line [tex]x+5y=-7[/tex]
The solution of the system of inequalities is the shaded area between the two dashed lines
If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area
Two points in the solution are
(1,2) and (2,-1)
see the attached figure