Step-by-step explanation:
a1 is the first term. In this case, 2.
r is the common ratio. Each term is multiplied by -3 to get the next term, so r = -3.
an = 2 (-3)ⁿ⁻¹
What is the area of the trapezoid? Leave the answer in simplest radical form. The figure is not drawn to scale.
Answer:
• 72 ft²
Step-by-step explanation:
The bottom side length of the triangle is the difference between the top base length and the bottom base length:
13 ft - 5 ft = 8 ft
The vertical side length of the triangle is the same, because the triangle is an isosceles right triangle.
Since we know the base lengths and height of the trapezoid, we can use the usual formula for the area:
A = (1/2)(b1 +b2)h
= (1/2)(5 ft + 13 ft)(8 ft) = 72 ft²
At a seaport, the depth of the water, h metres, at time t hours, during a certain day is given by h=2.5 sin 2π (t−4) /12.4 + 6.2
What is the minimum depth of the water?
9.2 m
5.2 m
8.7 m
7.7 m
Answer:
5.2 m
Step-by-step explanation:
5.2 m
To find the minimum depth of the water, we look at the minimum of the function h, given by the equation h = 2.5 sin 2π (t−4) /12.4 + 6.2. The minimum depth is -2.5 + 6.2 = 3.7m, but this option is not provided.
Explanation:In this mathematics problem, we are given a sinusoidal function representing the depth of water, h, at a seaport over time, t. The equation is h = 2.5 sin 2π (t−4) /12.4 + 6.2.
To find the minimum depth of the water, we need to focus on the properties of the sine function, which varies from -1 to 1. Therefore, the minimum value of 2.5 * sin(2π(t−4)/12.4) is -2.5 when sin(x) = -1.
By adding 6.2 to the minimum value of the function (-2.5), we obtain -2.5 + 6.2 = 3.7, which is the minimum value of h. However, this option is not provided in the choices. There seems to be a mistake in the given problem or its options.
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Sienna wants to set up a special fund so she can save to buy presents for her friends and family throughout the year. If her gift purchases last year totalled $580, estimate how much she should save each month to have approximately the same amount available for gifts next year? a. Approximately $480 b. Approximately $58 c. Approximately $48 . d. Approximately $96
Answer:
c. $48
Step-by-step explanation:
Answer:
C. Approximately $48
Step-by-step explanation:
Given,
Total amount she have to save this year = $ 580,
The number of months in a year = 12,
So, the amount saved by her in each month
[tex]=\frac{\text{Total amount}}{\text{Number of months}}[/tex]
[tex]=\frac{580}{12}[/tex]
= $ 48.333333..
≈ $ 48
Hence, OPTION C is correct.
P(getting exactly 7 correct) = 0.0031
P(getting exactly 8 correct) = 0.000386
P(getting exactly 9 correct) = 2.86 × 10–5
P(getting exactly 10 correct) = 9.54 × 10–7
Describe the pattern in the probability of getting greater numbers of successes.
Answer:
Sample Response: The probability gets smaller and approaches 0 because 9 or 10 successes in 10 trials is unlikely.
The pattern observed is that the probability of getting a higher number of correct answers decreases exponentially as the number of correct answers increases.
We have given probabilities for getting exactly 7, 8, 9, and 10 correct answers in a sequence of trials.
P(getting exactly 7 correct) = 0.0031P(getting exactly 8 correct) = 0.000386P(getting exactly 9 correct) = 2.86 × 10⁻⁵P(getting exactly 10 correct) = 9.54 × 10⁻⁷To describe the pattern, we can observe how the probabilities change as the number of correct answers increases.
Let's calculate the Ratios Between Successive Probabilities:
Ratio of P(8 correct) to P(7 correct)Ratio of P(9 correct) to P(8 correct)Ratio of P(10 correct) to P(9 correct)1. [tex]\frac{P(\text{8 correct})}{P(\text{7 correct})} = \frac{0.000386}{0.0031} = 0.1245[/tex]
2. [tex]\frac{P(\text{9 correct})}{P(\text{8 correct})} = \frac{2.86 \times 10^{-5}}{0.000386} = 0.0741[/tex]
3. [tex]\frac{P(\text{10 correct})}{P(\text{9 correct})} = \frac{9.54 \times 10^{-7}}{2.86 \times 10^{-5}}= 0.0334[/tex]
Analysis of the Pattern:
The probabilities decrease rapidly as the number of correct answers increases. The ratios themselves are decreasing, which indicates that the reduction in probability is not linear but rather exponential or follows a more pronounced pattern of decay.
This kind of pattern is typical in scenarios where the events are rare or become increasingly unlikely as the number of successes increases, such as in the binomial or geometric distributions.
Complete question:
P(getting exactly 7 correct) = 0.0031
P(getting exactly 8 correct) = 0.000386
P(getting exactly 9 correct) = 2.86 × 10⁻⁵
P(getting exactly 10 correct) = 9.54 × 10⁻⁷
Describe the pattern in the probability of getting greater numbers of successes.
Problem Page A principal of $2100 is invested at 7.75% interest, compounded annually. How much will the investment be worth after 12 years?
Answer:
After 12 years the investment will be worth $5145.
Step-by-step explanation:
The formula used for compounded interest is:
A = P(1+r/n)^nt
where,
A = future value
P = Principal Amount
r = interest rate
n = no of times interest is compounded
t = time
In the question given:
A=?
P = $2100
r = 7.75% or 0.0775
n = 1
t= 12
A= 2100*(1+0.0775/1)^1*12
A= 2100 *(1+0.0775)^12
A= 2100 *(1.0775)^12
A= 2100 * 2.45
A= 5145
So, after 12 years the investment will be worth $5145.
Write
3919
in expanded form.
Answer:
Expanded form means to write the standard form as an equation with addition
so, 3919 would be 3000 + 900 + 10 + 9
Step-by-step explanation:
[tex]\text{Hey there!}[/tex]
[tex]\text{Write 3,919}[/tex]
[tex]\text{Expanded form is where you basically when you write the numbers in a}[/tex] [tex]\text{individual formation (e.g. a + a + a + a)}[/tex]
[tex]\text{3 = 3,000 since it's in the THOUSANDS place}[/tex]
[tex]\text{9 = 900 since it's in the HUNDREDS place}[/tex]
[tex]\text{1 = 10 because it is in the TENS place}[/tex]
[tex]\text{9 = 9 because it is in the ONES place}[/tex]
[tex]\boxed{\boxed{\text{Answer: 3,000 + 900 + 10 + 9}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Answer:
a= -2
b= 3
Step-by-step explanation:
solving for a:
-6 times what equals 12?
-2
solving for b:
when multiplying two variables that have exponents you simply add the two exponents together. so to find b you want to subtract 2 from 5
A= square of 3. B=2 to the square root of 3. C= square root of 25. D= square root of 16. Which expressions result in a rational number? Select all that apply.
Answer:
square root of 25 and square root of 16
Step-by-step explanation:
Parking Lot A has twice as many cars as Parking Lot B. After 10 cars draw away from Parking lot A, and 13 cars moved from parking lot A to Parking lot B, Parking lots have the same amount of cars. How many cars were there in each Parking Lot?
PLEASE HELP ASAP
Answer:
a=72 and b=36
Step-by-step explanation:
A=2B
A-10-13=B+13
Answer:
Number of cars in Parking lot A = 72 and in Parking Lot B = 36
Step-by-step explanation:
Let the number of cars in parking A is = A and in parking B is = B
Now we will make the equations
" Parking lot A has twice as many cars as Parking lot B"
A = 2B ------(1)
"After 10 cars draw away form parking lot A, and 13 cars moved from parking lot A to parking lot B then both the lots have same amount of cars."
A - 10 - 13 = B + 13
A - 23 = B +13
A = B + 13 + 23
A = B + 36 ------(2)
Now we equate the values of A in both the equations
2B = B + 36
2B - B = 36
B = 36
From equation 1
A = 2B
A = 2×(36) = 72 cars
Therefore, number of cars in Parking lot A = 72 and in Parking Lot B = 36
A dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 m/sec, while the cat can run at a speed of 24 m/sec. How soon will the dog catch the cat if the dog starts running after the cat?
Answer:
33.33
Step-by-step explanation:
A farmer has a square field that measures 100 yards on side. The field had a watering system that sweeps a large circle from the center of the field. The arm of the watering system is 50 yards long. What percentage of the field is watered?
Answer:
hdndhehhe
Step-by-step explanation:
shshheheuesuusuausshhshshshshshhehshshsgshshshshsh I just do it for points lol hahahdjejejdbjejdjrjdjdjfjfkskdkdnfnjjjjdhdhdhdhjdjdjjdjfjfdjsjdjfjdjfjfjjfjfisndjfbsisbiabsiwhwiwu2828akbdidbsjdiebeieheieb POINTS HAHA LOLCorrelation Coefficients. If the formula _____ were used to find the r-value of the following data, what would be the value of y?
A. 5
B. 9.
C. 7
D. 3
Answer: 0.9839
Step-by-step explanation:
X Values
∑ = 15
Mean = 3
∑(X - Mx)2 = SSx = 10
Y Values
∑ = 35
Mean = 7
∑(Y - My)2 = SSy = 50
X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 22
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 22 / √((10)(50)) = 0.9839
Meta Numerics (cross-check)
r = 0.9839
Answer:
C. 7Step-by-step explanation:
According to the problem, we have to find [tex]y[/tex] which refers to the mean of y-values.
So, we just have to find the mean:
[tex]y=\frac{3+5+6+9+12}{5}=\frac{35}{5}=7[/tex]
Therefore, the right answer is C.
Remember that the mean is defined as the quotient betwene the sum of all values, and the total number of them. In this case, the sum is 35 and the total number is 5.
Polonium-210 is a radioactive substance with a half life of 138 days. If a nuclear facility is handling 265 grams of polonium-210, then how many grams of polonium-210 will be left after 250 days.
The half life is 138 days, meaning exactly half of the material will decay after this time. Use this information to find the decay factor [tex]k[/tex]:
[tex]\dfrac12=e^{138k}\implies k=-\dfrac{\ln2}{138}[/tex]
Then after 250 days, there will be
[tex]265e^{250k}\approx75.492[/tex]
grams left.
Answer:
[tex]\boxed{\text{75.5 g}}[/tex]
Step-by-step explanation:
The amount of substance decreases by 50 % every half-life.
Thus, 50 % of the substance remains at the end of each half-life.
The exponential function is
[tex]a = a_{0}\left( \dfrac{1}{2}\right)^{x}[/tex]
where x = the number of half-lives.
Data:
a₀ = 265 g
[tex]t_{\frac{1}{2}} = \text{138 da}[/tex]
t = 250 da
Calculations:
(a) Calculate x
[tex]x = \dfrac{250}{138} \approx 1.812[/tex]
(b) Calculate a
[tex]a = 265\left( \dfrac{1}{2}\right)^{1.812}\\\\a = 265 \times 0.2849 = \boxed{\textbf{75.5 g}}[/tex]
1. Find f(x) if it is known that f(x+5)=x+12.
2. Find f(x) if it is known that f(x−5)=1.2x−6.
Answer:
1. f(x)=x+7
2. f(x)=1.2x
Step-by-step explanation:
1. If f(x+5)=x+12, then substitute
[tex]t=x+5\Rightarrow x=t-5[/tex]
Hence,
[tex]f(t)=(t-5)+12\\ \\f(t)=t+7[/tex]
Now change t into x:
[tex]f(x)=x+7[/tex]
2. If f(x-5)=1.2x-6, then substitute
[tex]t=x-5\Rightarrow x=t+5[/tex]
Hence,
[tex]f(t)=1.2(t+5)-6\\ \\f(t)=1.2t+6-6\\ \\f(t)=1.2t[/tex]
Now change t into x:
[tex]f(x)=1.2x[/tex]
Pepper jackie has 5.8 kg of rainbow sprinkles.If she divides them equally into 8 star containers, how much will be in each star?
Answer:
Step-by-step explanation:
Divide 5.8/8
If a diameter of a cylinder is 5 yd and the height is 8 yd what is the volume?
Answer:
[tex]\large\boxed{V=50\pi\ yd^3\approx157\ yd^3}[/tex]
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have the diameter d = 2r = 5yd → r = 2.5yd and the height H = 8yd.
Substitute:
[tex]V=\pi(2.5)^2(8)=\pi(6.25)(8)=50\pi\ yd^3\\\\\pi\approx3.14\to V\approx(50)(3.14)=157\ yd^3[/tex]
Which of the following best describe a parabola
Answer:
Option B
Step-by-step explanation:
We know that a parabola is a set of points that are equidistant from a given line, which is the directrix, and a given fixed point called the focus.
So the correct option is option B.
Answer: Option 'B' is correct.
Step-by-step explanation:
Parabola is a curve in which any given point is at equal distance from focus i.e. a fixed point and directrix i.e. a fixed line.
So, it is the set of all points forming the curve that is equidistant from a single point and a single line.
Hence , option 'B' is correct.
The sum of two numbers is 57, and their difference is 27. What are the two numbers?
Answer:
Answer: x = 32, y = 25
Step-by-step explanation:
You can write 2 equations that meet the criteria:
The sum of two numbers is 57
x + y = 57
The difference is 7
x - y = 7
Solve the second equation for x, and substitute in the first equation to solve for y
- solve the second equation for x.
Add y to both sides of the equation
x - y + y = 7 + y
x = 7 + y
- substitute x = 7 + y into the first equation
x + y = 57
(7 + y) + y = 57
7 + 2y = 57
Subtract 7 from both sides of the equation
7 - 7 + 2y = 57 - 7
2y = 50
Divide both sides of the equation by 2 to solve for y
y=25
Insert y = 25 into either equation and solve for x
x - y = 7
x - 25 = 7
Add 25 to both sides of the equation
x - 25 + 25 = 7 + 25
x = 32
Answer: x = 32, y = 25
As a check, plug these values into both equations to make sure that it works
Mary and her sister mona decide to rent a paddleboat for 2 hours at a total cost of $25 which statement describes the relationship
No hay relaion porque su hermana "mona", es su mascota
There are 3 times as many females as males on the maths course at university. What fraction of the course are female? Give your answer in its simplest form.
There are 3 times as many females as males in a maths course, giving a ratio of 3:1. The fraction of the course that is female is therefore 3/(3+1), simplifying to 3/4.
Explanation:If there are three times as many females as males in the course, this implies a ratio of females to males of 3:1, which means for every 3 females, there's one male. However, we're interested in the fraction of the course that is female, so we're looking at the fraction of total participants (females + males) that are female.
To get this, we add females and males together to get the total number of participants. There are 3 'parts' females and 1 'part' males, for a total of 4 parts. Each 'part' represents a group of students, so the total number of students is divided into 4 equal parts.
The fraction of the maths course that are females is therefore the number of parts that are female (3) over the total number of parts (4). So the fraction is 3/4.
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use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
Answer:
Second Option
671 m²; 725 m²
Step-by-step explanation:
The lateral area of a triangular prism is:
[tex]A_L = Ph[/tex]
Where P is the perimeter of the triangular base and h is the height of the prism.
In this case, the perimeter of the triangular base is:
[tex]P = 9 + 6+ 10.82\\\\P = 25.82\ m[/tex]
Then the height is 26 m
Then the lateral area of the prism is:
[tex]A_L = 25.82 * (26)\\\\A_L = 671\ m ^ 2[/tex]
Therefore the surface area of the triangular prism is:
[tex]A = 2A_B + A_L[/tex]
Where [tex]A_B[/tex] is the area of the base.
[tex]A_B = \frac{bh}{2}[/tex]
Where b is the base of the triangle and h is the height
In this case:
[tex]b = 9\ m\\\\h = 6\ m\\\\A_B = \frac{9 * 6}{2}\\\\A_B = 27\ m ^ 2[/tex]
Finally
[tex]A = 2 * 27 + 671\\\\A = 54 + 671\\\\A = 725\ m ^ 2[/tex]
The answer is 671 m² and 725 m²
Answer:
[tex]671m^{2};725m^{2}[/tex]
Step-by-step explanation:
what is the percent increase from 25 to 500
Answer:
200
Step-by-step explanation:
25 is 1/4 of 100. 25 x 4 = 100. 100 x 5 = 500
What is the solution to the system of equations that contains −3x + y = 3 and 2x − y = −1? no solution (−1, 3) infinite number of solutions (−2, −3)
Answer:
A) −3x + y = 3
B) 2x − y = −1 Adding both equations:
-x = 2
x = -2 y = -3
Step-by-step explanation:
Answer:
D). (-2, -3)
x = -2 y = -3
Step-by-step explanation:
The base of a right pentagonal prism has an area of 20 square inches. if the prism has an altitude of 8 inches, determine and state the volume of the prism, in cubic inches.
Answer:
160 in³
Step-by-step explanation:
The volume of a prism is given by the formula ...
V = Bh
where B is the area of the base and h is the height. Filling in the given numbers, you have ...
V = (20 in²)(8 in) = 160 in³
The volume of the prism is 160 cubic inches.
Final answer:
The volume of a right pentagonal prism can be found by multiplying the base area by the height of the prism. In this case, the volume is 160 cubic inches.
Explanation:
To find the volume of a right pentagonal prism, we need to multiply the area of the base by the height of the prism. In this case, the area of the base is 20 square inches and the altitude (height) is 8 inches. So, the volume can be found by multiplying 20 by 8.
Volume = Base Area x Height
Volume = 20 square inches x 8 inches = 160 cubic inches
Therefore, the volume of prism is 160 cubic inchinches
can someone help me on these two equations
#1.A cafe offers senior citizens a 15% discount off its regular price of $8.95 for the dinner buffet. How much of a discount does a senior citizen receive off of the $8.95 price?
$1.42
$1.49
$1.34
$1.65
#2.Use an equation to find a part. Round answer to the nearest tenth.
48% of 83 is what number?
39.8
43.2
172.9
159.6
Number 1, the answer is C: $1.34 and number 2 the answer is A:$39.48
Answer 1 one is C next one is A
Step-by-step explanation:
What statement BEST explains the relationship between numbers divisible by 5 and 10 A) a number that is divisible by 10 is also factors of 5.B) some of the numbers that are divisible by 10 are also divisible by 5.C) numbers that is divisible by 10 are never divisble by 5.D) a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
Answer:
D
Step-by-step explanation:
The best answer is D.
A number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
Final answer:
The correct statement is that a number divisible by 10 is also divisible by 5 because 5 is a factor of 10. Any number ending in 0 can be divided by both 10 and 5 to yield whole numbers, confirming this relationship. So, option D is correct.
Explanation:
The statement that BEST explains the relationship between numbers divisible by 5 and 10 is 'a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10'. This is because any number that ends with a 0 is divisible by 10, and since 10 is made up of 2 and 5, that same number must also be divisible by 5. For example, take the number 30; it ends in a 0, so it is divisible by 10. When you divide 30 by 10, you get 3, which shows that 10 is a factor of 30. Now, if you take 30 and divide it by 5, you also get a whole number, which is 6 in this case. This further confirms that any number divisible by 10 will also be divisible by 5.
The probability that a person at a show has seen the band play live before is 60%. A "superfan" is defined as someone who has seen the band play live at least 5 times. The probability that a person at a show is a "superfan" is 20%. Two people are selected at random. What is the probability that both of them have both seen the band perform live before, and are "superfans?"
Answer:
pretty sure the answer is 35%
Step-by-step explanation:
because thats what i got on my quiz and it was right
Please answer I’ll rate brainlyest
Answer:
Marginal distribution of political party. Choice B
Step-by-step explanation:
The Democrat is a political party. The voters are registered as either, Democrats, Republicans or Others. This implies that a voter selected at random regardless of gender will either be a Democrat a Republican or affiliated to Other political parties.
Therefore, the percent of all voters that are registered Democrats is part of the marginal distribution of political party
5(y+1)-7 = 3(y-1)+2y
y = ?
Answer:
no solutionStep-by-step explanation:
[tex]5(y+1)-7=3(y-1)+2y\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\5y+5-7=3y-3+2y\qquad\text{combine like terms}\\\\5y+(5-7)=(3y+2y)-3\\\\5y-2=5y-3\qquad\text{subtract}\ 5y\ \text{from both sides}\\\\-2=-3\qquad\bold{FALSE}[/tex]
What are the outputs of the following function?
{-3, 0, 1, 9}
{-3, -2, 0, 1, 9}
{-2}
{-3, -2}
Answer:
-2
Step-by-step explanation:
The output of the function shown is -2 for each of the four inputs.
Answer:
-2
Step-by-step explanation:
-2