Answer:
225
Step-by-step explanation:
15(1+15/2) *2= 240-15=225
The sum of the arithmetic series given by the terms (2n - 1) for n=1 to 5 is 25, computed using the formula for the sum of an arithmetic series.
The series in question is an arithmetic series with a difference of 2 and the sum of the first n terms can be represented by the formula for the sum of an arithmetic series, Sn = n/2[2a + (n-1)d], where 'a' is the first term and 'd' is the common difference between the terms.
In the provided series, each term is of the form (2n - 1) starting with n=1 and going till n=5. So the first term, a = 2(1) - 1 = 1, and the common difference, d = 2 since each subsequent term increases by 2.
We can compute this sum directly by evaluating S5, using the formula for an arithmetic series: S5 = 5/2[2(1) + (5-1)(2)] = 5/2[2 + 8] = 5/2[10] = 25. So, the sum of the series is 25.
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 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
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]
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
The dolphins at the sea aquarium are fed 2 1/3 buckets of fish each day. The walruses are fed 5 times as much fish as the dolphins. How many buckets of fish are the walruses fed each day?
The total number of buckets of fish walruses were fed each day is
A = 35/3 buckets or 11 2/3 buckets
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total number of buckets of fish walruses were fed each day be = A
Now , the equation will be
The number of buckets of fish dolphins were fed each day = 2 1/3 buckets
The value 2 1/3 = 7/3 buckets
And ,
The number of buckets of fish walruses were fed each day = 5 x number of buckets of fish dolphins were fed each day
Substituting the values in the equation , we get
The number of buckets of fish walruses were fed each day = 5 x 7/3
The number of buckets of fish walruses were fed each day = 35/3 buckets
Number of buckets of fish walruses were fed each day = 11 2/3 buckets
Therefore , the value of A is 11 2/3 buckets
Hence , The total number of buckets of fish walruses were fed each day is
A = 35/3 buckets or 11 2/3 buckets
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Final answer:
To determine how much fish the walruses are fed, multiply the 2 1/3 buckets of fish fed to dolphins by 5. The calculation gives us an answer of 11 2/3 buckets of fish fed to walruses each day.
Explanation:
The dolphins at the sea aquarium are fed 2 1/3 buckets of fish each day. To find out how much the walruses are fed, we have to multiply the quantity of fish fed to dolphins by 5, since walruses are fed 5 times as much.
First, convert 2 1/3 to an improper fraction: 2 1/3 = 7/3.
Now, multiply 7/3 by 5 to get the walruses' daily fish intake in buckets.
7/3 × 5 = 35/3.
35/3 is an improper fraction, and when converted to a mixed number, it equals 11 2/3 buckets of fish per day.
Hence, the walruses at the sea aquarium are fed 11 2/3 buckets of fish each day.
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:
5 . 3n
A. 15,30,45,60
B.5,15,45,135
C.0,15,45,135
D.15,45,135,405
Answer:
3n
Step-by-step explanation:
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:
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:
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
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
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.
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
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
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
Identify the cross section of the solid shown in the diagram.
A.
hexagon
B.
pentagon
C.
octagon
D.
tetrahedron
The cross section is A. Hexagon, a 6-sided figure.
Answer:
Hexagon
Step-by-step explanation:
A polygon are plane figure with more than 3sides e.g Pentagon , hexagon, heptagon etc.
Based on the diagram the cross section of the solid contains a six sided plane figure known as a hexagon.
An hexagon is a polygon with six equal sides and angles.
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]
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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what are the steps to solving this equation?
35 + 3x – 11 = 23
The first step is to combine like terms, 35 and 11 are both integers without variables, so we can combine.
24+3x= 23
Now we subtract 24 from 23 to isolate 3x, and we get -1.
3x=-1
To solve we just need to divide -1 by 3.
Answer: -1/3
The value of x after solving the equation will be equal to -1/3
What is an equation?
The expression is defined as the relationship between the numbers and variables and are arranged in the form of an equation.
The first step is to combine like terms, 35 and 11 are both integers without variables, so we can combine.
24+3x= 23
Now we subtract 24 from 23 to isolate 3x, and we get -1.
3x=-1
To solve we just need to divide -1 by 3.
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Which situation involves descriptive statistics?
Answer:
Eighty percent of the recipes in a cookbook require salt.
Step-by-step explanation:
The above statistic describes the entire population of recipes in the cookbook. It is not projecting anything about the population based on a sample.
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.
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:
heeeeeeeeeeeeeeeellllllllpppppppp
Answer:
Answer (a):
distance traveled per revolution = 1.5 feet
Answer (b):
slope = 1.5 feet per revolution
Step-by-step explanation:
We have been given a graph which shows number of revolutions v/s distance traveled in feet.
Answer (a):
Now we need to find about how far does Miguel travel per revolution. That means find distance traveled in 1 revolution.
From graph we see that 10 revolution corresponds to 15 feet.
then 1 revolution = 15/10 = 1.5 feet
hence final answer is 1.5 feet.
Answer (b):
slope means [change in y-value] / [change in x-value]
From graph we see that 10 revolution corresponds to 15 feet.
then slope = 15/10 = 1.5 feet per revolution
Answer a is 1.5 and so is b
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
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.
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
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]
3. For the following geometric sequence, determine a1 and r and find an explicit formula for the sequence: 2, -6, 18, -54…
a. What is a1?
b. What is the common ratio r?
c. Write an explicit formula for an using the formula for geometric sequences an = a1*(r)n – 1.
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
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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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