(a) How many integers are in the list 1800, 1801, 1802, . . . , 3000?
(b) How many integers in the list 1800, 1801, 1802, . . . , 3600 are divisible by 3?
(c) How many integers in the list 1800, 1801, 1802, . . . , 3000 are divisible by 5?
(d) How many integers in the list 1800, 1801, 1802, . . . , 3000 are divisible by 3 and by 5?
(e) How many integers in the list 1800, 1801, 1802, . . . , 3000 are divisible by 3 or by 5?
Answers
If the list of integers is given then it can be found by subtracting the starting value from the ending value and adding 1,
(a) To find the number of integers in the list 1800, 1801, 1802, ..., 3000, we subtract the starting value (1800) from the ending value (3000) and add 1. Therefore, there are 3000 - 1800 + 1 = 1201 integers in the list.
(b) To determine the number of integers divisible by 3 in the list, we divide the difference between the starting and ending values by 3 and add 1. So, (3600 - 1800) / 3 + 1 = 601 integers are divisible by 3.
(c) Following the same approach, we divide the difference between the starting and ending values by 5 and add 1. Thus, (3000 - 1800) / 5 + 1 = 241 integers are divisible by 5.
(d) To find the integers divisible by both 3 and 5, we consider the multiples of their least common multiple, which is 15. We divide the difference by 15 and add 1: (3000 - 1800) / 15 + 1 = 120 integers are divisible by both 3 and 5.
(e) To determine the integers divisible by 3 or 5, we calculate the sum of integers divisible by 3 (601) and integers divisible by 5 (241) and subtract the integers divisible by both 3 and 5 (120): 601 + 241 - 120 = 721 integers are divisible by either 3 or 5.
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Related Questions
A group of students were given a personality test to determine if they were Type A or Type B. The results are given in the table.
Туре А 55
Туре В 48
10th Grade 11th Grade
75
22
How does P(10th Grade u Type A) compare with P(10th Grade[Type A)?
O There is not enough information.
• P(10th Grade u Type A) = P(10th Grade|Type A)
• P(10th Grade u Type A) > P(10th Grade|Type A)
• P(10th Grade u Type A) < P(10th Grade|Type A)
Answers
There is not enough information to compare the two probabilities.
To compare P(10th Grade u Type A) with P(10th Grade | Type A), let's break down what each probability represents.
P(10th Grade u Type A) refers to the probability of a student being in the 10th grade and also being Type A.
This probability can be calculated by dividing the number of students who are both in the 10th grade and Type A by the total number of students.
P(10th Grade | Type A) refers to the probability of a student being in the 10th grade given that they are Type A.
This probability can be calculated by dividing the number of Type A students who are in the 10th grade by the total number of Type A students.
Based on the given table, we have the following information:
Type A: 55 students
Type B: 48 students
10th Grade: 75 students
11th Grade: 22 students
To calculate the probabilities, we need additional information about how the Type A and Type B students are distributed across the 10th and 11th grades.
Without this information, we cannot determine the values of P(10th Grade u Type A) or P(10th Grade | Type A).
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Kelsey and Julia both leave the coffee shop at the same time, but in opposite directions. If Julia travels 9 mph faster than Kelsey and after 7 hours they are 259 miles apart, how fast is each traveling
Answers
Kelsey is traveling at a speed of 14 mph, while Julia is traveling at a speed of 23 mph.
Let's denote the speed of Kelsey as x mph. Since Julia travels 9 mph faster than Kelsey, her speed can be expressed as (x + 9) mph. In 7 hours, the total distance covered by both Kelsey and Julia is 259 miles.
Using the formula distance = speed × time, we can write the following equation for Kelsey:
Distance traveled by Kelsey = Kelsey's speed × time
= x mph × 7 hours
= 7x miles
Similarly, for Julia:
Distance traveled by Julia = Julia's speed × time
= (x + 9) mph × 7 hours
= 7(x + 9) miles
According to the problem, the total distance covered is 259 miles, so we can set up the equation:
Distance traveled by Kelsey + Distance traveled by Julia = Total distance
7x + 7(x + 9) = 259
Simplifying the equation:
7x + 7x + 63 = 259
14x = 196
x = 14
Therefore, Kelsey's speed is 14 mph, and Julia's speed is (14 + 9) mph = 23 mph.
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What is the explicit formula for the sequence {3, 8, 13, 18, ...}?
an = 3 – 5(n − 1)
O an = 3 +5,-1
An = 3 + 5(n − 1)
an = 3 + an-1
Answers
an=3+5(n-1)
Just in case you can't see what is says it says Which point has coordinates (1,-5)
A B C D please help me
Answers
Answer:
D
Step-by-step explanation:
the x value = 1 so move to the right 1 mark on the graph and since y = -5 you move down 5 marks on the graph and you get you answer
hope this helps!
plz mark me brainliest if this helped!
have a great day!
solve the question.
Answers
Answer: 1
\((\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1\)
Step-by-step explanation:
Please help thank you so much
Answers
Answer:
no
when you enter the point into the equation and solve, it does not work
Answer:
NO
Step-by-step explanation:
Need answer asapppp I have 10 min only!!!
Answers
can someone help with this algebra problem?
Answers
Answer:
g(1) = 1
Step-by-step explanation:
Since 1 ≠ -2 and 1 ≠ -1
Then we must use the expression:
g(x) = x³ - x² + 1 ,to calculate g(1).
Therefore
g(1) = (1)³ - (1)² + 1
= 1 - 1 + 1
= 0 + 1
= 1
an island is 1 mi due north of its closest point along a straight shoreline. a visitor is staying at a cabin on the shore that is 15 mi west of that point. the visitor is planning to go from the cabin to the island. suppose the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph. how far should the visitor run before swimming to minimize the time it takes to reach the island? round your answer to three decimal places and omit units from the answer box.
Answers
if the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph., then the visitor would run 14 .45 miles before swimming to minimize the time it takes to reach the island .
we are given that an island is 1 mi due north of its closest point along a straight shoreline., where the visitor is staying at a cabin on the shore that is 15 mi west of that point, in some point the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph. Considering x be the distance the visitor runs. so the total time will be :
Time (T)= x/6 + √((15-x)²+1²)/2.5
Differntiating both sides respect to x , we get
dT/dx = 1/6 -(15-x)/√(15-x)²+1)/2.5
=>1/6 = (15-x)/√(15-x)²+1)/2.5
=>6(15-x) = 2.5√(15-x)²+1)
Now considering 15 - x = y, we get
=>6y = 2.5√(y²+1)
=>36y² = 6.25y² + 6.25
=>29.75y² = 6.25
y = √(25/119), therefore ,x = 15 - √(25/119) = 14 .45
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If the average rate of inflation over the last hundred years was 3. 22%, what amount of money one hundred years ago would be equivalent to a million dollars today? Show your work.
Answers
If the average rate of inflation over the last hundred years was 3.22%, the amount of money one hundred years ago would be equivalent to a million dollars today is approximately 968,805 dollars.
If the average rate of inflation over the last hundred years was 3.22%, we have to determine the amount of money one hundred years ago would be equivalent to a million dollars today.
We know that formula of inflation is:
inflation = (FP−IP)/IP × 100
where, IP stands for the initial basket price or price index.
FP stands for the basket's final price or the price index.
From the question, inflation = 3.22%, FP = 1,000,000
Now putting the values in the formula
3.22 = (1,000,000 - IP)/IP × 100
Divide by 100 on both side, we get
0.0322 = (1,000,000 - IP)/IP
Multiply by IP on both side, we get
0.0322IP = 1,000,000 - IP
Add IP on both side, we get
1.0322IP = 1,000,000
Divide by 1.0322 on both side, we get
IP = 968,804.5
IP = 968,805(approx)
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7.7 is what percent of 16? round to the nearest hundredth?
Answers
Answer:
7.7 x x/100 = 16
x100 x100
7.7x = 1,600
Divide by 7.7 on both sides:
X = 207.79 around 208
Answer:48.13%
Step-by-step explanation:
7.7÷16×100=48.125%
Rounded to nearest hundredth=48.13%
Víctor desea colocar mayólicas cuadradas al piso de dos patios. Para este propósito dispone de dos tipos de mayólicas: tipo A y tipo B. Las medidas de cada mayólica tipo A son 45 cm x 45 cm. Mientras que las medidas de cada mayólica tipo B son 30 cm x 30 cm. Ambos patios tienen forma cuadrada y son de diferentes tamaños. Para iniciar su trabajo, Víctor coloca 9 mayólicas del tipo A en cada lado del primer patio, mientras que en el segundo patio coloca 12 mayólicas del tipo B en cada lado. ¿Qué patio tiene mayor área en metros cuadrados? ¿Cuál es la diferencia entre las áreas de los patios, en metros cuadrados?
Answers
Answer:
El primer patio, con cada mayólica tipo A, tiene mayor área.
La diferencia entre las áreas de los patios es 3.4425 m²
Step-by-step explanation:
Sabes que las medidas de cada mayólica tipo A son 45 cm x 45 cm y Víctor coloca 9 mayólicas del tipo A en cada lado del primer patio. Entonces para calcular las medidas de cada lado del patio si colocas las mayólicas debes multiplicar la medida de una por la cantidad de Víctor coloca:
9*45 cm= 405 cm
Siendo la mayólica un cuadrado, donde todos los lados son iguales y que en este caso mide 45 cm, entonces el otro lado del patio también medirá 405 cm.
Siendo el patio un cuadrado, cuya área es el producto entre dos lados, su superficie es:
405 cm* 405 cm= 164,025 cm²
Siendo 1 cm² igual a 0.0001 m², entonces el área tiene un valor de 16.4025 m².
Sabes que las medidas de cada mayólica tipo B son 30 cm x 30 cm y Víctor coloca 12 mayólicas del tipo B en cada lado del segundo patio. Entonces para calcular las medidas de cada lado del patio si colocas las mayólicas debes multiplicar la medida de una por la cantidad de Víctor coloca:
12*30 cm= 360 cm
Siendo la mayólica un cuadrado, donde todos los lados son iguales y que en este caso mide 30 cm, entonces el otro lado del patio también medirá 360 cm.
Siendo el patio un cuadrado, cuya área es el producto entre dos lados, su superficie es:
360 cm* 360 cm= 129,600 cm²
Siendo 1 cm² igual a 0.0001 m², entonces el área tiene un valor de 12.9600 m².
Entonces el primer patio, con cada mayólica tipo A, tiene mayor área.
La diferencia es el resultado de la resta o sustracción. En este caso entonces la diferencia entre las áreas de los patios es:
16.4025 m² - 12.9600 m²= 3.4425 m²
La diferencia entre las áreas de los patios es 3.4425 m²
If the length of a rectangle is five less than three times its width and the perimeter is 105
inches, what is its width? Length?
Answers
Answer:
Mark me Brainliest please
Answer : W = 14.375 inches
L = 38.125 inches
Step-by-step explanation:
Suppose the length of the rectangle is : L
and Width of the Rectangle is : W
As per the the given question
L = 3W -− 5 ---------- (1) // Length is five less than three times its width
Given Perimeter = 105 inches
2( L + W ) = 105 ---------- (2)
Put the value of L from equation (1) to equation (2)
2( 3W -− 5 + W)= 105
6W -− 10 + 2W = 105
8W -− 10 = 105
8W = 115
W = 14.375
Put the value of W in the equation (1)
L = 3W -− 5
L = 3*∗14.375 -− 5
L = 43.125 -− 5
L = 38.125
Answer : W = 14.375 inches
L = 38.125 inches
find all solutions of the equation 3sin2x−7sinx 2=0 in the interval [0,2π).
Answers
The equation 3sin^2(x) - 7sin(x) - 2 = 0 has two solutions in the interval [0, 2π): x = π/6 and x = 5π/6.
To find the solutions, we can start by factoring out sin(x) from the equation:
sin(x) * (3sin(x) - 7sin(x^2)) = 0
Now, we have two possibilities:
1. sin(x) = 0
This occurs when x = 0 and x = π since sin(0) = 0 and sin(π) = 0.
2. 3sin(x) - 7sin(x^2) = 0
To solve this part of the equation, we need to examine the interval [0, 2π) and find the values of x that satisfy the equation.
Let's rewrite the equation as:
sin(x) * (3 - 7sin(x)) = 0
From this, we can deduce two possibilities:
a) sin(x) = 0
This condition was already considered in the first part, and we found the solutions x = 0 and x = π.
b) 3 - 7sin(x) = 0
Solving this equation for sin(x), we get:
sin(x) = 3/7
To find the solutions, we can use the inverse sine function (sin^(-1)):
x = sin^(-1)(3/7)
Using a calculator or reference, we can find the approximate value of sin^(-1)(3/7) to be approximately 0.428 radians.
Since the interval is [0, 2π), we need to find all the values of x that satisfy the equation in this interval. By analyzing the unit circle, we find that sin(x) = 3/7 in the first and second quadrants.
Therefore, the approximate solutions in the interval [0, 2π) are x ≈ 0.428 radians, x = π/2, and x = π.
In summary, the solutions to the equation 3sin(2x) - 7sin(x^2) = 0 in the interval [0, 2π) are x = 0, x = π/2, and x = π.
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please help! i can never understand these problems
Answers
Answer:
1234567891011121314151617181920
An experiment will be conducted in which 20 pepper plants are randomly assigned to two groups. The plants in group 1 will receive the current fertilizer, fertilizer a, and the plants in group 2 will receive a new fertilizer, fertilizer b. All other growing conditions, including amount of sunlight and water, will be kept the same for the two groups. The growth of the pepper plants will be compared for the two groups. What are the experimental units in this experiment?.
Answers
Answer: E. The 20 plants in the two groups
Step-by-step explanation: experimental units are individuals on which the experiment is being performed. In this case the pepper plants are being used to test the effectiveness of the new fertilizer.
find inverse function for y=6x-11
Answers
the answer is in the pic
2) The Club Auto Parts Company has just recently been organized. It is expected to experience no growth for the next 2 years as it identifies its market and acquires its inventory. However, Club will grow at an annual rate of 5% in the third and fourth years and, beginning with the fifth year, should attain a 10% growth rate which it will sustain thereafter. The last dividend paid was $0.50 per share. Club has a cost of capital of 12%. What should be the present price per share of Club common stock?
Answers
Answer:
$20.84
Step-by-step explanation:
div 1 = $0.50
div 2 = $0.50
div 3 = $0.50 x 1.05 = $0.525
div 4 = $0.525 x 1.05 = $0.55125
years 5 and beyond we need to use the growing perpetuity formula:
stock price = [div 4 x (1 + g)] / (r - g) = ($0.55125 x 1.1) / (12% - 10%) = $30.32
now to determine the current value of the stocks we must calculate the present value of the future dividends and stock price:
stock price = $0.50/1.12 + $0.50/1.12² + $0.525/1.12³ + $0.55125/1.12⁴ + $30.32/1.12⁴ = $0.45 + $0.40 + $0.37 + $0.35 + $19.27 = $20.84
Is the question ''how many cars were sold each day this month'' statistical or not?
Answers
2+3=95
4+5=259
6+7=4913
8+9=?
Answers
Answer:
8117Step-by-step explanation:
by considering 2 + 3 = 95
3² = 9
2 + 3 = 5
by considering 4 + 5 = 259
5² = 25
4 + 5 = 9
by considering 6 + 7 = 4913
7² = 49
6 + 7 = 13
by considering 8 + 9 = ????
9² = 81
8 + 9 = 17
∴ 8 + 9 = 8117
Think about the function f(x) = 3 - 2x.
What does the notation f(0) mean?
Answers
3 - (2*0) => 3-0 = 3
so the answer is 3
Answer:
the answer is 3
6) What is the measure of angle bpc?
Answers
100 POINNTTSSThe following box plot shows the class scores on a particular math test:
box plot with number line titled percent with 40 as the minimum, 70 as quartile 1, 80 as the median, 95 as quartile 3, and 100 as the maximum
Which of the following data sets is represented in the box plot?
{40, 55, 55, 85, 85, 100}
{0, 40, 70, 80, 95, 100}
{70, 70, 75, 80, 85, 95}
{40, 70, 70, 80, 80, 95, 95, 100}
Answers
Answer: are you in the algerbra in flvs ? lol just wondering
Step-by-step explanation:
it would be the last option or
(40, 70, 70, 80, 80, 95, 95, 100)
have a great day :)
The following data sets are represented in the box plot
(40, 70, 70, 80, 80, 95, 95, 100)
We have given that,
the class scores on a particular math test box plot with a number line titled percent with 40 as the minimum, 70 as quartile 1, 80 as the median, 95 as quartile 3, and 100 as the maximum
What is the box plot?A boxplot is a graph that gives you a good indication of how the values in the data are spread out.
The following data sets are represented in the box plot
(40, 70, 70, 80, 80, 95, 95, 100).
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What is the difference between a leg and a hypotenuse?
Answers
Answer:
Legs - the sides that form the right angle of a right triangle.
Hypotenuse - the side opposite the right angle of a right triangle.
Step-by-step explanation:
Every triangle has 3 sides.
Certain special triangle have specific names assigned to their sides.
A right triangle has one right angle and two acute angles. The two sides that form the right angle of a right triangle are called legs. The third side of the right triangle is called hypotenuse. The hypotenuse is opposite the right angle and does not help form the right angle.
What outcome is likely to occur for a hypothesis test evaluating a treatment that has a very large and robust effect?
Answers
For the given statement, we have to correctly rejecting the null hypothesis.
According to the statement
we have to find the outcome when hypothesis test evaluating a treatment that has a very large and robust effect.
For this purpose, we know that the
A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
And according to the given statement it is clear that the by this we have to rejected this hypothesis.
because this treatment and the large effects are not possible for the independent values of the hypothesis.
In other words, we can say that the we have to correctly rejecting the null hypothesis.
So, For the given statement, we have to correctly rejecting the null hypothesis.
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Can someone pls help me ASAPP
Answers
the answer is 48 square 72
Step-by-step explanation:
72+46=48square and 48square x 0
Question 1
1 pts
What is the area formula of a square?
O A=b.h
O A=b.h: 2
A = (b+b)h = 2
Answers
Giving Brainliest If You answer this correct
Answers
Answer:
magnitude is always postive
so, it will be +2.5 , so C
Answer:
I think the answer is the third choice.
Step-by-step explanation:
The answer makes the most sense to my sense of mathematics.
Suppose your daily revenue from selling used DVDs is
R(t) = 100 + 10t (0 ≤ t ≤ 5)
dollars per day, where t represents days from the beginning of the week, while your daily costs are
C(t) = 87 + 5t (0 ≤ t ≤ 5)
dollars per day. Find the area between the graphs of R(t) and C(t) for 0 ≤ t ≤ 5.
$
What does your answer represent?
average revenue per dayaverage cost per day average profit per daytotal revenue for the weektotal cost for the weektotal profit for the week
Answers
Area between graphs is 127.5 square units. Interpretation area represents difference between revenue and cost functions over interval [0, 5].
Functions represent revenue and cost per day area represents accumulated profit over same period.
It represents total profit for week (from day 0 to day 5) in dollars.
To find the area between the graphs of R(t) and C(t) for 0 ≤ t ≤ 5,
Calculate the definite integral of the difference between the two functions over the given interval.
Let's denote the area as A,
A = ∫₀⁵ (R(t) - C(t)) dt
Substituting the functions for R(t) and C(t),
A = ∫₀⁵ ((100 + 10t) - (87 + 5t)) dt
Simplifying
A = ∫₀⁵ (13 + 5t) dt
To evaluate the integral, use the power rule of integration,
A = [13t + (5t²)/2] evaluated from t = 0 to t = 5
Now substitute the upper and lower limits into the equation,
A = [13(5) + (5(5)²)/2] - [13(0) + (5(0)²)/2]
= [65 + (5(25))/2] - [0 + 0]
= [65 + 125/2] - [0]
= 65 + 62.5
= 127.5
Therefore, the area between the graphs of R(t) and C(t) for 0 ≤ t ≤ 5 is 127.5 square units.
Now let's interpret what this answer represents in the context of the problem,
The area represents the accumulated difference between the revenue and cost functions over the interval [0, 5].
Since the functions represent revenue and cost per day, the area represents the accumulated profit over the same period.
Hence, the answer represents the total profit for the week (from day 0 to day 5) in dollars.
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what equations equals 28
Answers
The solutions to the equations are:
x = 21,
x = 7,
4 * 7 = 28,
3³ - 2³ = 19, and 30 - 2 = 28.
We have,
x + 7 = 28
To solve for x, we can subtract 7 from both sides of the equation:
x + 7 - 7 = 28 - 7
x = 21
So, the solution to the equation x + 7 = 28 is x = 21.
2x + 14 = 28
To solve for x, we can subtract 14 from both sides of the equation:
2x + 14 - 14 = 28 - 14
2x = 14
Next, we divide both sides of the equation by 2 to isolate x:
2x/2 = 14/2
x = 7
Therefore, the solution to the equation 2x + 14 = 28 is x = 7.
4 * 7 = 28
This equation is already solved.
The product of 4 and 7 is 28.
So, the equation 4 * 7 = 28 is true.
3³ - 2³ = 28
To solve this equation, we need to evaluate the exponentials:
3³ - 2³ = 27 - 8 = 19
Therefore, the equation 3³ - 2³ = 28 is not true; the correct value is 19.
30 - 2 = 28
This equation is already solved.
The difference between 30 and 2 is indeed 28.
So, the equation 30 - 2 = 28 is true.
Thus,
The solutions to the equations are:
x = 21,
x = 7,
4 * 7 = 28,
3³ - 2³ = 19, and 30 - 2 = 28.
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The complete question:
x + 7 = 28
2x + 14 = 28
4 * 7 = 28
3^3 - 2^3 = 28
30 - 2 = 28