Answer:
The sequence is arithmetic
Step-by-step explanation:
we know that
In an arithmetic sequence, the difference between consecutive terms is always the same and is called common difference
In this problem we have
[tex]3,9,15,21,...[/tex]
Let
[tex]a1=3, a2=9,a3=15,a4=21[/tex]
[tex]a4-a3=21-15=6[/tex]
[tex]a3-a2=15-9=6[/tex]
[tex]a2-a1=9-3=6[/tex]
The sequence is arithmetic
The common difference is equal to [tex]6[/tex]
What is the point in the middle of a circle called?
A. Radius
B. Center
C. Circumference
D. Epicenter
Answer:
center
Step-by-step explanation:
The point in the middle of a circle called, B. Center
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know, The largest chord that passes through the center of a circle is called a diameter.
All the other line segments that can be drawn with endpoints touching the circumference of a circle are called chords.
The radius is half the length of the largest chord(diameter).
A circle is defined as if we fix a point and mark points in a plane such that each point is equidistant from that fixed point a circle will be formed.
That fixed point is called the center of a circle.
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What is the solution to the following of equations {5x-3y=34 x-2y=4?
The main tank has a radius of 70 feet. What is the volume of the quarter-sphered sized tank? Round your answer to the nearest whole number.
expand and simplify (2t-3)^2
How to write 7 95/125 as a decimal?
4.5 3.9 4.258 3.75 4.256 from least to greatest
How many different strings can be made from the letters in MISSISSIPPI, using all the letters and having no consecutive S's? ...?
Each figure represents a Real Number and no denominators are zero. Choose the
correct statement and briefly explain why the others are not correct.
A) a/b+ c/d= a+c/bd
B) a/b+c/d= a+c/b+d
C) a/b+c/d= ad+bc/bd
What is the solution to 4n-6=10n?
Probability with Huntington's disease?
Huntington disease is a rare degenerative human disease determined by a dominant allele, HD. The disorder is usually manifested after the age of 45. A young man has learned that his father has developed the disease; his mother does not have the disease (and does not carry to HD disease allele).
What is the probability that the young man will later develop the disease?
If the young man has a child with a woman who does not carry the HD disease allele, what is the probability that their first child will be affected by Huntington disease as ...?
The young man has a 50% chance of developing Huntington's disease, as he can inherit the HD allele from his father. Similarly, if he carries the HD allele and has a child with a woman who does not carry the HD allele, their child has a 50% risk of inheriting and developing the disease.
Explanation:Huntington's disease is associated with genetics and can be passed from parents to offspring. If this young man's father suffers from the condition due to a dominant allele, HD, and his mother does not carry the HD allele, he has a 50% chance of inheriting and later developing the disease. This probability arises because the offspring inherits one allele from each parent.
If the young man has a child with a woman who does not carry the HD disease allele, the child's risk of developing the condition depends on whether the father carries the HD allele. If the father does not carry the HD allele, the probability that their first child would be affected by Huntington's disease is 0%. If the father does carry the HD allele, the risk would be 50% as the child will inherit one allele from the each parent (one from the father who might have HD and one from the mother who does not carry the HD allele).
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What number is 32% of 75?
Which of the following equations could be used to solve the problem?
n = 0.32(75)
0.32n = 75
n = 75 ÷ 0.32
A science experiment calls for mixing 3 2/3 cups of distilled water with 1 3/4 cups of vinegar and 2/3 cups of liquid detergent. How much liquid, in all, in cups, is needed?
Answer:
D) 6 1/12
Have a good day.
Answer:
D. It’s right
Step-by-step explanation:
The perimeter of a square is equal to the perimeter of an equilateral triangle. The length of a side of the square is given by x, and the length of a side of the equilateral triangle is given by x=1. Which equation can be used to find the value of x?
To solve for x, given that the perimeter of a square is equal to the perimeter of an equilateral triangle, the equation 4x = 3(x + 1) can be used.
Explanation:To find the value of x when the perimeter of a square is equal to the perimeter of an equilateral triangle, we set up an equation. Since the side of the square is given by x, and the perimeter of a square is 4 times the length of a side, the perimeter of the square is 4x. The length of a side of the equilateral triangle is given by x + 1, and since the perimeter of the equilateral triangle is 3 times the length of a side, its perimeter is 3(x + 1). Setting these two perimeters equal to each other gives us the equation 4x = 3(x + 1).
Find the most general antiderivative of the function.
g(t) = (5 + t + t^2)/ square root of t
To find the most general antiderivative of the function g(t) = (5 + t + t^2) / sqrt(t), rewrite the function using inverse trigonometric functions and integrate it with respect to x, before substituting x back in terms of t to get the most general antiderivative.
Explanation:To find the most general antiderivative of the function, g(t) = (5 + t + t^2) / sqrt(t), we can rewrite the function using inverse trigonometric functions. Let x = sqrt(t), then t = x^2. Substituting this into the function gives us g(x^2) = (5 + x^2 + x^4) / x. Now, we can integrate this function with respect to x to find the antiderivative. The antiderivative of (5 + x^2 + x^4) / x is 5x + (x^3/3) + (x^5/5) + C, where C is the constant of integration. Finally, we substitute x back in terms of t to get the most general antiderivative of g(t).
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Which function represents exponential decay?
f(x) =1/2 (3/2)^x
f(x) =1/2 (-3/2)^x
f(x) =4 (-2/3)^x
f(x) = 4 (2/3)^x
The function [tex]f(x) = 4 (2/3)^x[/tex] represents exponential decay, as the base of the exponent (2/3) is between 0 and 1.
The function which represents exponential decay is the one where the base of the exponent is between 0 and 1 (0 < b < 1). Out of the given options, [tex]f(x) = 4 (2/3)^x[/tex] represents an exponential decay function since (2/3) is a positive fraction less than 1.
In contrast, a base greater than 1, a negative base, or a base of 1 would not represent decay: a base greater than 1 represents exponential growth; a base of 1 would be constant (no growth or decay); and a base that is negative would not be a standard exponential decay because it would lead to oscillation between positive and negative values.
Which is the conclusion of this statement?
If a and b are negative, then a + b is negative.
A. If a and b are negative, then a + b is negative.
B. If a + b is negative, then a and b is negative.
C. a and b are negative.
D. a + b is negative.
What is the least common denominator of 5/12 and 4/9
Rishi Maharan’s charge account statement shows an unpaid balance of $6,752.22. The monthly finance charge is 1.85% of the unpaid balance. After the finance charge was applied, Rishi has made new purchases of $150.75. What is the new account balance?
$7,027.89
$7,030.67
$6,902.97
$6,877.14
The requreid new account balance is approximately $7,027.89, which is option A.
What is a finance charge?A finance charge is a fee charged by a lender or creditor for the use of credit or the extension of existing credit. It is typically calculated as a percentage of the unpaid balance on a credit account or loan and is added to the account balance as an additional cost to the borrower.
The finance charge can be calculated as:
1.85% of $6,752.22 = 0.0185 x $6,752.22 = $124.98
Adding this finance charge to the unpaid balance gives:
$6,752.22 + $124.98 = $6,877.20
Finally, adding the new purchases to this balance gives:
$6,877.20 + $150.75 = $7,027.95
So, the new account balance is approximately $7,027.89, which is option A.
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Which statement correctly describes the end behavior of y = -3x5 + 5x2 +2x + 1
A)
The graph rises to the left and falls to the right.
B)
The graph falls to the left and rises to the right.
C)
The graph rises to the left and rises to the right.
D)
The graph falls to the left and falls to the right.
Which of the following is an inequality that represents the following scenario: Peter is at a local burger shop. He wants to purchase burgers and fries from the store. The cashier tells him that burgers are $5 each and fries are $2 each. Peter has only $15 to spend on food. Let y represent the number of fries purchased and let x represent the number of burgers purchased
5x+2y >/= 5
Answer: 2 burgers and 2 fries if he has only $15
Burgers=$5 each
Fries=$2 each
5+5=10
2+2=4
which comes out to $14 so the max he can get is 2 each
1.There are 10 kids running a race. How many ways are there for them to come in first, second, and third place?
2.In a drawing, a jar holds the numbers 1 to 8. If you draw three numbers to form a three-digit number (without replacement), what is the probability you will draw 135?
Answer:
1: 720
2: [tex]\frac{1}{336}[/tex]
Step-by-step explanation:
1: There are 10 kids in a race so the number of ways such that they come first , second and third=10×9×8
=720
(since the first place is occupied by any one of the ten students i.e. we have ten choices after occupying first position there are only 9 students left for second position and after occupying second for the third position only 8 choices are left)
2: We have to find the probability such that there is no replacement such that we draw 135.
for the first position we have to find the probability([tex]P_{1}[/tex]) that '1' comes out of 8 numbers=[tex]\frac{1}{8}[/tex]
similarly for second choice we could not take 1 as there is no replacement
so probability that 3 comes([tex]P_{2}[/tex]) =[tex]\frac{1}{7}[/tex]
similarly probability that 5 comes at third position([tex]P_{3}[/tex]) = [tex]\frac{1}{6}[/tex]
hence, probability that 135 is drawn= [tex]\frac{1}{8}\times\frac{1}{7}\times\frac{1}{6}=\frac{1}{336}[/tex]
The following bar graph shows the amount of time Latisha participated in an exercise program over a four-week period. If Latisha wants to make the increase over time appear larger, what could she do to the graph?
a. use a smaller range on the vertical scale
b. use a larger range on the vertical scale
c. use different colored bars
Answer:
The bar graph is given ,which shows the amount of time Latisha participated in an exercise program over a four-week period.
If amount of exercising , that is increase over time appear larger
She must use a larger range on the vertical scale.There will be no change in width of bar graph, as coloring the bar graph with different color will make no sense.
Pictorial representation of this problem is depicted below:
Option (B) is true.Use a larger range on the vertical scale.
This answer is correct in the sense that , if time of exercise increases,
Otherwise, if you increase the width between two whole numbers, the graph will appear larger.That is between if width between 0 to 1 is 1 cm than increase it by 1.5 cm or 2 cm, that will make the bar graph larger.
Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±7).
To find the standard form equation of a hyperbola with given vertices and foci, calculate the values of a and b using distances from the origin, and then insert into the standard form equation (y²/a²) - (x²/b²) = 1. The final equation for the hyperbola with vertices at (0, ±2) and foci at (0, ±7) is 45y² - 4x² = 180.
To find the equation of a hyperbola in standard form, we need the vertices and the foci. Given that the vertices are at (0, ±2), we know that the hyperbola is vertical, and the distance between the vertex and the center, which is the origin, is 2 units, so a=2. Since the foci are at (0, ±7), the distance from the center to a focus is 7 units, which means c=7.
With these values, we can calculate b by using the relationship c² = a² + b². Plugging in the known values gives us 7² = 2² + b², so b² = 49 - 4 = 45. Therefore, b = √45.
The standard form equation of a vertical hyperbola with a center at the origin is (y²/a²) - (x²/b²) = 1. Replacing a and b with the found values, the equation becomes (y²/4) - (x²/45) = 1. Multiplying through by 180, which is the least common multiple of 4 and 45, we get the equation in standard form: 45y² - 4x² = 180.
write a fraction with a denominater of 6 that is greater than 4/2
If two triangles are congruent, then the six ___ parts are congruent.
Answer:
If two triangles are congruent, then the six corresponding parts are congruent.
Step-by-step explanation:
If two triangles are congruent, then each part of the triangle is congruent to the corresponding part in the other triangle.
With reference to the above congruent triangle rule, we get;
If two triangles are congruent, then the six corresponding parts are congruent.
Why would you want to solve a literal equation for a variable when you could simply plug in known values and then solve the resulting linear equation?
Solving literal equations for a variable is beneficial for finding general solutions that apply to multiple situations, saves time by avoiding repetitive calculations, and reduces potential errors when working with complex numbers.
Why Solve Literal Equations for a Variable
Solving a literal equation for a variable is fundamental in mathematics because it allows one to find a general solution that can apply to various situations. Instead of replacing a variable with a given number each time, which can be time-consuming and error-prone especially when dealing with long decimals and complex fractions, working with no numbers—just variables—simplifies the process. Having found the values that make the equation true, one can easily convert words to an algebraic expression or equation that best models a given problem. This results in the ability to find a solution more swiftly and with less room for error.
For example, in computer programs, solutions to equations are frequently required for multiple sets of input values. Algebraically solving an equation provides a general form that can easily be reused with different inputs, saving substantial time and resources. Additionally, in complex problems involving multiple unknowns, solving for one variable in terms of others can lead to a simplified equation, making it easier to solve the problem.
which ordered pair is a solution of y=-6x-7
Is the relation a function? {(14, 9), (15, 8), (8, 7), (1, 9), (15, 2)}
Jeans costs $15 each and shirts costs $9 each. You have at most $90 to spend clothing. You must purchase at least 3 pairs of jeans. Let x be the amount of jeans purchased and y be the amount of shirts purchased. What is a possible solution?
(4,-5)
(4, 5)
(4,2)
(2,4)
Answer: 4,2 is the correct answer
Step-by-step explanation:
Use the graph of the function h below to find the following.All values at which h has a local minimum
All local minimum values of h
If there is more than one answer, separate them with commas.
Don't want an answer, just want to know what I'm looking for, maybe an example.
The local minimum values of h are -3 and 0, and occur at the points (-2,-3) and (3,0).
From the graph, we can see that:
Local minimum values of h occur at (-2,-3) and (3,0)
Local minimum values of h are -3 and 0 respectively.
To find the local minimum values of h, we look for the points on the graph where the function changes from decreasing to increasing. These points are called local minimums.
From the graph, we can see that h changes from decreasing to increasing at the points (-2,-3) and (3,0). Therefore, these are the local minimum values of h.
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