The area of the circle with the given circumference is: 42.25π in.².
What is the Area and Circumference of a Circle?Area = πr²
Circumference = 2πr.
Given the following:
Circumference of the circle = 13π in.
Find the radius (r):
2πr = 13π
Divide both sides by 2π
2πr/2π = 13π/2π
r = 13/2
r = 6.5
Area = πr² = π(6.5²) = 42.25π in.²
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Christine is putting money into a savings account. She starts with $650 in the savings account, and each week she adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Christine has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.
Total amount of money in the savings account after 11 weeks is $1310.
Total money in the account =
Initial Money + Money added per week x Number of weeks
Given:
Initial Money = $650
Money added per week = $60
Total money in the account = S
Number of weeks = W
Substituting it in the above equation we get,
S = $650 + $60xW (General Equation)
Total amount of money in the savings account after 11 weeks
S = $650 + $60x11
S = $650 + $660
S = $1310
Thus total amount of money in the savings account after 11 weeks is $1310.
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the function f(x)=-x^2-x+15 is shown on the graph. what are donain and range of the function? t
Answer:
Domain: All real numbersRange: [tex]y \leq 61/4[/tex]Step-by-step explanation:
The domain is the set of x values.
The range is the set of y values.
just need the answer for E!!!!
maths functions
Answer: [tex]g(x) \ge f(x)[/tex] for all x such that [tex]x\le-2[/tex] or [tex]x\ge0[/tex]
Step-by-step explanation:
This question is essentially asking at what x values would the graph of g(x) be greater than (higher than) or equal to f(x).
In the graph, we can see that g(x) is greater than (or higher than) f(x) at all x's before (to the left of) point E and after (to the right of) point A. An easy way to find the points E and A is by setting f(x) = g(x).
[tex]f(x)=g(x)\\1-x^2=2x+1\\1=x^2+2x+1\\0=x^2+2x\\0=x(x+2)\\x=0\hspace{0.1cm}or\hspace{0.1cm}x=-2[/tex]
Since any value with x=-2 is left of the y-axis, we know that point E would have its x-coordinate as -2. Similarly, any point on the y-axis would have x=0; therefore, we can tell that point A would have its x-coordinate at 0.
If we remember that g(x) is greater than f(x) to the left of E and to the right of A, we can say that
[tex]g(x) \ge f(x)[/tex] for all x such that [tex]x\le-2[/tex] or [tex]x\ge0[/tex]
The accompanying table shows the number of bacteria present in a certain culture over a 6 hour period, where x is the time, in hours, and y is the number of bacteria. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, determine the number of bacteria present after 15 hours, to the nearest whole number.
The number of bacteria present after 15 hours is 18928
How to determine the exponential equation?An exponential equation is represented as;
y = ab^x
Where
a = y, when x = 0
From the table, we have:
y = 1796 when x = 0
So, we have:
y = 1796b^x
Also, we have the point (1, 2097)
This gives
2097 = 1796b^1
Divide by 1796
b = 1.17
Substitute b = 1.17 in y = 1796b^x
y = 1796(1.17)^x
This means that the exponential equation is y = 1796(1.17)^x
After 15 hours, we have:
y = 1796(1.17)^15
Evaluate
y = 18928
Hence, the number of bacteria present after 15 hours is 18928
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Max is thinking of a number, which he calls n. He adds 8 and then doubles the sum. What is Max's final number if his starting number is 7? i need help pls
Based on the given situation, Max final number if his starting number is 7 is -4.5
AlgebraUnknown number = nHe adds 8n + 8
then doubles the sum2(n + 8)
starting number = 7So,
2(n + 8) = 7
2n + 16 = 7
2b = 7 - 16
2n = -9
n = -9/2
n = -4.5
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A group of yeast cells grows by 75% every 3hrs. At 9am, there are 200 yeast cells [9 marks].
a) write an equation that models the number of cells, given the number of hours after 9am
b) Determine the number of yeast cells after 10 hours.
a) The exponential function that models the number of cells is: [tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
b) There will be 1292 cells after 10 hours.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]
In which:
A(t) is the amount after t hours.A(0) is the initial amount.r is the rate of change, as a decimal.n is the time it takes to change.For this problem, the parameters are:
A(0) = 200, r = 0.75, n = 3.
Hence the equation is:
[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]
[tex]A(t) = 200(1 + 0.75)^{\frac{t}{3}}[/tex]
[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
The number of cells after 10 hours is:
[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
[tex]A(10) = 200(1.75)^{\frac{10}{3}}[/tex]
A(10) = 1292.
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?? what’s these answers? part A,B and C
Answer:
you need to upload a pic so we can see what you're talking about
Factor x2 − 2x + 3. (1 point) (x − 3)(x − 1) (x + 3)(x + 1) (x − 3)(x + 1) Prime
Answer: for the factor one: The expression isn't factorable with rational numbers
Step-by-step explanation: Since the polynomial can be factored it isn't prime (i don't know if that is what you meant or not but I hope this helps and I got all of them correct )
help im low on my grade and it would help me alot
Answer:
3.5
Step-by-step explanation:
1 - (-2.5) = 1 + 2.5 = 3.5
The graph of y=x4 - 2x² + 1 is shown.
Which point is a relative maximum?
Answer: Point B
Reason:
This point is the highest point in the neighborhood or interval. Yes point D is higher up, but points immediately adjacent to point D are higher. This means D is not a relative max. We need a hill shape like where B is located. In contrast, point C is a relative minimum since it is at the bottom of the valley.
Solve the inequality for x.
5x-39-3(6-4x)
Simplify your answer as much as possible.
Answer:
= 5x-39-18-12x
=5x-12x-39-18
=-7x-57
What is the equation of the directrix?
The equation of the directrix is y = -5
How to determine the directrix equation?The equation is given as:
(x -1)^2 = 12(y + 2)
Express 12 as a product of 4 and 3
(x -1)^2 = 4 * 3(y + 2)
The parabola is represented as:
(x -h)^2 = 4p(y - k)
Where the directrix is
y = k - p
By comparison, we have:
k = -2 and p = 3
So, we have:
y = -2 - 3
Evaluate
y = -5
Hence, the equation of the directrix is y = -5
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cual es el valor de 4+x=9
Answer:
x=5
Step-by-step explanation:
Resolvamos tu ecuación paso a paso.
4+x=9
Paso 1: simplifica ambos lados de la ecuación.
x+4=9
Paso 2: Resta 4 de ambos lados.
x+4−4=9−4
x=5
Answer:
4+x=9
or, x=9-4
or, x=5
the value of x is 5
How many cubicle blocks each with ages of length 2 cm are needed to fill a rectangular box that has inside dimensions 10 cm x 12 cm x 60 cm
we conclude that 900 cubes enter in the given box.
How many blocks are needed to fill the box?
We need to find the volumes of both figures.
The blocks are cubes of 2cm by 2cm by 2cm, then the volume of each block is:
[tex]V = (2cm)^3 = 8cm^3[/tex]
The box has dimensions of 10cm by 12cm by 60cm, then the volume is:
[tex]V = 10cm*12cm*60cm = 7,200 cm^3[/tex]
The number of cubes that enter in the box is N such that:
[tex]N*8cm^3 = 7,200cm^3[/tex]
Solving for N, we get:
[tex]N = 7200cm^3/8cm^3 = 900[/tex]
In this way, we conclude that 900 cubes enter in the given box.
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Find the value of t0 such that the following statement is true: P(-t0 ≤ t ≤ t0) = .95 where df = 15. Group of answer choices
The value of To from the t table will be 2.131
How to get the value?The following can be deduced from the information:
P(-t0 < t < t0) = 0.95
2*P(t < t0) - 1 = 0.95
P(t < t0) = 0.975
df = 15
From t-table (column 1-0.975 = 0.025) in the row 15. Therefore, t0 = 2.131.
In conclusion, the answer is 2.131.
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Find the slope between the two points given. Then, use the slope and Point One to write the equation of the line in Point-Slope form. State the slope. Point One: (4,−3) Point Two: (−2,2)
The equation in point slope form is given as y+3 = -5/8(x-4)
Equation of a lineThe formula for calculating the equation of a line in point-slope form is expressed as:
y-y1= m(x-x1)
Given the coordinate point
Slope = 2-(-3)/-2-4
Slope = 5/-8
Determine the equation
y-(-3) =-5/8(x-4)
y+3 = -5/8(x-4)
Hence the equation in point slope form is given as y+3 = -5/8(x-4)
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Use an outside source to search for a quadratic equation that models something from your daily life. (Be sure to cite the source you use.)
Solve the equation in two ways.
Discuss which method you liked better and why.
In your responses to peers, compare and contrast your preferences for how to solve quadratic equations.
A quadratic equation that models something from one's daily life is when calculating areas, and determining a product's profit.
What is a quadratic equation?It should be noted that a quadratic equation means an algebraic equation of the second degree in x.
The quadratic equation in its standard form is ax² + bx + c = 0. Here, a and b are the coefficients, x is the variable, while c is the constant term.
Quadratic equations are used in everyday life, as when calculating areas, and the determination of a product's profit and formulating the speed of an object.
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Can you help me with this please?
The half-life of the given exponential function is of 346.57 years.
What is the half-life of an exponential function?It is the value of t when A(t) = 0.5A(0).
In this problem, the equation is:
[tex]A(t) = A(0)e^{-0.002t}[/tex].
In which t is measured in years.
Hence the half-life is found as follows:
[tex]0.5A(0) = A(0)e^{-0.002t}[/tex]
[tex]e^{-0.002t} = 0.5[/tex]
[tex]\ln{e^{-0.002t}} = \ln{0.5}[/tex]
[tex]0.002t = -\ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.002}[/tex]
t = 346.57 years.
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Mr. Bellman orders a cube of clay for each of his art classes. The height of the
cube is 20 inches. How much clay, in cubic inches, would Mr. Bellman order
for three classes?
Write and evaluate an expression to find your answer.
20 cubed is 20 times 20 and then that answer times 20.
length X width x height = cube
20 to the 3rd power or 203
A
B
C
60 cubic inches
400 cubic inches
8,000 cubic inches
Answer:
20 x 20 x 20 = 8000
The method in which all the elements of the set are written within brackets is called
Answer:
The set can be defined by listing all its elements, separated by commas and enclosed within braces. This is called the roster method.
Step-by-step explanation:
Mark me as Brainy.
Find the missing coordinate.
x = cos t
y = sin t
(-1, [?])
Answer:
0
Step-by-step explanation:
sin²t + cos²t = 1, so since cos²t = 1, sin²t = 0, and thus sint = y = 0.
Two friends, Jamie and Devin, are working together at the Sparrowtown Cafe today. Jamie works every 2 days, and Devin works every 7 days. How many days do they have to wait until they next get to work together?
Using the least common factor, they need to wait 14 days until they next get to work together.
How to find the time it takes for periodic events to repeat at the same time?To find the time that passes between the events happening at the same time, we need to find the least common multiple of the periods.
In this problem, the periods are of 2 days and 7 days, which already are prime numbers, hence:
lcm(2,7) = 2 x 7 = 14.
They need to wait 14 days until they next get to work together.
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A regular-size box of cereal measures 3 1/2 inches by 8 1/2 inches by 15 inches. The manufacturer also sells an individual-size box that has a volume that is 1 1/0 of the volume of the regular-size box.
What is the volume of the individual-size box of cereal?
Enter your answer as a mixed number in simplest form by filling in the boxes.
The individual-size box of cereal is a rectangular prism with a volume of 44.625 inches³.
What is the volume of a rectangular prism?The volume of rectangular prism of length l, width w and height h is given by:
V = lwh.
In this problem, the standard dimensions are:
l = 3(1/2) = 3 + 0.5 = 3.5 inches.w = 8(1/2) = 8 + 0.5 = 8.5 inches.h = 15 inches.The individual-size box has a 1/10 of the volume of the original box, hence:
V = 0.1 x 3.5 x 8.5 x 15 = 44.625 inches³.
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Rollin Corporation has 410,000 shares of 5$ per value common stock issued and outstanding. Record the following entries into the general journal
Answer:3522
Step-by-step explanation:222
2
he parallelogram on the left was dilated by a scale factor of 2 about point P . It was then transformed in another way to produce the parallelogram on the right. On a coordinate plane, parallelogram P has points (negative 4, 0), (negative 2, 0), (negative 3, negative 3), (negative 5, negative 3). Parallelogram P prime has points (3, 0), (7, 0), (5, negative 6), (1, negative 6). Which identifies the transformation that occurred after the dilation?
The transformation that occurred after the dilation of the parallelogram is a translation of 9 units to the right.
What is a parallelogram?A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram. If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is referred to as a parallelogram.
The initial parallelogram was dilated by a scale factor of 2 about point P.
The points of the initial parallelogram are: (-4, 0), (-2, 0), (-3, -3), (-5, -3).
The parallelogram obtained on dilation will have the points: (-6, 0), (-2, 0), (-4, -6), (-8, -6).
The points of the final parallelogram are: (3, 0), (7, 0), (5, -6), (1, -6).
(-6,0) →(3,0) ⇒ (x,y)→(x+h , y+k)
x = -6 , x+h = 3 ⇒ h=3-x = 3-(-6) = 9
y = 0 , y+k = 0 ⇒ k = 0
The transformation rule is (x,y)→( x+9 , y )
That is, a translation of 9 units to the right.
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Answer:
A. a translation of 9 units to the right
Step-by-step explanation:
Edge 2023
11. You want to save all the money you earn to buy a guitar that costs $400. You earn $9 per hour and
plan to work 15 hours each week for the next 3 weeks. Will you earn enough money in that time to buy
the guitar? Explain your answer.
Answer:
The answer is YES
Step-by-step explanation:
You want to save all the money you earn to buy a guitar that costs $400. You earn $9 per hour and
plan to work 15 hours each week for the next 3 weeks. Will you earn enough money in that time to buy
the guitar? Explain your answer.
15 hours × 3 weeks × $9 per hour
15 × 3 × 9 =
45 × 9 = 405$
The answer is YES
a polygon has two interior angles of 120 degree each and the others are 150 degree each calculate the number of sides and the sum of interior angles in a polygon
Answer:
10 sidesangles total 1440°Step-by-step explanation:
The formula for the total of interior angles can be used together with the given angle values to write an equation for the number of sides.
SetupThe total of interior angles of an n-sided polygon is 180°×(n -2). In the given n-sided polygon, two angles are 120° and (n -2) angles are 150°. The total of angles is the same either way it is computed:
2×120 +(n -2)150 = (n -2)180
SolutionSubtracting (n-2)150, we have ...
240 = 30(n -2)
8 = n -2 . . . . . . . . divide by 30
10 = n . . . . . . . . add 2
The polygon has 10 sides.
The total of interior angles is ...
angle sum = 180°×(10 -2) = 1440°
The sum of interior angles is 1440°.
Answer:
10 sides and
1440° total of interior angles.
Step-by-step explanation:
The number of degrees in a polygon (sum of interior angles) is:
(n - 2)×180
This is the total. Here, n is the number of sides (same as the number of angles)
In your question, 2 of the angles are 120° and the remaining angles are 150°.
If n is ALL the angles, then (n-2) is all the 150° angles because the other 2 are 120°
So we can write an equation:
Our polygon:
120°+120°+(n-2)150°
=
(n-2)180°
Combine like terms:
240+(n-2)150=(n-2)180
Use Distributive property.
240+150n-300=180n-360
Again, combine like terms.
300 = 30n
Divide.
10 = n
n is the number of sides (and angles).
Check:
Ten-sided shape:
(10-2)180
= 1440°
Our shape:
120°+120°+ 8(150°)
= 240° + 1200°
= 1440° Check!
39 kg Rice of taken out of a bag of rice. If 8/22 of the rice is left in the beg then find the quantity of rice the bag contained in the beginning
Answer:
429/7 kg or 61 2/7 kg
Step-by-step explanation:
I'll answer according to how I understand this problem, but I'm not sure this is correct.
"39 kg of rice is taken out of bag of rice. If 8/22 of the rice is left, what was the original weight of the rice in the bag?"
8/22 is a strange number to work with because it could have been given as 4/11. This is another reason I'm not too sure about this problem.
8/22 = 4/11
If 4/11 is left, then since 11/11 - 4/11 = 7/11, 7/11 of the rice remains.
7/11 x = 39
x = 39 × 11/7
x = 429/7
x = 61 2/7
What value of “a” would make the equation have no solution?
4(5x+1) = -2(ax+4)
Answer: a = -10
Concept:
When an equation has no solution, in most cases, it means that the variables are being canceled out, and left with unequal constants.
For example:
2x + 3 = 2 +2x
The 2x can be canceled out on both sides, which left us with:
3 = 2
3 does not equal to 2, therefore, it has no solution
Solve:
Given equation
4 (5x + 1) = -2 (ax + 4)
Expand the parenthesis
4 (5x) + 4 (1) = -2 (ax) + (-2) (4)
20x + 4 = -2ax - 8
According to the concept, we need to make the variables equal to cancel them out and left with unequal constants
20x = -2ax
Divide x on both sides
20x / x = -2ax / x
20 = -2a
Divide -2 on both sides
20 / -2 = -2a / -2
[tex]\Large\boxed{a=-10}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Primer numbers list maths
Answer:
1 - 100 primes numbers
Step-by-step explanation:
2,3,5,7,11,13,17,19,23,29,31,37,41,47,57,59,61,67,71,79,83,8797