The area of the circular manufactured good is given by:
[tex]A = 1.8146 \times 10^{16} \text{m}^2[/tex]
What is the area of a circle?The area of a circle of radius r is:
[tex]A = \pi r^2[/tex].
In this problem, the radius in meters is:
[tex]r = 7.6 \times 10^7[/tex]
Hence the area in m² is:
[tex]A = \pi (7.6 \times 10^7)^2 = 181.46 \times 10^{14} = 1.8146 \times 10^{16} \text{m}^2[/tex]
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From 4:00 to 5:00 p.m., the temperature dropped 6 °F. At 5:00 pm the temperature was 18°F. What was the temperature at 4:00 p.m.?
What is the central angle of a circle whose radius is 8cm and intercepted arc length is 7.2cm?
What is the radians as a decimal
Answer:
≈51.55
Step-by-step explanation:
∆/360 πD = 7.2
x/360 *22/7*16= 7.2
x/360 *50/2/7= 7.2
x/360 = 63/440
x =51.54545455
≈51.55
how many groups of 1/5 are in 4
Answer: 20
Step-by-step explanation: Since it is 1/5 you multiply the 5 by 4 and get 20.
Answer:
20
Step-by-step explanation:
It is 20 because you have to multiply the denominator by the whole number.
HELP ASAP!
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
Explain what the ratio 15:73 represents.
The ratio 15:73 represents the ratio of total athletes to 7th grade football players.
The ratio 15:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
The ratio 15:73 represents the ratio of 6th grade athletes to total athletes.
Answer:The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
Step-by-step explanation:
The average temperature for a country during September 2013 was 58.1 degrees Farenheit. This is 5.6 degrees Farenheit above the 20th-century average temperature for September. What was the country's 20th-century average temperature for September
Answer:
52.5
Step-by-step explanation:
58.1 - 5.6= 52.5
If the null hypothesis is µ ≥ 200, then a two-tail test is being conducted.
True Or False
Answer:
False
Step-by-step explanation:
A two-tailed test requires that the null hypothesis use the equal (=) sign. Rejection of the null can happen in either direction. (Ex. a test statistic that i either too high, or too low). Anything other than equal (Ex. the null hypothesis is either, "greater than or equal to", or, "less than or equal to"), indicates a one-tailed test.
7. The length (in centimeters) of a scalloped hammerhead shark can be
modeled by the function = 266-219e-0.05t, where t is the age (in years) of
the shark.
a. How old is a shark that is 200 centimeters long?
2.11
b. How long is a shark that is twice as old as the shark in part (a)?
Answer: a. To find the age of a shark that is 200 centimeters long, we can set the function equal to 200 and solve for t:
L = 266 - 219e^(-0.05t)
200 = 266 - 219e^(-0.05t)
Solving this equation for t, we get t ≈ 2.11 years.
b. To find the length of a shark that is twice as old as the shark in part (a), we can substitute 2.11*2= 4.22 for t into the function:
L = 266 - 219e^(-0.05(4.22))
This will give us the length of the shark that is twice as old as the shark in part (a) in centimeters.
Need this answer please
Answer:
P = 5x + 33 = 58
Q = R = 3x+46 = 61
Step-by-step explanation:
angles in a triangle add up to 180 degrees
the angles in an isosceles triangle that correspond to the two congruent sides (are opposite the sides) are also congruent
that means that angle R = angle Q because QP and RP are congruent
angles = 5x+33, 3x+46, 3x+46
5x+33 + 3x+ 46 + 3x+46 = 180
11x + 125 = 180
subtract 125 from both sides to isolate the x and its coefficient
11x = 55
divide both sides by 11 to find x
x = 5
P = 5x + 33 = 58
Q = R = 3x+46 = 61
what is 47,925 as a mixed number
47.925 can be written as a mixed number as 47(925/1000).
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
47.925
This can be written as,
= 47925 / 1000
Now,
47925 = 47000 + 925
1000 x 47 = 47000
So,
47925/1000
= 47(925/1000)
Thus,
The mixed number is 47(925/1000)
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a single line divides a plane into two regions. two lines (by crossing) can divide a plane into four regions; three lines can divide it into seven regions. let pn be the maximum number of regions into which n lines divide a plane, where n is a positive integer recurrence formula
The P(n) represents the maximum no of regions into which n lines divide the plain then P(k) = P(k-1) + k. (b). The formula for P(n) is [tex]1+{ }^{n+1} c_2\end{aligned}$[/tex]. (c). The 5152 regions can divide the plane for 100 lines.
When no. lines are drawn, we get one plain region.
Let the number of regions when divided by lines be represented by
P(0), P(1), P(2), P(3), P(n)
Therefore P(0) = 1
P(1) = 2
P(1) = P(0) + 1
P(2) = P(1) + 2
P(3) = P(2) + 3
P(4) = P(3) + 4………………….
P(n) = P(n-1) + n
Therefore, if P(n) represents the maximum no. of regions into which n lines divide the plain
Then P(k) = P(k-1) + k
(b).
⇒ P(0) = 1
⇒P(n) = P(n-1) + n
= P(n-2) + (n-1)+n
= P(n-3) + (n-2) +(n-1)+n……..
= P(0) + 1 + 2+ 4=3 + 4 + 5 +……+n
= P(0) + (Sum of the first n natural numbers)
[tex]$$\begin{aligned}& =P(0)+\frac{n(n+1)}{2} \\& =1+{ }^{n+1} c_2\end{aligned}$$[/tex]
Therefore, the formula for P(n) is [tex]1+{ }^{n+1} c_2\end{aligned}$[/tex].
(c)
Compute the value for n=100
[tex]$$1+{ }^{n+1} c_2=1+{ }^{101} c_2=1+\frac{101 \times 102}{2}=5152$$[/tex]
Therefore, the 5152 regions can divide the plane for 100 lines.
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A single line divides the plane into two regions. Two lines (by crossing) can divide the plane into four regions; three lines can divide it into seven regions, etc. Let P(n) be the maximum number of regions into which n lines divide a plane, where n is a positive integer.
(a) Derive a recurrence relation for P(k) in terms of P(k-1) for all integers [tex]$k \geq 2$[/tex].
(b) Use iteration to find an explicit (closed) formula for P(n).
(c) Into how many regions can 100 lines divide the plane?
How do you Graph Y=1/2x-4
Answer:
To graph the equation y = 1/2x - 4, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
In this equation, the slope is 1/2, and the y-intercept is -4. The slope represents the steepness of the line, and the y-intercept is the point at which the line crosses the y-axis.
To graph the equation:
Plot the y-intercept, which is (-0, -4)
Using the slope, we can pick a second point on the line. The slope of 1/2 tells us that for every 2 units in the x direction, we will move 1 unit in the y direction. So we can pick a point that is 2 units to the right of the y-intercept, such as (2,0).
Connect the two points to get a straight line
The resulting graph will be a straight line that passes through the point (-0, -4) and (2, 0) and continues in both directions.
Alternatively, you can use a table of values to plot the points that belongs to the line and connect them, for example:
x | y
-2 | -5
-1 | -4.5
0 | -4
1 | -3.5
2 | -3
These are few points on the graph and with more points you can connect them and see the shape of the graph.
Step-by-step explanation:
Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 3
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 6
2 Superscript 4 x Baseline = 2 Superscript 3 x minus 3
The equivalent exponential equations are given as follows:
[tex]2^{4x} = 2^{3(x - 3)}[/tex]
How to obtain the equivalent exponential expression?The exponential expression for this problem is defined as follows:
[tex]2^{4x} = 8^{x - 3}[/tex]
The number eight is the third power of 3, that is:
8 = 2³.
The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:
[tex]8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}[/tex]
Meaning that the correct option is given by the fourth option.
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Nick has a checking account with the Park Slope Savings Bank. He writes both paper and electronic checks. For each transaction Nick enters the necessary information: check number, data, type of transaction, and amount. He uses E to indicate an electronic transaction. Determine the balance in his account after the Star Cable Co. check is written.
there is not enough information here to complete the problem.
there are 36 eggs in a crate if 24 are fried what percentage is left
Answer:
33.33%
Step-by-step explanation:
You start with 36 eggs, and 24 are removed and fried. This means that the remaining eggs are the difference of 36 and 24:
36 - 24 = 12
There are 12 eggs left! To find the percentage of remaining eggs, write a ratio comparing the number of eggs that remain to the original amount of eggs:
[tex]\frac{12}{36}[/tex]
Now, simplify the fraction into a decimal:
12 ÷ 36 = 0.3333...
Multiply a decimal by 100 to convert it to a percentage:
0.3333... ⋅ 100 = 33.33...%
Rounded to the nearest hundredth, the percent of remaining eggs is 33.33%
ANYONE GOOD AT MATH PLEASE I BEG OF YOU FOR HELP!
Answer: 5
Step-by-step explanation: To solve f(x), g(x), or f(g(x)) problems, we place the value of x in the functions with the value that we are given. This value will be f(g(5)) or g(3) or f(27). We plug in the number in the parentheses.
In this problem, we have to first plugin 5 to g(x) then plug g(5) into f(x).
First, we do g(5)=sqrt((5^2)+2). This gives us 3. Then we plug in 3 which is g(5) into f(x). This gives us f(g(5)) or f(3)=sqrt((3^3)-2) which is 5.
Solve the following problem using the substitution method. Please make sure to show all of your work.
x + y = 3
y = x + 5
Answer: x=-1,y=4
Step-by-step explanation:
x + y = 3
y = x + 5
subtract x from both sides of the equation so you get
x + y = 3
-x + y = 5
use the elimination method and you'll get
2y = 8
simplify and
y = 4
now use that to get x
x + 4 = 3
x = -1
Therefore, the answer is
x = -1, y = 4
Answer:
x=-1, y=4. (-1, 4).
Step-by-step explanation:
x+y=3
y=x+5
----------
x+(x+5)=3
x+x+5=3
2x+5=3
2x=3-5
2x=-2
x=-2/2
x=-1
y=-1+5=4
Let u = [ 14 -1] and v= [14 1] show that [h k] is in span {u,v} for all and k
How can it be shown that a vector b is in Span {u,v}? O A. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then bis in Span{u,v}. O B. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span {u,V}. C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then bis in Span{u,v}. O D. Determine if the system containing u, v, and b is consistent.
C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span{u,v} is correct.
To show that a vector b is in Span{u,v}, one way is to determine if it can be written as a linear combination of the vectors in the set, i.e., if there exist scalars h and k such that b = hu + kv. If this is the case, the system containing the equations hu + kv = b is consistent, meaning that there exist values of h and k that make the equation true. Therefore, if the system is consistent, it can be concluded that the vector b is in Span{u,v}.
Therefore, option C is the correct answer.
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Which graph is the graph of this function? F(x) = { 1/2x - 2 if x <_ 6 -x - 1 if x > 6
34x56x79447886447567
Consider the piecewise-defined function given by the graph. What are these values?
f(–3) =
f(–1) =
f(3) =
f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.
What are straight-line equations?
The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).
The variables x and y are related to coordinates on the line in the linear equation y = mx + c.
The formula y = mx + c yields a result for y when we enter a value for x.
As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.
According to our question-
m (x-x1) = y-y1 or
y = mx + c
Where,
Straight-line gradient, or m, is the line's slope.
The Cartesian coordinate that the line crosses is x1, y1.
the constant c
The calculation of the gradient (m) between any two locations on a line
m = Δy / Δx
f (-1) = Because x = -1, the function used is
y = 2, so f (-1) = 2 C) f (-3) = Because -3 -1,
the function used is y = -x-4, so f (-3) = - (- 3) -4 f (-3) = 3-4 f (-3) = -1 f (3) Since the function employed is
= -2x + 11 and x = 3, f (3) = -2 (3) +11, f (3) = -6 + 11, and f (3) = 5.
Hence, f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.
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Answer:-1
2
5
Step-by-step explanation:
simple answer
NO LINKS!!! Part 3
Find an exponential function y = ab^x form that satisfies the given information
f. passes through (-1, 72.73) and (3, 106.48)
g. passes through (-2, 351.56225) and (3, 115.2)
h. passes through (4, 405) and (9, 98415)
Answer:
[tex]\text{f)} \quad y=80(1.1)^x[/tex]
[tex]\text{g)} \quad y=225(0.8)^x[/tex]
[tex]\text{h)} \quad y=5(3)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Part (f)Given points:
(-1, 72.73)(3, 106.48)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 72.73=ab^{-1}[/tex]
[tex]\implies 106.48=ab^3[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{106.48}{72.73}=\dfrac{ab^3}{ab^{-1}}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=\dfrac{b^3}{b^{-1}}[/tex]
Solve for b:
[tex]\implies \dfrac{106.48}{72.73}=b^3 \cdot b^{1}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=b^{3+1}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=b^4[/tex]
[tex]\implies b=1.09998968...[/tex]
[tex]\implies b=1.1[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 72.73=a \cdot (1.09998968...)^{-1}[/tex]
[tex]\implies a=80.0022499...[/tex]
[tex]\implies a=80[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=80(1.1)^x[/tex]
---------------------------------------------------------------------------------------
Part (g)Given points:
(-2, 351.56225)(3, 115.2)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 351.56225=ab^{-2}[/tex]
[tex]\implies 115.2=ab^3[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{ab^3}{ab^{-2}}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{b^3}{b^{-2}}[/tex]
Solve for b:
[tex]\implies\dfrac{115.2}{351.56225}=b^3 \cdot b^{2}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=b^{3+2}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=b^5[/tex]
[tex]\implies b=0.800000113...[/tex]
[tex]\implies b=0.8[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 115.2=a(0.800000113...)^3[/tex]
[tex]\implies a=224.999904[/tex]
[tex]\implies a=225[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=225(0.8)^x[/tex]
---------------------------------------------------------------------------------------
Part (h)Given points:
(4, 405)(9, 98415)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 405=ab^4[/tex]
[tex]\implies 98415=ab^9[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{98415}{405}=\dfrac{ab^9}{ab^4}[/tex]
[tex]\implies 243=\dfrac{b^9}{b^4}[/tex]
Solve for b:
[tex]\implies 243=b^9 \cdot b^{-4}[/tex]
[tex]\implies 243=b^{9-4}[/tex]
[tex]\implies 243=b^{5}[/tex]
[tex]\implies b=3[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 405=a \cdot 3^4[/tex]
[tex]\implies 81a=405[/tex]
[tex]\implies a=5[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=5(3)^x[/tex]
can someone help me with these 2 Images, please? it's for geometry
Question 1
[tex]11+2x+29=x+28 \\ \\ 2x+40=x+28 \\ \\ x+40=28 \\ \\ x=-12[/tex]
Question 2
A, B, E
what is the value of K such that (x^3-2x^2+kx-12)/(x-5) has a remainder of 0
Answer:
k = -12.6
Step-by-step explanation:
Given rational polynomial:
[tex]\dfrac{x^3-2x^2+kx-12}{x-5}[/tex]
When we divide a polynomial f(x) by (x − d) the remainder is f(d).
If the remainder is zero, then (x - d) must be a factor of f(x).
If a cubic polynomial is divided by (x - d) then:
[tex]\implies (x-d)(ax^2+bx+c)[/tex]
where:
a is the leading coefficient-cd is the constantIf the constant of the cubic polynomial is -12 and d = 5:
[tex]\implies -cd=-12[/tex]
[tex]\implies -5c=-12[/tex]
[tex]\implies c=2.4[/tex]
The leading coefficient of the cubic polynomial is one. Therefore:
[tex]\implies (x-5)(x^2+bx+2.4)[/tex]
Expand and collect like terms:
[tex]\implies x^3+bx^2+2.4x-5x^2-5bx-12[/tex]
[tex]\implies x^3+(b-5)x^2+(2.4-5b)x-12[/tex]
The find the value of b, compare the coefficients of the term in x²:
[tex]\implies b-5=-2[/tex]
[tex]\implies b=3[/tex]
To find k, substitute the found value of b into the coefficient of x:
[tex]\implies k=2.4-5b[/tex]
[tex]\implies k=2.4-5(3)[/tex]
[tex]\implies k=-12.6[/tex]
Answer:
–12.6
Step-by-step explanation:
[tex] \frac{ \\ {x }^{3} - {2x}^{2} + kx - 12}{x - 5} = 0[/tex]
that means (x–5) is a factor of x³ – 2x² +kx – 12
since it resulted to zero according to the rules of zeros of polynomial.
x–5 = 0
x = 5
by substituting
f(x) = 5³ – 2(5)² + k(5) – 12 = 0
125 – 50 + 5k – 12 = 0
75 + 5k – 12 = 0
5k + 75 – 12 = 0
5k + 63 = 0
5k = –63
[tex] \frac{ \\ 5k}{5} = \frac{ - 63}{5} [/tex]
[tex]k = - 12.6 \: or \: - 12 \frac{3}{5} [/tex]
I hope I helped
Y=(x-2)^2+3 vertex form to standard form
The required vertex form of the given equation is y = x² - 4x + 7.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
y = (x - 2)² + 3
Simplifying the expression,
y = x² -4x + 4 + 3 {since (a - b)² = a² + b² -2ab}
y = x² - 4x + 7
Thus, the required vertex form of the given equation is y = x² - 4x + 7.
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Find the savings plan balance after 9 months with an APR of 3% and monthly payments of $200.
Answer: To calculate the balance of the savings plan after 9 months with an APR of 3% and monthly payments of $200, we need to take into account the interest earned on the account.
First, we will calculate the interest earned by multiplying the principal (initial amount) by the interest rate (APR) and the number of months.
Interest = Principal * Interest Rate * Number of months
Interest = 200 * 0.03 * 9 = 54
Then, we will add the interest earned to the total amount of payments made.
Total = Principal + Interest + Payments
Total = 200 + 54 + (200 * 9) = 200 + 54 + 1800 = 2054
So the savings plan balance after 9 months with an APR of 3% and monthly payments of $200 is $2054.
Step-by-step explanation:
I need help with this!!! What is the y intercept?
The point R(3, 3) is rotated 180 clockwise around the origin. what are the coordinates of the resulting point, R
Kristy made 33 cookies for a bake
sale. She is putting the cookies in
packages to sell. Each package will
hold 4 cookies. How many complete
packages of cookies can she make?
9. How many solutions does this system have? (1 point)
x-2y = 2
y=-2x+5
O infinitely many solutions.
Ono solutions
Otwo solutions.
one solution
The final statement is: The system of equations have unique solution.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: x-2y = 2 & y=-2x+5
Solving these two equations by method of substitution we get
x-2(-2x+5)=2
x+4x-10=2
5x=12
x=2.4
∴ y=2×2.4+5
=4.8+5
=9.8
Hence, The system has one solution.
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Given this equation...
4x - 1 6
--------- = -----
3x + 7 5
What is the value of x in this
proportion?
Answer:
x=91
Step-by-step explanation:
Follow the steps in the image.
add 16 to both sides
subtract 3 from both sides
divide by 1x
Plug answer back into equation
-Hope this helped
Francis buys a package of 450 plastic forks. He uses 315 of the plastic forks.
What percent of the plastic forks did Francis use? Show your work.
Francis purchases a package of 450 plastic forks but only uses 315 of them, therefore he uses 70% of the available supply.
what is percentage ?In math, a % is a number or ratio that is expressed as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," and "pc." However, the percent sign "%" is frequently used to indicate it. The percentages' total quantity has no dimensions. Percentages are fundamentally fractions when the denominator is 100. Put a percent sign (%) next to a number to indicate that it is a percentage. For instance, if you successfully answer 75 out of 100 questions on a test (75/100), you get a 75%. Divide the money by the total to get percentages, then multiply the resulting number by 100. The formula (value/total) x 100% is used to calculate the percentage.
given
Francis purchases 450 plastic forks and
utilizes 315 of them, for
a percentage of 315/450*100
= 70%.
Francis purchases a package of 450 plastic forks but only uses 315 of them, therefore he uses 70% of the available supply.
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