The below formula is used to find the circumference of a circle;
[tex]C=2\pi r[/tex]But we know that the diameter of a circle is expressed as;
[tex]d=2r[/tex]Let's replace 2r with d in the 1st equation, we'll then have;
[tex]C=\pi d[/tex]We've been told that the diameter of the circle is 20inches, if we substitute this value into our equation, we'll have;
[tex]C=20\pi[/tex]f(x+h)-f(x)
h
lim:
h→0
i) The average rate of change of f(x) over the interval [x, x + h]
ii) The slope of the line tangent to f(x) at the point (x, f(x))
iii) The slope of the line secant to f(x) over the interval [x, x + h]
iv) The derivative of f(x)
O A. ii and iii
O B. i and iii
O c. ii
OD. i
...
O E.
i and iv
O F. ii and iv
Answer: F
Step-by-step explanation:
(i) The interval is meant to have infinitesimal width because the limit is approaching 0.
(ii) This gives the derivative at [tex](x, f(x))[/tex], which is the same as the slope of the tangent line.
(iii) False, this deals with the tangent line, not the secant.
(iv) True by definition.
MP and MN are tangents to the circle.What is the value of x?133M90940NxºР17286
To get x, we will use the equation below:
[tex]\frac{1}{2}\lbrack(360-x)-x\rbrack=94[/tex]open the inner paremthesis
[tex]\frac{1}{2}\lbrack360-2x\rbrack=94[/tex]
open the parenthesis
180 - x = 94
collect like term
180 - 94 = x
86 = x
find the are and perimeter
L: Length
W: Width
The perimeter of a rectangle is:
[tex]P=2W+2L[/tex][tex]\begin{gathered} P=2(3ft)+2(5ft) \\ P=6ft+10ft \\ P=16ft \end{gathered}[/tex]The area of a rectangle is:
[tex]A=W\cdot L[/tex][tex]\begin{gathered} A=3ft\cdot5ft \\ A=15ft^2 \end{gathered}[/tex]Hello! I need some assistance with this homework question, pleaseQ12
Answer:
A(-1,4) and B(2,0)
Step-by-step explanation:
The quadratic parabola equation is represented as;
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex of the parabola} \end{gathered}[/tex]Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':
[tex]\begin{gathered} -1=a(-1-2)^2-5 \\ -1=9a-5 \\ 9a=4 \\ a=\frac{4}{9} \end{gathered}[/tex]Hence, the equation for the parabola:
[tex]f(x)=\frac{4}{9}(x-2)^2-5[/tex]Now, for the line since it is a horizontal line, the equation would be:
[tex]g(x)=5[/tex]Then, for (f+g)(x):
[tex]\begin{gathered} (f+g)(x)=\frac{4}{9}(x-2)^2-5+5 \\ (f+g)(x)=\frac{4}{9}(x-2)^2 \end{gathered}[/tex]Then, the graph for the composite function and the points that lie on the graph:
A(-1,4) and B(2,0)
If A and B are supplementary angles and A is nine times as large as B, find the measures of A and B.
Supplementary angles add up to 180°
A+ B = 180
A is 9 times as large as B.
A = 9B
We have the system of equations:
A+ B = 180
A = 9B
Put the second equation into the first one, and solve for B
(9B)+ B = 180
10B = 180
B= 180/10
B = 18
Replace the value of B on any equation and solve for A:
A = 9B
A= 9(18)
A= 162
A= 162°
B=18°
A manager measured the number of goods, y, that his company produced in a hours. The
company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45
goods.
Which equation, in point-slope form, correctly represents the goods produced by the company
after x hours?
Oy-45 = 5(x-9)
Oy+9= 5(x +45)
Oy 45= 5(x + 9)
Oy-9=5(x - 45)
Answer:
[tex]y-45=5(x-9)[/tex]
Step-by-step explanation:
Definition of the variables:
y = total number of goods produced.x = time in hours.Given information:
The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.As the rate of change is constant and linear, the rate of change is the slope of the line. Therefore, the slope is 5.
At hour 9 (x-value) the company had produced 45 (y-value) goods. Therefore, this can be represented by the point (9, 45).
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-45=5(x-9)[/tex]
Therefore, the equation that correctly represents the goods produced by the company after x hours is:
[tex]\boxed{y-45=5(x-9)}[/tex]
What is the mean of 3x, 4x - 5 and 2x - 1?
justify proposes each step
the answer is associative property of multiplicaction
because
A*(B*C)=(A*B)*C
Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given: XN NZ and NY = NW No; you cannot determine that the quadrilateral is a parallelogram. Yes; opposite sides are congruent. Yes; two opposite sides are both parallel and congruent. Yes; diagonals of a parallelogram bisect each other.
A parallelogram is a quadrilateral that has the following characteristics:
The opposite sides are parallel and congruent.
The opposite angles are congruent.
The consecutive angles are supplementary.
If any one of the angles is a right angle, then all the other angles will be at right angle.
The two diagonals bisect each other.
Since:
[tex]XN\cong NZ;NY\cong NW[/tex]We can conclude that the answer is:
Yes; diagonals of a parallelogram bisect each other.
Graph the reflection of the polygon in the given line #5 Y=2
We have the next image
the line of reflection is the line in red
the original polygon ABCD is the one in blue
the reflected polygon A'B'C'D' is the one in green
Seventeen percent of people say they've seen a ghost or felt its presence. If 10 people are asked, what is the probability that at least two have seen a ghost or felt its presence?Round your answer to at least three decimals.
Answer: the probability that at least two have seen a ghost or felt its presence is 0.527
Explanation:
In this scenario, it is either a person asked has seen seen a ghost or felt its presence or they have not. These outcomes are independent of each other. Thus, it's a binomial distribution. We would apply the formula for calculating binomial probability which is expressed as
P(x) = nCx * p^x * q^(n - x)
where
p = probability of success
q = 1 - p = probability of failure
n = sample size
x = number of successes
From the information given, we are concerned with the people that say they've seen a ghost or felt its presence. Thus,
p = 17% = 17/100 = 0.17
q = 1 - 0.17 = 0.83
n = 10
x = 2
We want to find P(x ≥ 2)
P(x ≥ 2) = 1 - [P(x = 0) + P(x = 1)
P(x = 0) = 10C0 * 0,17^0 * 0.83^(10 - 0) = 0.1552
P(x = 1) = 10C1 * 0,17^1 * 0.83^(10 - 1) = 0.3178
P(x ≥ 2) = 1 - (0.1552 + 0.3178) = 1 - 0.473
P(x ≥ 2) = 0.527
the probability that at least two have seen a ghost or felt its presence is 0.527
If r is the nominal rate and n is the number of times interest is compounded annually, then R=(1+r/n)^(n)-1 is the effective rate. Here, R represents the annual rate that the investment would earn if simple interest were paid. Use this formula to determine the effective rate for $1 invested for 1 year at 4.8% compounded semiannually.
Effective Rate in Compound Interest
Given r as the nominal rate of investment and n the number of times the interest is compounded annually, the formula for the effective rate is:
[tex]R=\mleft(1+\frac{r}{n}\mright)^n-1[/tex]We are required to find the effective rate for a rate of r=4.8% compounded semiannually. This means the value of n is 2 since there are two periods where interest is added to the principal per year.
Substituting the given values in the formula (recall r must be used as a decimal value, i.e. r=4.8/100=0.048):
[tex]R=(1+\frac{0.048}{2})^2-1[/tex]Calculating:
[tex]R=(1.024)^2-1=0.048576[/tex]The effective rate is 4.86%
Forty percent of 90 is what number
90 represents the 100%
Let's call x to the number that represents the 40%
To find the 40%, we can use the next proportion:
[tex]\frac{90}{x}=\frac{100\text{ \%}}{40\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 90\cdot40=100\cdot x \\ \frac{3600}{100}=x \\ 36=x \end{gathered}[/tex]36 is 40% of 90
Cynthia wants to buy a rug for a room that is 18ft wide and 28ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 264 square feet of carpeting. What dimensions should the rug have ?
SOLUTION
Let us use a diagram to illustrate the information, we have
Now, from the diagram, let the length of the uniform strip of floor around the rug be x, So, this means the length and width of the rug is
[tex]\begin{gathered} \text{length = 2}8-x-x=28-2x \\ \text{width = }18-x-x=18-2x \end{gathered}[/tex]Now, since she can afford to buy a rug of 264 square feet for carpeting, this means that the area of the rug is 264, hence we have that
[tex]\begin{gathered} \text{area of rug = (2}8-2x)\times(18-2x) \\ 264=\text{(2}8-2x)(18-2x) \\ \text{(2}8-2x)(18-2x)=264 \end{gathered}[/tex]Solving for x, we have
[tex]\begin{gathered} \text{(2}8-2x)(18-2x)=264 \\ 504-56x-36x+4x^2=264 \\ 504-92x+4x^2=264 \\ 4x^2-92x+504-264=0 \\ 4x^2-92x+240=0 \end{gathered}[/tex]Dividing through by 4 we have
[tex]\begin{gathered} x^2-23x+60=0 \\ x^2-20x-3x+60=0 \\ x(x-20)-3(x-20)=0 \\ (x-3)(x-20)=0 \\ x=3\text{ or 20} \end{gathered}[/tex]So from our calculation, we go for x = 3, because 20 is large look at this
[tex]\begin{gathered} \text{From the length which is (2}8-2x) \\ 28-2(20) \\ =28-40=-12 \end{gathered}[/tex]length cannot be negative, so we go for x = 3.
Hence the dimensions of the rug becomes
[tex]\begin{gathered} \text{(2}8-2x) \\ =28-2(3) \\ =28-6=22 \\ \text{and } \\ 18-2x \\ 18-2(3) \\ 18-6=12 \end{gathered}[/tex]So the dimension of the rug should be 22 x 12 feet
4. A 5% tax is added onto a $75 online order. How much are the taxes?
We have the following:
We know that 100% is the value of the purchase of $ 75, therefore, if we add 5%, it would be 105%, that is equal to 1.05, so we multiply the value of 75 by 1.05, and we are left with the following
[tex]\begin{gathered} 75\cdot1.05=78.75 \\ 78.75-75=3.75 \end{gathered}[/tex]Total value is $78.75 and taxes are 3.75
Graph the image of rectangular TUVW after a translation 5 units right and 4 units up.
From the rectangle TUVW, the coordinates of the points are shown below:
T(-5, -5), U(-1, -5), V(-1, 4), and W(-5, 4)
If TUVW is translated 5 units right and 4 units up, the coordinates of the new rectangle are in the form (x+5, y+4):
T'(0, -1), U'(4, -1), V'(4, 8), and W'(0, 8)
What are three ratios equivalent to 9/5?
The given ratio is 9/5
This ratio is already in the simplified form. To find equivalent ratios, we would multiply the numerator and denominator by constant numbers. We have
If we multiply by 2, it becomes
9 * 2/5 * 2 = 18/10
If we multiply by 3, it becomes
9 * 3/5 * 3 = 27/15
If we multiply by 4, it becomes
9 * 4/5 * 4 = 36/20
Thus, three equivalent ratios are
18/10, 27/15 and 36/20
Find the slope and the x- & y-intercepts of x + 2y = 6(5 pts) (Show work for finding X- & y-intercepts)
First, we need to write our equation in standard form — the y should be on the left- hand - side and the x should be on the right- hand side.
The first step is to subtract x from both sides, doing this we get:
[tex]2y=6-x[/tex]Now we divide both sides of the equation by 2 (this isolates the y on LHS), doing this gives us:
[tex]y\text{ = }\frac{6-x}{2}[/tex]which can also be written as
[tex]y=\frac{-x}{2}+3[/tex]The y-intercept is the point at which the line described by our equation intersects the y-axis. This intersection happens when x = 0; therefore, the y-intercept is
[tex]y=\frac{-0}{2}+\text{ 3}[/tex][tex]y=0\text{.}[/tex]The x-intercept is the point at which the line intersects the x-axis. This happens when y =0; therefore, the x-intercept is
[tex]0=\frac{-x}{2}+3[/tex][tex]-3\text{ = }\frac{-x}{2}[/tex][tex]x\text{ = 6.}[/tex]Now we see that the slope of the equation is -1/2 (the coefficient of x ). The y-intercept is y = 3 and the x-intercept is 6.
determine the interview on which the function is concave upward and concave downward
We have to identify the intervals where the function is concave upwards and where is concave downward.
We can differentiate them in a graph as:
We then have only one interval where the function is concave upwards: between x = -1 and x = 4. We can identify other intervals where the function is concave downwards and interrupted by discontinuities.
Then, we can write all the intervals as:
[tex]\begin{gathered} (-\infty,-5)\longrightarrow\text{Concave downward.} \\ (-5,-1)\longrightarrow\text{Concave downward.} \\ (-1,4)\longrightarrow\text{Concave upward}. \\ (4,\infty)\longrightarrow\text{Concave downward.} \end{gathered}[/tex]Which of the following are mathematical sentences? Check all that apply. A. 34 B. r + 7 = 4 C. 5g = 9 D. 4x E. 8r = 12 F. x = 1
The mathematical sentences that can be found in the sentence are:
B. r + 7 = 4 C. 5g = 9 D. 4x E. 8r = 12 F. x = 1What are mathematical sentences?A mathematical sentence can be described as the statement that comprises the two expressions nor more than two expression.
It should be noted that these two expressions can make use of the numbers as well as the variables and in some of the cases combination of them however the mathematical sentence do encompass the symbols which could be inform of equals, greater than, as well as less than.
Therefore, the options that are examples of mathematical sentences are option B C D E F.
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The mathematical sentences which can be found in the sentence are;
B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1
What are mathematical sentences?A mathematical sentence can be described as a statement that comprises two expressions or more than two expressions.
Expression can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Remember that these two expressions can make use of the numbers as well as the variables and in some cases a combination of them however the mathematical sentence does encompass the symbols which could be in form of equals, greater than, as well as less than.
Hence, the options that are examples of mathematical sentences are ; B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1
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22 8(11 + 2r) = 126r + 3
8(11 + 2r) = 126r + 3
first open the parenthesis
88 + 16r = 126r + 3
88 - 3 = 126r - 16 r
85 = 110r
divide both-side of the equation by 110
85/110 = r
r= 17/22
Write an equation and solve to find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?
The equation is -2n - 7.3 = 16 1/2
The value of the variable n = -11.9
STEP - BY - STEP EXPLANATION
What to find?
• Write the equation of the given statement.
,• The value of n.
Given:
find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?
To solve follow the steps below:
Step 1
Translate the given statement into equation.
Let n be the number.
-2n - 7.3 = 16 1/2
Step 2
Convert 16 1/2 to decimal.
-2n - 7.3 = 16.5
Step 3
Add 7.3 to both-side of the equation.
-2n = 16.5 + 7.3
Step 4
Simplify the right-hand side of the equation.
-2n =23.8
Step 5
Divide both-side of the equation by -2.
[tex]\frac{\cancel{-2}n}{\cancel{-2}}=\frac{23.8}{-2}[/tex]n = -11.9
Therefore, the value of the variable n = -11.9
URGENT!!! help!!!!!!!!!!!!!
Triangles' resemblance is reflected by their congruence. If the matching sides and angles of two triangles match, the triangles are said to be congruent.
For triangles, there are five primary congruency rules: Side-Side-Side is an SSS criterion. The side-angle-side SAS criterion. Angle, Side, Angle is an ASA criterion. Angle-Angle-Side is an AAS criterion.
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
An isosceles triangle in geometry is one with at least two equal-length sides. It is sometimes stated as having exactly two equal-length sides and other times as having at least two equal-length sides, with the latter version adding the equilateral triangle as one of the possible configurations.
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question 18:Evaluate: summation from n equals 2 to 8 of 12 times 4 tenths to the n plus 1 power period Round to the nearest hundredth. (1 point)
Given:
[tex]\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]Required:
Sum of the numbers
Explanation:
Let
[tex]A_n=\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]when n = 2, Aₙ becomes
[tex]A_2=12(0.4)^{2+1}=12\times(0.4)^3=0.768[/tex]when n = 3, Aₙ becomes
[tex]A_3=12(0.4)^{3+1}=12\times(0.4)^4=0.3072[/tex]when n = 4, Aₙ becomes
[tex]A_4=12(0.4)^{4+1}=12\times0.4^5=0.12288[/tex]
when n = 5, Aₙ becomes
[tex]A_5=12(0.4)^{5+1}=12\times0.4^6=0.049152[/tex]when n = 6, Aₙ becomes
[tex]A_6=12(0.4)^{6+1}=12\times0.4^7=0.0196608[/tex]when n = 7, Aₙ becomes
[tex]A_7=12(0.4)^{7+1}=12\times0.4^8=0.007866432[/tex]when n = 8, Aₙ becomes
[tex]A_8=12(0.4)^{8+1}=12\times0.4^9=0.003145728[/tex]So now,
[tex]\begin{gathered} A=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8 \\ \\ A=0.768+0.3072+0.12288+0.049152+0.0196608+0.00786432+0.003145728 \\ \\ A=1.277902848\approx1.28 \end{gathered}[/tex]Final answer:
The
The electronics company makes two types of switches. Type a takes 4 minutes to make and requires $3 worth of materials.Type b takes 5 minutes to make and requires $5 of materials. In the latest production bath, it took 32 hours to make these switches and the materials cost 1740. How many of each type of switch was made?
Let
x ------> number of switch type A
y -----> number of switch type B
so
Remember that
1 hour=60 min
32 hours=32*60=1,920 minutes
4x+5y=1,920 -------> equation 1
3x+5y=1,740 ------> equation 2
Solve the system of equations
Solve by graphing
using a graphing tool
see the attached figure
Solution is
x=180
y=240
therefore
the number of switch type A was 180the number of switch type B was 240You have been tracking an adult female Australian flatback sea turtle who weighs 25 kg. How many kilocalories must she consume each day to maintain her body weight?
The kilocalories that she must consume each day to maintain her body weight is 6250 kilocalories.
How to calculate the value?From the information, the person has been been tracking an adult female Australian flatback sea turtle who weighs 25 kg.
It should be noted that the requirements is 250kcal per kilograms.
Therefore, the calories will be:
= Weight × Required calories
= 250 × 25
= 6250 kcaloriies
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Angles A and B are supplementary angles. The measure of angle A is
73∘
What is the measure of angle B?
Answer:
17
Step-by-step explanation:
73+b=90
b=90-73
b=17
In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T(a,0). What are the coordinates of S?A. (a, b)B. (a+b, d)C. (a+b, b)D. (a, d)
In a parallelogram, the opposite sides are parallel.
This means that RS is parallel to OT. So, the y value of S is the same as the y value of R, which is d, so y = d. Thus:
[tex]S=(x,y)=(x,d)[/tex]Now, we need to find x.
Since the sides RO and ST are also parallel, the x distance from O to R is the same as the x distance from T to S.
The x distance from O to R is
[tex]b-0=b[/tex]The x distance from T to S is
[tex]x-a[/tex]Since these x distances are equal, then:
[tex]\begin{gathered} b=x-a \\ x=a+b \end{gathered}[/tex]Then, the coordinates of S are:
[tex](a+b,d)[/tex]Which corresponds to option B.
How many 7 digit phone numbers can be created if the first digit cannot be a zero, and the lastnumber must be an odd number?
Given:
Number of digits = 7
The first digit cannot be zero
Last number = odd number
The possible numbers between other than zero is 9
and there are 5 odd numbers.
Hence, the number of possible combinations is:
[tex]\begin{gathered} =\text{ 9 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 5} \\ =\text{ 4500000} \end{gathered}[/tex]Answer: Option A
About how much more is the total weight of the pacific halibut and conger than the weight of the yellowfin tuna ? Explain
The weight of pacific halibut is 459 pounds and weight of yellowfin tuna is 387 pounds.
There is 72 pounds more is the total weight of pacific halibut than the yellowfin tuna.