According to Polynomial System, the correct answer is that the roots of f(x) are (x+1).
A polynomial system (sometimes just a polynomial system) is a set of simultaneous equations f₁ = 0,..., fₙ = 0. where fi is a polynomial in multiple variables such as x₁,..., xₙ over the fields. k.
This is due to the zero product property that when two binomials are multiplied by 0, one of their factors must be 0.
A simple example of a system of polynomial equations is
x²+y²- 5 = 0
xy-2 = 0.
Its solutions are the four pairs (x, y) = (1, 2), (2, 1), (-1, -2), (-2, -1). These solutions are easily verified by substitution, but proving that there are no other solutions requires more work.
Based on above description, we can say that:
(x+1) must be 0.
(x+1)=0
x=-1
Thus, If (x-1)=0 then x is 1 instead of -1 in question.
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Write an equation of a circle whose
center is (-1,3) and passes through the
point (7,-2).
Answer: (x + 1)^2 + (y - 3)^2 = 65
Step-by-step explanation:
Answer: (x+1)²+(y-3)²=89
Step-by-step explanation:
An equation of a circle: (x-a)²+(y-b)=R²
The center of a circle is (-1,3), hence a=-1 b=3
(x-(-1))²+(y-3)=R²
(x+1)²+(y-3)²=R² (1)
Substitute the coordinate (7,-2) belonging to the circle into equation (1):
(7+1)²+(-2-3)²=R²
8²+(-5)²=R²
64+25=R²
89=R²
Thus, R²=89
Hence,
(x+1)²+(y-3)²=89
Simplify the expression
By simplifying the equation we can get 5y²+2y+0.4.
What is equation?An equation is said to be a formula that express the equality of two expressions. These two expressions on either side of the equal sign are called the "left side" and "right side" of the equation. We usually assume that the right-hand side of the expression is zero. This can be compensated for by subtracting the right side formula from the two side formulas, so there is no loss of generality.
The equation is representing direct proportion is, by the commenting them with equal sign.
4y²+4.1+7y-3.7-5y+y²
Reorder and gather like terms-
(1.4y²+y²)+(4.1-3.7)-(7y-5y)
Collect coefficients of likes terms
(1.4+1)y²+(4.1-3.7)-(7y-5y)×y
Calculate the sum or difference we can get
2.4y²+0.4+2y
Rewrite the expression
2.4y²+2y+0.4
Thus this is the correct answer .
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State what additional information is required in order that the triangles are congruent for the reason given.
The additional information is required in order that the triangles are congruent for the SSS congruent theorem is IW = IH
How to determine the additional information?From the question, we have the following parameters that can be used in our computation:
Triangles = IWO, and IHO
Given theorem = SSS
The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent
From the question, we can see that the following corresponding sides on the triangles have the same mark
W O and H O
A O and A O
This implies that these sides are congruent sides
For the triangle to be congruent by SSS, the following sides must also be congruent
IW must be congruent to IH
Hence, the additional information on the congruency of the triangles is IW = IH
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Leah Long bought one bond of Vick Company for 147. The original bond was 8.25 10. Leah wants to know the current yield. Help Leah with the calculation. (Round your answer to the nearest tenth percent.)
Hence, the current yield is [tex]1212.897[/tex]
What is the calculation?
A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or results.
Here given that,
Leah Long bought one bond of Vick Company for [tex]147[/tex]. The original bond was [tex]8.25 10[/tex].
So,
[tex]8.2510(147)=1212.897[/tex]
Hence, the current yield is [tex]1212.897[/tex]
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write the integer which is 9 units left from +4
Answer:
I believe the answer is 5
Step-by-step explanation:
If RV = 54, find XV.
Step-by-step explanation:
this is a structure of medians in the main triangle.
the center point X divides each median into parts in the ratio 2:1, with X being twice as far from the originating vertex than from the midpoint of the connected side.
so, RX is twice as long as XV.
RV = 54.
RX : XV = 2:1
that means RV consists of 2+1 = 3 equal parts. 2 of these parts are RX, and one part is XV.
how long is one part ?
54/3 = 18.
RX = 2×18, and XV = 1×18
XV = 18
The required measure of the XV in the triangle is 18.
What is the median?The Median is defined as the line joining the vertex of a triangle to the midpoint of the facing side of the triangle.
Triangle RST is given, which consists of median RV, TU, and SW. All the median of the triangle intersects at X.
Now, the property triangle states that the point of intersection of the median(i.e centroid) X divides the median in the ratio of 2:1,
So,XV = 1 / 3 of RV and RX = 2/3 of RV,
Now,
XV = RV/3
XV = 54 / 3
XV = 18
Thus, XV = 18.
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I've been stuck on this for 30 minutes. Anyone able to assist?
The value of the function at -4 is f(-4) = -14.
What is the value of a function?
When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The quantity that the function assumes for these argument values is the value of a function, given the value(s) assigned to its argument(s).
Given:
f(x) = 2x - 6
We have to find the value of f(-4).
So, plug x = -4 in the above equation.
Above equation becomes,
f(-4) = 2(-4) - 6
f(-4) = -8 - 6
f(-4) = -14
Hence, the value of the function at -4 is f(-4) = -14.
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Which is the same as sin^-1 x
arccos x
arcsin x
arctan x
The expression that is the same as sin⁻¹ x is (b) arcsin x
How to determine the equivalent expression?From the question, we have the following sine expression that can be used in our computation:
sin^-1 x
When this expression is rewritten, we have the following representation
sin⁻¹ x
The above expression is pronounced as arc-sin of x
And it can be represented as
arcsin x
This means that the equivalent expression of the given expression is (b) arcsin x
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A delicatessen is selling 16 ounce containers of potato salad, but a consumer group thinks they are putting less than 16 ounces into them. A random sample of 9 containers finds the following weights: {15.24, 14.82, 15.05, 15.40, 15.55, 15.20, 13.50, 14.50, 15.32} They test at the 2.5% level of significance.
There is not enough evidence to conclude that the company is putting less than 16 ounces into the salads.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the mean is less than 16 ounces, hence:
[tex]H_0: \mu \geq 16[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean is less than 16 ounces, hence:
[tex]H_1: \mu < 16[/tex]
We have a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.025 and 9 - 1 = 8 df, hence the critical value is of:
t = -2.306.
Hence the conclusion, considering the test statistic t, is reached as follows:
t > -2.306: not enough evidence that the mean is less than 16 ounces.t < -2.306: enough evidence that the mean is less than 16 ounces.What is the test statistic?The equation to calculate the test statistic is presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.From the given sample, the values of these parameters are given as follows:
[tex]\overline{x} = 13.84, \mu = 16, s = 3.285, n = 9[/tex]
Hence the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{13.84 - 16}{\frac{3.285}{\sqrt{9}}}[/tex]
t = -1.97 -> not enough evidence.
Missing InformationThe problem asks for the conclusion regarding the test of the hypothesis.
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Which equation represents the perimeter of rectangle ABCD?; How do you find the length and width of a rectangle when given the perimeter?; What is the formula for calculating perimeter of a rectangle?; How do you find the length of a rectangle with the perimeter?
The formula for calculating it is perimeter of the rectangle = 2(length + width), meaning that it is equal to twice the sum of its length and width.
Given that,
We have to find which equation perfectly describes the ABCD rectangle's perimeter? How do you determine a rectangle's length and width given its perimeter?
We know that,
The total length of a rectangle's outer boundary is known as its perimeter. The formula for calculating it is perimeter = 2(length + width), meaning that it is equal to twice the sum of its length and width.
The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in metres, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.
A rectangle has four 90° angles.
The diagonals of a rectangle are all of the same length.
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Use analysis of variance rather than a t test whenever the null hypothesis makes a claim about:____
The use of analysis of variance rather than a t-test for the null hypothesis claims more than two populations.
Analysis of Variance (ANOVA) is a statistical component used to evaluate variances throughout the method (or average) of various groups. A variety of eventualities use to decide if there's any distinction among the method of various groups. Student's t-test is used to compare means between two His groups and ANOVA is used to compare means between three or more His groups. ANOVA first obtains the common t-test. A significant t-test for the ANOVA test indicates at least one pair for which the mean difference was statistically significant.
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find the maclaurin expansion for the following functions and indicate for which values of x it actually represents the function
The maclaurin expansion for function eˣ is 1 + x + x²/2 + x³/6 + x⁴/24 + .....
A function's expansion series, which provides the function's derivatives' sum, is known as a Maclaurin series.
Series [f, x, 0, n] can be used to find a function's Maclaurin series up to order n.
When x = 0, it is a specific example of the Taylor series. The series of Maclaurin is provided by
[tex]f(x) = f(x_0) + f(x_0)(x - x_0) + \frac{f"(x_0)}{2!}(x - x_0)^2 + . . .[/tex]
The formula for maclurin series is :
[tex]f(x) = \sum^{\infty}_{n=0} \frac{f^n (x_0)}{n!} (x-x_0)[/tex]
Where,
f(xo), f’(xo), f’‘(xo)……. are the successive differentials when xo = 0.
Maclaurin expansion for the function eˣ
Firstly , We will derivate the function
f(x) = eˣ
=> f'(x) = e⁰ = 1
=> f''(x) = e⁰ = 1
=> f'''(x) = e⁰ = 1
and so on
Upon evaluation of all derivatives at x = 0, we obtain the value 1.
Moreover, f(0)=1, so we can deduce that the expansion of the Maclaurin Series as
=> eˣ = 1 + x + x²/2 + x³/6 + x⁴/24 + .....
The given question is incomplete , I answered the question in general according to the knowledge
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Rocky has $150 to spend on food this week. If he buys 120 Coconuts for $150, what is the average cost per coconut?
Answer:
$1.25
Step-by-step explanation:
150 / 120
Answer:
$1.25
Step-by-step explanation:
You can find the average cost per coconut by dividing the total price by the number of coconuts. 150 divided by 120 is $1.25. Therefore, each coconut costs $1.25.
Where in the equation of the line passing through the point (2,-14) and having a slope -4
Hence, the equation of the line is [tex]y=-4x-22[/tex].
What is the line of equation?
The equation of a line in a two-dimensional coordinate system is an equation including terms containing variables [tex]x[/tex] and [tex]y[/tex] separately with degree [tex]1[/tex].
Here given that,
The equation of the line passing through the point [tex](2,-14)[/tex] and having a slope [tex]-4[/tex].
Using the formula of line of slope
[tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope.
Here,
[tex]m=-4\\x=2\\y=-14[/tex]
So,
[tex]y=mx+c\\-14=-4(2)+c\\\\-14=8+c\\\\c=-14-8\\\\c=-22[/tex]
Hence, the equation of the line is [tex]y=-4x-22[/tex].
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For each of the following relations, please answer the following questions (briefly justify your answers). (i) (3 points) Is the relation a function? (ii) (3 points) If the relation is a function, what are its domain and image? (ii) (3 points) Is the inverse a function? If so, what is the inverse function? The relations of interest are
(a) {(z, y):,y Z,y-2) (c) f(x, y): z,y Z,r+ y 0) (e) {(x,y) E Z × Z : xly). (f) [(x, y): z, y e R, 2 y2 1) (2) (3 points each) Let A 1,2, 3,4]. Determine a codomain B and a function f: A- B such that the following hold (briefly justify your answers).
(a) f is onto B, but not one-to-one. (b) f is one-to-one, but not onto B (c) f is both one-to-one and onto B. (d) f is neither one-to-one nor onto B. Note: You might need to change your B from part to part.
The answer is (i)Yes the given relation is a function ,
(ii) the domain is Z and range is 2Z ,
(iii) the inverse is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 }
In the question ,
it is given that ,
the relation is S₁ = {(x,y) | x,y∈ Z : y = 2x }
Part(i) ,
We can say that Yes , the given relation is a function because for each
x ∈ Z , there exists a unique y ∈ Z .
Part(ii)
since the variable x , y ∈ Z , the input variable is x ,
so , the domain of the function will be Z , and
the Range of the function will be = 2Z .
Part(iii) ,
Since the given function is bijective function ,
the function will have an inverse .
given y = 2x ,
the inverse ⇒ x = y/2 .
so , the inverse function is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 } .
There fore , the relation is a function whose domain is Z and range is 2Z n and the inverse is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 } .
The given question is incomplete , the complete question is
For given relation , please answer the following questions (briefly justify your answers).
(i) Is the relation a function ?
(ii) If the relation is a function, what are its domain and image ?
(iii) Is the inverse a function ? If so, what is the inverse function ?
The relation is given as : S₁ = {(x,y) | x,y∈ Z : y = 2x }
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The diagram shows a cologne bottle that consists of a cylindrical base and a hemispherical top.Write an expression for the (a) cylinder's volume and (b) hemispherical top's volume.h=10 cm;r=5 cm
Cylinder's volume = πr^2h = π(5 cm)^2(10 cm) = 785.398 cm^3 and Hemispherical top's volume = 2/3πr^3 = 2/3π(5 cm)^3 = 523.598 cm^3
a) To calculate the volume of the cylinder, we need to use the equation for the volume of a cylinder, which is πr^2h, where π is pi, r is the radius, and h is the height. In this case, the radius is 5 cm and the height is 10 cm, so the equation becomes π(5 cm)^2(10 cm) = 785.398 cm^3.
b) To calculate the volume of the hemispherical top, we need to use the equation for the volume of a hemisphere, which is 2/3πr^3, where π is pi and r is the radius. In this case, the radius is 5 cm, so the equation becomes 2/3π(5 cm)^3 = 523.598 cm^3.
Cylinder's volume = πr^2h = π(5 cm)^2(10 cm) = 785.398 cm^3
Hemispherical top's volume = 2/3πr^3 = 2/3π(5 cm)^3 = 523.598 cm^3
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Match each number on the left with the correct description of the number on the right.
Answer options on the right may be used more than once.
-10
This is an integer.
This is a rational number, but not an integer.
This is an irrational number.
√5
-5.6
31/
π
The given number on the left can be matched with the correct description of the number on the right as :
-10 ;This is an integer.31/4 ;This is a rational number, but not an integer.π ,√5 ; This is an irrational number.What are integers and rational numbers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
logical quantity is A rational number is any fraction with a non-zero denominator. 1/2, 1/5, 3/4, and other like numbers are a few examples of rational numbers. The number "0" is also a rational number because there are various ways to express it, including 0/1, 0/2, and 0/3.
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Part C: Mr. Chin wants to add a rectangular desk that is 7 feet wide by 5 feet long. He says
he has enough space in the reading room to add the desk. Do you agree with Mr. Chin's
conjecture? Why or why not? Explain.
Not agree with the Mr. Chin's conjecture, because there may be space for the desk in the room but Mr. Chin not have the actual measurement, it may or may not fit the desk in room of given length and width.
What is conjecture?A good guess or an idea about a pattern is a conjecture. Speculate (about something) We can only speculate about the killer's thoughts. speculate that... He speculated that the population might double within a decade. speculate about something She speculated about the existence of a brand-new species.
A mathematical assertion that has not yet been thoroughly established is known as a conjecture. When one observes a pattern that is consistent across many cases, speculations result. However, just because a pattern applies to a lot of cases does not mean that it applies to all of them. To fully accept the mathematical observation, conjectures must be demonstrated. A theorem is formed when a conjecture is thoroughly demonstrated.
A crucial step in solving a problem is making a guess; It's more than just a tool for professionals in math. It is extremely uncommon for a problem's solution to be immediately apparent in everyday problem solving. Instead, the process of solving problems involves looking at the problem structure, looking at the cases, making a guess about the solution, and then proving that guess.
Hence, not agree with Mr. Chin's conjecture.
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A line passes through the points (-8, – 7) and (-6, – 3). What is its equation in slope-intercept form?
The equation in slope-intercept form would be; y = 5x + 33
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given that line passes through points (-8, – 7) and (-6, – 3).
Now we will write in slope-intercept form,
y = m x + b .
Now to find m, we use the formula;
m = y₂ - y₁ / x₂ - x₁
Then,
m = { -3 - (-7)} / { 6 - (-8)}
m = 4 / 14
m = 2/7
Thus, y = 5x +33
Therefore, its equation in slope-intercept form would be; y = 5x + 33
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Please help me asap, I’m struggling with this :(
Answer:
x≈33.36
Step-by-step explanation:
The marks on the lines mean they are the same lenth, that means the other two angles are both 29 degrees. Because triangle angles add up to 360, we can add the two 29 degree angles and subtract them from 360 to get the angle of the equation. From here we can solve to find x.
[tex]29+29=58[/tex]
[tex]360-58=302[/tex]
[tex]11x-65=302\\[/tex]
[tex]11x=367[/tex] (add 65 on both sides)
[tex]x[/tex]≅[tex]33.36[/tex] (divide 11 on both sides)
What value of x will make on similar to SRQ by the SSS similarity theorem?; What value of will make the triangles similar by the similarity theorem?; How do you find similar triangles in SSS?; How do you find the value of X that makes triangles similar?
The value of x will make on similar to SRQ by the SSS similarity theorem is 25.
From the figure :
NM = 10
SR = 20
NO = 8
QR = x
SAS Similarity Theorem:
states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
NO/NM = SR/QR
substitute the values
8/10 = 20/x
cross multiplication
8x = 200
dividing both sides by 8
x = 25
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Full question :
What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?What value of will make the triangles similar by the similarity theorem?; How do you find similar triangles in SSS?; How do you find the value of X that makes triangles similar?
16. Translate and solve the equation.
Seven less than twice a number is 15. Find the number.
A. O 12
B.11
C. 07
D. 22
Answer:
B) 11
Step-by-step explanation:
Let n = a number
2n - 7 = 15 Add 7 to both sides
2n - 7 + 7 = 15 + 7
2n = 22 Divide both sides by 2
[tex]\frac{2n}{2}[/tex] = [tex]\frac{22}{2}[/tex]
n = 11
Answer:
B. 11
Step-by-step explanation:
2a - 7 = 15
2a = 15 + 7
2a = 22
a = 22/2
a = 11
Check:
2*11 - 7 = 15
22 - 7 = 15
It takes an older computer twice as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 12 minutes to send out the email. How long will it take the older computer to send out the email on its own? Do not do any rounding.
The older computer takes 8 minutes to send out the email on its own.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Let , the older computer works at the rate of x.
According to the condition,
then the rate of work of newer computer is x/2.
And the combined work of both the computer = x/2 + x = 3x/2
It means that 3x = 12
then x = 4
Hence, x =8of the job per minute.
It means the older computer will make the entire job in 84 minutes.
Therefore, the older computer takes 8 minutes to send out the email on its own.
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plot the probability mass function of the sample mean of x1, ... , xn, when (a) n = 2; (a) n = 3. assume that the probability mass function of the xi is p{x = 0} = .2, p{x = 1} = .3, p{x = 3} = .5 in both cases, determine e[x ] and var(x ).
The probability mass function of the sample mean of x1, ... , xn, then the
Expectation [tex]E[X][/tex] = 1 and Variance [tex]Var[X][/tex] = 4.9
To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E(X)=μ=∑xP(x).
var(X)=∑(x−μ)2pX(x), where the sum is taken over all values of x for which pX(x)>0. So the variance of X is the weighted average of the squared deviations from the mean μ, where the weights are given by the probability function PX(x) of X.
Given that,
The probability mass function of the sample mean of x1, ... , xn,
p{x = 0} = 0.2, p{x = 1} = 0.3, p{x = 3} = 0.5
when (a) n = 2; (a) n = 3
Expectation is defined as
[tex]E[X][/tex] = ∑ˣ [tex]x P(X =x)[/tex]
We have
[tex]E[X][/tex] = ∑ [tex]x P(X =x)[/tex]
[tex]x[/tex]∈(2,3)
[tex]E[X][/tex] = [tex]P(X =0)+2P(X=1)+3P(X=3)[/tex]
[tex]E[X][/tex] = 0.2 + 0.3 + 0.5
[tex]E[X][/tex] = 1
Variance is defined as
[tex]Var[X][/tex] = E[(X-[tex]E[X]^{2}[/tex]]
[tex]Var[X][/tex] = [tex]E[X^{2}][/tex] - [tex](E[X])^{2}[/tex]
We get
[tex]E[X]^{2}[/tex] = [tex]1^{2} P[X=0]+2^{2} P[X=1]+3^{2} P[X=2][/tex]
[tex]E[X]^{2}[/tex] = 0.2 + 4(0.3) + 9(0.5)
[tex]E[X]^{2}[/tex] = 0.2 + 1.2 + 4.5
[tex]E[X]^{2}[/tex] = 5.9
Variance is defined as
[tex]Var[X][/tex] = [tex]E[X^{2}][/tex] - [tex](E[X])^{2}[/tex]
[tex]Var[X][/tex] = 5.9 - [tex]1^{2}[/tex]
[tex]Var[X][/tex] = 5.9 - 1
[tex]Var[X][/tex] = 4.9
Therefore,
The probability mass function of the sample mean of x1, ... , xn, then the
Expectation [tex]E[X][/tex] = 1 and Variance [tex]Var[X][/tex] = 4.9
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what is the remainder in the synthetic division below
The Remainder in the Synthetic division is three, for given problem
1 |__1___2__-3__3 is 3.
So, the correct option is option(c).
The Synthetic Division:
It is defined as the method of dividing the polynomial by the binomial is known as the synthetic division. It stands for polynomial division. Here, the division principle is performing in the coefficient of the polynomial.
We have given that the synthetic division is
1 |__1___2__-3__3
We find out the remainder in the synthetic division :
Multiply the carry-down value (i.e 1) by the test zero on the left, and carry the result(i.1×1 = 1) up into the next column inside:
1 | 1 2 -3 3
|______________
1
Add down the column( 2+1 = 3) :
1 | 1 2 -3 3
|____1_________
1 3
Multiply the previous carry-down value (i.e 3) by the test zero, and carry the new result up into the last column:
1 | 1 2 -3 3
|____1____3____
1 3 0
1 | 1 2 -3 3
|____1____3___0_
1 3 0 3
three, last carry-down value is the remainder.
Therefore, the remainder is 3. The option c is correct.
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Complete question:
What is the remainder in the synthetic division problem below?
a. 6
b. 4
c. 3
d. 5
Most of the cars the Green Pine Auto Dealership sells are minivans and sedans. In January, they sold 10 minivans and 20 sedans. In February, the dealership ran some promotions, and they sold 15 minivans and 25 sedans. During which month did the dealership sell a greater ratio of minivans to sedans?
Using the concept of ratio, the month of February had a better ratio in sales compared to January
What is RatioThe ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
This is the process of comparing two quantities against one another to determine their ratio against each other.
In the question given;
January = 10 minivans, 20 sedans
The ratio of minivans to sedan = 10 / 20 = 1/2
The ratio of minivans to sedan in January = 1/2
February = 15 minivans, 25 sedans
The ratio of minivans to sedans = 15/25 = 3/5
The month of February has the highest ratio
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On Abby Ellen’s graduation from law school, Abby’s uncle, Bull Brady, promised her a gift of $24,000 or $2,400 every quarter for the next 4 years after graduating from law school. If the money could be invested at 6% compounded quarterly, which offer should Abby choose? How much money will Abby have if she invests at 6% compounded quarterly? (Round your answer to the nearest cent.)
Abby choose:
Abby will have:
Abby will choose $2,400 every quarter for 4 years.
Abby will have $30455.65 if she invests at 6% compounded quarterly
What is interest rates?
The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
The formula of compounded quarterly is
A = P ( 1 + r/n)^(4t)
P = Principal = $24,000
n = 4
r = rate of interest = 6% = 0.06
t = time = 4 years
Putting the value of P, r, t in the formula of compounded quarterly:
A = 24000 ( 1 + 0.06/4)^(4×4)
A = 30455.65.
Future Value of an Ordinary Annuity
[tex]S = R[\frac{(1+i)^n-1}{i} ][/tex]
Where
S is the future value;
R is the periodic payment;
i is the interest rate per period;
n is the number of periods.
The value of R is $2,400, i = 0.06/4 = 0.015
n = (4 × 4) = 16
[tex]S = 2400[\frac{(1+0.015)^{16}-1}{0.015} ][/tex]
S = 43037.69
Abby choose: $2,400 every quarter for 4 years.
Abby will have $30455.65 if she invests at 6% compounded quarterly.
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which of the following is equivalent to
235,000,000,000?
A2.35 x 10-⁹
B 2.35 x 10-10
C 2.35 x 1011
D 2.35 x 1012
Answer:
C 2.35 x 10¹¹
Step-by-step explanation:
You want the number 235,000,000,000 written in scientific notation.
Place valueThe exponent of 10 when a number is written in scientific notation is the same as the exponent of 10 for the most significant digit when the number is written in expanded form using exponents.
235,000,000,000 = 2×10¹¹ +3×10¹⁰ +5×10⁹ +0×10⁸ +... +0
The place value multiplier for the most-significant digit is 10¹¹, so this is the multiplier when the number is written in scientific notation.
2.35×10¹¹
Find the average value of f(x)=−2sin(x)+5cos(x) over the interval [π,2π] .
The average value of the trigonometric equation f(x) = - 2 · sin x + 5 · cos x over the interval [π, 2π] is equal to 2 / π.
How to determine the average value of a function on a given intervalIn this question we find the definition of a trigonometric equation consisting in the sum of two trigonometric functions on a given interval [a, b], of which we must determine its average value by means of the following integral equation:
[tex]m = \frac{1}{b - a} \cdot \int\limits^b_a {f(x)} \, dx[/tex]
Where:
a - Lower boundb - Upper boundFirst, write the entire trigonometric equation and the bounds of the interval:
f(x) = - 2 · sin x + 5 · cos x, a = π, b = 2π
Second, obtain the result of the integral equation:
[tex]m = -\frac{2}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\sin x} \, dx + \frac{5}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\cos x} \, dx[/tex]
[tex]m = \frac{2}{\pi}\cdot \cos x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex] + [tex]\frac{5}{\pi}\cdot \sin x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex]
m = (2 / π) · (cos 2π - cos π) + (5 / π) · (sin 2π - sin π)
m = (2 / π) · (1 - (- 1)) + (5 / π) · (0 - 0)
m = 2 / π
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wich of the following statements are true
Answer:
A
Step-by-step explanation:
