Let 'y' represent the amount Margaret spent at the state fair.
Let 'x' represent the amount Nathan spent at the state fair.
In the next statement, Nathan spent $2 more than twice the amount that Margaret spent.
Mathematically,
[tex]x=2+2y\ldots\ldots.1[/tex]And also, we were told that Margaret and Nathan spent a total of $128 at the state fair.
Mathematically,
[tex]x+y=\text{ \$128}\ldots\ldots\ldots2[/tex]Let us substitute 'x'= 2+2y into equation 2 and solve for y.
[tex]\begin{gathered} x+y=128 \\ 2+2y+y=128 \\ 2y+y=128-2 \\ 3y=126 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{126}{3} \\ y=42 \end{gathered}[/tex]Therefore, the amount of money spent by Nathan will be,
[tex]\begin{gathered} x=2+2y \\ x=2+2(42)=2+84=86 \\ \therefore x=86 \end{gathered}[/tex]Hence, Nathan spent $86 at the fair.
Can you help me with this assignment
Those are vertical angles, therefore:
[tex]\begin{gathered} m\angle ONB=m\angle MNK \\ so\colon \\ m\angle ONB=85 \end{gathered}[/tex]Benjamin invested an amount of $12,000.00 in a mutual fund. After 4 years and 6 months the accumulated value of his investment was $13,407.58. What is the nominal interest rate of the investment if interest is compounded semi-annually?__________%
Given the following parameters
[tex]\begin{gathered} PV\Rightarrow\text{Present value}\Rightarrow12000.00 \\ T\Rightarrow\text{time}\Rightarrow4\text{years and 6 month} \\ FV\Rightarrow\text{Future Value}\Rightarrow13407.58 \\ n=2 \end{gathered}[/tex]To calculate the nominal rate, we will have to calculate the interest rate and the compounded period, the following formula will be used to find the interest rate and the compounded period.
[tex]\begin{gathered} i=(\frac{FV}{PV})^{\frac{1}{n}}-1 \\ m=\frac{n}{t} \end{gathered}[/tex]To find the value of the interest, we have
[tex]\begin{gathered} i=(\frac{13407.58}{12000.00})^{\frac{1}{2}}-1 \\ i=(1.117298333)^{\frac{1}{2}}-1 \\ i=1.057023336-1=0.05702336 \end{gathered}[/tex]To find the compounded period we will have that
[tex]\begin{gathered} m=\frac{n}{t} \\ n=2 \\ t=4.5 \\ m=\frac{2}{4.5} \\ m=0.4444444444 \end{gathered}[/tex]Thus, the nominal rate formula is given as;
[tex]\begin{gathered} j=m\times i \\ \end{gathered}[/tex]Substitute for m and i to find the nominal rate
[tex]\begin{gathered} i=0.05702336 \\ m=0.4444444444 \\ j=0.05702336\times0.4444444444 \\ j=0.02534371556\approx0.0253 \end{gathered}[/tex]The nominal rate in percentage is
[tex]\begin{gathered} j=0.0253\times100\text{ \%} \\ j=2.53\text{ \%} \end{gathered}[/tex]Hence, the nominal rate of the investment if interest is compounded semi-annually is 2.53%
The function g(x) approaches positive infinity as x approaches positive infinity. The zeros of the function are -1,2 and 4. Which graph best represents g(x)?
Explanation
We are asked to select the correct option for which g(x) approaches positive infinity as x approaches positive infinity.
Also, the zeros of the function are -1,2 and 4.
The correct option will be
Identify the transformations for the function below. Check all that applyf (x) = 2(x – 3)^3 + 2DilationHorizontal ShiftVertical ShiftReflection
The given function is,
[tex]f(x)=2(x-3)^3+2[/tex]The parent function of the given function can be identified as,
[tex]f(x)=x^3[/tex]A transformed function can be represented as,
[tex]f(x)=a(bx-h)^3+k[/tex]If k is a positive or a negative number, then function is shifted k units vertically.
So, comparing the equations, we find that in the given function k=2.
Hence, the function is vertically shifted.
A function f(x) is shifted h units horizontally if h is a positive or a negative number.
So, in the given function h=3.
Hence, the function is horizontally shifted.
If |a| >1 or 0<|a|<1, the function f(x) is dilated vertically by a scale factor of a units and if a is a negative number , the function is also reflected across the x axis.
In the given function, a=2.
So, f(x) is dilated, but not reflected.
If |b| >1 or 0<|b|<1, the graph of function f(x) is dilated by a scale factor of b units horizontally and if b is a negative number, the function is also reflected across the y axis.
In the given function, b=1.
So, f(x) is not dilated or reflected.
Hence, f(x) has undergone the transformations:
Dilation
Horizontal Shift
Vertical Shift
Suppose that $4000 is placed in a savings account at an annual rate of 9%, compounded monthly. Assuming that no
withdrawals are made, how long will it take for the account to grow to $6216?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
_ years
Answer:
below
Step-by-step explanation:
The equation to use
FV = PV ( 1 + i)^n FV = 6216 PV = 4000
i = decimal interest per period = .09/12
n = how many months?
6216 = 4000 ( 1 + .09/12)^n
6216/4000 = (1 + .09/12)^n
1.554 = 1.0075 ^n
log 1.554 / log(1.0075) = n = 59 months (approx 5 years )
Solve the system of two linear inequalities graphically.ſr<62-3Step 2 of 3 : Graph the solution set of the second linear inequality.AnswerKeyboThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (-)Enter two points on the boundary line:510-35Select the region you wish to be shaded:
Answer and Explanation:
Given the system of two linear inequalities;
[tex]\begin{gathered} x<6 \\ x\ge-3 \end{gathered}[/tex]To solve the above system of inequalities graphically, we follow the below steps;
Step 1: Graph the first inequality;
Since the first inequality has a less than sign, we'll shade the region to the left of the line.
Also, the first inequality does not have an equality sign, so the line will be a dashed line.
See below the graph of the first inequality;
Step 2: Graph the second inequality on the same grid;
Since the inequality has an equality sign, the line will be a solid line.
Also, the inequality has the greater than sign, so we'll shade the region to the right of the line
See below the image of the graph;
Step 3: The solution set of the two systems of inequalities is the region where the shading overlaps.
As can be seen in the above graph, the shaded region between the dashed line and the solid line is the solution of the system of inequalities.
The graph of the solution set of the second inequality is as shown below;
On the boundary line we can select the below points;
[tex]\begin{gathered} \lparen-3,5) \\ \lparen-3,-5) \end{gathered}[/tex]Correctnomial function with the stated properties. Reduce all fractions to lowest terms.Third-degree, with zeros of - 3, - 1, and 2, and passes through the point (3, 5).
We must construct a polynomial with the following characteristics:
0. degree: 3,
,1. zeros: x₁ = -3, x₂ = -1 and x₃ = 2,
,2. passes through the point (3, 5).
The general form for this polynomial is:
[tex]p(x)=a*(x-x_1)(x-x_2)(x_{}_{}-x_3).[/tex]Where a is a constant factor and x₁, x₂ and x₃ are the zeros of the polynomial.
Replacing the values of the zeros, we have:
[tex]p(x)=a*(x+3)(x+1)(x-2).[/tex]Using the condition that the polynomial passes through (3, 5), we have:
[tex]y=a*(3+3)(3+1)(3-2)=a*24=5.[/tex]Solving for a, we get a = 5/24. Replacing this value in the equation above, we get:
[tex]p(x)=\frac{5}{24}(x+3)(x+1)(x-2).[/tex]Answer[tex]p(x)=\frac{5}{24}(x+3)(x+1)(x-2)[/tex]The perimeter of a triangle ABC is 100 cm.The length of AB is 45 cm and the length of BC is 32 cm.What is the length ofCA?
Recall that the perimeter of the triangle ABC is given by the following formula:
[tex]Perimeter=AB+BC+CA\text{.}[/tex]Substituting the given data we get:
[tex]100\operatorname{cm}=45\operatorname{cm}+32\operatorname{cm}+CA\text{.}[/tex]Solving the above equation for CA we get:
[tex]\begin{gathered} CA=100\operatorname{cm}-45\operatorname{cm}-32\operatorname{cm} \\ =23\operatorname{cm}\text{.} \end{gathered}[/tex]Answer: The length of CA is 23cm.
Given Point A, what is the coordinate for A' after the following transformation has occurred?A (5,7)AC
Using the following given,
[tex]\begin{gathered} (x,y)\Rightarrow(x-5,-y+2) \\ (5,7) \end{gathered}[/tex]substitute the given coordinates to the new coordinates.
[tex](5,7)\Rightarrow(5-5,-7+2)[/tex]Simplify the coordinates.
[tex](5,7)\Rightarrow(0,-5)[/tex]Thus, the coordinates of A' is (0, -5).
The lengths of the four sides of a quadrilateral (in inches) are consecutive integers. If the perimeter is 110 inches, find the value of the longest of the four side lengths.
The value of the longest side of the quadrilateral is 29 inch when its perimeter is 110 inches.
Perimeter of quadrilateral
The sum of all length of sides of a quadrilateral is known as the Perimeter of quadrilateral.
For example, if ABCD is the quadrilateral, then its perimeter is calculated as,
P = AB + BC + CD + AD
Where
AB, Bc, CD, and Ad are the values of the sides of ABCD.
Given,
The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
Here we need to find the longest side value when the perimeter is 110 inches.
We know that, the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
So, let us consider the length of quadrilateral are x, x + 1, x + 2 and x + 3
Through this we have identified that the longest length = x + 3
We know that the perimeter is 110 inches.
So, it can be written as,
=> x + (x + 1) + (x + 2) + (x + 3) = 110
=> x + x + 1 + x + 2 + x + 3 = 110
=> 4x + 6 = 110
=> 4x = 110 - 6
=> 4x = 104
Therefore, the vale of x is 26 inch
Hence, longest length is calculated as,
=> x + 3
=> 26 + 3
=> 29 inch
Therefore, the value of the longest side of the quadrilateral (in inches) is 29 inch.
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which inequality is shown in the graph below? A x<2 B x>2 C y>2 S y<2
In the picture, we can see that the solution to the inequality are those x-values greater than 2 (2 is not included) no matter which value the y-variable has. This corresponds to: x > 2.
Solve the problem below, inputting your answer in decimal form.32 3/4 + 12 1/2
Answer:
45.25
Explanation:
To find the value of the expression given, we first convert the mixed numbers into fractions .
[tex]32\frac{3}{4}=32+\frac{3}{4}[/tex]multiplying 32 by 4/4 gives
[tex]undefined[/tex]A company wants to decrease their energy use by 15%. If their electric bill is currently $1,700 a month, what will their bill be if they are successful? Give your answer accurate to at least the nearest dollar.$
We will determine it as follows:
[tex]x=1700-1700(0.15)\Rightarrow x=1445[/tex]So, they will pay $1445 if they manage to decrease the consumption by 15%.
just need help and a simple way to solve this
ANSWER
The length of the third leg is
STEP-BY-STEP EXPLANATION:
The figure given is a right-angled triangle.
To find the third length of the triangle, we need to apply Pythagora's theorem
It states that
[tex]\begin{gathered} (Hypotenuse)^2=(opposite)^2+(adjacent)^2 \\ \end{gathered}[/tex]The third length of the triangle is the hypotenuse because it is the longest
[tex]\begin{gathered} (Hypotenuse)^2=4^2+2^2 \\ (Hypotenuse)^2\text{ = 16 + 4} \\ (Hypotenuse)^2\text{ = 20} \\ \text{ Take the squareroots of both sides} \\ \text{ }\sqrt[]{(Hypotenuse)^2\text{ }}\text{ = }\sqrt[]{20} \\ \text{Hypotenuse = }4.472 \\ \text{Hypotenuse }\approx\text{ 4.5} \end{gathered}[/tex]Hence, the length of the third leg is 4.5
The volume of a sphere is a function of it's radius, V=4/3* πr^3. evaluate the function for the volume of a volleyball with radius of 11.3 cm.Round to the nearest tenth.
Volume of sphere = 6040.9cm³
Explanation:
Volume of sphere = 4/3* πr³
radius = r = 11.3cm
if π = 3.14
[tex]\begin{gathered} \text{volume = }\frac{4}{3}\times3.14\times11.3^3 \\ \end{gathered}[/tex][tex]\begin{gathered} V\text{ = }\frac{4}{3\text{ }}\times3.14\times1442.897 \\ V=6040.929cm^3 \end{gathered}[/tex]Rounding to the nearest tenth:
Volume of sphere = 6040.9cm³
Same took out a loan for 6200 that charges an annual rate of 8.6% compounded quarterly. Answer each part. Sent picture
Given:
Sam took out a loan for 6200 that charges an annual rate of 8.6% compounded quarterly.
Required:
Find effective annual interest rate.
Explanation:
a).
We know compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Now,
[tex]undefined[/tex]b).
We know the effective annual interest rate
[tex]EAR=(1+\frac{i}{m})^m-1[/tex]EAR = Effective annual interest
i = Annual nominal rate of interest
m = No. of compounding periods in a year.
[tex]\begin{gathered} EAR=(1+\frac{0.086}{4})^4-1 \\ EAR=0.088813 \\ \text{ To find percentage multiply by 100 } \\ =0.088813\times100 \\ =8.8813\% \end{gathered}[/tex]Answer:
answered the question.
Find the equation of the line that has a slope of -2 and passes through point (-3 ,4)
Let's use the slope-point form to find the equation:
[tex]\begin{gathered} y-4=-2(x-(-3)) \\ \rightarrow y-4=-2(x+3) \\ \rightarrow y-4=-2x-6 \\ \rightarrow y=-2x-2 \\ \end{gathered}[/tex]Thereby, the equation of the line is:
[tex]y=-2x-2[/tex]A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam.
a. What are the null and alternative hypotheses for addressing the research question, "are average test scores different between the different teaching methods?"
b. What are the degrees of freedom associated with the F distribution for evaluating these hypotheses?
c. Suppose the p-value for this test is 0.0168. What would you conclude? (Be sure to specify your significance level.)
a. The hypotheses are:
Null hypothesis: the average test scores are the same for the different teaching methods.
Alternative hypothesis: the average test scores are different for the different teaching methods.
b. To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample
c. With a p value of of 0.0168 and using a standard significance level of 0.05, we will reject the null hypothesis as 0.0168 is less than 0.05 and conclude that the average test scores are different for the different teaching methods.
Hence we get the required answer.
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Solve the equation for X. Round the answer to three decimal places. 4^x = 6
Answer:
c. x =1.293
Explanation:
To solve the expression, we will apply the properties of the logarithms, so
[tex]\begin{gathered} 4^x=6 \\ \log 4^x=\log 6 \\ x\log 4=\log 6 \\ x=\frac{\log 6}{\log 4} \\ x=1.293 \end{gathered}[/tex]Therefore, the value for x is
c. x =1.293
State if the triangles in each pair are similar. If so, state how you know they are similar andcomplete the similarity statement.1) 2)
Triangles Similarity
For two shapes to be similar, two conditions must be satisfied:
* They must have the same angles.
* The side lengths must be in proportion
Let's focus on the image provided in problem 1.
We must try to find if the length sides of ABU and VWU are in proportion.
To do it, we find the ratio of the sides. If we find the same ratio of two pairs of sides, then the second condition is met.
pls help I've had a bad day and I've been trying to figure this out forever
the given expression is
4Ix-2I - 3
Difference of Squares gives which complex factors for the expression x2 +11?A. (x + W11)(x - 111)B. (x+in/11)(x +111)C. (x + 111)2(x - in 11)D. (x - iw/11)(x-in 11)SUBMIT
we have that
[tex](x+i\sqrt[\square]{11})\cdot(x-i\sqrt[\square]{11})=x^2-(i^2)(11)=x^2+11[/tex]answer is the first option
option A
Karmahhaze09 Can i have your number
Answer: irdk u yet so no
Step-by-step explanation:
A card is drawn randomly from a standard deck of cards. You win $5 if the card is adiamond or a king. What is the probability that you will win 5 dollars?
EXPLANATION
Let name event A as the event of drawing a Diamond and let us name event B as the event of drawing an King.
Now, we are required to find P(A union B)
We know that P(A union B) = P(A) + P(B) - P(A intersection B) … (i)
Let's suppose there are 52 cards in a standard deck.
A standard deck of cards has 13 diamonds and 4 kings
We have P(A) = 13/52 = 1/4, P(B) = 4/52 = 1/13
A intersection B denotes the case of the King of Diamonds whose probability = 1/52
Now plugging in these values to equation (i) and simplifying, we obtain the required probability as P(A union B) = 1/4 + 1/13 - 1/52 = 4/13
The probability is 4/13 or 0.307 or 30.7%
What are the zeroes of f(x) = x^2 + 5x + 6? (4 points)A) x = -2, -3B) x = 2,3C) x= -2,3D) x = 2, -3
You have the following function:
[tex]f(x)=x^2+5x+6[/tex]in order to find the zeros of the previous function, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are the coefficients of the polynomial. In this case:
a = 1
b = 5
c = 6
replace the previous values of the parameters into the formula for x:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(1)(6)}}{2(1)} \\ x=\frac{-5\pm\sqrt[]{25-24}}{2}=\frac{-5\pm1}{2} \end{gathered}[/tex]hence the solution for x are:
x = (-5-1)/2 = -6/2 = -3
x = (-5+1)/2 = -4/2 = -2
A) x = -2 , -3
Find the magnitude of the vector (-4,-4).Write your answer in simplified radical form.030/0 (0,0)ХX6?
Given the vector < -4, 4 >
The magnitude of the vector =
[tex]\sqrt[]{(-4)^2+(4)^2}=\sqrt[]{2\cdot4^2}=4\sqrt[]{2}[/tex]so, the answer will be:
[tex]4\sqrt[]{2}[/tex]⁰which of the following is the volume of a hemisphere with a radius of 8 inches?
The general expression for the volume of hemisphere is :
[tex]\text{ Volume = }\frac{2}{3}\Pi\text{ }\times radius^3\text{ }^{}^{}[/tex]In the given question we have radius = 8 inches
Substitute the value of r = 8 in the expression for the volume of hemisphere :
[tex]\begin{gathered} \text{ Volume = }\frac{2}{3}\Pi\text{ }\times radius^3\text{ }^{} \\ \text{Volume}=\frac{2}{3}\times3.14\times8^3 \\ \text{Volume =}1071.78666 \\ Volume\text{ = 1071.70 inches cubed} \end{gathered}[/tex]B) 1071.79 inches cube
Answer
Pleaseeeeee help
2x+7y=-5;(a,1)
Answer:
x= −5a/2 - 7y/2
I think. correct if wrong!!!
Reason
A library has 144 books. A long
shelf can fit 100 books. A short shelf can fit 10 books.
The books that are left over can be put in a bin.
Draw two ways to sort books on a shelf.
100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
Given, a library has 144 books. A long shelf can fit 100 books. A short shelf can fit 10 books.
The books that are left over can be put in a bin.
Now, we have to find the way to sort the books on a shelf.
So, we can put the books in this fashion,
100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
Hence, 100 books can be kept in the long shelf and the 10 books can be kept in the short shelf.
The remaining 34 books can be kept in the bin.
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221/34 simplifyed........................................
Consider the given expression,
[tex]\frac{3}{x+1}-\frac{1}{x-1}-\frac{2x}{x^2-1}[/tex]Consider the algebraic identity,
[tex]a^2-b^2=(a+b)(a-b)[/tex]Simplify the expression as,
[tex]\begin{gathered} \frac{3}{x+1}-\frac{1}{x-1}-\frac{2x}{(x-1)(x+1)} \\ \frac{3(x-1)-1(x+1)-2x(1)}{(x-1)(x+1)} \\ \frac{3x-3-x-1-2x}{(x-1)(x+1)} \\ \frac{-4}{(x-1)(x+1)} \\ \frac{-4}{x^2-1} \end{gathered}[/tex]Thus, the given expression is in simplified form gives,
[tex]\frac{3}{x+1}-\frac{1}{x-1}-\frac{2x}{x^2-1}=\frac{-4}{x^2-1}[/tex]