The number of words of the book Jimmy reads os 21,356, and the number of words of the book Bob reads is one-and-a-half times (that is, 1.5x) as many words, so to find the number of words Bob reads, we just need to multiply the number of words of Jimmy's book by the factor of 1.5:
[tex]21356\cdot1.5=32034[/tex]NEED HELP DUE BY WEDNESDAY OR TOMMOROW. Solve each of the equations and select the numbers that represent solutions to more than one of the six equations. Select all that apply. 4x-3=17. 8(x + 1) = 24. 5(x - 2) = 20. 34 - 7x = 20. 31 - x = 29. 3x +6=21. A. x=1. B. x=2. C. x=3. D. x=4.E. x=5. F. X = 6.
We are to solve for x in all the equations and select the ones that occur more than one solution.
Hence,
[tex]\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4}=5 \\ \therefore x=5 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2=6 \\ \therefore x=6 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 31-x=29 \\ 31-29=x \\ 2=x \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1=2 \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 14=7x \\ \frac{14}{7}=\frac{7x}{7} \\ 2=x \\ \Rightarrow x=2 \end{gathered}[/tex]Lastly,
[tex]\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3}=5 \\ \therefore x=5 \end{gathered}[/tex]Hence, the numbers that represent solutions to more than one of the six equations are
[tex]\begin{gathered} x=2\text{ \lparen Option 2\rparen} \\ x=5\text{ \lparen Option 5\rparen} \end{gathered}[/tex]Which of the following sets does the number - 12.12532 ... belong to?Select all correct answers.Select all that apply:Whole NumbersIntegersURational NumbersIrrational NumbersReal NumbersUNone of the Above
Answer:
Explanation:
Let's define each of the given types of numbers;
*Whole numbers are a set of all positive integers including 0. E.g 0, 1, 2,
*Integers
Which of the following polygons has reflective symmetry but not rotational symmetry?
a) square
b) regular decagon
c) kite
d) equilateral triangle
A kite has reflective symmetry but not rotational symmetry.
Define symmetry.In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more exact meaning of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.
Given,
A kite has reflective symmetry but not rotational symmetry.
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Need help with this question
Given: a quadratic function with vertex (2,3) opening upward .
Find: the given statement is true or false.
Explanation: if parabola has a vertex at (2,3) and opens upward, it has one real solution., (2,3) will be a lowest point. The vertex will be at lowest point, it will be minimum.
that means graph has no one real solution. hence it will never going to intersect. so this statement is false.
Final answer: the given statement is FALSE.
questionSuppose $24,000 is deposited into an account paying 7.25% interest, which is compoundedcontinuouslyHow much money will be in the account after ten years if no withdrawals or additional depositsare made?
This is a compound interest question and we have been given:
Principal (P) = $24000
Rate (r) = 7.25%
Years (t) = 10
However, we are told this value is compounded continuously. This means that for every infinitesimal time period, the value keeps being compounded.
The formula for finding the compound interest is:
[tex]\text{Amount}=P(1+\frac{r}{n})^{nt}[/tex]But because the compounding period is continuous and therefore, infinitesimal,
[tex]\begin{gathered} Amount=P(1+\frac{r}{n})^{nt} \\ But, \\ n\to\infty \\ \\ \therefore Amount=\lim _{n\to\infty}P(1+\frac{r}{n})^{nt} \end{gathered}[/tex]This is similar to the general formula for Euler's number (e) which is:
[tex]e=\lim _{n\to\infty}(1+\frac{1}{n})^n[/tex]Thus, we can re-write the Amount formula in terms of e:
[tex]\begin{gathered} \text{Amount}=\lim _{n\to\infty}P(1+\frac{r}{n})^{nt} \\ \text{This can be re-written as:} \\ \\ Amount=\lim _{n\to\infty}P(1+\frac{r}{n})^{\frac{n}{r}\times r\times t}\text{ (move P out of the limit because it is a constant)} \\ \\ \text{Amount}=P\lim _{n\to\infty}((1+\frac{r}{n})^{\frac{n}{r}})^{r\times t} \\ \\ \text{Amount}=P(\lim _{n\to\infty}(1+\frac{r}{n})^{\frac{n}{5}})^{rt} \\ \\ \text{but,} \\ e=(\lim _{n\to\infty}(1+\frac{r}{n})^{\frac{n}{r}} \\ \\ \therefore\text{Amount}=Pe^{rt} \end{gathered}[/tex]Therefore, we can find the amount of money in the account after 10 years:
[tex]\begin{gathered} \text{Amount}=Pe^{rt} \\ P=24000 \\ r=7.25\text{ \%=}\frac{7.25}{100}=0.0725 \\ t=10\text{ years} \\ \\ \therefore\text{Amount}=24000\times e^{10\times0.0725} \\ \\ \text{Amount}=24000\times2.06473 \\ \\ \therefore\text{Amount}=49553.546\approx49553.55 \end{gathered}[/tex]Therefore the amount after compounding continuously for 10 years is:
$49553.55
Bill has these expenditures for his utilities: December,
$234.45; January, $281.23; February, $284.33. What is his
average monthly expense for utilities?
The average monthly expenses for Bill's utilities is $266.67.
It is given in the question that:-
Expenditure in December by Bill = $ 234.45
Expenditure in January by Bill = $ 281.23
Expenditure in February by Bill = $ 284.33
We have to find the average monthly expenses for Bill's utilities.
We know that,
Average monthly expense for utilities = (Expenditure in December + Expenditure in January + Expenditure in February)/3
Hence, using the data given in the question, we can write,
Average monthly expense for utilities = (234.45 + 281.23 + 284.33)/3
Average monthly expense for utilities = 800.01/3 = $266.67
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2. Graph the following inequality on the axes provided below: 6x + 2y = 8 -10 8 6 4 2 -101-8-6 1-4-2 -2 2 4_LG_L 8 10 -4 -6 -8 -10 True or False: (1,1) is a solution to the inequality. Explain using evidence from your graph.
We are given the following inequality
[tex]6x+2y<8[/tex]Let us first convert the inequality into slope-intercept form
[tex]\begin{gathered} 6x+2y<8 \\ 2y<-6x+8 \\ y<-\frac{6x}{2}+\frac{8}{2} \\ y<-3x+4 \end{gathered}[/tex]Comparing this inequality with the standard slope-intercept form we see that
Slope = -3 and y-intercept = 4
So the graph of the inequality is
The area left to the red line represents the solution of the inequality.
Now we need to check if the point (1, 1) lies left to the red line.
We can clearly see that point (1, 1) is just left to the red line hence it is a solution.
Therefore, it is true.
13 nickels to 43 dimes in a reduced ratio form
The reduced ratio form of 13 nickels to 43 dimes is 13/86.
What is a ratio?
a ratio let us know that how many times one number contains another number.
We are given 13 nickels and 43 dimes.
We know that 1 dime equal to 2 nickels.
Hence 43 dimes equals 86 nickels.
Now we find the ratio of the 2.
Which will be [tex]\frac{13}{86}[/tex]
Hence the reduced ratio form is 13/86.
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Sketch the graph of a function that has a local maximum value at x = a where f'(a) is undefined.
Derivative and Maximum Value of a Function
The critical points of a function are those where the first derivative is zero or does not exist.
Out of those points, we may find local maxima or minima or none of them.
One example of a function with a derivative that does not exist is:
[tex]y=-x^{\frac{2}{3}}[/tex]This function has a local maximum at x=0 where the derivative does not exist.
The graph of this function is shown below:
kindly asking for help to clarify this question and mathematical problem .
As you can see the options A and B are decreasing, D is constant, therefore, the only increasing relationship is the option C
RATIOS/UNIT RATESRead and answer the question.Jessica sold 4 out of 32 boxes of the cookies her Girl Scout troop sold onSaturday. Select ALL the choices that display an equivalent ratio to thenumber of boxes Jessica sold to the total boxes sold.8 to 641:80 11O 21602:15
Evaluate the rational expression for the given x value. Express the answer as a fraction in simplest form.
Given the expression:
[tex]\frac{x-3}{2x+3}[/tex]We need to find the value of the expression when x = 7
So, we will substitute with x = 7 into the expression as follows:
[tex]\frac{7-3}{2\cdot7+3}=\frac{7-3}{14+3}=\frac{4}{17}[/tex]so, the answer will be 4/17
Use mental math to find all of the quotients equal to 50. Drag the correct division problems into the box.
4
,
500
÷
900
450
÷
90
45
,
000
÷
900
4
,
500
÷
90
450
÷
9
Quotients equal to 50
Answer: 45,000 ÷ 900=50
Step-by-step explanation:
Hey could someone help me out with this thank you
Karen will run more than 28
#8 help with algebra 2 question. That’s the only picture I have. I tried writing it out.
Solution:
Given a cosine function graph;
The general cosine function is
[tex]y=A\cos(Bx-C)+D[/tex]Where
[tex]\begin{gathered} A\text{ is the amplitude} \\ Period=\frac{2\pi}{B} \\ C\text{ is the phase shift} \\ D\text{ is the vertical shift} \end{gathered}[/tex]From the graph,
The midline is y = 1
The amplitude, A, is
[tex]\begin{gathered} A=4-1=3 \\ A=3 \end{gathered}[/tex]The amplitude, A is 3
Where,
[tex]\begin{gathered} Period=12 \\ Period=\frac{2\pi}{B} \\ 12=\frac{2\pi}{B} \\ Crossmultiply \\ 12B=2\pi \\ Duvide\text{ both sides by 12} \\ \frac{12B}{12}=\frac{2\pi}{12} \\ B=\frac{\pi}{6} \end{gathered}[/tex]The phase shift, C = 0, and the vertical, D, is 1
Thus, the equation of the graph is
[tex]\begin{gathered} y=A\cos(Bx-C)+D \\ Where \\ A=3 \\ B=\frac{\pi}{6} \\ C=0 \\ D=1 \\ y=3\cos(\frac{\pi}{6}x)+1 \end{gathered}[/tex]The graph is shown below
Hence, the equation is
[tex]y=3\cos(\frac{\pi}{6}x)+1[/tex]Please help me sketch a graph for this sequence (I've already solved it): 2/3, 1, 3/2, 9/4, 27/8
ANSWER and EXPLANATION
We have that the 1 - 5th terms of the sequence are:
2/3, 1, 3/2, 9/4 and 27/8
To plot the graph of this sequence, we have:
=> on the x axis, the term number (i.e. n = 1, 2, 3, 4, 5)
=> on the y axis, the term(i.e. a(n) 2/3, 1, 3/2, 9/4, 27/8)
We will plot the graph of n versus a(n).
That is:
That is the graph.
If Tanisha wants the top of the ladder to reach exactly 8 feet up the building, what is X, the distance between the building and the base of the ladder in feet?
Solution:
Given:
The right triangle can be sketched as shown below;
To get the distance between the building and the base of the ladder, we use the Pythagoras theorem since it is a right triangle.
[tex]\begin{gathered} \text{hypotenuse}^2=\text{adjacent}^2+\text{opposite}^2 \\ \\ \text{where;} \\ \text{hypotenuse}=10 \\ \text{adjacent}=x \\ \text{opposite}=8 \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} \text{hypotenuse}^2=\text{adjacent}^2+\text{opposite}^2 \\ 10^2=x^2+8^2 \\ 100=x^2+64 \\ 100-64=x^2 \\ 36=x^2 \\ x=\sqrt[]{36} \\ x=6 \end{gathered}[/tex]Therefore, the distance between the building and the base of the ladder in feet is 6 feet.
Divide the polynomial by the binomial. (Simplify your answer completely.)
(q² + 5q + 20) / (q + 8)
Answer:
It's already in its simplest form.
Step-by-step explanation:
Factorising QuadraticsI'm writing a book/document on this topic but it's not finished. I suspect there is an error in this question because it's practically impossible to factorise it into integers.
The quadratic polynomial in the numerator has imaginary roots because 5 squared is less than 20 times 4.
ax² + bx + c;
if ( b² < 4ac ) { 'solution is imaginary' }
The quadratic equation will explain the above.
Hello! I need some help with this homework question, please? The question is posted in the image below. Q17
The function being one-to-one implies that every value of x, has one one vaue of y, and every value of y, has one value of x.
The inverse uses the output(y value) as an input(x value) and spits it out to get the original x value inputted into f.
Using the given point ( 2, -5 ), it implies of f(2) = -5. Since the function is one-to-one, this implies that:
[tex]f^{-1}(-5)=2[/tex][tex]\text{Thus, the point on the graph of f}^{-1}\text{ is }(-5,2\text{ )}[/tex]Hence, the correct option is option B
What is the image point of (-12, —8) after the transformation R270 oD ?
Answer
(-12, -8) after R270°.D¼ becomes (-2, 3)
Explanation
The first operation represented by R270° indicates a rotation of 270° counterclockwise about the origin.
When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.
Then, the second operation, D¼ represents a dilation of the coordinate about the origin by a scale factor of ¼ given.
The coordinates to start with is (-12, -8)
R270° changes A (x, y) into A' (y, -x)
So,
(-12, -8) = (-8, 12)
Then, the second operation dilates the new coordinates obtained after the first operation by ¼
D¼ changes A (x, y) into A' (¼x, ¼y)
So,
(-8, 12) = [¼(-8), ¼(12)] = (-2, 3)
Hope this Helps!!!
Hallum hardware created flyers to advertise a carpet sale . A portion of the flyer is shown below. Based on the chart, which statement describes the relationship between area and the cost of carpet?
The correct statement is the relationship is proportional because the ratio of the area to the cost is constant.
Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area.
Ratio = cost / area
750 / 500 = 1.50
1500 / 1000 = 1.50
2,250 / 1500 = 1.50
3000 / 2000 = 1.50
Since the ratios are constant, the relationship is proportional.
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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant. Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area. Ratio = cost / area 750 / 500 = 1.50 1500 / 1000 = 1.502,250 / 1500 = 1.503000 / 2000 = 1.50 Since the ratios are constant, the relationship is proportional.
Gina left home, riding her bicycle at a rate of 25 miles per hour. Sean left 1 hour later, riding at a rate of 30 miles per hour. How long will it take Sean to catch up to Gina?
As per the distance formula, it take 1 hour of time for Sean to catch up to Gina.
Distance formula:
The equation that relates the distance, rate, and time is
d = rt
Where d represents the distance traveled, r represents the rate, and t represents the time.
Given,
Gina left home, riding her bicycle at a rate of 25 miles per hour. Sean left 1 hour later, riding at a rate of 30 miles per hour.
Here we need to find the time take by Sean to catch up Gina.
Let us consider x be the time when Gina left the home.
Then, Sean left 1 hour later from her time.
So, it can be written as,
=> x + 1
As the Distance traveled is the same, the ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases.
Therefore, the ratio of Speed in both cases
=> 25 : 30
=> 25/30
=> 5/6
Therefore, it can be written as,
x/x+1 = 5/6
When we cross multiply them, then we get,
5x + 5 = 6x
x = 5.
If Gina left at the time of 5, then Sean left at the time of 6.
So, it take 1 hour for Sean to catch up to Gina.
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Two functions, function A and function B, are shown below:Function Axy714816918Which statement best compares the rate of change of the two functions?The rate of change of both functions is 2.The rate of change of both functions is 3.The rate of change of function A is greater than the rate of change of function B.The rate of change of function B is greater than the rate of change of function A.
Answer
The rate of change of both functions is 2.
Explanation
To know the statement that best compares the rate of change of the two functions, we need to first calculate the rate of change for each function.
Rate of change of function A
Using x₁ = 7, y₁ = 14, x₂ = 8 and y₂ = 16
Rate of change = Δy/Δx
Δy = (y₂ - y₁) = 16 - 14 = 2
Δx = (x₂ - x₁) = 8 - 7 = 1
⇒ Rate of change = 2/1 = 2
Rate of change of function B
From the graph
Using coordinate x₁ = 2, y₁ = 4, x₂ = 3 and y₂ = 6
Rate of change = Δy/Δx
Δy = (y₂ - y₁) = 6 - 4 = 2
Δx = (x₂ - x₁) = 3 - 2 = 1
⇒ Rate of change = 2/1 = 2
Since the rate of both functions are the same (2), then the statement that best compares the rate of change of the two functions in the options given is "The rate of change of both functions is 2"
How are the strategies the same and how are they different
Diagram 1.
Strategy 1.
[tex]A_{Total}=253\cdot31=(200+50+3)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]\begin{gathered} A_{Total}=A_1+A_2+A_3+A_4+A_5+A_6 \\ =(200\cdot30)+(50\cdot30)+(3\cdot30)+(200\cdot1)+(50\cdot1)+(3\cdot1) \\ =6000+1500+90+200+50+3 \\ =7843 \end{gathered}[/tex]Diagram 2.
Strategy 2.
[tex]A_{Total}=253\cdot31=(253)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]A_{Total}=A_1+A_2=253\cdot30+253\cdot1=7590+253=7843[/tex]We can see that we got the same answer: Total area = 7843 quare units
The strategies are similar because they are dividing the total area into smaller ones and then add them together.
However, they are different in that diagram 1 has more areas that are smaller compared to diagram 2. Also, the divisions in diagram 1 are designed to make multiplications easier compared to diagram 2.
Property valued at $56,000 is assessed at of itsvalue. If the yearly tax is calculated as $3 per $100 ofassessed value, what is the yearly tax on this property?A. $ 420B. $1.120C. $1,260D. $1,680E $2,240
Since the yearly tax is calculated as $3 per $100 of assessed value, which is 3/4 of $56,000 , the yearly tax on this property can be calculated as: $56,000*3/4*$3/$100 = $ 1260. The answer is option C.
What is the Y intercept of the graph below? A. (0,-2)B. (0,-4) C. (0, 2) D. (0,4)
Recall that the y-intercept of a graph is the point where the graph intersects the y-axis.
From the given graph we get that the line intersects the y-axis at (0,2).
Answer: Option C.
how do I determine the hypotenuse, opposite, and adjacent angles when I'm only given sides and no angles?
[tex]\angle J = 90^{\circ}\\\\\cos (\angle K)=\frac{5}{23} \implies \angle K=\arccos(5/23)\\\\\sin (\angle I)=\frac{5}{23} \implies \angle I=\arcsin(5/23)[/tex]
Find ca^2+b^2=c^2 3^2+2^2=c^29+4=13
Substituting with a = 3 and b = 2, we get:
[tex]\begin{gathered} 3^2+2^2=c^2 \\ 9+4=c^2 \\ 13=c^2 \\ \sqrt[]{13}=c \\ 3.6\approx c \end{gathered}[/tex]Simplify the expression (6^2)^46^?
The given expression is
[tex](6^2)^4[/tex]We would apply the rule of indices or exponent which is expressed as
[tex]\begin{gathered} (a^b)^c=a^{bc} \\ \text{Therefore, the expression would be } \\ 6^{2\times4} \\ =6^8 \end{gathered}[/tex]4. Solve the polynomial.
7x³ + 21x² - 63x = 0
After solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}
What is a polynomial?An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² 4x + 7 is an illustration of a polynomial with a single indeterminate x.So, 7x³ + 21x² - 63x = 0:
Now, solve for x as follows:
7x³ + 21x² - 63x = 07x(x² + 3x - 9) = 0Zero factor principal, if ab = 0, then a = 0 and b = 0.
x = 0 and x² + 3x - 9 = 0Now, x² + 3x - 9 = 0:
x = [(-3 ± 3√5)/2]x = 0Therefore, after solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}
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