7.
10% = 6
25% = 15
50% = 30
20% = 12
_____________________
8.
a = 35
b = 105
c = 140
____________________________
9.
15 is 30% of 50.
_____________________________
10.
The punch recipe contains 25% lemonade:
24/6 = x/100
x=1/4 x 100 = 25%
_____________________________
11.
520
multiply 650 by 80 amd then divide by 100
or simply multiply 650 by 0.8
to get 520 students.
_______________________________________
12.
Number of items checked = 300
Defective items = 3%
Number of defective items =
Number of defective items =
Number of defective items = 9
Number of items worked = Total items - Number of defective items
Number of items worked = 300 - 9 = 291
291 items of checked items worked.
The functions f(x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval -1≤x≤4 goes from least to greatest.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for the rate of change
\(\begin{gathered} rate\text{ of change}=\frac{f(b)-f(a)}{b-a} \\ rate\text{ of change}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}\)STEP 2: Write the given intervals
\(-1\leq x\leq4\)STEP 3: Find the average rate of change of f(x)
\(\begin{gathered} Picking\text{ two points on the graphs, we have:} \\ (x_1,y_1)=\left(-1,5\right) \\ (x_2,y_2)=(4,0) \end{gathered}\)We substitute the coordinates into the rate of change formula:
\(rate\text{ of change}=\frac{0-5}{4-(-1)}=-\frac{5}{5}=-1\)STEP 4: Find the rate of change of g(x)
\(\begin{gathered} (x_1,y_1)=(-1,17) \\ (x_2,y_2)=(4,2) \\ rate\text{ of change}=\frac{2-17}{4-(-1)}=\frac{-15}{5}=-3 \end{gathered}\)STEP 5: Find the rate of change of h(x)
\(\begin{gathered} h(x)=-x^2-5x+37 \\ x_1=-1 \\ h(-1)=-(-1^2)-5(-1)+37=-1+5+37=41 \\ x_2=4 \\ h(4)=-(4^2)-5(4)+37=-16-20+37=1 \\ The\text{ new points become:} \\ (x_1,y_1)=(-1,41) \\ (x_2,y_2)=(4,1) \\ Average\text{ rate of change:} \\ \frac{1-41}{4-(-1)}=\frac{-40}{5}=-8 \end{gathered}\)STEP 6: Write the average rates of change for the functions
\(\begin{gathered} f(x)=-1 \\ g(x)=-3 \\ h(x)=-8 \end{gathered}\)The average rates of change in ascending order will be -8,-3,-1
Hence, the arrangement of the functions according to their ascending order of average rates of changes are:
\(h(x),g(x),f(x)\)Karl’s rectangular vegetable garden is 20 feet by 45 feet, and Makenna’s is 25 feet by 40 feet. Whose garden is larger in area?
Answer:
Makennas
Step-by-step explanation:
Area of rectangle = length * width
Area of Karl's garden = 20 * 45 = 900ft²
Area of Makenna's garden = 25 * 40 = 1000ft²
1000 is greater than 900 therefore makennas garden has a greater area than Karls garden
Hence, Makenna's garden is larger in area than Karl's because 1000 > 900.
Hoped this helped.
\(BrainiacUser1357\)
solve the system using elimination 2x+2y=62x-2y=6
Given the system of equations:
\(\begin{gathered} 2x+2y=6 \\ 2x-2y=6 \end{gathered}\)we can solve it using elimination by directly adding both equations to get the following:
\(\begin{gathered} 2x+2y=6 \\ 2x-2y=6 \\ ---------- \\ 4x=12 \\ \Rightarrow x=\frac{12}{4}=3 \\ x=3 \end{gathered}\)now that we have that x=3, we can find y using this value on any of the two equations:
\(\begin{gathered} 2x+2y=6 \\ x=3 \\ \Rightarrow2(3)+2y=6 \\ \Rightarrow6+2y=6 \\ \Rightarrow2y=6-6=0 \\ \Rightarrow2y=0 \\ y=0 \end{gathered}\)therefore, the solution of the system is (3,0)
8 and 3/4 into mixed number
Answer:
8 3/4 is a mixed number
Step-by-step explanation:
I don know how to explain
Which of the following tables represents a linear relationship that is also proportional?
(A)
x −1 0 1
y 0 2 4
(B)
x −3 0 3
y −2 −1 0
(C)
x −2 0 2
y 1 0 −1
(D)
x −1 0 1
y −5 −2 1
Answer: 我不知道你好
Step-by-step explanation:
Which equation is equivalent to -2(2 − 2x) = 4 − 8(1 − x)
0 = 4x
8 = 4x
4 = -4x
16 = -4x
Answer:
8 = 4x OR 0 = 4x
Step-by-step explanation:
I not %100 sure or it could be 0 = 4x
EITHERONE
Carmen draws this area model to help her divide 1,800 by 9. She says the
quotient is 20. Does Carmen's model make sense?
Use the drop-down menus to explain.
make sense.
2+2+2
G
2+2+2+2
Click the arrows to choose an answer from each menu.
Carmen's model is divided into 10 sections. The area of each section is
. This total
Choose...
Choose...
.The total area of all 10 sections is Choose...
equal to the dividend, 1,800. So, Carmen's model
Choose...
99x29x29x29x29x29x29x29x29x29x2
21
*
Answer:IF you divide 1800 divided by 9 you will get 200
The sum of a number and its reciprocal is 2 1/12 . Find the number.
The number we are looking for is 6/4, which is equivalent to 1 1/2.
To solve this problem
Let's start by setting up an equation using algebra. Let x be the number we are trying to find:
x + 1/x = 2 1/12
To solve for x, we need to get rid of the fraction on the right-hand side. We can convert the mixed number to an improper fraction:
x + 1/x = 25/12
Now we can multiply both sides by the denominator (12x) to eliminate the fractions:
12x(x + 1/x) = 12x(25/12)
Simplifying the left-hand side by distributing the 12x:
12x^2 + 12 = 25x
Bringing all the terms to one side:
12x^2 - 25x + 12 = 0
This is a quadratic equation in standard form, which we can solve using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 12, b = -25, and c = 12. Plugging in these values:
x = (-(-25) ± sqrt((-25)^2 - 4(12)(12))) / 2(12)
x = (25 ± sqrt(529)) / 24
Simplifying the square root:
x = (25 ± 23) / 24
There are two solutions:
x = 2 or x = 6/4
However, we need to check that these solutions satisfy the original equation:
2 + 1/2 = 2 1/2, which is not equal to 2 1/12
6/4 + 4/6 = 25/12, which does satisfy the equation
Therefore, the number we are looking for is 6/4, which is equivalent to 1 1/2.
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What does the number of solutions (none, one or infinite) of a system of linear equations represent?
Answer:
Step-by-step explanation:
If the number solution is none means, the two lines are parallel to each other and they will not intersect
If the number of solution is one, then the two lines intersect at one point which is the solution of the two equations
If there are infinite solutions, then the two lines coincide and so has infinite solutions.
Describe the end behavior of the function. Be specific!
What is the power of the function? What would the sign of the leading term be for this function?
What are the zero(s) of the function. Describe the nature of each zero in terms of multiplicity. Be specific and justify your answers!
What is the y-intercept? Write your answer as a point.
Write an equation of the polynomial function displayed above. Use what you have identified to construct a polynomial function. You can write your equation in factored form.
The power of the function is 4 and the leading term will be positive
The zeros of the function are
-2, -1, -1, 1
The nature of the zeros in terms of multiplicityThe zero that occurs at -2 and 1 has a multiplicity of 1. while the zero at -1 have a multiplicity of 2.
The y-intercept is where the graph cuts the y-axis and this is at
(0, -2) written as a pointEquation of the polynomial function
f(x) = a(x + 2) (x +1)² (x - 1)
using point (0, -2) to solve for a
-2 = a(0 + 2) (0 +1)² (0 - 1)
-2 = a(2) (1)² (--1)
-2 = -2a
a = 1
hence the equation is f(x) = (x + 2) (x +1)² (x - 1)
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A line is parallel to y = 3x - 12 and
intersects the point (1, -2). What is the
equation of this parallel line?
y = [?]x + [ ]
Answer: y = 3x - 5
Step-by-step explanation:
find the slope of the original line and use the point slope formula y- y1 =m(x-x1) to find the line parallel to y = 3x - 12.
Answer:
The equation of the original line that is parallel to the given line and intersects the point (1, -2) is y = 3x - 5.Solution:
Given:
Parallel line = y = 3x - 12Point = (1, -2)Step-by step explanation:
Step-1 ⇒ Let's first make a graph. (My graph is in the picture below.)Step-2 ⇒ Now, using the given equation, create the parallel line on the graph. (My original line is colored in red)Step-3 ⇒ Write down the point (1, -2) on the graph (The point is marked by a black dot).Step-4 ⇒ Lastly, draw the line such that it can intersect the points given and it is parallel to the given line. Result ⇒ Your equation should be y = 3x - 5.Conclusion:
We can conclude that the equation of the original line that is y = 3x - 5.
Determine whether or not the following variable is a rank and give the units. Student ratings of a course on a 5-point Likert scale
B. The ratings are not ranks and have no units
C. The ratings are not ranks and the units are Likerts
D. The ratings are ranks and have no units
C. The ratings are not ranks and the units are Likerts.
In the context of student ratings of a course on a 5-point Likert scale, let's analyze the options further:
A. The ratings are ranks and have no units: In a ranking system, the responses would be ordered or ranked in a specific sequence. For example, if the students were asked to rank the course from best to worst, their responses would be assigned specific positions or ranks. However, in a Likert scale, the responses are not based on relative ranking but rather on levels of agreement or disagreement. Therefore, the ratings in this case are not ranks.
B. The ratings are not ranks and have no units: This option is accurate. The responses on a Likert scale do not represent ranks because they do not indicate a specific ordering or hierarchy. Each response on the 5-point Likert scale represents a different level of agreement or disagreement, rather than a rank.
C. The ratings are not ranks and the units are Likerts: This option is the most appropriate choice. Likert scales use response categories (e.g., strongly agree, agree, neutral, disagree, strongly disagree) instead of ranks. The units associated with this variable would be "Likerts" to indicate the scale used.
D. The ratings are ranks and have no units: This option is not applicable since the ratings on a 5-point Likert scale are not considered ranks.
Therefore, option C is the correct answer. The ratings on a 5-point Likert scale are not ranks, and the units associated with this variable are "Likerts" to represent the scale used.
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Convert binary 11011.10001 to octal, hexadecimal, and decimal.
Binary number 11011.10001 can be converted to octal as 33.21, to hexadecimal as 1B.4, and to decimal as 27.15625.
To convert binary to octal, we group the binary digits into sets of three, starting from the rightmost side. In this case, 11 011 . 100 01 becomes 3 3 . 2 1 in octal.
To convert binary to hexadecimal, we group the binary digits into sets of four, starting from the rightmost side. In this case, 1 1011 . 1000 1 becomes 1 B . 4 in hexadecimal.
To convert binary to decimal, we separate the whole number part and the fractional part. The whole number part is converted by summing the decimal value of each digit multiplied by 2 raised to the power of its position. The fractional part is converted by summing the decimal value of each digit multiplied by 2 raised to the power of its negative position. In this case, 11011.10001 becomes (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) + (1 * 2^-1) + (0 * 2^-2) + (0 * 2^-3) + (0 * 2^-4) + (1 * 2^-5) = 16 + 8 + 0 + 2 + 1 + 0.5 + 0 + 0 + 0 + 0.03125 = 27.15625 in decimal.
Note: The values given above are rounded for simplicity.
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What is 2 divided by 1/4.
Answer:
8
Step-by-step explanation:
you basically multiply 2 by 4 anyways hope this helps
Two lines and a transversal form corresponding angles that are congruent. Describe the two lines.
The lines are perpendicular.
There is not enough information.
The lines are parallel
The given statement, "Two lines and a transversal form corresponding angles that are congruent," indicates that the lines are parallel. This is known as the Corresponding Angles Postulate or the Corresponding Angles Theorem.
According to the Corresponding Angles Postulate, when a transversal intersects two parallel lines, the corresponding angles formed on the same side of the transversal are congruent. In other words, if the corresponding angles are congruent, then the lines must be parallel.
This implies that the two lines never intersect and maintain a constant distance between each other. When a transversal intersects them, the corresponding angles formed on the same side of the transversal are equal.
If the lines were perpendicular, the corresponding angles formed on the same side of the transversal would not be congruent but rather supplementary, meaning their sum would be 180 degrees.
Therefore, based on the given information, we can conclude that the lines are parallel.
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5, 3, 2, 6, 5, 2,5
mean:
median:
mode:
range:
Answer:
mean: 4
median: 5
mode: 5
range: 4
Given the equation y = 2/3 x − 2, what is the value of x when y = 10?
Step-by-step explanation:
Y is equal to:
2/3x - 2 = 10
2/3x = 10 + 2
2/3x = 12
3/3x = (12 ÷ 2) × 3
x = 18
Not sure but its worth a try.
if 4x ≤ g(x) ≤ 2x4 − 2x2 + 4 for all x, evaluate lim x→1 g(x). If 4x = g(x) = 2x4 – 2x2 + 4 for all x, evaluate lim g(x). x →1
=============================================
Reason:
Let
f(x) = 4xh(x) = 2x^4-2x^2+4If we want to evaluate this limit
\(\displaystyle \lim_{\text{x}\to1} g(\text{x})\)
Then we need to evaluate these limits as well: \(\displaystyle \lim_{\text{x}\to1} f(\text{x}) \ \text{ and } \lim_{\text{x}\to1} h(\text{x})\)
This is because g(x) is bound entirely by these lower and upper functions. Refer to the squeeze theorem for more information.
To evaluate those two other limits, we simply plug x = 1 into each function.
You should find that:
f(1) = 4h(1) = 4Each function results in 4 when x = 1. This then extends to the idea that f(x) approaches 4 when x approaches 1; similarly, h(x) approaches 4 when x approaches 1.
Therefore, g(x) must approach this same y value to be contained within both these boundaries. These two boundaries squeeze or pinch g(x) into one possible option here.
how many rectangles can be made with an area of 144cm whose sides are whole numbers? PLSSS Helpp!
Give the answer in simplest form:
3/8 of 48 = n n = _____
Answer: n= 18
Step-by-step explanation: 3/8 of 48 is the same as 3/8 times 48
Answer:
18
Step-by-step explanation:
48 divided into 8 parts is 6
3x6=18
Prove that d/dx (csc (x)) = -csc(x)*cot(x). Fill in the blanks
step 1: d/dx(csc(x))=(d/dx)(1/blank)
step 2: =(blank)(0)-1(blank)
step 3: (blank)/(sin^2x)
step 4: -(1/sin x)*(blank/sin x)
step 5: = -csc(x)*cot(x)
We will use the first principle of differentiation, to prove the function.
What is the first principle of differentiation?y = f(x) with respect to its variable x. If this limit exists and is finite, then we say that: Wherever the limit exists is defined to be the derivative of f at x.
Given function cosec x
d(cscx)dx = d(1/sinx)dx
= limh→0 1/sin(x+h)-1/sinx / (x+h)-x
= limh→0 sinx - sin(x + h)/sinxsin(x + h) /h
= limh→0 sinx - sin(x + h) / h sinx sin(x + h)
= limh→0 -(sin(x + h) - sinx)/h sinx sin(x + h)
= limh→0 - (sin(x + h) - sinx)h × 1/limh→0 sinx sin(x + h)
= -cosx × 1/sin2x
= -cosx/sinx × 1/sinx
= -cotx cscx
Therefore, proved the derivative of cosec x to be -cot x cosec x using the first principle of differentiation.
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the tangent line to the graph of =() at the point (9,32) has the equation =4−4. (a) find ′(9). ′(9) = 4 (b) find the instantaneous rate of change of with respect to at =9.
The instantaneous rate of change of g(x) with respect to x at x = 9 is 4.To find the derivative of the function g(x) at x = 9, denoted as g'(9), we can use the equation of the tangent line given as f'(9) = 4.
The derivative of a function represents its rate of change at a specific point. In this case, the derivative g'(x) at x = 9 is given as 4, which means that at that point, the function g(x) has a slope of 4. The tangent line to the graph of g(x) at (9,32) has this slope of 4, indicating the instantaneous rate of change of g(x) with respect to x at x = 9.
This means that for a small change in x around x = 9, the corresponding change in g(x) is approximately 4 times that of x. Thus, the instantaneous rate of change of g(x) with respect to x at x = 9 is 4, indicating how quickly g(x) is changing at that particular point.
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A stackable CD rack holds 20 CDs and costs $3. Mark has a collection of 120 CDs. How much will it cost him to buy enough racks to hold all of his CDs?
Answer:
You would need $18 total to buy the racks needed.
Step-by-step explanation:
First, every 20 CDs needs a new rack, so you would divide 120 by 20.
120 / 20 = 6 racks
Second, you would multiply the price ($3) of a rack by how many racks needed.
3 * 6 = $18
When interpreting f(7, 31) = 4.78, p > 0.05, how many subjects were tested in this simple one-way anova?
39 subjects were tested in this simple one-way ANOVA.
The df for F distribution is (treatment df, error df)
Using given information
Treatment df = 7
Error df = 31
Total df= 7+31 = 38
Again, total df = N-1, N= number of subjects tested
Then, N-1 = 38
=> N= 39
One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.
The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.
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(Please help)
Rewrite the following questions to make them a statistical question.
1. Can I do a cartwheel?
2. How many pets do I have?
3. What is my favorite movie?
4. How tall am I?
5. What is my bedtime on a school night?
Answer:
1. How many students at the play ground can do a cartwheel
2. How many pets so the kids in my class have
3. What are the students in my schools favorite movie
4. How tall are the people in the store
5. What is the bedtime of the students in my class on a school night
Step-by-step explanation:
A statistical question is a question that varies in answers. Like if you ask how tall am I, you will get only one answer. But if you ask how tall are the people in the store the answers will vary.
Hope this helped :)
consider the initial value problem y′′ 36y=e−t, y(0)=y0, y′(0)=y′0. suppose we know that y(t)→0 as t→[infinity]. determine the solution and the initial conditions.
The complementary solution to the homogeneous equation y'' - 36y = 0 is y_c(t) = c1e^(6t) + c2e^(-6t), where c1 and c2 are arbitrary constants.
To find the particular solution to the non-homogeneous equation y'' - 36y = e^(-t), we can guess a particular solution of the form y_p(t) = Ate^(-t), where A is a constant to be determined.
Taking the derivatives, we have y_p'(t) = Ae^(-t) - Ate^(-t) and y_p''(t) = -2Ae^(-t) + Ate^(-t).
Substituting these into the original equation, we get:
(-2Ae^(-t) + Ate^(-t)) - 36(Ate^(-t)) = e^(-t).
Simplifying, we have:
(-2A - 36A) e^(-t) + (A - 36A)t e^(-t) = e^(-t).
To satisfy this equation, we must have:
-38Ae^(-t) + (A - 36A)t e^(-t) = e^(-t).
Comparing the coefficients, we get:
-38A = 1, and
A - 36A = 0.
Solving these equations, we find A = -1/38.
Therefore, the particular solution is y_p(t) = (-1/38)te^(-t).
The general solution to the non-homogeneous equation is y(t) = y_c(t) + y_p(t) = c1e^(6t) + c2e^(-6t) - (1/38)te^(-t).
Since we know that y(t) approaches 0 as t approaches infinity, we can conclude that the constant terms c1 and c2 must be 0. Therefore, the particular solution with the initial conditions y(0) = y0 and y'(0) = y'0 is:
y(t) = -(1/38)te^(-t).
To summarize:
Solution: y(t) = -(1/38)te^(-t).
Initial Conditions: y(0) = y0 and y'(0) = y'0.
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What is the difference of the lengths of and ? use the value = 3.14, and round the answer to two decimal places. a. 1.25 units b. 1.57 units c. 2.56 units d. 2.84 units
The difference between the length of arc BD and CE is 1.57 units
Length of an arclength of arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleTherefore,
BD = 45 / 360 × 2 × 3.14 × 6 = 1695.6 / 360 = 4.71 units
CE = 45 / 360 × 2 × 3.14 × 8 = 2260.8 / 360 = 6.28 units
Therefore, the difference between the length of arc BD and CE is as follows:
6.28 - 4.71 = 1.57 units
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Answer:
1.57 units
Step-by-step explanation:
A triangle is shown below what is the measure of
Answer:
70 Degrees
Step-by-step explanation:
All triangles add up to 180 degrees so add 44+26=70 180-70= 110 so remaining angle is 110. A straight line is 180 degrees so using the remaining angle of the blue triangle we find that 180-110=70 so B is 70 degrees.
Answer:
\(70\textdegree\)
Step-by-step explanation:
The Exterior Angle Theorem states that in a triangle, the measure of an exterior angle is equal to the sum of its two remote interior angles.
In this case, the exterior angle is ∠\(B\) and the remote interior angles measure \(44\textdegree\) and \(26\textdegree\), so \(m\)∠\(B=44+26=70\textdegree\). Hope this helps!
PLS ANSWER QUICK W EXPLANATION
Answer:
A
Step-by-step explanation:
you multiply the previous term by 4 each time, so the base is 4.
That leaves A and B remaining.
If we substitute x = 1 into the two answers, A gives you 8 like in the problem while B gives you 4.
So the answer must be A
Answer:
A
Step-by-step explanation:
When you plug in each of the x, you get the right output.
2 x (4^1)= 8
2 x (4^2) = 2 x 16 =32
2 x (4^3)= 2 x 64= 128
2 x (4^4)= 2 x 256= 512
mary receives $100 for her birthday. her grandma told her she can only spend half of the money each day. if she obeys her grandma on what day would she have spent the last of the money