The percentage rise of Jane= 7%.
What is percentage ?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentage Increase/ Rise and Decrease/ Fall
The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.
% increase = [(New number – Original number)/Original number] x 100
where,
increase in number = New number – original number
Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100.
% decrease = [(Original number – New number)/Original number] x 100
Where decrease in number = Original number – New number
So basically if the answer is negative then there is a percentage decrease.
In the given question , Jane earns initially = £11 400 per year
After rise Jane earns = £12 198 per year.
Percentage rise = [(New number – Original number)/Original number] x 100
Percentage rise = [( 12198 – 11400)/11400] x 100
= [( 798)/11400] x 100= 0.07 × 100 = 7%
So the percentage rise of Jane= 7%.
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Which of the following is an arithmetic sequence? A. 1, 0, 1, 0, 1, 0, ...B. 800, 200, 50, ...C. 10, 7, 4, 1, -2, ...D. 1, 3, 9, 27,...
Given:
The sequences in options.
Required:
Which of the sequence is an arithmetic sequence.
Explanation:
The arithmetic sequence has a common ration, that is equal for every pair of number
[tex]d=a_2-a_1,d=a_3-a_2[/tex]Now, in option c
[tex]\begin{gathered} d=7-10=-3 \\ d=4-7=-3 \\ d=1-4=-3 \end{gathered}[/tex]So, common ratio is -3 and hence sequence is arithmetic sequence.
Answer:
So, option c is correct.
2. The line plot shows the results of a survey about kitchen sinks. Kitchen Sink Survey + 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Capacity (gallons) Write a paragraph summarizing the data set. In your summary include the following A description of the data, including the unit of measure The number of data values The shape of the distribution The value of an appropriate measure of center The value of an appropriate measure of spread
Given: The information and line plot showing
..
From the plot we can write a table of values for the data
From the table we can get the mean
[tex]\begin{gathered} M_{\text{ean}}=\frac{\Sigma fx}{\Sigma f} \\ M_{\text{ean}}=\frac{(12\times0+13\times1+\ldots+24\times1+25\times0)}{1+2+4+5+...+1+0} \\ M_{\text{ean}}=\frac{354}{21} \\ M_{\text{ean}}=16.86 \\ M_{\text{ean}}\approx17 \end{gathered}[/tex]The standard deviation
[tex]\begin{gathered} S_{\text{tandard deviation}}=\sqrt[]{\frac{\Sigma f(x-\mu)^2}{\Sigma f}} \\ S_{\text{tandard deviation}}=\sqrt[]{\frac{0(12-17)^2+1(13-17)^2+\cdots+1(24-17)^2}{21}} \\ S_{\text{tandard deviation}}=\sqrt[]{\frac{150.571}{21}} \\ S_{\text{tandard deviation}}=2.68 \end{gathered}[/tex]ANSWER SUMMARY
It can be observed that the capacity of the kitchen sink ranges from 12 gallons to 25 gallons. There are 21 kitchen sink with different capacity in gallons. The shape of the distribution is skewed right with an appropriate measure of centre (that is the mean) as 17 gallons. The measure of spread including the range (between 13 gallons to 24 gallons) is 11 gallons, the median is 16 gallons sink and the standard deviation is 2.68 gallons
Answer:
poopsicle
Step-by-step explanation:
Perform the indicated operation 4.8L +12.6L
To perform a operation with the same variable (L), add or subtract the coefficients before the variable and keep the variable.
4.8 L + 12.6 L
(4.8 + 12.6) L
17.4L
Answer: 17.4 L.
what's false 16 / 10 equal 25 / 40
10/16 = 25/40
Divide each
0.625 = 0.625
Second option:
15/60= 35/140
0.25 = 0.25
Third option
24/36=50/75
0.6666= 0.6666
Fourth option
14/35=35/70
0.4=0.5
FALSE
A. 12in ^2B. 30 in ^2C. 24 in ^2 D. 27 in 2pls help with guided practice
The given figure is a parallelogram. The formula for determining the area of a parallelogram is expressed as
Area = base * height
From the diagram,
base = 9 inches
height = 3 inches
Area = 9 * 3 = 27 in^2
The correct option is D
Find the value of x and the value of y.A. x = 15, y = 10sqrt3B. r = 20, y = 10sqrt3C. r = 20sqrt3, y = 5sqrt3D. x=15, y = 5sqrt3
To find the values of x and y it is necessary to use trigonometric ratios.
To find x it is necessary to use sine. Sine is the ratio between the opposite side to a given angle and the hypotenuse. In this case, the given angle is 60°, the opposite side is x and the hypotenuse is 10 sqrt 3. Use this information to find x:
[tex]\begin{gathered} \sin 60=\frac{x}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\sin 60=x \\ x=15 \end{gathered}[/tex]To find y it is necessary to use cosine. It is the ratio between the adjacent side to a given angle and the hypotenuse. The given angle is 60°, the adjacent side is y and the hypotenuse is 10 sqrt 3. Follow the same procedure as with sine:
[tex]\begin{gathered} \cos 60=\frac{y}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\cos 60=y \\ y=5\sqrt[]{3} \end{gathered}[/tex]The correct answer is D. x=15, y=5sqrt3.
A rock is thrown upward from the top of a 80-foot high cliff overlooking the ocean at a speed of 64 feetper second The rock's height above ocean can be modeled by the equationH (t) = -16t^2 +64t + 80.a. When does the rock reach the maximum height?The rock reaches its maximum height after ________second(s).b. What is the maximum height of the rock?The maximum height obtained by the rock is_______feet above sea level.c. When does the rock hit the ocean?The rock hits the ocean after_____seconds.
Given:
The speed is 64 feet per second.
The height of the high cliff is 80 feet.
The function is
[tex]H(t)=-16t^2+64t+80[/tex]a)
We need to find the maximum value of t in the given function to find a time when the rock reaches its maximum height.
Differentiate the given equation, we get
[tex]H^{\prime}(t)=-16(2t)^{}+64[/tex][tex]H^{\prime}(t)=-32t^{}+64[/tex]Set H'(t)=0 and solve for t.
[tex]0=-32t^{}+64[/tex]Adding 32t on both sides, we get
[tex]0+32t^{}=-32t+64+32t[/tex][tex]32t^{}=64[/tex]Dividing both sides by 32, we get
[tex]\frac{32t}{32}^{}=\frac{64}{32}[/tex][tex]t=2[/tex]Hence the rock reaches its maximum height after 2 seconds.
b)
Substitute t=2 in the given equation to find the maximum height of the rock.
[tex]H(2)=-16(2)^2+64(2)+80[/tex][tex]H(2)=144[/tex]Hence the maximum height obtained by the rock is 144 feet above sea level.
c)
Substitute H(t)=0 in the given function to find the time when the rock hit the ocean.
[tex]0=-16t^2+64t+80[/tex]Dividing both sides by (-16), we get
[tex]0=-\frac{16t^2}{-16}+\frac{64t}{-16}+\frac{80}{-16}[/tex][tex]0=t^2-4t-5[/tex][tex]t^2-4t-5=0[/tex][tex]t^2+t-5t-5=0[/tex][tex]t(t+1)-5(t+1)=0[/tex][tex](t+1)(t-5)=0[/tex][tex](t+1)=0,(t-5)=0[/tex][tex]t=-1,t=5[/tex]Omitting the negative value, we get t= 5 seconds.
Hence the rock hits the ocean after 5 seconds.
Sophie put $3330 in a savings account at a simple interest rate of 7.4% per year.
Adam put $2795 in a savings account at a simple interest rate of 8.1% per year.
Who will have earned more interest after 5 years? How much more?
Sophie earned more simple interest of $100.
Simple interest is a short and easy technique for calculating the interest price on a mortgage. simple interest is decided with the aid of multiplying each day's interest charge via the most important by the variety of days that elapse among bills.
To calculate Simple interest, multiply the main quantity by using the interest charge and the time. The method written out is Simple interest = principle x interest price x Time." This equation is the most effective way of calculating interest.
Calculation:-
For Sophie
SI = PRT/100
= ($3330 × 7.4 × 5 ) /100
= $1232
For Adam
SI = PRT/100
= ($2795 × 8.1 × 5 ) /100
= $1132
Therefore, Sophie earned more interest of $1232 - $1132 = $100
simple interest is based on the most important amount of a loan or the primary deposit in a financial savings account. simple interest doesn't compound, and because of this a creditor will most effectively pay interest on the foremost amount, and a borrower might in no way have to pay extra interest at the previously amassed interest.
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if f(x) = 13 when f(x)=5x -√8, find x.
Given that we have the function f(x) = 5x-√8, it is equal to 13 at some value of x. This relation can be written in equation as
[tex]5x-\sqrt[]{8}=13[/tex]Move √8 to the other side of the equation so that only the term with x will be left on the left-hand side. We have
[tex]5x=13+\sqrt[]{8}[/tex]Divide both sides by 5, we get
[tex]\begin{gathered} \frac{5x}{5}=\frac{13+\sqrt[]{8}}{5} \\ x=\frac{13+\sqrt[]{8}}{5} \end{gathered}[/tex]The square root of 8 can be further simplified as
[tex]\sqrt[]{8}=\sqrt[]{4\cdot2}=2\sqrt[]{2}[/tex]Hence, the value of x can also be rewritten as
[tex]x=\frac{13+2\sqrt[]{2}}{5}[/tex]Thus, the value of x to satisfy f(x) = 13 when f(x)=5x -√8 is
[tex]x=\frac{13+\sqrt[]{8}}{5}=\frac{13+2\sqrt[]{2}}{5}=\frac{13}{5}+\frac{2\sqrt[]{2}}{5}[/tex]what is the perimeter? and what unit should i use?
The given information is:
- 7-gon: it has 7 sides.
- a=15 ft
- s=14 ft
The perimeter, is the sum of the side lengths, as it has 7 sides, then its perimeter is:
[tex]\begin{gathered} P=7s \\ P=7*14ft \\ P=98ft \end{gathered}[/tex]Now, the area is given by the formula:
[tex]\begin{gathered} A=\frac{7}{2}(s*a) \\ \\ A=\frac{7}{2}(14ft*15ft) \\ \\ A=\frac{7}{2}(210ft^2) \\ \\ A=\frac{1470ft^2}{2} \\ \\ A=735ft^2 \end{gathered}[/tex]The area is 735 square feet
Solve x2-12x + 11 = 0 by completing the square.
Given: A quadratic equation-
[tex]x^2-12x+11=0[/tex]Required: To solve the equation by completing the square method.
Explanation: The general form of a quadratic equation is-
[tex]ax^2+bx+c=0[/tex]The given equation can be solved by the method of completing the square by adding and subtracting the term-
[tex](\frac{b}{2})^2[/tex]Hence, the given equation can be written as-
[tex]x^2-12x+36-36+11=0[/tex]Now solving further as-
[tex]\begin{gathered} x^2-2\times6\times x+6^2-25=0 \\ (x-6)^2=25 \\ (x-6)=\sqrt{25} \\ (x-6)=\pm5 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} x-6=5\text{ or } \\ x-6=-5 \end{gathered}[/tex]This gives-
[tex]\begin{gathered} x=11\text{ or} \\ x=1 \end{gathered}[/tex]Final Answer: The solution to the equation is x=11 or x=1.
In the figure below, AB is an angle bisector. What is the value of x? Show and explain work
Since AB is the angle bisector:
[tex]\begin{gathered} m\angle CAB=m\angle DAB \\ so\colon \\ 33=4x+1 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 4x=33-1 \\ 4x=32 \\ x=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Answer:
x = 8
Probability of dependent events2/5EspanolA department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 5 live in the town of Gaston,2 live in Pike, and 2 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Gaston? Write your answer as afraction in simplest form.0DOХ5?
Given there are 9 customers who have entered the drawing, 5 live in the town of Gaston, 2 live in Pike, and 2 live in wells. Two winners will be selected at random.
We have to find the probability that both winners live in Gaston.
The probability that the first winner selected is from Gaston is:
[tex]P(A)=\frac{5}{9}[/tex]The probability that the second winner selected is from Gaston is:
[tex]P(B|A)=\frac{4}{8}=\frac{1}{2}[/tex]The probability that both winners live in Gaston is:
[tex]\begin{gathered} P(A\cap B)=P(A)\cdot P(B|A) \\ =\frac{5}{9}\cdot\frac{1}{2} \\ =\frac{5}{18} \end{gathered}[/tex]Thus, the answer is 5/18.
5 markers cost $6.55.Which equation would help determine the cost of 4 markers?
5 markers -------> $6.55
4 markers -------> x
[tex]undefined[/tex]Help Dalton explain his work. Complete the paragraph.One way to show that FGHI is a rectangle is to show that all 4 of its angles are rightangles. So, I found the slope of each side. The slope of FG and IH wasTheslope of FI and GH wasThen I knew that ZF, LG, ZH, and ZI were all rightangles becauselines have
ANSWERS
...The slope of FG and IH was 4/5. The slope of FI and GH was -5/4. Then I knew that ∠F, ∠G, ∠H, and ∠I were all right angles because perpendicular lines have opposite reciprocal slopes.
EXPLANATION
The slope of a line is given by,
[tex]m=\frac{\Delta y}{\Delta x}[/tex]For lines FG and IH, the slope is,
[tex]m_{FG}=m_{IH}=\frac{8}{10}=\frac{4}{5}[/tex]Similarly, the slope of lines FI and GH is,
[tex]m_{FI}=m_{GH}=\frac{5}{-4}=-\frac{5}{4}[/tex]Note that the slopes are opposite reciprocals, which makes each pair of lines perpendicular lines.
Find the measure of chord EF. Enter your numerical answer.
Notice that each chord (CD and EF) defines a segment in the circle whose arc length has the same value. Thus, the length of both chords has to be the same; then,
[tex]\begin{gathered} CD=EF \\ \Rightarrow9x-1=41-5x \\ \Rightarrow14x=42 \\ \Rightarrow x=3 \end{gathered}[/tex]Finding the length of EF,
[tex]\begin{gathered} x=3 \\ \Rightarrow EF=41-5*3=26 \end{gathered}[/tex]Therefore, the answer is 26
A city is built on the banks of a river and some islands in the river. The map below shows the bridges connecting the various land masses. Draw a graph that models the connecting relationships in the map below. The vertices represent the land masses and the edges represent bridges connecting them. Is it possible to find a circuit through the city that uses each bridge once? If so, enter the sequence of land masses(vertices) visited, for example ABDEA. If it is not possible, enter DNE. Use Fleury's algorithm and show all work and the graph as demonstrated in class.
We can graph the model as:
The Fleury's algorithm start with any vertex, and then select an edge that start from this vertex and go to another vertex. Then we pick another edge that starts from the last vertex, and so on. The condition is that all the vertices in the graph are always connected to each other: that is, there is always a path to conect any two vertices.
We start with A.
We can go to C, then B, then D, then E, then A.
After this part, we are left with these edges:
As the last vertex was A, we start from there.
We go to D, then to B, then to C, then to A again and we end in E.
We are never able to go back to the vertex we start (A), so there is no possible sequence.
Answer: DNE
Disprove each statement , and then find all values of a and b for which the statement happens to be true . Explain your results If f(x) = x ^ (1/3) does f(a + b) = f(a) + f(b) ?
We are given the following function:
[tex]f(x)=x^{\frac{1}{3}}[/tex]To determine the value of f(a) we will replace the value of "x" for "a" in the function:
[tex]f(a)=a^{\frac{1}{3}}[/tex]Using the same procedure we determine the value of f(b):
[tex]f(b)=b^{\frac{1}{3}}[/tex]Now we determine the value of f(a+b):
[tex]f(a+b)=(a+b)^{\frac{1}{3}}[/tex]We are asked about the equatity:
[tex]f\mleft(a+b\mright)=f\mleft(a\mright)+f\mleft(b\mright)[/tex]replacing the values we get:
[tex](a+b)^{\frac{1}{3}}=a^{\frac{1}{3}}+b^{\frac{1}{3}}[/tex]We get an equality that is not true for any value of "a" and "b" since the left expression can't be converted into the right expression for any "a" or "b". The statement is false.
The statement could be right if "a" or "b" equal zero, for example, let's take a = 0, we get:
[tex](0+b)^{\frac{1}{3}}=(0)^{\frac{1}{3}}+b^{\frac{1}{3}}[/tex]Simplifying:
[tex]b^{\frac{1}{3}}=b^{\frac{1}{3}}[/tex]Which is a true statement. .
Simplify the following union and/or intersection.Answer(-∞, 3] n [3, 13)
Given:
[tex](-\infty,3]\cap[3,13)[/tex]Required:
Simplify the intersection.
Explanation:
The given intersection is
[tex](-\infty,3]\cap[3,13)[/tex]The first interval includes the values greater than
[tex]-\infty[/tex]to equal 3 and the second interval includes the values from 3 to less than 13.
The intersection in both intervals is only the value 3.
Final Answer:
The intersection value is 3.
How many radians are in a full rotation around a circle, or 360°?
Given:-
A full rotation.
To find the correct radians.
So as we know full rotation means 360 degree.
Also we know,
[tex]\pi=180[/tex]So for getting 360 degree. we get,
[tex]2\times180=360[/tex]So the required solution is,
[tex]2\pi[/tex]Jack needs to order some new supplies for the restaurant where he works. The restaurant needs at least 711 glasses. There are currently 206 glasses. If each set on sale contains 10 glasses, write and solve an inequality which can be used to determine ss, the number of sets of glasses Jack could buy for the restaurant to have enough glasses.
Jack needs to buy at least 51 sets of glasses to ensure that the restaurant has enough glasses.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Let s be the number of sets of glasses that Jack needs to buy.
According to the problem, the restaurant needs at least 711 glasses, and currently has 206. So Jack needs to buy:
711 - 206 = 505 glasses
Since each set contains 10 glasses, the total number of glasses Jack can buy is:
10s
To have enough glasses, the total number of glasses Jack buys must be greater than or equal to 505. So we can write the inequality:
10s ≥ 505
To solve for s, we can divide both sides by 10:
s ≥ 50.5
Since s must be a whole number (you can't buy half a set of glasses), we round up to the nearest integer:
s ≥ 51
Therefore, s ≥ 51.
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> Next question Get a similar question You can retry this a 8.1 ft 9.7 10.6 Name the Shape: • triangle trapezoid kite parallelogram
The given figure is has three sides and three vertices : Triangle
In the given triangle, height = 9.7 ft, base = 8.1 ft,
Area of triangle = 1/2 x Base x Height
Area of traingle = 1/2 x 8.1 x 9.7
Area of traingle = 39.28 ft²
Area of the given figure = 39.28 ft²
The following sequence has a degree of 3:3, -4, -23, -60, -121, -212, -339, ....TrueFalse
-4 -23 -60 -121 -212 -339
27 37 61 91 127
False, this sequence does not have a degree of 3
graph the equation shown below by transforming the given graph of the parent function. y = 2x²
We have that the parent function is multiplied by 2, therefore, the graph for y = 2x^2 will compress in comparison with the graph of y=x^2
Both graphs would looke like this:
where the black graph represents the functon y = 2x^2 and the red graph represents the function y = x^2
The number of protozoa in a biology laboratory experiment is given by the polynomial functionp(t) = 0.02t^4 + 0.3t^3 + 7t^2, where p is the number of protozoa after t hours.Step 2 of 2: How many protozoa are present after 2 days? Round your answer to the nearest wholenumber.
In order to calculate the number of protozoa after 2 days (that is, 48 hours), let's use t = 48 in the function p(t) and calculate its value:
[tex]\begin{gathered} p(t)+0.02t^4+0.3t^3+7t^2 \\ p(48)=0.02\cdot48^4+0.3\cdot48^3+7\cdot48^2 \\ p(48)=0.02\cdot5308416+0.3\cdot110592+7\cdot2304 \\ p(48)=106168.32+33177.6+16128 \\ p(48)=155473.92 \end{gathered}[/tex]Rounding to the nearest whole number, the number of protozoa is 155474.
Find the lowest multiple of each group.show the factors you used.1. 5,20,28
Given the following question:
1, 5, 20, 28
1 = 1
5 = 5
20 = 2 × 2 × 5
28 = 2 × 2 × 7
2 × 2 × 5 × 7
2 × 2 = 4
4 × 5 = 20
20 × 7 = 140
LmM = 140
Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. What is the probability distribution forthe 30 pieces of fruit, in the order listed?FruitNumber ofpiecesProbabiltyApples Bananas62
Answer:
D.
Explanation:
We were given that:
A company provides fruit for its employees
The employees can pick among five kinds of fruit
The fruits obtained this week is:
Apples = 6 pieces
Bananas =2 pieces
Lemons = 10 pieces
Oranges = 8 pieces
Pears = 4 pieces
Total = 30 pieces
The probability distribution for this is given by:
[tex]\begin{gathered} P(apples)=\frac{Number\text{ of apples}}{Total}=\frac{6}{30}=\frac{1}{5} \\ P(apples)=\frac{1}{5} \\ \\ P(bananas)=\frac{Number\text{ of bananas}}{Total}=\frac{2}{30}=\frac{1}{15} \\ P(bananas)=\frac{1}{15} \\ \\ P(lemons)=\frac{Number\text{ of lemons}}{Total}=\frac{10}{30}=\frac{1}{3} \\ P(lemons)=\frac{1}{3} \\ \\ P(oranges)=\frac{Number\text{ of oranges}}{Total}=\frac{8}{30}=\frac{4}{15} \\ \\ P(pears)=\frac{Number\text{ of pears}}{Total}=\frac{4}{30}=\frac{2}{15} \\ P(pears)=\frac{2}{15} \\ \\ \therefore P=\frac{1}{5},\frac{1}{15},\frac{1}{3},\frac{4}{15},\frac{2}{15} \end{gathered}[/tex]Therefore, the answer is D
13. If a trapezoid has base lengths of 18and 40, what is the length of themedian?I●
The median of a trapezoid is a straight line that goes from the midpoint of one of the sides to the midpoint of the opposite side and is parallel to both bases.
Its length is the average of the lengths of both bases:
[tex]median=\frac{(upper.base+lower.base)}{2}[/tex]One of the bases of the trapezoid has a length of 18 units and the other base has a length of 40 units. Average both bases to determine the length of the median:
[tex]\begin{gathered} median=\frac{18+40}{2} \\ median=\frac{58}{2} \\ median=29 \end{gathered}[/tex]The length of the median is 29 units.
three points a b and c exist in space such that b is between a and C it is known that AB = 7 , BC= 4 and AC = 9 . Ar epoints a b and c Collinear? give a written explanation supported by mathematical evidence for your answer.
Points are collinear if they are in the same line.
So:
AB+BC = AC
Replacing with the values given:
7+4 = 9
11 =9 False
A,b, and c aren't collinear.
What is the range of the function?2.-54-3-22-1-2 -3 -4
We need to find the range of a function given in graph form. The graph is shown below:
So we need to recall what Range is: the set of y-values that are in fact connected to x-values in our function.
So looking at the image given we realize that the curve that represents such connection does not go further up in the y-axis than the value y = 4.
On the other hand, since the image has branches going down, it seems that all the values for y are represented in that portion of the lower part of the graph.
We can then say that the set of y-values of the Range is defined as:
(in set-builder notation form) ;
[tex]\text{Range}=\left\lbrace y\right|y\leq4\}[/tex]which reads as:
Range = the set of all the y-values that are less than or equal to 4.