Let's begin by listing out the information given to us:
Old Price = $54
New Price = $74
The percentage change is given by:
[tex]\begin{gathered} \text{\%}\Delta=\frac{|OldPrice-NewPrice|}{OldPrice}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{|54-74|}{54}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{|-20|}{54}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{20}{54}\cdot100\text{\%} \\ \text{\%}\Delta=37.04\text{\%} \\ \text{\%}\Delta\approx37\text{\%} \end{gathered}[/tex]V8 Splash $2.28 64 oz Walmart 0.04 cents per ozV8 Splash $ 2.49 64 oz Kroger 3.89 cents per ozWhich is the better deal?
Given:
V8 Splash $2.28 64 oz Walmart 0.04 cents per oz
V8 Splash $ 2.49 64 oz Kroger 3.89 cents per oz.
Best deal is
V8 Splash $2.28 64 oz Walmart 0.04 cents per oz
what is 6 exponent 7 * 4 exponent 4 * 2 / 6 exponent 5 * 4 exponent 4 * 2.2
given
[tex]\frac{6^7\cdot4^4\cdot2}{6^5\cdot4^4\cdot2^2}[/tex][tex]=6^{7-5}\cdot4^{4-4}\cdot2^{1-2}=6^2\cdot4^0\cdot2^{-1}=\frac{6^2\cdot1}{2}=\frac{36}{2}=18[/tex]Note 4 exponent 0 = 1
.converge or diverge? If it converges, to what value does it converge?
Given the series;
[tex]\sum ^{\infty}_{n\mathop=0}3(\frac{1}{5})^{n-1}[/tex]To obtain the sum of the series above and decide if it converges or diverges, we will
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}0}3(\frac{1}{5})^{n-1}=\sum ^{\infty}_{n\mathop{=}0}3(5)^{-(n-1)} \\ =\sum ^{\infty}_{n\mathop{=}0}3(5)^{(1-n)} \\ =\sum ^{\infty}_{n\mathop{=}0}15\times5^{-n} \\ =15\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n \end{gathered}[/tex]Simplify the resulting geometric series and decide if it converge or diverge
[tex]\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n\Rightarrow is\text{ an infinite geometric series, with first term a= 1 and common ratio r=}\frac{1}{5}[/tex]Solve for the sum to infinity of the geometric series
[tex]S_{\infty}=\frac{a}{1-r}=\frac{1}{1-\frac{1}{5}}=\frac{1}{\frac{4}{5}}=\frac{5}{4}[/tex]The sum of the series wil be
[tex]15\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n\Rightarrow15\times\frac{5}{4}=\frac{75}{4}[/tex]Hence,
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}0}3(\frac{1}{5})^{n-1}=\frac{75}{4} \\ \text{The series converges} \end{gathered}[/tex]12)50 students took a quiz with five questions. The frequency table below shows the results of the quiz. Use the frequency table to answer the following questions. ValueFrequencyRelative FrequencyCumulative Frequency040.084180.1612260.1218320.04204150.3355150.350
e) Finding how many students answered at most 4 questions.
The number of students that answered at most 4 questions correctly is:
Students answered 0 questions correctly + Students answered 1 question correctly + Students answered 2 questions correctly + Students answered 3 questions correctly + Students answered 4 questions correctly
So, the number of students is:
4 + 8 + 6 + 2 + 15 = 35
35 students answered at most 4 questions correctly.
f) Finding the sum of relative frequency.
The sum of relative frequency is:
0.08 + 0.16 + 0.12 + 0.04 + 0.3 + 0.3
Sum = 1.
The sum of the relative frequency in a distribution is always 1.
g) Creating a histrogram
To create a histogram, create a bar for each result correct. The values of the frequency will be used in the y-axis.
Select the correct answer from each drop-down menu.Phyllis bought 21 feet of wood to frame a window. If she makes a triangular window, what is the greatest area the window can have?For a given perimeter, the triangle with the largest perimeter isv triangle. Using this type of triangle, the sides wouldmeasureSo, the greatest area the window could be is aboutsquare feet
Equilateral Triangles
An equilateral triangle has all of its three sides of the same measure. Suppose the side length of an equilateral triangle is L.
The perimeter of such a triangle is:
P = 3L
Phyllis bought 21 feet of wood to frame a triangular window. This corresponds to the perimeter of the triangle, so we can calculate the side length:
L = P/3
L = 21 feet / 3
L = 7 feet.
Now we know the length of the side of the triangle, we calculate the area by using the formula:
[tex]A=\frac{\sqrt[]{3}}{4}L^2[/tex]Substituting L = 7 feet:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(7ft)^2 \\ A=\frac{\sqrt[]{3}}{4}49ft^2 \\ \text{Calculating:} \\ A\approx21.22ft^2 \end{gathered}[/tex]Lana owns an office supply shop. At the beginning of each school year, she chooses two or three products to donate to the local middle school.
The table shows the school supplies that Lana has in her shop and how many of each kind she has in stock. Lana is considering different options of supplies to donate. For each option, determine the greatest number of identical boxes she could pack and the number of each supply item she could put in the boxes.
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
A option 1: pencils and erasers: ____boxes with ____ pencils and ____ erasers
B option 2: notebooks and folders: ____ boxes with ____notebooks and ____ folders in each box.
C option 3: erasers, markers, and folders: ____ boxes with ____ erasers ____ markers and ____ folders in each box.
Option-1: 221 boxes with 78 pencils and 143 erasers.
Option-2: 525 boxes with 195 notebooks and 330 folders in each box.
Option-3: 583 boxes with 143 erasers 110 markers and 330 folders in each box.
Given that,
Owning an office supplies store is Lana. Each school year, she selects two or three items to give to the neighborhood middle school.
We have to find the correct answer for the given options.
The table is
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
Option1:
Pencils and erases:
78+143=221
221 boxes with 78 pencils and 143 erasers.
Option 2:
Notebooks and folders:
195+330=525
525 boxes with 195 notebooks and 330 folders in each box.
Option 3:
Erasers, markers, and folders:
143+110+330= 583
583 boxes with 143 erasers 110 markers and 330 folders in each box.
To learn more about box visit: https://brainly.com/question/28013200
#SPJ1
A car's rear windshield wiper rotates 135°. The total length of the wiper mechanism is 21 inches and the length of the wiper blade is 12 inches. Find the area wiped by the wiper blade. (Round your answer to one decimal place.)
The area wiped by the wiper blade is 424.08 in².
How to find the area?Using this formula to find the area
A= 1/2r² Ф
Where:
A = Area
r = Radius
Let plug in the formula
A = [1/2 × (21)² × 135° ×π /180 ] - [1/2 × (21 -12)² × 135° ×π /180 ]
A = [1/2 × (21)² × 135° ×π /180 ] - [1/2 × (9)² × 135° ×π /180 ]
A = [1/2 × (441) × 135° ×π /180 ] - [1/2 × (81) × 135° ×π /180 ]
A = 519.54 - 95.43
A = 424.08 in²
Therefore the area is 424.08 in².
Learn more about area here:https://brainly.com/question/25292087
#SPJ1
Which expressions are equivalent to the one below? Check all that apply.ln(e5)A.1B.5C.5 • ln eD.5e
SOLUTION:
We want to find the equivalent expression to;
[tex]ln(e^5)[/tex]We can rewrite it as;
[tex]\begin{gathered} 5ln(e) \\ =5 \end{gathered}[/tex]Thus, the answers are;
[tex]5Ine\text{ }and\text{ }5[/tex]OPTION B and C
Find a recursive formula for the following sequence:4, 11, 25, 53, 109, ...
Notice the following pattern in the given sequence:
[tex]\begin{gathered} 11=4\cdot2\text{ +3,} \\ 25=11\cdot2+3, \\ 53=25\cdot2+3, \\ 109=53\cdot2+3. \end{gathered}[/tex]Therefore, the n-term of the sequence has the following form:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]Answer:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]Determine the interest rate capitalized once in a year which can triple any amount in 6 years
ANSWER
interest rate = 20%
EXPLANATION
let P = x, A = 3x, t = 6 and R = ?
[tex]A\text{ = P}\ast(1+R)^t[/tex][tex]\begin{gathered} 3x=x(1+R)^6 \\ 3=(1+R)^6 \\ 1+R=3^{\frac{1}{6}} \\ 1+R\text{ = 1.2} \\ R\text{ = 1.2 - 1} \\ R\text{ = 0.2} \\ R\text{ = 20\%} \end{gathered}[/tex]jessica needs to bake 50 muffins her baking pan holds 12 muffins how many rounds of baking will she need to do
Let x be the number of rounds of baking. Jessica's baking pan holds 12 muffins. Total 50 muffins is to be made. Hence, we can write,
[tex]\begin{gathered} 12x=50 \\ x=\frac{50}{12}=\frac{25}{6}=4\frac{1}{6} \end{gathered}[/tex]So, we obtained that x is equal to 4 1/6. The number of rounds cannot be a fraction. Here, the number of rounds is equal to the sum of 4 and a fraction 1/6. So, we can say that 5 rounds is needed to make 50 muffins.
1. On a number line, graph the solution to the inequality -5(x + 1) > 7x +31? Also, write thesolution in interval notation.
We have the following:
[tex]\begin{gathered} -5\cdot\left(x+1\right)>7x+31 \\ -5x-5>7x+31 \\ -5x-5+5>7x+31+5 \\ -5x-7x>7x+36-7x \\ -12x>36 \\ x>\frac{36}{-12} \\ x<-3 \end{gathered}[/tex]interval notation:
[tex](-\infty,-3)[/tex]graph:
MATH HELP WILL MARK BRAINLEST
Evaluate the following expression.C(8,3)C=combinations
The formula for combination is
nCr = n!/(n - r)!r!
C represents the number of combinations
n represents the total number of objects to choose from
r represents the number of items selscted from n
From the information given,
n = 8 and r = 3
8C3 = 8!/(8 - 3)!3!
= 8! /5!3!
= 8 * 7 * 6 * 5 * 4 * 3!/5 * 4 * 3 * 2 * 1 * 3!
The 3! cancels out. It becomes
8 * 7 * 6 * 5 * 4 /5 * 4 * 3 * 2 * 1
= 6720/120
= 56
The answer is 56
REWRITE EACH PROBLEM AS A MULTIPLICATION QUESTION!!!Students were surveyed about their favorite colors. 1/4 of the students preffered red, 1/8 of the students blue, and 3/5 of the remaining students preffered green. If 15 students preffered green, how many student were surveyed?
Let there are x total student surveyed, the 1/4x students prefer red, 1/8x prefer blue.
Determine the remaining students.
[tex]\begin{gathered} S=x-\frac{x}{4}-\frac{x}{8} \\ =\frac{8x-2x-x}{8} \\ =\frac{5}{8}x \end{gathered}[/tex]Determine the students that prefer green.
[tex]\frac{3}{5}\cdot\frac{5}{8}x=\frac{3x}{8}[/tex]The students who preferred green is 15. So equation for x is,
[tex]\begin{gathered} \frac{3x}{8}=15 \\ x=\frac{15\cdot8}{3} \\ =40 \end{gathered}[/tex]So total students that were surveyed is equal to 40.
1,1,2,6,24,_,_,_,_A) explain and complete the sequenceB) write an explicit and recursive formula for the sequence
As you can notice, this sequence is detailed as follows:
[tex]\begin{gathered} 1\cdot1=1 \\ 1\cdot2=2 \\ 2\cdot3=6 \\ 6\cdot4=24 \end{gathered}[/tex]Now, let's find the next four terms:
[tex]\begin{gathered} 24\cdot5=120 \\ 120\cdot6=720 \\ 720\cdot7=5040 \\ 5040\cdot8=40320 \end{gathered}[/tex]A possible formula could be:
[tex]a_n=n\cdot a_{n-1}[/tex]Where "n" is the number of the term given and it starts from 1. (a0 is 1) This is:
[tex]\begin{gathered} a_1=1.a_{1-1}=1\cdot a_0=1_{} \\ a_2=2\cdot a_{2-1}=2\cdot a_1=2 \\ a_3=3\cdot a_{3-1}=3\cdot a_2=6 \\ \text{and so on } \end{gathered}[/tex]-9 is to the _____ of -3 on a number line so -9 is _____ than -3.right left more less
Answer:
-9 is to the left of -3
-9 is less than -3
Explanation:
If we're to write -9 and -3 on a number line from right to left, we'll see that -3 is going to come before -9, which means that -9 is to the left of -3.
On a number line, any number to the left of another number is less than the other number.
Since -9 is to the left of -3, so -9 is less than -3
1.Given the Graph Circle One: Arithmetic, Geometric, or Neither Circle One: Common Ratio or Common difference: recursive formula-explicit formula-find the 5th term-
We can see in the graph that for every increment in x, the y-value is halved (that is, multiplied by 1/2).
Since the y-values are being multiplied for every increment of x, we have a geometric sequence or function.
Also, the function has a common ratio, which is the value 1/2 that multiplies y for every increment of x.
Last, we have a recursive formula: each value of y is half of the previous value of y (a_n = (1/2) * a_(n-1))
In order to find the explicit formula, since we have an exponential function, we can use the model y = a*b^x.
Using the points (1, 32) and (2, 16), we have:
[tex]\begin{gathered} 32=a\cdot b^1\to a=\frac{32}{b} \\ 16=a\cdot b^2\to b^2=\frac{16}{a}=\frac{16b}{32}\to b=\frac{1}{2} \\ 32=a\cdot\frac{1}{2}\to a=64 \end{gathered}[/tex]So the explicit function is y = 64 * (1/2)^x.
Looking at the graph, the 5th term of the sequence (x = 5) is found by halving the value y = 8 two times, so the 5th term is 2.
Do You Know How? In 3-8, estimate each product using rounding or compatible numbers. 4. 104 x 0.33 3. 0.87 x 112 0.90x110=99 6. 0.54 x 24 5. 9.02 x 80 9x80=720 7. 33.05 x 200 a. 0,79 x 51
Estimating Products
Some operations can be estimated and its results approximated by using rounding and number that are easier to calculate.
For example the product 0.87*112 can be estimated by using 0.9 (a very close rounded number) and 110 instead of 112. One of the factors was rounded up and the other was rounded down. The product should be very close to the real exact product.
Now for 104*0.33. 104 can be rounded to 100 and it can be easily multiplied by 0.33. 100*0.33 = 33
0.54*24 can be estimated as 0.5*26=13 or as 0.6*30=18
33.05*200 is approximated as 33*200 = 6600
0.79*51 is estimated as 0.8*50 = 400
Some of the estimations above can be challenged and some people can propose better combinations for more accurate results. It's a subjective task.
Kelly and nadir both had maths tests last week, Kelly scored 47/68 and nadir scored 35/52. Who got the higher percentage score
Answer:
Kelly got a higher percentage score.
Step-by-step explanation:
35 / 52 = 0.673
47 / 68 = 0.691
Calculate the percent error. Darwin’s coach recorded that he had bowled points out of in a bowling tournament.
Given:
The recorded value is 250 points.
The true value is 300 points.
To find the percent error:
Using the formula,
[tex]P\text{ercent error}=\frac{|recorded\text{ value}-\text{true value|}}{\text{True value}}\times100\text{ \%}[/tex]On substitution we get,
[tex]\begin{gathered} =\frac{|250-300|}{300}\times100 \\ =\frac{50}{300}\times100 \\ =16.67\text{ \%} \end{gathered}[/tex]Hence, the percent error is 16.67 %.
what is the correct trigonometric ratio for the tangent of A?
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the figure,
opposite =8 and adjacent= 15
[tex]\tan A=\frac{8}{15}[/tex]In the diagram, line AB is parallel to DE. Also, line DE is drawn such that the length of line DE is half the length of line AB. If sin A=0.5, then what is sin E?
By alternate interior angle theorem. Angle A is congruent with Angle E.
This makes ΔAFB similar to ΔEFD.
IF sin A = 0.5, then sin E is also equal to 0.5.
The volume of dis rectangular prism is zero. Seven to a cubic yards. What is the value of C in yards?
To get the volume of a prims, we do the products of the base times its height.
Being a rectangular prims, the area of its base is the product of its dimesions, so the volume of a rectangular prism is simply the product of its three dimensions:
[tex]V=l\cdot w\cdot h=1.3\cdot1.4\cdot c=1.82c[/tex]Since the volume is equal to 0.728 yd³, we have:
[tex]\begin{gathered} 0.728=1.82c \\ c=\frac{0.728}{1.82}=0.4 \end{gathered}[/tex]So, the measure of c is 0.4 yards.
The table below shows the probability distribution of a random variable X Х P(X) -10 0.07 -9 0.09 -8 0.67 -7 0 -6 0.17 What is the expected value of X? Write your answer as a decimal.
Teshawn, this is the solution to the problem:
We use the following formula to calculate the expected value of x, as follows:
Expected value of x = -10 * 0.07 + - 9 * 0.09 + -8 * 0.67 + -7 * 0 + -6 * 0.17
Expected value of x = -0.7 + -0.81 + - 5.36 + 0 + - 1.02
Expected value of x = -0.7 - 0.81 - 5.36 - 1.02
Expected value of x = -7.89
Suppose your final grade in this class is based on the following system:Class participation 10% homework 20%test average 30% final exam 25%quiz average 15%Given the grades listed below, what would your final grade in the class be?test grades(78, 87, 93, 75) quiz average (85)Class participation (95) homework(75)final exam(63)choices:A. 83B. 70C. 88D. 78
to find a percentage we multiply by the number and divide by 100
class participation
[tex]\begin{gathered} 95\times\frac{10}{100} \\ =9.5 \end{gathered}[/tex]homework
[tex]\begin{gathered} 75\times\frac{20}{100} \\ =15 \end{gathered}[/tex]test average
first find the average
[tex]\begin{gathered} \frac{78+87+93+75}{4} \\ =83.25 \end{gathered}[/tex]then the percentage
[tex]\begin{gathered} 83.25\times\frac{30}{100} \\ =24.975 \end{gathered}[/tex]Final Exam
[tex]\begin{gathered} 63\times\frac{25}{100} \\ =15.75 \end{gathered}[/tex]Quiz average
[tex]\begin{gathered} 85\times\frac{15}{100} \\ =12.75 \end{gathered}[/tex]finally we add to get the final grade
[tex]\begin{gathered} 9.5+15+24.975+15.75+12.75 \\ =77.97 \end{gathered}[/tex]the final grade is 78
The mean height of men is known to 5.9 ft with a standard deviation of 0.2 ft. The height of a man (in ft) corresponding to a z-score of 2 is:Group of answer choices6.16.36.25.9
The average height is μ= 5.9ft and has a standard deviation of σ=0.2ft.
You have to determine the height (X) for the Z-score z=2
To determine this value, you have to use the formula of the standard deviation:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]First, write the equation for X:
-Multiply both sides by sigma:
[tex]\begin{gathered} Z\sigma=\sigma\frac{X-\mu}{\sigma} \\ \\ Z\sigma=X-\mu \end{gathered}[/tex]-Add mu to both sides of it:
[tex]\begin{gathered} (Z\sigma)+\mu=X-\mu+\mu \\ X=(Z\sigma)+\mu \end{gathered}[/tex]Replace the expression obtained for X with the known values of z, sigma, and mu
[tex]\begin{gathered} X=2\cdot0.2+5.9 \\ X=\text{0}.4+5.9 \\ X=6.3 \end{gathered}[/tex]The height of a man that corresponds to z=2 is 6.3 ft
If Guillermo deposits $5000 into an account paying 6% annual interest compounded monthly, how long until there is $8000 in the account?
We have the following:
The formula in this case is the following:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]solving for t:
replacing
A is 8000, P is 5000, n is 12 and r is 6% (0.06)
[tex]\begin{gathered} 8000=5000(1+\frac{0.06}{12})^{12t} \\ \frac{8000}{5000}=1.005^{12t} \\ \ln (\frac{8}{5})=12\cdot t\ln (1.005)_{} \\ t=\frac{\ln (\frac{8}{5})}{12\ln (1.005)} \\ t=7.85 \end{gathered}[/tex]therefore, the answer is 7.9 years
Bob's Car Wash had to close 26 days last year because of bad weather. If last year had 365 days, what is the ratio of days closed to days open for Bob's Car Wash?OA. 26 to 339OB. 26 to 365OC. 365 to 26OD. 339 to 26
Days closed = 26
Days open = Total days - days closed = 365 -26 = 339
Days closed to days open:
26 to 339
when plqying a math game in class you drew 5 cards and had to find the sum of the numbers. your numbers were -9 3 2 - 5 4. what was the sum of your hand
We are required to sum up the numbers obtained. Our approach is to add the negative numbers separately and the positive numbers separately and then add up both.
[tex]\begin{gathered} (-9)+3+2+(-5)+4=3+2+4+(-9)+(-5) \\ 3+2+4=9 \\ -(9+5)=-14 \\ \text{Adding both} \\ 9+(-14)=9-14=-5 \end{gathered}[/tex]-5 is our answer.