The markup amount on the sweater of cost price $15 is $3.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A clothing store buys a sweater for $15 before marking it up by 1/5.
So, the markup amount can be obtained if we multiply the cost price by the fraction of mark up which is,
= 15×(1/5).
= 3.
The markup price is $3.
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verify that (sin x -cos x)^2 =1-2 sin x cos x is an identity
By trigonometric formulas and algebra properties, the equivalence between the trigonometric expression (sin x - cos x)² and the trigonometric expression 1 - 2 · sin x · cos x.
How to prove the equivalence between two trigonometric expressions
In this problem we need to prove if the trigonometric expression (sin x - cos x)² is equivalent to the trigonometric expression 1 - 2 · sin x · cos x, this can be proved by trigonometric formulas and algebra properties. First, write the initial expression:
(sin x - cos x)²
Second, expand the binomial:
sin² x - 2 · sin x · cos x + cos² x
Third, use the fundamental trigonometric expression:
1 - 2 · sin x · cos x
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NO LINKS!! Fredrico's Bank will you decide how often your interest will be computed, but with certain restrictions. Read the following options. What is the best deal after one year? Justify your answer.
Compounded quarterly; annual interest rate is 7.875%
========================================================
Explanation:
Let's say we are depositing P = 100 dollars, and we leave it in the account for a timespan of t = 1 year.
This will apply for options A through E.
-------------------
If we go with option A, then we would have n = 1 and r = 0.08
Use the compound interest formula to get the following:
A = P*(1+r/n)^(n*t)
A = 100*(1+0.08/1)^(1*1)
A = 108
We'll have $108 dollars in the account at the end of 1 year if we go with option A. The amount of interest only is A-P = 108-100 = 8 dollars.
-------------------
For option B, we have: n = 4 and r = 0.07875
A = P*(1+r/n)^(n*t)
A = 100*(1+0.07875/4)^(4*1)
A = 108.110625948487
A = 108.11
So far option B is slightly better since you've earned an extra $0.11, aka 11 cents.
-------------------
For option C, we have: n = 4 and r = 0.07875
A = P*(1+r/n)^(n*t)
A = 100*(1+0.0775/12)^(12*1)
A = 108.031299777277
A = 108.03
This amount is less compared to the $108.11 with option B. Therefore, option B is still the best so far.
-------------------
For option D, we have: n = 52 and r = 0.07625
A = P*(1+r/n)^(n*t)
A = 100*(1+0.07625/52)^(52*1)
A = 107.917207523206
A = 107.92
This is worse compared to option C.
Option B is still the best so far.
-------------------
For option E, we have: n = 365 and r = 0.075
A = P*(1+r/n)^(n*t)
A = 100*(1+0.075/365)^(365*1)
A = 107.787584644
A = 107.79
---------------------
Here's a table comparing the balance after 1 year for options A through E. Those balances all have a starting point of $100 as the deposit.
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Option} & \text{Balance after 1 year}\\\cline{1-2}A & \$108\\\cline{1-2}\boldsymbol{B} & \boldsymbol{\$108.11}\\\cline{1-2}C & \$108.03\\\cline{1-2}D & \$107.92\\\cline{1-2}E & \$107.79\\\cline{1-2}\end{array}[/tex]
Option B is the best choice earning the most ($108.11) if you deposit $100.
There's nothing special about the $100, so feel free to change it to something else to try other starting deposits. You'll find that option B will still provide the highest return.
Answer:
B
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedUse the Compound Interest Formula with the given values for each option to calculate a final equation where A equals a multiple of P.
The option with the greatest coefficient of P is the account which yields the highest interest after one year, and is therefore the best deal.
Option AGiven:
r = 8% = 0.08n = 1 (annually)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.08}{1}\right)^1[/tex]
[tex]\implies \sf A=1.08P[/tex]
Option BGiven:
r = 7.875% = 0.07875n = 4 (quarterly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.07875}{4}\right)^{4 \cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.0196875)^4[/tex]
[tex]\implies \sf A=1.081106259P[/tex]
Option CGiven:
r = 7.75% = 0.0775n = 12 (monthly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.0775}{12}\right)^{12\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.006458333\right)^{12}[/tex]
[tex]\implies \sf A=1.080312998P[/tex]
Option DGiven:
r = 7.625% = 0.07625n = 52 (weekly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.0765}{52}\right)^{52\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.001471154\right)^{52}[/tex]
[tex]\implies \sf A=1.079441506P[/tex]
Option EGiven:
r = 7.5% = 0.075n = 365 (daily)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.075}{365}\right)^{365\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.000205479\right)^{365}[/tex]
[tex]\implies \sf A=1.077875846P[/tex]
Summary[tex]\begin{array}{|c|l|}\cline{1-2} \sf Answer\;Option & \sf Coefficient\;of\;P\\\cline{1-2} A & 1.08\\\cline{1-2} B & 1.081106259\\\cline{1-2} C & 1.080312998\\\cline{1-2} D & 1.079441506\\\cline{1-2} E & 1.077875846\\\cline{1-2} \end{array}[/tex]
Therefore, the option with the greatest coefficient of P and therefore the best deal is option B.
Four students in Mr. Morales' math classes are
conducting surveys in their school. They each
handed out 100 surveys. The table shows the
response rates of each student's survey.
Response Rates
Min-seo: 4 out of 5 students responded
Orlando: 8 out of 10 students responded
Jian: 3 out of 4 students responded
Leona: 10 out of 12 students responded
2. Did Min-seo and Orlando get the same ratio of responses? Explain.
3. Did Jian and Leona get the same ratio of responses? Explain.
Min-Seo and Orlando have the same ratio of responses but Jian and Leona do have not the same ratio of responses.
What is ratio?The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.
As per the given information in the question,
The ratios given in the question are,
2.
The ratio obtained by Min-SEO = 4/5 and,
The ratio obtained by Orlando = 8/10
The ratio in the simplest form will be: 4/5
This means that Nin-SEO and Orlando have the same ratio of responses.
3.
The ratio obtained by Jian = 3/4 and,
The ratio obtained by Leona = 10/12
The simplest form of ratio = 5/6
This means that Jian and Leona do have not the same ratio of responses.
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Can someone help me with this problem?
Answer:
$33
Step-by-step explanation:
l=prt = 30 × 0.05 × 2=3
total save = 30+ 3= 33
"2. Compare and contrast the two major sects of Islam, Sunni and Shia, by filling out the table below. (10 points)
Similarities in the sects Differences between the sects"
The similarity is that Sunni and Shia Muslims agree on the fundamental tenets of Islam, such as worshiping Allah as God, acknowledging Muhammad (Peace Be Upon Him) as the Prophet, and adhering to the Quran's teachings.
The difference is that Shia place a greater emphasis on Muhammad's family ancestry through a succession of Imams than Sunnis do on imitating the Prophet and his example.
What is the Similarities and difference between the difference Islamic sect?All Shia and Sunni Muslims recognize the importance of the Quran; contrary to popular belief, Shi'a does not use a corrupted version of the Quran.
Shi'a and Sunni Muslims both use the Hadith, though they often prefer different collections of sayings.
They have different perspectives on imams. Imams are considered saints in Sunni Islam and must have a strong commitment to the Quran and Sunnah in order to be nominated. In Shia Islam, however, only God has the authority to name an imam. Only imams in Shia Islam have the authority to translate the Quran.
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For what value of x is line m parallel to line n?
Answer: x=-2
Step-by-step explanation:
they’re corresponding angles meaning they’re congruent or equal to each other then solve like any other problem
what is the reciprocal of 8?
Answer:1/8
Step-by-step explanation:
The reciprocal of a number is what you multiply by a number to give 1. Therefore
8x = 1
x = 1/8
Given the function y = -5x +4, what is the range of the function if the domain is {-2, 0,5}
Answer:
range is { - 21, 4 , 14 }
Step-by-step explanation:
the domain gives the value of x , the input
the range is the corresponding values of y, the output
substitute values of x from the domain into the function
x = - 2 : y = - 5(- 2) + 4 = 10 + 4 = 14
x = 0 : y = - 5(0) + 4 = 0 + 4 = 4
x = 5 : y = - 5(5) + 4 = - 25 + 4 = - 21
then range is { - 21, 4 , 14 }
Daniel rollerbladed 3 1/4 miles in 4 minutes. What was his speed in miles per hour?
Answer: 48 3/4 miles/hour.
Step-by-step explanation: To find Daniel's speed in miles per hour, we need to first convert the time he rollerbladed to hours. We can do this by dividing the number of minutes he rollerbladed by 60 minutes per hour, as follows:
time in hours = 4 minutes / 60 minutes/hour = 1/15 hours
We can then use the formula for speed, which is distance divided by time, to find Daniel's speed in miles per hour as follows:
speed in miles per hour = distance in miles / time in hours
speed in miles per hour = 3 1/4 miles / 1/15 hours
speed in miles per hour = 3 1/4 miles * 15 hours/1
speed in miles per hour = 48 3/4 miles/hour
Therefore, Daniel's speed in miles per hour was 48 3/4 miles/hour.
Answer:
Check explanation!
Step-by-step explanation:
Daniel rollerbladed at 15 mph, we know this because 60 divided by 4 = 15 (number of minutes in an hour divided by his time = answer)
so daniel rollerbladed at 15 mph
right triangleXYZ with hypotenuse line segment YZ, the length of line segment XY is b units long, and the length of line segment XZ is three times the length of line segment XY
The length of the hypotenuse side of the right triangle ΔXYZ, found using Pythagorean Theorem is b·√(10)
What is Pythagorean Theorem?Pythagorean Theorem indicates that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the square of the legs of the right triangle.
The specified parameters of triangle are;
The hypotenuse of the triangle, ΔXYZ = [tex]\overline{YZ}[/tex]
The length of the legs of the right triangle are;
[tex]\overline{XY}[/tex] = b, and [tex]\overline{XZ}[/tex] = 3 × [tex]\overline{XY}[/tex]
Therefore;
[tex]\overline{XZ}[/tex] = 3 × b (substitution property of equality)
The length of the hypotenuse side can be calculated as follows;
Therefore;, according to Pythagorean theorem, we get;
[tex]\overline{YZ}[/tex]² = [tex]\overline{XY}[/tex]² + [tex]\overline{XY}[/tex]²
[tex]\overline{YZ}[/tex]² = b² + (3·b)² = b² + 9·b² = 10·b²
[tex]\overline{YZ}[/tex] = [tex]\sqrt{10\cdot b^2} = b \cdot \sqrt{10}[/tex]
The length of the hypotenuse side , [tex]\overline{YZ}[/tex] = b·√(10)
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The ratio x:y is equal to is 2 : 5, and y is 80% of z. Write an equation to represent the proportional relationship between x and z.
Answer:
z = 3.125 * x
Step-by-step explanation:
since y is 80 percent of z, we can represent it in the form of a ratio as 80:100.
Simplify it down: 80:100 = 8:10 = 4:5
therefore x:y = 2:5
and y:z = 4:5
"y" is common in both of these ratios. Therefore we now have to make the value of Y same in both of the ratios. Therefore we find the least common multiple of both the y values which is 5 and 4. It is 20.
Now we make the value of y in both the ratios 20. So we need to multiply 5 in 2:5 by 4. Since we multiplied one of the values by 4 we have to multiply the other one as well (2*4). Now our new ratio for x:y is 8:20. Do the same for the other ratio. the other ratio is 4:5. the y value here is 4. 4 needs to be multiplied by 5 to become 20. Therefore multiply 4 by 5 and multiply 5 by 4. our new ratio for y:z is 20:25
As you can see both the y values are similar now.
x:y = 8:20
y:x = 20:25
therefore we can now write x:y:z as 8:20:25
that also means that x:z is now 8:25.
Now we know that when x is 8 z is 25. in this case. 8 and 25 are directly proportional.
therefore we can write an equation as
25 = k*8
k = 25/8
k = 3.125
therefore z = 3.125 * x
two more than a certian number is 15 less than the product of 7/8 and the number
The number is -136.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Let the number be x.
Given that, two more than the number, x, is 15 less than the product of 7/8 and the number, therefore:
x + 2 = (7/8)x - 15
x - (7/8)x = -15 -2
x/8 = -17
x = -136
Hence, the number is -136.
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What is Four divided by 1 8. It’s a faction the one and eight
Answer: 32
Step-by-step explanation:
4 ÷ 1/8
You can reduce the expression by cancelling out common factors;
4/1 ÷ 1/8
Cross cancel the ones, and then multiply 4 and 8
4 x 8 = 32
[(1 1/4 - 3/4) · (- 2/3) ³] ÷ (-4)
What is the value of the expression
Answer:
Step-by-step explanation:
1 1/4-3/4=5/4-3/4=(5-3)/4=2/4=1/2
(-2/3)3=-8/27
HELP!! 30 POINTS!!
What is the correlation of the data shown?
0
1
-0.5
-1
The correlation of the data shown on the graph is 0
How to determine the correlation?In this question, the graph represents the given parameter
From the graph, we have the following observations
The x values is on the horizontal axisThe y values is on the vertical axisAs the x values increase, the y values do not follow a patternWhen the change (increase) in the x values causes a random change (increment) in the y values, then the correlation is 0
From the list of options, we have
-1, -0.5 and 1 are not zero i.e. 0
This means that the correlation is (a) 0
Hence, the correlation of the data is 1
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Determine the values of A, B, and C when y- 7= 3(x-4) is written in standard form, Ax+By = C.
Answer:
A = 3
B = -1
C = 5
Step-by-step explanation:
y - 7 = 3(x - 4) Distribute the 3
y - 7 = 3x -12 subtract y from both sides
-7 = 3x -y -12 Add 12 to both sides
5 =3x -y Flip the equation around the equal sign
3x -y = 5
The 3 is the A, -1 is the B and 5 is the C.
4. Which of the triangles below is not a right triangle?
3 cm, 4 cm, 5 cm
27 cm, 36 cm, 45 cm
6 ft, 8 ft, 12 ft
√6in, √10in, √4in
Answer:
3cm,4cm,5cm
Step-by-step explanation:
5 is the longest side ( the hypotenuse)
and by Pythagoras theorem x=√(3²+4²)
= √(9+16)
=√(25)
= 5
so 3cm,4cm,5cm is a right angle triangle.
x=√(27²+36²)
=√(729+ 1296)
=√2025
=45
so 27cm,36cm,45cm is a right angle triangle
to find out if a triangle is a right angle triangle try applying the law of Pythagoras theorem to see if it matches, and if it matches then it is a right angle triangle but if it doesn't then it's not a right angled triangle Try for the last two and put it down the comments I'll try to checkwhich figure should be next, following the pattern?
The figure that should be the next, following the pattern is option (b)
How to determine the next figure?The missing information that completes this question is added as an attachment
From the attached figure, we have the following pattern:
Each of the figure represents the alphabet letter PThe next figure is gotten by rotating the current figure by 45 degrees to the right i.e. in clockwise directionWhen the pattern is studied carefully, we can see that the next figure is the figure in option (b)
This is so because the figure in option (b) is gotten by rotating the last figure in the pattern by 45 degrees to the right
Hence, the conclusion about the figure that should be the next figure is that the next figure should be figure (b)
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The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.
Find log0.81 rounded to the nearest tenth.
The value of the logarithm of 0.81 for logarithm properties is equal to - 0.1.
How to determine the value of a logarithm
Herein we must use logarithm properties to simplify a given logarithm and solve the resulting expression. The properties to be used in this question are described below:
㏒ (a / b) = ㏒ a - ㏒ b
㏒ aᵇ = b · ㏒ a
First, write the logarithmic equation:
㏒ 0.81
㏒ 81 / 100
Second, use the logarithmic property for a division:
㏒ 81 - ㏒ 100
Third, use the logarithmic property for a power:
㏒ 3⁴ - ㏒ 10²
4 · ㏒ 3 - 2 · ㏒ 10
4 · ㏒ 3 - 2
4 · 0.477 - 2
- 0.092
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The frame of a bicycle weighs 16 pounds. Each tire weighs 9 ounces. The seat weighs 12 ounces. The handlebars weigh 24 ounces. How many pounds does the bicycle weigh?
The weight of the bicycle is 19.375 pounds.
Define weight.In physics and engineering, the weight of an object refers to the gravitational force that pulls on it. Weight is frequently described as a scalar quantity that measures the gravitational force's strength.
The weight of the frame of the bicycle= 16 pounds
1 pound= 16 ounces
Therefore, 16 pounds= 16 x 16 = 256 ounces
The weight of one tire= 9 ounces
Therefore, the weight of two tires= 9 x 2 = 18 ounces
The weight of the seat= 12 ounces
The weight of handlebars= 24 ounces
Therefore, the total weight of the bicycle = 256 + 18 + 12 + 24
= 310 ounces
Therefore, the bicycle weighs 310 ounces
That is 310/ 16 = 19.375 pounds
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What is the distance between Texas 2.6* 10 to the 5th power square miles and Rhode Island 1.21 * 10 to the 3rd power square miles what is the difference between them I need it in scientific notation
The distance between Texas and Rhode Island will be;
⇒ 2.59 × 10⁵ square miles
What is mean by Subtraction?
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
Texas 2.6* 10 to the 5th power square miles and Rhode Island 1.21 * 10 to the 3rd power square miles.
Now,
Since, Texas 2.6* 10 to the 5th power square miles and Rhode Island 1.21 * 10 to the 3rd power square miles.
Hence, The distance between Texas and Rhode Island will be find as;
⇒ 2.6 × 10⁵ - 1.21 × 10³
⇒ 260 × 10³ - 1.21 × 10³
⇒ (260 - 1.21) × 10³
⇒ 258.79 × 10³
⇒ 2.59 × 10⁵ square miles
Thus, The distance between Texas and Rhode Island will be;
⇒ 2.59 × 10⁵ square miles
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Please help! The answer is the slope and it needs to be rounded to 3 decimal places.
The slope is 0.003
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
the coordinates are (12000, 20) and (18000, 2)
so, slope= 18 / 6000
= 0.003
The 3 in the thousandths place rounds down to 3, or stays the same, because the digit to the right in the ten thousandths place is 0.003.
Hence, the slope is 0.003.
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Solve the following equations
25x²-4=0
Answer: x= (2)/5 & x= (-2)/5
Step-by-step explanation:
Factor Form:
1. Use the sum product patturn
25x^2-4=0 → 25x^2+10-10-4=0
2. Common factors from each pair
25x^2+10-10-4=0 → 5x(5x+2)-2(5x+2)=0
3. Rewrite the factored form
5x(5x+2)-2(5x+2)=0 → (5x+2)(5x-2)=0
4. Create separate equations
(5x+2)(5x-2)=0 → 5x+2=0 5x-2=0
5. Solve
5x+2=0 5x-2=0 → x=(2)/5 x=(-2)/5
how much would it cost to replace all the windows on all the buildings in the united states?
24 - 10x = 9 (ignore---------------------------------------------------------------------------------------------------------------)
[tex]\fbox{x=$\dfrac{3}{2}$}[/tex] or [tex]\fbox{x=1.5}[/tex]
Simplify Equation:
[tex]24-10x=9[/tex]
[tex]-10x+24=9[/tex]
Subtract 24 from both sides:
[tex]-10x+24-24=9-24[/tex]
[tex]-10x=-15[/tex]
Divide both sides by -10:
[tex]\dfrac{-10x}{-10} =\dfrac{-15}{-10}[/tex]
[tex]x=\dfrac{3}{2}[/tex] or [tex]x=1.5[/tex]
Whats the answer please help its worth 10 points!
What is the ratio of shaded to unshaded squares in the grid below?
Group of answer choices
3/5
5/8
1/3
Answer:
1/3
Step-by-step explanation:
shaded is 10 and unshaded is 15
so the answer is 1/3 because
5 can be multiplied both sides
5 times 3 is 15
5 times 1 is 5
So both sides can be multiplied by 5
Answer: alt account
Step-by-step explanation:
[tex]y= 4\\y = \frac{8}{3} x - 4\\[/tex]
Answer: x=3
Step-by-step explanation:
Assuming you want to solve the system,
You are already given y = 4, so plug 4 in for the other y in the other equation.
[tex]y=\frac{8}{3} x-4\\\\4=\frac{8}{3} x-4\\4+4=\frac{8}{3} x-4+4\\\frac{3}{8}\times 8=\frac{3}{8} \times\frac{8}{3}x\\\\x=3[/tex]
Anna works at an electronics
store as a salesperson. Anna earns a 5% commission a
the total dollar amount of all
phone sales she makes, and earns a 7% commission Or
all computer sales. Anna made a total of $2100 in sales
and earned $119 in
commission. Write a system of equations that could be used to determine the dollar
amount of phone sales Anna made and the dollar amount of computer sales she
made. Define the variables that you use to write the system.
Let
Let p be the amount of sales (in dollars) of phones.
Let c be the amount of sales (in dollars) of computers.
Equation 1: sales
p + c = 2100
the amount of all sales is 2100
Equation 2: commission
0.05p + 0.07c = 119
5% commission on phones plus 7% commission on computers totals to 119