Answers
1.I WILL USE CROSS MULTIPLICATION
[tex] \frac{ - n}{4} = 13 \\ - n = 13(4) \\ - n = 52 \\ \frac{ - n}{ - 1} = \frac{52}{ - 1} \\ n = - 52[/tex]
2.
[tex] \frac{3x}{4} - 5 = 4 \\ \frac{3x}{4} (4) - 5(4) = 4(4) \\ 3x - 20 = 16 \\ 3x = 16 + 20 \\ 3x = 36 \\ \frac{3x}{3} = \frac{36}{3} \\ x = 12[/tex]
ATTACHED IS THE SOLUTION.
Related Questions
Question 54 what I’m suppose to do it says I have to evaluate
Answers
Craig deposited $727 in a savings account earning 15% interest, compounded annually.To the nearest cent, how much will he have in 5 years?$
Answers
The compound interest formula is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A is the final amount, P is the principal, r is the interest rate (as a decimal), n is the number of times the interest is applied per year, and t is the number of years.
Given that the interest is compounded annually, then n = 1.
Substituting with P = $727, r = 0.15, n = 1, and t = 5 years, we get:
[tex]\begin{gathered} A=727\cdot(1+0.15)^5 \\ A=1462.26\text{ \$} \end{gathered}[/tex]In 5 years, he will have $1,462.26
Tell me if Soup B, Soup C, Soup D, and Soup E either have the same price per can as Soup A, or they do not have the same price per can as Soup A
Answers
Answer:
• Same price per can as Soup A: C, E.
,• Do not have the same price per can as Soup A are: B, D
Explanation:
In order to determine which cans have the same price per can as Soup A, first, determine the price per can for Soup A.
Ted bought 4 cans of Soup A for $6.00.
[tex]\text{Price per can for Soup A}=\frac{\$6.00}{4\text{ cans}}=\$1.50\text{ per can}[/tex]Next, determine the price per can for Soup B, C, D and E.
Soup B: 2 cans for $5.
[tex]\text{Price per can for Soup B}=\frac{\$5.00}{2\text{ cans}}=\$2.50\text{ per can}[/tex]Soup C: 3 cans for $4.50.
[tex]\text{Price per can for Soup C}=\frac{\$4.50}{3\text{ cans}}=\$1.50\text{ per can}[/tex]Soup D: 5 cans for $5.50.
[tex]\text{Price per can for Soup D}=\frac{\$5.50}{5\text{ cans}}=\$1.10\text{ per can}[/tex]Soup E: 6 cans for $9.
[tex]\text{Price per can for Soup E}=\frac{\$9}{6\text{ cans}}=\$1.50\text{ per can}[/tex]Therefore:
Those that have the same price per can as Soup A
• Soup C
,• Soup E.
Do not have the same price per can as Soup A are:
• Soup B
,• Soup D
In a rectangle, one side is 6 cm longer than the other. The area of the rectangle is 520cm2. Determine the longest side of the rectangle.
Answers
From the given informatio, we can draw the following picture:
where x denote the shorter side of the rectangle and x+6 the longest one. Since the area of the rectangle is equal to the base times the height, we have
[tex]A=(x+6)x[/tex]Since the area is 520 square centimeters, we have
[tex]520=(x+6)x[/tex]Then, by distributing the variable x into the parentheses, we have the following equation:
[tex]x^2+6x=520[/tex]or equivalently,
[tex]x^2+6x-520=0[/tex]So, we can to apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]coming from the quadratic polynomial:
[tex]ax^2+bx+c=0[/tex]By comparing this polynomial with ours, we can note that
[tex]\begin{gathered} a=1 \\ b=6 \\ c=-520 \end{gathered}[/tex]so, we get
[tex]x=\frac{-6\pm\sqrt{6^2-4(1)(-520)}}{2}[/tex]which gives
[tex]\begin{gathered} x=\frac{-6\pm\sqrt{2116}}{2} \\ x=\frac{-6\pm46}{2} \end{gathered}[/tex]Then, we have 2 possible solutions:
[tex]\begin{gathered} x=\frac{-6+46}{2}=\frac{40}{2}=20 \\ and \\ x=\frac{-6-46}{2}=\frac{-52}{2}=-26 \end{gathered}[/tex]However, since the dimension are always positive numbers, the searched side measure 20 cm. In other words, the shorter side measures 20cm and the longest one 20+6=26 cm. Therefore, the answer is: 26 centimeters.
For Suav's lemonade recipe, 6 lemons are required to make 10 cups of lemonade. At what rate are lemons being used in cups of lemonade per lemon?
Answers
Given:
To make a lemonade recipe, 6 lemons are required to make 10 cups of lemonade.
Aim:
We need to find the rate of cubs of lemonade per lemon.
Explanation:
[tex]10\text{ cups : 6 lemons}[/tex]Divide both sides by 10.
[tex]\frac{10}{10}\text{ cups: }\frac{6}{10}\text{ lemon}[/tex][tex]\text{cup : }\frac{3}{5}\text{ lemon}[/tex][tex]\text{cup per lemon = }\frac{3}{5}\text{ }[/tex]Final answer:
Hence 3/5 rate of lemons being used in cups of lemonade per lemon.
fill in the missing value in the given equivalent ratios 7:5= ___:35
Answers
we have the ratio
7:5 -------> x:35
To obtain 35 from 5, you must multiply the ratio by 7 on both sides
so
7(7) :5(7) ------> 49:35
Find the closest fractional equivalent for the following decimal measurement using the given denominator.0.842 in. (16ths)
Answers
Given:
[tex]0.842[/tex]Required:
To find the closest fractional equivalent for the following decimal measurement.
Explanation:
Consider the given decimal number
[tex]0.842[/tex]Multiply to remove 3 decimal places. Here, you multiply top and bottom by 1000.
[tex]\frac{0.842}{1}\times\frac{1000}{1000}[/tex][tex]=\frac{842}{1000}[/tex]Now divide 2 on both side, we get
[tex]=\frac{421}{500}[/tex]Final Answer:
The closest fractional equivalent for 0.842 is
[tex]\frac{421}{500}[/tex]Which function produces a range of {−11, −5,1,4,10} given a domain of {−2,0,1,3,5}?
f(x) = −2x − 5f(x) = −2x − 5
f(x) = x + 2f(x) = x + 2
f(x) = −3x + 4f(x) = −3x + 4
f(x) = −5x + 3f(x) = −5x + 3
Answers
Answer: C
Step-by-step explanation:
i did the same assignment so it should be right
can you help me with steps and i only need help with #8
Answers
We have to find the slope for the lines AC and DB that are:
[tex]\begin{gathered} ac=\frac{-2-3}{-1-4}=-\frac{5}{3} \\ bd=\frac{3--2}{2--7}=\frac{5}{9} \end{gathered}[/tex]so we have that the equations are:
[tex]\begin{gathered} 5x+3y=-11 \\ 5x-9y=-17 \end{gathered}[/tex]having that we get that
[tex]-12y=-6\rightarrow y=0.5\rightarrow5x+1.5=-11\rightarrow x=-\frac{12.5}{5}=-2.5[/tex]so the answer is (-2.5,0.5)
Explain 2 different ways to solve for the derivative s(θ)=200sinθcosθ
Answers
To find the derivative of the function s we can use the two following approaches:
0. Product rule.
,1. Using trigonometric identities.
Product rule.
We know that the product rule states that:
[tex]\frac{d}{dx}(fg)=f^{\prime}g+fg^{\prime}[/tex]Using this rule in this case we will have:
[tex]\begin{gathered} \frac{ds}{d\theta}=\frac{d}{d\theta}(200\sin\theta\cos\theta) \\ =200\frac{d}{d\theta}(\sin\theta\cos\theta) \\ =200(\cos\theta\frac{d}{d\theta}\sin\theta+\sin\theta\frac{d}{d\theta}\cos\theta) \\ =200(\cos\theta\cos\theta+\sin\theta(-\sin\theta)) \\ =200(\cos^2\theta-\sin^2\theta) \end{gathered}[/tex]Therefore, using the product rule, we have that:
[tex]\frac{ds}{d\theta}=200(\cos^2\theta-\sin^2\theta)[/tex]Using trigonometric identities.
We can also calculate the derivative if we remember that:
[tex]\sin2\theta=2\sin\theta\cos\theta[/tex]Then, in this case we have:
[tex]\begin{gathered} \frac{ds}{d\theta}=\frac{d}{d\theta}(200\sin\theta\cos\theta) \\ =100\frac{d}{d\theta}(2\sin\theta\cos\theta) \\ =100\frac{d}{d\theta}\sin2\theta \\ =100(2\cos2\theta) \\ =200\cos2\theta \end{gathered}[/tex]Therefore, using trigonometric identities, we have that:
[tex]\frac{ds}{d\theta}=200\cos2\theta[/tex]Note: Both results are equivalent, to prove it we just need to remember that:
[tex]\cos^2\theta-\sin^2\theta=\cos2\theta[/tex]If we use this identity in the first result we get the second one.
Factor the expression using the GCF 36-70x
Answers
Here, we want to factor the expression using the GCF
The greatest common factor is 2
So we have the factoring as;
[tex]36-70x\text{ = 2(18-35x)}[/tex]What are the polar coordinates of A? Give an exact answer.
Answers
Answer:
To find coordinate of A, it is (6,-6) in polar coordinate.
we know that,
The polar coordinate system as a method in which a point is described by its distance from a fixed point at the center of the coordinate space known as a pole and by the measurement of the angle formed by a fixed-line and a line from the pole through the given point.
In the polar coordinate system, the coordinates of a point are represented as,
[tex](r,\theta)[/tex]where r is the distance of the point from the pole, and θ is the measure of the angle.
we know that,
[tex]r^2=x^2+y^2[/tex][tex]\theta=tan^{-1}(\frac{y}{x})[/tex]we get,
(x,y)=(6,-6)
x=6, y=-6
Using this we get,
[tex]r^2=6^2+(-6)^2[/tex][tex]r^2=36+36[/tex][tex]r^2=72[/tex][tex]r=8.48[/tex]Then,
[tex]\theta=tan^{-1}(\frac{-6}{6})[/tex][tex]\theta=tan^{-1}(-1)[/tex][tex]\theta=-\frac{\pi}{4}[/tex]we get the polar coordinate of A is,
[tex](r,\theta)=(8.48,-\frac{\pi}{4})[/tex]Use long division to divide. Specify the quotient and the remainder.(−x2 − 1) ÷ (x + 1)quotient remainder
Answers
Solution
The quotient is
[tex]1-x[/tex]The remainder is
[tex]-2[/tex]Find the output, y, when the input, 2, is 6. y = y 8. 6+ 4+ 2 + -6 2 4 6 8 -4+ -6+
Answers
Step by step: a painting costs $225. If the sale price is $191.25, what is the percent discount?
Answers
Given:
The cost of the painting = $225
The sales price of the painting = $191.25
To find:
the percent discount
To determine the percent discount, we will apply the formula:
[tex]\text{ \% discount = }\frac{original\text{ price - sales price}}{original\text{ price}}\times100[/tex][tex]\begin{gathered} \text{ \% discount = }\frac{225\text{ - 191.25}}{225}\times100 \\ \\ \text{ \% discount = }\frac{33.75}{225}\times100 \end{gathered}[/tex][tex]\begin{gathered} \text{ \% discount = 0.15 }\times\text{ 100} \\ \\ Percent\text{ discount = 15\%} \end{gathered}[/tex]Maria loves the lunch combinations at Diner's Delite. Today, however, she wants adifferent combination than the ones listed on the menu.Two burgers, one french fries $7.55One coke, one burger, one french fries $8.10Two cokes, two burgers $9.90Assume that the price of a combo meal is the same price as purchasing each itemseparately. Find the price for a burger, a coke, and french fries.burger $2.20 french fries S3 15. coke S2.75burger: S3 15. french fries $2.20, coke S2.75burger $1.20, french fries: $3.15 coke: $3.75burger $2.78, french fries: S3 10 coke S2.22
Answers
Let b be the price of the burger, c the price of the coke, and f the price of the french fries, then we can set the following system of equations:
[tex]\begin{gathered} 2b+f=7.55, \\ b+c+f=8.10, \\ 2c+2b=9.90. \end{gathered}[/tex]Subtracting the second equation from the first one we get:
[tex]b-c=7.55-8.10=-0.55.[/tex]Now, subtracting the two times the above equation from the third equation we get:
[tex]\begin{gathered} 2c+2b-2b+2c=9.90-2(-0.55), \\ 4c=11, \\ c=\frac{11}{4}=2.75\text{.} \end{gathered}[/tex]Substituting c=2.75 in the third equation and solving for b we get:
[tex]\begin{gathered} 2(2.75)+2b=9.90, \\ 2b=9.90-5.5=4.4, \\ b=2.2\text{.} \end{gathered}[/tex]Finally, substituting b=2.2 in the first equation and solving for f we get:
[tex]\begin{gathered} 2(2.2)+f=7.55, \\ f=7.55-4.4=3.15\text{.} \end{gathered}[/tex]Answer: The burger costs $2.20, the price of the french fries is $3.15, and the price of the coke is $2.75.
Determine the discriminant, and then state the nature of the solutions. 9x^2-30x+25=0The discriminant tells us there is Answer
Answers
To answer this question, we need to remember was the discriminant of a quadratic equation means. The discriminant is given by the following formula:
[tex]D=b^2-4ac[/tex]The values of a, b, and c, are:
• a is the leading coefficient (or quadratic coefficient)
,• b is the linear coefficient
,• c is the constant-coefficient
We can see this in the general formula:
[tex]ax^2+bx+c[/tex]In this case, we have that the polynomial:
[tex]9x^2-30x+25=0[/tex]Then
• a = 9
,• b = -30
,• c = 25
If we use the formula of the discriminant, we have:
[tex]D=b^2-4ac\Rightarrow D=(-30)^2-4(9)(25)=900-900=0[/tex]When we have that the discriminant of the polynomial is equal to 0, then the parabola that represents the quadratic formula will have only one x-intercept. It has one real solution. However, this solution is a multiplicity, that is this solution is
The coordinates of the point A are (10,-5) and the coordinates of point B are(0, -5). What is the distance, in units, between the point A and point B?
Answers
Given:
The coordinates of the point A, (x1, y1)=(10, -5).
The coordinates of the point B, (x2, y2)=(0,-5).
The expression for the distance between points A and B is,
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Substitute the values.
[tex]\begin{gathered} D=\sqrt[]{(0-10)^2+(-5-(-5)^{})^2} \\ D=\sqrt[]{10^2+0} \\ D=10 \end{gathered}[/tex]Therefore, the distance between points A and B is 10 units.
Calculate the standard deviation and variance of the given random sample data. Round to two decimal places.
Answers
The standard deviation = 7.65
The variance = 58.55
Explanation:The given data are:
x = 19.9, 3.7, 24.6, 4.9, 13.5, 4.4, 19, 18.1
The mean is calculated as:
[tex]\begin{gathered} \mu=\frac{\sum x}{N} \\ \mu=\frac{19.9+3.7+24.6+4.9+13.5+4.4+19+18.1}{8} \\ \mu=\frac{108.1}{8} \\ \mu=13.5125 \end{gathered}[/tex]The standard deviation is given by the formula:
[tex]\begin{gathered} SD=\sqrt{\frac{\sum(x-\mu)^2}{N}} \\ SD=\sqrt{\frac{(19.9-13.5125)^2+(3.7-13.5125)^2+(24.6-13.5125)^2+(4.9-13.5125)^2+(13.5-13.5125)^2+(4.4-13.5125)^2+(19-13.5125)^2+(18.1-13.5125)^2}{8}} \\ SD=7.65 \end{gathered}[/tex]The variance = SD²
The variance = 7.65²
The variance = 58.55
Given that 20 degrees is the measure of a central angle of a regular polygon, show how you would determine the number of sides.
Answers
The central angle is given 20 degrees.
ExplanationTo determine the number of sides.
[tex]\frac{360\degree}{20\degree}=18[/tex]AnswerHence the number of sides is 18.
What are the value o x and y in this equation: 7y + 3x =9
Answers
The given equation is expressed as
7y + 3x = 9
To solve for x, the first step is to subtract 7y from both sides of the equation. It becomes
7y - 7y + 3x = 9 - 7y
3x = 9 - 7y
We would divide both sides of the equation by 3. it becomes
3x /3 = 9/3 - 7y/3
x = 3 - 7y/3
To solve for y, the first step is to subtract 3x from both sides of the equation. It becomes
7y + 3x - 3x = 9 - 3x
7y = 9 - 3x
We would divide both sides of the equation by 7. it becomes
7y/7 = 9/7 - 3x/7
y = 9/7 - 3x/7
Jonathan's checking balance is -45 dollars. After receiving his allowance he deposits $7 into the account. What is the balance of the account after Jonathan's deposit?
Answers
Given,
The initial balance in the account is - 45 dollars.
The amount he deposite in the account is $7.
The balance of the account after Jonathan's deposit is,
[tex]\text{Balance of the account=initial balance+deposite amount}[/tex]Substituting the values then,
[tex]\text{Balance of the account=-}45+7=-38[/tex]Hence, the balance of the account after Jonathan's deposit is $-38.
Solve for the given variable 1) 7(y + 3) = 5y + 82) 4(3r + 5) = -8(2r + 1)3) 19/4 - 7/2a = -1/4a + 3/2
Answers
1) 7(y + 3) = 5y + 8
distributing,
7(y) + 7(3) = 5y + 8
7y + 21 = 5y + 8
5y is adding on the right, then it will subtract on the left
21 is adding on the left, then it will subtract on the right
7y - 5y = 8 - 21
2y = -13
2 is multiplying on the left, then it will divide on the right
y = -13/2
2) 4(3r + 5) = -8(2r + 1)
distributing,
4(3r) + 4(5) = -8(2r) + 8(1)
12r + 20 = -16r + 8
16r is subtracting on the right, then it will add on the left
20 is adding on the left, then it will subtract on the right
12r + 16r = 8 - 20
28r = -12
r = -12/28
r = -3/7
3)
[tex]\frac{19}{4}-\frac{7}{2}a=-\frac{1}{4}a+\frac{3}{2}[/tex]7/2a is subtracting on the left, then it will add on the right
3/2 is adding on the right, then it will subtract on the left
[tex]\begin{gathered} \frac{19}{4}-\frac{3}{2}=\frac{1}{4}a+\frac{7}{2}a \\ \frac{19-3\cdot2}{4}=\frac{1+7\cdot2}{4}a \\ \frac{13}{4}=\frac{15}{4}a \end{gathered}[/tex]15/4 is multiplying on the right, then it will divide on the left
[tex]\begin{gathered} \frac{13}{4}\cdot\frac{4}{15}=a \\ \frac{13}{15}=a \end{gathered}[/tex]Peppermints $2.37 per pound. Candy corn $5.78 per pound. Tootsie Roll $7.61 per pound. Jellybeans $8.96 per pound. Great pops $1.25 for three. Swirly pops $19.39 for a dozen. Strawberry Pop $4.54 for six. Gumballs $.75 per spin grab bag $6.52 per pound. Gum drops $3.23 per scoop. 1. Aubrey wants to buy candy for goodie bags for her birthday party she was going to buy 6 pounds of jellybeans. How much will Aubrey pay for the candy?2. Abigail bought 4 pounds of peppermints and Sophia bought 3 pounds of grab bag candy who spent less money. 3. How much last did she spend from question number two. 4. How much does each swirly pop cost 10th one you need to know how many swirly pops are in a dozen 12 hint to round your answer to be only two decimal places since your answers is in money. 5. If five gumballs are released with each spin how much would each gumball cost. 6. David and Mary sweat the cost of 1 pound of each jelly beans one scoop of gum jobs in 1 pound of peppermints how much would they pay. 7. Sheryl Paul and three of their friends split 8 pounds of turkey rolls how much does each person pay rent pay close attention to the number of people sweating the candy also round your answer to the nearest cent two decimal places Sheryl Paul and three of their friends split 8 pounds of turkey rolls how much does each person pay rent pay close attention to the number of people sweating the candy also round your answer to the nearest cent two decimal places. 8. Candy corn went on sale for half price the week of Halloween how much wood 5 pounds of candy corn be at the sale price. 9. Fred bought 12 strawberry pops force into the gumball machine and three scoops of gum drops how much did he spend.
Answers
ANSWER
$53.76
EXPLANATION
1) Aubrey wants to buy 6 pounds of jellybeans.
One pound of jellybeans costs $8.96.
To get the price of 6 pounds, we have to multiply the price of one pound by 6.
That is:
[tex]6\cdot\text{ 8.96 = \$}53.76[/tex]She will pay $53.76 for the candy
suppose a normal distribution has a mean of 62 and a standard deviation of4. What is the probability that a data value is between 54 and 66? Round youranswer to the nearest tenth of a percent
Answers
Solution
For this case we have the following info given:
[tex]X\approx N(62,4)[/tex]and we want to find this probability:
P(54And we can use the z score and we have:
[tex]z=\frac{54-62}{4}=-2[/tex][tex]z=\frac{66-62}{4}=1[/tex]And we have this:
[tex]P(54And the final answer would be 81.9%find the length of each side of an equilateral triangle with the perimeter of 57 in
Answers
Let each side of the equilateral triangle be x
since it has 3 sides, then
x + x + x = 57
3x = 57
Divide both-side of the equation by 3
x = 19
Length of each side is 19 in
What is the value of 2 for the following data to three decimal places?OA. 0.867X34LO57y245610 20
Answers
Explanation
We are given the data below:
We are required to determine the value of r² using the table above.
This is achieved thus:
- Using a graphing calculator, we have:
- From the graph above, we have:
[tex]r^2=0.8674[/tex]Hence, the answer is:
[tex]r^2\approx0.867[/tex]Option A is correct.
A driver travels 288 miles in 6 hours. What is the driver’s speed, in miles per hour?
Answers
The driver's speed is 48 miles per hour
Here, we want to calculate the speed
Mathematically;
[tex]\begin{gathered} \text{speed = }\frac{dis\tan ce}{\text{time}} \\ \\ =\text{ }\frac{288\text{ miles}}{6\text{ hours }}\text{ = 48 miles per hour} \end{gathered}[/tex]For the function, find the intervals where it is increasing and decreasing, and JUSTIFY your conclusion. Construct a sign chart to help you organize the information, but do not use a calculator. f(x) = xex 1
Answers
First we have to derivate the function
[tex]\begin{gathered} f(x)=xe^{\frac{1}{x}}\rightarrow \\ f^{\prime}(x)=e^{\frac{1}{x}}+x\cdot(e^{\frac{1}{x}}\cdot\frac{-1}{x^2})=e^{\frac{1}{x}}(1-\frac{1}{x}) \end{gathered}[/tex]We have to find when the derivate is 0
[tex]e^{\frac{1}{x}}(1-\frac{1}{x})=0\rightarrow1-\frac{1}{x}=0\rightarrow x=1[/tex]we have to consider x=0, because we can not divide by 0
so for a number lower than 0 we get that
[tex]f^{\prime}(x)>0[/tex]so it is increasing
for a number between 0 and 1 we get
[tex]f^{\prime}(x)<0[/tex]so it is decreasing
for a number greater than 1 we get
[tex]f^{\prime}(x)>0[/tex]it is increasing
A contestant on a quiz show gets 150 points for every correct answer and loses 250 points for each incorrect answer. After answering 20 questions, the contestant has 200 points. How many question has the contestant answered correctly? ard
Answers
Given data:
The points obtained after getting correct answer is c=150.
The points losses after getting incorrect answer is i=250.
The expression for total questions is,
[tex]\begin{gathered} c+i=20 \\ i=20-c \end{gathered}[/tex]The expression for total marks is,
[tex]150c-250i=200[/tex]Substitute (20-c) for i in the above expression.
[tex]\begin{gathered} 150c-250(20-c)=200 \\ 150c-5000+250c=200 \\ 400c=5200 \\ c=13 \end{gathered}[/tex]The numbers of incorrect questions are,
[tex]\begin{gathered} i=20-13 \\ =7 \end{gathered}[/tex]Thus, the numbers of correct questions are 13, and numbers of incorrect questions are 7.
