Answer:
j = -2
Step-by-step explanation:
It usually works well to start by eliminating parentheses.
15j +6 = 6j -12
Now you can subtract 6j from both sides to get the variable term on one side of the equation only:
9j +6 = -12
And you can subtract 6 from both sides to get the variable term by itself:
9j = -18
Now, dividing by the coefficient of the variable gives you the solution:
j = -2
The solution is j = -2.
Answer:
j = -2
Step-by-step explanation:
3 (5j + 2) = 2 (3j - 6)
15j + 6 = 6j - 12
15j - 6j = - 12 - 6
9j = - 18
j = - 18/9
j = - 2
The points A, B, and C reside on a line segment. B is the midpoint of AC. If line AB measures 6 units in length, what is the length of line AC?
Answer:
12 units
Step-by-step explanation:
A-------6--------B-------?--------C
Midpoint is center that divides the line segment into two equal halves.
∴ AB = BC
If line AB measures 6 units in length, then, line BC will measure 6 units in length.
AB = BC = 6 units
AC = AB + BC
AC = 6 units + 6 units
AC = 12 units
OR
We can say If B is the midpoint of AC, then AC is twice as long as AB.
AC = 2AB
AC = 2 × 6 units
AC = 12 units
Therefore, the length of line AC is 12 units.
The quadratic equation 8x²+12x-14 has two real roots. What is the sum of the squares of these roots?
Answer:
The real roots are
[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]
The sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]
Step-by-step explanation:
The given quadratic equation is [tex]8x^2+12x-14[/tex] has two real roots.
To find the roots .
[tex]8x^2+12x-14=0[/tex]
Dividing the above equation by 2
[tex]\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}[/tex]
[tex]4x^2+6x-7=0[/tex]
For quadratic equation [tex]ax^2+bx+c=0[/tex] the solution is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Where a and b are coefficents of [tex]x^2[/tex] and x respectively, c is a constant.
For given quadratic equation
a=4, b=6, c=-7
[tex]x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}[/tex]
[tex]=\frac{-6\pm\sqrt{36+112}}{8}[/tex]
[tex]=\frac{-6\pm\sqrt{148}}{8}[/tex]
[tex]=\frac{-6\pm\sqrt{37\times 4}}{8}[/tex]
[tex]=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}[/tex]
[tex]=\frac{-6\pm\sqrt{37}\times 2}{8}[/tex]
[tex]=2\frac{(-3\pm\sqrt{37})}{8}[/tex]
[tex]=\frac{-3\pm\sqrt{37}}{4}[/tex]
[tex]x=\frac{(-3\pm\sqrt{37})}{4}[/tex]
The real roots are
[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]
Now to find the sum of the squares of these roots
[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}[/tex]
[tex]=\frac{-6}{4}[/tex]
[tex]=\frac{-3}{2}[/tex]
[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}[/tex]
Therefore the sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]
Johnny has 7 different colored marbles in his bag. In how many ways can he choose three different marbles from his bag to play a game?
Answer:
35
Step-by-step explanation:
Use the combination formula:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
Substitute known values:
[tex]C(7,3)=\frac{7!}{3!(7-3)!}=35[/tex]
We don't use the permutation formula since the order of the drawn marbles does not matter.
Answer: 35
Step-by-step explanation:
He can choose 3 marbles from 7 distinct marbles in (7/3) ways
C(7/3) = 7!/(3!-(7-3)!)
= 7*6*5*4/4*3*2
= 35
Say you flip a coin seven times. What is the probability the number of heads will be even?
Answer:
The probability the number of heads will be even is 0.4922.
Step-by-step explanation:
Consider the provided information.
It is given that coin flip seven times.
Thus, the total number of possible outcomes are: [tex]2^7[/tex]
We want heads will be even.
Even numbers are 2, 4, 6.....
Thus, the possible case are: 2 heads, 4 heads or 6 heads.
The required probability is:
[tex](^7C_2+^7C_4+^7C_6)\times\frac{1}{2^7}=\left(\frac{7!}{2!5!}+\frac{7!}{4!3!}+\frac{7!}{6!1!}\right)\frac{1}{128}\approx 0.4922[/tex]
Hence, the probability the number of heads will be even is 0.4922.
A football team plays in a large stadium. With a ticket price of $19, the average attendance at recent games has been 50 comma 000. A market survey indicates that for each $1 increase in the ticket price, attendance decreases by 300. a. Express the number of spectators at a football game, N, as a function of the ticket price, x. b. Express the revenue from a football game, R, as a function of the ticket price, x.
Answer:
Part 1: N(x) = 50,000 - 300(x-19)
Part 2: R(x) =-300x² + 55700x
Step-by-step explanation:
Given,
The original price of each ticket = $ 19,
The original attendance = 50,000
Part 1 :
∵ For the each $1 increase in the ticket price, attendance decreases by 300.
Let x represents the price of each ticket after increment,
Thus, if price increment = (x-19) dollars,
New attendance, N(x) = 50,000 - 300(x-19)
Part 2 :
Since, revenue = price of each ticket × attendance
Thus, the revenue from the football game,
R(x) = x(50,000 - 300(x-19))
R(x) = 50000x - 300x²+ 5700x
⇒ R(x) =-300x² + 55700x
A collection of dimes and quarters is worth $9.55. If the quarters were dimes and the dimes were quarters, the total value would be 7.60. Find the number of each coin.
Number of dimes are 18 and number of quarters are 31
Solution:
Let "d" be the number of dimes
Let "q" be the number of quarters
value of 1 dime = $ 0.10
value of 1 quarter = $ 0.25
A collection of dimes and quarters is worth $9.55
value of 1 dime x number of dimes + value of 1 dime x number of quarters = 9.55
0.10d + 0.25q = 9.55 ---------- eqn 1
If the quarters were dimes and the dimes were quarters, the total value would be 7.60
quarters were dimes means , q = d
dimes were quarters means d = q
0.25d + 0.10q = 7.60 ----- eqn 2
Let us solve eqn 1 and eqn 2 to find "d" and "q"
Multiply eqn 1 by 2.5
0.25d + 0.625q = 23.875 ---- eqn 3
Subtract eqn 2 from eqn 3
0.25d + 0.625q = 23.875
0.25d + 0.10q = 7.60
( - ) ----------------------
0.525q = 16.275
q = 31
Substitute q = 31 in eqn 1
0.10d + 0.25q = 9.55
0.10d + 0.25(31) = 9.55
0.10d + 7.75 = 9.55
0.10d = 1.8
d = 18
Thus dimes are 18 and number of quarters are 31
Answer:
i needed the answer to this too!! have a good life
Suppose the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs." That is, if P = profit, then P X 0.75 0.05. Use a linear transformation of your results in (a) and (b) to find the mean and standard deviation for P.
Answer:
Step-by-step explanation:
Given that the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs."
i.e. Profit
= P(x) = 0.75 x - 0.05 where x is the no of dvds sold
E(x) = [tex]E(0.75x-0.05)\\= E(0.75x) -E(0.05)\\= 0.75E(x) -0.05[/tex]
(using linear transformation rules for mean)
VarP(x) = [tex]Var(0.75 x - 0.05)\\= Var(0.75x)\\= 0.75^2 Var(x)[/tex]
Hence std dev P(X) = 0.75 std dev (x)
Please... ?
The first term of an infinite geometric progression is 5 and the sum of its terms is 20. What is the common ratio of the progression?
Answer:
The common ratio of the progression is 3/4Explanation:
A geometric progression is a sequence of terms in which the consecutive terms have a constant ratio; thus, each term is equal to the previous one multiplied by a constant value:
[tex]First\ term=a_1\\\\ Second\ term=a_2=a_1\times r\\\\ Third\ term=a_3=a_2\times r=a_1\times r^2\\\\n_{th}\ term=a_n=a_{n-1}\times r=a_1\times r^{n-1}[/tex]
A infinite geometric progression may have a finite sum. When the absolute value of the ratio is less than 1, the sum of the infinite geometric progression has a finite value equal to:
[tex]S_{\infty}=\frac{a_1}{1-r}[/tex]Thus, the information given translates to:
[tex]a_1=5\\ \\ S_{\infty}=20=\frac{5}{1-r}[/tex]
Now you can solve for the constant ratio, r:
[tex]1-r=\frac{5}{20}\\ \\ r=1-\frac{5}{20}\\ \\ r=\frac{15}{20}\\ \\ r=3/4[/tex]
The common ratio of the infinite geometric progression with the first term of 5 and a sum of 20 is 0.75.
The question pertains to finding the common ratio of an infinite geometric progression (GP) when given the first term and the sum of all its terms. The first term is known as 5, and the sum of the infinite GP is 20. To find the common ratio, we use the formula for the sum of an infinite GP, which is S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.
Plugging in the given values, we have:
20 = 5 / (1 - r)
We can solve for r by multiplying both sides by (1 - r) and then simplifying:
20(1 - r) = 5
20 - 20r = 5
15 = 20r
r = 0.75
Thus, the common ratio of the infinite GP with a first term of 5 and a sum of 20 is 0.75.
If [x] denotes the least integer greater than or equal to x and [x/2] = 0, which of the following could be the value of x?A. -2B. -3/2C. 1/2D. 1E. 2
Answer:
B) -3/2
Step-by-step explanation:
If [x/2]=0 then x/2 is a number such that the least integer greater than or equal to x/2 is 0. We can rewrite this as the inequality x/2≤0. Then, the value of x in C, D and E is wrong because they are positive numbers, then x/2 would be a positive number which contradicts this inequality.
Now, 0 is the least integer that satisfies this inequality, therefore we cannot have that x/2≤-1 since -1 is an integer and -1<0. Then x/2>-1. This discards A as wrong, because for x=-2, x/2=-1, contrary to x/2>-1.
Thus B is the right answer. To verify, if x=-3/2, then x/2=-3/4 and we have that -1<-3/4≤0 as required.
The length of a rectangle is 3 m less than the diagonal and the width is 8 m less than the diagonal. If the area is 74 m^2, how long is the diagonal in meters? Round your answer to the nearest tenth.
Answer:
14.5 m
Step-by-step explanation:
Let x represent the length of the diagonal. Then the length of the rectangle is (x-3) and its width is (x-8). The area is the product of these, so is ...
(x -3)(x -8) = 74
x^2 -11x +24 = 74 . . . . eliminate parentheses
x^2 -11x = 50 . . . . . . . .subtract 24
x^2 -11x +30.25 = 80.25 . . . . add 30.25 to complete the square
(x -5.5)^2 = 80.25 . . . . . . write as square
x - 5.5 = √80.25 ≈ 8.958 . . . . take the square root
x = 8.958 + 5.5 = 14.458 . . . . .add 5.5
The length of the diagonal is about 14.5 meters.
Answer:
Step-by-step explanation:
The diagram of the rectangle, ABCD is shown in the attached photo. The diagonal of the rectangle forms a triangle, ABC
Applying Pythagoras theorem,
d^2 = (d - 8)^2 + (d - 3 )^2
d^2 = d^2 - 16d + 64 + d^2 - 6d + 9
d^2 = 2d^2 - 22d + 73
d^2 - 22d + 73 = 0
d^2 = 22d - 73 - - - - - - 1
If the area is 74 m^2, it means that
(d- 8)(d- 3) = 74
d^2 - 11d + 24 = 74
d^2 = 74 - 24 + 11d
d^2 = 50 + 11d - - - - - - - -2
Equating equation 1 and 2, it becomes
22d - 73 = 50 + 11d
22d - 11d = 50 + 73
11d = 123
d = 123/11 = 11.182
diagonal = 11.2 m to the nearest tenth.
A virus takes 8 days to double its original population (A=2A0). How long will it take to quadruple its population? Round to the nearest tenth.
Answer:
It takes 16 days to quadruple its population.
Step-by-step explanation:
The population of the virus can be represented by the following exponential function.
[tex]A(t) = A_{0}e^{rt}[/tex]
In which A(t) is the population after t days, [tex]A_{0}[/tex] is the initial population and r is the growth rate.
In this problem, we have that:
[tex]A(8) = 2A_{0}[/tex]
So, we use this to find the value of r.
[tex]A(t) = A_{0}e^{rt}[/tex]
[tex]2A_{0} = A_{0}e^{8r}[/tex]
[tex]e^{8r} = 2[/tex]
Applying ln to both sides
[tex]8r = 0.6931[/tex]
[tex]r = 0.0867[/tex]
How long will it take to quadruple its population?
This is t when [tex]A(t) = 4A_{0}[/tex]
[tex]A(t) = A_{0}e^{rt}[/tex]
[tex]4A_{0} = A_{0}e^{0.0867t}[/tex]
[tex]e^{0.0867t} = 4[/tex]
Again we apply ln to both sides.
[tex]0.0867t = 1.39[/tex]
[tex]t = 16[/tex]
It takes 16 days to quadruple its population.
The number of days it takes to quadruple it's population is; 16days
According to the question;
The virus takes 8 days to double it's original population.Therefore;
8days = 2A.
We are required to determine how long it will take to quadruple it's population;
Let no. of days required = x days.
8days =======2A x days =======4ABy cross multiplication; we have;
2Ax = 32ABy dividing through by 2A; we have;
x = 16 days.Read more:
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The researcher has limited resources. He sends 9 emails from a Latino name, and 14 emails from a non-Latino name. For the Latino names, the mean response time was 421 minutes (standard deviation of 82 minutes). For the non-Latino names, it was 366 minutes (standard deviation of 101 minutes). Calculate the standard error for the difference in means.
Answer: 38.41 minutes
Step-by-step explanation:
The standard error for the difference in means is given by :-
[tex]SE.=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma^2_2}{n_2}}[/tex]
where , [tex]\sigma_1[/tex] = Standard deviation for sample 1.
[tex]n_1[/tex]= Size of sample 1.
[tex]\sigma_2[/tex] = Standard deviation for sample 2.
[tex]n_2[/tex]= Size of sample 2.
Let the sample of Latino name is first and non -Latino is second.
As per given , we have
[tex]\sigma_1=82[/tex]
[tex]n_1=9[/tex]
[tex]\sigma_2=101[/tex]
[tex]n_2=14[/tex]
The standard error for the difference in means will be :
[tex]SE.=\sqrt{\dfrac{(82)^2}{9}+\dfrac{(101)^2}{14}}[/tex]
[tex]SE.=\sqrt{\dfrac{6724}{9}+\dfrac{10201}{14}}[/tex]
[tex]SE.=\sqrt{747.111111111+728.642857143}[/tex]
[tex]SE.=\sqrt{1475.75396825}=38.4155433158\approx38.41[/tex]
Hence, the standard error for the difference in means =38.41 minutes
Nell's mom makes chocolate milk with 30\text{ mL}30 mL30, start text, space, m, L, end text of chocolate syrup for every 222 ounces of milk. Nell's dad adds 65\text{ mL}65 mL65, start text, space, m, L, end text of chocolate syrup for every 555 ounces of milk. Whose chocolate milk is more chocolatey?
Answer:
Hence Nell's mom Chocolate milk is more Chocolaty.
Step-by-step explanation:
Given:
Chocolate syrup used by Nell's mom = 30 ml
Amount of milk used = 2 ounces.
We will first find Amount of chocolate syrup used in 1 ounce of milk.
Now In 2 ounces of milk = 30 ml of chocolate syrup.
So in 1 ounce of milk = Amount of Chocolate syrup used for 1 ounce milk.
By using Unitary method we get;
Amount of Chocolate syrup used for 1 ounce milk= [tex]\frac{30}{2}=15\ ml[/tex]
Hence For every 1 ounce of milk Nell's mom uses 15 ml of chocolate syrup.
Also Given:
Chocolate syrup used by Nell's dad = 65 ml
Amount of milk used = 5 ounces.
We will first find Amount of chocolate syrup used in 1 ounce of milk.
Now In 5 ounces of milk = 65 ml of chocolate syrup.
So in 1 ounce of milk = Amount of Chocolate syrup used for 1 ounce milk.
By using Unitary method we get;
Amount of Chocolate syrup used for 1 ounce milk= [tex]\frac{65}{5}=13\ ml[/tex]
Hence For every 1 ounce of milk Nell's dad uses 13 ml of chocolate syrup.
Since The amount of chocolate syrup used by Nell's mom is more than Nell's dad.
Hence Nell's mom Chocolate milk is more Chocolaty.
Answer:
They are both the same
Step-by-step explanation:
A certain drug dosage calls for 460 mg per kg per day and is divided into four doses (1 every 6 hours). If a person weighs 229 pounds, how many milligrams of the drug should he receive every 6 hours?
Final answer:
For a 229-pound individual, they should receive approximately 11947 mg of the drug every 6 hours.
Explanation:
The student is asking how to calculate the appropriate dosage of a medication based on a person's weight. Specifically, the problem is determining how many milligrams of a drug should be administered every 6 hours when the dosage calls for 460 mg per kg per day and the person weighs 229 pounds.
First, we convert the person's weight from pounds to kilograms, knowing that 1 pound is approximately 0.453592 kg. So, 229 pounds is equal to 229 × 0.453592 kg = 103.890648 kg.
Next, we calculate the daily dosage in milligrams using the provided dosage requirement of 460 mg per kg per day:
103.890648 kg × 460 mg/kg = 47789.09808 mg per day.
Since the medication is divided into four doses, we divide the daily total by 4 to find the amount per dose:
47789.09808 mg ÷ 4 = 11947.27452 mg per dose.
Therefore, the individual should receive approximately 11947 mg of the drug every 6 hours.
What term is used to describe the graphical representation of the change in microbial population over time?
Answer:
The term exponential is often used.
Step-by-step explanation:
The term exponential is used to represent changes in population over time. The idea of (positive) exponential is that the higher the number, the higher the growth. You can relate this with a population, because the higher the population, the more opportunities for it to multiply, thus, the higher it grows.
Usually the way to meassure the population of an species after certain number of years x, you use an exponential function of the form
[tex] f(x) = K_0 * a^x [/tex]
For certain constants K₀ and a. K₀ is the initial population at the start of the experiment and a number of exponential growth. Essentially, the population of the species is multiplied by a during each year.
For example, if K₀ = 1000 and a = 2, then the population at the start of the experiment is 1000. After the first year is 1000*2 = 2000 and after the second year it is 2000*2 = 4000. Note that, not only the population grow during the years, but also the amount that the population increases also grow: in the first year it grows 1000, and between the first and second year it grows 2000.
1. In the triangle below, determine the value of c.
2. In the triangle below, what ratio is tan P?
a. p/r
b. r/q
c. r/p
d. p/q
Answer:
2. a. [tex]\displaystyle \frac{p}{r}[/tex]
1. [tex]\displaystyle 15,35842773 ≈ c[/tex]
Step-by-step explanation:
2. Extended Information on Trigonometric Ratios
[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ[/tex]
__________________________________________________________
1. We have to determine which trigonometric ratio[s] to use, depending on what is given to us, and in this case, we will be using the secant [or cosine] ratio:
[tex]\displaystyle sec\:43° = \frac{21}{c} → \frac{21}{sec\:43°} ≈ c → 15,35842773 ≈ c \\ \\ OR \\ \\ cos\:43° = \frac{c}{21} → 21cos\:43° ≈ c → 15,35842773 ≈ c[/tex]
ONCE AGAIN...
Extended Information on Trigonometric Ratios
[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ[/tex]
I am joyous to assist you anytime.
Answer:
15.36.
p/r.
Step-by-step explanation:
cos 43 = c/21
c = 21 cos 43
c = 15.36.
Tan P = opposite side / adjacent side
= p/r.
In the figure, BP is an angle bisector of ∠CBD.
Find x if m∠1 = 4x - 8 and m∠2 = 3x + 2.
A) 5
B) 7
C) 9
D) 10
Answer:
9
Step-by-step explanation:
Susan wanted to know if aerobic exercise caused more weight loss than just walking. Susan had her experimental group do aerobic exercise for 20 minutes, 4 days a week. She weighed each subject before the experiment started and again 3 months into the experiment. The independent variable in her experimental research was _____
Answer:
Independent variable : Anaerobic Exercise
Step-by-step explanation:
The dependent variable is known as the variable of interest or "Y" and usually the independent variables are expressed by "X".
The independent variable is the "variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable"
For this case our independent variable would be the anerobic exercise, since we want to se the effect of the exercise on the weigth loss, so then our dependent variable would be th weigth loss.
And for this case we can check the hypothesis with a paired t-test if we use the same individuals.
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations we can use it.
The independent variable in Susan's experimental research on weight loss is the introduction of aerobic exercise. How much weight loss is achieved can have multiple contributing factors, including individual differences. Incorporating moderate to vigorous physical activity is crucial for weight control and may need to be adjusted based on individual needs.
The independent variable in Susan's experimental research is the type of exercise performed by the subjects — specifically, the aerobic exercise. This is because the independent variable is the factor that the researcher manipulates to determine if it causes a change in another variable. In this case, the independent variable is the introduction of aerobic exercise compared to just walking. Susan's goal is to measure the effects of aerobic exercise on weight loss among the participants over a period of 3 months.
Variations in weight loss outcomes in a workout program can be attributed to individual differences such as metabolism, diet, genetics, lifestyle, and adherence to the exercise regimen. For effective weight control, research suggests a combination of aerobic activity and muscle-strengthening exercises. Susan can compare her findings to these variables to gain insight into the weight loss effects of aerobic exercise.
For those looking to use physical activity for weight loss and control, it might make sense to increase either the intensity or the minutes per week of physical activity, depending on their individual circumstances. Incorporating moderate to vigorous aerobic activity combined with a reduction in caloric intake can help meet weight-control goals for many adults.
A costumer walked into a restaurant and purchased 4 chicken sandwiches and 5 large sodas for $22.50. The customer behind him bought 7 chicken sandwiches and 6 large sodas for $35.25. How much does a chicken sandwich cost and how much is a large soda?
Set up an equation for each customer:
4C + 5S = 22.50
7C + 6S = 35.25
Multipyy the first equation by -1.75 to make the 4C the inverse of 7c:
4C + 5S = 22.50 x -1.75 = -7C - 8.75S = -39.375
Now add the two equations to eliminate the C variable:
7C +6S = 35.25 + -7C - 8.75S = -39.375
= -2.75S = -4.125
Divide both sides by -2.75 to solve for S:
S = -4.125 / -2.75
S = 1.50
The price of a soda is $1.50
Now replace S in an equation with 1.50 and solve for C:
4C + 5(1.50) = 22.50
Simplify:
4C + 7.50 = 22.50
Subtract 7.50 from both sides:
4C = 15
Divide both sides by 4:
C = 15/4
C = 3.75
The sandwich costs $3.75
Soda = $1.50
Sandwich = $3.75
Answer: the cost of a chicken sandwich is $3.75
the cost of a large soda is $1.5
Step-by-step explanation:
Let x represent the cost of a chicken sandwich.
Let y represent the cost of a large soda.
A costumer walked into a restaurant and purchased 4 chicken sandwiches and 5 large sodas for $22.50. This means that
4x + 5y = 22.5 - - - - - - - -1
The customer behind him bought 7 chicken sandwiches and 6 large sodas for $35.25. This means that
7x + 6y = 35.25 - - - - - - - - - -2
Multiplying equation 1 by 7 and equation 2 by 4, it becomes
28x + 35y = 157.5
28x + 24y = 141
Subtracting
11y = 16.5
y = 16.5/11 = 1.5
Substituting y = 1.5 into equation 1, it becomes
4x + 5 × 1.5 = 22.5
4x + 7.5 = 22.5
4x = 22.5 - 7.5 = 15
x = 15/4 = 3.75
Find the area of the shaded region of the circle. Round to the nearest hundredth.
160.78
615.75
547.62
454.97
Answer:Area of shaded region is 454.97
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area of circle = πr^2
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
r = 14
Area of the circle = 3.14 × 14^2 = 615.44
The shaded area is a sector
Area of a sector is expressed as
Area = #/360 × πr^2
Where
# = 94 = central angle
Area of sector = 94/360 × 3.14 × 14
= 160.68
Area of shaded region would be
615.44 - 160.68
= 454.97
Answer:
454.97 unit^2.
Step-by-step explanation:
The area of the whole circle = pi r^2
= 14^2 pi.
As there are 360 degrees in a circle the area of the shaded region , by proportion = [ (360 - 94) / 360 ] * 14^2 pi
= 454.972 unit^2.
In Mathopolis, an adult is a person 21 years of age or older and a child is a person under 21 years of age. Exactly half of the adults in Mathopolis are female, and exactly half of the female adults have exactly one biological child. Nobody else has a child, and there are no other children. What percent of the people of Mathopolis are children?
Answer:
20%
Step-by-step explanation:
If there are 4 adults, 2 are female, and 1 of those has 1 child. Then the population is 4 adults and 1 child. The children make up 1/5 = 20% of the population.
Answer
20%
Step-by-step explanation:
Aops Question
There is a 0.9991 probability that a randomly selected 31-year-old male lives through the year. A life insurance company charges $166 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $90 comma 000 as a death benefit. Complete parts (a) through (c) below.
a. From the perspective of the 31-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If the 31-year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why?
Answer:
a) Monetary values corresponding to the two events are:
-In case of surviving the year = -166$
-In case of a death in the year = 89834$
b) Expected value of the purchasing the insurance is -85 $
c) Yes, insurance company can make a profit with this policy.
Step-by-step explanation:
a) The man need to pay 166$ first to enroll the insurance policy. If he survives within a year, he will lose 166$. Otherwise, if he dies within a year he will profit 89834$.
b) Expected value of the purchasing the insurance as following:
-In case of surviving the year:
Value: -166$
Probability: 0,9991
-In case of death in a year
Value: 89834$
Probability: 0,0009
Expected value is E(x) = -166×0,9991 + 89834×0,0009 = -85 $
c) Lets consider that 10000 different 31 year old man enrolled to this insurance policy. According to probability of death, 9 out of 10000 man expected to be dead within the year. Therefore, company need to pay 9*90000 = 810000$ to their costumers. But, company will collect 10000*166=1660000$ from their costumers in the beginning of the year
So, it is expected that company is going to profit 1660000-810000=850000$ per year.
The monetary values corresponding to surviving or not surviving for a 31-year-old male are $166 and $90,000 respectively. The expected value for the male purchasing the policy is $83.75. The insurance company can expect to make a profit from many such policies.
Explanation:a. From the perspective of the 31-year-old male, the monetary value of surviving the year is $166 (the cost of the insurance). The monetary value of not surviving is $90,000 (the death benefit).
b. To find the expected value, we multiply the probability of each outcome by its corresponding monetary value and sum them. The expected value is calculated as: (0.9991 * $166) + (0.0009 * (-$90,000)) = $164.75 + (-$81) = $83.75.
c. The insurance company can expect to make a profit from many such policies. This is because the expected value for the 31-year-old male is positive ($83.75), meaning that on average the insurance company will earn more in premiums than it pays out in benefits.
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A savings account is started with an initial deposit of $600. The account earns 2.1 % interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
Answer: it will take 14 years
Step-by-step explanation:
A savings account is started with an initial deposit of $600. This means that the principal P is
P = 600
It was compounded annually. This means that it was compounded once in a year. Therefore,
n = 1
The rate at which the principal was compounded is 2.1%. So
r = 2.1/100 = 0.021
The duration of time that for which the money stayed in the account is t years. So
Time = t
The formula for compound interest is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years. Therefore,
a) the equation to represent the amount of money in the account as a function of time in years would be
A = 600 (1+0.021/1)^1×t
A = 600 (1.021)^t
b) the amount of time it takes for the account balance to reach $800 would be
800 = 600 (1.021)^t
Dividing both sides of the equation by 600, it becomes
1.33 = (1.021)^t
t = 14
A bicycle store costs $1750 per month to operate. The store pays an average of $65 per bike. The average selling price of each bicycle is $115. How many bicycles must the store sell each month to break even?
Answer:
The store must sell 35 bikes to break even.
Step-by-step explanation:
115-65 = 50. 1750 divided by 50 = 35.
Answer:you must sell 35 bikes each month to break even
Step-by-step explanation:
The point at which you break even is the point when there is neither profit nor loss. It mean that
Revenue - cost = 0
Revenue = cost
The cost of operating the bicycle per month is $1750
The store pays an average of $65 per bike. Let x represent the number of bikes that the store gets in a month. The total cost of x bikes would be
1750 + 65x
The average selling price of each bicycle is $115. Total revenue from x bikes would be
115 × x = 115x
Therefore, to break even,
1750 + 65x = 115x
115x - 65x = 1750
50x = 1750
x = 1750/50 = 35
A vegetable garden and it's around a pasta shaped like a square that together are 12 ft wide. A path is 1 feet wide. If one bag of gravel covers 9 square feet, how many bags are needed to cover the path? Round your answers to the nearest tenth.
The overall width of the path and garden is 12 feet.
The area of the entire garden and path is 12 x 12 = 144 square feet.
The path is 1 foot wide, so the garden would be 12 - 2 = 20 feet wide.
The area of the garden only would be 10 x 10 = 100 square feet.
The area of the path only = 144 - 100 = 44 square feet.
1 bag covers 9 square feet:
44 / 9 = 4.88
You would need 5 bags.
In the parallelogram below, W = ?
The value of w in the given figure of parallelogram is, w = 37 degrees.
We can see that the diagonals of the parallelogram divided it into four number of parallelogram.
We know that the sum of all interior angles of a triangle is 180 degrees according to Angle Sum Property of Triangle.
So, from the given figure we can see that in a triangle the interior angles are w, 2w and 69 degrees.
According to Angle Sum Property,
w + 2w + 69 = 180
3w = 180 - 69 = 111
w = 111/3 = 37
Hence the value of w in the given parallelogram is 37 degrees.
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What would be added to the price of a $22,500 car if the DMV fees for title and license were 1.5%?
A. $3,375
B. $337.50
C. $450
D. $22,837.50
Answer:
B. $337.50
Step-by-step explanation:
1.5% of $22,500 is 337.5
Answer:
B. $337.50
Step-by-step explanation:
The amount of fluid excreted as urine each day averages approximately less than how many liters?
Answer: Averages less than 2litres per day
Step-by-step explanation:
The normal range of urine excreted per day is between 1 to 2 litres, but the kidney must produce a minimum urine volume of 500mL per day, to get rid of body waste, anything below that is abnormal, and not good for the body
3/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?A. 1/2B. 2/3C. 11/15D. 23/30E. 4/5
Answer:
option C
Step-by-step explanation:
[tex]\dfrac{3}{5}[/tex] class left [tex]\dfrac{2}{5}[/tex] of the class left.
now,
[tex]\dfrac{1}{3}[/tex] of stayed did not want to go so, [tex]\dfrac{2}{3}[/tex] of the student wanted to go.
[tex]\dfrac{1}{2}[/tex] of the stayed student join the trip.
number of student that stayed and wanted to go are
=[tex]\dfrac{2}{5}\times \dfrac{2}{3}\times \dfrac{1}{2}[/tex]
=[tex]\dfrac{2}{15}[/tex]
fraction of class on the field trip
= [tex]\dfrac{3}{5}+\dfrac{2}{15}[/tex]
= [tex]\dfrac{11}{15}[/tex]
Hence, the correct answer is option C
Mitch and Tom are playing a video game. Mitch has eight less than triple the points that Tom has. If Mitch has 79 points how many points does Tom have?
Tom has 29 points in the video game whereas mitch has 79 points.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, Tom and Mitch are engaged in video game gaming. Tom has eight more points than Mitch does, but not by much. Let points of mitch be y and points of tom be x.
Based on the given conditions, formulate y = 3x -8
Rearrange unknown terms to the left side of the equation: 3x = 79 + 8
Calculate the sum or difference: 3x = 87
Divide both sides of the equation by the coefficient of the variable: x = 87/3
Cross out the common factor: x = 29
Therefore, Tom has 29 points in the video game.
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By solving the equation 3T - 8 = 79, we find that Tom has 29 points.
Explanation:The student is asking a mathematical word problem that involves forming and solving an equation. To find how many points Tom has, we need to work with the information given: Mitch has eight less than triple the points that Tom has, and Mitch has 79 points.
Let's define Tom's points as 'T'. The problem tells us that Mitch's points are eight less than triple Tom's points, which can be written as the equation: 3T - 8 = 79.
Now we solve for 'T':
Add 8 to both sides of the equation: 3T = 79 + 8Calculate the sum: 3T = 87Divide both sides by 3: T = 87 / 3Calculate the division: T = 29Tom has 29 points.