Justin is taking an anti-flammatory drug and he must receive 6 milligrams for each 17 kg of weight.
Justin's weight is 244 pounds i.e., 110.677 Kg.
Theerfore, the amount of anti flammatory drug he needs is
[tex]\frac{6}{17}\times110.677\approx39.063[/tex]Therefore, Justing needs 39.063 miiligrams of anti flammatory drug.
Determine the probability of being dealt 4 Aces of cards, from a deck of 52 playing cards, with a replacement.
Before finding the probability of being dealt 4 Aces of cards, let's find the probability of being dealt an Ace card on each draw.
The probability of getting an specific card from a deck is given by the ratio between the amount of this specific card and the total amount of cards. We have 4 Aces in a deck, and 52 cards, therefore, the probability of getting an Ace is
[tex]\frac{4}{52}=\frac{1}{13}[/tex]Since the cards are replaced, it is the same probability of getting an Ace on each draw.
Each draw is an independent event, the probability of them happening simultaneously is given by their product. The probability of being dealt 4 Aces of cards with a replacement is
[tex]\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}=\frac{1}{13^4}=\frac{1}{28561}=0.00003501277\ldots[/tex]Can you please help me out
ANSWER:
A. 2.2%
STEP-BY-STEP EXPLANATION:
We can calculate the probability using the quotient of the area of the small circle and the area of the entire rectangular sector, like this:
[tex]\begin{gathered} p=\frac{A_c}{A_r} \\ A_c=\pi\cdot r^2 \\ A_r=l\cdot w \end{gathered}[/tex]In the circle the radius is 6 inches and in the rectangle the length is 84 inches and the width is 60 inches.
Therefore we replace and we have:
[tex]\begin{gathered} A_c=3.14\cdot6^2=113.04 \\ A_r=84\cdot60=5040 \\ p=\frac{113.04}{5040}=0.022=2.2\text{\%} \end{gathered}[/tex]Bill flip a coin and roll a dice independent or dependent
Dependent Events where what happens depends on what happened before, such as taking cards from a deck makes less cards each time.
Independent Events which we learn about here.
Bill flipping a coin and rolling a dice are independent events. Flipping a coin doesn't depend on rolling a die.
AnswerIndependent
Suppose cone a is similar to cone b and the scale factor between the solids is 3:2, respectively. If the height of cone a is 15 inches, determine the height of cone b.
The height of cone is 10 inches.
What is cone?
A cone is indeed a three-dimensional geometric shape with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex. A cone is made up of a collection of line segments, half-lines, as well as lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex. The base may only be a circle, any closed one-dimensional figure, any one-dimensional quadratic shape in the plane, or any combination of the above and furthermore all the enclosed points, depending on the author.
What is the formula for finding the height of a cone?
The cone height formula calculates the height of the cone. The height of the cone using cone height formulas are, h = 3V/πr 2 and h = √l2 - r2, where V = Volume of the cone, r = Radius of the cone, and l = Slant height of the cone.We know that
If two figures are similar, then the ratio of its corresponding sides is proportional
Let x----> the height of cone B
using proportionality
3/2 = 15/x
x = 2 * 15/3
x = 10 inches
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i need helppp!!!!!!!!
Answer:
5
Step-by-step explanation:
y=x+5 cuz it works out for everything
At a fundraiser hosted by a local restaurant, customers can pay as much or as little as they like for a meal, as long as they pay at least $1. any profits are donated to a local charity. one evening, the mean (average) price paid per customer was $55. one more customer walked in and paid $70 for a meal, bringing the average up to $56. what is the highest possible price that a customer could have paid for their meal that evening? do you think the amounts in your solution are reasonable.
in your solution are reasonable for this situation?
The highest possible price that a customer could have paid for their meal that evening exists $ 757. Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.
How to estimate the highest possible price that a customer could have paid for their meal that evening?When determining the mean (average) of a group of values, we add up the values in the group and divide that total by the number of values in the group. As a result, the average of the set's values divided by the total number of values is equal to the set's values' sum.
Let n represent how many people were in the store that evening. Thus, a total of 56n was paid that evening by all customers. The bill for the last customer's meal was $70.00. There were (n-1) customers who had already paid a total of (56n-70) dollars before this one arrived. The average cost per customer at that time was $55 dollars.
From the above information, we get
[tex]$\frac{56 n-70}{n-1} &=55 \\[/tex]
simplifying the above equation, we get
56n - 70 = 55(n - 1)
56n - 70 = 55n - 55
n = 15
Since n = 15, it follows that there were 15 customers that evening, and the total amount paid by all customers stood therefore 56 n = 56(15) = 840 dollars.
To estimate the highest possible price that a customer could have paid for their meal that evening, we will assume that 13 of the customers paid the lowest possible price of $ 1. Then the remaining customer would have paid 840 - 13 × 1 - 70 = 757 dollars.
Therefore, the highest possible price that a customer could have paid for their meal that evening exists $ 757.
Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.
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Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $7,500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011? Last week, he made $ in commission.
EXPLANATION
Let's see the facts:
%Earns= 13% commission/week
Last week sold = $7,500
In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:
$Earns = 0.13 (decimal form)*$7,500
Earns = $975
Last week, he made $975 in commission.
If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year
16. Describe, step-by-step how to find the slope of a line through two points.
Answer:
1. find the 2 points and determine their coordinates.
2. determine the difference in the rise or y-coordinates.
3. determine the difference in the run or x-coordinates.
4. place the rise over the run and divide to find slope
I need help to find x and could you explain it also please
6) How long will it take for an investment to double in value if it earns 4.75% compoundedcontinuously?A) 14.593 yearsB) 15.711 years C) 23.129 years D) 7.296 years
A quantity that is compounded continuously follows the next equation:
[tex]A=Pe^{rt}[/tex]Where:
[tex]\begin{gathered} A=\text{ amount in time ''t''} \\ P=\text{ initial amount} \\ r=\text{ rate of interest in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Now, the interest rate in decimal notation is determined by dividing the percentage by 100:
[tex]r=\frac{4.75}{100}=0.0475[/tex]Now, we are asked to determine the time required for the quantity to double. Therefore, we need to determine "t" when:
[tex]A=2P[/tex]Substituting in the formula we get:
[tex]2P=Pe^{rt}[/tex]Now, we can cancel out the "P":
[tex]2=e^{rt}[/tex]Now, we solve for "t". First, we take the natural logarithm to both sides:
[tex]ln2=lne^{rt}[/tex]Now, we use the following property of logarithms:
[tex]lnx{}^y=ylnx[/tex]Applying the property we get:
[tex]ln2=rtlne[/tex]We have that:
[tex]lne=1[/tex]Therefore:
[tex]ln2=rt[/tex]Now, we divide both sides by "r":
[tex]\frac{ln2}{r}=t[/tex]Now, we substitute the value of "r":
[tex]\frac{ln2}{0.0475}=t[/tex]Solving the operations:
[tex]14.593=t[/tex]Therefore, the right option is A.
Zachary is paying his dad back for the money he borrowed to pay for a car repair. The amount that he owes his dad is shown in the graph
Answer:
so you need to divide this and turn it into a coefficient for the answer
Step-by-step explanation:
Select the correct answer.
Solve the system of equations.
y=x-5
y=x-5x+3
O A. (4,-3) and (2,-1)
О в.
(4,-1) and (2,-3)
O C.
(-4,-9) and (-2,-7)
O D.
(4,-9) and (2,-7)
The value of x is -2 and the value of y is -7. The correct option is C.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the equations are y = x - 5 and y = 5x + 3. The value of x and y will be calculated by solving the equations,
y=x-5
y=5x+3
x -5 = 5x + 3
-4x = 8
x = -2
The value of y will be calculated as,
y = x - 5
y = -2 - 5
y = -7
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To save money for her son's college tuition, Mary invests $98 every month in an annuity that pays 6.1% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 21 years.
Given
Monthly deposit = $98
Rate = 6.1%
Number of years = 21
Find
Total value of the annuity in 21 years.
Explanation
Total value of annuity is given by
[tex]FV=A[\frac{(1+\frac{r}{m})^{mt}-1}{\frac{r}{m}}][/tex]where FV is a future value
so ,
[tex]\begin{gathered} FV=98[\frac{(1+\frac{0.061}{12})^{12\times21}-1}{\frac{0.061}{12}}] \\ \\ \end{gathered}[/tex]now solve this to obtain the future value .
[tex]\begin{gathered} FV=98\times509.227229162 \\ FV=49904.26 \end{gathered}[/tex]Final Answer
Therefore , the future value is $49904.27
Which of the following equations is equivalent to 2/3x- 1/2Y=6
O4x - 3y = 36
2x - y = 36
O 2x - y = 6
Answer:
4x - 3y = 36
Step-by-step explanation:
⅔x-½y=6
just multiply both sides by the LCM which is 6
6×⅔x-6×½y=6×6
4x-3y=36
Subject :- Optional Mathematics
Topic :- Fraction
The value of x is 0.94 or 3.34 with the functions given.
The function is given as:
f = (x, 4 x - 17)
g = (x, (2 x + 8) / 5)
We get that:
g⁻¹ (x) = (2 x + 8) / 5
f o f (x)
= f (f (x))
= (4x [ 4x - 17] - 17)
= 16 x² - 68 x - 17
ATQ:
16 x² - 68 x - 17 = (2 x + 8) / 5
80 x² - 340 x - 85 = 2 x + 8
80 x² - 342 x - 93 = 0
Solving the equation:
D = b² - 4 ac
D = (-342)² - 4 (80) (-93)
D = 36681
x = (342 ± √36681) / 2(80)
x = (342 ± 191.52) / 160
x = 0.94 or x = 3.34
Therefore, the value of x is 0.94 or 3.34 with the functions given.
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Alicia has at most $196 to buy a new baseball gloves and a new baseball hat. What inequality can represent this?
Alicia has at most $196 this means that her amount of money is less or equal than $196, we can express this as an inequality, like this:
[tex]\text{y}\leq\text{ \$}196-x[/tex]Where x represents the cost associated with the hat and the gloves and y is the money that left after the purchase of these articles
In Mrs. Stone's class, 18 out of 30 student turned in their homework on time. What percent of the class turned their homework in on time?
Which ordered pair is a solution for this system of linear inequalities?
2x + 3y < 12
3x - 2y ≥ 18
A. (5,0)
B. (3,-1)
C. (-1,3)
D. (4,-9)
The ordered pair that is a solution for the inequality 2x + 3y < 12 and
3x - 2y ≥ 18 is
D. (4,-9)How to find the solutionThe solution is sought by substituting to each of the pair to the equation and comparing the answers
for D. (4,-9)
2 * 4 + 3 * -9 < 12
-19 < 12 correct
3x - 2y ≥ 18
3 * 4 - 2 * -9 ≥ 18
30 ≥ 18 correct
This proves that option D is the correct option
trying for A. (5,0)
2 * 5 + 3 * 5 < 12
25 < 12 incorrect
3x - 2y ≥ 18
3 * 5 - 2 * 0 ≥ 18
15 ≥ 18 incorrect
trying for B. (3,-1)
2 * 3 + 3 * -1 < 12
3 < 12 correct
3x - 2y ≥ 18
3 * 3 - 2 * -1 ≥ 18
11 ≥ 18 incorrect
When any part is incorrect the pair is not a solution
trying for C. (-1,3)
2 * -1 + 3 * 3 < 12
7 < 12 correct
3x - 2y ≥ 18
3 * -1 - 2 * 3 ≥ 18
-9 ≥ 18 incorrect
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Lu's deposit includes two checks: $123.45 and $432.90; cash: 3 one-dollar bills, 9 five-dollar bills, 5 ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. Find the total deposit.
$556.35
$648.35
$660.32
$721.31
Answer:
The total deposit is $721.31.
Step-by-step explanation:
4x+2y=2 and y=-3x+2 slove the system of equations
The solution of the given system of equations is x =1 and y = -1.
What is a system of equations?In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
Given is a system of equations; 4x+2y=2 and y=-3x+2
Solving the equation by substitution, we get,
4x+2(-3x+2) = 2
4x-6x-4 = 2
-2x+4 = 2
-2x = -2
x = 1
Put x = 1 in any of the given equation,
y = -3*1+2
y = -3+2
y = -1
Hence, The solution of the given system of equations is x =1 and y = -1.
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Hello! Having a little trouble on this question, thanks for your help!
The graph of the function:
[tex]g(x)=ln(4-x)[/tex]Can be obtained by using the parent function:
[tex]f(x)=ln(x)[/tex]Whose graph is shown below:
We must first turn x into -x by making a reflection over the y-axis. This way, the function becomes:
[tex]f(-x)=ln(-x)[/tex]And the graph is:
Finally, we just add 4 to x to translate the graph 4 units to the right to get our desired function:
[tex]g(x)=f(4-x)=ln(4-x)[/tex]The graph is shifted 4 units to the right as shown:
use the distributive property to solve 4 × ( 10 + 7)
Given the expression:
[tex]4\ast(10+7)[/tex]Let's solve the expression using distributive property.
To use distributive property, distribute the term ouside the parentheses to the terms in the parentheses.
Apply distributive property:
[tex]a\ast(b+c)=ab+ac[/tex]Distribute 4 to the values inside the parentheses:
[tex]\begin{gathered} 4\ast(10+7) \\ \\ =4(10)+4(7) \\ \\ =40+28 \\ \\ =68 \end{gathered}[/tex]ANSWER:
68
can you help me on this?
Answer:
The answer is run because the line is going down.
Step-by-step explanation:
One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 5 or a Club. Note that the ace is considered a low card.The probability that the card selected is less than 5 or a club is.(Type an integer or a simplified fraction.)
The total number of cards in a deck of cards is: 52
The total number of club cards is: 13
The total number of cards that less than 5 is: 8.
The probability of selecting a club card is,
[tex]\begin{gathered} P(Club)=\frac{Total\text{ number of club cards}}{\text{Total number of cards}} \\ =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]The probability of selecting a card that is less than five is,
[tex]\begin{gathered} P(card<5)=\frac{8}{52} \\ =\frac{2}{13} \end{gathered}[/tex]The total number of club card that is less than 5 is 3.
The probability of selecting a club card and a card that is less than 5 is,
[tex]P\text{ (club and less than 5)}=\frac{3}{52}[/tex]The probability of selecting a card that is a club or less than 5 is,
[tex]\begin{gathered} P\text{ (Club or less than5)}=P(Club)+P\text{(card less than 5)-P(Club and less than 5)} \\ =\frac{1}{4}+\frac{2}{13}-\frac{3}{52} \\ =\frac{21}{52}-\frac{3}{52} \\ =\frac{9}{26} \end{gathered}[/tex]Thus, the probability of selecting a club card or card that is less than 5 is 9/26.
Write the system of linear equations represented by the augmented matrix. (Use variables x, y, and z, if applicable.)1 - 1 21-30 1 -1 50 0 1-5Use back-substitution to solve the system.(x, y, z) =
The augmented matrix represents the following system of linear equations:
[tex]\begin{gathered} x-y+2z=-3 \\ y-z=5 \\ z=-5 \end{gathered}[/tex]Use back substitution. It means, use the value of z given in the last equation, to find y in the second equation, and then, use these values to find x in the first equation:
[tex]\begin{gathered} y-z=5 \\ y-(-5)=5 \\ y+5=5 \\ y=5-5 \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} x-y+2z=-3 \\ x-0+2(-5)=-3 \\ x-10=-3 \\ x=-3+10 \\ x=7 \end{gathered}[/tex]The solution of the system is (x, y, z)=(7, 0, -5)
Can someone help? :)
The slope of the given line is 2
What is slope of a line?
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
m = [tex]tan\theta[/tex]
If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
slope = [tex]\frac{y_2-y_1}{x_2 - x_1}[/tex]
The given line passes through ( 0, 5) and (-2, 1) .
Slope of the line =
[tex]\frac{1-5}{-2-0}\\\\\frac{-4}{-2}\\\\2[/tex]
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which of the following value are solutions to the inequality -5>6x+9
Given:
The inequality is,
[tex]-5>6x+9[/tex]Required:
To choose the correct value for the given inequality.
Explanation:
Consider the given inequality,
[tex]-5>6x+9[/tex]Consider the first option, 6
Put x=6 in to the given inequality, we get
[tex]\begin{gathered} -5>6\times6+9 \\ -5>36+9 \\ -5>45 \end{gathered}[/tex]Clearly the statement is false.
Now consider the next option, 4
Put x=4 in to the given inequality, we get
[tex]\begin{gathered} -5>6\times4+9 \\ -5>24+9 \\ -5>33 \end{gathered}[/tex]Clearly the statement is false.
Now consider the next option, 0
Put x=0 in to the given inequality, we get
[tex]\begin{gathered} -5>6\times0+9 \\ -5>9 \end{gathered}[/tex]Clearly the statement is false.
Final Answer:
There is no values in the given options .
A ship travels from Akron (A) on a bearing of 030° to Bellvilie (B),90km away. It then travels to Comptin (C) which is 310 km due east of Akron (A).Draw a diagram showing the movement of the ship indicate:a.)Northb.)the distances travelledc.)the know angles
Given: The bearing and distance of a ship from Akron(A) through Bellville(B) to Compton(C)
To Determine: The distance travelled and the angles
Solution
The diagram of the journey can be represented as shown below
Let us solve for BC using cosine rule
[tex]\begin{gathered} BC^2=AB^2+AC^2-2(AB)(AC)cosA \\ BC^2=90^2+310^2-2(90)(310)(cos60^0) \\ BC^2=8100+96100-27900 \\ BC^2=76300 \\ BC=\sqrt{76300} \\ BC=276.22km \\ BC\approx276km \end{gathered}[/tex]The total distance travelled is
[tex]\begin{gathered} Total-distance=AB+BC+AC \\ =90km+276km+310km \\ =676km \end{gathered}[/tex]Using sine rule, we can determine the measure of angle C
[tex]\begin{gathered} \frac{AB}{sinC}=\frac{BC}{sinA}=\frac{AC}{sinB} \\ \frac{90}{sinC}=\frac{276}{sin60^0}=\frac{310}{sinB} \\ \frac{90}{sinC}=\frac{276}{sin60^0} \\ sinC=\frac{90(sin60^0)}{276} \\ sinC=\frac{155.88}{276} \\ sinC=0.5648 \\ C=sin^{-1}(0.5648) \\ C=34.39^0 \end{gathered}[/tex]Also know that the sum of angles in a triangle is 180 degree. Therefore
[tex]\begin{gathered} A+B+C=180^0 \\ 60^0+B+34.39^0=180^0 \\ B+94.39^0=180^0 \\ B=180^0-94.39^0 \\ B=85.61^0 \\ B\approx85.6^0 \end{gathered}[/tex]The bearing of Compton from Bellville(B) is
[tex]Bearing(C-from-B)=90^0+34.39^0=124.39^0\approx124.4^0[/tex]The bearring of Akron(A) from Compton(C) is
[tex]Bearing(A-from-C)=270^0+34.39^0=304.39^0\approx304.4^0[/tex]In summary
The total distance travelled is 676km
The bearing of Compton from Bellville is 124.4 degrees, and the bearing of Akron from Compton is 304.4 degrees
A full-grown monarch caterpillar weights 0.75 grams, has a length of 5 centimeters, and is about 2.5 centimeters around. How can the surface area of the caterpillar be estimated?
A ___ can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of ___ square centimeters.
The choices for the first blank are:
*rectangular prism
*triangular prism
*sphere
*cylinder
The choices for the second blank are:
*13.5
*6.75
*49.1
*117.8
A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.3 cm²
A full-grown monarch caterpillar is of cylinder shape . so , the option 4th is correct for first blank.
Surface area of cylinder is 2πrh + 2πr²
where r is radius of circle and h is height of cylinder
here , length of caterpillar is 5cm and radius is 2.5cm
Surface area = 2πrh + 2πr²
= 2π(5)(2.5) + 2π(2.5)²
= 2π(12.5) + 2π(6.25)
putting π = 3.14
=78.5+39.25
=117.8 cm²
Rewriting the sentence
A cylinder can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of 117.8 square centimeters.
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Answer: A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.8 square centimeters
(if your on PLATO) if not then 117.8
To rent a moving truck for the day, it costs $75 plus $1.50 for each mile, m, driven. Which expression represents the cost, in dollars, to rent the moving truck?
The expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression to represent the total cost will be:
The truck costs $75.And an extra $1.50 for every mile.The expression that gives the total cost.
Let, the number of miles are 'n' and the total cost be 'C'.
Now,
1.50n + 75 = C
Therefore, the expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.
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