Given
[tex]P=600e^{0.03t}[/tex]Find
time,t
Explaination
[tex]\begin{gathered} P=600e^{0.03t} \\ 708=600e^{0.03t} \\ 1.18=e^{0.03t} \end{gathered}[/tex]Taking log on both sides
[tex]\begin{gathered} ln(1.18)=0.03t \\ 0.165514438=0.03t \\ t=5.5\text{ sec} \end{gathered}[/tex]Final Answer
t = 5.5 sec
Which is greater ? 3/5 or 0.14
3/5 = 0.60
0.6 > 0.14
Then, 3/5 is greater than 0.14
What is a system of equations? • An equation with no variables •An equation with more than one variable •Two or more equations with one variable •Two or more equations that share variables
A system of equations is two or more equations with the same variables.
Example:
[tex]\begin{gathered} y=3x+8 \\ 2y=5x-9 \end{gathered}[/tex]Two equations with variables x and y
Translate the following phrase into an algebraic expression. Do not simplify.y divided by the product of 9 and x
To translate the phrase "y divided by the product of 9 and x" into an algebraic expression.
The algebraic expression is
[tex]\frac{y}{9\times x}=\frac{y}{9x}[/tex]Hence, the algebraic expression is
[tex]\frac{y}{9x}[/tex]amma send yo a pic of the work
Graph of inequality
[tex]2x+4y<8[/tex]This is:
a. Is (3,9) a solution to y<16−x ? b. Is (4,11) a solution to y≤14−x ? c. Is (5,10) a solution to y>15−x ? d. Is (6,15) a solution to y≥16−x ?
Let the point (x,y) = (3,9) and the inequality y<16−x. If the point (x,y) is a solution to this inequality then replacing the coordinates of the point (x,y) on the inequality, the inequality would be true. Let's check this:
[tex]9<16−3[/tex]this is equivalent to saying:
[tex]9<13[/tex]this is true, thus (3,9) is a solution to y<16−x.
Similarly consider the point (4,11) and the inequality y≤14−x. Thus:
[tex]11≤14−4[/tex]this is equivalent to:
[tex]11≤10[/tex]this is a contradiction, so we can conclude that the point (4,11) is not a solution to y≤14−x.
Now, consider the point (5,10) and the inequality y>15−x. Then:
[tex]10>15−5[/tex]this is equivalent to:
[tex]10>10[/tex]this is a contradiction, so we can conclude that the point (5,10) is not a solution to y>15−x.
Finally, consider the point (6,15) and the inequality y≥16−x. Then:
[tex]15≥16−6[/tex]this is equivalent to:
[tex]15≥10[/tex]this is true, thus (6,15) is a solution to y≥16−x.
We can conclude that the correct answer is:
Answer:a) (3,9) is a solution to y<16−x.
b) (4,11) is not a solution to y≤14−x.
c) (5,10) is not a solution to y>15−x.
d) (6,15) is a solution to y≥16−x.
Write an equation of the line containing the point (3,1) and perpendicular to the line 2x - 3y = 4.The equation of the line is____(Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer. Do notfactor.)
Two lines are perpendicular when the multiplication of their slopes is equal to -1.
To find the slope of the line 2x - 3y = 4, we have to isolate y, as follows:
[tex]\begin{gathered} 2x-3y=4 \\ -3y=4-2x \\ y=\frac{4-2x}{-3} \\ y=\frac{4}{-3}+\frac{-2x}{-3} \\ y=-\frac{4}{3}+\frac{2}{3}x \end{gathered}[/tex]Its slope is 2/3, then the slope of the perpendicular line is:
[tex]\begin{gathered} m\cdot\frac{2}{3}=-1 \\ m=-1\cdot\frac{3}{2} \\ m=-\frac{3}{2} \end{gathered}[/tex]The slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
Replacing with m = -3/2 and point (3,1):
1 = -3/2(3) + b
1 = -9/2 + b
1 + 9/2 = b
11/2 = b
The equation of the line is y = -3/2x + 11/2
consider the expressions 3x + 12; 3x + 4; x + 12; 12+ 3x which of the expressions would give a different answer than 3(x + 4) when x = 2
From the expression in the end, we can distribute the multiplication by 3 to get:
[tex]3(x+4)=3x+12[/tex]The order of the addtion doesn't change the result, so these three expression are the same for every value of x:
[tex]3(x+4)=3x+12=12+3x[/tex]But the other two, 3x + 4 and x + 12, are not the same, so we can check if they will give the same result.
The result for 3(x + 4) is and x = 2 is:
[tex]3(x+4)=3(2+4)=3\cdot6=18[/tex]And the results for 3x + 4 and x + 12 when x = 2 are:
[tex]\begin{gathered} 3x+4=3\cdot2+4=6+4=10 \\ x+12=3+12=15 \end{gathered}[/tex]Which are not the same as 18.
Thus, the expressions that would give different answer are 3x + 4 and x + 12.
Plot the image of point P under a translation by 5 units to the left and 3 units up.
In order to translate 5 units to the left and 3 units up, we need to decrease 5 units of the x-coordinate and increase 3 units of the y-coordinate.
Looking at the graph, the coordinates of point P are (3, -4).
So, subtracting 5 units from the x-coordinate and adding 3 units to the y-coordinate, we have:
[tex]\begin{gathered} P(3,-4)\\ \\ P^{\prime}(3-5,-4+3)=P^{\prime}(-2,-1) \end{gathered}[/tex]Therefore the image of point P after the translation is located at (-2, -1).
write the equation in STANDARD FORM!
y=2x+3/7
Standard form: [tex]Ax+By=C[/tex]
A, B and C are integersTo arrange a given linear equation into standard form, we are looking to put x and y onto one side of the equation.
Solving the QuestionWe're given:
[tex]y=2x+\dfrac{3}{7}[/tex]
⇒ Typically, we don't include any fractions in standard form. Multiply everything by 7 to get rid of the fraction:
[tex]7y=14x+3[/tex]
⇒ Move 14x to the other side:
[tex]-14x+7y=3[/tex]
⇒ A is typically positive. Divide everything by -1 to make A positive:
[tex]14x-7y=-3[/tex]
Answer[tex]14x-7y=-3[/tex]
Need help with question 5? just the answer and work
SOLUTION:
Step 1:
In this question, we are asked to find the equation of the circle with the given characteristics in standard form:
Step 2:
We need to get the distance between the two points:
(11 , - 7 ) and ( 17 , 13 )
[tex]\begin{gathered} d\text{ =}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ where\text{ \lparen x}_1,\text{ y}_1)\text{ = \lparen 11, - 7\rparen} \\ \text{and } \\ (x_2,\text{ y}_2)\text{ = \lparen 17, 13\rparen} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt{(17-11)^2+\text{ \lparen13-\lparen-7\rparen\rparen}^2} \\ d\text{ = }\sqrt{6^2+\text{ \lparen13+7\rparen}^2} \\ d\text{ =}\sqrt{36+400} \\ d\text{ =}\sqrt{436} \\ Radius\text{ =}\frac{\sqrt{436}}{2} \end{gathered}[/tex]Next:
[tex]\begin{gathered} Using\text{ the equation of a circle in standard form, we have that:} \\ (x-a)^2+\text{ \lparen y-b\rparen}^2\text{ = r}^2 \\ where\text{ \lparen a , b \rparen= \lparen}\frac{11+17}{2},\text{ }\frac{-7+13}{2})\text{ = \lparen}\frac{28}{2},\text{ }\frac{6}{2})\text{ = \lparen 14, 3\rparen} \\ r=\frac{\sqrt{436}}{2} \\ and \\ r^2\text{ =\lparen}^\frac{\sqrt{436}}{2})^2=\frac{436}{4}=\text{ 109} \end{gathered}[/tex][tex]\begin{gathered} (x-14)^2+\text{ \lparen y - 3\rparen}^2=\text{ 109} \\ (Equation\text{ of the circle in standard form\rparen} \\ \end{gathered}[/tex]The graph is as follows:
using the distance formula from above find the distance between (-15,-18) and (18,-2). round to the nearest tenth.using the distance formula from above find the distance between (5,9) and (-7,-7). round to the nearest tenth.using the distance formula from above find the distance between (3,8) and (9,10). round to nearest tenth.
Answer:
[tex]\begin{gathered} 1.\text{ }d=36.7 \\ 2.\text{ }d=20 \\ 3.\text{ }d=6.3 \end{gathered}[/tex]Step by step explanation:
The distance between two points is represented by the following expression:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]1. Then, for (-15, -18) and (18, -2)
[tex]\begin{gathered} d=\sqrt[]{(18-(-15))^2+(-2-(-18))^2} \\ d=\sqrt[]{(33)^2+(16)^2} \\ d=\sqrt[]{1089+256} \\ d=\sqrt[]{1345} \\ d\approx36.67 \\ \text{Rounding to the nearest tenth:} \\ d=36.7 \end{gathered}[/tex]2. Now, for (5,9) and (-7,-7)
[tex]\begin{gathered} d=\sqrt[]{(-7-5)^2+(-7-9)^2} \\ d=\sqrt[]{(-12)^2+(-16)^2} \\ d=\sqrt[]{144+256} \\ d=\sqrt[]{400} \\ d=20 \end{gathered}[/tex]3. Finally, for (3,8) and (9,10)
[tex]\begin{gathered} d=\sqrt[]{(9-3)^2+(10-8)^2} \\ d=\sqrt[]{6^2+2^2} \\ d=\sqrt[]{36+4} \\ d=\sqrt[]{40} \\ d=2\sqrt[]{10} \\ \text{Rounding to the nearest tenth:} \\ d=6.3 \end{gathered}[/tex]Which two of the following numbers have the same value? 4 power of 2 and 5 power of 2 2power of 4 and 4 power of 2 2 power of 4 and 3 power of 3 3 wer of 3 and 4 power of 2
How do you solve this 2 step equation and find the missing letter K? K-10/2=-7
Answer:
Given that,
To solve for k,
[tex]\frac{k-10}{2}=-7[/tex][tex]k-10=-7\times2[/tex]we get,
[tex]k-10=-14[/tex][tex]k=-14+10[/tex][tex]k=-4[/tex]Answer is: k=-4
A trivia contest awards $102 for first place, $68 for second place, $34 for third place, and $17 for fourth place . The function can be written bas ordered pairs :{(1,102),(2,68),(3,34),(4,17)}. Express this function as a table, a graph, and a mapping diagram.
The function denoted by the ordered pairs, (1, 102), (2, 68), (3, 34), (4, 17) can be shown on a tale as follows
As a graph, this is shown below;
Note that the graph drawn above uses 25 units on 1 cm on the y-axis, and 1 unit to 1 cm on the x-axis. Also, its not drawn to perfection as the "points where the x any y values intersect should all fall perfectly on the line of the function.
the Cruz family is buying a custom-made cover for their swimming pool shown below the cover cost $2 and ninety-five per square foot how much will the cover cost ?.round to the nearest cent .
The total cost is $1627.55 , or $1627 and fifty-five
Which statement illustrates the distributive property?OA. 9+ (5i -12i) = (9 + 5i) — (9 + 12i)OB. 9(5i -12i) = 9(5i) — 12i--OC. 9(5i + 12i) = 9(12i + 5i)OD. 9(5i -12i) = 9(5i) — 9(12i)-
Given:
Four options are given.
Required:
Find the option that states the distributive property.
Explanation:
The distributive property is stated as:
[tex]a(b\pm c)=ab\pm ac[/tex]In the given options
[tex]9(5i-12i)=9(5i)-9(12i)[/tex]Final Answer:
Option D is the correct answer.
Un givenue Coordinates . Problem 1 Dilation: Coordinates: A(2,-4), B(2,-2), C(4,0), D(4,-4)
To solve we appply dilation for each point
[tex]\begin{gathered} A(2,-4)\times\frac{1}{2}=A^{\prime}(1,-2) \\ \\ B(2,-2)\times\frac{1}{2}=B^{\prime}(1,-1) \\ \\ C(4,0)\times\frac{1}{2}=C^{\prime}(2,0) \\ \\ D(4,-4)\times\frac{1}{2}=D^{\prime}(2,-2) \end{gathered}[/tex]Solve this percent mixture problem using a system of linear equationsThe royal fruit company produces two types of fruit drinks. The first type is 20% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 160 pints of a mixture that is 85% pure fruit juice? First Fruit Drink= Pints Second Fruit Drink= Pints
Let x and y represent the amount of the first and second type of fruit drinks (respectively) that are used to create the fruit drink that contains 85% fruit juice.
The total volume of the mixture is x+y and it must be equal to 160:
[tex]x+y=160[/tex]Since the first mixture contains 20% fruit juice, only 0.2x of the volume x is pure fuit juice. The total amount of fruit juice in the mixture will be 0.2x plus y, and must be equal to 85% of 160:
[tex]0.2x+y=0.85\cdot160[/tex]We got a system with two variables and two equations. Solve the system of equations using the elimination method:
[tex]\begin{gathered} x+y=160 \\ 0.2x+y=0.85\cdot160 \\ \Rightarrow x-0.2x+y-y=160-0.85\cdot160 \\ \Rightarrow0.8x=160-136 \\ \Rightarrow0.8x=24 \\ \Rightarrow x=\frac{24}{0.8} \\ \therefore x=30 \end{gathered}[/tex]Replace x=30 into the first equation to find the value of y:
[tex]\begin{gathered} x+y=160 \\ \Rightarrow30+y=160 \\ \Rightarrow y=160-130 \\ \Rightarrow y=130 \end{gathered}[/tex]Then, 30 pints of the 20% pure fruit juice and 130 pints of the 100% pure fruit juice are needed to produce 160 pints of the 85% pure fruit juice mixture.
Therefore, the answer is:
[tex]\begin{gathered} \text{First fruit drink = 30 pints} \\ \text{Second fruit drink = 130 pints} \end{gathered}[/tex]3n+6=15 please solve for n.
Isolate the variable term by subtracting 6 from both sides of the equation.
[tex]\begin{gathered} 3n=15-6 \\ 3n=9 \end{gathered}[/tex]Divide both sides of the equation by 3.
[tex]\begin{gathered} \frac{3n}{3}=\frac{9}{3} \\ n=3 \end{gathered}[/tex]Therefore, the value of n is 3.
Write the slope intercept form of the equation 11x-4y=32
our equation is
[tex]11x-4y=32[/tex]to write the slope intercept form we need to solve the equation for Y
then
[tex]\begin{gathered} -4y=32-11x \\ 4y=-32+11x \\ y=\frac{-32+11x}{4} \\ \\ y=-8+\frac{11}{4}x \\ \\ y=\frac{11}{4}x-8 \end{gathered}[/tex]The table shows conversions of common units of length. Unit of LengthCustomary System UnitsMetric System Units1 inch2.54 centimeters1 foot0.3048 meters1 mile1.61 kilometersHow many miles are equivalent to 800 meters? Round answer to the nearest hundredth.0.50 miles1.29 miles2.62 miles4.97 miles
1 mile = 1.61 kilometers
1000 meters = 1 kilometer
First, express the meters as kilometers-
800 meters / 1000 = 0.8 kilometers
Now, divide 0.8 km by 1.61 km per mile
0.8 / 1.61 = 0.49 = 0.50 miles
An economist wants to estimate the mean per capita income in thousands of dollars for a major city in California. He believes that the mean income is $24.4 and the standard deviation is known to be $8.1. How large of a sample would be required in order to estimate the mean per capita income at the 80% level of confidence with an error of at most $0.24 round your answer to the next integer
Explanation:
The formula for calculating the MSE and then the confidence interval is as follows:
[tex]MSE\text{ = z * }\frac{\sigma}{\sqrt{n}}[/tex]We are given that the standard deviation is $8.1 and that MSE = $0.24.
We are also told that the confidence level is 80%. The corresponding z value at 80% is 1.28
We are then required to calculate n:
[tex]\begin{gathered} 0.24\text{ = 1.28 * }\frac{8.1}{\sqrt{n}} \\ \frac{16}{3}\text{ = }\frac{\sqrt{n}}{8.1} \\ 43.2\text{ = }\sqrt{n} \\ 1866.24\text{ = n} \\ n\text{ }\approx\text{ 1866} \end{gathered}[/tex]Answer: n = 1866
The volume of this triangular prism is 144 cubic feet. What is the value of s?
Solve the following for a:-2 + a=1
a = 3
Explanations:The given equation is:
- 2 + a = 1
Collect like terms:
This means that the -2 will cross the equality sign to the Right Hand Side to become +2
The equation will then become:
a = 1 + 2
a = 3
⇒I will use the additive inverse to solve the problem.
[tex]-2+(2)+a=1+(2)\\a=3[/tex]
GOODLUCK!!
Find an equivalent equation in rectangular coordinates.r(1 - 2 cos θ) = 1
SOLUTION
The given equation is:
[tex]r(1-2\cos\theta)=1[/tex]Rewrite the equation
[tex]r-2r\cos\theta=1[/tex]Recall that
[tex]r=\sqrt{x^2+y^2}x=rcos\theta[/tex]Substituting these values gives
[tex]\begin{gathered} \sqrt{x^2+y^2}-2x=1 \\ (\sqrt{x^2+y^2})^2=(1+2x)^2 \\ x^2+y^2=1+4x^2+4x \\ 1+4x^2+4x-x^2-y^2=0 \\ 3x^2-y^2+4x+1=0 \end{gathered}[/tex]Therefore the required equation is
[tex]3x^{2}-y^{2}+4x+1=0[/tex]Use the expression 10 x ? Where represents a factor between 1 and 9.What is true about the digit in the ones place of each product? Explain.3rd grade student
In mathematics, every integer in a number has a place value. Therefore, the place value of a number is the value represented by a digit in a number based on its position in the number.
For example, consider the number 30.
3 is in the tens place while,
0 is in the ones place.
Going by the above explanation:
The digit in the ones place in each of the products (10,20,30,40,50,...90) is 0
For every product obtained, it will always have a ones place value of 0
Use the rule to write the first 12 in the pattern. Discribe another pattern in the numbers. 1. Rule: Subtract 7 First Term: 95____________________________________________________________________________________________________2. Rule: Add 15 Subtract 10 First Term:4____________________________________________________________________________________________________
we have
1. Rule: Subtract 7 First Term: 95
so
a1=95
a2=95-7=88
a3=88-7=81
a4=81-7=74
a5=74-7=67
a6=67-7=60
a7=60-7=53
a8=53-7=46
a9=46-7=39
a10=39-7=32
a11=32-7=25
a12=25-7=18
we have that
the general equation in this arithmetic sequence is
an=a1+d(n-1)
we have
a1=95
d=-7
substitute
an=95-7(n-1)
an=95-7n+7
an=102-7n2. Rule: Add 15 Subtract 10 First Term:4
the rule add 15 and subtract 10 is the same that the rule add 5
so
a1=4
a2=4
8. A hair stylist at Pierre's hair salon earns $6.80 per hour plus tips.The stylist works 40 hours per week with tips of about $240 per week. Findthe total weekly earnings.A.493.00B.512.00C. $625.00
1) Gathering the data
6.80h + t=E
h=hours
t=tips
E=Earnings
2
Help i need this quick!!Ms. Howard is comparing the cost to attend two different preschools. a Preschool A charges a $40.00 registration fee plus $5.00 per day of attendance. • Preschool B does not charge a registration fee but charges $7.50 per day of attendance. At what number of days will the cost of attendance be the same for both preschools? A. 3 days B. 6 days C. 16 daysD. None of these
Given data:
The given registration fees for preschool A is c=$40.00.
The given attendence fees for preschool A is a=$5.00/day.
The given attendence fees for preschool B is b=$7.50/day.
The total fees for school A is,
[tex]S_A=40+5x[/tex]The total fees for school B is,
[tex]S_B=7.5x[/tex]The cost of both preschool is same.
[tex]\begin{gathered} (40+5x)=7.5x \\ 40=2.5x \\ x=16 \end{gathered}[/tex]Thus, the option (C) is correct.
a college lacrosse team will play 18 games next fall. each game can result in one of 3 outcomes; a win, a loss, or a tie. find the total possible number of outcomes for the season record.
Each game has 3 possible outcome so there are 3 different outcomes for game 1
The same can happen for game 2
and for game 3 and so on for each game
There are 18 games
3 *3*3*3*3 .......*3 18 times
3^18
387420489 different possible outcomes