Answer:
300 -- venue cost24 -- cost for each couplex -- the number of couples24x the cost associated with all couple300+24x -- the total cost for the danceStep-by-step explanation:
Given the scenario that cost is $300 for the venue and $24 for each couple attending a dance at that venue, you want to know the meaning of the variables and terms in 300 +24x.
ComparisonYou can compare the terms, coefficients, and variables in the given expression with the parts of the problem statement.
300 is a constant term that corresponds to "$300 for a venue rental'24 is a coefficient that corresponds to "$24 for each couple"x is a variable representing the number of "couple that attends"24x is a term representing the cost associated with "$24 for each couple that attends"That is, the cost associated with the number of people attending is $24 times the number of couples: 24x. The expression 300+24x is the total of the fixed venue cost and the per-couple costs
Solve the missing angles by using trig function Answer Choices: A. 57.4B. 53.1
We can relate an angle x to its opposite leg and its adjacent leg, by means of the trigonometric function tangent of x, like this:
[tex]\tan (x)=\frac{\text{opposite}}{\text{adjacent}}[/tex]Then we can find the value of the angle by applying the inverse function of tangent, like this:
[tex]x=\tan ^{-1}(\frac{opposite}{adjacent})[/tex]Let's replace the values from the figure into this equation to find x, like this:
[tex]\begin{gathered} x=\tan ^{-1}(\frac{25}{16}) \\ x\approx57.4 \end{gathered}[/tex]Then, x equals 57.4°
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
[tex]x^2+y^2=400[/tex]
a) find dy/dt given x=16, y=12 and dy/dt=7
b) find dx/dt given x=16, y=12, and dy/dt =-3
For the given equation: x² + y² = 400, the required values of dy/dt and dx/dt are [(-28)/3] and 4 respectively.
What are differentiable functions?
If the derivative f '(a) exists at each point in its domain, then f(x) is said to be differentiable at the point x = a. Given two functions g and h, where y = g(u) and u = h(x). A function is referred to as a composite function if its definition is y = g [h (x)] or goh(x). Therefore, fog is also differentiable and (fog)'(x) = f'(g(x) if g (x) and h (x) are two differentiable functions. g’(x).
Given, the equation for x and y is: x² + y² = 400
Differentiating the equation above with respect to t using chain rule, we have: (2x)(dx/dt) + (2y)(dy/dt) = 0 -(i)
Rearranging (i) for dy/dt, we have: dy/dt = (-x/y)(dx/dt) - (ii)
Again, rearranging (i) for dx/dt, we have: dx/dt = (-y/x)(dy/dt) - (iii)
For (a), x = 16, y = 12 and dx/dt = 7, thus dy/dt using (ii) can be written as:
dy/dt = (-x/y)(dx/dt) = (-16/12)*7 = (-4/3)*7 = (-28)/3
For (b), x = 16, y = 12 and dy/dt = -3, thus dx/dt using (iii) can be written as:
dx/dt = (-y/x)(dy/dt) = (-12/16)*(-3) = (4/(-3))*(-3) = 4
Therefore, for the given equation: x² + y² = 400, the required values of dy/dt and dx/dt are [(-28)/3] and 4 respectively.
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find the slope of a line that is PARALLEL to y=3/5x-2
Parallel lines have the same slope.
In this case, the slope of the line is 3/5.
Then, any line that satisfies y=3/5*x+C, being C any constant, is parallel to our line.
Then, when C=0 for example, we have the line y=3/5*x that is parallel and goes through the center of coordinates (0,0).
Graphically, we can see that they a re parallel:
Answer: y = 3/5*x + C, with C=constant. There are infinte solutions if no other restriction is made, so for example y=3/5*x is parallel to y=3/5*x-2.
Seth earns $25 a day and $3 for each ticket he sells at the local theatre. Write and solve aninequality that can be used to find how many tickets he must sell in a day to earn at least $115.Solve.
Seth earns $25 a day and also she earns $3 for each ticket he sells at the local theatre.
Therefore $25 is the independent value and $3 is the dependent value because it depends on how many tickets are sold.
We can write the next expression:
[tex]25+3x[/tex]Now, we need to make an inequality about he must sell at least $115 in a day.
The word "at least" means greater than or equal to, therefore:
[tex]25+3x\ge115[/tex]Now, let's solve the inequality:
Subtract both sides by 25:
[tex]25-25+3x\ge115-25[/tex][tex]3x\ge90[/tex]Then, divide both sides by 3:
[tex]\frac{3x}{3}\ge\frac{90}{3}[/tex]Simplify:
[tex]x\ge30[/tex]A committee of eight math instructors and ten science instructors need to select two people from each group to send to a conference. What is the probability of selecting two math instructors and two science instructors?
Choosing two math instructors out of 8 would be
[tex]P=\frac{2}{8}=\frac{1}{4}[/tex]Choosing two science instructors out of 10 would be
[tex]P=\frac{2}{10}=\frac{1}{5}[/tex]Given that they are independent events, we multiply their probabilities
[tex]P=\frac{1}{4}\times\frac{1}{5}=\frac{1}{20}[/tex]Hence, the probability of selecting two math instructors and two science instructors is 1/20.
8) Remus earns $.15 per unit for the work he does. For all units heproduces in a week, over 1,000, he receives $.20. What were his weeklyearnings if he produced 1,420 units?
You have the following information:
- Remus earns $.15 per unit
- For units he produced over 1,000 he receives $.20
- He produced 1,420 units
In order to determine what were the weekly earnings, you first take into account the earnings for the first 1,000 units:
0.15 x 1,000 = 150
Next, you calculate the earnings for the units over 1,000, which are 420:
0.20 x 420 = 84
Next, you sum both contributions:
150 + 84 = 234
Hence, the weekly earning os Ramus were of $234
There are 10 males and 18 females in the Data Management class. How many different committees of 5 students can be formed if there must be 3 males and 2 femalesA: 18360B: 2600C: 98280D: 15630
Answer:
A: 18360
Explanation:
The number of ways of combinations to select x people from a group of n people is calculated as
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]Since we need to form committees with 3 males and 2 females, we need to select 3 people from the 10 males and 2 people from the 18 females, so
[tex]10C3\times18C2=\frac{10!}{3!(10-3)!}\times\frac{18!}{2!(18-2)!}=120\times153=18360[/tex]Therefore, there are 18360 ways to form a committee.
So, the answer is
A: 18360
Mai made $192 for 12 hours of work at the same rate how many hours would she have to work to make $128? Please help
We were told that Mai made $192 for 12 hours of work. This means that the amount that she made per hour is
192/12 = $16
Given that her constant rate is $16 per hour,
let x = the number of hours would she have to work to make $128. Then, we have the following equations
1 = 16
x = 128
By crossmultiplying, we have
16x = 128
x = 128/16
x = 8
She has to work for 8 hours
what is the equation
In the graph you can see that the line passes through 2 points (-4,0) and (0,2). With them you can obtain the equation of the line. First you find the slope of the line with the following equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Where} \\ m\colon\text{ Slope of the line} \\ (x_1,y_1)\colon\text{ Coordinates of first point }on\text{ the line} \\ (x_2,y_2)\colon\text{ Coordinates of second point }on\text{ the line} \end{gathered}[/tex]So you have,
[tex]\begin{gathered} (x_1,y_1)=(-4,0) \\ (x_2,y_2)=(0,2) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-0}{0-(-4)} \\ m=\frac{2}{4}=\frac{1}{2} \end{gathered}[/tex]Now, with the point slope equation you can obtain the equation of the line
[tex]\begin{gathered} y-y_1=m(x_{}-x_1) \\ y-0=\frac{1}{2}(x-(-4)) \\ y=\frac{1}{2}(x+4) \\ y=\frac{1}{2}x+\frac{1}{2}\cdot4 \\ y=\frac{1}{2}x+\frac{4}{2} \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]Therefore, the equation of the line is
[tex]y=\frac{1}{2}x+2[/tex]Comparing Two Linear Functions (Context - Graphically)
start identifying the slope and y-intercept for each high school.
The slope represents the growth for each year, in this case for high school A is 25 and for high school B is 50.
The y-intercept is the number of students that are enrolled currently, in this case for A is 400 and for B is 250.
The complete equations in the slope-intercept form are
[tex]\begin{gathered} A=25x+400 \\ B=50x+250 \end{gathered}[/tex]Continue to graph the equations
High school B is projected to have more students in 8 years.
Give the degree of the polynomial.
-v^8u^9 + 6x - 16u^6x^2v^6 - 5
Answer: nonic
Step-by-step explanation:
Hi can you help me find the correct match to each question?
GIVEN:
We are given a set of 4 statements as indicated in the attached image.
Required;
Determine whether each statement is TRUE or FALSE.
Solution;
(1) Look at the digit to the right of the digit to which you are rounding to tell whether to round up or leave it the same.
This statement is TRUE
(2) If the digit to the right of the digit to which you are rounding is four or less, you keep the digit the same.
This statement is TRUE.
(3) If the digit to the right of the digit to which you are rounding is five or more, you keep the digit the same.
This statement is FALSE.
(4) Look at the digit to the left of the digit to which you are rounding to tell whether to round down or leave it the same.
This statement is FALSE.
HELP PLEASEEEEE!!!!!!
A rational number that is between -0.45 and -0.46 is -0.455.
What is the rational number?The values given are negative decimal numbers. A decimal is a method that is used to write non-integers. An example of a decimal is 0.48. A negative number is a number whose value is less than one.
A rational number is a number that can be expressed as a fraction of two integers
Examples of rational numbers are 2 , -0.455.
-0.455 can be expressed as an integer of -0.22750 and 0.22750.
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In 2000, the population of a town was 46.020. By 2002 wpulation had increased to52,070. Assuming that the towns population is increasing linearly answer the followingquestions.a.What is the population of the town by 2006?
We know that the population increased linearly, so an adequate model for the population P in year t is:
[tex]P(t)=m\cdot t+b[/tex]We know that in 2000 the population is 46,020.
In 2002 the population is 52,070.
This are two points of the line that can be written as (2000, 46020) and (2002, 52070).
Then, we can calculate the slope m as:
[tex]m=\frac{P_2-P_1}{t_2-t_1}=\frac{52070-46020}{2002-2000}=\frac{6050}{2}=3025[/tex]With the slope value we can write the equation in slope-point form:
[tex]\begin{gathered} P-P_0=m(t-t_0) \\ P-46020=3025(t-2000) \\ P=3025(t-2000)+46020 \end{gathered}[/tex]With the linear equation defined like this (we don't need to calculate the y-intercept), we can calculate the population expected for 2006:
[tex]\begin{gathered} P(2006)=3025(2006-2000)+46020 \\ P(2006)=3025\cdot6+46020 \\ P(2006)=18150+46020 \\ P(20060)=64170 \end{gathered}[/tex]Answer: the population in 2006 is expected to be 64,170.
NO LINKS!! Describe the domain and range (in BOTH interval and inequality notation) for each function shown part 1a
Answer:
Domain as an inequality: [tex]\boldsymbol{\text{x} < 6 \ \text{ or } \ -\infty < \text{x} < 6}[/tex]
Domain in interval notation: [tex]\boldsymbol{(-\infty, 6)}[/tex]
Range as an inequality: [tex]\boldsymbol{\text{y} \le 6 \ \text{ or } \ -\infty < \text{y} \le 6}[/tex]
Range in interval notation: [tex]\boldsymbol{(-\infty, 6]}[/tex]
=========================================================
Explanation:
The domain is the set of allowed x inputs. For this graph, the right-most point is when x = 6. This endpoint is not part of the domain due to the open hole. The graph goes forever to the left to indicate [tex]\text{x} < 6[/tex] but I think [tex]-\infty < \text{x} < 6[/tex] is far more descriptive.
The second format directly leads to the interval notation of [tex](-\infty, 6)[/tex]
Always use parenthesis for either infinity. We use a parenthesis for the 6 to tell the reader not to include it as part of the domain.
------------------------
The range is the set of possible y outputs.
The highest y can get is y = 6
Therefore, y = 6 or y < 6
The range can be described as [tex]\text{y} \le 6 \ \text{ or } \ -\infty < \text{y} \le 6[/tex] where the second format is better suited to lead directly to the interval notation [tex](-\infty, 6][/tex]
Use a square bracket to include the 6 as part of the range. We don't have any open holes at the peak mountain point.
Answer:
[tex]\textsf{Domain}: \quad (-\infty, 6) \quad -\infty < x < 6[/tex]
[tex]\textsf{Range}: \quad (-\infty,6] \quad -\infty < y\leq 6[/tex]
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values).
The range of a function is the set of all possible output values (y-values).
An open circle indicates the value is not included in the interval.
A closed circle indicates the value is included in the interval.
An arrow show that the function continues indefinitely in that direction.
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.Inequality notation
< means "less than".> means "more than".≤ means "less than or equal to".≥ means "more than or equal to".From inspection of the given graph, the function is not continuous and so the domain is restricted.
There is an open circle at x = 6.
Therefore, the domain of the function is:
Interval notation: (-∞, 6)Inequality notation: -∞ < x < 6From inspection of the given graph, the maximum value of y is 6.
The function continues indefinitely to negative infinity.
Therefore, the range of the function is:
Interval notation: (-∞, 6]Inequality notation: -∞ < y ≤ 6which of the relationships below represents a function with the same rate of change of the function y= -4x + 2
Given data:
The given equation of the line is y= -4x + 2.
Substitute 0 for x in the given equation.
[tex]\begin{gathered} y=-4(0)+2 \\ =2 \end{gathered}[/tex]Substitute 1 for x in the given equation.
[tex]\begin{gathered} y=-4(1)+2 \\ =-2 \end{gathered}[/tex]Thus, option (D) is correct.
How many liters of paint must you buy to paint the walls of a rectangular prism-shaped room that is 20 m by 10 m with a ceiling height of 8 m if 1 L of paint covers40 m2? (Assume there are no doors or windows and paint comes in 1-L cans.)
17 Liters
Explanation
Step 1
find the total area to paint
we need to assume the floor wont be painted, so the total are to paint is
the are of a rectangle is gieven by:
[tex]Area=length*width[/tex]so, the total area will be
[tex]\begin{gathered} total\text{ surface area=\lparen20*10\rparen+2\lparen20*8\rparen+2\lparen10*8\rparen} \\ total\text{ surface area=200+2\lparen160\rparen+2\lparen80\rparen} \\ total\text{ surface area=200+320+160} \\ total\text{ surface area=680 m}^2 \end{gathered}[/tex]so , the area to paint is 680 square meters
Step 2
finally, to know the number of Liters need , divide the amount ( total area) by the rate of the paitn, so
[tex]\begin{gathered} paint\text{ needed=}\frac{total\text{ area}}{rate\text{ paint}} \\ paint\text{ needed=}\frac{680m^2}{40\frac{m^2}{L}}=17Liters \end{gathered}[/tex]so, the total paint needes is 17 Liters, and paint comes in 1-L cans, so
[tex]\begin{gathered} 17\text{ Liters} \\ 17\text{L}\imaginaryI\text{ters\lparen}\frac{1\text{ Can}}{1\text{ L}})=17cans \end{gathered}[/tex]therefore, the answer is
17 Liters
I hope this helps you
Please help me
I give brainliest
worth 15 points
The amount of money in a bank account is given by the function y = 200(1+0.05), where y is in dollars and t is measured in months since the account was opened.
What is the percent rate of growth of the bank account?
Enter your answer in the box.
Answer:
60% annual rate
Step-by-step explanation:
Your equation is incorrect
It should be Y = 200 (1+.05)^t
T is the number of compounding periods per year (12 to a year)
.05 is the periodic interest rate ( 1/12 th of the annual)
.05 * 12 = .6 Which is 60% <=====REALLY high annual rate!
Find the equation of the tangent line to the curve y = x^3- 4x - 5 at the point (2, -5).Tangent Line Equation:
Let's find the derivative of y:
[tex]\begin{gathered} y=x^3-4x-5 \\ \frac{dy}{dx}=3x^2-4 \end{gathered}[/tex]Evaluate the derivative for x = 2:
[tex]\frac{dy}{dx}\begin{cases} \\ x=2\end{cases}=3(2)^2-4=12-4=8[/tex]Now, we have the slope, let's use the point-slope formula to find the equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ _{\text{ }}where\colon \\ (x1,y1)=(2,-5) \\ m=8 \\ y+5=8(x-2) \\ y+5=8x-16 \\ y=8x-21 \end{gathered}[/tex]Answer:
y = 8x - 21
1. Are these ratios equivalent? 8:7 and 4:2
EXPLANATION
The answer is no, because 8:7 and 4:2 are different relationships.
Match each expression on the left to its equivalent value on the right. Some answer options on the right will not be used.
Let us write out our expressions:
[tex]\begin{gathered} -29+(-7) \\ -34+(-94) \\ -8+(-14) \\ -12+(-48) \end{gathered}[/tex]The trick here is to get rid of the minus, then solve the sum as usual, and add a minus to the result. Let us do that for each of them:
-29+(-7)] Step one gives us:
[tex]29+7[/tex]Step two gives us:
[tex]36[/tex]Step three gives us:
[tex]-36[/tex]Then, -29+(-7) should be linked to -36.
-34+(-94)] Step one gives us:
[tex]34+94[/tex]Step two gives us:
[tex]128[/tex]Step three gives us:
[tex]-128[/tex]Thus, -34+(-94) should be linked to -128.
-8+(-14)] Step one gives us:
[tex]8+14[/tex]Step two gives us:
[tex]22[/tex]And step three gives us:
[tex]-22[/tex]This implies that -2+(-14) should be linked to -22.
-12+(-48)] Step one gives us:
[tex]12+48[/tex]Step two gives us:
[tex]60[/tex]And step three gives us:
[tex]-60[/tex]Then, -12+(-48) should be linked to -60.
8. A certain virus infects one in every 700 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (a) Find the probability that a person has the virus given that they have tested positive. (b) Find the probability that a person does not have the virus given that they have tested negative.
Part a
Find the probability that a person has the virus given that they have tested positive
Probability in fraction form
p=(1/700)*(90/100)=90/70,000
simplify
P=9/7,000Part b
Find the probability that a person does not have the virus given that they have tested negative
Probability in fraction form
P=(699/700)*(10/100)
P=6,990/70,000
simplify
P=699/7,000Haley spent 1/2 oven hour playing on her phone that used up 1/9 of her battery how long would she have to play on her phone to use the entire battery
1/2 hour playing -- 1/9 battery
1 hour playing -- 2/9 battery
1 1/2 hours playing --- 3/9 battery
2 hours playing ------ 4/9 battery
2 1/2 hours playing ---- 5/9 battery
3 hours playing ----- 6/9 battery
3 1/2 hours playing --- 7/9 battery
4 hours playing -----8/9 battery
4 1/2 hours playing ---- 9/9 battery
9/9 represent the entire battery so che can play 4.5 hours on her phone
it can be represented into a fraction as
[tex]4.5=4\frac{1}{2}=\frac{9}{2}[/tex]The volume of a rectangular prism is 2 x cubed + 9 x squared minus 8 x minus 36 with height x + 2. Using synthetic division, what is the area of the base?
2 x cubed + 13 x squared + 18 x
2 x cubed + 5 x squared minus 18 x
2 x squared + 13 x + 18
2 x squared + 5 x minus 18
Answer:
2 x squared + 5 x minus 18
Step-by-step explanation:
Hope this helps sorry if not right
Answer: D
Step-by-step explanation: EDGE
Given a function described as the equation y= 4x - 4, what is y when x is 1, 2, and 3?A 2, 8, 16B 4,8, 12C 0,4,8D 0, 6, 12
Answer
C. 0, 4, 8
Explanation
Given function:
y = 4x - 4
What to find:
To find y when x = 1, 2, and 3
Step-by-step solution:
When x = 1
y = 4(1) - 4
y = 4 - 4
y = 0
When x = 2
y = 4(2) - 4
y = 8 - 4
y = 4
When x = 3
y = 4(3) - 4
y = 12 - 4
y = 8
find the value of tan A in simplest radical form
In the given right angle triangle BCA : BC = 5, CA = 3 and BA = root 34
From the trignometric ratio of right angle triangle :
The tangent of angle is the ratio of the Adjacent side to the opposite side
[tex]\tan \theta=\frac{Opposite\text{ side}}{Adjacent\text{Side}}[/tex]In the given triangle, the side opposite to angle A = BC and adjacent side CB
Substitute the value :
[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ side}}{Adjacent\text{Side}} \\ \tan A=\frac{BC}{CB} \\ \tan A=\frac{5}{3} \\ \tan A=1.66 \\ \\ ^{} \end{gathered}[/tex]The value of tanA = 5/3 or 1.66
the area of a trapezoid is given by the formula A= h(a+b)/2. solve for the formula for b.
The formula is
[tex]A=\frac{(a+b)\cdot h}{2}[/tex]To solve for b, first, we multiply the equation by 2
[tex]\begin{gathered} 2A=2\cdot\frac{(a+b)\cdot h}{2} \\ 2a=(a+b)\cdot h \end{gathered}[/tex]Then, we divide the equation by h
[tex]\begin{gathered} \frac{2A}{h}=\frac{(a+b)h}{h} \\ \frac{2A}{h}=a+b \end{gathered}[/tex]At last, we subtract a from each side
[tex]\frac{2A}{h}-a=a-a+b[/tex]Hence, the final expression is[tex]b=\frac{2A}{h}-a[/tex]Which postulate or theorem proves that ∆ABC and ∆EDC are congruent?
O AAS Congruence Theorem
O HL Congruence Theorem
O SAS Congruence Postulate
O SSS Congruence Postulate B
Use the graph of the function y= f(x) below to answer the questions
a)
We need to find the value of f(-3), that means we need to find the value of the y-coordinate when the x-coordinate is -3
As we can see in the graph
f(-3)=-5
Therefore f(-3) is negative
The answer for this part is NO
b)
if f(x)=0, that means that we are looking for the x-intercepts
x=-2
x=1
x=4
The answer is -2,1,4
c)
We need to know for what values of x f(x)<0
In this case in interval notation
[tex]\lbrack-3,2)\cup(1,4)[/tex]Suppose a certain company sells regular keyboards for $82 and wireless keyboards for $115. Last week the store sold three times as many regular keyboards as wireless. If total keyboard sales were $5,415, how many of each type were sold?how many regular keyboards?how many wireless keyboards?
Given:
A set 3 regular and 1 wireless keyboard,
Regular keyboards = $ 82
Wireless keyboards = $ 115
Total keyboards sales = $ 5415
Find-:
(a) how many regular keyboards?
(b) how many wireless keyboards?
Explanation-:
A set of 3 regular and 1 wireless keyboard would sell for:
[tex]\begin{gathered} =3\times82+115 \\ \\ =246+115 \\ \\ =361 \end{gathered}[/tex]For, the given sales, the number of sets sold:
Total keyboard sales = $5415
[tex]\begin{gathered} =\frac{5415}{361} \\ \\ =15 \end{gathered}[/tex]Since there are 3 regular keyboards in each set,
The regular keyboard is:
[tex]\begin{gathered} =3\times15 \\ \\ =45\text{ Regular Keyboards} \end{gathered}[/tex]The regular keyboard is 45.
Wireless keyboard is 15.
