Answer:
To find the total price, we need to add the tip and tax to the total bill amount.
First, we need to find the amount of the tip. To do this, we will multiply the total bill by 22% (or 0.22):
$45.65 x 0.22 = $10.04
This means the tip amount is $10.04.
Next, we need to find the amount of tax. To do this, we will multiply the total bill by 5% (or 0.05):
$45.65 x 0.05 = $2.28
This means the tax amount is $2.28.
Finally, we can find the total price by adding the total bill, tip, and tax together:
$45.65 + $10.04 + $2.28 = $57.97
Therefore, the total price is $57.97.
#4:
Victoria is solving the equation x-3-4. Some
of her steps are shown below.
• equation 1: x-3=4 5
21
• equation 2:
2
3
X-3=
5
2
• equation 3: x-3+3=¹+3
21
5
Which statement correctly explains whether equation 3
in Victoria's work is valid in solving the equation?
It is not valid because because Victoria should subtract 3
instead of adding 3.
It is valid because -3+3=0.
It is not valid because Victoria did not also add 3 to
It is valid because because Victoria added the same amount
to each side of the equation.
The statement "It is valid because Victoria added the same amount to each side of the equation" correctly explains whether equation 3 in Victoria's work is valid in solving the equation.
What explanation is suitable?In equation 3, Victoria added 3 to both sides of the equation x-3=4/21. This operation is valid because she added the same amount (3) to both sides, which maintains the equality between the two sides of the equation. The resulting equation is x-3+3=4/21+3, which simplifies to x=4/21+63/21 or x=67/21.
Therefore, equation 3 is a valid step in solving the equation x-3=4/21.
learn more about simplification: https://brainly.com/question/28595186
#SPJ1
Help me I don’t under stand this!
Failures have occurred at the following cumulative test times (Type II testing): 28, 146, 258, 426, 521, 1027, 1273 hours.
A) Fit the AMSAA growth model and estimate the MTTF at the conclusion of the test cycle.
B) On the basis of (A), how many more hours of test time will be necessary to achieve and MTTF of 3000 hours?
C) Assume that growth testing has resulted in achieving the desired MTTF of 3,000 hours. How many items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available? (Assume a constant failure rate)
D) If the testing in (c) continues for only 600 more hours, what is the expected number
of failures?
AMSAA growth model
The MTTF at the conclusion of the test cycle is 232.59 hours. 22423.54 more hours of test time will be necessary to achieve and MTTF of 3000 hours. 52.15 items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available. If the testing continues for only 600 more hours, 1.75 is the expected number of failures.
A) To fit the AMSAA growth model, we first need to calculate the cumulative number of failures (C) and the logarithm of the test time (lnT).
| Test Time (T) | C | lnT |
|---------------|---|-----|
| 28 | 1 | 3.33|
| 146 | 2 | 4.98|
| 258 | 3 | 5.55|
| 426 | 4 | 6.05|
| 521 | 5 | 6.26|
| 1027 | 6 | 6.93|
| 1273 | 7 | 7.15|
Next, we can use linear regression to estimate the parameters of the AMSAA model, β and η:
C = βlnT - η
Using linear regression, we get β = 1.11 and η = 3.82.
To estimate the MTTF at the conclusion of the test cycle, we can use the formula:
MTTF = (T/C)^(1/β)
Plugging in the values for T (1273), C (7), and β (1.11), we get:
MTTF = (1273/7)^(1/1.11) = 232.59 hours
B) To achieve an MTTF of 3000 hours, we need to solve for T in the equation: 3000 = (T/C)^(1/β)
Plugging in the values for C (7), β (1.11), and rearranging the equation, we get:
T = 3000^(β) * C = 3000^(1.11) * 7 = 23696.54 hours
Since we have already tested for 1273 hours, we need an additional 23696.54 - 1273 = 22423.54 hours of test time to achieve an MTTF of 3000 hours.
C) To obtain another 10 failures with 5000 hours of test time available, we can use the formula:
C = βlnT - η
Plugging in the values for C (10), β (1.11), η (3.82), and T (5000), and rearranging the equation, we get:
10 = 1.11ln(5000) - 3.82
ln(5000) = (10 + 3.82)/1.11 = 12.47
5000 = e^(12.47) = 260753.13
Therefore, we need to place 260753.13/5000 = 52.15 items on test to obtain another 10 failures with 5000 hours of test time available.
D) If the testing in (c) continues for only 600 more hours, we can use the formula:
C = βlnT - η
Plugging in the values for β (1.11), η (3.82), and T (600), and rearranging the equation, we get:
C = 1.11ln(600) - 3.82 = 1.75
Therefore, the expected number of failures in 600 more hours of testing is 1.75.
For more such questions on Growth model.
https://brainly.com/question/30500128#
#SPJ11
Concepts to make sure are (re)-discussed: Isolating the radical Checking for extraneous solutions Solving rational exponents in equations- more than one solution Sample problems: 1. V4x + 1 - Vx+ 10 = 2. V2x+30 = (x+3)
To solve the given equations, we need to follow these steps:
1. Isolate the radical on one side of the equation.
2. Square both sides of the equation to eliminate the radical.
3. Solve the resulting equation for the variable.
4. Check for extraneous solutions by plugging the solution back into the original equation.
5. If there are rational exponents, use the same steps but raise both sides of the equation to the reciprocal of the exponent.
Let's apply these steps to the sample problems:
1. V4x + 1 - Vx+ 10 = 2
First, isolate the radical on one side:
V4x + 1 = Vx+ 10 + 2
V4x + 1 = Vx+ 12
Next, square both sides to eliminate the radical:
(4x + 1) = (x+ 12)^2
4x + 1 = x^2 + 24x + 144
Solve for x:
0 = x^2 + 20x + 143
Using the quadratic formula:
x = (-20 ± √(20^2 - 4(1)(143)))/(2(1))
x = (-20 ± √(400 - 572))/2
x = (-20 ± √(-172))/2
x = (-20 ± √172i)/2
There are no real solutions for this equation.
2. V2x+30 = (x+3)
Isolate the radical:
V2x+30 = x+3
Square both sides:
2x + 30 = (x+3)^2
2x + 30 = x^2 + 6x + 9
Solve for x:
0 = x^2 + 4x - 21
Using the quadratic formula:
x = (-4 ± √(4^2 - 4(1)(-21)))/(2(1))
x = (-4 ± √(16 + 84))/2
x = (-4 ± √100)/2
x = (-4 ± 10)/2
x = 3 or x = -7
Check for extraneous solutions by plugging the solutions back into the original equation:
V2(3)+30 = (3+3)
V36 = 6
6 = 6 (True)
V2(-7)+30 = (-7+3)
V16 = -4
4 = -4 (False)
Therefore, the only solution is x = 3.
To know more about rational exponents refer here:
https://brainly.com/question/3009444
#SPJ11
A pack of 8 collectable cards contains 1 rare card, 3 uncommon cards, and 4 common cards. If Javier has 45 packs of cards, how many more uncommon cards does he have than rare cards?
Javier has 90 more uncommon cards than rare cards.
To find out how many more uncommon cards Javier has than rare cards, we need to multiply the number of packs he has by the number of each type of card in a pack, and then subtract the number of rare cards from the number of uncommon cards. We can do this with the following equation:
Uncommon cards - Rare cards = Difference
First, we'll multiply the number of packs by the number of each type of card:
45 packs × 3 uncommon cards = 135 uncommon cards
45 packs × 1 rare card = 45 rare cards
Now we'll subtract the number of rare cards from the number of uncommon cards to find the difference:
135 uncommon cards - 45 rare cards = 90
So, the number of uncommon cards is 90 more than the rare cards.
Learn more about Difference here: https://brainly.com/question/17695139.
#SPJ11
need help with 7 A & B? “Quadratic Functions” algebra 1
The required solutions are as follows,
(a) The parabola will open downwards and have a maximum.
(b) The axis of symmetry for this function is t = 15.
A parabola is a cross-section cut out of the cone and represented by an equation shown in the question.
Here,
(a) The function C(t) is a quadratic function with a coefficient of -0.2 in front of the t² term. Since this coefficient is negative, the parabola will open downwards and have a maximum.
(b) The axis of symmetry of a quadratic function in the form of f(x) = ax² + bx + c is given by the formula x = -b/2a.
In this case, the function is C(t) = -0.2t² + 6t + 28.5, so a = -0.2 and b = 6. Thus, the axis of symmetry is:
t = -b/2a = -6/(2*(-0.2)) = 15
Therefore, the axis of symmetry for this function is t = 15.
Learn more about parabola here:
brainly.com/question/4074088
#SPJ1
Find the measure of the central angle indicated. Lines that appear to be diameters, are diameters.
The measure of the central angle indicated is 60°.
Define central angle?The central angle of a circle is the angle that an arc takes up in the centre. The radius vectors are what make up the angle's arms.
The formula for calculating a central angle is: Central Angle = Arc length (AB) / Radius (OA) = (s 360°) / 2r, where "s" stands for arc length and "r" for circle radius.
Now here in the given diagram,
Let x equal the desired angle.
The central angle that we need to find is:
Now x = 360-120-(90+90)
⇒ x = 360-300
⇒ x = 60°
To know more about central angle, visit:
https://brainly.com/question/15698342
#SPJ1
A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event, what is the probability the player makes zero of their next three free throws? (A) 0.064 (B) 0.216 (C) 0.784 (D) 0.936 (E) None of these
A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event,the probability the player makes zero of their next three free throws is 0.064. The correct answer is A.
The probability that a middle school basketball player makes zero of their next three free throws can be calculated using the formula P(A) = P(A')ⁿ, where P(A) is the probability of the event occurring, P(A') is the probability of the event not occurring, and n is the number of trials.
In this case, P(A) is the probability of the player making zero free throws, P(A') is the probability of the player missing a free throw (1 - 0.6 = 0.4), and n is the number of free throws (3).
Using the formula, we can calculate the probability of the player making zero free throws as follows:
P(A) = P(A')ⁿ
P(A) = (0.4)³
P(A) = 0.064
Therefore, the correct answer is (A) 0.064.
Learn more about probability at https://brainly.com/question/20913662
#SPJ11
write these number in standard form seventeen thousand
Answer:
17,000
Step-by-step explanation:
17000 in words is written as Seventeen-thousand. The number 17000 represents a value equivalent to it.
Fifth order linear ODE with one real root r and two complex
roots a ± bi and c ± di. From the given information, determine its
general solution.
The general solution of a fifth order linear ODE with one real root r and two complex roots a ± bi and c ± di can be determined by using the fact that the general solution of a linear ODE is the sum of the solutions corresponding to each of the roots.
For the real root r, the solution is given by:
y1 = C1 * e^(r*x)
For the complex roots a ± bi, the solution is given by:
y2 = C2 * e^(a*x) * cos(b*x) + C3 * e^(a*x) * sin(b*x)
For the complex roots c ± di, the solution is given by:
y3 = C4 * e^(c*x) * cos(d*x) + C5 * e^(c*x) * sin(d*x)
The general solution of the fifth order linear ODE is the sum of these solutions:
y = y1 + y2 + y3
= C1 * e^(r*x) + C2 * e^(a*x) * cos(b*x) + C3 * e^(a*x) * sin(b*x) + C4 * e^(c*x) * cos(d*x) + C5 * e^(c*x) * sin(d*x)
This is the general solution of the fifth order linear ODE with one real root r and two complex roots a ± bi and c ± di.
Learn more about linear
brainly.com/question/15830007
#SPJ11
A box contains color of markers black and red the ratio of black markers to red markers is 7 : 2 if there are 144 markers the box how many markers are there of each type PLSSS HELP ANSWER ANS EXPLAIN PLSSS
Answer:
see below
Step-by-step explanation:
put paragraph of words into summarised information 1st.
ie
black : red : total
7 : 2 : 7+2 = 9 is total units
total units = 9 (which is 144 markers)
so 1 unit is .....
144 ÷ 9 = 16 markers
black = 7units
7 x 16 markers = ans
red = 2 units
2 x 16 = ans
There are 12 boys and 13 girls in my 3rd period class. How many pairs can I make if I choose
one boy and one girl?
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)
The properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms ln(√z) = (1/2)ln(z)
What is the logarithms?
Logarithms are mathematical functions that help to solve exponential equations. They are used to express very large or very small numbers in a more convenient and manageable way.
We can use the property of logarithms that states:
logb (a∙c) = logb a + logb c
to expand the expression as a sum of logarithms:
ln(√z) = ln(z^(1/2))
Using the power rule of logarithms, we can simplify this as:
ln(z^(1/2)) = (1/2)ln(z)
Hence, we can write:
ln(√z) = (1/2)ln(z)
To learn more about logarithms, Visit
https://brainly.com/question/25710806
#SPJ1
HI I have this project due tomorrow and I need to know what type of histogram this is
The given histogram is right skewed type.
What is a histogram?A histogram is a graphic representation of data in a grouped frequency distribution with continuous classes.
They are similar to a bar graphs, but there are no gaps between the consecutive rectangles.
Histograms are widely used for ranging data into groups. It is a highly practical graph due to its clarity and simplicity.
Histogram :-
It is a collection of rectangles next to one another, where each bar represents a different type of data.
In this context, frequency refers to the number of times a number appears in statistical data.
It is known as a frequency distribution when shown in a table.
Here, the distribution here is skewed to the left. Therefore, it is also referred to as a negatively skewed histogram graph.
Hence, the given histogram is right skewed type.
Learn more about histograms, click;
https://brainly.com/question/30354484
#SPJ1
What is the volume of a cylinder with a radius of 3 feet and a height of 4 feet? Use 3.14 for pi. Round to the nearest hundredth.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\pi (3)^2(4)\implies \stackrel{ \pi =3.14 }{V=113.04}[/tex]
How to find the Zeros, Multiplicity, and Effect?
f(x)=-8x^(3)-20x^(2)
The Zeros of the equation would be x = -5/2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given the equation as;
[tex]f(x)=-8x^3-20x^2[/tex]
We can factor;
4x^2 ( 2x+5)
Using the zero product property
2x = 0
2x + 5 = 0
x = -5/2
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ1
How to find the least common denominator of 1/6x + 3/8?
Answer:
Step-by-step explanation:
The least common denominator for 1/6 + 3/8 is 24
first find the multiples of 6 and 8
6= 6, 12, 18, 24, 30
8 = 8, 16, 24, 32
Next circle the number that appear in both
That number will be 24 which is the least common denominator.
A social media survey found that 75% of parents are "friends" with their children on a certain online networking site. A random sample of 160 parents was selected.
a. Calculate the standard error of the proportion.
b. What is the probability that 125 or more parents from this sample are "friends" with their children on this online networking site?
c. What is the probability that between 120 and 128 patents
The formula for standard error of proportion is √(pq/n) where p is the sample proportion, q = 1-p, and n is the sample size. Here, the sample proportion is 0.75, q is 0.25, and n is 160. Therefore, the standard error of proportion is √(0.75*0.25/160) = 0.035
The probability that between 120 and 128 patents (inclusive) are friends with their children can be calculated using the z-score formula:
z = (x - np)/√(npq)
where x is the number of parents between 120 and 128 who are friends with their children,
np = 160*0.75 = 120, and pq = 160*0.25 = 40.
Therefore,√(npq) = √(120*40) = 24.49
z = (120 - 120)/24.49 = 0
z = (121 - 120)/24.49 = 0.04
z = (122 - 120)/24.49 = 0.08
z = (123 - 120)/24.49 = 0.12
z = (124 - 120)/24.49 = 0.16
z = (125 - 120)/24.49 = 0.2
z = (126 - 120)/24.49 = 0.24
z = (127 - 120)/24.49 = 0.29
z = (128 - 120)/24.49 = 0.33
Using a z-table or a calculator, the probability that z is between 0 and 0.33 is 0.1292. Therefore, the probability that between 120 and 128 parents are friends with their children is 0.1292.
To know more about probability refer here:
https://brainly.com/question/11234923
#SPJ11
In this caee there are no restricoions onb1b2, andbnso the zystern has the uniquex1=−40b1+16b2+9bj,x1=1b1−5b2−3b3+x1=5b2−2b2−bjfor all values ofb1,b2, andb3. Exercise set 1,6 7.−1x1+5x1=band using Theorm i.6. 2x1+2x2=b11.xk+x2=25x3+6x2=9 2. 4x1−5x3=−12x1−5x2=9the bri natue ike aviten 3.x1+3x2+x1=42x1+2x4+x1=−12x5+2x1+x4=4.4x3+3x2+2r5a 4 asind matrar fa tindu3xx+3xz+2xy=2xz+xn=5Q.x1−4x1=4x1+2x2+x2+x1L.B4=t1by=is.x+y+z=5 6. −x−2y−3z=0x+y−4z=10(y+x+4y+4z=7−4x+y+8=04.3x+7y+9z=4−ay−2x−4y−4tan 14. −x1+4x1+f1=x1+9x2+2x1=dx1+2r1=1r11b3=a1d2=1. Thue Iatsa Eneriaes.
It seems like the question is asking about a system of equations with no restrictions on the variables b1, b2, and b3. However, the question is filled with typos and formatting errors that make it difficult to understand the exact problem and provide an accurate answer. It would be best to ask the student to clarify the question and provide a properly formatted version of the problem before attempting to answer.
Learn more about system of equations
brainly.com/question/12895249
#SPJ11
(2)
Solve the inequality 2r - 5 ≤ 9 and present your answer in interval
notation.
The solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].
To solve the inequality 2r - 5 ≤ 9, we need to isolate the variable r on one side of the inequality. Here are the steps to do so:
Step 1: Add 5 to both sides of the inequality to eliminate the -5 on the left side. This gives us: 2r ≤ 14Step 2: Divide both sides of the inequality by 2 to isolate the variable r. This gives us: r ≤ 7Now, we can present our answer in interval notation. Interval notation is a way to represent an interval on the number line. It is written in the form of [a, b], where a and b are the endpoints of the interval. The square brackets mean that the endpoints are included in the interval.
Since our inequality is r ≤ 7, our interval notation would be (-∞, 7], where -∞ represents negative infinity and 7 is the endpoint. The square bracket on the 7 means that 7 is included in the interval.
Therefore, the solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].
For more information about inequality, visit:
https://brainly.com/question/30238989
#SPJ11
Chose all the asswer that describe the quadrilateral ABCD if AB // CD, AB=9 CD=9
In the quadrilateral ABCD if AB ||CD and AB=9 as well as are CD=9. Then, quadrilateral ABCD is both parallelogram and trapezium.
Explain about the features of trapezium and parallelogram? A trapezium is still a two-dimensional quadrilateral with two parallel opposed sides that is made up of four straight lines. The base and legs of the trapezium are the opposing parallel sides, which are referred as the base and indeed the non-parallel sides, respectively. It has four sides plus four corners and is a closed plane shape.Parallelogram's characteristics
The different sides are distributed uniformly and parallel.Angles on either side are equal.The following or neighboring angles are supplemental.All of the angles will end up being right angles when any of them is a right angle.In the quadrilateral ABCD:
AB ||CD AB = CD = 9.Thus, the quadrilateral ABCD is both parallelogram and trapezium.
Explain about the features of trapezium?Know more about trapezium
https://brainly.com/question/27929782
#SPJ1
Find the measurements of X
pt 3
Answer:
180 p
Step-by-step explanation:your welcome
Point W(-6, 7) is rotated 90° clockwise where is W
Check the picture below.
please help me for 20 poins!!
Answer: C, 2 2/8
Step-by-step explanation: To turn a mixed number into an improper fraction, multiply the whole number by the denominator. Then, add the numerator. So in this example it would be:
4 3/8 = 35/8
2 1/8 = 17/8
Now, since the denominators are equivalent, all we need to do is subtract the numerators.
35/8 - 17/8 = 18/8
The answer needs to be changed back to a mixed number. For this problem, there is an easy way to do this.
18/8 = 8/8 + 8/8 +2/8, which as a mixed number would be 2 2/8.
So the correct choice would be (C).
whats the answer? I have to finish this quiz since I missed it
Answer:
Step-by-step explanation:
For this triangle, we can find the angle adjacent to side length 4 using trig:
tan(theta) = 7/4
theta = tan^-1(7/4)
theta = 60.26
Now we use sine to find x:
sin(60.26) = 7/x
x = 7/sin(60.26)
x = 8.06
I don't know how far you need to round, so it can either be this or 8.1
Hope this helps!
Please help this is he and I’m so confused
Answer: 5.25
Step-by-step explanation:
In the picture there is a smaller triangle inside a bigger triangle. You have to find the size it grows by dividing a side of the bigger triangle to the same side of the smaller triangle.
16.8/6.4 = 2.625
Then you find x by multiplying the adjacent side by the size it grows.
2*2.626 = x
2*2.626 = 5.25
Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?
An expression that shows the total area of five rooms is (3 × 13²) + (2 × 15²)
The correct answer is an option (A)
Let 'a' represents the side length of the square rooms measuring 13 ft each and 'b' represents the side length of the square rooms measuring 15 ft each.
We know that the formula for the area of a square is A = s²
where 's' is the side of a square.
Sides of three square rooms measure 13 feet each.
So, the area of the three rooms would be:
A₁ = 3 × a²
A₁ = 3 × 13²
And sides of two square rooms measure 15 feet each.,
So, the area of the two rooms would be:
A₂ = 2 × b²
A₂ = 2 × 15²
Total area of the five rooms A = A₁ + A₂
So, we get an expression:
A = 3 × 13² + 2 × 15²
A = 3 × 169 + 2 × 225
A = 957 ft²
Therefore the total area of the five rooms be 957 ft².
Learn more about an expression here:
brainly.com/question/30091997
#SPJ4
The complete question is:
Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?
a.(3 × 13^2) + (2 × 15^2)
b.(2 × 13^3) + (2 × 15^2)
c.(3 × 15^2) + (2 × 13^2)
d.(3 × 13^2) × (2 × 15^2)
Find the volume of the composite figure below.
Show work.
Answer:
1278in^3
Step-by-step explanation:
21×8=168
168×6=1008in^3
5×9=45
45×6=270in^3
1008+270=1278in^3
If M<1 = 140 what is M <4
Answer:
I think its 560
Step-by-step explanation:
pls help me
Let f(t) = 10 and g(t) = 65t. The distance, in miles, that a car is from a city can be modeled by f(t) + g(t), where t represents time, in hours. Riordan claims that the car is 150 miles from the city after 2 hours of driving, since (10 + 65) = 75(2) = 150. Decide if Riordan is correct. If he is correct, enter 150 below. If he is incorrect, enter the correct distance. miles
Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:
d(t) = f(t) + g(t) = 10 + 65t
So, after 2 hours of driving, the distance that the car has traveled from the city is:
d(2) = 10 + 65(2) = 10 + 130 = 140 miles
Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.
Step-by-step explanation: