Answer:
The answer is 24
Step-by-step explanation:
Each quart contains 4 cups of soup. So, one gallon of soup contains 16 cups of soup. Therefore, 1 1/2 gallons of soup contains 16+8 = 24 cups. Therefore, the chef can serve 1 1/2 gallons of soup as 24 one-cup servings.
100 POINTS
PLEASE PROVIDE STEPS. FOR BOTH
FIND THE INTEGRALS
Answer:
8. -⅓ cos³x + C
9. sec x + eˣ + C
Step-by-step explanation:
8. ∫ sin x cos²x dx
If u = cos x, then du = -sin x dx.
∫ -u² du
-⅓ u³ + C
-⅓ cos³x + C
9. ∫ (sec x tan x + eˣ) dx
∫ sec x tan x dx + ∫ eˣ dx
These are both standard integrals:
sec x + eˣ + C
Question 8:
∫sinxcos²xdx
∫-u²du (let u = cos(x))
-∫u²du
-u(^2+1)/2+1
-cos^(2+1)(x)/2+1
-1/3cos³(x)
-1/3cos³(x) + C
Question 9:
∫(secxtanx + eˣ)dx
∫sec(x)tan(x)dx + ∫eˣdx (apply sum rule)
sec(x) + eˣ (sec(x)tan(x)dx = sec(x) and eˣdx = eˣ)
sec(x) + eˣ + C
Best of Luck!
The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tower. The height, h, of the penny is recorded after each second, t, in the table. Write an equation for the curve of best fit, then find the approximate height of the penny after 7 seconds.
Answer:
The equation for the height of the penny in function of time is:
[tex]h(t)=1451-16t^2[/tex]
After 7 seconds, the penny will be at a height of 667 feet.
Step-by-step explanation:
The penny will have a free fall.
The initial velocity is zero, and the initial height is h(0)=1,451.
The acceleration will be the gravity, that has a value g=32 ft/s^2.
Then, we can model this starting by the speed:
[tex]dv/dt=-g\\\\v(t)=v_0-gt=-gt[/tex]
Then, the height becomes:
[tex]dh/dt=v(t)=-gt\\\\h(t)=h_0-\dfrac{gt^2}{2}=1451-\dfrac{32}{2}t^2\\\\\\h(t)=1451-16t^2[/tex]
The approximate height of the penny after 7 seconds can be calculated as:
[tex]h(7)=1451-16(7^2)=1451-16*49=1451-784=667[/tex]
After 7 seconds, the penny will be at a height of 667 feet.
Trisomy 18 (T18) is a rare genetic disorder that severely disrupts a baby's development prior to birth. Many die before birth and most die before their first birthday. T18 occurs in only 1 in 2500 pregnancies in the U.S. A genetic test on the mother's blood can be done to test for T18 in her baby. The overall probability of a positive test result is 0.010384. The probability of a positive test result for a baby with T18 is 0.97. The probability of a negative test result for a baby without T18 is 0.99. A mother's blood tests positive for T18. What is the probability that her baby has T18
Answer:
3.74% probability that her baby has T18
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test.
Event B: The baby having T18.
T18 occurs in only 1 in 2500 pregnancies in the U.S.
This means that [tex]P(B) = \frac{1}{2500} = 0.0004[/tex]
The probability of a positive test result for a baby with T18 is 0.97.
This means that [tex]P(A|B) = 0.97[/tex]
The overall probability of a positive test result is 0.010384.
This means that [tex]P(A) = 0.010384[/tex]
What is the probability that her baby has T18
[tex]P(B|A) = \frac{0.0004*0.97}{0.010384} = 0.0374[/tex]
3.74% probability that her baby has T18
In how many ways can a member of a hiring committee select 3 of 12 job applicants for further consideration?
Answer: 220
Step-by-step explanation:
When we wanto to create a group of K elements for a set of N elements (where the order of the K elements does not matter, so we do not considerate the permutations of the K elements), the number of possible combinations is:
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here N = 12 and K = 3
[tex]C = \frac{12!}{9!*3!} = \frac{12*11*10}{3*2} = 220[/tex]
So there are 220 possible combinations
Answer:
220
Step-by-step explanation:
Write the equation of the circle graphed below
Answer: (x-1)² + (y-2)² = 6.25
Step-by-step explanation:
The standard equation of a circle is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius. The center of this circle is (1,2) and the radius is 2.5, so the equation of this circle would be (x-1)² + (y-2)² = 6.25
Answer:
(x-1)² + (y-2)² = 6.25
Step-by-step explanation:
What goes into the boxes
Answer:
See explanation
Step-by-step explanation:
[tex]6 {c}^{2} + 2 {c}^{4} - c \\ \\ standard \: form = \red{ \boxed{ \bold{2 {c}^{4} + 6 {c}^{2} - c}}} \\ \\ degree = \purple{ \boxed{ \bold{4}}} \\ \\ leading \: coefficient = \orange{ \boxed{ \bold{1}}}[/tex]
€1.4 m
1.9 m
Tim has to cover 3 tanks completely with paint.
Each tank is in the shape of a cylinder with a top and a bottom.
The tank has a diameter of 1.4 metres and a height of 1.9 m.
A tin of paint covers 5 m
Find the total surface area of the 3 tanks and state how
many tins of paint Tim will need to buy
You must show your working
Total marks 5
Answer:
Step-by-step explanation:
Since each tank is cylindrical, we would apply the formula for determining the total surface area of a cylinder which is expressed as
Total surface area = 2πr² + 2πrh
Where
r represents the height of the cylinder.
h represents the height of the cylinder.
π = 3.14
From the information given,
Height = 1.9
Diameter = 1.4
Radius = diameter/2 = 1.4/2 = 0.7
Total surface area = 2 × 3.14 × 0.7² + 2 × 3.14 × 0.7 × 1.9 = 3.0772 + 8.3524 = 11.4296 m²
Total surface area of the 3 cylinders = 11.4296 × 3 = 34.29 m²
Since a tin of paint covers 5 m², the number of tins paints that Tim will need to buy is
34.29/5 = 6.858
Since the tins of paint must be whole numbers, he needs to buy 7 tins of paints.
The average lifetime of a set of tires is three years. The manufacturer will replace any set of tires failing within two years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within two years of the date of purchase?
Answer:
48.67% probability that the tires will fail within two years of the date of purchase
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
In this question:
[tex]m = 3, \mu = \frac{1}[3}[/tex]
[tex]P(X \leq 2) = 1 - e^{-\frac{2}{3}} = 0.4867[/tex]
48.67% probability that the tires will fail within two years of the date of purchase
Three methods, A, B and C, are available for teaching a certain industrial skill. The failure rate is 15% for A, 5% for B and 10% for C. The method A is used 30%, B is used 40% and C is used 30% of the time. A worker is taught the skill by one of the methods but fails to learn it correctly. a. (10 points) What is the probability that he was taught by method A? b. (5 points) What is the probability of B given A?
Answer:
a) so the correct answer is that the probability that method A has been taught is 0.4737
b) the probability that B receives A is 0.5
Step-by-step explanation:
With the previous data we know that 3 methods teach an industrial skill and when putting into practice a worker does not learn, we have the failure rates like this:
method A fails 15%
method B fails: 5%
method C fails: 10%
usage percentages:
A: 30%
B: 40%
C: 30%
a) the probability that method A has been taught is as follows:
P (failure rate) = P (A) * P (failure rate A) + P (B) * P (failure rate B) + P (C) * P (failure rate C)
we replace the data obtaining:
P = 0.3 * 0.15 + 0.4 * 0.05 + 0.3 * 0.1 = 0.095
P ( failure rate A) = P (A) * P (failure rate A) / P (failure rate)
we replace the data obtaining:
0.3 * 0.15 / 0.095 = 0.4737
so the correct answer is that the probability that method A has been taught is 0.4737
b) the probability that B receives A is as follows:
P (B | A) = P (B) = 0.50
Shira packs 170 lemon bars in boxes for the bake sale. Each box holds 8 lemon bars. She takes home the lemon bars tha are leg over after she has filled as many boxes as possible. Ahora use partial quotients to find how many boxes of lemon bars she can fill to sell at the bake sale. She finds only two partial quotients when she divides. Use the numbers in the box to answer the questions
1 2 7 8 20 21 23 27 29
Question:
1. How many full boxes of lemon bars can Shira fill?
2. How many delicious lemon bars will she be taking home?
Answer:
1. Number of filled box = 21
2. Number of take home = 2
Step-by-step explanation:
Given
Number of lemon bars = 170
Each bar contains 8 lemon bars
Required
(1) & (2)
To calculate the number of boxes Shira can fill, we simply divide the total number of bars by constituents of each bar .
i.e.
Number of filled box = 170/8
Number of filled box = 21.25
But here, we only need the quotient of the division because it represents the filled boxed.
So,
Number of filled box = 21
Calculating the number of take home.
We'll follow the same steps as (1) above but here, we only need the remainder of the division.
When 170 is divided by 8, the remainder is 2.
So, number of boxes she'll take home is 2.
See calculation below
Number of take home = 170 % 8
Number of take home = 2
Omar purchased a used vehicle for $6,500 one year ago. He drove 12,000 miles during the year and kept a record of all his expenses. The variable costs totaled $1,972.50, and the fixed costs totaled $2,476.25. What was the cost per mile for Omar to operate his vehicle last year?
1 point
$0.16
$0.20
$0.37
$2.70
Answer: $0.16
Step-by-step explanation:
Hi, to answer this question we simply have to divide the variable cost ($1,972.50) by the number of miles driven (the variable; 12,000 miles)
Mathematically speaking:
1,972.50 /12000 = 0.16
The cost per mile for Omar to operate his vehicle last year was $0.16
Feel free to ask for more if needed or if you did not understand something.
tommy has a car with a 22-gallon gas tank that yields 16 miles per gallon. How far can he drive on a full tank of gas?
Answer:
On a full tank of gas, Tommy can drive a distance:
D = 22 x 16 = 352 miles
Hope this helps!
:)
Answer:352 miles
Step-by-step explanation:
1 gallons for 16 miles
22 gallons for ______
For 22 gallons 22x16=352 miles
State if the two vectors are parallel, orthogonal, or neither.
u=18i+8j
v=9i+4j
Answer:
Parallel, since [tex]\vec u = 2\cdot \vec v[/tex].
Step-by-step explanation:
The relation between both vectors is determined by the use of the dot product, whose expression is:
[tex]\cos \theta = \frac{\vec u \bullet \vec v}{\|\vec u\| \|\vec v\|}[/tex]
Where:
[tex]\cos \theta = 1[/tex] if vectors are parallel to each other and [tex]\cos \theta = 0[/tex] if vectors are orthogonal. Then, norms and dot product are calculated hereafter:
[tex]\|\vec u\| = \sqrt{18^{2}+8^{2}}[/tex]
[tex]\|\vec u\| \approx 19.698[/tex]
[tex]\|\vec v \| = \sqrt{9^{2}+4^{2}}[/tex]
[tex]\|\vec v\| \approx 9.849[/tex]
[tex]\vec u \bullet \vec v = (18)\cdot (9) + (8)\cdot (4)[/tex]
[tex]\vec u \bullet \vec v = 194[/tex]
[tex]\cos \theta = \frac{194}{(19.698)\cdot (9.849)}[/tex]
[tex]\cos \theta = 1[/tex]
The two vectors are parallel to each other, which is also supported by the fact that one vector is multiply of the other one. That is,
[tex]18i + 8j = 2\cdot (9i + 4j)[/tex]
[tex]\vec u = 2\cdot \vec v[/tex]
Consider the following parametric equation. x equals (t plus 5 )squared; y equals t plus 8; negative 10 less than or equals t less than or equals 10 (a) Eliminate the parameter to obtain an equation in x and y. (b) Describe the curve and indicate the positive orientation. (a) Eliminate the parameter to obtain an equation in x and y. Choose the correct equation below. A. y equals StartRoot x plus 3 EndRoot B. y equals (x plus 3 )squared C. y equals x squared plus 3 D. y equals 3 plus or minus StartRoot x EndRoot (b) Describe the curve and indicate the positive orientation. A. -15 15 -5 15 x y
Answer:
a) D. y = 3 ±√x
b) parabola opening to the right
Step-by-step explanation:
(a) Solving for t in the equation for y:
y = t+8
t = y -8 . . . . subtract 8
Substituting into the equation for x, we have ...
x = ((y -8) +5)^2 = (y -3)^2
Solving for y, we get
±√x = y -3 . . . . . take the square root
y = 3 ±√x
__
(b) The equation describes a parabola that opens to the right.
1a. Find the set of possible and actual zeros according to the rational root theorem using f(x)=3x^3+13x^2+16x+4
1b. Zeros Multiplicity Cross/Turn
|____|_________|_________|
|____|_________|_________|
c. End Behavior:
d. Y-int:
e. Graph.
2. Divide using synthetic Division: x^4-6x^2-2/x-2
3. Diving Using Long Division: 3x^3+5x^2+4x+1/3x+2
4. Using synthetic division and the remainder theorem to find P(c) if P(x)=4x^3+6x^2+4x+3 and c=-1
5. Use synthetic division and the given factor to completely factor each polynomial function and find the zeros: y=x^3+6x^2+3x-10;(x-1)
Factored Form:
Zeros:
Answer:.....
Step-by-step explanation:
......
Round 299 to the nearest hundred. Enter your answer in the box below.
Answer:
300
Step-by-step explanation:
hundreds tens ones
2 9 9
We look at the tens
It is 5 or higher so we round up the hundreds place
2 becomes 3
300
Answer:
300
Step-by-step explanation:
its obv 300 because 299 is greater than 249 and if it is less than 249 it is rounded to 200.
What’s the correct answer for this?
Answer:
perpendicular linesssssssss
The answer is B. perpendicular lines. This is because only perpendicular lines can form 4 congruent angles when they intersect (all 4 angles will be 90 degrees).
6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its
center, spread, and overall shape.
6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a
measure of variation describes how its values vary with a single number.
6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
TASK: You are an employee at a small company. In this company, there are 10 employees who make
$15,000/yr, one manager who makes $100,000/yr, and one CEO who makes $2,000,000/yr. An
employee complained about the salaries to the Department of Labor and the company was brought
under investigation. The CEO responded to the Department of Labor saying:
"The average salary in my company is $187,500. There is no need for concern."
The Data
Employee 2
Employee 3
Employee 4
Employee 5
Employee 6
Employee 1
$15,000
$15,000
$15,000
$15,000
$15,000
$15,000
Employee 7
Employee 8
Employee 9
Employee 10
Manager
CEO
$15,000
$15,000
$15,000
$15,000
$100,000
$2,000,000
Day 1
I.
Which measure of central tendency did the CEO use to describe his company's salaries? (Mean,
Median, Mode)
Was the CEO telling the truth? Explain.
Was the CEO's response a fair description of what is happening in the company?
II.
II.
If you know geometry please answer
-geometry
Answer:
8
Step-by-step explanation:
Find the value of P(7,2)
Answer: 42
Step-by-step explanation:Its a permutation problem!
You roll two dice. How many ways can you
roll a sum of 8 or a sum of 10?
Answer:
5 different ways
Step-by-step explanation:
for the 8
2 and 6
3 and 5
4 and 4
for then tens
5 and 5
4 and 6
Which statements are true? Check all that apply.
A: StartRoot 1.8 EndRoot < 1.8
B: StartRoot 1.8 EndRoot greater-than 1
C: StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
D: 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
E: StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
F: StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
Answer:
The answer is all of them except the last one so... A,B,C,D,E.
Step-by-step explanation:
To indicate that we want both the positive and the negative square root of a radicand we put the symbol ± (read as plus minus) in front of the root. Zero has one square root which is 0. Negative numbers don't have real square roots since a square is either positive or 0.
Answer:
A,B,C,D,and E
Step-by-step explanation:
Convert kg into dg
1) 0.089kg
2) 0.0659 kg
Answer:
?/????????
Step-by-step explanation:
Answer:
Question 1: 890dg
Question2: 659dg
Step-by-step explanation:
1kg=10000dg
Question 1:
0.089kg=0.089 x 10000=890
0.089kg=890dg
Question 2:
0.0659kg=0.0659 x 10000=659
0.0659kg=659dg
4. The Gold family sold their house for $450,000. They paid a realty
company 6% for selling the house. How much money did they pay the
company? *
Answer:
27,000
Step-by-step explanation:
$450,000 x 0.06= $27,000
0.06 is the 6% that you multiply by the total amount they earned to see how much they paid the realty company.
Over what interval is the graph of f(x) = -(x + 8)2 – 1 decreasing?
0 (-8, 0)
O (8, 0)
(- 0,8)
(-∞, -8)
Answer:
(-8, infinity)
Step-by-step explanation:
it's the first option on edge
The solution is, : The given function f(x) is decreasing on the interval :
(-8, +∞).
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The function is given to be : f(x) = (x + 8)² - 1
To find the interval of decreasing, first find the critical points of the function f(x)
f(x) = (x + 8)² - 1
⇒ f'(x) = 2(x + 8)
Critical Point : x = -8
Now, Intervals are : (-∞ , -8) and (-8, +∞)
For the interval : (-∞ , -8)
f'(x) > 0 ⇒ f(x) is increasing on this interval.
For the interval : (-8, +∞)
f'(x) < 0 ⇒ f(x) is decreasing on this interval.
Hence, The given function f(x) is decreasing on the interval : (-8, +∞).
To learn more on function click:
brainly.com/question/21145944
#SPJ7
John wants to invest P dollars at a 4% interest rate. After 5 years the investment will be worth 2000 dollars. How much will it be worth in 11 years?
Answer:
About $2530.63
Step-by-step explanation:
The formula for this kind of calculation is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where P is the initial investment, r is the interest rate, n is the number of times you compound your investment per year, and t is the number of years. Assuming that you compound yearly, plugging in the numbers that you have given, you are left with:
[tex]2000=P(1+\frac{0.04}{1})^{t}[/tex]
[tex]2000=P\cdot (1.04)^5\\P\approx 1643.85\\A=1643.85 \cdot (1.04)^{11}\approx $2530.63[/tex]
Hope this helps!
Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
Answer:
93.25% probability that they have taken this steroid
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test
Event B: Taking the steroid.
Suppose the probability of an athlete taking a certain illegal steroid is 10%.
This means that [tex]P(B) = 0.1[/tex]
Given that the athlete has taken this steroid, the probability of a positive test result is 0.995.
This means that [tex]P(A|B) = 0.995[/tex]
Positive test:
99.5% of 10%(If the athlete has taken).
100-99.2 = 0.8% of 100-10 = 90%(Athlete has not taken)
Then
[tex]P(B) = 0.995*0.1 + 0.008*0.9 = 0.1067[/tex]
Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.1*0.995}{0.1067} = 0.9325[/tex]
93.25% probability that they have taken this steroid
How do I type in exponents
Answer:
on what
Step-by-step explanation: normaly you have a button that you can have certain characters
Consider the graph of the exponential function, y =3(2)^x. The x- intercept of the graph is
Answer:
the x intercept is 2
Step-by-step explanation:
I just went over this unit
Answer:
2
Step-by-step explanation:
If 32x+1 = 3x+5, what is the value of x?
2
3
4
6
Answer:4
Step-by-step explanation:
