Answer:
Step-by-step explanation:
put x=r cos θ
y=r sin θ
r²cos²θ-r²sin²θ=3rsin θ
r²(cos²θ -sin²θ)=3r sin θ
r²cos 2θ=3rsinθ
r cos 2θ=3 sin θ
r=3sec 2θ sin θ
what are the coordinates of point b on ac such that ab=2/5ac
Answer:
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]
= [tex]-\frac{36}{7}[/tex]
y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]
= [tex]\frac{40}{7}[/tex]
Therefore, coordinates of pint B will be,
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
WHY CAN'T ANYONE HELP ME :( Solve the formula for the specified variable. tex]D=\frac{1}{4}fk for f.
Answer:
4d/k or [tex]\frac{4d}{k}[/tex]
Step-by-step explanation:
first multiply both sides by four
you will have 4d=fk
then divide by k
4d/k=f
Help ASAP!!!
A recursive sequence is a sequence where each term is found by adding a common difference
True or false
Answer:
True
Step-by-step explanation:
Classify the polynomial 2x^3+6x^2-4 by the number of terms. binomial. trinomial. cubic. quadratic.
Answer:
monomial
Step-by-step explanation:
A sample of 250 observations is selected from a normal population with a population standard deviation of 25. The sample mean is 20. Determine the standard error of the mean. (Round your answer to 3 decimal places.)
Answer:
The standard error of the mean is [tex]\sigma _{\= x } = 1.581[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 250
The standard deviation is [tex]\sigma = 25[/tex]
The sample mean is [tex]\= x = 20[/tex]
The standard error of the mean is mathematically represented as
[tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x } = \frac{25 }{\sqrt{250} }[/tex]
[tex]\sigma _{\= x } = 1.581[/tex]
perform the division...please!
Answer:
-7/3x + 3
Step-by-step explanation:
Answer:
(9x-7)/3x or (3-7/3x)
Step-by-step explanation:
Divide each term of numerator by denominator.
-28x^5/12x^6 +36x^6/12x^6
-7/3x +3
College Calculus - hyperbolic functions (see attachment)
Answer:
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
Step-by-step explanation:
Using the fundamental theorem of calculus
Taking the derivative of the integral gives back the function
Since the lower limit is a constant when we take the derivative it is zero
d/dx [tex]\int\limits^x_4 {g(t)} \, dt = g(x)[/tex]
g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))
Replacing t with x
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
What is the best way to remember the 6 trigonometric ratios?
Answer:
SOHCAHTOA
Step-by-step explanation:
Usually, in American schools, the term "SOHCAHTOA" is used to remember them. "SOH" is sine opposite hypotenuse, "CAH" is cosine adjacent hypotenuse, and "TOA" is tangent opposite adjacent. There is also Csc which is hypotenuse/opposite, Sec which is hypotenuse/adjacent, and Cot is adjacent/opposite.
Answer: SOHCAHTOA
Step-by-step explanation:
The pneumonic I learned is SOH-CAH-TOA. it says that Sin = opposite/hypotenuse. Cos = adjacent/hypotenuse. Tan = opposite/adjacent.
Hope it helps <3
in the life of a car engine, calculatedin miles, is normally distributed, with a mean of 17,000 miels and a standard deviation of 16,500 miles, what should be the guarantee period if the company wants less than 2% of the engines to fail while under warranty g
Answer:
the guarantee period should be less than 136010 miles
Step-by-step explanation:
From the given information;
Let consider Y to be the life of a car engine
with a mean μ = 170000
and a standard deviation σ = 16500
The objective is to determine what should be the guarantee period T if the company wants less than 2% of the engines to fail.
i.e
P(Y < T ) < 0.02
For the variable of z ; we have:
[tex]z = \dfrac{x - \mu }{\sigma}[/tex]
[tex]z = \dfrac{x - 170000 }{16500}[/tex]
Now;
[tex]P(Y < T ) = P( Z < \dfrac{T- 170000}{16500})[/tex]
[tex]P( Z < \dfrac{T- 170000}{16500})< 0.02[/tex]
From Z table ;
At P(Z < -2.06) ≅ 0.0197 which is close to 0.02
[tex]\dfrac{T- 170000}{16500}<- 2.06[/tex]
[tex]{T- 170000}<- 2.06({16500})[/tex]
[tex]{T- 170000}< - 33990[/tex]
[tex]{T}< - 33990+ 170000[/tex]
[tex]{T}<136010[/tex]
Thus; the guarantee period should be less than 136010 miles
A sample of bacteria is growing at an hourly rate of 10% compounded continuously. The sample began with 4 bacteria. How many bacteria will be in the sample after 18 hours?
Answer:
24
Step-by-step explanation:
The computation of the number of bacteria in the sample after 18 hours is shown below:
We assume the following things
P = 4 = beginning number of bacteria
rate = r = 0.1
Now
We applied the following formula
[tex]A = Pe^{rt}[/tex]
[tex]= 4\times e^{18\times0.1}[/tex]
[tex]=4e^{1.8}[/tex]
[tex]= 4\times6.049647464[/tex]
= 24
We simply applied the above formula to determine the number of bacteria after the 18 hours
Questions:
1. What do you notice about how the angles fit together around a point?
2. What is the measure of a straight angle?
3. Describe the relationship amoung the measure of the angles of ∆ABC
4. The triangle sum theorem states that forma ∆ ABC, m<A + m<A = 180°. Is this true? Explain
1. The angles form a straight angle
2. A straight angle is defined to be 180 degrees
3. The three angles of any triangle always add to 180, as the diagram shows.
4. This is false. We need to add the three different angles A,B,C to get 180. Adding angle A to itself may not lead to 180. A+A = 180 only happens when angle A is a right angle (90 degree angle).
Solve the equation below for x. -1 2(3x - 4) = 11
Answer:
x= 37/36
Step-by-step explanation:
−12(3x−4)=11
Step 1: Simplify both sides of the equation.
−12(3x−4)=11
(−12)(3x)+(−12)(−4)=11(Distribute)
−36x+48=11
Step 2: Subtract 48 from both sides.
−36x+48−48=11−48
−36x=−37
Step 3: Divide both sides by -36.
−36x
−36
=
−37
−36
x=
37
36
Answer:
x=
37
36
-1/2(3x-4) = 11
Multiply both sides by -2:
3x-4 = -22
Add 4 to both sides:
3x = -18
Divide both sides by 3:
X = -6
A card is drawn from a well shuffled deck of 52 cards. What is the probability of drawing an ace or a 9? Round to nearest thousandth
Answer:
.154
Step-by-step explanation:
There are 52 cards
There are 4 aces and 4 9's for a total of 8 cars
P (ace or 9) = number of aces or 9's / total
= 8/52 = 2 /13 =.153846154
To the nearest thousandth
= .154
Answer:
0.154
Step-by-step explanation:
We want to find the probability of drawing an ace or a 9.
P(ace or 9)= aces and 9s / total cards
There are 4 aces and 4 9s in a standard deck of cards. This means there is a total of 8 aces and 9s.
In a standard deck of cards, there is a total of 52 cards.
P(ace or 9)= aces and 9s / total
aces and 9s= 8
total= 52
P(ace or 9)= 8/52
This fraction can be simplified. Both the numerator and denominator can be evenly divided by 4.
P(ace or 9)= (8/4) / (52/4)
P(ace or 9)= 2/13
P(ace or 9)= 0.153846153846154
Round to the nearest thousandth. The 8 in the ten thousandth place tell sus to round the 3 up to a 4.
P(ace or 9) = 0.154
The probability of drawing an ace or 9 is 0.154
x/3 ≥−33 solve for x answer must be simplified
Answer:
[tex]\boxed{x\geq -99}[/tex]
Step-by-step explanation:
[tex]\frac{x}{3} \geq -33[/tex]
[tex]\sf Multiply \ both \ sides \ by \ 3.[/tex]
[tex]\frac{x}{3} (3) \geq -33(3)[/tex]
[tex]x\geq -99[/tex]
Answer:
[tex]\boxed{\red{x \geqslant - 99}}[/tex]
Step-by-step explanation:
[tex] \frac{x}{3} \geqslant - 33 \\ x \geqslant - 33 \times 3 \\ x \geqslant - 99[/tex]
hope this helps you!
The Escobar family and the Johnson family each used their sprinklers last month. The water output rate forthe Escobar family's sprinkler was 20 gallons per hour. The water output rate for the Johnson family's sprinkler was40 gallons per hour. The families used their sprinklers for a combined total of 32 hours, resulting in a total wateroutput of 960 gallons. How many hours was each family’s sprinkler used?
Answer:
J = 32
E = 0
Step-by-step explanation:
E is the number of hours for the Escobar family
J is the number of hours for the Johnson family
E + J = 32
E * 20 + J * 30 = 960
Multiply the first equation by -20 so we can use elimination
-20 E -20 J = -640
Add this to the second equation
E * 20 + J * 30 = 960
-20 E -20 J = -640
---------------------------------
10 J = 320
Divide by 10
J = 32
Now find E
E + J = 32
E + 32 = 32
E = 0
PLEASEEEEE HELPPOO
For Individual or Group Explorations
Maximizing the Total Profit
Payles at The Christmas Store very periodically with a high ef 550.000 in December
the Christmas Stove also comes the Powe, where profits reach a high of $80,000
in Aurust and a few of $20,000 in February Assume that the profit function for
Crm Store
Save
40
20
10
1 2 3 4 5 6 7 8 9 10 11 12
Month
a) Write the profit function for The Christmas Store as a function of the month
and sketch its graph
b)
Write the profit function for The Pool Store as a function of the month and
sketch its graph.
are are length
Write the total profit as a function of the month and sketch its graph. What is
the period?
are inside the
est enth of a
Use the maximum feature of a graphing calculator to find the owner's maxi-
mum total profit and the month in which it occurs.
Find the owner's minimum total profit and the month in which it occurs.
We know that y -a sin x + bcos x is a sine function. However, the sum of
two arbitrary sine or cosine functions is not necessarily a sine function. Find an
example in which the graph of the sum of two sine functions does not look like
a sine curve.
Explain.
is tangent to one
Answer:
what
Step-by-step explanation:
What is the square root of nine?
Answer:
3 or -3
Step-by-step explanation:
sqrt(9)
What number multiplied by itself will give you 9
3*3 =9
-3 * -3 =9
The square root of 9 is 3 or -3
Pls help!! Thank you sooooo much if you help me on this, pls show proof
Answer:
√468 = 6√13
Step-by-step explanation:
ABCDEF is a regular hexagon of side length 6.
A'B'C'D'E'F' is the reflection of ABCDEF across BC.
The line FE' is the line from F to E'. It is also the hypotenuse of the right triangle FEE'. FE = 6, and EE' = 4a, where a is the apothem of the hexagon.
To find the apothem, draw the 30-60-90 triangle formed by the apothem and the radius (essentially 1/12th of the hexagon).
Using properties of a 30-60-90 triangle:
a = (6/2)√3
a = 3√3
4a = 12√3
Using Pythagorean theorem:
x² = (6)² + (12√3)²
x² = 36 + 432
x = √468
x = 6√13
Need help finding the length
Answer:
27
Step-by-step explanation:
First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.
Answer:
27 unitsStep-by-step explanation:
Perimeter of rectangle is 2(l) + 2(w).
The perimeter is given 100 units.
2(4x-1) + 2(3x+2) = 100
Solve for x.
8x-2+6x+4=100
14x+2=100
14x=98
x=7
Plug x as 7 for the side WX.
4(7) - 1
28-1
= 27
please help Find: ∠x ∠a ∠b
Answer:
x = 22
<a = 88°
<b = 92°
Step-by-step explanation:
To solve for x, <a, and <b, we'd need to recall some of the properties of parallel lines, then apply them in solving this problem.
To find the value of x, recall that consecutive interior angles are supplementary. (5x - 18), and (3x + 22) are consecutive interior angles. Therefore:
[tex] (5x - 18) + (3x + 22) = 180 [/tex]
Solve for x
[tex] 5x - 18 + 3x + 22 = 180 [/tex]
[tex] 5x + 3x - 18 + 22 = 180 [/tex]
[tex] 8x + 4 = 180 [/tex]
Subtract 4 from both sides:
[tex] 8x + 4 - 4 = 180 - 4 [/tex]
[tex] 8x = 176 [/tex]
Divide both sides by 8
[tex] \frac{8x}{8} = \frac{176}{8} [/tex]
[tex] x = 22 [/tex]
=>Find <a:
According to the properties of parallel lines, alternate interior angles are equal. Therefore:
<a = 3x + 22
Plug in the value of x
<a = 3(22) + 22 = 66 + 22
<a = 88°
=>Find <b:
According to the properties of parallel lines, corresponding angles are said to be equal. Therefore,
<b = 5x - 18
Plug in the value of x to find <b
<b = 5(22) - 18
<b = 110 - 18 = 92°
Write 3 expressions containing exponents so that each expression equals 81
Answer:
9x9= 81
3x3x3x3=81
81 to the first power.
Step-by-step explanation:
I hope this helps in any way:)
0.3% of a country has a certain disease. The test for the disease has a sensitivity of 92% (i.e., of those we know have the disease, the test comes back positive 92% of the time.) It has a specificity of 96% (i.e., of those who do NOT have the disease, the test comes back negative 96% of the time.) Determine the ACCURACY of this test (round to 5 decimals) Remember, ACCURACY is correct values (i.e. true positives true negatives)
Answer:
0.95988 (Accuracy of the test )
Step-by-step explanation:
To determine the accuracy of this test we have to list out the given values
Prevalence rate of the disease = 0.3% = 0.003
sensitivity rate of the disease = 92% = 0.92
specificity rate for the test = 96% = 0.96
The accuracy of the test can be found using this equation
Accuracy = sensitivity * prevalence + specificity ( 1 - prevalence )
= 0.92 * 0.003 + 0.96 ( 1 - 0.003 )
= 0.00276 + 0.95712
= 0.95988
What is the missing term that makes these ratios equivalent? 1.5:3, 31.5:____
=========================================
Work Shown:
1.5/3 = 31.5/x
1.5x = 3*31.5 cross multiply
1.5x = 94.5
x = 94.5/1.5 dividing both sides by 1.5
x = 63
-----------
An alternative equation to solve is
1.5/31.5 = 3/x
1.5x = 31.5*3
1.5x = 94.5
The remainder of the steps are the same as in the previous section above.
what is 328.1 × 0.63 what answer
Answer:206.703
Step-by-step explanation: you have to multiply 328.1 times 0.63 then you get your answer.
Answer:
206.703
Step-by-step explanation:
328.1 × 0.63=206.703
Ifx + iy = 1
1+i/
1-i
prove that, x² + y² = 1
HI MATE
Need answers!!!!! ASAPPP
Answer:
t
Step-by-step explanation:
a hardware store ordered cartons of hammers at 100$ per carton and cartons wrenches at 150$ per carton if there were a total of 25 cartons in this order And the total cost of the order was 3,000$ how many cartons of hammers were ordered
Answer:
15 cartons of Hammers were ordered
Step-by-step explanation:
Cost per carton of Hammer = $100
Cost per carton of Wrenches = $150
Total Carton = 25
Total Cost = $3,000
Required
Determine the numbers of Hammer and Wrenches
Represent the hammers with H and the wrenches with W
So;
[tex]H + W = 25[/tex]
and
[tex]100H + 150W = 3000[/tex]
Make W the subject of formula in the first equation:
[tex]H + W = 25[/tex]
[tex]W = 25 - H[/tex]
Substitute 25 - H for W in the second equation
[tex]100H + 150(25 - H) = 3000[/tex]
[tex]100H + 3750 - 150H = 3000[/tex]
Collect Like Terms
[tex]100H - 150H = 3000 - 3750[/tex]
[tex]-50H = -750[/tex]
Divide both sides by -50
[tex]\frac{-50H}{=50} = \frac{-750}{-50}[/tex]
[tex]H = \frac{-750}{-50}[/tex]
[tex]H = 15[/tex]
Hence, 15 cartons of Hammers were ordered
Find the hcf of 15a²b² and -24ab | plzzz solve
Answer:
[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all, let's find the factors of these two numbers and I will put in boxes the common factors.
[tex]15a^2b^2=\boxed{3}\cdot 5\cdot \boxed{a} \cdot a \cdot \boxed{b} \cdot b \\ \\ \\-24ab=(-1)\cdot 2 \cdot \boxed{3} \cdot 4 \cdot \boxed{a} \cdot \boxed{b}[/tex]
The Highest Common Factor (HCF) is found by finding all common factors and selecting the largest one. So, in this case, it gives
[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Nakashima Gallery had the following petty cash transactions in February of the current year. Nakashima uses the perpetual system to account for merchandise inventory. Feb 2 Write a $400 check to establish a petty cash fund. Feb 5 Purchased paper for the copier for $14.15 that is immediately used. Feb 9 Paid $32.50 shipping charges (transportation in) on merchandise purchased for resale, terms FOB shipping point. These costs are added to merchandise inventory. Feb 12 Paid $7.95 postage to deliver a contract to a client Feb 14 Reimbursed Adina Sharon, the manager, $68 for mileage on her car. Feb 20 Purchased office paper for $67.77 that is immediately used. Feb 23 Paid a courier $20 to deliver merchandise sold to a customer, terms FOB destination. Feb 25 Paid $13.10 shipping charges (transportation in) on merchandise purchased for resale, terms FOB shipping point. These cost are added to merchandise inventory. Feb 27 Paid $54 for postage expenses Feb 28 The fund had $120.42 remaining in the petty cashbox. Sorted the petty cash receipts by accounts affected and exchanged them for a check to reimburse the fund for expenditures. Feb 28 The petty cash fund amount is increased by $100 to a total of $500
Answer:
1. Debit Petty cash for $400; and Credit Cash for $400.
2. Total petty cash payment = $270.57
3(a) Cash reimbursement is $279.58; and Cash over and short is $9.01.
3(b) Debit Petty cash for $100; and Credit Cash for $100.
Step-by-step explanation:
Note: This question is not complete. The full complete question is therefore provided before answering the question. See the attached pdf file for the full question.
The explanations to the answers are now given as follows:
1. Prepare the journal entry to establish the petty cash fund.
Note: See the journal entry in the attached excel file
2. Prepare a petty cash payments report for February with these categories: delivery expense, mileage expense, postage expense, merchandise inventory (for transportation-in), and office supplies expense. Sort the payments into the appropriate categories and total the expenditures in each category.
Note: See the petty cash payments report in the attached excel file.
3. Prepare the journal entries for required 2 to both (a) reimburse and (b) increase the fund amount.
Note: See the journal entries (a) and (b) in the attached excel file
3(a) Reimburse Workings:
w.1: Calculation of Cash reimbursement
Cash reimbursement = Petty cash fund - Petty cash fund balance = $400 - $120.42 = $279.58
w.2: Calculation of the Cash over and short
Cash over and short = Cash reimbursement – Total expenses = $279.58 - $270.57 - $120.42 = $9.01
A bag of 20 tulip bulbs purchased from a nursery contains 10 red tulip bulbs, 7 yellow tulip bulbs, and 3 purple tulip bulbs. What is the probability of randomly selecting a purple tulip bulb from the bag
Answer:
3/20
Step-by-step explanation:
since there is a total of 20 tulips that would be your denominator then your numerator would be the number of purple tulips which would be 3 so you probability of randomly selecting a purple tulip would be 3/20