Calc AB! Please show work, the answers are provided. I need all work for part A AND B!!!
Need ASAP!
Answers
Step-by-step explanation:
24. A
B' ( t ) = 10 [ 20 CDS ( t/10) ] = 2 COS ( t/10 )
B' ( 7 ) = 1.5
After 7 days the number of beds in use is increasing at the rate of 1 1/2 beds per day.
24.B
2 COS ( t/10) =0
using calculator t = 15.7
B (12) = 20 Sin (1.2) + 50 = 68.6 = 69
B (15.7) = 20 Sin (1.57) + 50 = 70
B (20) = 20 SIn (20) + 50 = 68.25 = 68
Maximum number of beds in use occurs in afternoon of 15th day and is 70 beds.
I hope that helps and I hope it's right
Related Questions
The students want to make care packages for unhoused people for winter season. They would like to put 5 boxes of tissues into each care package. If they have 450 boxes pack, how many tissue boxes will they need to complete the boxes?
Answers
Answer: 50 tissue boxes
Step-by-step explanation:
The students want to make care packages for unhoused people for winter season.
They would like to put 5 boxes of tissues into each care package.
If they have 450 boxes pack, to determine how many tissue boxes that they need to complete the boxes, we will divide the total number of boxes pack that they have by the number of tissues that will go into one pack. It becomes
450/9 = 50
The office building is 48 floors high. Half of the floors have 18 windows each and half of the floors have 36 windows each. How many windows does the building have in all?
Answers
Answer:
1296 windows
Step-by-step explanation:
HALF of the floors, means
HALF of 48, that is:
48 * 0.5 = 24
Thus, we can say:
24 floors each have 18 windows, and
24 floors each have 36 windows
Total Number of Windows:
24 * 18 = 432 windows
24 * 36 = 864 windows
Total = 432 + 864 = 1296 windows
Answer:
1296 windows are present in the building
Explanation:
Given the office building is 48 floors high
Half of floors have 18 windows each
Then , half of floors =[tex]\frac{48}{2}[/tex] = 24 floors
Total windows on half of the floors, that is 24 floors
= [tex]18\times 24[/tex]
= 432 windows
Also, half of the floors have 36 windows each
Total windows on rest half floors (24 floors)
=[tex]36 \times 24[/tex]
= 864 windows
Total windows = 432 + 864 = 1296 windows
Therefore, 1296 windows are present in the building
Harry has a small business cleaning kitchens and bathrooms. He usually cleans a bathroom in 1 hour and cleans a kitchen in 45 minutes. He never works more than 15 hours in a week. Harry earns $60 per bathroom and $20 per kitchen job. He does not do more than 8 bathroom jobs per week (the smell gets to him). Find a combination of bathroom and kitchen jobs per week that will maximize his income and state the amount.
Answers
Answer:
8 bathroom jobs and 9 kitchen jobs
Step-by-step explanation:
B=60
K=20
8*60=480
9*20=180
that would give harry 660 dollars in a week. HOWEVER- we have to make sure that its equal to or less than 15 hours of work.
8*1h= 8 hours in bathroom
9*45m=6.75hr in kitchen
8 hours+6.75 hours=14.75hr 14.75 hr<15hr so it works.
A rectangular area of 36 f t2 is to be fenced off. Three sides will use fencing costing $1 per foot and the remaining side will use fencing costing $3 per foot. Find the dimensions of the rectangle of least cost. Make sure to use a careful calculus argument, including the argument that the dimensions you find do in fact result in the least cost (i.e. minimizes the cost function).
Answers
Answer:
x = 8,49 ft
y = 4,24 ft
Step-by-step explanation:
Let x be the longer side of rectangle and y the shorter
Area of rectangle = 36 ft² 36 = x* y ⇒ y =36/x
Perimeter of rectangle:
P = 2x + 2y for convinience we will write it as P = ( 2x + y ) + y
C(x,y) = 1 * ( 2x + y ) + 3* y
The cost equation as function of x is:
C(x) = 2x + 36/x + 108/x
C(x) = 2x + 144/x
Taking derivatives on both sides of the equation
C´(x) = 2 - 144/x²
C´(x) = 0 2 - 144/x² = 0 ⇒ 2x² -144 = 0 ⇒ x² = 72
x = 8,49 ft y = 36/8.49 y = 4,24 ft
How can we be sure that value will give us a minimun
We get second derivative
C´(x) = 2 - 144/x² ⇒C´´(x) = 2x (144)/ x⁴
so C´´(x) > 0
condition for a minimum
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2z2i + y2z2j + xyzk, S is the part of the paraboloid z = x2 + y2 that lies inside the cylinder x2 + y2 = 16, oriented upward.
Answers
Answer:
[tex]\displaystyle \iint_S {\text{curl \bold{F}} \cdot} \, dS = \boxed{\bold{0}}[/tex]
General Formulas and Concepts:
Calculus
Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Methods: U-Substitution + U-Solve
Multivariable Calculus
Partial Derivatives
Triple Integrals
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Integral Conversion [Cylindrical Coordinates]:
[tex]\displaystyle \iiint_T {f(r, \theta, z)} \, dV = \iiint_T {f(r, \theta, z)r} \, dz \, dr \, d\theta[/tex]
Vector Calculus
Surface Area Differential:
[tex]\displaystyle dS = \textbf{n} \cdot d\sigma[/tex]
Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]
[tex]\displaystyle \text{div \bf{F}} = \nabla \cdot \textbf{F}[/tex][tex]\displaystyle \text{curl \bf{F}} = \nabla \times \textbf{F}[/tex]Stokes’ Theorem:
[tex]\displaystyle \oint_C {\textbf{F} \cdot } \, d\textbf{r} = \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma[/tex]
Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \textbf{F} (x, y, z) = x^2z^2 \hat{\i} + y^2z^2 \hat{\j} + xyz \hat{\text{k}}[/tex]
[tex]\displaystyle \text{Region:} \left \{ {{\text{Paraboloid:} \ z = x^2 + y^2} \atop {\text{Cylinder:} \ x^2 + y^2 = 16}} \right[/tex]
Step 2: Integrate Pt. 1
Find div F:[tex]\displaystyle \text{div } \textbf{F} = \frac{\partial}{\partial x} x^2z^2 + \frac{\partial}{\partial y} y^2z^2 + \frac{\partial}{\partial z} xyz[/tex][div F] Differentiate [Partial Derivatives]:
[tex]\displaystyle \text{div } \textbf{F} = 2xz^2 + 2yz^2 + xy[/tex][Divergence Theorem] Substitute in div F:
[tex]\displaystyle \iint_S {\text{curl } \textbf{F} \cdot} \, dS = \iiint_D {2xz^2 + 2yz^2 + xy} \, dV[/tex]
Step 3: Integrate Pt. 2
Convert region from rectangular coordinates to cylindrical coordinates.
[tex]\displaystyle \text{Region:} \left \{ {{\text{Paraboloid:} \ z = x^2 + y^2} \atop {\text{Cylinder:} \ x^2 + y^2 = 16}} \right \rightarrow \left \{ {{\text{Paraboloid:} \ z = r^2} \atop {\text{Cylinder:} \ r^2 = 16}} \right[/tex]
Identifying limits, we have the bounds:
[tex]\displaystyle \left\{ \begin{array}{ccc} 0 \leq z \leq r^2 \\ 0 \leq r \leq 4 \\ 0 \leq \theta \leq 2 \pi \end{array}[/tex]
Step 4: Integrate Pt. 3
[Integral] Substitute in variables and region:[tex]\displaystyle \iint_S {\text{curl } \textbf{F} \cdot} \, dS = \int\limits^{2 \pi}_0 \int\limits^4_0 \int\limits^{r^2}_0 {r \bigg( 2z^2r \cos \theta + 2z^2r \sin \theta +r^2 \cos \theta \sin \theta \bigg)} \, dz \, dr \, d\theta[/tex]
We evaluate the Stokes' Divergence Theorem Integral using basic integration techniques listed under "Calculus".
[tex]\displaystyle \begin{aligned}\iint_S {\text{curl } \textbf{F} \cdot} \, dS & = \int\limits^{2 \pi}_0 \int\limits^4_0 \int\limits^{r^2}_0 {r \bigg( 2z^2r \cos \theta + 2z^2r \sin \theta +r^2 \cos \theta \sin \theta \bigg)} \, dz \, dr \, d\theta \\& = \frac{1}{3} \int\limits^{2 \pi}_0 \int\limits^4_0 {zr^2 \bigg[ 2z^2 \big( \cos \theta + \sin \theta \big) + 3r \sin \theta \cos \theta \bigg] \bigg| \limits^{z = r^2}_{z = 0}} \, dr \, d\theta \\\end{aligned}[/tex]
[tex]\displaystyle \begin{aligned}\iint_S {\text{curl } \textbf{F} \cdot} \, dS & = \frac{1}{3} \int\limits^{2 \pi}_0 \int\limits^4_0 {r^5 \bigg[ 2r^3 \big( \cos \theta + \sin \theta \big) + 3 \sin \theta \cos \theta \bigg]} \, dr \, d\theta \\& = \frac{1}{54} \int\limits^{2 \pi}_0 {r^6 \bigg[ 4r^3 \big( \cos \theta + \sin \theta \big) + 9 \sin \theta \cos \theta \bigg] \bigg| \limits^{r = 4}_{r = 0}} \, d\theta \\\end{aligned}[/tex]
[tex]\displaystyle \begin{aligned}\iint_S {\text{curl } \textbf{F} \cdot} \, dS & = \frac{2048}{27} \int\limits^{2 \pi}_0 {\cos \theta \Big( 9 \sin \theta + 256 \Big) + 256 \sin \theta} \, d\theta \\& = \frac{-1024}{243} \bigg[ 4608 \cos \theta - \bigg( 9 \sin \theta + 256 \bigg)^2 \bigg] \bigg| \limits^{\theta = 2 \pi}_{\theta = 0} \\& = \boxed{\bold{0}}\end{aligned}[/tex]
∴ we have calculated the Stokes' Theorem integral with the given region and function using the Divergence Theorem.
---
Learn more about multivariable Calculus: https://brainly.com/question/13933633
---
Topic: Multivariable Calculus
The Stokes' theorem is applied to convert a surface integral of a curl of a vector into a line integral. This is done by identifying the curl of the given vector field F and setting up the limits of the integral based on given bounds. The integral is then evaluated.
Explanation:Stokes' theorem is used in vector calculus to simplify certain types of surface integrals. It transforms a surface integral of a curl of a vector field into a line integral. F(x, y, z) = x2z2i + y2z2j + xyzk, here, is the given vector field. The surface S is the part of the paraboloid that lies within the cylinder x² + y² = 16. The theorem is used to evaluate the integral S curl F · dS, by treating the surface integral as a line integral. The line integral can be easier to evaluate. The exact process involves identifying the curl of F, setting up the bounds of the integral based on the restrictions given, and then computing the integral.
Learn more about Stokes' Theorem here:https://brainly.com/question/10773892
#SPJ3
An investor has $80,000 to invest in a CD and a mutual fund. The CD yields 8% and the mutual fund yields 6%. The mutual fund requires a minimum investment of $9,000, and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the return? What is the maximum return?
Answers
Answer:
mutual fund: $9000CDs: $71000return: $6220, an average of 7.775%Step-by-step explanation:
Since the mutual fund is the lower yield vehicle, only the minimum should be invested there.
The investments and returns should be ...
mutual fund: $9000, return = 6% × $9000 = $540
CD: $71000, return = 8% × $71000 = $5680
The maximum return is ...
$540 +5680 = $6220
To maximize the return, we need to find the amount to be invested in CDs and the mutual fund. The amount to be invested in CDs is $53,333.33 and the amount to be invested in the mutual fund is $26,666.67. The maximum return is $5,333.33.
Explanation:To maximize the return, we need to find the amount to be invested in CDs and the mutual fund. Let's assume the amount invested in the mutual fund is x dollars. Since the investor requires at least twice as much to be invested in CDs, the amount invested in CDs will be 2x dollars. The total investment amount is $80,000, so we can write the equation: x + 2x = $80,000. Simplifying the equation, we have 3x = $80,000. Dividing both sides by 3, we get x = $26,666.67 (rounded to two decimal places).
The amount to be invested in CDs is 2 times x, which is $53,333.33 (rounded to two decimal places). Therefore, the maximum return can be calculated by multiplying the amount invested in CDs and the mutual fund by their respective interest rates and adding them. The return from the CDs would be 8% of $53,333.33 and the return from the mutual fund would be 6% of $26,666.67. Calculating the returns and adding them, we get the maximum return as $5,333.33 (rounded to two decimal places).
Learn more about investment here:https://brainly.com/question/34489138
#SPJ3
The thermostat in Steffi’s house is set to 56°F. The actual temperature variance in her house can be modeled by the inequality |t − 56|= 3. Plot the range of possible temperatures in her house.
Answers
Answer:
Step-by-step explanation:
|t − 56|= 3 states that the temperature, t, can be as low as (56-3)°F, or 53°F, and as high as (56+3)°F, or 59°F.
On a number line, plot a dark dot at both 53°F and 59°F, and then connect these two dots with a solid line.
The maximum and minimum values of temperature are 59°F and 53°F respectively.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
Given the inequality
|t − 56|= 3
Now,
Taking positive value ;
t - 56 = 3
t = 59
Now taking negative value
-(t-56) = 3
t = -3 + 56 = 53
Hence "The maximum and minimum values of temperature are 59°F and 53°F respectively".
For more about inequality,
brainly.com/question/20383699
#SPJ2
A rectangle is drawn on a coordinate grid. The equation for one side of the rectangle is 2x – 5y = 9. Which could be the equation of another side of the rectangle?
Answers
Answer:
[tex]25x+10y+18=0[/tex]
Step-by-step explanation:
We are given that a rectangle in which the equation of one side is given by
[tex]2x-5y=9[/tex]
We have to find the equation of another side of the rectangle.
We know that the adjacent sides of rectangle are perpendicular to each other.
Differentiate the given equation w.r.t.x
[tex]2-5\frac{dy}{dx}=0[/tex] ([tex]\frac{dx^n}{dx}=nx^{n-1}[/tex])
[tex]5\frac{dy}{dx}=2[/tex]
[tex]\frac{dy}{dx}=\frac{2}{5}[/tex]
Slope of the given side=[tex]m_1=\frac{2}{5}[/tex]
When two lines are perpendicular then
Slope of one line=[tex]-\frac{1}{Slope\;of\;another\;line}[/tex]
Slope of another side=[tex]-\frac{5}{2}[/tex]
Substitute x=0 in given equation
[tex]2(0)-5y=9[/tex]
[tex]-5y=9[/tex]
[tex]y=-\frac{9}{5}[/tex]
The equation of given side is passing through the point ([tex]0,-\frac{9}{5})[/tex].
The equation of line passing through the point [tex](x_1,y_1)[/tex] with slope m is given by
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values then we get
[tex]y+\frac{9}{5}=-\frac{5}{2}(x-0)=-\frac{5}{2}x[/tex]
[tex]y=-\frac{5}{2}x-\frac{9}{5}[/tex]
[tex]y=\frac{-25x-18}{10}[/tex]
[tex]10y=-25x-18[/tex]
[tex]25x+10y+18=0[/tex]
Hence, the equation of another side of rectangle is given by
[tex]25x+10y+18=0[/tex]
Answer:
y=2/5x-9
I just answered this and got it right.
Step-by-step explanation:
Choose the slope-intercept equation of the line that passes through the point (-2, 4) and is parallel to y = -3x + 6.
y = 1/3 x + 14/3
y = 3x + 10
y = -3x - 2
y = - 1/3 x + 10/3
Answers
Answer:
y = -3x - 2
Step-by-step explanation:
Parallel lines have the same slope. The only answer choice with the same slope (x-coefficient = -3) as the given line is the one shown above.
Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros of f (x )equals x cubed plus 5 x squared plus 7 x plus 6f(x)=x3+5x2+7x+6. What are the possible numbers of positive real zeros?
Answers
Answer:
0
Step-by-step explanation:
All of the terms have positive signs, so there are no sign changes. Zero sign changes means there are zero positive real roots.
Consider the given function and the given interval.
f(x) = 3 sqrt x, [0, 16]
(a) Find the average value fave of f on the given interval
(b) Find c such that fave = f
(c). (Round your answer to three decimal places.)
Answers
Answer:
(a) fave = 8
(b) c = 64/9
(c) c ≈ 7.111
Step-by-step explanation:
(a) The average value of the function is its integral over the interval, divided by the width of the interval.
[tex]f_{ave}=\displaystyle\frac{1}{16-0}\int_0^{16} {3x^{\frac{1}{2}}} \, dx=\left.\frac{x^{3/2}}{8}\right|_0^{16}=8[/tex]
__
(b) We want ...
f(c) = 8
3√c = 8 . . . . . use f(c)
√c = 8/3 . . . . . divide by 3
c = (8/3)² . . . . square
c = 64/9
__
(c) c ≈ 7.111
To find the average value of a function, evaluate the definite integral over the interval and divide by the length of the interval.
Explanation:To find the average value of a function on a given interval, we need to evaluate the definite integral of the function over the interval and divide it by the length of the interval.
For the given function f(x) = 3√x on the interval [0, 16], the average value fave is given by:
fave = (1/[16-0]) * ∫(0 to 16) 3√x dx
Simplifying this integral, we get:
fave = 3/16 * (2/3) * (16^(3/2) - 0^(3/2)) = 4(16 - 0) = 64
Learn more about Average value of a function here:https://brainly.com/question/32589988
#SPJ3
Consider an employee's whose earnings, in dollars, are according to the continuous stream f(t)=5,000e0.1t for t>0, where t is measured in years. How many years will it take them to earn a combined total of $100,000? Give your answer in years to the nearest year.
Answers
It will take approximately 10.986 years for the employee to earn a combined total of $100,000. Rounding to the nearest year, it will take approximately 11 years for the employee to reach this earnings milestone.
To determine how many years it will take for the employee to earn a combined total of $100,000, we need to set up and solve the following integral:
[tex]\[ \int_{0}^{t} 5000e^{0.1\tau} \, d\tau = 100,000 \][/tex]
Here, [tex]\( t \)[/tex] represents the time in years. The integral represents the accumulated earnings from the start (0 years) to t years based on the continuous stream function[tex]\( f(\tau) = 5000e^{0.1\tau} \).[/tex]
Let's solve this integral:
[tex]\[ \int_{0}^{t} 5000e^{0.1\tau} \, d\tau = \left. \frac{5000}{0.1}e^{0.1\tau} \right|_{0}^{t} \][/tex]
Evaluate this at the upper and lower limits:
[tex]\[ \frac{5000}{0.1}e^{0.1t} - \frac{5000}{0.1}e^{0.1 \times 0} \][/tex]
Simplify:
[tex]\[ 50000(e^{0.1t} - 1) \][/tex]
Now, set this expression equal to the target earnings of $100,000 and solve for t :
[tex]\[ 50000(e^{0.1t} - 1) = 100,000 \][/tex]
Divide both sides by 50000:
[tex]\[ e^{0.1t} - 1 = 2 \][/tex]
Add 1 to both sides:
[tex]\[ e^{0.1t} = 3 \][/tex]
Now, take the natural logarithm (ln) of both sides:
[tex]\[ 0.1t = \ln(3) \][/tex]
Solve for t:
[tex]\[ t = \frac{\ln(3)}{0.1} \][/tex]
Using a calculator:
[tex]\[ t \approx \frac{1.0986}{0.1} \]\[ t \approx 10.986 \][/tex]
20% 20 % of the tickets sold at a water park were adult tickets. If the park sold 55 55 tickets in all, how many adult tickets did it sell?
Answers
There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor, position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 10 candidates qualified for 3 of the positions. Determine the number of different ways that 3 positions can be filled by these applicants.a.30.b.720.c. none of these choices.d. 10.e. 120
Answers
Answer:
The correct option is B) 720.
Step-by-step explanation:
Consider the provided information.
We have 10 candidates those qualified for 3 of the positions.
There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor, position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position.
For Position 1 we have 10 choices, if we select 1 out of 10 candidates we are left with 9 candidates.
For position 2 we have 9 candidates, if we select 1 out of 9 candidates we are left with 8 candidates.
For position 3 we have 8 candidates.
Therefore, the number of ways are: [tex]10\times 9\times 8=720[/tex]
The number of different ways that 3 positions can be filled by these applicants is 720.
Hence, the correct option is B) 720.
Correct Option Is (e. 120.) The number of different ways that 3 positions can be filled by the applicants is 120.
Explanation:To determine the number of different ways that 3 positions can be filled by these applicants, we can use the concept of combinations. Since there are 10 candidates and the order of the positions does not matter, we can use the combination formula. The number of combinations of 10 candidates taken 3 at a time is given by:
C(10, 3) = 10! / (3!(10-3)!)
Simplifying this expression, we get:
C(10, 3) = 10! / (3!7!)
Calculating the factorial values, we have:
C(10, 3) = 10 * 9 * 8 / (3 * 2 * 1) = 120
Therefore, the number of different ways that 3 positions can be filled by these applicants is 120.
Learn more about Combinations here:https://brainly.com/question/39347572
#SPJ3
Giovanni orders a pastry from the bakery. The price of the pastry before tax is $4.50. Giovanni wants to know the total price including a 10% sales tax.
Answers
Answer:
4.95
Step-by-step explanation:
You take the 4.50 and multiply it by 1.10 and it equals 4.95. Also I did it and I got it right.
The total price of the pastry is $4.95.
Given to usprice of the pastry = $4.50
sales tax = 10%
Sales taxThe sales tax on the pastry is 10% of the price of the pastry.
Tax on pastry = price of the pastry x percentage of sales tax
[tex]= \$4.50 \times 10\%\\= 4.5\times \dfrac{10}{100}\\= 4.50 \times 0.1\\= 0.45[/tex]
therefore, the tax on the pastry will be $0.45
Total price of the pastryTotal price of the pastry = Price of the pastry + tax on the pastry
= $4.50 + $0.45
= $4.95
Hence, the total price of the pastry is $4.95.
Learn more about Tax:
https://brainly.com/question/1362871
Coach A is offering her services for an initial $6,925 in addition to $450 per hour. Coach B is offering her services for an initial $5,000 in addition to $725 per hour. When will the two coaches charge the same amount of money? The two coaches will charge the same amount of money after
Answers
Answer:
The two coaches will charge the same amount of money after working for 11 hours
Step-by-step explanation:
Let us assume for m hours, they both will charge same amount.
For COACH A:
The initial Fee = $ 6,925
The per hour fee = $450
So, the fees in m hours = m x ( Per hour fees) = m x ($450) = 450 m
So, the total fees of Coach A in m hours = Initial Fee + fee for m hours
= $ 6,925 + 450 m
⇒ The total fees of Coach A in m hours = $ 6,925 + 450 m .... (1)
For COACH B:
The initial Fee = $ 5,000
The per hour fee = $725
So, the fees in m hours = m x ( Per hour fees) = m x ($725) = 725 m
So, the total fees of Coach B in m hours = Initial Fee + fee for m hours
= $ 5,000 + 725 m
⇒ The total fees of Coach B in m hours =$ 5,000 + 725 m .... (2)
Now, for m hours , they both charge the SAME AMOUNT fees
⇒$ 6,925 + 450 m = $ 5,000 + 725 m ( from (1) and (2))
or, 6925 - 5000 = 725 m - 450 m
or, 1925 = 175 m
or,m = 1925 / 175 = 11
or, m = 11
Hence, the two coaches will charge the same amount of money after working for 11 hours.
A certain company has 255 employees. If an employee is to be selected at random from the company's employees, is the the probability less than 1/2 that the employee selected will be a woman who has a college degree?
(1) 130 of the company's employees do not have a college degree
(2) 125 of the company's employees are men
Answers
Answer:
a) 125 < 128
b) The maximum probability that all 130 women are with college degree is 130 < 128 (this is not possible)
The minimum probability that none of the 130 women are college holders = 0 < 128 (this is possible)
Step-by-step explanation:
Total number of employees = 255
If the probability is less than 1/2 that the employee selected will be a woman who has college degree, we have
Women with college degree < 255/2
< 128
a) if 130 of the company employee do not have college degree, we consider that all the college degree holders are women.
The women with college degree = 255 - 130
= 125
Therefore; 125 < 128 ( this is possible)
b) If 125 of the company employees are men, the number of women = 250 -125
= 130 women
The maximum probability that all 130 women are with college degree is 130 < 128 (this is not possible)
The minimum probability that none of the 130 women are college holders = 0 < 128 (this is possible)
Use the confidence interval to find the estimated margin of error. Then find the sample mean.
A biologist reports a confidence interval of (3.8,4.8 )when estimating the mean height (in centimeters) of a sample of seedlings.
Answers
Answer: The estimated margin of error = 0.5 centimeter
The sample mean = 4.3 centimeters
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm E[/tex]
or [tex](\overline{x}-E,\ \overline{x}+E)[/tex]
, where [tex]\overline{x}[/tex] = sample mean.
E = Margin of error .
The given confidence interval : (3.8,4.8 )
Lower limit : [tex]\overline{x}-E=3.8[/tex] (1)
Upper limit = [tex]\overline{x}+E=4.8[/tex] (2)
Eliminate equation (1) from (2) , we get
[tex]2E=1.0\\\\\Rightarrow\ E=\dfrac{1}{2}=0.5[/tex]
⇒ The estimated margin of error = 0.5 centimeter
Add (1) and (2) ,we get
[tex]2\overline{x}-E=8.6\\\\\Rightarrow\ \overline{x}=\dfrac{8.6}{2}=4.3[/tex]
⇒ The sample mean = 4.3 centimeters
All questions answer help me! I need it right now! Step by step explain please!
Answers
Answer:
C
Step-by-step explanation:
Just by looking at the chart the answer concludes the correct equation for the graph hope this helps CORRECT ME IF I'M WRONG
ps: is that you on your profile picture?
Answer:
A
Step-by-step explanation:
1.9
A
A mixture of 5 pounds of fertilizer A, 13 pounds of fertilizer B, and 4 pounds of fertilizer C provides the optimal nutrients for a plant. Commercial brand X contains equal parts of fertilizer B and fertilizer C. Commercial brand Y contains one part of fertilizer A and two parts of fertilizer B. Commercial brand Z contains two parts of fertilizer A, five parts of fertilizer B, and two parts of fertilizer C. How much of each fertilizer brand is needed to obtain the desired mixture?
Answers
The optimal mixture to compose the desired fertilizer can be obtained using 17 lbs of Brand X, 6 lbs of Brand Y, and 8 lbs of Brand Z.
Explanation:To solve this problem, let us denote X as the amount of brand X, Y as the amount of brand Y, and Z as the amount of brand Z. Since brand X contains equal parts of fertilizers B and C, and the optimal nutrients contain 13 lbs of B and 4 lbs of C, we can say that X = 13 lbs + 4 lbs = 17 lbs.
Brand Y contains one part of A and two parts of B. As we know from the problem that we need 5 lbs of A and 13 lbs of B, we get the equation Y = 5/3 lbs + 13/3 lbs = 6 lbs of Y. This equation is derived from the fact that for every 3 lbs of Y, you get 1.lb of A and 2 lbs of B.
Lastly, brand Z contains two parts of A, five parts of B, and four parts of C. So, Z could be calculated by the combined remainder of A, B and C i.e. (5 - 5/3 lbs) of A, (13 - 13 lbs) of B, and (4 - 4 lbs) of C which will get you approximately 8 lbs of brand Z.
So, you would need roughly 17 lbs of brand X, 6 lbs of brand Y, and 8 lbs of brand Z to create the desired fertilizer mixture.
https://brainly.com/question/30233543
#SPJ12
A random number generator is used to create a list of 300 single-digit numbers. Of those 300 numbers, 146 are odd and 154 are even. The number 8 was generated 22 times. What is the experimental probability of an even number other than 8 being generated
Answers
Answer:
0.44
Step-by-step explanation:
The total numbers drawn = 300
Out those 146 are odd and 154 are even.
The number 8 was drawn = 22 times
So, the number of times an even number other than 8 = 154 -22 = 132
The experimental probability = The number of favorable outcomes ÷ The number of possible outcomes.
The experimental probability of an even number other than 8 being generated = [tex]\frac{132}{300}[/tex]
Simplify the above fraction to decimal, we get
= 0.44
Therefore, the answer is 0.44
Amaya has a store credit of 50.86 she plans to purchase a video game for $24.97 and a golf club accessory for $6.99 how much store credit will she have left
Answers
Amaya will have $18.90 store credit left.
Step-by-step explanation:
Available store credit = $50.86
Cost of video game = $24.97
Cost of golf club accessory = $6.99
Total amount spent = Cost of video game + cost of golf club accessory
[tex]Total\ amount\ spent=24.97+6.99\\Total\ amount\ spent=\$31.96[/tex]
Remaining store credit = Available store credit - total amount spent
[tex]Remaining\ store\ credit=50.86-31.96\\Remaining\ store\ credit=\$18.90[/tex]
Amaya will have $18.90 store credit left.
Keywords: Addition, subtraction
Learn more about addition at:
brainly.com/question/11566221brainly.com/question/12896802#LearnwithBrainly
I love sharks! In fact, before I became a statistician, I wanted to be a marine biologist specializing in shark research (I even went to school for it for a little while). Of particular interest to me were hammerheads and great whites.
Great white sharks are big and hungry. The lengths of 44 great white sharks tagged near False Bay, South Africa had a mean of 15.6 ft with standard deviation 2.5 feet. Based on this sample, is there evidence that the mean length of great white sharks near False Bay are greater than 15 feet? Use a significance level, α = 0.10.
State the null hypothesis.
Answers
Answer:
Null hypothesis: [tex]\mu \leq 15[/tex]
Alternative Hypothesis: [tex]\mu >15[/tex]
We have enough evidence to reject the null hypothesis at 10% level of significance.
Step-by-step explanation:
1) Data given
n =44, representing the sample size
[tex]\bar X=15.6ft[/tex] represent the sample mean for the length of great white sharks
[tex]s=2.5ft[/tex] represent the sample standard deviation for the length of great white sharks
[tex]\alpha =0.1[/tex] significance level for the test
2) Formulas to use
On this case we are intereste on the sample mean for the length of great white sharks, and based on the paragraph the hypothesis are given by:
Null hypothesis: [tex]\mu \leq 15[/tex]
Alternative Hypothesis: [tex]\mu >15[/tex]
since we have n>30 but we don't know the population deviation [tex]\sigma[/tex] so we will can use the t approximation. The sample mean have the following distribution
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
Based on this the statistic to check the hypothesis would be given by:
[tex]t=\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex]
Replacing the values given we have:
[tex]t_{calc}=\frac{15.6-15}{\frac{2.5}{\sqrt{44}}}=1.592[/tex]
We can calculate the degrees of freedom with:
[tex]df=n-1=44-1=43[/tex]
With [tex]\alpha[/tex] and the degrees of freedom we can calculate the critical value, since [tex]\alpha=0.1[/tex] we need a value from the t distribution with 43 degrees of freedom that accumulates 0.1 of the area on the right or 0.9 of the area on the left.
We can use excel, a calculator or a table for this, calculating this value we got:
[tex]t_{(43,critc)}=1.302[/tex]
Since our calculatesd value was [tex]t_{calc}=1.592>t_{crit}[/tex], we can reject the null hypothesis at 0.1 level of significance.
Other way in order to have a criterion for reject or don't reject the null hypothesis is calculating the p value, on this case based on the alternative hypothesis the p value would be given by:
[tex]p_v=P(t_{(43)}>1.592)=0.0594[/tex]
So then [tex]p_v <\alpha[/tex] so we have enough evidence to reject the null hypothesis at 10% level of significance.
A rectangle is drawn so that the width is 3 feet shorter than the length. The area of the rectangle is 28 square feet. Find the length of the rectangle.
Answers
Answer:
7 feet
Step-by-step explanation:
Assuming the dimensions are integers, we can look at the factors of 28:
28 = 1·28 = 2·14 = 4·7
The last pair differs by 3, so can be the solution to the problem.
The length of the rectangle is 7 feet.
Write the equation of the linear relationship in slope-intercept form, using decimals as needed.
x 25 35 45 55
y 92.5 87.5 82.5 77.5
The equation that represents this relationship is y = ?
Answers
The equation of the linear relationship given the x and y coordinates is calculated in slope-intercept form by finding the slope and y-intercept. In this case, the equation of the line is y = -0.5x + 95.
Explanation:In mathematics, the equation of a linear relationship can be represented in the slope-intercept form, which is y = mx + c.
Where, 'm' is the slope of the line and 'c' is the y-intercept.
Given the x and y coordinates, we can calculate the slope 'm' using the formula, m = (y2 - y1) / (x2 - x1).
For example: m = (87.5-92.5) / (35-25) = -5 / 10 = -0.5. So the slope 'm' is -0.5.
Now we can find the y-intercept 'c' by substituting the known x,y coordinates and the slope into the equation and solving for 'c'. Let's take x = 25 and y = 92.5, substituting these values, we will get c = y - mx = 92.5 - (-0.5 * 25) = 95.
So, the equation of the straight line in slope-intercept form is y = -0.5x + 95.
Learn more about Equation of Line here:https://brainly.com/question/21511618
#SPJ12
2. Which coordinate divides the directed line segment from –10 at J to 23 at K in the ratio of 2 to 1? Explain.
A. 1
2. 11
C. 12
Answers
Answer:
12
Step-by-step explanation:
x=(-10×1+23×2)÷(2+1)=36/3=12
Final answer:
The coordinate that divides the line segment from -10 at J to 23 at K in the ratio of 2 to 1 is C) 12.
Explanation:
The coordinate that divides the line segment from -10 at J to 23 at K in the ratio of 2 to 1 is 12.
To find this coordinate, we can use the concept of a section formula. Let the ratio be m:n. The coordinate divided is [tex](\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n})[/tex]. Substituting the values, we get [tex](\frac{2 ( 23) + 1 ( -10)}{2+1}, \frac{2 (0) + 1 ( 2)}{2+1})[/tex] = (12, 0).
Therefore, the required coordinate that divides the line segment in the ratio of 2 to 1 is C) 12.
At a recent track meet the fastest time in the 40-yard dash was 4.37 seconds on the slowest time was 5.08 seconds what is the difference between the fastest and slowest time
Answers
The difference between the fastest and slowest time in the 40-yard dash is 0.71 seconds.
Explanation:The difference between the fastest and slowest time in the 40-yard dash can be found by subtracting the slowest time from the fastest time. In this case, the fastest time was 4.37 seconds and the slowest time was 5.08 seconds. To find the difference, we subtract 5.08 seconds from 4.37 seconds.
The difference between the fastest and slowest time is 0.71 seconds.
Learn more about Difference between fastest and slowest time here:https://brainly.com/question/30292758
#SPJ12
Long-term studies of Belding's ground squirrels show that immigrants move nearly 2 km from where they are born and make up 1 to 8% of the males and 0.7 to 6% of the females in other populations. On an evolutionary scale, why is this significant?
Answers
Answer:
It is significant because when they migrate from one place to other it becomes a source of genetic diversity between them and other population.
Step-by-step explanation:
A sumo wrestling ring is circular and has a circumference of 4.6\pi \text{ meters}4.6π meters4, point, 6, pi, start text, space, m, e, t, e, r, s, end text. What is the area AAA of the sumo wrestling ring in square meters? Give your answer in terms of \piπpi. A=A=A, equals \text{m}^2m 2
Answers
Answer:
The area of the sumo wrestling ring is [tex]5.29 \pi[/tex]
Step-by-step explanation:
The circumference of the circular sumo wrestling ring is [tex]4.6\pi[/tex], that means its radius [tex]r[/tex] is:
[tex]2\pi r=4.6\pi[/tex]
[tex]r=\frac{4.6}{2} =\boxed{2.3\:meters.}[/tex]
Now once we have the radius [tex]r[/tex] of the sumo wrestling ring we can find its area [tex]A[/tex] by the following formula:
[tex]A=\pi r^2[/tex]
Putting in the value of [tex]r=2.3\:meters[/tex] we get:
[tex]A=\pi (2.3m)^2=\boxed{5.29\pi\:\:m^2}[/tex]
Therefore the area of the sumo wrestling ring is [tex]{5.29\pi\:\:m^2[/tex]
Answer:
5.29pi
Step-by-step explanation:
Which is the best interpretation of the solution set for the compound inequality?
3(2x + 1) > 21 or 4x + 3 < 3x +7
no solution
3
Ox<3 or x > 4
all real numbers
Answers
For this case we must find the solution set of the given inequalities:
Inequality 1:
[tex]3 (2x + 1)> 21[/tex]
Applying distributive property on the left side of inequality:
[tex]6x + 3> 21[/tex]
Subtracting 3 from both sides of the inequality:
[tex]6x> 21-3\\6x> 18[/tex]
Dividing by 6 on both sides of the inequality:
[tex]x> \frac {18} {6}\\x> 3[/tex]
Thus, the solution is given by all the values of "x" greater than 3.
Inequality 2:
[tex]4x + 3 <3x + 7[/tex]
Subtracting 3x from both sides of the inequality:
[tex]4x-3x + 3 <7\\x + 3 <7[/tex]
Subtracting 3 from both sides of the inequality:
[tex]x <7-3\\x <4[/tex]
Thus, the solution is given by all values of x less than 4.
The solution set is given by the union of the two solutions, that is, all real numbers.
Answer:
All real numbers