Answer:
t=4 seconds to reach the cannon floor
Step-by-step explanation:
ax^2+bx+c=0
0=-16t^2+255
-255=-16t^2
t^2=15.9375
t= 3.99
round it up...
t=4 seconds to reach the cannon floor
hope this helps!!! :)
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
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.
All questions answer help me! I need it right now! Step by step explain please!
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
Traci collects donations for a dance marathon. One group of sponsors will donate a total of $15 for each hour she dances. Another group of sponsors will donate $110 no matter how long she dances. What number of hours should Traci dance if she wants to raise at least $500?
Answer:
she will need to dance for 26 hours
Step-by-step explanation:
500=15(26)+110
Answer:
26 hours
Step-by-step explanation:
One group will donate $15 per hour, while the other is offering a flat sum of $110. She wants $500, so we can set up the equation
15x + 110 = 500 (with x being the number of hours Traci dances). You subtract 110 from 500 to isolate the variable with its coefficient, resulting in
15x = 390 . Then, dividing 390 by 15 to get x by itself, the answer of 26 hours is found.
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.
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
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?
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:
answer correctly / explain a lil.
Which relation could be rewritten using FUNCTION notation?
A) x = 3
B) x + y = 3
C) x + y2 = 3
D) x2 + y2 = 3
Answer:
B) x + y = 3
Step-by-step explanation:
This is a specific way to give details without a detailed written explanation of the function. There will be NO exponents when trying to find out information about something:
[tex]\displaystyle x + y = 3 → y = -x + 3[/tex]
I am joyous to assist you anytime.
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.
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: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: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
Need help with this I am not good in Geometry
Answer:
Step-by-step explanation:
Lines p and line r are parallel. This actually means that they will extend continuously without meeting at a point.
Let us assign an alphabet to an angle to make it easy for reference. The diagram is shown in the attached photo
From the photo,
Angle T is equal to 34 degrees. This is because angle T and 34 degrees are corresponding angles.
Angle G = angle T. This is because angle T is vertically opposite to angle G. Therefore
G = 34 degrees
If the length of a rectangle is given by the expression 2 153 and the width is given by 4 68 , which radical expression represents the perimeter of the rectangle? A) 6 34 B) 14 17 C) 28 17 D) 32 17
Answer:
C) 28√17
Step-by-step explanation:
The perimeter is twice the sum of the two given side lengths, so is ...
P = 2(L +W) = 2(2√153 +4√68)
= 2(6√17 +8√17) = 2(14√17)
P = 28√17 . . . . . matches choice C
_____
This is about simplifying radicals. The applicable rules are ...
√(ab) = (√a)(√b)
√(a²) = |a|
__
153 = 9×17, so √153 = (√9)(√17) = 3√17
68 = 4×17, so √68 = (√4)(√17) = 2√17
_____
Comment on the problem presentation
It would help if there were actually radicals in the radical expressions. We had to guess based on the spacing and the answer choices.
In any event, this problem can be worked with a calculator. Find the perimeter (≈115.45) and see which answer matches that. (That's what I did in order to verify my understanding of what the radical expressions were.)
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?
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
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.
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 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
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
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?
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
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.
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.
Are triangles △ABCtriangle, A, B, C and △DEFtriangle, D, E, F similar? To answer, try to map △ABCtriangle, A, B, C onto △DEFtriangle, D, E, F using the interactive widget.
Answer:
From three condition the it is proved that Δ ABC and Δ DEF are similar Triangles .
Step-by-step explanation:
Given as :
To Proof : Triangle Δ ABC and Triangle Δ DEF are similar
There are three methods for two Triangles to be similar
A ) SAS i.e side angle side
B ) AA i.e angle angle
C ) SSS i.e side side side
Now,
A) If two triangle have a pair of equal corresponding angles and sides are proportional then triangle are similar
So, If in Δ ABC and Δ DEF
∠ B = ∠ E
and , [tex]\dfrac{AB}{DE}[/tex] = [tex]\dfrac{BC}{EF}[/tex]
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e SAS similarity
B ) If two triangles have equal corresponding angles , then triangles are similar .
So, If in Δ ABC and Δ DEF
∠ B = ∠ E and ∠ A = ∠ D
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e AA similarity
C ) If two triangles have three pairs of corresponding sides proportional then triangles are similar .
So, If in Δ ABC and Δ DEF
[tex]\dfrac{AB}{DE}[/tex] = [tex]\dfrac{BC}{EF}[/tex] = [tex]\dfrac{AC}{DF}[/tex]
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e SSS similarity
Hence From three condition the it is proved that Δ ABC and Δ DEF are similar Triangles . answer
Answer: Neither
Step-by-step explanation:
Got it wrong bc of the person it top of me but yea
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.
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
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?
Please show ALL WORK
WILL MARK BRAINLIEST
Which inequality is graphed below?
y ≥ -2|x - 1| + 3
y ≤ -2|x - 1| + 3
y ≤ -2|x + 1| - 3
y ≥ -2|x + 1| + 3
Answer
The answer
it is y ≥ -2|x + 1| + 3
since the -2 or A controls the negative or positive of an absolute value graph its negative so it's down.
| x+1| if it's like that then you must reverse the sign so it is -1
and for the +3 that controls your vertical line meaning up or down. & in this case it went up so its +3
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.
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]
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
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 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.
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.
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?
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
In a recent month, 88% of automobile drivers filled their vehicles with regular gasoline, 2% purchased midgrade gas, and 10% bought premium gas. Given that a driver bought regular gas, 28% paid with a credit card; given that they bought midgrade and premium gas, 34% and 42% respectively, paid with a credit card. Suppose we select a customer at random.
a. Draw a tree diagram to represent this situation.
b. What is the probability that an automobile driver filled with regular gasoline AND paid with a credit card?
c. What is the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card?
d. What’s the probability that the customer paid with a credit card?
Answer:
b) 0.2464
c) 0.0580
d) 0.2952
Step-by-step explanation:
Probability of those that purchased regular gas = 88% = 0.88
2% purchased mid grade gas
10% purchased premium gad
Given that a driver bought regular gas, 28% paid with credit card
Given that a driver bought mid grade gas, 34% paid with credit card
Given that a driver bought premium gas, 42% paid with credit card
Let R represent drivers that bought regular gas
Let M represent drivers that bought mid grade gas
Let P represent drivers that bought premium gas
Let C represent credit card payment
Let NC represent non-credit card payment
Pr(R) = 88% = 0.88
Pr(M) = 2% = 0.02
Pr(P) = 10% = 0.10
Pr(C|R) = 28%= 0.28
Pr(C|M) = 34%= 0.34
Pr(C|P) = 42%= 0.42
Pr(NC|R) = 1 - 0.28= 0.72
Pr(NC|M) = 1 - 0.34 = 0.66
Pr(NC|P) = 1 - 0.42 = 0.58
Using multiplication rule
Pr(AnB) = Pr(A) * Pr(B|A) = Pr(B) * Pr(A|B)
Using conditional probability,
P(B|A) = Pr(AnB) / Pr(A)
Pr(CnR) = Pr(R) * Pr(C|R)
= 0.88*0.28
= 0.2464
Pr(CnM) = Pr(M) * Pr(C|M)
= 0.02*0.34
= 0.0068
Pr(CnP) = Pr(P) * Pr(C|P)
= 0.10*0.42
= 0.0420
b) the probability that an automobile driver filled with regular gasoline AND paid with a credit card =
Pr(CnR)
= 0.2464
c) the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card = Pr(P n NC) = Pr(NC|P) * Pr(P)
= 0.58 * 0.10
= 0.0580
d) The probability of those that paid with credit card is given as
Pr(CnR) + Pr(CnM) + Pr(CnP)
= 0.2464 + 0.0068 + 0.042
= 0.2952
This problem involves calculating different probabilities pertaining to customers' selection of gas type and payment method. These probabilities are found by multiplying corresponding probabilities together for intersecting events, and adding different possibilities together for compound events.
Explanation:The subject of this question is probability, used in Mathematics. Let's solve each part step-by-step:
a. Drawing a tree diagram is a bit tricky in text form, however, it would start with a broad branch representing the initial choice of gas type. This would split into three branches for regular, midgrade, and premium. From each of these, two branches would sprout for the methods of payment: credit card or not credit card. b. The probability that an automobile driver filled with regular gasoline AND paid with a credit card is found by multiplying the probability of each event. So, 0.88 (probability filling with regular gas) * 0.28 (probability of paying with a credit card given that they bought regular gas) = 0.2464 or 24.64%. c. Similarly, the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card is calculated as 0.10 (probability filling with premium gas) * 0.58 (probability of not paying with a credit card given that they bought premium gas) = 0.058 or 5.8%. d. The probability a random customer paid with a credit card can be found by adding up the possibilities for each gas type: (0.88 * 0.28) + (0.02 * 0.34) + (0.10 * 0.42) = 0.2464 + 0.0068 + 0.042 = 0.2952 or 29.52%. Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
ASAP PLZ!!! Select the correct answer. Which equation cannot be solved by factoring? A. x2 + 5x − 4 = 0 B. x2 + 6x + 9 = 0 C. x2 + 3x − 4 = 0 D. x2 − x − 6 = 0
Answer:
Step-by-step explanation:
We have four equations here. Let's actually solve them, using factoring if possible and some other method if factoring is not possible.
A) x^2 + 5x + 4 factors into (x + 1)(x + 4), but x^2 + 5x - 4 does not.
B) x^2 + 6x + 9 factors into (x + 3)^2.
C) x^2 + 3x - 4 factors into (x + 4)(x - 1).
D) x^2 - x - 6 factors into (x - 3)(x + 2)
x^2 + 5x - 4 = 0 can be solved, but not by factoring.
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?
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.
Calvin thinks a certain potato chip maker is putting less product in their personal-sized bags of chips. In the past, these bags contained one ounce of product. Calvin conducted a test of H0:μ=1vs. HA:μ<1. From a random sample of 23 bags of potato chips he calculated a p - value of 0.086 for the sample.
(a) At a 5% level of significance, is there evidence that Calvin is correct? (Type Yes or No):
(b) At a 10% level of significance, is there evidence that he is correct? (Type Yes or No):
Answer:
a) There are no evidence that Calvin is correct.
b) There are evidence that Calvin is correct.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 1 ounce
Sample size, n = 23
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 1\text{ ounce}\\H_A: \mu < 1\text{ ounce}[/tex]
P-value = 0.086
a) Significance level = 5% = 0.05
Since
P-value > Significance level
We fail to reject the null hypothesis and accept it. Thus, the chips bag contain one ounce of product. Thus, there are no evidence that Calvin is correct.
b) Significance level = 10% = 0.10
Since
P-value < Significance level
We reject the null hypothesis and accept the alternate hypothesis. Thus, the chips bag contain less than one ounce of product. Thus, there are evidence that Calvin is correct.
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
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)
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.
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
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
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
A pick-up truck with two passengers weighs about 14100 N. In good driving conditions around a curve, the maximum friction with the road is equal to the truck's weight. What is the minimum safe curve radius that the truck could negotiate at 26.2 m/s?
Answer:
r=68.64 m
Step-by-step explanation:
Given that
Weight ,wt= 14100 N
mass m = 1410 kg ( g = 10 m/s²)
Friction force = Weight
Fr= 14100 N
v= 26.2 m/s
Lets take radius of the curve = r
To balance the truck ,radial force should be equal to the friction force
[tex]\dfrac{mv^2}{r}=Fr[/tex]
mv² = Fr x r
1410 x 26.2² = 14100 x r
r=68.64 m
Therefore radius of the curve will be 68.64 m
Answer - r=68.64 m
The minimum safe curve radius that the truck could negotiate at 26.2 m/s in good driving conditions is approximately 78.94 meters. This relies on the principles of centripetal force and friction, and requires converting the weight of the truck into its mass. The resulting radius ensures that the centripetal force, provided by the friction between the tires and the road, is enough to keep the truck on its path.
Explanation:The subject of this question is related to Centripetal Force and Friction in physics. Centripetal force is the net force on an object moving in a circular path and it points towards the center of the circular path. This force keeps the object moving along this path and is provided by the frictional force between the truck's tires and the road.
In this case, if friction equates to the weight of the truck (14100 N), it will be the centripetal force. The equation for centripetal force is given by:
Fc = mv²/rwhere Fc is the centripetal force, m is the mass of the object, v is the velocity of the object and r is the radius of the circular path. We can arrange this formula to calculate the safe curve radius(r) the truck can negotiate:
r = mv²/FcHowever, in this case, the mass of the truck is given as a force (Weight = 14100 N). So first we need to convert this weight into mass. We can do this by using the formula: Weight = mass (m) × acceleration due to gravity (g). Here, g = 9.8 m/s²:
m = Weight / g = 14100 N / 9.8 m/s² = 1438.78 kgNow we can substitute m = 1438.78 kg, v = 26.2 m/s and Fc = 14100 N into our radius equation to find the minimum safe curve radius for the truck:
r = (1438.78 kg × (26.2 m/s)²) / 14100 N = 78.94 mSo, the minimum safe curve radius that the truck could negotiate at 26.2 m/s in good driving conditions is approximately 78.94 meters.
Learn more about Centripetal Force and Friction here:https://brainly.com/question/32206643
#SPJ11