ANSWER
[tex]-10s^2-2s-5[/tex]EXPLANATION
Given
[tex]\mleft(-12s^2+10s-3\mright)+\mleft(2s^2-12s-2\mright)[/tex]removing the brackets, we have;
[tex]-12s^2+10s-3+2s^2-12s-2[/tex]collecting like terms, we have
[tex]\begin{gathered} -12s^2+2s^2+10s-12s-3-2 \\ \end{gathered}[/tex]adding similar terms, we have;
[tex]-10s^2-2s-5[/tex]The solution is
[tex]-10s^2-2s-5[/tex]Need help determining if h. F(x)= 3^x is even, odd or neither
Recall that:
1) f(x) is an even function if:
[tex]f(-x)=f\mleft(x\mright).[/tex]2) f(x) is an odd function if:
[tex]f(-x)=-f(x).[/tex]Now, notice that:
[tex]\begin{gathered} f(-x)=3^{-x}\ne3^x=f(x), \\ f(-x)=3^{-x}\ne-3^x=-f(x). \end{gathered}[/tex]Therefore f(x)=3^x is neither an even function nor an odd function.
Answer: Neither an even function nor an odd function.
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 12.5 ft by 13.5 ft by 13 ft. The container is entirely full. If, on average, its contents weigh 0.18 pounds per cubic foot, and, on average, the contents are worth $7.18 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
The volume of a right rectangular prism is given by
[tex]V=\text{height}\times length\times width[/tex]From the given information, we know that
[tex]\begin{gathered} \text{ height=13.5 ft} \\ \text{ length=13 ft} \\ \text{width = 12.5 ft} \end{gathered}[/tex]So, the volume is given by
[tex]V=13.5\times13\times12.5ft^3[/tex]which gives
[tex]V=2193.75ft^3[/tex]Now, since the content weigh 0.18 pound per cubic foot and worth $7.18 per pound, the value of the container is given by,
[tex]\text{ Value=}2193.75\times0.18\times7.18[/tex]Therefore, by rounding to the nearest cent, the answer is:
[tex]\text{Value}=\text{ \$2835.20}[/tex]In circle D with the measure of minor aré CE = 162 degrees, find m of CFE
SOLUTION
Step 1: Make a more comprehensive sketch of the question.
The measure of CFE is 81 degrees.
An object moves at a rate of 9,400 inches each week. How many feet does it move per minute?
To answer this question, we need to transform each of the values into the corresponding other units:
• Inches ---> Feet
,• Week ---> minutes
And we also have here a ratio:
• Inches/week ---> Feet/minute.
Then we can proceed as follows:
Inches to FeetWe know that the conversion between inches and feet is:
[tex]1ft=12in[/tex]Then
[tex]1in=\frac{1}{12}ft[/tex]If we have 9,400 inches, then:
[tex]9400in=\frac{9400}{12}ft\Rightarrow9400in=783ft+\frac{1}{3}ft=783.33333333ft[/tex]Week to minutesWe know that:
[tex]1\text{hour}=60\min [/tex]In one day we have 24 hours, then:
[tex]24\text{hours}=24\cdot60\min =1440\min [/tex]Then we have 1440 minutes in a day. A week has 7 days. Therefore, we will have:
[tex]1440\frac{\min}{day}\cdot7days=10080\min [/tex]Therefore, we have that there are 10,080 minutes in one week.
Now, to find the ratio of feet per minute, we need to divide:
[tex]\frac{783\frac{1}{3}ft}{10080\min}=0.0777116402116\frac{ft}{\min }[/tex]In summary, we can say that the object moves:
[tex]0.0777116402116\frac{ft}{\min }[/tex]into the
convert 85 degrees to radians
To convert 85 degrees to radians, consider:
[tex]\pi=180^o^{}[/tex]Let
[tex]x=85^o[/tex]Then
[tex]\begin{gathered} 180x=85\pi \\ x=\frac{85\pi}{180} \\ \\ =\frac{17}{36}\pi \end{gathered}[/tex]David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
Given,
The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair.
Explain what each part of the expression represents in the context of the problem.
Now, According to the question:
Given the following algebraic expression:
0.07r + (r – 20)
In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.
What each part of the expression represents in the context of the problem include the following:
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
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distance between (11,-5) and (0,1)
Here,point can be written as:
[tex]\begin{gathered} x1=11, \\ y1=-5 \\ x2=0 \\ y2=1 \end{gathered}[/tex]The formula for the distance between the points as follows;
[tex]\begin{gathered} d=\sqrt{(x1-x2)^2+(y1-y2)^2} \\ d=\sqrt{(11-0)^2+(-5-1)^2} \\ d=\sqrt{121+36} \\ d=\sqrt{157} \\ d=12.53 \end{gathered}[/tex]Thus, the distance between the point is 12.53.
Solve for w.4w²-24w=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution".W =0U08Nosolution
ANSWER
[tex]\begin{equation*} w=0,\text{ }w=6 \end{equation*}[/tex]EXPLANATION
We want to solve the given equation for w:
[tex]4w^2-24w=0[/tex]To do this, we have to factorize the equation and simplify it.
Let us do that now:
[tex]\begin{gathered} (4w*w)-(4w*6)=0 \\ \\ 4w(w-6)=0 \\ \\ \Rightarrow4w=0\text{ and }w-6=0 \\ \\ \Rightarrow w=0,\text{ }w=6 \end{gathered}[/tex]That is the answer.
3(4x+1)^2-5=25 using square root property
Answer:
[tex]x=\frac{-1+\sqrt{10}}{4}\text{ or }x=\frac{-1-\sqrt{10}}{4}[/tex]Explanation:
Given the equation:
[tex]3\left(4x+1\right)^2-5=25[/tex]To solve an equation using the square root property, begin by isolating the term that contains the square.
[tex]\begin{gathered} 3(4x+1)^{2}-5=25 \\ \text{ Add 5 to both sides of the equation} \\ 3(4x+1)^2-5+5=25+5 \\ 3(4x+1)^2=30 \\ \text{ Divide both sides by 3} \\ \frac{3(4x+1)^2}{3}=\frac{30}{3} \\ (4x+1)^2=10 \end{gathered}[/tex]After isolating the variable that contains the square, take the square root of both sides and solve for the variable.
[tex]\begin{gathered} \sqrt{(4x+1)^2}=\pm\sqrt{10} \\ 4x+1=\pm\sqrt{10} \\ \text{ Subtract 1 from both sides} \\ 4x=-1\pm\sqrt{10} \\ \text{ Divide both sides by 4} \\ \frac{4x}{4}=\frac{-1\pm\sqrt{10}}{4} \\ x=\frac{-1\pm\sqrt{10}}{4} \end{gathered}[/tex]Therefore, the solutions to the equation are:
[tex]x=\frac{-1+\sqrt{10}}{4}\text{ or }x=\frac{-1-\sqrt{10}}{4}[/tex]
Using solving systems using elimination addition method3x-7y=5-3x+7y=-9help
In the elimination method, we need to eliminate one of the variables using addition or subtraction.
In this case, if we add both equations, we have that:
Since we obtained a FALSE result, we can say that this system of linear equations has NO SOLUTIONS.
In summary, using the elimination method, we add both equations. The result for that was a false r
simplify the following expression:7^-6 × 7^3
To solve this question, we will apply the knowledge of exponents and indices
The values have the same bases (7) but different powers and they are separated by a multiplication sign.
So we can use the law:
[tex]a^{x\text{ }}\text{ x a}^{y\text{ }}=a^{x\text{ + y}}[/tex]so that
[tex]7^{-6}\text{ x 7}^3=7^{-6\text{ + 3}}[/tex]on simplifying will give
[tex]7^{-3}[/tex]=>
[tex]7^{-3}\text{ =}\frac{1}{7^3}[/tex]One thousand Charity raffle tickets are sold for $1 each. Winning tickets will be drawn in order,1st,2nd,3rd. First prize is $500. Second prize is $300. Third prize is $150. Tickets are replaced after each drawing so the probability of being draw for each prize is 1/1000. What is the expected value? I am stuck on this question and need help
Answer:
-$0.05
Explanation:
The expected value can be calculated as the sum of each possible prize multiplied by its probability. You will buy a ticket for $1 and there is a probability of 1/1000 to win the $500, a probability of 1/1000 to win $300, and a probability of 1/1000 to win $150, then the expected alue is
[tex]\begin{gathered} E=-1+500(\frac{1}{1000})+300(\frac{1}{1000})+150(\frac{1}{1000}) \\ E=-1+0.5+0.3+0.15 \\ E=-0.05 \end{gathered}[/tex]Therefore, the expected value is -$0.05.
Find the x- and y-intercepts of the graph of the equation.5x + 3y = 15x−intercept (x, y) = ( ) y−intercept (x, y) = ( )
Consider that the intercept form of equation of a line whose x-intercept is (a,0) and y-intercept is (0,b), is given by,
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]The equation of the line is given as,
[tex]5x+3y=15[/tex]Convert this equation into intercept form,
[tex]\begin{gathered} \frac{5x}{15}+\frac{3y}{15}=1 \\ \frac{x}{3}+\frac{y}{5}=1 \end{gathered}[/tex]Comparing with the standard equation,
[tex]\begin{gathered} a=3 \\ b=5 \end{gathered}[/tex]Thus, the x-intercept and y-intercept of the equation, respectively, are,
[tex](3,5)\text{ and }(0,5)[/tex]Solve the following expression when
r = 22
r
11+3+r
11 +3 + r
11+3 = 14
So 14 + 22 is 36
Ans:36
Hope this helps!
A pendulum swings through an angle of 14° each second. If the pendulum is 14 cm in length and the complete swing from right to left last two seconds what area is covered by each complete swing?
Answer;
[tex]\text{Area = 47.90 cm}^2[/tex]Explanation;
Firstly, we need a diagrammatic representation to get what is described in the question.
We have this as follows;
Now, from what we have here, the total angle swept by the pendulum moving from left to right is 28 degrees
To get the area, we simply need to find the area of the sector formed by the by pendulum
Mathematically, we have the area of a sector calculated as follows;
[tex]A\text{ = }\frac{\theta}{360}\times\pi\times R^2[/tex]theta is the angle made by the pendulum in one complete swing which is 28 degrees
pi is 22/7
R is the length of the pendulum which is 14 cm
Substituting these values in the formula above, we have it that;
[tex]\begin{gathered} A=\frac{28}{360}\times\frac{22}{7}\times14^2 \\ \\ A=47.90cm^2 \end{gathered}[/tex]represent the following expressions as a power of the number a (a≠0):
(a^-1*a^-2)^-2
By using some exponent properties, we will see that the expression can be written as:
a^6
How to simplify the expression?
Here we need to use some exponent properties, these are:
(x^n)^m = x^(n*m)x^(-n) = (1/x)^nx^n*x^m = x^(n + m)Here we have the expression:
(a^(-1)*a^(-2))^(-2)
Using the third property we can write:
(a^(-1)*a^(-2))^(-2) = (a^(-1 - 2))^(-2) = (a^(-3))^(-2)
Now we use the first property:
(a^(-3))^(-2) = a^(-3*-2) = a^6
That is the expression simplified.
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The difference between the graph of a radical function and the graph of a rational function
The difference between the graph of a radical function and that of a rational function is:
A radical graph is drawn from a function that contains a root, it could be a square root, cube root, etc. Whenever you are graphing a radical function, we first need to consider the domain. Because of the square root sign, the domain and range are always restricted.
But a rational graph is drawn from the ratio of two polynomial functions where the function in the denominator is not equal to zero. A rational graph is characterized by asymptotes.
The major difference would be that a radical graph has a restricted domain due to the root, and usually without an asymptote, while a polynomial graph has a restricted domain and sometimes range which forms the asymptote (vertical, horizontal asymptote).
Jackie planted a tomato plant that was 4 inches tall. The plant grew by 150% of its height after 3 weeks. How tall was the plant after the 3 weeks?
1) Problems like these, we can solve by writing an equation.
2)Since that tomato plant grew 150% after three weeks we can write the following
[tex]\begin{gathered} 4\cdot(1+1.5)= \\ 4(2.5)=10 \\ \end{gathered}[/tex]Note that in the parentheses we have the factor of growth. Since it's 150% we can add to 1 and write 1 +1.5=2.5
3) Thus, the answer is:
[tex]10\:inches[/tex]simply
i^3+i^20
show work
==================================================
Explanation:
Recall that
i = sqrt(-1)
Squaring both sides gets us
i^2 = -1
Now let's multiply both sides by i
i*i^2 = i*(-1)
i^3 = -i
Repeat the last step
i^3 = -i
i*i^3 = i*(-i)
i^4 = -i^2
i^4 = -(-1)
i^4 = 1
----------------------------
Here's a summary so far
i^0 = 1i^1 = ii^2 = -1i^3 = -ii^4 = 1The pattern repeats every 4 items. This means we'll divide the exponent by 4 and look at the remainder.
20/4 = 5 remainder 0
Therefore i^20 = i^0 = 1
Or we can think of it like this
i^20 = (i^4)^5 = 1^5 = 1
----------------------------
This means we can then say
i^3 + i^20 = -i + 1 = 1 - i
The basic wage earned by a truck driver for a 40 - hour week is $560 How can I calculate the hourly rate for overtime, the driver is paid one and a half times the basic hourly?
First, find the hourly rate by dividing the total wage of $560 by the amount of time worked, which is 40 hours:
[tex]\frac{\text{\$}560}{40h}=\text{ \$}14\text{ per hour}[/tex]To find the hourly rate for overtime, multiply the basic hourly rate by 1.5:
[tex](\text{\$}14\text{ per hour})\times1.5=\text{ \$}21\text{ per hour}[/tex]Therefore, the hourly rate for overtime is $21.
NO LINKS!! Please help me with this problem
0.3821, 0.8745
========================================================
Work Shown:
pi/2 = 3.14/2 = 1.57 approximately
The solutions for t must be in the interval 0 ≤ t ≤ 1.57
[tex]3\cos(5t)+3 = 2\\\\3\cos(5t) = 2-3\\\\3\cos(5t) = -1\\\\\cos(5t) = -1/3\\\\5t = \cos^{-1}(-1/3)\\\\5t \approx 1.9106+2\pi n \ \text{ or } \ 5t \approx -1.9106+2\pi n\\\\t \approx \frac{1.9106+2\pi n}{5} \ \text{ or } \ t \approx \frac{-1.9106+2\pi n}{5}\\\\[/tex]
where n is an integer.
Let
[tex]P = \frac{1.9106+2\pi n}{5}\\\\Q = \frac{-1.9106+2\pi n}{5}\\\\[/tex]
Then let's generate a small table of values like so
[tex]\begin{array}{|c|c|c|} \cline{1-3}n & P & Q\\\cline{1-3}-1 & -0.8745 & -1.6388\\\cline{1-3}0 & **0.3821** & -0.3821\\\cline{1-3}1 & 1.6388 & **0.8745**\\\cline{1-3}2 & 2.8954 & 2.1312\\\cline{1-3}\end{array}[/tex]
The terms with surrounding double stars represent items in the interval 0 ≤ t ≤ 1.57
Therefore, we end up with the solutions 0.3821 and 0.8745 both of which are approximate.
You can use a graphing tool like Desmos or GeoGebra to verify the solutions. Be sure to restrict the domain to 0 ≤ t ≤ 1.57
Answer:
[tex]\textsf{c)} \quad 0.3821, \; 0.8745[/tex]
Step-by-step explanation:
Given equation:
[tex]3 \cos (5t)+3=2, \quad \quad 0\leq t\leq \dfrac{\pi}{2}[/tex]
Rearrange the equation to isolate cos(5t):
[tex]\begin{aligned}\implies 3 \cos(5t)+3&=2\\3 \cos(5t)&=-1\\\cos(5t)&=-\dfrac{1}{3}\end{aligned}[/tex]
Take the inverse cosine of both sides:
[tex]\implies 5t=\cos^{-1}\left(-\dfrac{1}{3}\right)[/tex]
[tex]\implies 5t=1.91063..., -1.91063...[/tex]
As the cosine graph repeats every 2π radians, add 2πn to the answers:
[tex]\implies 5t=1.91063...+2\pi n, -1.91063...+2 \pi n[/tex]
Divide both sides by 5:
[tex]\implies t=0.38212...+\dfrac{2}{5}\pi n,\;\; -0.38212...+\dfrac{2}{5} \pi n[/tex]
The given interval is:
[tex]0\leq t\leq \dfrac{\pi}{2}\implies0\leq t\leq 1.57079...[/tex]
Therefore, the solutions to the equation in the given interval are:
[tex]\implies t=0.3821, \; 0.8745[/tex]
which equation represents the function modeled by the graph? (picture of graph below)
Answer:
The parent function of the graph is given below as
[tex]y=\sqrt[3]{x}[/tex]The parent function has undergone transformation
Hence,
Using a graphing calculator, we will have the graph be
Hence,
The final answer is
[tex]\Rightarrow f(x)=\sqrt[3]{4x+2}[/tex]The FIRST OPTION is the right answer
O DESCRIPTIVE STATISTICInterpreting relative frequency-histogramsStudents at a major university in Southern California are complaining about a serious housing crunch. Many of the university's students, they complain, have tocommute too far to school because there is not enough housing near campus. The university officials' response is to perform a study. The study, reported in theschool newspaper, contains the following histogram summarizing the commute distances for a sample of 100 students at the university:Relative frequencyCommute distance (in miles)Based on the histogram, find the proportion of commute distances in the sample that are at least 16 miles. Write your answer as a decimal, and do not roundyour answer
Since the graph gives us the relative frequency we just have to add those who are more or equal to 16; in this case we have to add 0.11 and 0.06, therefore the proportion in this case is 0.17
octavius wants to write the equation of a line perpendicular to y=-4x + 5 that passes through the point (8,-3). Describe the mistake octavius made and write the correct equation of the line.
The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:
[tex]y = \frac{1}{4} x-5[/tex].
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given equation of line is:
y=-4x + 5
Let [tex]m_{1}[/tex] be the slope of given line
Then,
[tex]m_{1}[/tex] = -4
Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line
As we know that product of slopes of two perpendicular lines is -1.
[tex]m_{1}*m_{2} = -1\\- 4*m_{2}=-1\\ m_{2} = \frac{1}{4}[/tex]
The slope intercept form of line is given by
[tex]y = m_{2}x+c[/tex]
[tex]y = \frac{1}{4} x+c[/tex]
to find the value of c, putting (4,-1) in equation
[tex]-3= \frac{1}{4} *8+c\\-3-2 = c\\c = -5[/tex]
Putting the value of c in the equation
[tex]y=\frac{1}{4} x-5[/tex]
Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is [tex]y=\frac{1}{4} x-5[/tex].
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In planning her retirement, Liza deposits some money at 4.5% interest, with twice as much deposited at 5%. Find the amount deposited at each rate if the total annual interest income is $1595.
Let
x ----> amount deposited at 4.5%
y ----> amount deposited at 5%
we have that
y=2x----> equation A
4.5%=0.045
5%=0.05
so
0.045x+0.05y=1,595 ----> equation B
solve the system
substitute equation A in equation B
0.045(x)+0.05(2x)=1,595
solve for x
0.045x+0.10x=1,595
0.145x=1,595
x=11,000
Find y
y=2(11,000)=22,000
The amount deposited at 4.5% was $11,000 and the amount deposited at 5% was $22,000The table below shows distance as it relates to how many seconds have passed.1510time(seconds)distance, y =y = f(x)(meters)30150 300Write a formula to describe the distance as a linear function of time.
please help me thank you
which methods correctly solve for the variable x in the equation 2/5m = 8?
Ok, so the equation is (2/5)m=8
1st option: Divide by 2 on both sides, then multiply by 5 on both sides:
[tex]\begin{gathered} \frac{2}{10}m=4 \\ \frac{10}{10}m=20 \\ m=20 \end{gathered}[/tex]2nd option: Multiply both sides by 5/2
[tex]\begin{gathered} \frac{2}{5}\cdot\frac{5}{2}m=8\cdot\frac{5}{2} \\ m=20 \end{gathered}[/tex]3rd option: First dristibute 2/5 to (m=8), the multiply by 5/2 in both sides
[tex]\begin{gathered} \frac{2}{5}m=8 \\ \frac{5}{2}\cdot\frac{2}{5}m=8\cdot\frac{5}{2} \\ m=20 \end{gathered}[/tex]4th option: Divide both sides by 2/5:
[tex]\begin{gathered} \frac{\frac{2}{5}}{\frac{2}{5}}m=8\cdot\frac{5}{2} \\ m=20 \end{gathered}[/tex]5th option: First, multiply by 5. Then, divide by 2.
[tex]\begin{gathered} 5\cdot\frac{2}{5}m=40 \\ 2m/2=40/2 \\ m=20 \\ \end{gathered}[/tex]All the methods are correct
-Зе - 10 - 4Solve and graph the inequality
The given inequality is expressed as
[tex]\begin{gathered} -\text{ 3e - 10 }\leq-4 \\ \end{gathered}[/tex]We would add 10 to both sides of the inequality. It becomes
[tex]\begin{gathered} -\text{ 3e - 10 + 10 }\leq-\text{ 4 + 10} \\ -\text{ 3e }\leq6 \end{gathered}[/tex]We would divide both sides by - 3. This would cause the inequality symbol to reverse. It becomes
[tex]\begin{gathered} \frac{-3e}{-3}\text{ }\ge\frac{6}{-3} \\ e\text{ }\ge-2 \end{gathered}[/tex]The graph would be
The shaded circle at the position of - 2 indicates that- 2 is inclusive
a large human population of both globally and within individual countries has been a concern since the time of Thomas Malthus. country X is 95% desert. the government of country X is concerned about not having enough arable land (land capable of being used to grow crops) in the country to produce the food needed to feed its population without increasing food imports the demographic for Country X for the year 2020 is provided in the table below. 1. calculate the national population growth rate for a country X 2. using the rule of 70 calculate the doubling time for this population
Firstly, we want to calculate the growth rate of the population
While birth would increase the population, death and migration will decrease the population
So when we subtract the migration rate and the death rate from the birth rate, we can get the population growth rate;
Thus, we have;
[tex]\begin{gathered} \frac{38}{1000}\text{ - (}\frac{24}{1000}\text{ + }\frac{2}{1000}) \\ \\ =\text{ }\frac{38}{1000}\text{ - }\frac{26}{1000} \\ \\ =\text{ }\frac{12}{1000} \end{gathered}[/tex]The national population growth rate for a country X is 12/1000
Secondly, we are to use the rule of 70 to calculate the doubling time for the population
Mathematically;
[tex]\begin{gathered} No\text{ of years to double = }\frac{70}{\text{annual growth rate}} \\ \\ No\text{ of years to double = 70 divided by }\frac{12}{1000} \\ \\ No\text{ of years = 70 }\times\frac{1000}{12}=5833\frac{1}{3}years^{} \\ \\ \frac{1}{3}\text{ years is same as 4 months} \\ \\ So\text{ it will take 5833 years and 4 months for the population to double} \end{gathered}[/tex]