The cotangent is given by the cosine over the sine.
If the cotangent is positive and the sine is positive, that means the cosine is also positive.
Now, in order to find the value of cos(x), we can use the following property:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (0.4)^2+\cos ^2(x)=1 \\ 0.16+\cos ^2(x)=1 \\ \cos ^2(x)=1-0.16 \\ \cos ^2(x)=0.84 \\ \cos (x)=0.917 \end{gathered}[/tex]A line passes through the point (-2,-7) and has a slope of 4
Answer:
y= 4x +1
Step-by-step explanation:
The equation of a line, in slope-intercept form, is given by y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is 4, m= 4.
Substitute m= 4 into y= mx +c:
y= 4x +c
To find the value of c, substitute a pair of coordinates the line passes through.
When x= -2, y= -7,
-7= 4(-2) +c
-7= -8 +c
c= -7 +8
c= 1
Substitute the value of c into the equation:
Thus, the equation of the line is y= 4x +1.
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Is there one line that passes through the point (3, 5) that is parallel to the lines represented by y = 2x - 4 and y = x - 4Explain.
If two lines are parallel, it means that they have the same slope. The given lines are
y = 2x - 4 and y = x - 4
The slope intercept form of a straight line is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
By comparing both equations with the slope intercept form,
For y = 2x - 4
Slope, m = 2
For y = x - 4
Slope, m = 1
We can see that the slopes are not eaual. Thus, the lines are not parallel.
Also, we can conclude that there is no line that passes through the point (3,5) that is parallel to both lines
There is no line that passes through the point (3,5) that is parallel to both lines.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
If two lines are parallel, it means that they have the same slope. The given lines are
y = 2x - 4 and y = x - 4
By comparing both equations with the slope-intercept form,
For y = 2x - 4
Slope, m = 2
For y = x - 4
Slope, m = 1
We can see that the slopes are not equal. Thus, the lines are not parallel.
Also, we can conclude that there is no line that passes through the point (3,5) that is parallel to both lines.
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Check off all of the equations that would give infinitely many solution
All of the equations that would give infinitely many solutions are given as follows:
[tex]\begin{gathered} 1)\text{ 3x + 12 = 3x + 12} \\ 2)\text{ 2\lparen3x - 4\rparen = 6x - 8} \end{gathered}[/tex]Thus the correct answer is option 3 and option 5.
product of the equationa^4•a^6
Okay, here we have this:
Considering the provided operation, we are going to perform it, so we obtain the following:
Let us remember that when two terms with the same base are multiplied, then the base is preserved and the exponents are added, in this case we have:
[tex]\begin{gathered} a^4\cdot a^6 \\ =a^{(4+6)} \\ =a^{10} \end{gathered}[/tex]Finally we obtain that the operation is equal to a^10.
On the graph below, what is the length of side AB? B ...
The distance between two points in the plane is:
[tex]d(P,Q)=\sqrt[]{(x_2-x_1)^2+(y_2}-y_1)^2[/tex]The points A and B have coordinates A(5,3) and B(5,6). Then the distance between them is:
[tex]\begin{gathered} d(A,B)=\sqrt[]{(5-5)^2+(6-3)^2} \\ =\sqrt[]{(3)^2} \\ =\sqrt[]{9} \\ =3 \end{gathered}[/tex]Therefore, the length of the side AB is 3 units.
Julie can run 3 laps in 9 minutes. At this rate, how many laps can she run in 24 minutes?
Answer:
Julie can run 12 laps
Step-by-step explanation:
9 min = 3 laps
9 x 2 = 18 = 6 laps
9 cant fit into 24 again
24 - 18 = 6
6 + 6 = 12 laps
3. At which of the following angles is the tangent function undefined?(1) 0 =180°(3) 0 = 45°(4) 0 =-360°(2) 0=-90°
The correct answer is angle 90 degrees.
Explanation:
The tangent of angle 90 degrees is undefined.
[tex]undefined[/tex]12)If the legs of a right triangle are 6 cm and 5 cm, find the area of the triangle.A)11 cm2B)15 cm2C)30 cm2D)60 cm2
The expression below is scientificnotation for what number? 4.58 • 10^-2
We are given the number in scientific notation:
[tex]4.58\times10^{-2}[/tex]To convert it to decimal format, we need to move the decimal point two spaces to the left.
Since we don't have enough digits before the decimal point, we add two zeros before the 4:
[tex]004.58\times10^{-2}[/tex]Now we move the point as required:
[tex]004.58\times10^{-2}=0.0458[/tex]The required number is 0.0458
You live 3 miles from collage and 2 miles from the business where you work.Let d represent the distance between your work and the collage write an inequality involving d.
The inequality involving the distance is 3 > d > 2.
What is an inequality?An inequality is simply used to illustrate the expressions that aren't equal. This can be illustrated through the use of greater than, less than, etc.
When you live live 3 miles from collage and 2 miles from the business where you work. This will be expressed thus
Let d represent the distance between your work and the collage and the inequality is 3 > d > 2.
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what is the minimum surface area that such a box can have
Given a rectangular box with an open top and square base, the dimensions of the box are:
[tex]a\times a\times b[/tex]The volume can be calculated as:
[tex]V=a\cdot a\cdot b=a^2\cdot b[/tex]The area of the sides is:
[tex]A_L=a\cdot b[/tex]The area of the base:
[tex]A_B=a^2[/tex]There are 4 lateral sides and 1 base (the top is open), so the total surface area is:
[tex]A_{\text{total}}=4\cdot A_L+A_B=4\cdot a\cdot b+a^2[/tex]We have a fixed volume of 2048 in³, then:
[tex]\begin{gathered} a^2\cdot b=2048 \\ b=\frac{2048}{a^2} \end{gathered}[/tex]Using this result on A_total:
[tex]A_{\text{total}}=4\cdot a\cdot\frac{2048}{a^2}+a^2=\frac{8192}{a}+a^2[/tex]To find the minimum surface area, we take the derivative:
[tex]\begin{gathered} \frac{dA_{total}}{da}=-\frac{8192}{a^2}+2a=0 \\ a^3=4096 \\ a=16 \end{gathered}[/tex]Now, we calculate the minimum total area using a:
[tex]A_{\text{total}}=\frac{8192}{16}+16^2=768in^2[/tex]Find the surface area of the prism. 8 cm. 3 cm. 3 cm. 3 cm.) - 3 cm. Surface Area cm2
Surface area of a rectangular prism:
[tex]\begin{gathered} SA=2(l\cdot h+w\cdot h+l\cdot w) \\ l=\text{lenght} \\ w=\text{width} \\ h=\text{height} \end{gathered}[/tex]For the given prims:
l=8cm
w=3cm
h=3cm
[tex]\begin{gathered} SA=2(8\operatorname{cm}\cdot3\operatorname{cm}+3\operatorname{cm}\cdot3\operatorname{cm}+8\operatorname{cm}\cdot3\operatorname{cm}) \\ SA=2(24cm^2+9cm^2+24cm^2) \\ SA=2(57cm^2) \\ SA=114cm^2 \end{gathered}[/tex]Then, the surface area is 114 square centimetersLogan wants to know how many skateboards have defective parts. He inspects 20000 skateboards and keeps track of the number of defects per board. Use his probability distribution table to find the expected value for defects on a skateboard.(Rest of the problem needs to be sent as an image)a. 1/25b. 4/25c. 3/25d. 2/25
ANSWER:
2nd option: 4/25
STEP-BY-STEP EXPLANATION:
To find the expected value of the distribution, we multiply each outcome by its probability and the sum of this would be the expected value, like so:
[tex]\begin{gathered} E(x)=0\cdot\frac{9}{10}+1\cdot\frac{1}{20}+2\cdot\frac{1}{25}+3\cdot\frac{1}{100} \\ \\ E(x)=0+\frac{1}{20}+\frac{2}{25}+\frac{3}{100} \\ \\ E(x)=\frac{5}{100}+\frac{8}{100}+\frac{3}{100}=\frac{16}{100}=\frac{4}{25} \end{gathered}[/tex]Therefore, the correct answer is the 2nd option: 4/25
I need to know the initial size of the culture Find the doubling period Find the population after 65 min When will the population reach 10000
Given:
The population was 100 after 10 mins.
The population was 1500 after 30 mins.
To fill the blanks:
Explanation:
According to the problem, we write,
[tex]\begin{gathered} P=P_0e^{kt} \\ 100=P_0e^{10k}.........(1) \\ 1500=P_0e^{30k}............(2) \end{gathered}[/tex]Dividing equation (2) by equation (1), we get
[tex]\begin{gathered} \frac{1500}{100}=\frac{P_0e^{30k}}{P_0e^{10k}} \\ 15=e^{20k} \\ ln15=20k \\ 2.708=20k \\ k=\frac{2.708}{20} \\ k=0.1354 \end{gathered}[/tex]So, the equation becomes,
[tex]P=P_0e^{0.1354t}....................(3)[/tex]a) To find: The initial population
When P = 100 and t = 10, then the initial population would be,
[tex]\begin{gathered} 100=P_0e^{0.1354(10)} \\ 100=P_0e^{1.354} \\ 100=P_0(3.873) \\ P_0=\frac{100}{3.873} \\ P_0\approx25.82 \end{gathered}[/tex]Therefore, the initial population is 25.82.
b) To find: The doubling time
Using the formula,
[tex]\begin{gathered} t=\frac{\ln2}{k} \\ t=\frac{\ln2}{0.1354} \\ t=5.1192 \\ t\approx5.12mins \end{gathered}[/tex]The doubling time is 5.12 mins.
c) To find: The population after 65 mins
Substituting t = 65 and the initial population is 25.82 in equation (3) we get,
[tex]\begin{gathered} P=25.82e^{0.1354(65)} \\ P\approx171467.56 \end{gathered}[/tex]Therefore, the population after 65 mins is 171467.56.
d) To find: The time taken for the population to reach 10000
Substituting P = 10000 and the initial population is25.82 in equation (3) we get,
[tex]\begin{gathered} 10000=25.82e^{0.1354t} \\ e^{0.1354t}=\frac{10000}{25.82} \\ e^{0.1354t}=387.297 \\ 0.1354t=\ln(387.297) \\ 0.1354t=5.959 \\ t=\frac{5.959}{0.1354} \\ t\approx44.01 \end{gathered}[/tex]Therefore, the time taken for the population to reach 10000 is 44.01 mins.
Final answer:
• The initial population is 25.82.
,• The doubling time is 5.12 mins.
,• The population after 65 mins is 171467.56.
,• The time taken for the population to reach 10000 is 44.01 mins.
Part 1: Factorial! 3. What are the pros and cons to using the factorial function on your calculator in terms of understanding and/or thecalculation itself?
Explanation
We are required to determine the pros and cons of using the factorial function on the calculator.
Hence, the answers are:
- Pros
• It makes calculation easier.
,• It makes calculations to be done in an efficient manner.
,• It helps students to solve complicated questions seamlessly.
- Cons
• It cannot help with large numbers as the calculator has limited space for answer preview.
,• It does not help to understand better how the calculation is done.
Find the degree of the polynomial.2x6 − 4x2 + 3x − 1
Given:
There are given the equation:
[tex]f(x)=2x^6-4x^2+3x-1[/tex]Explanation:
According to the question, we need to find the degree.
So,
From the concept of degrees:
The degree is the largest exponent of the variable.
Final answer:
Hence, the value of the degree is 6.
You buy items costing $3000 and finance the cost with a simple interest fixed installment loan at 5% simple interest per year. The finance charge is $600.a) How many years will you be paying?b) What is your monthly payment?
Given:
The principal amount is P = $3000.
The rate of interest is r = 5% = 0.05.
The interest rate is A = $600.
The objective is,
a) To find the number of years.
b) To find the monthly payment.
Explanation:
a)
The general formula for simple interest is,
[tex]A=P\times n\times r\text{ . . . . . .(1)}[/tex]To find n:
On plugging the given values in equation (1),
[tex]\begin{gathered} 600=3000\times n\times0.05 \\ n=\frac{600}{3000\times0.05} \\ n=4 \end{gathered}[/tex]b)
Since, the total amount of the item can be calculated as,
[tex]T=A+P\text{ .. . . . (2)}[/tex]On plugging the obtained values in equation (2),
[tex]\begin{gathered} T=600+3000 \\ T=3600 \end{gathered}[/tex]To find monthly payment:
Now, the monthly payment can be calculated as,
[tex]m=\frac{T}{n\times12}\text{ . . . . .(3)}[/tex]Here, m represents the monthly payment, the product of 12 is used to convert the number of years into the number of months.
On plugging the obtained values in equation (3),
[tex]\begin{gathered} m=\frac{3600}{4\times12} \\ m=75 \end{gathered}[/tex]Hence,
a) The number of years is 4 years.
b) The monthly payment is $75.
I can't find the coordinates of midpoint D , must simplify
We have to find the midpoint coordinates (D) of segment AB.
We can calculate the coordinates of the midpoint as:
[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2}=\frac{-6x+(-2x)}{2}=\frac{-8x}{2}=-4x \\ \\ y_M=\frac{y_A+y_B}{2}=\frac{4y+(-4y)}{2}=\frac{4y-4y}{2}=0 \end{gathered}[/tex]Answer: D = (-4x, 0)
43% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor theuse of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight(a) P(3) =(Round to three decimal places as needed.)
EXPLANATION:
According to the established pattern that only 43 out of 100 adults favor the use of drones, now we must find out from the only twelve adults surveyed how much corresponds to 43 percent.
The first thing we must do is make the relation 12 equals 100, then 43 percent how much?
[tex]\begin{gathered} 12\rightarrow100 \\ x\leftarrow43 \\ x=\frac{12\times43}{100} \\ \textcolor{#FF7968}{x=5.16}\text{\textcolor{#FF7968}{ ; }} \\ \text{the answer is }\text{\textcolor{#FF7968}{5.16 }}\textcolor{#FF7968}{that}\text{\textcolor{#FF7968}{ is less than eight }}\text{; } \end{gathered}[/tex]need help with part a with a summary and all work shown to help me understand better
ANSWER:
[tex]\left(16u^{\frac{1}{3}}\right)^{\frac{3}{4}}=8\sqrt[4]{u}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]\left(16u^{\frac{1}{3}}\right)^{\frac{3}{4}}[/tex]When you raise an exponent to another exponent, multiply therefore:
The area of a parallelogram is 22, and the lengths of its sides are 9.2 and 2.6. Determine, to the nearest tenth of a degree, the measure of the obtuse angle of the parallelogram.
The measure of obtuse angle of the parallelogram is 113.12° .
The Area of Parallelogram with sides a and b and the angle between them as x° is given by the formula .
Area of Parallelogram = a×b×Sin(x)°.
In the question ,
it is given that
the area of the parallelogram is = 22
length of one side of parallelogram = 9.2
length of other side of parallelogram = 2.6 .
Substituting the values in the Area formula , we get
22 = (9.2)×(2.6)×Sin(x)°
22 = 23.92×Sin(x)°
Sin(x)° = 22/23.92
Sin(x)° = 0.9197
x = 66.88°
Since this is an acute angle , we will subtract it from 180° to find the obtuse angle .
So , obtuse angle = 180-66.88 = 113.12°
Therefore , the measure of obtuse angle of the parallelogram is 113.12° .
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what is the approximation of 3√200
Given the expression:
[tex]\text{ }\sqrt[3]{200}[/tex]Let's simplify the expression and convert its decimal form to get its approximation.
We get,
[tex]\text{ }\sqrt[3]{200}\text{ = }\sqrt[3]{8\text{ x 25}}[/tex][tex]\text{ =2 }\sqrt[3]{25}[/tex]In decimal form:
[tex]\text{ 2 }\sqrt[3]{25}\text{ = 2 x 2.92401773821 = 5.84803547643 }\approx\text{ 5.8}[/tex]Therefore, the approximate equivalent of 3√200 is 5.8.
Hi, I need help on this. the sentence says Write the Numbers that represent each Expression
H = 1, P =2, R = 3 B = -1, C = -2, A = -3, Q = -5
Explanation:
For the first number line:
From the tick mark to the tick mark with 4, there are 4 tick marks
Distance from 0 to 4 = 4 - 0 = 4
Each tick mark = 4/4 tick marks
Each tick mark = 1
This means each tick mark increases by 1 to the right after 0 and decreases by one to the left before zero.
H, P and R are after 0
H = 0 + 1 = 1
P = 1 + 1 = 2
R = 2 + 1 = 3
B, C, A and Q are all before 0
B = 0 - 1 = -1
C = -1 - 1 = -2
A = -2 - 1 = -3
Q = -4 - 1 = -5
For the 2nd number line:
from 0 to 100, there 5 tick marks
Distance from 0 to 100 = 100 - 0 = 100
Each tick mark = 100/5 tick marks
Each tick mark = 20
This means each tick mark after zero increases by 20 to the right and decreases to the before 0 by 20.
A, L and M are after zero
Number before A is 20, increasing the number by 20
A = 20 + 20 = 40
L = 40 + 20 = 60
M = 60 + 20 = 80
J, P, T, V are before zero
Number before J = 0, decreasing by 20
J = 0 - 20 = -20
P = -20 - 20 = -40
T = -40 - 20 = -60
V = -60 - 20 = -80
Find the slope of the line that passes through (4,2) and (2,1) which set up in the formula is correct? Select all that apply.
The formula for calculating the slope of a line passing through the points (x1, y1) and (x2, y2) is expressed as:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}\text{ }or\text{ }\frac{y_1-y_2}{x_1-x_2}[/tex]Given the coordinate points (4,2) and (2,1), the possible set up formulas are:
[tex]\begin{gathered} x_1=4 \\ y_1=2 \\ x_2=2 \\ y_2=1 \end{gathered}[/tex][tex]\begin{gathered} slope=\frac{1-2}{2-4} \\ slope=\frac{2-1}{4-2} \end{gathered}[/tex]This are the slopes of the line formula
For the data shown in the scatter plot, which is the best estimate of r?The answer choices are .94 .-45 .-94 .45
Pearson's correlation coefficient, r, measures the linear relationship between two variables. The correlation coefficient can take a range of values from +1 to -1.
• A value of 0 indicates that there is no association between the two variables.
,• A value ,greater than 0, indicates a ,positive association., That is, as the value of one variable increases, so does the value of the other.
,• A value ,less than 0, indicates a ,negative association,; that is, as the value of one variable increases, the value of the other decreases.
Graphically,
In this case, you can see that as the value of a variable x increases, the value of the variable y other decreases. Then, the correlation coefficient of these two variables is negative.
Also, you can see that the values of the variables do not completely fit a line but are very close to one.
Therefore, the best estimate of r is -.94.
I am not good at word problems this is a project so need extra help
M = $6,400
C = $3,600
CD interest = $180
Money market interest = $256
Here, we want to start by completing the chart
We proceed as follows;
Let us take it line by line
a) The rate for the CD account is 5%
Writing this as decimal is 5/100 = 0.05
b) The time for the CD account is 1 year
Next line;
a) Principal invested in money market is $M
b) The time is also 1 year
Next line;
The interest earned on investment is the sum of both
That will be;
0.05c + 0.04m
So, let us write the equations to solve simultaneously;
[tex]\begin{gathered} c\text{ + m = 10,000} \\ 0.05c\text{ + 0.04m = 436} \\ \text{second equation multiplied through by 100;} \\ 5c\text{ + 4m = 43,600} \\ \text{From i;} \\ c\text{ = 10,000-m} \\ \text{put this into the multiplied equation} \\ 5(10,000-m)\text{ + 4m = 43600} \\ 50,000\text{ - 5m + 4m = 43600} \\ m\text{ = 50,000-43600} \\ m\text{ = 6400} \\ c\text{ = 10,000-6400} \\ c\text{ = 3,600} \end{gathered}[/tex]So, let us fill the last parts;
a) $3,600 + $6,400 = Total $10,000 invested
b) CD interest is 0.05 c = 0.05 (3,600) = $180
Money market interest = 0.04M = 0.04 (6,400) =$256
$180 + $256 = $436 total interest
In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of dfeet below the surface, is given by the following equation:4dP = 14 +11If a scientific team uses special equipment to measures the pressure under water and finds it to be 318pounds per square foot, at what depth is the team making their measurements?Answer: The team is measuring atfeet below the surface.
1) Given this equation for Pressure, we need to plug into p the pressure of 318 lbs/ft² to get the depth according to the model described by this equation.
2) So, we can write out:
[tex]\begin{gathered} P=14+\frac{4d}{11} \\ 318=14+\frac{4d}{11} \\ 11\times318=11\times(14+\frac{4d}{11}) \\ 3498=154+4d \\ 3498-154=4d \\ 3344=4d \\ 4d=3344 \\ \frac{4d}{4}=\frac{3344}{4} \\ d=836ft \end{gathered}[/tex]Note that we multiplied both sides by 11 to get rid of the fraction.
Thus this is the depth below the surface that generates such pressure
Y.11 Multi-step problems with customary uni You have prizes to reveal! Go to your Tracy decides to take her puppy for a walk. After 90 feet, they stop to smell some roses. Then, Tracy runs into a friend 200 yards up the road. They start talking, and soon it's time for Tracy to go home. So, she and her puppy head back to her house. How many feet long was Tracy's walk? feet Submit
Given:
The distance travelled by Tracy till she stopped to smell roses, x=90 feet.
The distance from roses to the friend, y=200 yards.
The distance travelled by Tracy one side,
[tex]\begin{gathered} D=x+y \\ =90\text{ f}eet+200\times3feet \\ =90\text{ f}eet+600\text{ f}eet \\ =690\text{ f}eet \end{gathered}[/tex](1 yard=3 feet).
Now, the total distance travelled byTracy both sides is,
[tex]\begin{gathered} d=2D \\ =2\times690\text{ f}eet \\ =1380\text{ f}eet \end{gathered}[/tex]Therefore, Tracy walk was 1380 feet long.
which function is best represented by this graphA) f(x) = x² - 3x + 8B) f(x) = x² - 3x - 8C) f(x) = x² + 6x + 8D) f(x) = x² + 6x - 8
Solution:
Given the graph;
The axis of symmetry and vertex of the graph are;
[tex]\begin{gathered} x=-3 \\ (-3,-1) \end{gathered}[/tex]Also, the x-intercepts are;
[tex](-4,0),(-2,0)[/tex]And the y-intercep is;
[tex](0,8)[/tex]Thus, the function that best represents the graph is;
[tex]f(x)=x^2+6x+8[/tex]CORRECT OPTION: C
Simplify [tex]{({4e}^{ - 8x})}^{0.5} [/tex]with no negative exponents. thanks!
Explanation
Given the following expression
[tex]\begin{gathered} \text{Simplify (4 }e^{-8x})^{\frac{1}{2}} \\ \text{This expression can be written as} \\ (4\cdot\text{ }e^{-8x})^{\frac{1}{2}} \\ \text{Splitting the expression, we can have the below expression} \\ (4)^{\frac{1}{2}}\cdot(^{}e^{-8x})^{\frac{1}{2}} \\ \text{According to the law of indicies} \\ x^{\frac{1}{2}}\text{ = }\sqrt[]{x} \\ \text{Hence, we have the following expression} \\ \sqrt[]{4\text{ }}\cdot\text{ (}e^{-8x\cdot\text{ }\frac{1}{2}}) \\ 2\cdot\text{ }e^{-4x} \\ 2e^{-4x} \\ \text{Therefore, the simplified form is 2}e^{-4x} \\ \frac{2}{e^{4x}} \end{gathered}[/tex]