10 ptsQuestion 3Find the measure of each interior angle. Round to the nearest hundredth.4x(6x - 90)(3x + 31)(7x+19)X=(4x)" =(6x - 90)(7x + 19)° =(3x + 31)º =
Answers
Alexandre, this is the solution:
Let's recall that the interior angles of a rhombus add up to 360 degrees.
Upon saying that, we have:
4x + 3x + 31 + 6x - 90 + 7x + 19 = 360
20x - 40 = 360
Adding 40 at both sides:
20x - 40 + 40 = 360 + 40
20x = 400
Dividing by 20 at both sides:
20x/20 = 400/20
x = 20
Now, we can calculate each of the angles and prove they add up to 360 degrees, as follows:
• 4x = 4 * 20 =, 80
,• 3x + 31 = 3 * 20 + 31 = 60 + 31 =, 91
,• 7x + 19 = 7 * 20 + 19 = 140 + 19 = ,159
,• 6x - 90 = 6 * 20 - 90 = 120 - 90 = ,30
80 + 91 + 159 + 30 = 360
Related Questions
I need help question 10 b and c
Answers
Part b.
In this case, we have the following function:
[tex]y=5(2.4)^x[/tex]First, we need to solve for x. Then, by applying natural logarithm to both sides, we have
[tex]\log y=\log (5(2.4^x))[/tex]By the properties of the logarithm, it yields
[tex]\log y=\log 5+x\log 2.4[/tex]By moving log5 to the left hand side, we have
[tex]\begin{gathered} \log y-\log 5=x\log 2.4 \\ \text{which is equivalent to} \\ \log (\frac{y}{5})=x\log 2.4 \end{gathered}[/tex]By moving log2.4 to the left hand side, we obtain
[tex]\begin{gathered} \frac{\log\frac{y}{5}}{\log2.4}=x \\ or\text{ equivalently,} \\ x=\frac{\log\frac{y}{5}}{\log2.4} \end{gathered}[/tex]Therfore, the answer is
[tex]f^{-1}(y)=\frac{\log\frac{y}{5}}{\log2.4}[/tex]Part C.
In this case, the given function is
[tex]y=\log _{10}(\frac{x}{17})[/tex]and we need to solve x. Then, by raising both side to the power 10, we have
[tex]\begin{gathered} 10^y=10^{\log _{10}(\frac{x}{17})} \\ \text{which gives} \\ 10^y=\frac{x}{17} \end{gathered}[/tex]By moving 17 to the left hand side, we get
[tex]\begin{gathered} 17\times10^y=x \\ or\text{ equivalently,} \\ x=17\times10^y \end{gathered}[/tex]Therefore, the answer is
[tex]f^{-1}(y)=17\times10^y[/tex]Use the information given to find the equation of the line using the point-slope formula (y-y_1=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).(0,3) with a slope of 4The point slope form is (y-Answer)=Answer(x-Answer)Converting it to slope intercept form gives us y=Answerx+Answer
Answers
we have
m=4
point (0,3)
y-y1=m(x-x1)
substitute given values
y-3=4(x-0) ----> equation in point slope formConvert to slope-intercept form
y=mx+b
y-3=4x
adds 3 both sides
y=4x+3 ----> equation in slope-intercept form(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) And determine the quadrants of A+B and A-B.
Answers
Given that:
[tex]\cos A=\frac{5}{13}[/tex]Where:
[tex]0And:[tex]\cos B=\frac{3}{5}[/tex]Where:
[tex]0You need to remember that, by definition:[tex]\theta=\cos ^{-1}(\frac{adjacent}{hypotenuse})[/tex]Therefore, applying this formula, you can find the measure of angles A and B:
[tex]A=\cos ^{-1}(\frac{5}{13})\approx67.38\text{\degree}[/tex][tex]B=\cos ^{-1}(\frac{3}{5})\approx53.13\text{\degree}[/tex](a) By definition:
[tex]\sin \mleft(A+B\mright)=sinAcosB+cosAsinB[/tex]Knowing that:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]You can substitute the known values into the equation in order to find the opposite side for angle A:
[tex]\begin{gathered} \sin (67.38\text{\degree)}=\frac{opposite}{13} \\ \\ 13\cdot\sin (67.38\text{\degree)}=opposite \\ \\ opposite\approx12 \end{gathered}[/tex]Now you know that:
[tex]\sin A=\frac{12}{13}[/tex]Using the same reasoning for angle B, you get:
[tex]\begin{gathered} \sin (53.13\text{\degree)}=\frac{opposite}{5} \\ \\ 5\cdot\sin (53.13\text{\degree)}=opposite \\ \\ opposite\approx4 \end{gathered}[/tex]Now you know that:
[tex]\sin B=\frac{4}{5}[/tex]Substitute values into the Trigonometric Identity:
[tex]\begin{gathered} \sin (A+B)=sinAcosB+cosAsinB \\ \\ \sin (A+B)=(\frac{12}{13})(\frac{3}{5})+(\frac{5}{13})(\frac{4}{5}) \end{gathered}[/tex]Simplifying, you get:
[tex]\begin{gathered} \sin (A+B)=\frac{36}{65}+\frac{20}{65} \\ \\ \sin (A+B)=\frac{36+20}{65} \end{gathered}[/tex][tex]\sin (A+B)=\frac{56}{65}[/tex](b) By definition:
[tex]\sin \mleft(A-B\mright)=sinAcosB-cosAsinB[/tex]Knowing all the values, you get:
[tex]\begin{gathered} \sin (A-B)=(\frac{12}{13})(\frac{3}{5})-(\frac{5}{13})(\frac{4}{5}) \\ \\ \sin (A-B)=\frac{36-20}{65} \\ \\ \sin (A-B)=\frac{16}{65} \end{gathered}[/tex](c) By definition:
[tex]\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B}[/tex]By definition:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]Therefore, in this case:
- For angle A:
[tex]\tan A=\frac{12}{5}[/tex]- And for angle B:
[tex]\tan B=\frac{4}{3}[/tex]Therefore, you can substitute values into the formula and simplify:
[tex]\tan (A+B)=\frac{\frac{12}{5}+\frac{4}{3}}{1-(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{1-\frac{48}{15}}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{-\frac{11}{5}}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex](d) By definition:
[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\cdot\tan B}[/tex]Knowing all the values, you can substitute and simplify:
[tex]\tan (A-B)=\frac{\frac{12}{5}-\frac{4}{3}}{1+(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A-B)=\frac{\frac{16}{15}}{\frac{21}{5}}[/tex][tex]\tan (A-B)=\frac{16}{63}[/tex](e) Knowing that:
[tex]\sin (A+B)=\frac{56}{65}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex]Remember the Quadrants:
By definition, in Quadrant II the Sine is positive and the Tangent is negative.
Since in this case, you found that the Sine is positive and the Tangent negative, you can determine that this angle is in the Quadrant II:
[tex]A+B[/tex]What is the seventy-seven is forty-six more than r
Answers
Answer: 77 = 46 + r, r = 31
Step-by-step explanation:
We will write an equation to represent this situation. Then, we will solve for r by isolating the variable.
Seventy-seven is forty-six more than r.
77 is forty-six more than r.
77 = forty-six more than r.
77 = 46 more than r.
77 = 46 + r
77 = 46 + r
(77) - 46 = (46 + r) - 46
31 = r
r = 31
(2i) - (11+2i) complex numbers
Answers
Hope this helps :)
write 2500g in appropriate prefix pls.
Answers
Answer: 2.5kg
Step-by-step explanation:
I am assuming you mean to simplify it. So 2.5kg
1g=1000kg
2500/1000=2.5
0.2x + 0.21x - 0.04 = 8.16Solve for "x".
Answers
Given the folllowing equation:
[tex]0.2x+0.21x-0.04=8.16[/tex]You need to solve for "x" in order to find its value. To do this, you can follow the steps shown below:
1. You can apply the Addition property of equality by adding 0.04 to both sides of the equation:
[tex]\begin{gathered} 0.2x+0.21x-0.04+(0.04)=8.16+(0.04) \\ 0.2x+0.21x=8.2 \end{gathered}[/tex]2. Now you need to add the like terms on the left side of the equation:
[tex]0.41x=8.2[/tex]3. Finally, you can apply the Division property of equality by dividing both sides of the equation by 0.41:
[tex]\begin{gathered} \frac{0.41x}{0.41}=\frac{8.2}{0.41} \\ \\ x=20 \end{gathered}[/tex]The answer is:
[tex]x=20[/tex]what is 0.024 ÷ 0.231
Answers
Answer:
0.10389610389
Step-by-step explanation:
Hi!
I plugged it into a calculator:
0.024 ÷ 0.231 = 0.10389610389
Have a great day! :)
**Determine the x-value at which the-following function touches but does not cross the x-axis:3x^3- 182 + 27x
Answers
Okay, here we have this:
We need to identify the x-value at which the-following function touches but does not cross the x-axis in the following function: 3x^3- 18^2 + 27x. So, considering that if is a zero with even multiplicity, the graph touches the x-axis and bounces off of the axis. And if it is a zero with odd multiplicity, the graph crosses the x-axis at a zero.
According with this let's
*Statistical question: Is the proportion of inner-city families living on a subsistence income: 20%? Two hundred families were randomly selected for the survey
and 38 were found to have income at the subsistence level. Use the formal critical value method at 5% level of significance.
List the assumptions pertaining to this procedure.
Answers
Since the critical value of the test is greater than the absolute value of the test statistic, there is not enough evidence to conclude that the proportion is different of 20%.
Hypothesis tested and critical valueAt the null hypothesis, it is tested if the proportion is of 20%, that is:
[tex]H_0: p = 0.2[/tex]
At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:
[tex]H_1: p \neq 0.2[/tex]
We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:
|z| = 1.96.
Test statisticThe test statistic is given by the rule presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In the context of this problem, the parameters are given as follows:
[tex]p = 0.2, n = 200, \overline{p} = \frac{38}{200} = 0.19[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.19 - 0.2}{\sqrt{\frac{0.2(0.8)}{200}}}[/tex]
z = -0.35.
|z| < 1.96, hence there is not enough evidence to conclude that the proportion is different of 20%.
More can be learned about the use of the z-distribution to test an hypothesis at https://brainly.com/question/13873630
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An observer in a lighthouse 350 ft above sea level observes two ships directly offshore. The angles of depression to the shops are 4 degree and 6.5 degree. How far apart are the ships?
Answers
The two ships are 1933.32 ft apart
Explanation:Given:
The height of the lighthouse = 350 ft
The angles of depression to the ships are 4 degree and 6.5 degree
To find:
the distance between the two ships
To determine the distance, we will use an illustration of the situation
First we will find the value of y as we need to know this value to get x
To get y, we will apply tan ratio (TOA)
[tex]\begin{gathered} tan\text{ 6.5\degree = }\frac{opposite}{adjacent} \\ opp\text{ = 350 ft} \\ adj\text{ = y} \\ tan\text{ 6.5\degree = }\frac{350}{y} \\ y(tan\text{ 6.5\degree\rparen= 350} \\ y\text{ = }\frac{350}{tan\text{ 6.5}} \\ y\text{ = 3071.9106 ft} \end{gathered}[/tex]Next is to find x using tan ratio (TOA):
[tex]\begin{gathered} angle\text{ = 4\degree} \\ tan\text{ 4\degree= }\frac{opposite}{adjacent} \\ \\ opposite\text{ = 350 ft} \\ adjacent\text{ = y + x} \\ tan\text{ 4\degree= }\frac{350}{y\text{ + x}} \end{gathered}[/tex][tex]\begin{gathered} tan\text{ 4 = }\frac{350}{3071.9106+x} \\ \frac{350}{tan\text{ 4}}\text{ = 3071.9106 + x} \\ 5005.2332\text{ = 3071.9106 + x} \\ x\text{ = 1933.3226} \\ \\ The\text{ ships are 1933.32 ft apart \lparen nearest hundredth\rparen} \end{gathered}[/tex]Enter a rule for each function f and g, and then compare their domains, ranges, slopes, and y-intercepts.The function f(x) has a slope of -2 and has a y-intercept of 3. The graph shows the function g(x).
Answers
The rule of the function f(x) is : -2x + 3
To find the rule of the function g(x) let's calculate the slope of the line
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-11-5}{4-0}=\frac{-16}{4}=-4[/tex]The slope of the line is -4 and the intercept is 5 ( from the graph).
The rule of the function g(x) is : -4x + 5
The domains of f(x) and g(x) is All real numbers, because there is not any number of x which doesn't have a corresponding y-coordinate.
The ranges of f(x) and g(x) is All real numbers, because there is not any number of y which doesn't have a corresponding x-coordinate.
The slope of f(x) is greater than g(x) (-2 is greater than -4)
The y-intercept of f(x) is less than the y-intercept of g(x).(3 is less than 5)
Need help figuring out if the following is Real or Complex Question number 10
Answers
Explanation:
We have the expression:
[tex]i^3[/tex]where i represents the complex number i defined as follows:
[tex]i=\sqrt{-1}[/tex]To find if i^3 is real or complex, we represent it as follows:
[tex]i^3=i^2\times i[/tex]And we find the value of i^2 using the definition of i:
[tex]i^2=(\sqrt{-1})^2[/tex]Since the square root and the power of 2 cancel each other
[tex]\imaginaryI^2=-1[/tex]And therefore, using this value for i^2, we can now write i^3 as follows:
[tex]\begin{gathered} \imaginaryI^3=\imaginaryI^2\times\imaginaryI \\ \downarrow \\ \imaginaryI^3=(-1)\times\imaginaryI \end{gathered}[/tex]This simplifies to -i
[tex]\imaginaryI^3=-\imaginaryI^[/tex]Because -i is still a complex number, that means that i^3 is a complex number.
Answer: Complex
Find 2 given that =−4/5 and < < 3/2
Answers
Find 2 given that =
−4/5 and < < 3/2
we know that
sin(2x) = 2 sin(x) cos(x)
so
step 1
Find the value of cos(x)
Remember that
[tex]\sin ^2(x)+\cos ^2(x)=1^{}[/tex]we have
sin(x)=-4/5
The angle x lies on III quadrant
that means
cos(x) is negative
substitute the value of sin(x)
[tex]\begin{gathered} (-\frac{4}{5})^2+\cos ^2(x)=1^{} \\ \\ \frac{16}{25}+\cos ^2(x)=1^{} \\ \\ \cos ^2(x)=1-\frac{16}{25} \\ \cos ^2(x)=\frac{9}{25} \\ \cos (x)=-\frac{3}{5} \end{gathered}[/tex]step 2
Find the value of sin(2x)
sin(2x) = 2 sin(x) cos(x)
we have
sin(x)=-4/5
cos(x)=-3/5
substitute
sin(2x)=2(-4/5)(-3/5)
sin(2x)=24/25Find the volume of this triangular prism.Be sure to include the correct unit in your answer.8 cm7 cm→5 cm
Answers
The formula to find the volume of a triangular prism is the following:
[tex]V=\frac{1}{2}h\cdot b\cdot w[/tex]where:
h - height
b - base length
w - width
for this problem:
h = 8 cm
b = 5 cm
w = 7 cm
then
[tex]V=\frac{1}{2}8\cdot5\cdot7[/tex]solving this, we obtain that the volume of the triangular prism is 140 cm^3 or cubic centimeters
What is the first operation that should be performed to calculate (3 + 2) × 6÷5 - 4?
A) addition
B) division
C) subtraction
D) multiplication
Answers
Answer: A) addition
Step-by-step explanation:
because of BODMAS, you need to do the bracket first
(3+2)
11. The population of the District of Columbia was approximately 572 thousand in 2000 and had been growing by about 1.15% per year.(a) Write an explicit formula for the population of DC t years after 2000 (i.e. t=0 in 2000), where Pt is measured in thousands of people.Pt = (b) If this trend continues, what will the district's population be in 2025? Round your answer to the nearest whole number. thousand people(c) When does this model predict DC's population to exceed 800 thousand? Give your answer as a calendar year (ex: 2000).During the year
Answers
Given:
Population in 2000 = 572 thousand
Rate of growth per year = 1.15%
Let's solve for the following:
(a) Explicit formula for the population years after 2000.
Where:
In year 2000, t = 0
To write the explicit formula, apply the exponantial growth function formula:
[tex]f(t)=a(1+r)^t[/tex]Where:
a is the initial amount
r is the growth rate.
Thus, we have:
[tex]\begin{gathered} P_t=572(1+\frac{1.15}{100}_{^{}})^t \\ \\ P_t=572(1+0.0115)^t \end{gathered}[/tex]Therefore, the explicit formula for the population years after 2000 is:
[tex]P_t=572(1.0115)^t[/tex](b) What will be the district's population in 2025.
Where:
In the year 2000, t = 0
In the year 2025, t will be = 25
To find the population in 2025, substitute 25 for t in the explicit formula for evalaute:
[tex]\begin{gathered} P_{25}=572(1.0115)^{25} \\ \\ P_{25}=572(1.330905371) \\ \\ P_{25}=761.28\approx761 \end{gathered}[/tex]The population in 2025 if the trend continues will be approximately 761 thousand.
(c) When does the model predict the population to exceeed 800 thousand.
Substitute 800 for Pt and solve for t.
We have:
[tex]\begin{gathered} P_t=572(1.0115)^t \\ \\ 800=572(1.0115)^t \end{gathered}[/tex]Divide both sides by 572:
[tex]\begin{gathered} \frac{800}{572^{}}=\frac{572(1.0115)^t}{572} \\ \\ 1.3986=1.0115^t \end{gathered}[/tex]Take the natural logarithm of both sides:
[tex]\begin{gathered} \ln (1.3986)=\ln (1.0115)^t \\ \\ \ln (1.3986)=t\ln (1.0115) \\ \\ 0.33547=0.01143t \end{gathered}[/tex]Divide both sides by 0.01143:
[tex]\begin{gathered} \frac{0.33547}{0.01143}=\frac{0.01143t}{0.01143} \\ \\ 29.3=t \\ \\ t=29.3\approx29 \end{gathered}[/tex]When t = 29, the year is 2000 + 29 = 2029
Therefore, using this model, DC's population will exceed 800 thousand in the year 2029.
ANSWERS:
[tex]\begin{gathered} (a)P_t=572(1.0115)^t \\ \\ (b)=761\text{ thousand people} \\ \\ (c)\text{ 20}29 \end{gathered}[/tex]I don't understand please explain in simple words the transformation that is happeningwhat is the function notation
Answers
We have the next functions
[tex]f(x)=5^x^{}[/tex][tex]g(x)=2(5)^x+1[/tex]Function notation
[tex]g(x)=2(f(x))+1[/tex]Describe the transformation in words
we have 2 transformations, the 2 that multiplies the function f(x) means that we will have an expansion in the y axis by 2, the one means that we will have a shift up by one unit
I need help finding 5 points. the vertex, 2 to the left of the vertex, and 2 points to the right of the vertex.
Answers
Let's convert the given equation first into a vertex form.
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the vertex.
The vertex form of the equatio that we have is:
[tex]y=-2(x-0)^2+0[/tex]Hence, the vertex of the equation is at the origin (0, 0).
Since "a" is negative, our parabola is opening downward.
Let's identify two points to the left of the vertex. Let's say at x = -1. Replace "x" with -1 in the equation.
[tex]\begin{gathered} y=-2(-1)^2 \\ y=-2(1) \\ y=-2 \end{gathered}[/tex]Hence, we have a point to the left of the parabola at (-1, -2).
Let's say x = -2. Replace "x" with -2 in the equation.
[tex]\begin{gathered} y=-2(-2)^2 \\ y=-2(4) \\ y=-8 \end{gathered}[/tex]Hence, we also have another point to the left of the parabola at (-2, -8).
If our x is to the right of the vertex, say, x = 1. Replace "x" with 1 in the equation.
[tex]\begin{gathered} y=-2(1)^2 \\ y=-2(1) \\ y=-2 \end{gathered}[/tex]We have a point to the right of the parabola at (1, -2).
If x = 2, let's replace "x" with 2 in the equation.
[tex]\begin{gathered} y=-2(2)^2 \\ y=-2(4) \\ y=-8 \end{gathered}[/tex]Hence, we also have another point to the right of the parabola at (2, -8).
The graph of this equation is:
Find the product. Write your answer in scientific notation. (6.5 X 10^8) X (1.4 x 10^-5) =
Answers
Evaluate the product of the expression.
[tex]\begin{gathered} (6.5\times10^8)\cdot(1.4\times10^{-5})=6.5\cdot1.4\times10^{8-5} \\ =9.1\times10^3 \end{gathered}[/tex]So answer is 9.1X10^3.
I need these answers quickly. If I don't get them by midnight ill cry.
Answers
This is because the y intercept represents how much water is in the tank when the time = 0 minutes, and at 0 minutes Jack hasn’t opened the valve yet and no water has been lost.
Slope of Linear EquationsWhich description best compares the graph given by the following equations:23-5y = 82Y == -6Choose one. 4 pointsO parallelO perpendicularintersecting but not perpendicularO coinciding
Answers
Answer:
The two lines are parallel.
Explanation:
We have the equations:
[tex]\begin{gathered} 2x-5y=8 \\ y=\frac{2}{5}x-6 \end{gathered}[/tex]Let's solve the first one for y, so we get the same formatting on both euqations:
[tex]\begin{gathered} 2x-5y=8 \\ 5y=2x-8 \\ y=\frac{2}{5}x-\frac{8}{5} \end{gathered}[/tex]SInce the two lines have the same slope, 2/5, the two lines are parallel.
a circular cylinder with a diameter of 12 cm and a height of 27 cm is filled with water. An aquarium is in the shaoe of a rectangular prism with the dimensions 35 cm 40cm by 42cm. what isvthe maximum number of full cylinders that can be poured into the fish tank without overflowing it?
Answers
Given data:
The diameter of cylinder is d=12 cm.
The height of the cylinder is h= 27 cm.
The dimension of the aquarium is V=(35 cm)(40 cm)( 42 cm).
The volume of the cylinder is,
[tex]\begin{gathered} V^{\prime}=\frac{\pi}{4}(d)^2h \\ =\frac{\pi}{4}(12cm)^2(27\text{ cm)} \\ =3053.628cm^3 \end{gathered}[/tex]The volume of the aquarium is,
[tex]\begin{gathered} V=(35\text{ cm)(40 cm)(42 cm)} \\ =58800cm^3 \end{gathered}[/tex]The number of cylinders that can be pour into aquarium is,
[tex]\begin{gathered} n=\frac{V}{V^{\prime}} \\ =\frac{58800}{3053.628} \\ =19.25 \end{gathered}[/tex]Thus, the number of cylinders that can be pour into aquarium is 19.25.
How to find the area of a regular hexagon with a radius of 12 inches? Please help
Answers
Can someone help me with this math question. I just need to see the work.
pic of question below
Answers
The polar coordinates for each point are given as follows:
a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]
b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]
Polar coordinatesSuppose we have a point with Cartesian coordinates given as follows:
(x,y).
The polar coordinates will be found as follows:
r² = x² + y².θ = arctan(y/x).For item a), the Cartesian coordinates are as follows:
(-4, 4).
Hence the polar coordinates will be given as follows:
r² = (-4)² + (4)² -:> r = sqrt(32) = 2sqrt(5).θ = arctan(-4/4) = arctan(-1) = -45º = 2pi - pi/4 = 7pi/4.For item a), the Cartesian coordinates are as follows:
(3, 3sqrt(3)).
Hence the polar coordinates will be given as follows:
r² = (3)² + (3sqrt(3))² = 9 + 27 = 36 -> r = sqrt(36) = 6.θ = arctan(3sqrt(3)/3) = arctan(sqrt(3)) = 60º = pi/3.More can be learned about polar coordinates at https://brainly.com/question/7009095
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Draw the following vectors using the scale 1 cm = 50 km/h. Plant the tail at the origin. A. 200 km/h on a bearing of 020° B. 75 km/h S 10° W C. 350 km/h NE
Answers
Solution
a)
200 km/h on a bearing of 020°
Scale 1 cm = 50 km/h.
[tex]Length\text{ = }\frac{200}{50}\text{ = 4cm}[/tex]b)
B. 75 km/h S 10° W
[tex]Lenght\text{ = }\frac{75}{50}\text{ = 1.5cm}[/tex]C. 350 km/h NE
[tex]Length\text{ = }\frac{350}{50}\text{ = 7cm}[/tex]You want to build a sandbox that can hold50,445 cubic inches of sand. If the sandbox is to be59 in. long and57 in. wide, how tall will it need to be?
Answers
Volume of sandbox (to be built) = 50,445 cubic inches
A sandbox is the shape of a cuboid and is calculated by the formula
[tex]\text{volume = length }\cdot\text{ wi}\differentialD tth\text{ }\cdot\text{ height }\Rightarrow\text{ v = l }\cdot\text{ w }\cdot\text{ h}[/tex]Volume = Length * Width * Height
Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?
50,445 = 59 * 57 * h
Make h the subject of the formula, we have:
h = 50445 / (59 * 57) = 15 in
Sara spent 35 minutes on math homework and 20 minutes on reading homework. Mia spent a total of 40
minutes on reading and math homework. How much longer did Sara spend on her homework than Mia?
Answers
Sara spent 15 minutes longer than (the difference is 15 min) Mia in her homework.
According to the question,
We have the following information:
Sara spent 35 minutes on math homework and 20 minutes on reading homework. Mia spent a total of 40 minutes on reading and math homework.
So, it means that the total time spent by Sara in her homework is:
35+20 minutes
55 minutes
So, the differences between their time spent in her homework (will give us the more time taken by Sara) is:
Time spent by Sara in her homework-time spent by Mia in her homework
(55-40) minutes
15 minutes
Hence, Sara spent 15 more minutes than Mia.
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Use the change of base formula and a calculator to evaluate the logarithm
Answers
The change of base formula states that:
[tex]\log _bx=\frac{\ln x}{\ln b}[/tex]this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.
In this case we have:
[tex]\begin{gathered} x=14 \\ b=\sqrt[]{3} \end{gathered}[/tex]Then, using the change of base formula, we have:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln 14}{\ln \sqrt[]{3}}[/tex]Once we have the expression we just evaluate the expression on the right to get the appoximation we need:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln14}{\ln\sqrt[]{3}}\approx4.804[/tex]Four research teamed each used a different method to collect data on how fast a new strain of maize sprouts. Assume that they all agree on the sample size and the sample mean ( in hours). Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation
Answers
We need to identify the team that has the smallest sample standard deviation.
In order to do so, we need to find the stand deviation of each experiment based on the confidence level and confidence interval of each of them.
A. A confidence level of 99.7% corresponds to a confidence interval of 3 standard deviations above and 3 standard deviations below the mean.
Thus, for the confidence interval 42 to 48, the mean is 45. And the standard deviation is given by:
[tex]\begin{gathered} 3\sigma=48-45=3 \\ \\ \sigma=\frac{3}{3} \\ \\ \sigma=1 \end{gathered}[/tex]B. A confidence level of 95% corresponds to a confident interval of 2 standard deviations above and 2 standard deviations below the mean.
Thus, for the confidence interval 43 to 47, the mean is 45. And the standard deviation is given by:
[tex]\begin{gathered} 2\sigma=47-45=2 \\ \\ \sigma=\frac{2}{2} \\ \\ \sigma=1 \end{gathered}[/tex]C. A confidence level of 68% corresponds to a confident interval of 1 standard deviation above and 1 standard deviation below the mean.
Thus, for the confidence interval 44 to 46, the mean is 45. And the standard deviation is given by:
[tex]\begin{gathered} \sigma=46-45 \\ \\ \sigma=1 \end{gathered}[/tex]D. Again, we have a confidence level of 95%, which corresponds to 2 standard deviations.
Thus, for the confidence interval 44 to 46, the mean is 45. And the standard deviation is given by:
[tex]\begin{gathered} 2\sigma=46-45=1 \\ \\ \sigma=\frac{1}{2} \\ \\ \sigma=0.5 \end{gathered}[/tex]Therefore, the team that has the smallest sample standard deviation is:
Answer