Recall the Pythagorean identity,
[tex]\sec^2\theta=1+\tan^2\theta[/tex]
So we have
[tex]\sec^2\theta=4+2\tan^2\theta[/tex]
[tex]1+\tan^2\theta=4+2\tan^2\theta[/tex]
[tex]-3=\tan^2\theta[/tex]
But squaring any real number always gives a non-negative number, so there are no real solutions to this equation.
The ratio of the number of boys to the number of girls in a class is 12:13 What percentage of the class are boys?
48%
Step-by-step explanation:
add the ratio together which is 25
pick the ratio of boy
divide 12 by 25 and multiply 100
12/25×100= 48%
Answer:
48%
Step-by-step explanation:
b/g=12/13
so b/12=g/13=k
b=12k
g=13k
so b+g=25k so k=b+g/25
b=12*(b+g)/25=12*4*(b+g)/25*4=48(b+g)/100
so 48% are boys
What is the quotient?
(6 * 108) = (1.5 * 10-4)
4 x 1012
4 x 104
4 x 10-32
410-2
Answer:
(A)[tex]4X10^{12}[/tex]
Step-by-step explanation:
Given the quotient:
[tex]\dfrac{6*10^8}{1.5*10^{-4}}[/tex]
To evaluate, we first separate the given expression as follows.
[tex]=\dfrac{6}{1.5}X\dfrac{10^8}{10^{-4}}[/tex]
Next, we apply the division law of indices to the powers of 10.
Division Law of Indices: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]=4X10^{8-(-4)}\\=4X10^{8+4}\\=4X10^{12}[/tex]
Therefore, our quotient is [tex]4X10^{12}[/tex].
The correct answer is A.
What is a tangent line in relation to a circle?
Answer:
A tangent to a circle is a straight line which touches the circle at only one point.
Step-by-step explanation:
This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.
Log 3 base 6 + log 8 base 6 - log 4 base 6
Step-by-step explanation:
Refer The attachment.
What is the solution to the equation? 5 = two-fifths a 2 4 and three-fifths 12 and one-half 25
Answer:
12 1/2
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of a.
5 = (2/5)a
5(5/2) = (2/5)(5/2)a
25/2 = a
12 1/2 = a . . . . written as a mixed number
The solution is 12 1/2.
Answer:
12 1/2
Step-by-step explanation:
According to the picture, whats the answer?
Answer:
84 meters
Step-by-step explanation:
5 x 6 = 30 hypotenuse side not shown
3 x 4 ÷ 2 x 2 = 12 red (both ends)
3 x 6 = 18 green side
6 x 4 = 24 blue side
PLEASE HELP
Sara and Sam are each working on a science project in which they need to research the individual masses of the nine planets (including the dwarf planet Pluto as the ninth planet). Sara completes her data for the planets' masses in kilograms while Sam's data is in milligrams.
Sara:
Approximate how many times greater Saturn's mass is than Mercury's.
A: 2,000,000
B: 200,000
C: 20,000
D: 2,000
Please answer quick
Taylor is playing a board game with two friends, using a single dice, one friend rolled a one, and the other friend rolled a three. Taylor need to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning. What is the sample space for Taylor’s calculation?
A. [4,5,6]
B. [2,4,5,6]
C. [1,3]
D. [1,2,3,4,5,6]
Answer:
it is a
Step-by-step explanation:
its the only possible answer. :)
let me know if i am wrong!
What is the circumference of a circle with a radius of 91 mm? (use 22/7 for pi; show your work in numbers)
Answer:
[tex] \boxed{Circumference \: of \: circle = 572 \: mm} [/tex]
Step-by-step explanation:
Radius (r) = 91 mm
[tex]Circumference \: of \: circle = 2\pi r \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \frac{22}{7} \times 91 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 22 \times 13 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 44 \times 13\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 572 \: mm[/tex]
If Josh invests $500 in a 5-year fixed interest savings bond that pays 5% per annum, how much will his entire investment be worth at the end of the term?
Answer:
$638.14
Step-by-step explanation:
Our equation is [tex]p*(1+x)^{t}[/tex], with p being the starting amount, x being the interest rate, and t being the time. Plugging our variables in, we get
[tex]500*(1+0.05)^{5}[/tex] = around 638.14
Josh will receive $638 at the end of the term.
Josh invests $500 in a 5-year fixed interest savings bond that pays 5% per annum,
What is cost price?Cost price is that price for buyer which he pays to seller for an object or product.
Principle amount = $500
Rate = 5 %
Tenure = 5 years
Amount = principle (1+R)^tenure
= 500 (1+5/100)^5
= $638
Thus, Josh will receive $638 at the end of the term.
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help Marshmello ok xd
Answer:
84
Step-by-step explanation:
We simply plug in 1.75 for x into y = 48x, and when we do so we get y = 48 * 1.75 = 84 cups of coffee. Hope this helps!
Answer:
B) 84
Step-by-step explanation:
48 times x is the cups of coffee sold in x hours.
if x = 1.75, then you times 48 by 1.75
48 x 1.75 = 84
What’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
The equation of circle is :
(x−a)² + (y−b)² = r²
So the equation is
(x-3)² + (y-(-2))² = (6)²
Where center = (a,b) = (3,-2) and
Radius = r = 6
Vivek plans to survey 10 randomly chosen residence out of the 280 people that live in his community about plans for new neighborhood dog park describe one way he can make the sample to represent the population of residence *hint how will you pick those 10 people*
Step-by-step explanation:
To randomly pick the 10 people needed in the sample, it can be done this way
1. Define the population: in this case, the total population is 280 and expressed as N and since we are interested in everyone in the neighborhood with no exclusion, our sampling frame is thus 280 people.
2. Choose your sample size: As given in the question, our sample size is to randomly pick 10 people expressed as n.
3. List your population and then assign numbers to each unit in the population: Getting the list of all 280 people in the population and then assigning numbers from 1 to N - in this case 1 - 280.
4. Then find random numbers using the random number table to help select your 10 people sample making them a representative of the population in residence.
A clothing company produces denim jeans. The jeans are made and sold with either a regular cut or a boot-cut. To estimate the proportion of all customers in Tacoma, WA, who prefer boot-cut jeans, a marketing researcher examined sales receipts for a random sample of 178 customers who purchased jeans from the firm’s Tacoma store. 56 of the customers in the sample purchased boot-cut jeans. Construct the 99% confidence interval to estimate the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans and interpret the confidence interval (please write the interval boundaries to THREE decimal places
Answer:
99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].
Step-by-step explanation:
We are given that a marketing researcher examined sales receipts for a random sample of 178 customers who purchased jeans from the firm’s Tacoma store. 56 of the customers in the sample purchased boot-cut jeans.
Firstly, the Pivotal quantity for 99% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of customers who purchased boot-cut jeans = [tex]\frac{56}{178}[/tex] = 0.315
n = sample of customers = 178
p = population proportion of customers who prefer boot-cut jeans
Here for constructing 99% confidence interval we have used One-sample z test for proportions.
So, 99% confidence interval for the population proportion, p is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99
P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex], [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]
= [ [tex]0.315-2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }[/tex] , [tex]0.315+2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }[/tex] ]
= [0.225 , 0.405]
Therefore, 99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].
The interpretation of the above confidence interval is that we are 99% confident that the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans will lie between 0.225 and 0.405.
The string of a kite is 100 meters long and it makes an angle of 60° with the ground. What is the height of the kite?
Show your work please)
Answer:
50√3 ≈ 86.6 m
Step-by-step explanation:
The geometry can be modeled by a right triangle with the height of the kite being the leg opposite the 60° angle. The hypotenuse has the given length of 100 m.
The mnemonic SOH CAH TOA reminds you that the relation between angles and the sides of interest here is ...
Sin = Opposite/Hypotenuse
sin(60°) = (kite height)/(100 m)
kite height = (100 m)·sin(60°) = (100 m)(√3)/2
kite height = 50√3 m ≈ 86.6 m
Grace swam 0.6 kilometers during her first week of training and 0.25 kilometers during her second week of training. How many kilometers did she swim in all?
A.3.1 kilometers
B.8.5 kilometers
C.0.31 kilometers
D.0.85 kilometers
Answer:
she will cover a distance of 0.85 km.
Step-by-step explanation:
We have,
Grace swam 0.6 kilometres during her first week of training and 0.25 kilometres during her second week of training.
It is required to find total distance covered by her in all.
It can be calculated simply adding the distance covered in first and second week of training. So,
Total distance, D = 0.6 km +0.25 km = 0.85 km
Hence, she will cover a distance of 0.85 km.
12m by 7m what is the area
Answer:
multiply 12*7
Step-by-step explanation:
Answer:
84 m²
Step-by-step explanation:
12 times 7 (for a rectangle)
FOR BRAINLIEST only RIGHT ANWERS
Answer:
Length of arc: 6π
Step-by-step explanation:
~ Let us answer this question in terms of π, remaining so ~
1. Assume that this is a complete circle, for the moment being. The chord with length of 12 units would act as the diameter, and using that information we could determine the circumference of this complete circle...which will help us in the future. Apply the formula π * d as such: π * 12 ⇒ 12π to get the circumference as 12π.
2. Knowing that the length of the complete circle's circumference is 12π, this arc is part of a semicircle, meaning that it's value would be half of that of the complete circle's circumference, or in other words: 12π/2 ⇒ Answer ~ Length of arc: 6π
Answer:Length of arc: 6π
Step-by-step explanation:
CALC HELP!!! WILL MARK BRAINLIEST
Consider the parametric equations below.
x = t2 − 2, y = t + 1, −3 ≤ t ≤ 3
(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
(b) Eliminate the parameter to find a Cartesian equation of the curve. for −2 ≤ y ≤ 4
Answer:
(a) In attachment
(b) x = y² - 2y - 1, −2 ≤ y ≤ 4
Step-by-step explanation:
(a)
The graph of the given parametric equation is given in the attachment.
The direction in which the curve is traced as t increases, is indicated by black arrows.
(b)
To eleminate the parameter t, we simultaneously solve both the equations.
So, we have the equations:
x = t² - 2 ----- equation (1)
y = t + 1 ----- equation (2)
So, from equation (2), we have:
t = y - 1
Substituting this in equation (1), we get:
x = (y - 1)² - 2
x = y² - 2y + 1 - 2
x = y² - 2y - 1
Now, for limits of y, we use equation (2)
For initial limit, t = -3
y = - 3 + 1 = - 2
For final limit, t = 3
y = 3 + 1 = 4
Therefore, the final relation after eliminating t is:
x = y² - 2y - 1, −2 ≤ y ≤ 4
The Cartesian equation of the curve after eliminating the parameter t is expressed below.
[tex]x=y^2-2y-1[/tex]
For, the y values of, [tex]-2 \leq y \leq 4[/tex]
What is a parametric equation?The parametric equation is the type of equation in which the variable which is in depended on on is known as parameter. The dependent function in this equation is defined as the continuous function of that variable.
The first equation given in the problem is,
[tex]x = t^2 - 2 \\t^2=x+2[/tex]
The second equation given in the problem is,
[tex]y = t + 1\\t=y-1[/tex]
Put the values of t in the modified first equation as,
[tex](y-1)^2=x+2\\y^2+1-2y-2=x\\x=y^2-2y-1[/tex]
The values of t are between -3 to 3.
[tex]-3 \leq t \leq 3[/tex]
The value of t is -3 then the value of y will be -2 and when the value of t is 4 then the value of y will be 4 from equation 2.
Hence, the Cartesian equation of the curve after eliminating the parameter t is expressed below.
[tex]x=y^2-2y-1[/tex]
For, the y values of, [tex]-2 \leq y \leq 4[/tex]
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Circle B is shown. Line segments C B, D B, and E B are radii. Angle C B E is 52 degrees and angle E B D is 160 degrees. What is the measure of Arc C E D? 106° 108° 148° 212°
Answer it would be 212 :)
Step-by-step explanation:
The measure of arc CED in the circle given is: D. 212°.
What is the Measure of an Arc of a Circle?Measurement of an arc of a circle = measure of its central angle.
Thus:
Measure of arc CED = angle CBE + angle EBD
Substitute
Measure of arc CED = 52 + 160
Measure of arc CED = 212°
Therefore, the measure of arc CED in the circle given is: D. 212°.
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Sin2x + cos3x expand the expression
Step-by-step explanation:
Use double and triple angle identities:
sin(2x) + cos(3x)
2 sin x cos x + 4 cos³x − 3 cos x
What is the slope, m, and y-intercept for the line that is plotted on the grid below? On a coordinate plane, a line goes through points (0, 4) and (negative 2, 0).
Answer:
On a coordinate plane, a line (y = mx + b) goes through point A(0, 4), then it has point A as y-intercept (the point with x component is 0). And it goes through B(-2, 0).
Denote that line: y = mx + b
=> m*0 + b = 4 (it goes through A(0, 4))
=> b = 4
=> m*2 + 4 = 0 (it goes through B(-2, 0))
=> m = -2
=> Slope m = 2 and y-intercept (0, 4)
Hope this helps!
:)
Answer:
Slope: 2
y-intercept: 4
Step-by-step explanation:
m = (0-4)/(-2-0) = -4/-2 = 2
y -4 = 2(x - 0)
y = 2x + 4
An experienced landscaper thought it would be funny to play a joke on some rookie landscapers. The rookies were given the measurements, l e n g t h equals 4 space cube root of 24 f t space a n d space w i d t h equals 6 space cube root of 3 space f t , and asked to find the exact area (no decimals) of the rectangular region they would be working with. Show the equation and all work needed to find the exact area in simplest form. Be sure to write a sentence explaining your answer. Don’t forget the label! Note: we want the exact area, which is not a decimal. Instead, provide the answer in simplest radical form.
Answer:
48∛9 ft²
Step-by-step explanation:
The length (L) and width (W) are given by:
[tex]L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}[/tex]
Since this is a rectangular region, the area is given by:
[tex]A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2[/tex]
The answer can be further simplified by factoring as follows:
[tex]A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2[/tex]
The exact area is its simplest form is 48∛9 ft²
Match the expressions to their limit values.
Answer:
Step-by-step explanation:
individual health insurance is usually less expensive than group health insurance
true or false?
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
How is 3 help me please
Step-by-step explanation:
Square root 8 = 2 square root 2
If 8=10 and 1=7,which describes all the lines that must be parallel?
Only lines rand s must be parallel.
Only lines tand u must be parallel.
Lines rand s and lines t and u must be parallel.
Neither lines r and s nor lines t and u must be parallel.
Answer:
C: Lines r and s and lines t and u must be parallel.
Step-by-step explanation:
The true statement is (c) Only lines r and s must be parallel.
How to determine the true statementFrom the figure, we can see that:
Lines r and s point in the same direction, while lines t and u point in the same direction
If angle 8 = angle 10 and angle 1 = angle 7, then it means that:
Lines r and s must be parallel.
Line t and u may or may not be parallel.
Hence, the true statement is (c) Only lines r and s must be parallel.
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a desert tray has three slices of cake, three key lime pies, and four ice cream sundaes. What is the probability of the next two customers both select key lime pie?
Answer:
The probability of the next two customers both select key lime pie is 1/15
Step-by-step explanation:
No. of slices of cakes = 3
No. of key lime pies = 3
No. of ice cream sundaes = 4
Total deserts = 3+3+4=10
We are supposed to find The probability of the next two customers both select key lime pie
Probability of selecting key lime pie by first customer =[tex]\frac{3}{10}[/tex]
So,Total deserts =10-1=9
No. of key lime pies = 3-1=2
So,Probability of selecting key lime pie by second customer = [tex]\frac{2}{9}[/tex]
So,the probability of the next two customers both select key lime pie=[tex]\frac{3}{10} \times \frac{2}{9} =\frac{1}{15}[/tex]
Hence the probability of the next two customers both select key lime pie is 1/15
S500 invested at 4% compounded annually for 10 years.
Hello there!
$500 invested at 4% compounded annually for 10 years
time: 10 years
compound: annually
interest: 4%
y = 500(1.04)^10
1.04^10 = 1.48
500 x 1.48 = 740
Value after 10 years: $740
Answer:
$740.12
Step-by-step explanation:
The amount is multiplied by 1.04 each year, so after 10 years, the balance will be ...
$500(1.04^10) = $740.12
Write the formula to calculate how much dough is prepared in x hours.
10 kilograms of prepared dough in 5 hours
Answer: D(x) = 2kg/h*x
where x is the number of hours.
Step-by-step explanation:
The information that we have is:
in 5 hours, we can prepare 10kg of dough.
With this, we can find the rate per hour, to do this we find the quotient:
R = 10kg/5h = 2kh/h
This meeans that in one hour, we can make 2kg of dough.
Then, in x hours, we can make x times 2kg of dough, then the equation will be:
D(x) = 2kg/h*x
where x is the number of hours.