Answers
Answer:
B.
Step-by-step explanation:
The first number minus the 2nd number will close off the distance.
Related Questions
.Tom is throwing darts at a target. In his last 30 throws, Tom has hit the target 20 times. You want to know the estimated probability that exactly one out of the next three throws does not hit the target.
Answers
Step-by-step explanation:
In his last 30 throws, Tom hit the target 20 times and missed 10 times.
p = probability he misses the target = ⅓
q = probability he hits the target = ⅔
Using binomial probability:
P = nCr (p)^r (q)^(n-r)
Given n = 3, r = 1, p = ⅓, and q = ⅔:
P = ₃C₁ (⅓)¹ (⅔)³⁻¹
P = (3) (⅓) (⅔)²
P = 4/9
There is a 4/9 probability that he misses exactly 1 of his next 3 throws.
By applying binomial probability, the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target is 4/9.
How to determine the estimated probability?In order to determine the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target, we would apply binomial probability equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
Based on the information given, we can deduce the following points:
Probability that Tom misses the target (p) = 10/30 = ⅓Probability that Tom hits the target (q) = 20/30 = ⅔Number of next throws (n) = 3.Number of throws taken at a time (r) = 1.Substituting the given parameters into the equation, we have;
P = ³C₁ × (⅓)¹ × (⅔)³⁻¹
P = 3 × (⅓)¹ × (⅔)²
P = 3 × ⅓ × (⅔)²
P = 1 × 4/9
P = 4/9.
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Evaluate the line integral c (2x3 − y3) dx + (4x3 + y3) dy where c is the unit circle, and verify green's theorem for this case
Answers
Parameterize [tex]C[/tex]
[tex]x=\cos t[/tex]
[tex]y=\sin t[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\langle2x^3-y^3,4x^3+y^3\rangle[/tex] along [tex]C[/tex] is
[tex]\displaystyle\int_0^{2\pi}\langle2\cos^3t-\sin^3t,4\cos^3t+\sin^3t\rangle\cdot\langle-\sin t,\cos t\rangle\,\mathrm dt[/tex]
[tex]\displaystyle=\int_0^{2\pi}(4\cos^4t-2\cos^3t\sin t+\cos t\sin t^3+\sin^4t)\,\mathrm dt=\boxed{\frac{15\pi}4}[/tex]
By Green's theorem, the line integral is equivalent to
[tex]\displaystyle\iint_{x^2+y^2\le1}\left(\frac{\partial(4x^3+y^3)}{\partial x}-\frac{\partial(2x^3-y^3)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_{x^2+y^2\le1}(12x^2+3y^2)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^1(12r^2\cos^2\theta+3r^2\sin^2\theta)r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^1(9r^3\cos^2\theta+3r^3)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{15\pi}4}[/tex]
To evaluate the line integral along the unit circle, we can parametrize the circle using x = cos(t) and y = sin(t). The resulting integral is 6 times the integral of cos squared(t) times cos(t).
Explanation:To evaluate the line integral, we need to parametrize the unit circle. Let's use x = cos(t) and y = sin(t) as the parameterization. The differential arc length is given by ds = √(dx² + dy²) = dt. Substituting these into the line integral, we get:
∫(2cos³(t) - sin³(t)) dt + ∫(4cos³(t) + sin³(t)) dt = ∫(6cos³(t)) dt
Since the unit circle can be parameterized from 0 to 2π, the integral becomes:
∫[6cos³(t)] dt = 6 ∫[(cos(t))³] dt = 6 ∫[cos³(t)] dt = 6[∫(cos²(t)cos(t)) dt]
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He function h(t) = 210 – 15t models the altitude of a hot air balloon over time t, in minutes. Explain what h(10) means in the context of the real-world scenario, and how to find its value.
Answers
Answer:
Step-by-step explanation:
h(10) would be the height of the balloon at 10 seconds
I don't understand this. Can someone please help me?
Answers
Answer:
a) 16 in²
b) 20 cm²
Step-by-step explanation:
In any prism, a cross section parallel to parallel faces will have the same shape and area as either of those faces. (That is why we say a prism has a uniform cross section.)
a) The face(s) parallel to the cut plane are squares 4 in on a side, so that is the shape of the cross section. Its area is (4 in)² = 16 in².
__
b) The face(s) parallel to the cut plane are rectangles 4 cm by 5 cm. That is the shape of the cross section. Its area is (4 cm)(5 cm) = 20 cm².
If [tex]\alpha[/tex] = 65° and j = 11 mm, what is the value of h to the nearest tenth of a millimeter?
A. 4.7 mm
B. 12.1 mm
C. 5.1 mm
D. 8.6 mm
Answers
Answer:
C. 5.1 mm
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan alpha = opposite/ adjacent
tan alpha = j/h
tan 65 = 11/h
Multiply both sides by h
h tan 65 = 11/h *h
h tan 65 = 11
Divide each side by tan 65
h tan 65 / tan 65 = 11 / tan 65
h = 11 / tan 65
h =5.12938424
To the nearest tenth
h = 5.1
Answer:
12.1
Step-by-step explanation:
20 points One diagonal of a rhombus has endpoints (-10, 1) and (2, 9).
What are the endpoints of the other diagonal?
(-7, 7) and (-1, 3)
(-4, 7) and (2, 7)
(-2, 2) and (-6, 8)
(-6, 2) and (-2, 8)
Answers
Final answer:
To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other. The endpoints of the other diagonal are (-7, 7) and (-1, 3). Therefore, Option A is the correct answer.
Explanation:
To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other, meaning they intersect at their midpoints. We can find the midpoint by taking the average of the x-coordinates and the average of the y-coordinates of the given endpoints of the first diagonal.
For the given endpoints (-10, 1) and (2, 9), the midpoint would be ((-10 + 2)/2, (1 + 9)/2), which simplifies to (-4, 5).
Since the diagonals bisect each other, the other diagonal would have the same midpoint. Therefore, the endpoints of the other diagonal would be (-4, 5) and the reflection of (-4, 5) across the midpoint of the given diagonal, which is the midpoint of (-10, 1) and (2, 9). Thus, the correct answer is (-4, 5) and its reflection across (-4, 5), which is (-7, 7) and (-1, 3).
Tony spent $100 on books to give away as prizes to his students. At the store, he bought 4 more books than planned, spending $5 per book. Which equation can be used to find the number of books he originally wanted to buy. X
Answers
Answer:
[tex]5x=100[/tex]
[tex]x=20\ books[/tex]
Step-by-step explanation:
I'm going to assume that all books cost the same.
Let
x ------> the number of books he originally wanted to buy
we know that
[tex](x+4)(5)=100+4(5)[/tex]
[tex]5x+20=100+20[/tex]
[tex]5x=100[/tex] -----> equation that can be used to find the number of books he originally wanted to buy
solve for x
[tex]x=100/5[/tex]
[tex]x=20\ books[/tex]
Nick has 21 pencils and Lance has 63 pencils.
Tony spent a total of $100 on books. Since he bought 4 more books than he originally planned, and each book cost $5, let's denote the original number of books he planned to buy as x. Therefore, the total number of books he ended up buying would be x + 4. Given that the cost of each book is $5, we can establish the equation 5(x + 4) = 100 to represent the total expenditure on books.
To find the number of books he originally wanted to buy, we will solve for x in the equation above:
Multiply 5 by the quantity x + 4 to obtain the left side of the equation.
Set that result equal to 100, as this is the total amount spent.
Solve the equation for x by first distributing the 5, which gives us 5x + 20 = 100, and then subtracting 20 from both sides of the equation to get 5x = 80.
Finally, divide both sides by 5 to find the value of x, which results in x = 16.
Therefore, Tony originally planned to buy 16 books.
The student council at Sparrowtown High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $10 per shirt, plus a setup fee of $72. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
(Algebra 2)
Answers
step by step:
first make an equation with the amount of sold shirts being equal to cost of making them -
12x=10x+72 where x is the number of shirts
then, subtract 10x from 12x to get the variable on the same side -
2x=72
finally, divide by 2 to isolate x
x=36 shirts
to figure out the cost, substitute 36 for x in 10x+72
10(36)+72= 360+72= $432
PLEASE HELP
In the proof of the Law of Cosines, the equation c^2=h^2+(b-x)^2was created using the Pythagorean theorem. Which equation is a result of expanding (b-x)^2?
A.c^2=h^2+b^2-x^2
B.c^2=h^2+b^2-2bx+x^2
C. c^2=h^2+b^2+x^2
not D
Two construction workers, Tyrone and Diego, are standing 15 yards apart, looking up at a piano hanging between the two men from a crane. Tyrone is staring at the piano with an angle of elevation of 65°, and Diego is looking up with an angle of elevation of 77°. What is the distance between Tyrone and the piano? Round the answer to the nearest tenth.
9.0 yd
16.1 yd
22.1 yd
23.7 yd
Answers
Answer:
Q1 B
Q2 23.7yd
Step-by-step explanation:
Solution of Q2 is in the picture
Answer:
a) [tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]
Therefore letter B is the correct answer.
b) TP = 23.7 yards
Step-by-step explanation:
a) We can rewrite [tex](b-x)^{2}[/tex] as (b-x)(b-x), so we have a product of two binomials. We can use the FOIL method to multiply it:
[tex](b-x)(b-x)=b^{2}-bx-bx+x^{2}=b^{2}-2bx+x^{2}[/tex]
so the the Law of Cosines equation will be write as:
[tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]
Therefore letter B is the correct answer.
b) Here we can use the Law of sines.
TP is the distance between Tyrone and the pianoDP is the distance between Diego and the pianoTD is the distance between Diego and Tyrone.∠A angle between TD and TP = 65°
∠B angle between TD and DP = 77°
∠C angle between TP and DP = 180° - 77° - 65° = 38°
The equation is:
[tex]\frac{TP}{sin(B)}=\frac{TD}{sin(C)}[/tex]
[tex]\frac{TP}{sin(77)}=\frac{15}{sin(38)}[/tex]
Solving it for TP, we have:
[tex]TP=sin(77)\frac{15}{sin(38)}=23.7 yards[/tex]
I hope it helps you!
The growth of a new strain of bacteria is represented by y=79.31(1.48)x where x represents the number of days and y represents the number of bacteria. Which is the best prediction for the number of bacteria on day 7?
Answers
Answer:
1234
Step-by-step explanation:
Put the number in the expression and do the arithmetic.
y = 79.31(1.48^7) ≈ 79.31 × 15.554 ≈ 1233.56 ≈ 1234
Answer: There are 1233.55 bacteria on day 7.
Step-by-step explanation:
Since we have given that
[tex]y=79.31(1.48)^x[/tex]
Here, x represents the number of days.
y represents the number of bacteria.
We need to find the number of bacteria on day 7.
So, we put x = 7 as there are 7 days given.
So, our equation becomes,
[tex]y=79.31(1.48)^7\\\\y=1233.55[/tex]
Hence, there are 1233.55 bacteria on day 7.
Determine the height of the triangle.
Round to the nearest foot.
a. 12 ft c. 10 ft
b. 14 ft d. 18 ft
Please select the best answer from the choices provided
Answers
Answer:
Option B is correct.
Step-by-step explanation:
We need to find the height of triangle.
The triangle is right angled triangle
We are given Hypotenuse = 25
Perpendicular = h
and angle Ф = 34°
We know that sinФ = Perpendicular / Hypotenuse
sin 34° = h / 25
0.56 = h/25
=> h = 0.56 * 25
=> h = 14 ft
So, the height of triangle is h= 14 ft
So, Option B is correct.
Answer:
It's B!
Step-by-step explanation:
I just took it! Have a good day.
Really trying to pass this exam and graduate can someone smart please help me with these problems im running out of time ..
Answers
Answer:
1172.08 square inches
Step-by-step explanation:
Total surface area is area of all the surfaces.
Cylinder:
Top surface = πr^2 = π(4)^2 = 16(3.14) = 50.24
Lateral Surface = 2πrh = 2π(4)(9) = 72π = 72(3.14) = 226.08
Rectangular Prism:
2 sides = 2*(11*11) = 242
front and back = 2*(16*11) = 352
bottom = 16 * 11 = 176
Top part (it is top rectangle - bottom of cylinder) = (16*11) - (π(4)^2) = 125.76
Adding all up, we get:
50.24 + 226.08 + 242 + 352 + 176 + 125.76 = 1172.08 square inches
The longer leg of a 30°-60°-90° triangle measures [tex]9\sqrt{3}[/tex] inches. What is the length of the shorter leg?
A. 18 inches
B. [tex]18\sqrt{3}[/tex] inches
C. [tex]9\sqrt{3}[/tex] inches
D. 9 inches
Answers
Answer:
D. 9
Step-by-step explanation:
The Pythagorean triple for a 30-60-90 right triangle is (x, x√3, 2x). The side across from the 30° angle is x, the side across from the 60° angle is x√3, and the side across from the right angle is 2x (which is also the hypotenuse). If the side across from the 60° angle is given as 9√3, we can set that equal to the identity for that leg:
9√3 = x√3 and solve for x. Divide both sides by the √3 to get that x = 9
Answer:
The correct answer is option D. 9
Step-by-step explanation:
Points to remember
It a right triangle with angles 30°, 60 and 90° the n the sides are in the ratio,
Shorter leg : longer leg : hypotenuse = 1 : √3 : 2
To find the length of shorter leg
Here it is given that, longer length = 9√3
We have,
Shorter leg : longer leg : hypotenuse = 1 : √3 : 2 = Shorter leg : 9√3: hypotenuse
Therefore shorter leg = 9√3/√3 = 9
The revenue each season from tickets at the theme part is represented by t(x) = 5x. The cost to pay the employees each season is represented by r(x) = (1.5)x. Examine the graph of the combined function for total profit and estimate the profit after four seasons.
A. 1
B. 5
C. 10
D. 15
Answers
Answer: D. 15
Step-by-step explanation:
Given : The revenue each season from tickets at the theme part is represented by [tex]t(x) = 5x[/tex] .
The cost to pay the employees each season is represented by [tex]r(x) = (1.5)x[/tex].
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15
The correct option is d. 15, is the estimated profit after four seasons, rounded to the nearest integer.
Given : The revenue each season from tickets at the theme part is represented by t(x) = 5x .
The cost to pay the employees each season is represented by r(x) = (1.5)x.
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15
Suppose you have a bucket of sand containing 5.5 billion grains of sand ( 5.5×109 grains). Most of the grains of sand are white, but there are some brown grains mixed evenly throughout. If the concentration of brown sand is 2.0% , how many grains of brown sand are in the bucket?
Answers
Answer:
1.1×10^8
Step-by-step explanation:
2% of 5.5 billion is ...
2×10^-2 × 5.5×10^9 = 11×10^7 = 1.1×10^8
About 1.1×10^8 grains of brown sand are in the bucket.
Answer:
Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].
Step-by-step explanation:
Total number sand grains in the bucket =[tex] 5.5\times 10^9 grain[/tex]
Concentration of brown sand grains = 2.0%
Number of brown brain in the bucket be x
[tex]\%=\frac{\text{Brown sand grains}}{\text{Total sand grains}}\times 100[/tex]
[tex]2.0\%=\frac{x}{5.5\times 10^9 grain}\times 100[/tex]
[tex]x=1.1\times 10^8 grains[/tex]
Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].
Please answer this question for 30 points and brainliest!!
Answers
Answer:
2.5 cm
Step-by-step explanation:
The ratio of side lengths of similar figures is the same as the ratio of any linear measure on those figures, including perimeter. The second figure's perimeter is 10/16 of that of the first figure, so the shortest side of the second figure will also be 10/16 of the length of the shortest side of the first figure.
(10/16)×(4 cm) = 2.5 cm
The shortest side of the second polygon has a length of 2.5 cm.
Match the red graph above to the corresponding equation
Answers
Answer:
y = -1/3·x³
Step-by-step explanation:
The function is odd (symmetrical about the origin), so corresponds to a function of odd degree. It is shorter and wider than the parent x³ function, so has a vertical scale factor less than 1. The appropriate choice is ...
y = -1/3x³
The corresponding equation that matches the red graph include the following: A. [tex]y=-\frac{1}{3} x^3[/tex].
What is a cubic root function?In Mathematics and Euclidean Geometry, a radical function, cubic function or a cube root function can be represented by using the following mathematical equation:
[tex]f(x)=a\sqrt[3]{x-h} +k[/tex]
where:
h represent the horizontal shift.k represent the vertical shift.By critically observing the graph shown above, we can logically deduce that the red graph represents a cubic function with an odd degree because it is symmetrical about the origin. Also, the parent cubic function [tex]f(x)=x^3[/tex] was vertically compressed by a factor that is less than 1, which is 1/3;
[tex]y=-\frac{1}{3} x^3[/tex]
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Using the graph below, select all statements that are true.
A. f(0.6)=0
B. f(-3.2)=-3
C. f(5.1)=5
D. This is the graph of the greatest integer function.
E. This graph is one-to-one.
Answers
Answer:
A. f(0.6)=0
C. f(5.1)=5
D. This is the graph of the greatest integer function.
Step-by-step explanation:
The graph maps each x-value to the largest integer less than or equal to that value. That is the definition of the "greatest integer" function.
The "greatest integer" of -3.2 is -4, so B is not a correct choice. The graph does not pass the horizontal line test, so the function is not one-to-one, and E is not a correct choice.
Answer:
C, D, E
Step-by-step explanation:
Given the conditional statement: p → ~q Choose the logically equivalent statement.
A. p → q
B. ~p → q
C. q → p
D. q → ~p
Answers
Answer: The correct option is
(D) q → ~p.
Step-by-step explanation: We are given to select the statement that is logically equivalent to the conditional statement p → ~q.
We know that
two conditional statements are said to be logically equivalent if the truth tables of both the statements are same.
That is, they have same truth values under similar conditions.
The truth table is given by
p q ~p ~q p → ~q p → q ~p → q q → p q → ~p
T T F F F T T T F
T F F T T F T T T
F T T F T T T F T
F F T T T T F T T
So, the truth values of p → ~q is same as the truth values of q → ~p. They must be logically equivalent.
Thus, option (D) is CORRECT.
Answer:
D). q → ~p
Step-by-step explanation:
I just did the assignment on Edge... It's 100% correct... Hope this helps!!
Also heart and rate if you found this answer helpful... Have a nice day!! :)
A rectangular garden measures 3 feet by 15 feet the gardener decides to extend the garden 1 foot in each of the four directions what is the perimeter of the new garden in feet
Answers
The perimeter of the new garden after extension is 44 feet.
Explanation:To find the perimeter of the new garden, we need to determine the dimensions after the extension. The original garden measures 3 feet by 15 feet, and the gardener decides to extend it by 1 foot in each direction. This means the new dimensions are 5 feet by 17 feet.
To find the perimeter, we add up all the sides of the rectangle. The formula for the perimeter of a rectangle is:
P = 2(l + w)
where P represents the perimeter, l represents the length of the rectangle, and w represents the width of the rectangle. Plugging in the values, we have:
P = 2(5 + 17) = 2(22) = 44 feet
Therefore, the perimeter of the new garden is 44 feet.
For the function f(x)=[tex]\frac{\sqrt{x} }{5} +2[/tex]
A. ƒ –1(x) = 25(x – 2)2, x ≥ 2
B. ƒ –1(x) = 25x2 – 2, x ≥ 0
C. ƒ –1(x) = 5(x – 2)2, x ≥ 0
D. ƒ –1(x) = 25(x – 2)2, x ≥ 0
Answers
Answer:
[tex]f^{-1}(x)=25(x-2)^2[/tex]
Step-by-step explanation:
The inverse function can be found by solving ...
f(y) = x
(√y)/5 +2 = x
(√y)/5 = x -2 . . . . . subtract 2
√y = 5(x -2) . . . . . . multiply by 5
y = 25(x -2)² . . . . . square both sides
The inverse function is ...
[tex]f^{-1}(x)=25(x-2)^2[/tex]
_____
About the graph
The inverse of a function is its mirror image across the line y = x.
A game has a rectangular board with an area of 44 in2. There is a square hole near the top of the game board in which you must not toss in a bean bag. The square has side lengths of 3 in. What is the probability of not tossing the bag through the hole?
A)9/44
B)3/9
C)3/44
D)35/44
Answers
The probability of not tossing the bag through the hole is D) 35 / 44
How to find the probability ?
To find the probability of not tossing the bean bag through the hole, you need to calculate the area of the board where you can toss the bag and then divide it by the total area of the board.
Find the area where you can toss the bag (not through the hole), subtract the area of the hole from the total area:
Area to toss the bag = Total area - Area of the hole
Area to toss the bag = 44 in² - 9 in²
= 35 in²
Ccalculate the probability of not tossing the bag through the hole:
Probability = (Area to toss the bag) / (Total area)
Probability = 35 in² / 44 in²
Probability = (5 x 7) / (4 x 11)
Probability = 5/4 x 7/11
Probability = (5 x 7) / (4 x 11)
Probability = 35/44
An hour of CFL use consumes 10-2 kWh (kilowatt – hour), if each kilowatthour of electricity use is equivalent to 3.6 X 106 joules of energy, then find out the energy in joules used by the CFL in one hour
Answers
Answer:
[tex]3.6*10^{4}\ joules[/tex] or [tex]36,000\ joules[/tex]
Step-by-step explanation:
Let
x -----> the energy in joules used by the CFL in one hour
we know that
using proportion
[tex]\frac{1}{3.6*10^{6}}\frac{kWh}{joules} =\frac{10^{-2}}{x}\frac{kWh}{joules}\\ \\x=(3.6*10^{6})(10^{-2})\\ \\x=3.6*10^{4}\ joules[/tex]
or
[tex]36,000\ joules[/tex]
Please Help!! 35 Points!!!
Insert <, >, or = to make the sentence true.
12 __ 25
>
=
Answers
[tex]\frac{1}{2}[/tex] > [tex]\frac{2}{5}[/tex]
The wider/open part of the symbol (aka the mouth) faces the larger number, which in this case is [tex]\frac{1}{2}[/tex].
Hope this helped!
~Just a girl in love with Shawn Mendes
A point on the terminal side of an angle theta is given. Find the value of the indicated trigonometric function of theta.
Given (-4,-1), find sec(theta)
Answers
Answer:
-√17/4
Step-by-step explanation:
Because both the x- and the y-coordinates of (-4, -1) are negative, the angle, theta, is in Quadrant III.
tan theta = opp/adj = vertical side / horizontal side = 4/1, or just 4.
The two coordinates are the legs (both shorter than the hypotenuse) of the triangle formed by this terminal side / point.
The length of the hypotenuse is found using the Pythagorean Theorem and is:
√[ (1)² + (4)² = √17.
Again remembering that our terminal side is in Quadrant III,
sin Ф = opp/hyp = -1/√17
cos Ф = adj/hyp = -4/√17
tan Ф = opp/adj = 4 (see discussion above)
The instructions are to "find sec(theta)." The sec function is the inverse of the cos function. Here cos Ф = -4/√17, and so the secant of this angle is
the inverse (reciprocal) of the cosine, and is thus -√17/4
The value of sec(theta) is found by first determining the radius using the Pythagorean theorem and then calculating the reciprocal of the cosine function, which in this case is -√17/4.
Explanation:To find the secant of angle theta (sec(θ)) when given a point (-4,-1) on its terminal side, we first need to understand that sec(θ) = 1/cos(θ). Since cos(θ) is the x-coordinate of the point on the unit circle divided by the radius, we need to find the radius of the circle that would pass through the point (-4, -1). This radius can be found using the Pythagorean theorem.
Let's calculate the radius (r):
r = √((-4)^2 + (-1)^2)
r = √(16 + 1)
r = √17
Now, since the x-coordinate is -4, cos(θ) = -4/r. Plugging in the value of r, we get:
cos(θ) = -4/√17.
Therefore, sec(θ) is the reciprocal of cos(θ):
sec(θ) = -√17/4.
Need help with this one, no clue how to solve this. If someone could explain what's going on like I'm 5 it'd be much appreciated.
Find x.
Answers
Question 10
cos 45 = x/10
cos 45(10) = x
(1/sqrt{2})*10 = x
10/sqrt{2} = x
Rationalize the denominator.
[10/sqrt{2}] • [sqrt{2}/sqrt{2}] = x
10•sqrt{2} ÷ 2 = x
5• sqrt{2} = x
A random sample of 64 freshmen spent an average of 14 hours per week watching television. the sample standard deviation was 32 hours per week. what is the critical value for a 95% confidence interval for the population mean?
Answers
Answer:
+/- 1.9983
Step-by-step explanation:
The critical values for a confidence interval for the population mean, with population standard deviation not known, are obtained from the student's t distribution.
The sample size is given as 64. The degrees of freedom will thus be;
sample size - 1 = 64 - 1 = 63
The confidence level is given as 95%. The level of significance will thus be;
100 - 95 = 5%.
The area in the right-tail will thus be 2.5%. Therefore, we looking for a t-value such that the area to its right is 2.5% and the degrees of freedom being 63. From the t-tables we have;
+/- 1.9983
What is 3/4 times 710?
Answers
Answer:
532.5 or 532[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
3/4 x 710
= 3 x 710 ÷ 4
= 532.5 or 532[tex]\frac{1}{2}[/tex]
Final answer:
To find 3/4 times 710, multiply 710 by 3 to get 2130, then divide that result by 4 to get 532.5. Therefore, 3/4 times 710 equals 532.5.
Explanation:
The question asks for the result of multiplying 3/4 with 710. To perform this calculation we simply take the number 710 and multiply it by the fraction 3/4. Multiplying a whole number by a fraction involves multiplying the numerator of the fraction by the whole number and then dividing the result by the denominator of the fraction.
Here's a step-by-step breakdown:
Multiply the whole number 710 by the numerator of the fraction, 3.710 × 3 = 2130.Divide the result by the denominator of the fraction, 4.
2130 ÷ 4 = 532.5.
Therefore, 3/4 times 710 is 532.5.
The ages of sunitha and raseeda are in ratio of 7:8 ten years from now there ages will be 9:10 find there present age
Answers
Answer:
Sunitha: 35Raseeda: 40Step-by-step explanation:
Both numbers of the ratio units used to express the ratio in ten years are 2 higher than at present. Thus, each ratio unit must stand for 5 years. That would make their current ages ...
Sunitha: 7·5 = 35
Raseeda: 8·5 = 40
_____
If you can't figure the answer right away from the change in ratio units, then you may need to write a couple of equations:
s/r = 7/8(s+10)/(r+10) = 9/10These can be translated to standard form, which may make some methods of solution easier:
7r -8s = 09r -10s = 10These have solution (r, s) = (40, 35).
Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. Determine the period of the function and explain what it represents. Include the maximum and minimum temperatures in your answer.
Answers
Answer with explanation:
Temperature in the living room =68°F
The equation which satisfies ,the room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies
t=2 Cos (0.21 m) +68----------(1)
⇒To determine the period of the function
Z= A cos (sx+q)+r
As period of cos x is 2 π.
So,the given function has period
[tex]=\frac{2\pi}{s}[/tex]
So, the period of function 1, is given by
[tex]=\frac{2\pi}{0.21}[/tex]
⇒The meaning of period of the function is that after every period of [tex]=\frac{2\pi}{0.21}[/tex] the temperature of the room increases or decreases by an integer equal to 2.
⇒Cosine function has maximum value of 1 , and Minimum value of -1.
-1 ≤ Cos x ≤ 1
So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature
And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature
Final answer:
The period of the cosine function used to model the room temperature controlled by a thermostat is about 29.9155 minutes. This is the time it takes for the temperature to complete one full cycle of oscillation between the maximum of 70°F and the minimum of 66°F.
Explanation:
Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. This function describes a cosine wave, typical for oscillator systems like a thermostat regulating room temperature. To determine the period of the function, we examine the cosine part of the equation.
The general form of a cosine function is y = A cos(Bx + C) + D, where the period is 2π/B. Here, A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift. In Felicity's thermostat function, B = 0.21. The period of the function is therefore 2π/0.21, which is approximately 29.9155 minutes. This period represents the time it takes for the room temperature to go from a maximum value back to that value again after one complete cycle.
The max temperature is 2 + 68 = 70°F, and the min temperature is -2 + 68 = 66°F. These represent the highest and lowest temperatures the room will reach with the current thermostat settings.