Base your answer to the question on the diagrams shown below.
What is the probability of drawing a red card and then spinning a 1?
Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
From the given picture, the total number of cards = 5
The number of red card = 2
Thus, the probability of drawing a red card P(red)=[tex]\frac{2}{5}[/tex]
Also, total number of digits on spinner = 8
Number of 1's=4
Thus, the probability of spinning a 1 P( spinning 1)=[tex]\frac{4}{8}=\frac{1}{2}[/tex]
Since both the events of drawing a red card and spinning a 1 are independent events, therefore, the probability of drawing a red card and then spinning a 1=[tex]\text{ P(red)}\times\text{P( spinning 1)}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}[/tex]
2. Which of the following is equivalent to 5455 cm3?
(
0.5455 L
5.455 L
54.55 L
5455 L
A line passes through the points (-6,4) and (-2,2). Which is the equation of the line?
Answer:
The equation of the line is [tex]y=\frac{-1}{2}x+1[/tex]
Step-by-step explanation:
1. The equation of the line that passes through two points can be expresed as:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex] (Eq.1)
where [tex]x_{1}[/tex], [tex]x_{2}[/tex], [tex]y_{1}[/tex] and [tex]y_{2}[/tex] are the given points.
2. Name the points:
[tex]x_{1}[/tex]=-6
[tex]x_{2}[/tex]=-2
[tex]y_{1}[/tex]=4
[tex]y_{2}[/tex]=2
3. Replace the points in the Eq.1:
[tex]\frac{y-4}{x-(-6)}=\frac{2-4}{-2-(-6)}[/tex]
[tex]\frac{y-4}{x+6}=\frac{2-4}{-2+6}[/tex]
[tex]\frac{y-4}{x+6}=\frac{-2}{4}[/tex]
[tex]\frac{4(y-4)}{x+6}=-2[/tex]
[tex]4(y-4)=-2(x+6)[/tex]
[tex]4y-16=-2x-12[/tex]
[tex]4y=-2x-12+16[/tex]
[tex]4y=-2x+4[/tex]
[tex]y=\frac{-2x+4}{4}[/tex]
[tex]y=\frac{-2x}{4}+\frac{4}{4}[/tex]
[tex]y=\frac{-1}{2}x+1[/tex]
If the radius of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?
a. 3 7 π inches
b. 7 2 π inches
c. 7 3 π inches
d. 7 6 π inches
The correct answer to this problem C.)7/3
What is the best first step in solving the equation 4 + squrt(6x) = 5?
Help on both 13 and 14. Show work please
1. For which angle is secant undefined?
a. 30°
b. 45°
c. 180°
d. 270°
2. Which of the following is csc(-166°) equal to?
a. csc(14°)
b. -csc(14°)
c. -csc(-14°)
d. csc(166°)
1. The secant is defined as the inverse function of co-secant or cos function
Hence when the cosine is 0, the secant is 1/0 which is undefined. So, when cosine is 0, secant is undefined
Cos 30 = [tex] \sqrt{3} /2 [/tex]
Cos 45 = [tex] 1/\sqrt{2} [/tex]
Cos 180 = -1
cos 270 =0
Since cos 270 is 0, secant of 270 is undefined
Answer is d: 270
2. cosec (-x) = - cosec (180 -x)
We have cosec(-166) = - cosec (180-14) = -cosec (14)
Alternatively we can confirm this as csc (-166) = -4.133565 and -csc(14) = -4.133565; Hence, we can reconfirm that the answer arrived at is right
Therefore csc (-166) = -csc(14) (Option B) is the right answer
The equation $1.50p + $5.00 = $14.00 shows the total cost of picking p pounds of blueberries at a local blueberry farm. how many pounds of blueberres were picked/
How to find the sum of the squares of the lengths of the legs of a triangle of a=(-6,11) b=(2,8) c=(-1,0)?
To find the sum of the squares of the lengths of the legs of a triangle, use the distance formula to calculate the length of each leg and then square these lengths, summing the squares of the two legs that do not form the hypotenuse.
Explanation:To find the sum of the squares of the lengths of the legs of a triangle with vertices A=(-6,11), B=(2,8), and C=(-1,0), we first calculate the length of each leg using the distance formula, which is √((x2-x1)² + (y2-y1)²). For AB, AC, and BC we find distances:
AB = √((-6-2)² + (11-8)²)AC = √((-6+1)² + (11-0)²)BC = √((2+1)² + (8-0)²)Then, we square each leg's length:
AB² = ((-6-2)² + (11-8)²)AC² = ((-6+1)² + (11-0)²)BC² = ((2+1)² + (8-0)²)Finally, we sum up the squares of AB and AC because they represent the legs of the triangle:
Σ(leg squares) = AB² + AC²The sum of the squares of the lengths of the legs has now been found.
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Randall bought a bond with a face value of $6000 and a coupon rate of 7.25%. the bond will mature in 5 years. how much interest will he receive semiannually?
Answer:
Face value of bond = $ 6000
Rate of interest =7.25 %
The Bond will mature in 5 years.
If the interest is semiannually , the rate of interest will reduce to half.
So, new rate of interest will be [tex]\frac{7.25}{2}=3.625[/tex]
Formula for simple interest
[tex]=\frac{\text{Principal}\times Rate \times time}{100}[/tex]
Interest after 6 months will be
[tex]=\frac{6000 \times 3.625 \times 1}{100}\\\\=60 \times 3.625\\\\=217.5[/tex]
So, interest that Randall will receive after six months = $ 217.50
Please help :)
Solve the system of equations and choose the correct answer from the list of options.
d + e = 1
−d + e = −5
Label the ordered pair as (d, e). (4 points)
(0, 0)
(3, −2)
(−2, 3)
(−3, 0)
(3, -2)
Given equations are
d+e=1
-d+e=-5
We need to find d and e.
What is system of equations?A system of equations is a set of one or more equations involving a number of variables
The system of equations are
d+e=1....(1)
-d+e=-5....(2)
d=1-e (from 1)
Substitute d in (2)
-(1-e)+e=-5
-1+e+e=-5
-1+2e=-5
2e=-5+1
2e=-4
e=-2
Now substitute value of e in (1)
d-2=1
d=1+2
d=3
Therefore the ordered pair for d + e = 1 and −d + e = −5 is (3, -2)
i.e value of d=3 and e=-2
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Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
A. y = –x + 1
B. 3x − 4y = −4
C. 4x − 3y = −3
D. y – 2 = –(x – 4)
E. y + 2 = (x + 4)
Find the first five terms of the sequence: an = 5an – 1 + 2; a1 = 3.
a) {3, 17, 87, 437, 2187}
b) {3, 15, 75, 375, 1875}
c) {3, 12, 17, 22, 27}
d) {3, 11, 27, 59, 123}
What is the 12th term of the sequence?
3, −9, 27, −81, 243, ...
The 12th term of the sequence 3, -9, 27, -81, 243, ... is 177,147.
Explanation:The given sequence is: 3, -9, 27, -81, 243, ...
To find the 12th term, we can observe that the sequence alternates between positive and negative, and each term is obtained by multiplying the previous term by -3. Starting with 3 as the first term, we can find the 12th term using the formula:
an = a1 * (-3)n-1
Substituting the values, we have:
a12 = 3 * (-3)12-1a12 = 3 * (-3)11a12 = 3 * (-32)5a12 = 3 * 95a12 = 3 * 59049a12 = 177,147Final answer:
The 12th term of the geometric sequence is -531441, found by using the formula for the nth term of a geometric series with a first term of 3 and a common ratio of -3.
Explanation:
The sequence given is geometric with each term being multiplied by -3 to obtain the next term. To find the 12th term of the sequence, we can use the formula for the nth term of a geometric sequence: Tn = a * rn-1, where a is the first term, r is the common ratio, and n is the term number.
For the given sequence, the first term a is 3 and the common ratio r is -3. The 12th term is found by placing these values into the formula:
T12 = 3 * (-3)12-1
T12 = 3 * (-3)11
T12 = 3 * (-177147)
T12 = -531441
Therefore, the 12th term of the sequence is -531441.
Anna has leaned a ladder against the side of her house. The ladder forms a 72º angle with the ground and rests against the house at a spot that is 6 meters high. What length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?
Answer:
The best approximation of AB is 2 meters.Step-by-step explanation:
Notice that this situation models a right triangle, when the height, which is a leg of the triangle, is 6 meters.
Also, we know the angle between the ladder and the ground, which is 72°.
To find the distance from A to B, which from the bottom of the ladder to the bottom of the wall, we just need to use trigonometric reasons.
[tex]tan(72\°)=\frac{opposite \ leg}{adjacent \ leg}[/tex]
Why we use tangent? Because it relates both legs where we just need to find the adjacent one.
[tex]tan(72\°)=\frac{6}{AB}\\AB=\frac{6}{tan(72\°)} \\AB \approx \frac{6}{3} \\AB \approx 2 \ m[/tex]
Therefore, the best approximation of AB is 2 meters.
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years. Five years after Brian's initial investment, Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar)
Compound interest formula is [tex]A = P(1+r)^t[/tex]
Where P is the principal amount
r is the rate of interest
t is number of years
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years
P = 10,000 , r= 4% = 0.04 , t =10
Plug in all the values
[tex]A = 10000(1+0.04)^{10}[/tex] = 14,802.44
Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.
P = 10,000 , r= 7% = 0.07 , t =5
Plug in all the values
[tex]A = 10000(1+0.07)^5[/tex] = 14,025.52
Brian balance after the interest period = $ 14,802.44
Chris balance after the interest period = $ 14,025.52
Balance in Brian's account is more than Chris account
A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
pair of intersecting lines
degenerate ellipse
degenerate hyperbola
line
point
degenerate parabola
Answer:
degenerate hyperbola
pair of intersecting lines
Step-by-step explanation:
There was a sample of 200 milligrams of a radioactive substance to start a study. since then, the sample has decayed by 5.4% each year. let t be the number of years since the start of the study. let y be the mass of the sample in milligrams. write an exponential function showing the relationship between y and t .
The exponential function representing the relationship between the mass y of a radioactive sample in milligrams and t years since the start of the study is y = 200(1 - 0.054)^t.
The student is given a starting mass of a radioactive substance and the percentage of the mass that decays each year. To write an exponential function that models this situation, we consider the initial mass, which is 200 milligrams, and the decay rate, which is 5.4% per year. The relationship between the mass y and the time t in years can be represented by the formula y = 200(1 - 0.054)^t.
Using an exponential decay model, we understand that the amount of substance decreases by a certain percentage each year. To account for this, we raise the base (1 - 0.054) to the power of t, representing the number of years, which gives us the factor by which the original mass has reduced.
What's the diameter of a cirlce eith an area of 615.75?
What is the equation of the line that passes through (7, 4) and (4, -2)?
a) y = 2x - 10
b) y = -2x - 10
c) y = -2x + 18
d) y = 2x + 18
Solution:
we have been asked to find the equation of the line that passes through (7, 4) and (4, -2).
First we will find the slope of the line using the formula
[tex] m=\frac{y_2-y_1}{x_2-x_1} [/tex]
Plugin the given values we get
[tex] m=\frac{-2-4}{4-7}=\frac{-6}{-3}=2 [/tex]
Now using the point slope form of a straight line
[tex] (y-y_1)=m(x-x_1) [/tex]
Plugin the values
[tex] (y-4)=2(x-7)\\
\\
y=2x-14+4\\
\\
y=2x-10\\ [/tex]
Hence the correct option is a.
A student takes a 15 question
a. True
b. False quiz and guesses at every answer. what is the probability that the student gets exactly 10 questions right, given that the student got the first question right?
ABC Bookstore sells new books, n, for $12, and used books, u, for $8. The store earned $112 revenue last month. The store sold 4 more used books than new books. Using the substitution method, how many new and old books did ABC bookstore sell?
A.n = 4; u = 8
B.n = 8; u = 4
C.n = 8; u = 12
D.n = 12; u = 8
Due tomorrow help please
which graph shows the solution set of the compound inequality 1.5x-1>6.5 or 7x+3<-25
Answer:
It's B
Step-by-step explanation:
Whats the distance between points C(0, 4), T(-6, -3)
a √(37)
b √(85)
c √(109)
what is the height of the beach sign?
and what is the height of the beach umbrella?
I'm not sure if both images were attached, oops. but please help! I'll mark as brainliest! thank you!
A cylindrical tank has a radius of 4.5 ft and an altitude of 14 ft. If a gallon of paint will cover 130 ft squared ft2 of surface, how much paint in gallons is needed to put two coats of paint on the entire surface of the tank? Aswer: To put two coats of paint on the entire surface of the tank, ______ full gallons of pain are needed.
Books spontaneously catch on fire in temperatures at or above 451, degree Fahrenheit. Write an inequality that is true only for temperatures (t)(t)left parenthesis, t, right parenthesis at which books spontaneously catch on fire.
Compare the exponential and logarithmic models of population growth
What is the domain for the piece of the function represented by f(x) = x + 1?
Answer:
All real numbers
Step-by-step explanation:
The domain of the function represented by f(x) = x + 1 is the all real numbers as there is only addition involved in the function so putting any number as input will not lead the function to infinity.