Final answer:
The probability of drawing a spade, putting it back, and then drawing another spade is 6.25%. This is calculated by multiplying the probability of drawing a spade twice with replacement.
Explanation:
The probability of drawing a spade from a standard deck of 52 cards is 13/52, since there are 13 spades in a deck. If you replace the card and reshuffle, the condition remains the same for the second draw.
Therefore, the probability of drawing another spade is also 13/52. To find the combined probability of two independent events, you multiply the probabilities of both events occurring.
Thus, the probability of drawing a spade, replacing it, and then drawing another spade is:
(13/52) × (13/52)
When you calculate that, you get:
= 169/2704
= 0.0625 or 6.25%
This means that there is a 6.25% chance of drawing a spade, replacing it, and drawing another spade on two consecutive draws from a standard deck of cards.
List the 6 congruency statements given ABC = DEF
Answer:
∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF
Step-by-step explanation:
Given that triangles ABC and DEF are congruent. Now we need to choose correct congruency statements from the given choices.
We know that corresponding angles of congruent triangles are equal so we can write:
∠A ≅ ∠D
∠B ≅ ∠E
∠c ≅ ∠F
We know that corresponding sides of congruent triangles are equal so we can write:
AB = DE
BC = EF
AC = DF
comparing these with given choices we see that, First choice is correct.
The car at each vertex of a Ferris wheel holds a maximum of 5 people. The sum of the measures of the angles of the Ferris wheel is 7740º. What is the maximum number of people that the Ferris wheel can hold?
225
300
250
200
Answer:
225
Step-by-step explanation:
The sum total of all the angles is 7,740 degrees,
The formula for the interior angle is 180(n - 2) where n is the number of sides in the polygon
Set this equal to 7740
180 (n-2) = 7740
Divide each side by 180
180/180 (n-2) = 7740/180
n-2 =43
Add 2 to each side
n-2+2 = 43+2
n = 45
Each vertex hold 5 people so take n and multiply by 5
45*5 = 225
The Ferris wheel holds 225 people
Find the coordinates of the center of the given circle. (x - 5)2 + (y + 3)2 = 25
Answer:
The center is at (5, -3) and the radius is 5
Step-by-step explanation:
The equation for a circle is given by
(x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center of the circle and r is the radius of the circle.
(x - 5)2 + (y + 3)2 = 25
Rewriting the equation
(x - 5)2 + (y - -3)2 = 5^2
The center is at (5, -3) and the radius is 5
When the lights go out at the store at night there's a 15% off sign hanging out by the make up counter what is a number as a decimal and a fraction in simplest form
Answer:
As per the given statement: when the lights go out at the store at night there's a 15% off sign hanging out by the make up counter.
To find the number as a decimal and a fraction in simplest form.
Given the Number = 15%.
If we convert any number from percent to decimal divide by 100 and remove the % sign.
[tex]\frac{15}{100} = 0.15[/tex]
Then the given number in decimal is, 0.15
Now, to convert this percent into fraction;
[tex]\frac{15}{100}[/tex]
Divide both numerator and denominator by 5 to get;
[tex]\frac{\frac{15}{5} }{\frac{100}{5} } = \frac{3}{20}[/tex]
Therefore, the given number in fraction is; [tex]\frac{3}{20}[/tex]
Leah loves chicken wings and is comparing the deals at three different restaurants. Buffalo Bills has 88 wings for \$7$7. Buffalo Mild Wings has 1212 wings for \$10$10. Wingers has 2020 wings for \$17$17. Which restaurant offers the lowest price per wing?
Answer:
Buffalo mild wings offers the lowest price per wing ($0.83).
Step-by-step explanation:
Let us find unit price per buffalo wing of each restaurant.
[tex]\text{Unit rate for buffalo bills}=\frac{\$7}{8\text{ wings}}[/tex]
[tex]\text{Unit rate for buffalo bills}=\frac{\$0.875}{\text{ wing}}[/tex]
Upon rounding our answer to nearest cent we will get,
[tex]\text{Unit rate for buffalo bills}=\frac{\$0.88}{\text{ wing}}[/tex]
Therefore, buffalo bills offers each wing for $0.88.
[tex]\text{Unit rate for buffalo mild wings}=\frac{\$10}{12\text{ wings}}[/tex]
[tex]\text{Unit rate for buffalo mild wings}=\frac{\$0.83333}{\text{ wing}}[/tex]
Upon rounding our answer to nearest cent we will get,
[tex]\text{Unit rate for buffalo mild wings}=\frac{\$0.83}{\text{ wing}}[/tex]
Therefore, buffalo mild wings offers each wing for $0.83.
[tex]\text{Unit rate for wingers}=\frac{\$17}{20\text{ wings}}[/tex]
[tex]\text{Unit rate for wingers}=\frac{\$0.85}{\text{ wing}}[/tex]
Therefore, wingers offers each wing for $0.85.
We can see that buffalo mild wings offers the lowest price per wing that is $0.83 per wing.
help? anyone please thank youuuuuuuuu
Is it asking about the slope of this vertical line? if so, then the answer is "undefined". The rise is any number you want, let's say 1, and the run is 0
slope = rise/run = 1/0 = undefined
you cannot divide by zero
A convex polyhedron has 6 vertices and 12 faces. How many edges does it have?
Please help me and I will give you the Brainliest answer
Answer:
16 edges.
Step-by-step explanation:
We will use Euler's polyhedron formula to solve for the edges of our convex polyhedron.
Euler's polyhedron formula is: [tex]V+F-E=2[/tex], where,
V= Vertices of polyhedron,
F= Faces of polyhedron,
E= Edges of polyhedron.
Let us substitute V=6 and F=12 in Euler's formula to find number of edges of our polyhedron.
[tex]6+12-E=2[/tex]
[tex]18-E=2[/tex]
Let us subtract 18 from both sides of our equation.
[tex]18-E-18=2-18[/tex]
[tex]-E=2-18[/tex]
[tex]-E=-16[/tex]
[tex]E=16[/tex]
Therefore, our convex polyhedron will have 16 edges.
How are vectors used in real life?
Answer:
Vectors can be used in sports to define how a baseball player moves to catch a high fly baseball they can also be used with aircrafts.
Remember that science uses vectors to describe anything that has both a direction and a magnitude (size or quantity). These are drawn as pointed arrows, which length represents the magnitude. They are very used to locate persons or objects as the final direction can be predicted using a reference point, an stimated speed and direction. Vectors are also usefull to predict what would happen if two objects come into contact, an example would be predicting the movement of billiard balls, or calculating the trajectory of a golf ball.
Matt has a full jar of marbles he gave Kayla 3/4 and Marbles and Kayla return 1/3 of the jars worth of Marvel's to the jar how much are the jars now full marbles
Answer:
Matt has 7/12 of the jar of marbles left.
Step-by-step explanation:
In order to find this, simply subtract the 3/4 from the full jar (1) and then add 1/3. They will need common denominators to complete this operation.
1 - 3/4 + 1/3 = Amount
12/12 - 9/12 + 4/12 = Amount
7/12 = Amount
In a right triangle ?ABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find: The median to side BC The length of the angle bisector of angle ?A.
Answer:
Median is sqrt61
Step-by-step explanation:
Calculate s26 for the arithmetic sequence in which a14=4.1 and the common difference is d=1.7
Answer:
The value of [tex]s_{26}=84.5[/tex]
Step-by-step explanation:
We have given [tex]a_{14}=4.1[/tex]
d=1.7
We have to find [tex]s_{26}[/tex]
So, [tex]a_{14}=a+13d[/tex] from the formula
[tex]a_n=a+(n-1)d[/tex]
When n=14
[tex]a_{14}=a+(14-1)(1.7)=a+13(1.7)[/tex]
[tex]4.1=a+22.1[/tex]
[tex]-18=a[/tex]
[tex]a=-18[/tex]
Using the formula:
[tex]s_n=\frac{n}{2}[2a+(n-1)d[/tex]
When n=26
[tex]s_{26}=\frac{26}{2}[2(-18)+(26-1)(1.7)][/tex]
On simplification we get:
[tex]s_{26}=84.5[/tex]
The order of several matrices are given. A = 3x2 B = 3x5 C = 2x3 D = 5x7 E = 3x5 Which can be multiplied?
Answer:
A/C and B/D and C/E
Step-by-step explanation:
given the order of 2 matrices
(m × n)(p × q)
For the matrices to be conformable for multiplication
The number of columns in the first must equal the number of rows in the second
That is n = p and the resulting product has order m × q
From the order of matrices given
A and C, B and D, C and E can be multiplied
The matrices that can be multiplied are A*C, C*A, B*D, and E*D, as the number of columns in the first matrix equals the number of rows in the second.
Explanation:In matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Therefore, given the order of the matrices A = 3x2, B = 3x5, C = 2x3, D = 5x7, and E = 3x5, the possible matrix multiplications are: A*C, C*A, B*D, and E*D. For instance, you can multiply A (which is 3x2) with C (which is 2x3) because the number of columns in matrix A is equal to the number of rows in matrix C.
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Taylor Scuff leased a new sports car and is certain she can keep under the 12,000 miles allowed a year. The $2,200 due at signing includes the title and license fee. Her monthly lease payments are $700 a month. If the total lease cost is $27,400, for how many months does the lease last?
Answer:
The number of months does the lease last are 36 months.
Step-by-step explanation:
Let us assume that the number of months be x.
As given
Taylor Scuff leased a new sports car and is certain she can keep under the 12,000 miles allowed a year.
The $2,200 due at signing includes the title and license fee.
Her monthly lease payments are $700 a month.
If the total lease cost is $27,400.
Than the equations becomes
2200 + 700x = 27400
700x = 27400 - 2200
700x = 25200
[tex]x = \frac{25200}{700}[/tex]
x = 36
Therefore the number of months does the lease last are 36 months.
help picture down here
Answer:
it would be 8 hours
Answer:
I got 7.2 hours
Step-by-step explanation:
make a proportion such as 5/12=3/x and cross multiply then solve the rest
what is 14.5% of 8600 meters?
Answer: 1.247 kilometers
Step-by-step explanation: multiply 8600 by 0.145 so 8600 times 0.145=1247
Carly drove cross-country on vaction. Her average speed was 56 miles per hour. How far did she go in 24 hours?
Answer:
1344 miles
Step-by-step explanation:
using the relationship between distance/ speed / time
distance = speed × time, then
distance = 56 × 24 = 1344 miles travelled
To determine the distance traveled, we use the formula 'Distance = Speed x Time'. Based on Carly's average speed of 56 miles per hour for 24 hours, she traveled a total of 1,344 miles.
Explanation:In this problem, we're being asked to calculate how far Carly drove across the country in 24 hours if her average speed was 56 miles per hour. To find the distance she traveled, we can make use of the formula Distance = Speed x Time. So, for this particular situation:
Distance = 56 mph x 24 hours = 1,344 miles
Therefore, Carly drove 1,344 miles in 24 hours with an average speed of 56 miles per hour.
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A tiger can eat food that weighs up to 15% of its body weight.If a tiger can eat 75 pounds of food, how much does a tiger weigh?
Answer:
500 pounds
Step-by-step explanation:
By proportion :-
15% of the tigers weight = 75 pounds
1% .................................... = 75/15 pounds
100% .................................. = 75*100 / 15 pounds
= 7500 / 15
= 500 pounds
PLEASE HELP ASAP WILL MARK BRAINLYIST
SEE PICTURES
Answer:
Problem One: D
Problem Two: B
Step-by-step explanation:
Problem One
A and B are both wrong for the same reason. The graph for both of them will increase. Any time you raise a base greater than 1 to a power, the graph goes up. See below. The red graph is y = 12*1.1^2
The question is giving you a big hint by showing you which point to look at. When x = 1, y = 8. What will do that?
Is it 12 * 1/2 or is it 12 * 2/3
I think you will find it is 12*2/3 So the answer is D
Part B
This one is just the opposite, only now you have to figure out which graph you are getting. A is the only one that is obviously wrong. When x = 1, A will give
40* 1.5 which is 60 which is not enough.
C is too large. 40 * 3.25 = 130 so that does not describe the graph when x = 1.
So B and D are your only choices. D is still a little too big. See if you can get D to be 100 when D = 1
That leaves you with b
y = 40 * 2.25 = 90 which is just what you want.
The lengths of two sides of a triangle are 3 inches in 8 inches find the range of possible links for the third side S
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
1. a ≤ 3 ≤ 8 then a + 3 > 8 → a > 8 - 3 → a > 5 FALSE, because a ≤ 3.
2. 3 ≤ a ≤ 8 then 3 + a > 8 → a > 5 therefore 5 < a ≤ 8
3. 3 ≤ 8 ≤ a then 3 + 8 > a → 11 > a → a < 11 therefore 8 ≤ a < 11.
Answer: 5 < a < 11 → S = (5, 11)The range of possible links for the third side s is 5 < s < 11
What is a triangle ?A triangle is a polygon with three sides , three vertices and three angles.
It is known that if a, b and c are the lengths of the sides of a triangle and
then
a + b > c
b+c > a
c+a > b
Then the length of the third side lies between
8-3 < s < 8+3
5 < s < 11
Therefore the range of possible links for the third side s is 5 < s < 11
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You buy clothing at a sale.You buy sneakers at 2/3 of their original price of $60, a sweater at 7/10 of it original price of $35, and a jacket at 5/6 of its original price of $45.
a. How much money did you spend?
b. How much money did you save?
c. What fraction of the total original price did you save?
Answer:
a. $102 b. $38 c. 19/70.
Step-by-step explanation:
a. You spent 2/3 * 60 + 7/10 * 35 + 5/6 * 45
= $102.
b. Cost before the sale discount = 60 + 35 + 45 = $140 , so the amount you saved = 140 - 102 = $38.
c. Fraction on original price saved = 38/140 = 19/70.
Money spent is $102. Money saved is $38. The fraction of the total original price saved is 19/70.
a. How much money did you spend?
Sneakers: 2/3 of $60 = $40
Sweater: 7/10 of $35 = $24.50
Jacket: 5/6 of $45 = $37.50
Total spent = $40 + $24.50 + $37.50 = $102
b. How much money did you save?
Original total price = $60 + $35 + $45 = $140
Amount saved = $140 - $102 = $38
c. What fraction of the total original price did you save?
Fraction saved = Amount saved / Total original price = $38 / $140 = 19/70
Write a linear equation in slope intercept form to model the situation and internet company charges $4.95 per month plus $2.50 for each hour of use how much would it cost in a month when you use the internet for 14 hours
Answer:
it cost $39.95 in a month when you use the internet for 14 hours
Step-by-step explanation:
internet company charges $4.95 per month plus $2.50 for each hour
Let x be the amount of hours internet used
for 1 hour, charge is 2.50
for x hours , charge is 2.50x
To get linear equation we use y=mx+b
m is the slope and b is the fixed cost
fixed cost b= 4.95 and slope m = 2.50
So equation becomes y = 2.50x + 4.95
we need to find the cost y for 14 hours
So we plug in 14 for x and find out y
y = 2.50(14) + 4.95= 39.95
Final answer:
The linear equation to model the monthly cost of internet use is y = 4.95 + 2.50x. For using the internet for 14 hours, the total cost would be $39.95.
Explanation:
The student is asking for a linear equation in slope-intercept form to model the monthly cost of internet usage based on the number of hours used. The internet company charges a monthly subscription fee plus an additional fee per hour of use. The equation to represent this situation is y = 4.95 + 2.50x, where y represents the total monthly cost in dollars and x represents the number of hours the internet is used. To calculate the cost for 14 hours of use in a month, we substitute x with 14: y = 4.95 + 2.50(14), which equals $39.95 for the month.
Stefan sells jin a bicycle for $114 and a helmet for $18. The toltal cost for jin is 120% of what stefan spent originally to buy the bike and helmet. How much did stefan spend originally? How much money did he make by selling the bicycle and helmet to jin?
Answer:
Stefan spend originally $110 and the money stefan make by selling the bicycle and helmet to jin is $22 .
Step-by-step explanation:
As given
Stefan sells jin a bicycle for $114 and a helmet for $18.
Total cost of the bicycle and helmet = $114 + $18
= $132
The total cost for jin is 120% of what stefan spent originally to buy the bike and helmet.
120% is written in the decimal form.
[tex]= \frac{120}{100}[/tex]
= 1.20
Let us assume that the Stefan spend originally for bike and helmets be x.
Than the equation becomes
1.20 × x = 132
1.20x = 132
[tex]x = \frac{132}{1.20}[/tex]
x = $110
Therefore stefan spend originally be $110 .
Now find out how much money did he make by selling the bicycle and helmet to jin .
Money make by Stefan = Total selling cost of helmet and bicycle - Total amount of stefan spends for purchasing.
Money make by Stefan = 132 - 110
Money make by Stefan = $22
Therefore the money stefan make by selling the bicycle and helmet to jin is $22 .
Stefan's original expenditure for the bicycle and helmet was $110. He made a profit of $22 by selling these items to Jin.
Explanation:Stefan sold the bicycle and helmet to Jin for a total of $132 ($114 + $18). We know that this amount represents 120% of what Stefan originally spent. To determine Stefan's original expenditure, we'll therefore divide the total amount he earned by 120 and then multiply by 100 (as the cost is 100% for him). So, Stefan's original expenditure would be (132/120)*100 = $110.
Now, to determine Stefan's profit, we subtract his original expenditure from the amount for which he sold the items to Jin. That is, $132 - $110 = $22. So, Stefan made a $22 profit from selling the bicycle and helmet.
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A clothing store has a going-out-of business sale. They are selling pants for $8.99 and shirts for $3.99. You can spend as much as $60 and want to buy at least two pairs of pants.
The question deals with budgeting $60 to buy as many pants and shirts as possible, with at least two pairs of pants to be bought. After purchasing two pairs of pants, the remaining budget can be divided by the price of the remaining item to get the possible quantity.
Explanation:The subject of this question is
Mathematics
, specifically budgeting and maximizing purchases under a fixed budget. You have $60 to spend and each pair of pants costs $8.99, while shirts cost $3.99. If you want to buy at least two pairs of pants, your initial expense will be $8.99 x 2 = $17.98. After buying two pairs of pants, you will have $60 - $17.98 = $42.02 left to spend on either more pants or shirts. Divide this remaining amount by the price of the item you want to buy more of (either pants or shirts) to see how many more items you can purchase. Remember to round the result down to the nearest whole number, since you can't buy a fraction of an item.
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Which radical expression represents the perimeter of a triangle if the side lengths of the triangle are given by the expressions 13√80 , 3√125, and √500 ? A) 16 √5 B) 26√5 C) 39√5 D) 77√5
Answer:
D
Step-by-step explanation:
so basically to add up radicals you need to make the number inside the square root the same. what you have to do to do that is find squares inside the number as a factor.
13√80=13*2√20=13*2*2√5=52√5
3√125=3*5√5=15√5
√500=10√5
so all of them have 5 in the square root so you can add them up to equal 77√5
To find the perimeter of a triangle with given radical expressions for side lengths, simplify each expression and add them up. The correct answer is D) 77√5.
Explanation:The perimeter of a triangle is the sum of the lengths of all three sides. So, to find the perimeter of the triangle given the side lengths as radical expressions, we need to simplify and add them up.
The given side lengths are: 13√80 , 3√125, and √500.
Simplify each radical expression:
13√80 = 13 * √(16 * 5) = 13 * (4 * √5) = 52√5
3√125 = 3 * √(25 * 5) = 3 * (5 * √5) = 15√5
√500 = √(100 * 5) = 10√5
Now, add up the simplified radical expressions: 52√5 + 15√5 + 10√5 = (52 + 15 + 10)√5 = 77√5.
Therefore, the correct answer is D) 77√5, which represents the perimeter of the triangle.
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Sonya wants to sew ribbon along each side of a square pillow. If the pillow has an area of 144 square inches, how much ribbon would she buy to have the exact amount she needs
Monica has a bag of marbles. There are 4 red marbles and 7 blue marbles and 5 yellow marbles in a bag. Monica will randomly pick two marbles out of the bag replacing the first marble before picking the second marble. What is the probability of Monica picking a red and then blue marble?
Answer:
[tex]\frac{7}{64}\approx 0.11[/tex]
Step-by-step explanation:
We have been given that there are 4 red marbles and 7 blue marbles and 5 yellow marbles in a bag. Monica will randomly pick two marbles out of the bag replacing the first marble before picking the second marble.
Since Monica will replace the first marble before picking the second marble, therefore, probability of both events will be independent and probability of occurring one event will not affect the probability of second event's occurring.
Since the probability of two independent compound events is always the product of probabilities of both events.
[tex]P(\text{A and B})=P(A)*P(B)[/tex]
Now let us find probability of picking a red marble out of 16 (4+7+5) marbles.
[tex]P(Red)=\frac{\text{Total red marbles}}{\text{Total marbles}}[/tex]
[tex]P(Red)=\frac{4}{16}[/tex]
Probability of picking blue ball out of 16 (4+7+5) marbles:
[tex]P(Blue)=\frac{\text{Total blue marbles}}{\text{Total marbles}}[/tex]
[tex]P(Blue)=\frac{7}{16}[/tex]
Now let us find probability of Monica picking a red and then a blue marble.
[tex]P(\text{Red and Blue})=\frac{4}{16}\times \frac{7}{16}[/tex]
[tex]P(\text{Red and Blue})=\frac{1}{4}\times \frac{7}{16}[/tex]
[tex]P(\text{Red and Blue})=\frac{7}{4*16}[/tex]
[tex]P(\text{Red and Blue})=\frac{7}{64}[/tex]
[tex]P(\text{Red and Blue})=0.109375\approx 0.11[/tex]
Therefore, the probability of picking a red and then blue marble is [tex]\frac{7}{64}\approx 0.11[/tex].
A theme park has a tram that goes around the 2.5-mile perimeter of the park in 10 minutes. The equation s • (16) = 2.5 gives the speed of the tram. What exactly does s represent?
s in the expression s • (16) = 2.5 represents the speed in miles per hour.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
here,
A theme park has a tram that goes around the 2.5-mile perimeter of the park in 10 minutes.
So,
Speed = 2.5 miles / 10 minutes
Since, 1 hour = 60 minutes,
And 1 minute = 1/60 hours,
Now, converting the unit of speed of tram from miles per minute to miles per hour where,
Speed = 2.5 miles / 10 (1/60 hours)
Speed = s (say)
s = 2.5/ (1/6)
s (1/6) = 2.5
hence, s in the above expression represents the speed.
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Final answer:
The symbol 's' in the equation represents the speed of the tram in miles per minute
Explanation:
The student's question involves solving for the speed s of a tram that goes around the perimeter of a theme park. The equation provided is s (16) = 2.5, where s represents the speed of the tram in miles per minute. To find the value of s, we need to divide both sides of the equation by 16, which yields:
s = 2.5 / 16
Now, performing the division gives us:
s = 0.15625
Therefore, the speed of the tram is 0.15625 miles per minute.
Help please!!
For the following graph, what type of discontinuity occurs at x = 6 and what step of continuity is broken?
A) infinite and f(6) does not exist.
B) removable and f(6) does not exist.
C) jump and limx→6− f(x) ≠ limx→6+ f(x).
D) infinite and limx→6− f(x) ≠ limx→6+ f(x).
Answer:
A) Infinite and f(6) does not exist
Step-by-step explanation:
The three types of discontinuities are:
1. Removable or Hole: When the left hand limit is same as right hand limit but they are not equal to the value of function at x = 6.
Graphically if there exist a hole at the point x = 6, removable discontinuity occurs. But, it is not the case in the given graph.
2. Jump: When the left hand limit is not same as right hand limit.
But graphically, we see that both left and right limit at x=6 are tending to infinity i.e. both limits are same.
3. Infinite: It occurs when there exists vertical or horizontal asymptotes between the function and both limits tend to infinity.
Graphically, we see that the function has infinite discontinuity as there exist vertical asymptote and the value of function does not exist at x = 6.
Given sin(−θ)=−1/4 and tanθ=√15/15 . What is the value of cosθ ?
Answer:
[tex]\cos\left(\theta\right)=\frac{\sqrt{15}}{4}[/tex]
Step-by-step explanation:
Given that [tex]\sin\left(-\theta\right)=-\frac{1}{4}[/tex] and [tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex]
Using those values we need to find value of [tex]\cos\left(\theta\right)[/tex]
So let's begin with equation of [tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex] and simplify it to get value of [tex]\cos\left(\theta\right)[/tex]
[tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex]
[tex]\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}=\frac{\sqrt{15}}{15}[/tex]
[tex]\sin\left(\theta\right)=\frac{\sqrt{15}}{15}\cos\left(\theta\right)[/tex]
[tex]\sin\left(\theta\right)\cdot\frac{15}{\sqrt{15}}=\cos\left(\theta\right)[/tex]
[tex]\cos\left(\theta\right)=\sin\left(\theta\right)\cdot\frac{15}{\sqrt{15}}[/tex]
[tex]\cos\left(\theta\right)=-\sin\left(-\theta\right)\cdot\frac{15}{\sqrt{15}}[/tex] {since [tex]\sin\left(-\theta\right)=-\sin\left(\theta\right)[/tex] }
[tex]\cos\left(\theta\right)=-\sin\left(-\theta\right)\cdot\sqrt{15}[/tex]
[tex]\cos\left(\theta\right)=-\left(-\frac{1}{4}\right)\cdot\sqrt{15}[/tex]
[tex]\cos\left(\theta\right)=\frac{\sqrt{15}}{4}[/tex]
Answer:
[tex]\cos \theta = \frac{\sqrt{15}}{4}[/tex]
Step-by-step explanation:
The sine function is an odd function, that is:
[tex]\sin (-\theta) = - \sin \theta[/tex]
Then,
[tex]\sin \theta = \frac{1}{4}[/tex]
The cosine function is computed by the following relation:
[tex]\cos \theta = \frac{\sin \theta}{\tan \theta}[/tex]
[tex]\cos \theta = \frac{\frac{1}{4} }{\frac{\sqrt{15}}{15} }[/tex]
[tex]\cos \theta = \frac{\frac{1}{4} }{\frac{1}{\sqrt{15}} }[/tex]
[tex]\cos \theta = \frac{\sqrt{15}}{4}[/tex]
The original selling price of a single share of stock was d dollars. The selling price for a share of the same stock on a later date was represented by the expression 0.8(1.25d). Which description could explain what happened to the price of the share of stocks? A. The price increased by 25% and then decreased by 20%. B. None C. The price increased by 1.35% and then decreased by 15%. D. The price increased by 135% and then decreased by 85%. E. The price increased by 35% and then decreased by 0.15%.
Answer:
A
Step-by-step explanation:
The expression 1.25 d means 100% of the price +25% of the price. This means it increased by 25%. Multiplying it by 0.8 means it's value is only 80% of the value now which means it must of had a 20% decrease after increasing. It's now at it's original price.