Answer: $ 16.96
Step-by-step explanation:
Here, the present value of the loan, PV = $695.20
Annual Interest rate = 17.9%
⇒ Monthly interest rate = 17.9/12 = 1.41666666667
Thus, the monthly interest rate (decimal ) , r = 0.014167 ( approx)
Monthly payment, P = $ 325
Let the time period of the loan = n.
Since, [tex]P= \frac{r(PV)}{1-(1+r)^{-n}}[/tex]
⇒ [tex]325= \frac{0.014167(695.20)}{1-(1+0.014167)^{-n}}[/tex]
⇒ [tex]1-(1+0.014167)^{-n}= \frac{10.37008984}{325}[/tex]
⇒ [tex]1-(1+0.014167)^{-n}= 0.03190796873 [/tex]
⇒ n = 2.19
Thus, her total payment = 2.19 × 325 = 711.75
⇒ Her total interest = 711.75 - 695.20 = $16.55
Since only 16.96 is near to 16.55
Thus, second option is correct.
Mr. Andrews has a classroom of 45 students. He wants to divide them equally into 5 teams for a group project.
How many students will be on each team?
A) 7
B) 8
C) 9
D) 10 what the answer
Answer:
C) 9
Step-by-step explanation:
well 45/5 would eqaul 9 exactly
To find out how many students will be on each of Mr. Andrews' 5 teams, divide the total number of students, 45, by the number of teams, which results in 9 students per team. C is correct.
To determine how many students will be on each team when Mr. Andrews divides his classroom of 45 students equally into 5 teams, you need to divide the total number of students by the number of teams. This is a division problem in mathematics.
Here is the calculation:
Write down the total number of students: 45.
Write down the number of teams: 5.
Divide the total number of students by the number of teams:
45 ÷ 5 = 9.
So, there will be 9 students on each team, which corresponds to option C.
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0
0
2
1
cannot be determined
So to find the number of solutions this quadratic equation has without actually solving the equation, we are going to be using the discriminant formula. Plug in the numbers and solve:
[tex]D=5^2-4*1*7\\D=25-28\\D=-3[/tex]
Now, here are the rules with discriminants:
D > 0; there are 2 real solutions in the equationD = 0; there is 1 real solution in the equationD < 0; there are no real solutions in the equationAnswer:Since -3 is less than 0, this means that there are 0 real solutions in this equation.
Answer:
0 real solutions in this equation.
A jewelry salesperson earns 6two fifths ?% commission on all sales. Today she sold ?$5 comma 570 in jewelry. What is her total commission? earned?
Answer:
$356.48
Step-by-step explanation:
We have been given that a jewelry salesperson earns [tex]6\frac{2}{5}[/tex]% commission on all sales. Today she sold $5,570 in jewelry.
To find the total commission earned by salesperson is same as finding the [tex]6\frac{2}{5}[/tex]% of 5,570.
Let us convert [tex]6\frac{2}{5}[/tex] in decimal form.
[tex]6\frac{2}{5}=6.4[/tex]
[tex]\text{Total commission earned by salesperson}=\frac{6.4}{100}\times 5,570[/tex]
[tex]\text{Total commission earned by salesperson}=0.064\times 5,570[/tex]
[tex]\text{Total commission earned by salesperson}=356.48[/tex]
Therefore, the total commission earned by salesperson is $356.48.
What is the measure of YVZ
Answer:
D. 110 deg
Step-by-step explanation:
Angle YVZ and WVX are vertical angles.
A theorem states that vertical angles are congruent.
Angle YVZ is congruent to angle WVX.
m<YVZ = m<WVX = 110 deg
Answer:
110 degrees
Step-by-step explanation:
<YVZ is vertically opposite to a known angle <WVX
Vertically Opposite Angles are equal
<YVZ = WVX
<WVX = 110 degrees. Given
Therefore YVZ = 110 degrees. Property of Vertically opposite angles
What is the recursive rule for this geometric sequence?
1, 3, 9, 27, ...
Enter your answers in the boxes.
A recursive rule for a geometric sequence:
[tex]a_1\\a_n=r\cdot a_{n-1}[/tex]
[tex]a_1=1,\ a_2=3,\ a_3=9,\ a_4=27\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\to r=\dfrac{3}{1}=\dfrac{9}{3}=\dfrac{27}{9}=3\\\\\boxed{a_1=1,\qquad a_n=3\cdot a_{n-1}}[/tex]
As a rule of thumb, people should drink 1/2 ounce of water for each pound of body weight per day. How much water should a 145-pound person drink per day?
Answer: 72.5 ounces per day
After one week a music downloading site sold over 80,000 songs. After 4 weeks the music downloading site sold over 300,000 songs. Find the average rate of change of songs per week.
75,000 songs per week
80,000 songs per week
55,000 songs per week
73,334 songs per week
[tex]\bf \begin{array}{ccll} \stackrel{x}{weeks}&\stackrel{y}{songs}\\ \cline{1-2} 1&80000\\ 4&300000 \end{array}~\hspace{10em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{80000})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{300000}) \\\\\\ \stackrel{\textit{average rate of change}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{300000-80000}{4-1}\implies \cfrac{220000}{3}\quad \approx \quad 73333[/tex]
Ohn has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.
Answer:
Ohn has paid $5730 in first 20 installments
Step-by-step explanation:
As per the question Ohn payed the first installment =$100
Next month Ohn payed the installment = 1.1×$100
Similarly subsequent installment =1.1×1.1×$100
So we can write first 20 installments as
⇒100+100×1.1+100×1.1²+100×1.1³.........+100×[tex]1.1^{20}[/tex]
And we know in geometric series
1+x²+x³+...........[tex]x^{20}[/tex] = (1-[tex]x^{n-1}[/tex])÷(1-x)
Therefore sum of first 20 installments will be
⇒100(1+1.1²+1.1³............[tex]1.1^{20}[/tex] =(1- [tex]1.1^{20}[/tex])÷(1-1.1)
= 100(1-6.73)÷(-.1)
=100×5.73÷.1
= $5730
So Ohn has paid $5730
56 < 4x
Which phrase translates this expression?
A) 56 less than four times a number
B) four times a number less than 56
C) four times a number is less than 56
D) 56 is less than four times a number
what the answer
56 is less than four times a number representing the inequality 56 < 4x thus option (D) is correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given inequality,
56 < 4x
The sign "<" indicates that the value at the left of this sign will be smaller than the right.
Thus, 56 is less than four times the number.
Hence "56 is less than four times a number representing the inequality 56 < 4x".
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The phrase that accurately translates the expression "56 < 4x" is:
56 is less than four times a number.
The correct option is D.
We have the inequality
56 < 4x
Here, the symbol '<' shows less than relation.
So, this phrase represents the inequality statement correctly, stating that 56 is smaller than the result of multiplying four times a certain number (x).
Thus, 56 is less than four times a number.
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Math help please (80 points)
Answer:
1. x^4 -x^3 -4x^2 -3
a1 = -7.4
an = an-1 -13.8 (choice 1)
Step-by-step explanation:
f(x) = x^4 -x^2 +9
g(x) = x^3 +3x^2 +12
We are subtracting
f(x) -g(x) =x^4 -x^2 +9 - ( x^3 +3x^2 +12)
Distribute the minus sign
x^4 -x^2 +9 - x^3 -3x^2 -12
I like to line them up vertically
x^4 -x^2 +9
- x^3 -3x^2 -12
-------------------------
x^4 -x^3 -4x^2 -3
2. a1 = -7.4
To find the common difference, take term 2 and subtract term 1
-21.2 - (-7.4)
-21.2 + 7.4
-13.8
an = an-1 -13.8
Step-by-step explanation:
f(x) = x^4 -x^2 +9
g(x) = x^3 +3x^2 +12
We are subtracting
f(x) -g(x) =x^4 -x^2 +9 - ( x^3 +3x^2 +12)
Distribute the minus sign
x^4 -x^2 +9 - x^3 -3x^2 -12
I like to line them up vertically
x^4 -x^2 +9
- x^3 -3x^2 -12
-------------------------
x^4 -x^3 -4x^2 -3
2. a1 = -7.4
To find the common difference, take term 2 and subtract term 1
-21.2 - (-7.4)
-21.2 + 7.4
-13.8
an = an-1 -13.8
if you need anymore help just ask and if you wondering i found another question which its the same one as this one so her it is
A dress is selling for $100 after a 20 percent discount. What was the original selling price?
SHOW ALL WORK
Answer:
$125
Step-by-step explanation:
original cost - discount = discounted price
discount = original cost * .2
original cost - original cost *.2 = 100
Factor out the original cost
original cost ( 1-.2) = 100
original cost *.8 = 100
Divide each side by .8
original cost *.8/.8 = 100/.8
original cost = 125
Vanessa earns a base salary of $400.00 every week with an additional 5% comission on everything she sells.Vanessa sold $1650.00 worth of items last week.
Log 6 (1/36)
6 is the base. How to evaluate this?
We can write the argument of the logarithm as a power of 6:
[tex]\log_6\dfrac1{36}=\log_6\dfrac1{6^2}=\log_66^{-2}[/tex]
Then using the property that [tex]\log_ba^n=n\log_ba[/tex], we get
[tex]\log_6\dfrac1{36}=-2\log_66[/tex]
and since [tex]6=6^1[/tex], we have [tex]\log_66=1[/tex], so the value of this expression is simply -2.
The value of [tex]\(\log_6 \left(\frac{1}{36}\right)\)[/tex] is -2.
To evaluate [tex]\(\log_6 \left(\frac{1}{36}\right)\)[/tex], we can use properties of logarithms and exponents.
Let's set up the equation:
[tex]\[\log_6 \left(\frac{1}{36}\right) = x\][/tex]
This equation means:
[tex]\[6^x = \frac{1}{36}\][/tex]
We know that [tex]\(\frac{1}{36}\)[/tex] can be rewritten as [tex]\(6^{-2}\)[/tex] because:
[tex]\[36 = 6^2 \quad \text{so} \quad \frac{1}{36} = 6^{-2}\][/tex]
Thus, the equation [tex]\(6^x = \frac{1}{36}\)[/tex] becomes:
[tex]\[6^x = 6^{-2}\][/tex]
Since the bases are the same, we can equate the exponents:
x = -2
Therefore,
[tex]\[\log_6 \left(\frac{1}{36}\right) = -2\][/tex]
Can someone answer each step of this correctly?
About Slope - Intercept Form:
y = mx + bm is the slopeb is the y-interceptAbout Standard Form:
Ax + By = CA & B & C are integersA & B are both non-zeroThis form is good to use when wanting to find the x & y intercepts of a lineAbout Point - Slope Form:
Y - Y1 = m (x -X1)Y1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineOther Info:
Remember, y comes before the x An ordered pair from your problem: (-3,1), -3 is x & 1 is y & x is before the yAn ordered pair from your problem: (3,5), 3 is x & 5 is y & x is before the yFor the graph, the vertical line is yFor the graph, the horizontal line is xHope this information helps!!! :)
Use the substitution method to solve the system of equations. Choose the correct ordered pair. y = 5x + 7 x = 8 A. (8, 47) B. (0, 7) C. (8, 15) D. (0, 8)
Assuming the system is composed of the equations y = 5x+7 and x = 8, then the answer is (8,47) which is choice A
To get this answer, we simply replace x in the first equation with 8, and then compute
y = 5x+7
y = 5*8+7 .... replace x with 8
y = 40+7
y = 47
So together x = 8 and y = 47 pair up to get us the solution (x,y) = (8,47)
After solving the equation by substitution method, the correct pair for x and y will be (8, 47). Hence, option A is correct.
What is an equation?Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given data provided by the question,
The equation is,
y = 5x + 7
Substitute x = 8 in the equation,
y = 5 (8) + 7
y = 47.
So, after substituting the x=8 the value obtained for y is 47.
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Seattle, wa and san francisco, ca lie on the same longitudinal line. san francisco is at 38° latitude and seattle is at 47° latitude. if the earth is a sphere of radius 4000 miles, use arc length to find the distance between the cities. [use π = 3.14, and round to the nearest mile.]
Step 1.
Calculate measure of angle α:
[tex]47^o-38^o=9^o[/tex]
Step 2.
Calculate what fraction of the angle 360° is the angle α:
[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]
Step 3.
Calculate the circumference of the Earth (circle):
[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]
Step 4.
The length of arc is equal 1/40 of the circumference:
[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]
[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]
The distance between Seattle, WA, and San Francisco, CA, calculated using their latitudinal difference on a sphere with a radius of 4000 miles, is approximately 628 miles.
The question is asking for the distance between Seattle, WA and San Francisco, CA based on their respective latitudes and assuming they are on the same longitudinal line. To find the arc length and thus the distance between the two cities, you can use the formula for arc length on a sphere: [tex]\(Arc \ length = (\Delta Latitude \times \pi/180) \times \ Radius \ of\ Earth\)[/tex]. Here, [tex](\Delta Latitude\)[/tex] is the difference in latitude between the cities, which is [tex]\(47^\circ - 38^\circ = 9^\circ\)[/tex]. The radius of Earth is given as 4000 miles. Plugging these values into the formula, you get:
[tex]\(Arc \ length = (9 \times \pi/180) \times 4000\)[/tex]
[tex]\(Arc \ length = (9 \times 3.14/180) \times 4000\)\\\(Arc \ length = (0.157) \times 4000\)\\\(Arc \ length = 628 \ miles\)[/tex]
Therefore, the distance between Seattle and San Francisco, based on latitude and assuming they are directly north and south of each other, is approximately 628 miles.
If Julie needs 3 and 1/4 cups of oatmeal how many 1/4 cups of oatmeal will she use
Answer:
She will use 13 quarter cups of oatmeal
Step-by-step explanation:
3 1/4 = 13/4
x/4 = 13/4
4(x/4) = 4(13/4)
x = 13
HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4
Answer:
Option A is correct.
Value of [tex]S_{22} = 15.4[/tex]
Step-by-step explanation:
Given: [tex]a_{12} = 2.4[/tex] and common difference(d) = 3.4
A sequence of numbers is arithmetic i.e, it increases or decreases by a constant amount each term.
The sum of the nth term of a arithmetic sequence is given by;
[tex]S_n =\frac{n}{2}(2a+(n-1)d)[/tex], where n is the number of terms, a is the first term and d is the common difference.
We also know the nth tern sequence formula which is given by ;
[tex]a_n = a+(n-1)d[/tex] ......[2]
First find a.
it is given that [tex]a_{12} = 2.4[/tex]
Put n =12 and d=3.4 in equation [2] we have;
[tex]a_{12} = a+(12-1)(3.4)[/tex]
[tex]a_{12} = a+(11)(3.4)[/tex]
2.4 = a + 37.4
Simplify:
a = - 35
Now, to calculate [tex]S_{22}[/tex]
we use equation [1];
here, n =2 , a =-35 and d=3.4
[tex]S_{22} = \frac{22}{2}(2(-35)+(22-1)(3.4))[/tex]
[tex]S_{22} = (11)(-70+21(3.4))[/tex]
[tex]S_{22} = (11)(-70+71.4)[/tex]
[tex]S_{22} = (11)(1.4)[/tex]
Simplify:
[tex]S_{22} = 15.4[/tex]
Therefore, the sum of sequence of 22nd term i.e, [tex]S_{22} = 15.4[/tex]
Answer:
A. 15.4
Step-by-step explanation:
Rewrite the expression as a multiple of a sum of two numbers with no common factor. 27 + 21
Find the next term given in the sequence. 1.31, 2.54, 3.77, ....
Answer: The next term in the sequence is 5.
Step-by-step explanation: We are given to find the next term in the following sequence :
1.31, 2.54, 3.77, . . . .
We can see the following pattern in the consecutive terms of the given sequence :
[tex]2.54=1.31+1.23,\\\\3.77=2.54+1.23,\\\\\\\vdots~~~~~\vdots~~~~\vdots[/tex]
Therefore, the next term in the given sequence will be the last given term plus 1.23.
That is, the next term will be
[tex]3.77+1.23=5.00.[/tex]
Thus, the next term in the sequence is 5.
Kenya jumped 7 and 1 sixth feet. Janet jumped 6 and 1 third feet. How much farther did Kenya jump?
classify the sequence arithmetic , geometric, or neither
Answer:
Geometric
Step-by-step explanation:
Given terms are {3, -1, 1/3, -1/9............}
If we have common difference between the terms then it is arithmetic
If we have common ratio between the terms then it is Geometric
Difference of 3 and -1 is 4
Difference of 1/3 and -1 is -4/3
Common difference it not same so it is not Arithmetic
Now we check common ratio
we divide second term by first term
first term is 3 and second term is -1
[tex]\frac{-1}{3}[/tex]
now we check with next two terms
[tex]\frac{\frac{1}{3}}{-1}=\frac{-1}{3}[/tex]
common ratio is -1/3
So this is Geometric
Answer:
B so geometric :)
A point on the unit circle lies on the terminal side of an angle in standard position in Quadrant III .
Select from the drop-down menus to correctly complete each statement.
The cosine of the angle is . Negative or Positive
The sine of the angle is . Negative or Positive
The cosine of the angle is Negative.
The sine of the angle is Negative.
The given angle's terminal side resides in the third quadrant.
In the first quadrant, all trigonometric ratios are positive.
In the second quadrant, only sine and cosecant are positive.
In the third quadrant, only tangent and cotangent are positive.
In the fourth quadrant, only cosine and secant are positive.
In the third quadrant, both sine and cosine of given angle are negative.
Thus, the cosine of the given angle is Negative and
the sine of the given angle is Negative.
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Bryan started to evaluate a decimal expression. 2.5(42 ÷ 3.2 – 10(0.2) + 3)– 5.2 2.5(16 ÷ 3.2 – 10(0.2) + 3) – 5.2
Bryan's next step should look like: [tex]\[37.3 - 5.2\][/tex].
To evaluate the given expression, Bryan should follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).
Start with what's inside the parentheses:
[tex]\(42 / 3.2 = 13.125\)[/tex], and [tex]\(10(0.2) = 2\)[/tex]. So, inside the parentheses, we have: [tex]\(16 - 2 + 3 = 17\)[/tex].
Multiply and divide from left to right:
[tex]\(2.5 \times 17 = 42.5\).[/tex]
Substitute back into the expression:
[tex]\(42.5 - 5.2\).[/tex]
Complete the subtraction:
[tex]\(42.5 - 5.2 = 37.3\).[/tex]
Therefore, Bryan's next step should look like:
[tex]\[37.3 - 5.2\][/tex]
After this step, Bryan would perform the subtraction to find the final result. Following PEMDAS ensures that each operation is carried out correctly, leading to the accurate evaluation of the expression.
Can anyone please tell me what I’m doing wrong. It’s not giving me the full marks. The marks for this question is 4 but I only got 1.
Answer:
33%
Step-by-step explanation:
The area of the entire circle:
The radius is 4+3+3 = 10
Area of a circle= pi * r^2
Area of largest circle = pi * 10^2 = 100 pi
Area of blue ring = Area of blue circle - area of inner white circle
The blue circle has a radius of (4+3) = 7
The inner white circle had a radius of 4
Substituting what we know
Area of blue ring = Area of blue circle - area of inner white circle
= pi * r^2 - pi*r^2
= pi * 7^2 - pi *4^2
= 49pi - 16pi
= 33 pi
The percentage of the logo that is blue is the blue ring/ area of largest circle
percentage = 33 pi/100 pi
Canceling pi
percentage = 33/100
= 33 %
Which benefits do employers commonly offer to full-time employees?
Answer:
Employers offer bonuses ,health insurances, medical facilities ,residence facilities and other facilities to their full time employees.
Step-by-step explanation:
Employees play a vital role in progress of an organization.
they need inspiration to work better and to make company's rank better.
and for their inspiration and to enhance the relationship with employees, employers offer them bonuses,health insurances, medical facilities ,residence facilities and other facilities
Answer:
The common benefits of getting a full-time job are:
Health InsuranceSocial Security withholdings.Unemployment insurance.Periodic compensations.Remember that a full-time job has to have 40 hours per week. So, to compensate this amount of time spent in the company, they tend to "protect" their employees with better health insurance, their Social Security will give credits, which apply to retirement, and in case of accidents, their insurance will cover all costs.
All these variables make these jobs attractive in order to make people work even more.
A video streaming service offers unlimited movies for 15 dollars a month or 1.99 per movie. Which offer is better
Answer:15 dollar a month movie offer is
an empty kitchen cabinet has 8 shelves and each shelf can hold no more than 30 cans you want to arrange 40 cans in the kitchen cabinet so that the same number of cans is on each shelf that you use
(a) list the factors of 40
(b) list the factors of 40 that represent the number of cans that could be on each shelf
(c) how many different arrangements of cans are possible
(d) what are the possible arrangements of the cans
Answer:
(a)
[tex]40=1,2,4,5,8,10,20,40[/tex]
(b)
factor=5 can only hold it
(c)
Only one arrangement is possible
(d)
we can put 5 cans into all 8 shelves
(e)
[tex]40=8\times 5[/tex]
Step-by-step explanation:
We are given
an empty kitchen cabinet has 8 shelves
and each shelf can hold no more than 30 cans you want to arrange 40 cans in the kitchen cabinet
so that the same number of cans is on each shelf that you use
(a)
we can find all possible factors of 40
[tex]40=1,2,4,5,8,10,20,40[/tex]
(b)
Since, an empty kitchen cabinet has 8 shelves
so, one of factor of 40 must be 8
so,
[tex]40=8\times 5[/tex]
So, factor=5 can only hold it
(c)
Only one arrangement is possible
because there is only one such possible factor
[tex]40=8\times 5[/tex]
(d)
Since, we got
[tex]40=8\times 5[/tex]
So, we can put 5 cans into all 8 shelves
(e)
Since, there are 8 shelves
and we can put 5 cans on each shelves
so, possible arrangement is
[tex]40=8\times 5[/tex]
Answer:
(a) 40 = 1 x 40, 2 x 20, 4 x 10, or 5 x 8. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
(b) Factors: 5, 8, 10, 20
(c) 4, that is, the quantity of factors in (b)
(d) 5 cans in 8 shelves, 8 cans in 5 shelves, 10 cans in 4 shelves, 20 cans in 2 shelves.
3) A regulation basketball has a diameter of 9.4 inches. What is the volume of the ball?
Answer:
Volume = 434.89276543154 inch³
Step-by-step explanation:
volume = 4/3πr³
where r is the radius
r = 9.4/2
r = 4.7³
Volume = 4/3×π×4.73³
Volume = 434.89276543154 inch³
A standard deck of playing cards has 52 cards: 13 spades, 13 clubs, 13 hearts, and 13 dimonds. What is the probabipity of drawing a spade from a standard 52 card deck, replacing it, then drawing another spade? Show your work or explain how you got your answer.
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.