Step-by-step explanation:
To find the expected value of the number of bids won, E(X), we need to multiply each value of X with its corresponding probability and then sum these products.
E(X) = (X1 * P1) + (X2 * P2) + (X3 * P3)
Here, X1 = 0, X2 = 1, X3 = 2, and their corresponding probabilities are P1 = 0.81, P2 = 0.18, and P3 = 0.01.
E(X) = (0 * 0.81) + (1 * 0.18) + (2 * 0.01)
E(X) = (0) + (0.18) + (0.02)
E(X) = 0.20
The expected value of the number of bids won is 0.20.
4. What is the mean absolute deviation of the data below to the nearest hundredths?
(13, 16, 16, 17, 20, 20, 20, 21, 22)
Answer:
Exact form: 2.5185185185185
Simplified form: 2.52
Fraction form: 63/25
Step-by-step explanation:
Help me please for math
The total area of the composite figure is 17 square centimeters.
How to find the area of the figure?Remember that the area of a rectangle is equal to the product between its dimensions.
We can separate the figure into two rectangles, one of these rectangles is of 1cm by 2cm, then its area is:
A = 1cm*2cm = 2cm²
The other rectangle is of 3cm by 5cm, then its area is:
A' = 3cm*5cm = 15cm²
Adding that we get a total of:
total area = 2cm² + 15cm² = 17cm²
That is the area of the figure.
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O is the center of the regular decagon below. Find its area. Round to the nearest tenth if necessary. 14
The area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex]
To find the area of a regular decagon, we need to know either the side length or the apothem (the perpendicular distance from the center to a side). In this case, you have provided the radius of the decagon, which is 14 units.
For a regular decagon, the apothem (a) is related to the radius (r) by the formula:
[tex]a = r * cos(\pi/10)[/tex]
Let's calculate the apothem using the given radius:
[tex]a = 14 * cos(\pi/10) =12.149[/tex]
Now, we can calculate the area (A) of the regular decagon using the formula:
[tex]A = (5/2) * a^2 * tan(\pi/10)[/tex]
[tex]A = (5/2) * (12.149)^2 * tan(\pi/10) =195.7[/tex]
Rounding to the nearest tenth, the area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex].
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A lion can run 1.89 miles in distance. If 1 mile is the
same as 5,280 feet, what is the distance that a lion
can run in feet?
If $22,000 is invested in an account earning 4.5% interest compounded continuously,
determine how long it will take the money to quadruple. Round to the nearest year.
Use the model A = Pet where A represents the future value of P dollars invested at
an interest rate r compounded continuously for t years.
OA) 31 years
B) 36 years
OC) 3 years
D) 308 years
Answer:
31 years
Step-by-step explanation:
A = P(interest rate)^number of years (n)
if the money is to quadruple, A = 4 X 22,000 = 88,000.
P = investment amount = 22,000.
interest rate is 4.5%. so we have the whole (100%) + 4.5% = 1.045%.
n is number of years.
22,000 (1.045)^n = 88, 000
divide both sides by 22, 000:
(1.045)^n = 4
take logs for both sides:
log (1.045)^n = log 4
simplify using log laws (by bringing down the n):
n log (1.045) = log 4
divide both sides by log (1.045):
n = (log 4) / log (1.045)
= 31.49 (31 years to nearest year)
An end behavior model for f(x) = [tex](8x^6-16x^3+8)/4x^2-4x-24)[/tex]
2x^2.
2x^3.
2x^4.
2x^6.
This given function does not have an end behavior since it is not a polynomial.
What is the end behavior of a function?The end behavior of a function describes the behavior or trend of the function as the input values (x) approach positive or negative infinity. It helps us understand what happens to the function's values as x becomes very large or very small.
We have three possible cases of end behavior of a function which are;
When the value of x approaches positive infinityWhen the value of x approaches negative infinityWhen a function may have different behaviors for positive and negative infinity. In such cases, we specify the end behavior separately for positive and negative infinity.The end behavior of a function is often determined by using the leading term of the function, which is the term with the highest power of x.
In the given problem;
[tex]f(x) = \frac{8x^6 - 16x^3 + 8}{4x^2 - 4x - 24}[/tex]
The end behavior of this function does not exist because this function is not a polynomial
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Precalculus > M.12 Trigonometric ratios: find a side length 62D Find BC. B C BC= 00 12/31 √ 30° Write your answer in simplified, rationalized form. Do not round. D Learn with an example
PLEASE HELP ME
The length of BC is determined as 6√31 by applying trigonometry ratio.
What is the length of BC?The length of BC is calculated by applying the following formulas for trig ratios.
The trig ratio is simplified as;
SOH CAH TOA;
SOH ----> sin θ = opposite side / hypothenuse side
CAH -----> cos θ = adjacent side / hypothenuse side
TOA ------> tan θ = opposite side / adjacent side
The hypothenuse side of the right triangle is given as 12√31 and the opposite side is length BC.
The length of BC is calculated as follows;
sin 30 = BC / 12√31
BC = 12√31 x sin (30)
BC = 12√31 x ¹/₂
BC = 6√31
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I NEED HELP SOLVING THIS MATH PROBLEM PLEASE.
The ball's height is 11 meters after approximately 6.83 seconds and 0.17 seconds.
The height of the ball after t seconds is given by the equation h = 1 + 30t - 5t^2. To find all values of t for which the ball's height is 11 meters, we need to solve the equation [tex]1 + 30t - 5t^2 = 11[/tex].
[tex]30t - 5t^2 - 10 = 0[/tex]
[tex]t^2 - 6t + 2 = 0\\\\t = (6 \pm \sqrt{6^2 - 4(1)(2)}) / 2\\\\\t = (6 \pm \sqrt{32}) / 2\\\\t = (6 \pm 4\sqrt2 / 2\\\\t = 3 \pm 2\sqrt2[/tex]
Therefore, the values of t for which the ball's height is 11 meters are approximately 6.83 seconds and 0.17 seconds.
Rounding to the nearest hundredth, we get:
t ≈ 6.83 or t ≈ 0.17
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The pre image shown above is dilated by a scale factor of 1/2 about the center (1,-5). What is the location of the point C?
with scaling factor = 1/2 ,
the coordinate location of the dilated posit C is ( 2,-3)
Which inequality represents the values of x for which triangle ABC exists
After considering all the given options we come to the conclusion that the inequality that represents the values of x for the give triangle ABC is 15/11 < x < 17/5, which is Option A.
Here, the sides of a triangle should gradually satisfy the triangle inequality theorem which projects that the summation of the lengths considering any two sides of a triangle should be bigger than or equivalent towards the length of the third side.
Then, for the given sides of triangle ABC,
3x+1 + 16 > 8x
Applying this inequality,
x > 15/11
So,
16 + 8x > 3x+1
Applying simplification
x < 17/5
Hence , the inequality that represents the values of x for which triangle ABC exists is 15/11 < x < 17/5.
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PLEASE HELP!!!!!!! URGENT!!!!!
Use Law of Cosines. Find length of X. (Round final answer to one decimal place as needed. Round all intermediate values to two decimal places as needed.)
Answer: 23.80
Step-by-step explanation:
[tex]\sqrt{19^2+18^2-2*19*18cos(80)}[/tex]
You have a cylinder with a height of 8 centimeters and a radius of 3 centimeters. What is the volume. If you get the answer please add a explantion.
Answer:
The exact volume of the cylinder is 72π cubic centimeters, or approximately 226.19 cubic centimeters to two decimal places.
Step-by-step explanation:
The volume of a cylinder can be calculated using the formula:
[tex]\boxed{V = \pi r^2 h}[/tex]
where:
V is the volume.r is the radius.h is the height.Given values:
r = 3 cmh = 8 cmSubstitute the given values into the formula and solve for V:
[tex]\begin{aligned} \implies V&=\sf \pi \cdot 3^2 \cdot 8\\&=\sf \pi \cdot 9 \cdot 8\\&=\sf 72\pi \;cm^3\\&= \sf 226.19\; cm^3\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the volume of the cylinder is 72π cubic centimeters, or approximately 226.19 cubic centimeters to two decimal places.
1,6,9,1,6,9 what is a rule for the pattern?
The piecewise rule for the pattern is given as follows:
f(n) = 1 if n % 3 = 0.f(n) = 6 if n % 3 = 1.f(n) = 9 if n % 3 = 2.What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The pattern for this problem is given as follows:
1,6,9,1,6,9.
The period of the pattern is given as follows:
3 units.
The pattern of the function is constant, meaning that all the outputs for an input that is a multiple of 3 are of 1, if the remainder of the division is of 1 the output is of 6, and if the remainder of the division is of 2 the output is of 9.
Hence the pattern is defined as follows:
f(n) = 1 if n % 3 = 0.f(n) = 6 if n % 3 = 1.f(n) = 9 if n % 3 = 2.More can be learned about piece-wise functions at brainly.com/question/19358926
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An archaeologist finds a barren land with a large number of fossils of Dinosaurs. The number N(t) of fossils that can be found per cubic meter after t years can be determined by solving the equation:
Assuming that the initial number of fossils is 100, estimate the number of fossils after 10 years.
The assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.
To estimate the number of fossils after 10 years, we need to solve the given equation. However, since the equation is not provided, we'll assume a simple exponential decay model for the population of fossils.
Let's assume the equation for the population of fossils is:
N(t) = N0 * e^(-kt)
where:
N(t) is the number of fossils after t years,
N0 is the initial number of fossils,
k is a decay constant, and
e is the base of the natural logarithm (approximately 2.71828).
Since the initial number of fossils is given as 100, we have N0 = 100. Now, we need to find the value of the decay constant (k) to estimate the number of fossils after 10 years.
Without further information, it's challenging to determine the exact decay constant. However, let's assume a hypothetical value of k = 0.1 for this example.
Plugging the values into the equation, we get:
N(10) = 100 * e^(-0.1 * 10)
= 100 * e^(-1)
≈ 100 * 0.36788
≈ 36.788
So, with the assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.
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Answer:
B. 2333.59
Step-by-step explanation:
We have been given the following differential equation:
[tex]\dfrac{dN}{dt}=\dfrac{5000}{6+5t}[/tex]
To find the number of fossils N(t) after t = 10 years, we first need to solve the differential equation using integration and the given parameters to create an equation for N(t) in terms of t.
Solving a differential equation means using it to find an equation in terms of the two variables, without a derivative term.
Rearrange the equation so that all the terms containing N are on the left-hand side, and all the terms containing t are on the right-hand side:
[tex]1\;dN=\dfrac{5000}{6+5t}\; dt[/tex]
Integrate both sides:
[tex]\displaystyle \int 1 \;dN=\int \dfrac{5000}{6+5t}\; dt[/tex]
Use the following integration rules:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Integration rulest}\\\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\;\;(where $n$ is any constant value)\\\\\\$\displaystyle \int \dfrac{n}{a+bx}\:\text{d}x=\dfrac{n}{b}\ln |a+bx|+\text{C}$\\\\ \end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int 1\;dN&=\int \dfrac{5000}{6+5t}\; dt\\\\\implies N&=\frac{5000}{5}\ln \left|6+5t\right|+C\\\\N&=1000\ln \left|6+5t\right|+C\end{aligned}[/tex]
As the initial number of fossils is 100, then N = 100 when t = 0.
Substitute these values into the equation and solve for C:
[tex]100=1000\ln \left|6+5(0)\right|+C[/tex]
[tex]C=100-1000\ln (6)[/tex]
Therefore, the equation for N in terms of t is:
[tex]N=1000\ln \left|6+5t\right|+100-1000\ln(6)[/tex]
Use the quotient log rule to simplify:
[tex]N=1000\ln \left|6+5t\right|-1000\ln(6)+100[/tex]
[tex]N=1000\ln \left(\dfrac{\left|6+5t\right|}{6}\right)+100[/tex]
To estimate the number of fossils after 10 years, substitute t = 10 into the equation:
[tex]N=1000\ln \left(\dfrac{\left|6+5(10)\right|}{6}\right)+100[/tex]
[tex]N=1000\ln \left(\dfrac{56}{6}\right)+100[/tex]
[tex]N=2333.59\; \sf (2\;d.p.)[/tex]
Therefore, the number of fossils after 10 years is 2333.59.
what is capital and revenue expenditure?
Answer:
Capital expenditures are typically one-time large purchases of fixed assets that will be used for revenue generation over a longer period. Revenue expenditures are the ongoing operating expenses, which are short-term expenses used to run the daily business operations.
QUESTION 8 1 POINT
.
Find the GCF of the following three monomials:
21x³y5
63x5y²
45x¹y³
The greatest common factor (GCF) of the three monomial, 21x³y⁵, 63x⁵y² and 45x¹y³ is 3xy²
How do i determine the greatest common factor (GCF)?The greatest common factor (GCF) of the three monomials, 21x³y5, 63x5y² and 45x¹y³ can be obtained as follow:
First, we shall determine the factors of each monomials. This is illustrated below:
21x³y⁵ = 3 × 7 × x × x × x × y × y × y × y × y
63x⁵y² = 3 × 3 × 7 × x × x × x × x × x × y × y
45x¹y³ = 3 × 3 × 5 × x × y × y × y
Finally, we shall determine the greatest common factor (GCF) from the factors listed above. This is shown below:
3 × x × y × y = 3xy²
Thus, we can conlude that the greatest common factor (GCF) of the three monomials is 3xy²
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The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
The statements that will be true about parallelogram ABCD are: A, B, D, and E.
Properties of a Parallelogram -
Diagonals of a parallelogram bisect each other into congruent segments.
Opposite angles and sides of a parallelogram are always congruent.
Alternate interior angles are always congruent in measure.
Thus, the following would be true of parallelogram ABCD:
AP ≅ CP (congruent segment's of a bisected diagonal)
BC ≅ AD (congruent opposite sides)
∠CAD ≅ ∠ACB (congruent angles)
∠BPC ≅ ∠APD (congruent angles)
Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.
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the diagram shows a right triangle and the lengths of two of its sides in 11.9in and 7.9 and d what measurement is closest to the value of d inches
The measurement is closest to the value of d inches is 14. 28
How to determine the valueIt is important to note that the Pythagorean theorem is stated as;
The Pythagorean theorem states that the square of the longest leg or hypotenuse side of a triangle is equal to the sum of the squares of the other two sides.
This is represented as;
x²= y²+ z²
Now, substitute the values, we get;
x² = 11. 9² + 7.9²
Find the square values, we have;
x² = 141. 61 + 62. 41
add the values, we have;
x² = 204. 02
Now, find the square root of both sides, we get;
x = √204. 02
x = 14.28
Know that d = x = 14. 28
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Which is a whole number?
0.86
2/5
98
35%
Answer:
98 is a whole number
Step-by-step explanation:
0.86 is a decimal
2/5 is a fraction
35% is a percentage
Find the probability that a randomly
selected point within the square falls in the
red-shaded square.
1
1
3
P = [?]
3
Enter as a decimal rounded to the nearest hundredth.
The probability that a randomly selected point within the square falls in the red-shaded square is 0.11
Finding the probabilityFrom the question, we have the following parameters that can be used in our computation:
Red square of length 1White square of length 3The areas of the above shapes are
Red square = 1² = 1
White square = 3² = 9
The probability is then calculated as
P = Red square/White square
So, we have
P = 1/9
Evaluate
P = 0.11
Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.11
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Find the volume of a cylinder with a diameter of 20 km and a height of 5 km in terms of pie.
what is the volume of the cylinder?
Answer:
The volume of the cylinder is 500 π cubic kilometers.
Step-by-step explanation:
Formula: V = πr²h
r = d/2
r = 20km/2
r = 10 km
h = 5km
Solve for the volume using the formula.
Substitute the given
V = π(10km)²(5km)
V = 500π km³
I hope this helps you
Bookwork code: K27
,Calculator
allowed
A pendulum of length 18 cm is swinging from a fixed point, as shown.
Calculate the distance that the end of the pendulum travels when it swings
through an angle of 87°.
Give your answer in centimetres (cm) to 1 d.p.
87°
18 cm
The distance that the end of the pendulum travels when it swings is given by the relation D = 27.3 cm
Given data ,
A pendulum of length 18 cm is swinging from a fixed point
Now , it swings through an angle of 87°
So , Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
Now , D = ( θ/360 ) x 2πr
On simplifying , we get
D = ( 87 / 360 ) x 2 ( 3.14 ) ( 18 )
D = ( 0.241667 ) ( 113.04 )
D = 27.3 cm
Hence , the pendulum travels a distance of 27.3 cm
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You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2% APR compounded annually and the rest in a stock plan. Your stock plan increases in value 3% the first year, decreases 8% in value the second year, and increases 6% in value the third year. What are the balances for each account by the end of the third year and the total gain on your original saved amount?
Answer:
Step-by-step explanation:
Amount in 4.6% acct= 15000*(1/3)= 5000
Amount in bonds = 1/4*15000= 3750
Amount in stock= 15000-(5000+3750)= 6250
Amount in each account at the end of three years
5000*(1.046)^3= 5722.22668
3750*(1.052)^3=4365.94728
6250*1.03*(1-.08)*1.06= 6277.85
total: 5722.22668+4365.94728+6277.85=16366.02396
gain= 16366.02396-15000=1366.02396
or (16366.02396/15000)-1= 9.1068264%
See photo how to use distributive property of multiplication to simplify the expression.
The simplest form of the expression by the use of the distributive property is;
[tex]12x^2 + 24x + 9[/tex]
What is the distributive property?In mathematics, the distributive property, which explains how multiplication interacts with addition or subtraction, is a fundamental concept. By allocating or multiplying a number or term to each term enclosed by a set of parenthesis, it enables you to simplify expressions.
The distributive property is frequently employed in algebraic expressions, equation simplification, and polynomial operations. By spreading out the multiplication over addition or subtraction, it aids in simplifying complex statements and makes calculations easier to understand.
We know that;
[tex]3(4x^2 + 8x + 3)\\12x^2 + 24x + 9[/tex]
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Find the median and mode of the data.
3, 414, 334, 5, 212, 4, 823, 212
Median: 212
Mode: 212
The median and mode of the data set are 273 and 212 respectively.
What is the median?The median is the value that splits the mathematical numbers or expressions in half. The median value is the middle number of data points. To find the median first arrange the data points in ascending order.
To find the median, we need to arrange the numbers in order from least to greatest:
3, 4, 5, 212, 212, 334, 414, 823
There are 8 numbers in total, so the median is the average of the two middle numbers, which are 212 and 334.
Median = (212 + 334)/2 = 273
To find the mode, we need to identify the number(s) that occur most frequently. In this case, 212 appears twice, so it is the mode.
Mode = 212
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Is the relation a function? Explain.
A. No because for each input there is not exactly one output.
B. No because for each output there is not exactly one input.
C. Yes because for each input there is exactly one output.
D. Yes because for each output there is exactly one input.
The relation is a function because (d) Yes because for each output there is exactly one input.
Determining if the relation is a functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The graph can be represented as
x g(x)
-5 1
-2 0
-1 -1
0 2
1 3
5 1
The above table of values is a function
This is so because each output values have different input values.
i.e. it would pass the vertical line test when represented on a graph
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Exponent
T-Table
Coincident (Consistent
Dependent)
Systems of Equations
Inconsistent
Consistent Independent
1.
2.
3.
4.
5.
6.
A set of two or more equations
with the same variables.
A system of linear equations with
EXACTLY ONE solution.
A system of linear equations with
INFINITELY MANY solutions.
A system of equations with NO
solution.
A number representing how many
times the Base number should be
multiplied by itself.
A chart of the different values for
an equation or graph.
A set of two or more equations with the same variables.
A system of linear equations with EXACTLY ONE solution.
A system of linear equations with INFINITELY MANY solutions.
A system of equations with NO solution.
A number representing how many times the Base number should be multiplied by itself.
A chart of the different values for an equation or graph.
Systems of Equations:
A set of two or more equations with the same variables.
These equations are solved simultaneously to find the values of the variables.
Consistent Independent:
A system of linear equations with EXACTLY ONE solution.
This means that the lines represented by the equations intersect at a single point.
Consistent Dependent (Coincident):
A system of linear equations with INFINITELY MANY solutions.
In this case, the equations represent the same line or overlapping lines, and every point on the line is a solution.
Inconsistent:
A system of equations with NO solution.
This occurs when the lines represented by the equations are parallel and never intersect.
Exponent:
A number representing how many times the base number should be multiplied by itself.
For example, in the expression[tex]2^3,[/tex] the exponent is 3, which means 2 should be multiplied by itself 3 times [tex](2 \times 2 \times 2 = 8).[/tex]
T-Table:
A chart of the different values for an equation or graph.
It typically includes two columns: one for the input values (usually x) and one for the corresponding output values (usually y).
T-tables are helpful for understanding the relationship between the variables in an equation and for plotting points on a graph.
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factorise P(x)=2x*3-5.6x+1
After applying factorization of the given functions the evaluated expression comes out to be (2x + 1)(x² - x - 4.8), under the condition the given function is P(x)=2x × 3- 5.6x +1
In order to factorize the given polynomial P(x) = 2x³ - 5.6x + 1, we can apply the Rational Root Theorem. The theorem projects that in an incident when a polynomial has integer coefficients, then any rational roots must have a numerator that divides the constant term and a denominator that divides the leading coefficient.
For the given case, the leading coefficient is 2 and the constant term is 1.
Hence, any rational roots must be of the form p/q where p divides 1 and q divides 2. This elaborates that the possible rational roots are ±1/2 and ±1.
We can observe these roots applying synthetic division. Using synthetic division with root -1/2 gives us:
-1/2 | 2 0 -5.6 1
| -1 0.8 -0.5
-------------------
2 -1 -4.8 0.5
This means that P(x) can be factored as:
P(x) = (2x + 1)(x² - x - 4.8)
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=
A 12-sided die is rolled. The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a number less than 7.
The probability of rolling a number less than 7 is
(Type an integer or a simplified fraction.)
After considering all the given data we conclude that the the probability of rolling a number less than 7 is 1/2, under the condition that the set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12).
The evaluated probability of rolling a number less than 7 on a 12-sided die is the number of outcomes that are less than 7 divided by the total number of possible outcomes.
The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). There are 6 numbers less than 7 in this set (1,2,3,4,5,6) and 12 possible outcomes.
Hence , the probability of rolling a number less than 7 is:
6/12 = 1/2
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I'm giving the brainiest to the correct answer.
Answer:
$15,200
Step-by-step explanation:
You want to know the amount deposited at 1.5% that will earn the same simple interest in a year as $12,000 deposited at 1.9%.
InterestThe interest amount is given by the formula ...
I = Prt
For the two accounts, the interest and the time are the same, so we have ...
P1·r1 = P2·r2
12000·1.9% = P2·1.5% . . . . . . . . . . . equate interest amounts for t=1
P2 = 1.9/1.5·12000 = 15200 . . . . . . divide by 1.5%
Ruth deposited $15,200.
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