The probability that a sum of 9 on the 2 die will occur at least once is 217/729.
Sum of 9 in a pair of dice can occur in the following 4 ways.
3 + 6
4 + 5
5 + 4
6 + 3
Also, total number of ways = 6*6 = 36
Hence, probability of getting a sum of 9 = 4/36 = 1/9.
We know that,
Probability of getting a sum of 9 + Probability of not getting a sum of 9 = 1
Hence, we can write,
1/9 + Probability of not getting a sum of 9 = 1
Probability of not getting a sum of 9 = 8/9
Also,
Probability of getting the sum of 9 atleast 1 + probability of getting the sum 9 none of the times = 1
Hence, we can write,
Probability of getting the sum of 9 atleast once = 1 - probability of getting the sum 9 none of the times/
Probability of getting the sum of 9 atleast 1 = 1 - (8/9)*(8/9)*(8/9) = 1 - 512/729 = 217/729.
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Tom invested $2500 a year in a mutual fund for 15 years. If the market value of the fund increases 5% per year, what will be the value of the fund after 15 deposits?
The value of the mutual fund of Tom after 15 deposits will be $5197.320 .
In the question ,
it is given that , Tom invested $2500 in mutual fund for 15 years ,
So,
the investment amount(P) = $2500 .
time for investment(x) = 15 years
rate of increase(r) = 5% = 0.05
The amount of fund after 15 deposits can be calculated using the formula
amount = P*(1+r)ˣ
Substituting the values of P, x and r , we get
amount = 2500*(1 + 0.05)¹⁵
= 2500*(1.05)¹⁵
= 5197.320
Therefore , The value of the mutual fund of Tom after 15 deposits will be $5197.320 .
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A golf lesson lasts from 10:00 a.m. – 11:15 a.m. and includes a 15-minute break with equal lengths of time before and after the break. At what time should the break start?
A golf lesson lasts from 10:00 am - 11:15 am and includes a 15 minutes break with equal lengths of time before and after the break is at 10:30 am.
Total lesson time is 1 hour and 15 minutes (10:00 - 11:15)
There is 15 minutes break with equal lengths of time before and after break.
The lesson before the break is from 10 - 10:30
Therefore , break is at 10:30 am
Lesson resumes at 10:45 when break is over then lesson runs another 30 minutes until 11:15 am (10:45 - 11:15).
Therefore, the break is at 10:30 am in mid of 10:00 am - 11:15 am.
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Hi, can you help me answer this question please, thank you!
Given that
[tex]\begin{gathered} \mu_d=\mu_2-\mu_1=21.1 \\ s_d=14.9 \\ n=8 \end{gathered}[/tex]a) The formula for the test statistics for this sample is,
[tex]t=\frac{\mu_d}{s_d\sqrt[]{n}}[/tex]Therefore,
[tex]\begin{gathered} t=\frac{21.1}{14.9\times\sqrt[]{8}}=0.50067 \\ t=0.50067\approx0.501(3\text{ decimal places)} \\ \therefore t=0.501 \end{gathered}[/tex]Hence, the test statistic for this sample is
[tex]t=0.501[/tex]b)
A recipe that makes 10 pancakes calls for 13/4 cups of milk. If you want to scale down the recipe so that it makes only 2 pancakes, about how much milk should you use? A. 3/4 cup B. 1/2 cupC. 7/20 cup D. 3/10 cup E. 7/12 cup
13/20 cups
Explanations:The recipe makes 10 Pancakes with 13/4 cups of milk
The recipe will make 1 pancake with x cups of milk
[tex]\begin{gathered} x\text{ = }\frac{13}{4}\div10 \\ x\text{ = }\frac{13}{4}\times\frac{1}{10} \\ x\text{ = }\frac{13}{40} \\ \end{gathered}[/tex]The recipe will make 1 pancake with 13/40 cups of milk
The recipe will make 2 pancakes with (2 x 13/40) cups of milk
= 26 / 40
= 13 / 20
The recipe will make 2 pancakes with 13/20 cups of milk
Please answer correctly and tell me if its linear quadratic or exponential please.
Answer:
Exponential
Step-by-step explanation:
If the initial difference has the same value, the model will be linear.
If the value of the second difference is the same, the model will be quadratic.
If the difference has been calculated more than five times before duplicate values are discovered, the model might be exponential or involve another unique equation.
Hope this helps!
4. Find and interpret theaverage rate of change forthe interval. Show your work.1
Average rate of change = -2 celcius / hour
Interpretation: For every unit change in the time (x), there is a change of -2 celcius in the temperature
Explanations:The average rate of change is to be found for the interval:
[tex]1\text{ }\leq x\leq3[/tex]From the interval, we can deduce that:
[tex]x_1=1,x_2=3[/tex]Know the corresponding value of y for each value of x shown above:
[tex]\begin{gathered} \text{When x}_1=1,y_1=\text{ 6} \\ \text{When x}_2=3,y_2=\text{ 0} \end{gathered}[/tex]The average rate of cgange is given by the formula:
[tex]\begin{gathered} \frac{\delta y}{\delta x}=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \frac{\delta y}{\delta x}=\text{ }\frac{0-6}{3-1} \\ \frac{\delta y}{\delta x}=\frac{-6}{3} \\ \frac{\delta y}{\delta x}=-2 \end{gathered}[/tex]The rate of change for the interval is -2 celcius/hour
This can be interpreted as for every unit change in the time (x), there is a change of -2 celcius in the temperature
1. If DM = 35, what is the value of r?
DG=r + 3 GM=4r-28
Answer:
r=32
Step-by-step explanation:
when DM=35
then. 35=r+3
35-3=r
r=32 therefore, substitute into
second equation to solve GM
GM=4r-28
GM=128-28
GM=100
y=-2/3x+5 and goes through (0, -2)
with steps please
The equation of the line with coordinate (0, -2) that goes through y = -²/₃x + 5 is; y = -²/₃x - 2
What is the Equation of the Line?We know that the general formula for an equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, from the given equation of y = -²/₃x + 5, we can say that;
Slope; m = -²/₃
y-intercept = 5
Thus, equation of the new line would be;
y - (-2) = -²/₃(x - 0)
y + 2 = -²/₃x
y = -²/₃x - 2
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The mean Exam score on the SOC 15 Exam 2 is 84.28 with a standard deviation of 6.71Your friend scored an 86 on the exam. What percentage of students scored lower than your friendon the exam?
First, find the z-score of 86
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{86-84.28}{6.71} \\ z=\frac{1.72}{6.71} \\ z=0.2563 \end{gathered}[/tex]Rounding to the nearest hundredth, that is 0.26
Next, find z = 0.26 to the left of z in the z-table and we have the following
Multiply by 100%, and we have
[tex]\begin{gathered} P(z<0.26)=0.60257 \\ \\ 0.60257\cdot100\%=60.257\% \end{gathered}[/tex]Therefore, the percentage of students who scored lower than 86 is 60.257%.
Find the opposite of –15.
Answer:15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
If there is a negative sign just add a positive sign or remove the sign. And if it's a positive number add a negative sign.
Easy There we go!
Cuanto es 1 1/4 + 1/2 + 3 1/2 =?
Ayudaaa
Answer:
es 1 1/4 + 2/4 +3 2/4 = 5 1/4
5 1/4
help me on my hw! I don't understand (answers are already there but mine doesn't match any)
The answer is d. 82.1
Explanation:
Tan 75 = x/22
You have a tree in your yard that is 60 inches around. What is the diameter of the tree?
Given : a tree in your yard that is 60 inches around
60 inches represents the circumference of the tree
The circumference =
[tex]\pi\cdot d[/tex]Where d is the diameter of the tree
so,
[tex]\begin{gathered} \pi\cdot d=60 \\ \\ d=\frac{60}{\pi}\approx19.1 \end{gathered}[/tex]So, the answer is : the diameter of the tree is a bout 19.1 inches
Write three sentences that compare the values 12 and 3 in different ways
Given data:
The numbers given are 12 and 3.
The 12 and 3 are both positive integers in which 12 is greater than 3.
The 12 and 3 both lie on the right side of the number line in which 12 comes after 3, so 12 is bigger number than 3.
The 12 and 3 are both natural as well as rational number, 12 is nine more than 3.
DUE IN 40 MIN PLEASE HELP
Answer:
[tex]f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]
Step-by-step explanation:
The permissible values of x for a function is called the domain of the function. Permissible values mean that the function is real and defined.
The range of a function is the set of all y values for the domain
If a point on a graph is a filled circle, that point is included in the domain(x-value) and represents a ≤ or a ≥ inequality
If a point on a graph is an unfilled or hollow circle, that point is not included in the domain(x-value) and represents a < or a >inequality
Let's look at the three parts of the given piecewise graph
Piecewise part A
We see that the minimum and maximum values of x for this function are x = -2 and x = 1 respectively. The point corresponding to x= 1 is a hollow circle so it is not included in the domain whereas the point corresponding to x = -2 is included
Let's find the equation of this line:
Take 2 points on the line. We choose points (0, -4) and (1, -1)
Slope of this line is -1 -(-4)/(1-0) = (-1 + 4)/1 = 3
The y-intercept is -4
So equation of the line is y = 3x -4 for -2 ≤ x < 1
Proceeding in a similar manner we can determine the domain and function equation for the other two pieces, B and C
Piecewise part B
Domain of x : 1 ≤ x ≤5
Slope = (8-4)/(5-1) = 4/4 = 1
Equation is of the form y = 1x + b
To calculate b, plug in values of x = 1, y = 4 to get
4 = 1(1) + b
b = 3
Equation of this piecewise function is
y = x + 3 for 1 ≤ x ≤ 5
Piecewise Part C
This is a flat horizontal line at y = 8
So that is the equation of the line
The domain of this piece is 5 ≤ x ≤ 8
So we get y = 8 for [tex]$\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]
Normally, instead of using y we use f(x)
Putting all this together we get the piecewise function defined as
[tex]f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]
find the measure of Angel A? (Round your answer to the nearest whole number)
Answer:
Concept:
To figure out the measure of angle A, we will use the sine rule below
[tex]\begin{gathered} \frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC} \\ where, \\ a=37cm \\ c=29cm \\ C=50^0 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \frac{a}{sinA}=\frac{c}{sinC} \\ \frac{37}{sinA}=\frac{29}{sin50^0} \\ \end{gathered}[/tex]Cross multiply, we will have
[tex]\begin{gathered} \frac{37}{s\imaginaryI nA}=\frac{29}{s\imaginaryI n50^0} \\ 29\sin A=37\times sin50^0 \\ sinA=\frac{37sin50^0}{29} \\ sinA=0.9774 \\ find\text{ the arcsin} \\ A=\sin^{-1}0.9774 \\ A=77.79^0 \\ A\approx78^0(nearest\text{ whole number\rparen} \end{gathered}[/tex]Hence,
The measure of angle A to the nearest whole number is
[tex]\Rightarrow78^0[/tex]How do I solve this problem?By using the pythagorean identities.
Given the equation:
[tex]\sin ^2x(\csc ^2x-1)[/tex]Using the Pythagorean identities
so,
[tex]\csc ^2x-1=\cot ^2x[/tex]so, the equation will be:
[tex]\begin{gathered} \sin ^2x\cdot\cot ^2x \\ \\ =\sin ^2x\cdot\frac{\cos ^2x}{\sin ^2x} \\ \\ =\cos ^2x \end{gathered}[/tex]10^-6/10^-2 this is my question
Answer:
[tex] \frac{1}{10000} [/tex]
or Decimal
[tex]0.0001[/tex]
Step-by-step explanation:
Greetings !
look at the figure i have attached above
Hope it helps !!
6.25 ft7.25 cm11 cm8.921.6 m
The area of the shaded region can determined by substracting the area of rectangle from the area of triangle,
[tex]\begin{gathered} A=A_r-A_t \\ =14\operatorname{cm}\times25\operatorname{cm}-(\frac{1}{2}\times11\operatorname{cm}\times25) \\ =212.5cm^2 \end{gathered}[/tex]Thus, the area of the shaded region is 212.5 square centimeters.
Write the domain and range of g as intervals or unions of intervals
It's important to know that empty circles refer to open intervals or parenthesis.
In this case, we observe that the first interval of the domain is (-1, 1) and the second interval of the domain is (2, 5), so the whole domain would be the union of these two intervals.
[tex]\text{Domain}=(-1,1)\cup(2,5)[/tex]To obtain the range, let's observe the y-values. The function goes from y = -5 to y = 3, so the range would be
[tex]Range=(-5,3)[/tex]the store bought a bike from the factory for 90$ and sold it to Andre for 117 what percentage was the markup?
The markup percentage was
[tex]\begin{gathered} P=\frac{117-90}{90}\cdot100 \\ P=\frac{27}{90}\cdot100 \\ P=30 \end{gathered}[/tex]The markup percentage was 30%.
Keisha is making potato casserole for a party. she needs 3/2 of a potato per guest. how many potatoes will she need for 15 guest
Keisha needs 3/2 of potato per guest ( i.e one guest is equivalent to 3/2 potato)
Thus, for 15 guests
she needs;
[tex]\begin{gathered} 15\text{ }\times\frac{3}{2} \\ \frac{15\times3}{2}=\frac{45}{2} \\ 22\frac{1}{2} \end{gathered}[/tex]Keisha needs 45/2 potatoes for 15 guests
Carlos builds a robot that moves with small wheels. each wheel has six 5 inch long metal spokes that meet in the center what is the length of the arc
Answer:
Explanation:
a)
The formula for calculating the length of an arc is expressed as
Length of arc = θ/360 x 2πr
where
θ is the angle subtended at the center of the circle.
r is the radius of the circle
From the information given,
diameter = 5(length of each metal spoke)
r =diameter/2 = 5/2 = 2.5
Recall, the total angle in the circle is 360 degrees. There are 8 partitions. Angle between consecutive spokes is
360/8 = 45. Thus,
θ = 45
Length of are between consecutive spokes = 45//360 x 2 x π x 2.5
Length of are between consecutive spokes = 5π/8
b) The formula for calculating the area of a sector is expressed as
area of a sector = θ/360 x πr^2
By substituting the values,
area of a sector = 45/360 x π x 2.5^2
Area of sector = 25π/32 square inches
Can you please also give all forms of the end behavior such as ups/downs, as_,_ , and limits #25
The given function is a rational function
We will find the zeros of the denominator
[tex]\begin{gathered} 2x+1=0 \\ 2x=-1 \\ x=\frac{-1}{2} \end{gathered}[/tex]The end behavior of the function will be as follows:
[tex]\begin{gathered} x\rightarrow(-\frac{1}{2})^-;f(x)\rightarrow\infty \\ x\rightarrow(-\frac{1}{2})^+;f(x)\rightarrow-\infty \\ x\rightarrow\infty;f(x)\rightarrow\frac{1}{2} \\ x\rightarrow-\infty;f(x)\rightarrow\frac{1}{2} \end{gathered}[/tex]The graph of the function is as follows:
what is the arc measure of ct in radians? what is the arc length in feet?
We will determine the arch lenght (In radians) as follows:
*First: We transform the measure of the angle from degrees to radians, that is:
[tex]\theta=80\cdot\frac{\pi}{180}\Rightarrow\theta=\frac{4\pi}{9}[/tex]*Second: We find the arc length:
[tex]s=r\theta\Rightarrow s=(13.2)(\frac{4\pi}{9})[/tex][tex]\Rightarrow s=\frac{88}{15}\pi[/tex]So, the arc length for CT is 88pi/15 radians.
*Third: We find its measure in feet:
[tex]s\approx18.43[/tex]So, the arch length for CT in feet is approximately 18.43 feet.
Find LM tangent angle circle
Applying the two-tangent theorem, the length of LM is: A. 18.
What is the Two-Tangent Theorem?The two-tangent theorem states that if two tangents are drawn from a circle to meet at a point outside the circle, then the tangent segments are congruent to each other, that is they have equal lengths.
Segments LK and LM are tangent segments drawn to meet at the external point L. This means, the length of Lk and the length of LM would be equal to each other.
LK = 4x - 2
LM = 3x + 3
LK = LM
Substitute
4x - 2 = 3x + 3
Combine like terms
4x - 3x = 2 + 3
x = 5
LM = 3x + 3
Plug in the value of x
LM = 3(5) + 3
LM = 15 + 3
LM = 18
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A line contains points F, G, H, I, J. The space between F G is 2. The space between H and I is 1. The space between F and I is 7.
If FG = 2 units, FI = 7 units, and HI = 1 unit, what is GH?
3 units
4 units
5 units
6 units
The measure of GH is 4 units.
The correct option is (B)
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Given:
FG = 2 units, FI = 7 units, and HI = 1 unit
Now,
FI = FG+ GH +HI
7= 2 + GH + 1
7= 3 + GH
GH = 7-3
GH = 4 units
Hence, the measure of GH is 4 units.
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If n = 100 and p= 1/5, what is the mean and standard deviation of this binomial distribution?
The most appropriate choice for binomial distribution will be given by-
Mean of binomial distribution= 20
Standard deviation of binomial distribution = 16
What is binomial distribution?
Let there are n number of success or failure experiment called Bernouli trial and let p be the probability of success. Binomial distribution with parameters n and p is the probability distribution of p successes in n number of Bernouli trials.
Probability mass function of Binomial distribution
P(x = k) = [tex]n \choose k[/tex][tex]p^k(1-p)^k[/tex]
Here,
n = 100,
p = [tex]\frac{1}{5}\\[/tex]
1 - p = [tex]1 - \frac{1}{5}[/tex]
= [tex]\frac{5-1}{5}[/tex]
= [tex]\frac{4}{5}[/tex]
Mean of binomial distribution = np
= [tex]100 \times \frac{1}{5}\\[/tex]
=20
Standard deviation of binomial distribution =
[tex]100 \times \frac{1}{5}(1- \frac{1}{5})\\100 \times \frac{1}{5} \times \frac{4}{5}\\16[/tex]
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A group of friends were working on a student film. They spent all their budget on equipment and props. They spent $369 on equipment and 55% of the total budget on props. What was the total budget for their student film
Answer: t = 820
Step-by-step explanation:
1) Set up the equation
369 + 55%t = t
2) Simplify the percentage
369+ 0.55t = t
3) Minus 0.55 t on both sides
369 = 0.45t
4) Set t by itself.
t = 820
A price-taking firm makes air conditioners. The market price of one of its new air conditioners is $125. The firms total cost information is given in the table below
1. Calculating the marginal cost per day yields the following results:
Air conditioners Total cost Marginal cost
per day ($ per day) ($ per day)
1 100 100
2 150 50
3 220 70
4 310 90
5 405 95
6 510 105
7 650 140
8 800 150
2. To maximize profits, the price-taking firm should produce 6 air conditioners per day.
What is the profit-maximizing point?The profit-maximizing point or units is the output and price interaction that ensures that the marginal revenue equals the marginal cost.
The marginal revenue (MR) is the revenue earned from an additional unit. The marginal cost (MC) is the production cost per additional unit.
For price-taking firms, the maximum profit is achieved at the level of output where MC equals MR.
Market Price for one unit = $125
Air conditioners Total cost Marginal cost
per day ($ per day) ($ per day)
1 100 100 (100 - 0)
2 150 50 (150 - 100)
3 220 70 (220 - 150)
4 310 90 (310 - 220)
5 405 95 (405 - 310)
6 510 105 (510 - 405)
7 650 140 (650 - 510)
8 800 150 (800 - 650)
Thus, profit is not maximized where the MC exceeds the MR. Instead producing at that unit reduces profit.
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Question Completion:Total Cost Information
Air conditioners Total cost
per day ($ per day)
1 100
2 150
3 220
4 310
5 405
6 510
7 650
8 800
1. Calculate marginal cost per day, and enter your responses as whole numbers.
2. How many air conditioners should the firm produce per day if its goal is to maximize its profit? air conditioners per day.