A fiar coin is tossed 3 times in succession.
The results for each experiment is displayed as follows;
[tex]\begin{gathered} \text{HHH} \\ \text{HHT} \\ \text{HTH} \\ \text{THH} \\ \text{HTT} \\ \text{THT} \\ \text{TTH} \\ \text{TTT} \end{gathered}[/tex]On each toss from the above results, the probability of getting a tail would include all results that has a tail come up. That would be;
[tex]P\lbrack\text{Event\rbrack}=\frac{\text{Number of required outcomes}}{Number\text{ of all possible outcomes}}[/tex][tex]P\lbrack\text{tail\rbrack}=\frac{4}{8}[/tex]Note that to get a tail on the "second toss" would mean to get a result with a tail as the second out of three. We have 7 outcomes with tails. However 4 of these has a tail as a second outcome, hence we have the required outcome as 4 out of a total of 8.
ANSWER:
Probability of getting a tail on the second toss is
[tex]P\mleft\lbrace\text{tail}\mright\rbrace=\frac{1}{2}[/tex]I’ve attached my problem thank youfind the area of the shaded area
Giving the circle with 2 radius
Radius 1= 12
Radius 2=10
this figure is also known as a ring
the area of the ring is given by
[tex]A=\pi r1^2-\pi r2^2[/tex]this is just the difference of the area of the bigger circle less the smaller circle
then
[tex]A=\pi(r1^2-r2^2)[/tex][tex]A=\pi(12^2-10^2)[/tex][tex]A=\pi(44)[/tex][tex]A=44\pi=138.230[/tex]There are currently 400,000 cats in the San Diego area. The number of cats in San Diego increases each year by 2.5 % A) how many cats will there be in the year 2036 ? B) how long will it be before the number of cats doubles ?
a) 436529 cats b) Approximately 278 years
1) Gathering the data
400,000 cats
Increases yearly by 2.5%
2) Let's write that growth as a function. Note that we must rewrite 2.5% as purely decimal 0.0025. A growth of 2.5 must be written as 1.0025.
Because every time we multiply by 1.0025 we are multiplying the number and 2.5%. Considering that there are currently, in this 1st year 400,000 cats 2036 then this will be 35 years after
[tex]\begin{gathered} y=400000(1.0025)^n \\ y=400000(1.0025)^{35} \\ y=436529.23\text{ }\cong436,529\text{ } \end{gathered}[/tex]So considering we're in the first year, 35 years after in 2036 there'll be 436,529
b) Since n= is the number of years in that function, and y stands for the number of cats.
[tex]\begin{gathered} 800,000=400,000(1.0025)^n \\ \frac{800,000}{400,00}=\frac{400,000}{400,000}(1.0025)^n \\ 2=(1.0025)^n \\ \log 2\text{ =}\log (1.0025)^n \\ 0.3=^{}n1.08\cdot10^{-3} \\ n=\frac{0.3}{1.08\cdot10^{-3}} \\ n=277.8 \\ \end{gathered}[/tex]So, it will take at this rate approximately 278 years for the population of cats doubles.
13. Solve the inequality and share a graph on a number line
Given the following inequality:
[tex]-3(t\text{ - 2) }\ge\text{ -15}[/tex]We get,
[tex]-3(t\text{ - 2) }\ge\text{ -15}[/tex][tex]\frac{-3(t\text{ - 2)}}{-3}\text{ }\ge\text{ }\frac{\text{-15}}{-3}[/tex][tex]t\text{ - 2 }\ge\text{ }5[/tex][tex]t\text{ }\ge\text{ }5\text{ + 2}[/tex][tex]t\text{ }\ge\text{ }7[/tex]Graphing this on a number line will be:
568,319,000,000,000,000,000,000,000 in standard form
To write in standard form;
568,319,000,000,000,000,000,000,000
Move the decimal point backward till you reach the last number
Multiply by ten raise to the number of times you move the decimal point
That is;
568,319,000,000,000,000,000,000,000 = 5.68319 x 10^26
[tex]5.68319\text{ }\times10^{26}[/tex]if the endpoints of KB are K(-4, 5) and B(2, -5), what is the length of KB?
The length of the line can be found by distance formula as,
[tex]\begin{gathered} KB=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ KB=\sqrt[]{(2-(-4)_{})^2+(-5-5)^2} \\ KB=\sqrt[]{(2+4)^2+(-10)^2} \\ KB=\sqrt[]{6^2+100} \\ KB=\sqrt[]{36+100} \\ KB=\sqrt[]{136} \\ KB=11.66 \end{gathered}[/tex]PLS HELP FAST I WILL GIVE 25 POINTS simplify 10^6/10^-3. answers:A. 1/10^3. B. 1/10^18. C. 10^3. D. 10^9
D
Let's simplify that expression
1) Remember of the Exponents Rule, we have to subtract them
2) Note that for the exponents 6 -(-3) = 6+3 = 9 So it's D
i inserted a picture of the questionif it helps i can give you my answer to my previous question
In order to determine the time it takes for the music player to fall to the bottom of the ravine, we shall find the solutions of t as follows;
[tex]\begin{gathered} t=\sqrt[]{\frac{8t+24}{16}} \\ \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} t^2=\frac{8t+24}{16} \\ \text{Cross multiply and we'll have;} \\ 16t^2=8t+24 \\ \text{ Re-arrange the terms and we'll now have;} \\ 16t^2-8t-24=0 \end{gathered}[/tex]We can now solve this using the quadratic equation formula;
[tex]\begin{gathered} \text{The variables are;} \\ a=16,b=-8,c=-24 \\ t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(16)(-24)_{}}}{2(16)} \\ t=\frac{8\pm\sqrt[]{64+1536}}{32} \\ t=\frac{8\pm\sqrt[]{1600}}{32} \\ t=\frac{8\pm40}{32} \\ t=\frac{8+40}{32},t=\frac{8-40}{32} \\ t=\frac{48}{32},t=-\frac{32}{32} \\ t=1.5,t=-1 \end{gathered}[/tex]We shall now plug each root back into the original equation, as follows;
[tex]\begin{gathered} \text{Solution 1:} \\ \text{When t}=1.5 \\ t=\sqrt[]{\frac{8t+24}{16}} \\ t=\sqrt[]{\frac{8(1.5)+24}{16}} \\ t=\sqrt[]{\frac{12+24}{16}} \\ t=\sqrt[]{\frac{36}{16}} \\ t=\frac{6}{4} \\ t=1.5\sec \end{gathered}[/tex][tex]\begin{gathered} \text{Solution 2:} \\ \text{When t}=-1 \\ t=\sqrt[]{\frac{8(-1)+24}{16}} \\ t=\sqrt[]{\frac{-8+24}{16}} \\ t=\sqrt[]{\frac{16}{16}} \\ t=\frac{4}{4} \\ t=1 \end{gathered}[/tex]From the result shown the ballon will deploy after 1.5 seconds for the first solution.
However t = -1 cannot be a solution since you cannot have a negative time (-1 sec)
ANSWER:
t =1.5 is a solution
if frita goes to the mall, then alice will go to the mall
Given
The statements,
If Frita goes to the mall, then Alice will go to the mall.
If Wally goes to the mall, then Frita will go to the mall.
To find: The conclusion using the law of Syllogism.
Explanation:
It is given that,
If Frita goes to the mall, then Alice will go to the mall.
If Wally goes to the mall, then Frita will go to the mall.
That implies,
If Wally goes to the mall, then Frita will go to the mall.
If Frita goes to the mall, then Alice will go to the mall.
Here, consider the statement Wally goes to the mall as p, the statement Frita will go to the mall as q, and the statement Alice will go to the mall as r.
Therefore,
[tex]Conclusion:\text{ }If\text{ }Wally\text{ }goes\text{ }to\text{ }the\text{ }mall,\text{ }then\text{ }Alice\text{ }will\text{ }go\text{ }to\text{ }the\text{ }mall.[/tex]Hence, the answer is option C).
For each problem below find the missing factor by computing the inverse operation
Given:
There are given that the fraction:
[tex]4\frac{1}{2}-\text{ \lbrack \rbrack}=2\frac{7}{8}[/tex]Explanation:
Suppose missing information is x
Then,
Ater that we need to find the value of x
So,
[tex]4\frac{1}{2}-x=2\frac{7}{8}[/tex]Then,
[tex]\begin{gathered} 4\frac{1}{2}-x=2\frac{7}{8} \\ \frac{9}{2}-x=\frac{23}{8} \\ \frac{9}{2}-x-\frac{9}{2}=\frac{23}{8}-\frac{9}{2} \\ -x=\frac{23}{8}-\frac{9}{2} \end{gathered}[/tex]Now,
[tex]\begin{gathered} -x=\frac{23}{8}-\frac{9}{2} \\ -x=\frac{23-36}{8} \\ -x=\frac{-13}{8} \\ x=\frac{13}{8} \\ x=1\frac{5}{8} \end{gathered}[/tex]Final answer:
Hence, the missing factor is shown below:
[tex]x=1\frac{5}{8}[/tex]In your Grandpa Will's recipe for a marinade, each serving uses 3.5 tablespoons of ketchup and 7 tablespoons of vinegar. If 31.5 tablespoons of ketchup will be used for a larger batch of marinade, how much vinegar is needed? tablespoons of vinegar are needed. Submit answer
The rate of ketchup to vinegar should be preserved. Let V be the volume of vinegar that will be used for the larger batch of marinade. Since the recipe uses 7 tablespoons of vinegar for each 3.5 tablespoons of ketchup, then:
[tex]\frac{V}{31.5}=\frac{7}{3.5}[/tex]Then, the volume of vinegar for the larger batch of marinade can be calculated as:
[tex]\begin{gathered} V=\frac{7}{3.5}\times31.5 \\ =63 \end{gathered}[/tex]Therefore, 63 tablespoons of vinegar are needed.
33<=105/p what is the answer
The answer is p≤35/11.
From the question, we have
33≤105/p
⇒p≤105/33
⇒p≤35/11
Inequality:
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
When the symbols ">", "", "", or "" are used to connect two real numbers or algebraic expressions, that relationship is known as an inequality.
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Which of the following graphs could be a representation of a geometric sequence?Check all that apply.A.B.C.D.
SOLUTION:
We want to find the graph corresponding to a geometric sequence.
The equation of a geometric sequence is;
[tex]a_n=a_1(r)^{n-1}[/tex]This is clearly an exponential function with a starting value a.
The correct graphs are OPTION B and OPTION D
Please help me solve question 6 on this algebra assignment
At the zero of the function, f(x) = 0. Substituting f(x) = 0, we get:
[tex]0=\frac{3}{5}x-\frac{4}{3}[/tex]Adding 4/3 at both sides of the equation:
[tex]\begin{gathered} 0+\frac{4}{3}=\frac{3}{5}x-\frac{4}{3}+\frac{4}{3} \\ \frac{4}{3}=\frac{3}{5}x \end{gathered}[/tex]Multiplying by 5/3 at both sides of the equation:
[tex]\begin{gathered} \frac{5}{3}\cdot\frac{4}{3}=\frac{5}{3}\cdot\frac{3}{5}x \\ \frac{5\cdot4}{3\cdot3}=x \\ \frac{20}{9}=x \end{gathered}[/tex]Therefore the coordinates of the zero of the function are:
[tex](x,f(x))=(\frac{20}{9},0)[/tex]
On 14 would I solve the 32x + 72 or is that the answer. The app stopped in the middle of the other tutor
The given expression is 8(4x+9)
Multiplying 8 to each term of (2x+9), we get
[tex]8(4x+9)=8\times4x+8\times9[/tex][tex]=32x+72.[/tex]"Name the property used in the equation below
a) 3 x+9 y-1=3(x+3 y)-1
b) 7 x+5 y-5 y=7 x
c) (x-4)(x+3)=0
d) 4 x+5 x=5 x+4 x"
The property used in each equation are
a) 3x + 9y - 1 = 3(x + 3y) - 1 distributive property
b) 7x + 5y - 5y = 7x additive inverse property
c) (x - 4)(x + 3) = 0 distributive property
d) 4x + 5x = 5x + 4x commutative property
What is distributive property?The distributive property states that multiplying the total of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and adding the products together.
Additive inverse involves adding which involves two numbers that has opposite sign. the addition lead to zero
b) 7x + 5y - 5y = 7x
= 7x + 0
= 7x
What is commutative property?
This law basically asserts that while adding and multiplying numbers, you can rearrange the numbers in a problem without changing the solution.
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There are 14 girls and 12 boys in a class. What is the ratio of gris to students in simplest form
Number of girls = 14
Number of boys = 12
Number of students = 14 + 12 =26
Ratio of girls to students = 14/26 = 7 : 13
The constant of variation for a function is 2. Which of the following graphs best represents this situation
The required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
Given that,
To determine the graphs which show the constant of variation for a function is 2.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
in the graphs only graph, A and B show the given condition of the constant of variation for a function is 2. Because in both graphs shows that y = 2x and 2y = x.
Thus, the required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
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f(x)=4•2^2x,g(x)=2^4x+2, and h(x)=4^2x+1
Let's use the following property:
[tex]x^y\cdot x^z=x^{y+z}[/tex][tex]\begin{gathered} f(x)=4\cdot2^{2x} \\ g(x)=2^{4x+2}=2^{4x}\cdot2^2=4\cdot2^{4x} \\ h(x)=4^{2x+1}=4^{2x}\cdot2^{1^{}}=2\cdot4^{2x} \\ \text{Therefore:} \\ \text{None of them are equivalent} \end{gathered}[/tex]A couple took a small airplane for a flight to the wine country for a romantic dinner and then returned home. The plane flew a total of 5 hours and each way the trip was 233 miles. If the plane was flying at 170 miles per hour, what was the speed of the wind that affected the plane?
Answer:
114.26 miles per hour
Explanation:
Let us call
v = wind speed
Then
speed with the wind = 170 + v
speed against the wind = 170 -v
Therefore,
The time taken on the outward journey ( with the wind):
[tex]\frac{233}{170+v}[/tex]
Time take on the return journey
[tex]\frac{233}{170-v}[/tex]These two times must add up to 5 hours, the total time of the journey.
[tex]\frac{233}{170+v}+\frac{233}{170-v}=5[/tex]Solving the above equation for v will give us the wind speed.
The first step is to find the common denominator of the two rational expressions. We do this by multiplying the left rational expression by (180-v)/(180-v) and the right expression by (180 + v)/(180 + v).
[tex]\frac{170-v}{170-v}*\frac{233}{170+v}+\frac{233}{170-v}*\frac{170+v}{170+v}=5[/tex][tex]\frac{233(170-v)+233(170+v)}{(170-v)(170+v)}=5[/tex]Dividing both sides by 233 gives
[tex]\frac{(170-v)+(170+v)}{(170-v)(170+v)}=\frac{5}{233}[/tex]The numerator on the left-hand side of the equation simplifies to give
[tex]\frac{2\times170}{(170-v)(170+v)}=\frac{5}{233}[/tex][tex]\Rightarrow\frac{340}{(170-v)(170+v)}=\frac{5}{233}[/tex]Expanding the denominator gives
[tex]\operatorname{\Rightarrow}\frac{340}{170^2-v^2}=\frac{5}{233}[/tex][tex]\frac{340}{28900-v^2}=\frac{5}{233}[/tex]Cross multipication gives
[tex]5(28900-v^2)=340\times233[/tex]Dividing both sides by -5 gives
[tex]v^2-28900=-\frac{340\times233}{5}[/tex][tex]v^2-28900=-15844[/tex]Adding 28900 to both sides gives
[tex]v^2=13056[/tex]Finally, taking the sqaure root of both sides gives
[tex]\boxed{v=114.26.}[/tex]Hence, the speed of the wind, rounded to two decimal places, was 114.26 miles per hour.
4^2 * 4^3 simplified
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]4^2\ast4^3[/tex]STEP 2: Simplify the expression using the law of indices
[tex]\begin{gathered} \mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c} \\ 4^2\cdot \:4^3=4^{2+3} \\ =4^{\left\{2+3\right\}} \\ =4^5=1024 \end{gathered}[/tex]Hence, the evaluation gives:
[tex]1024[/tex]Select the correct answer.What is the image of this figure after this sequence of dilations?1. dilation by a factor of -1 centered at the origin2. dilation by a factor of 2 centered at (-1,1)
The coordinates of the original figure are:
(-2,1)
(3,1)
(1,3)
(-2,3)
A dilation by a negative scale factor produces an image on the other side of the center of enlargement.
As the first dilation is by a factor of -1 centered at the origin, the length of the sides doesn't change, but the new coordinates will be:
[tex](x,y)\to(kx,ky)[/tex]Apply this to the given coordinates:
[tex]\begin{gathered} (-2,1)\to(-1\cdot-2,-1\cdot1)\to(2,-1) \\ (3,1)\to(-1\cdot3,-1\cdot1)\to(-3,-1) \\ (1,3)\to(-1\cdot1,-1\cdot3)\to(-1,-3) \\ (-2,3)\to(-1\cdot-2,-1\cdot3)\to(2,-3) \end{gathered}[/tex]The image after the first dilation looks like this:
Now, the second dilation is by a scale factor of 2, centered at (-1,1).
As it is not centered in the origin, we can use the following formula:
[tex](x,y)\to(k(x-a)+a,k(y-b)+b)[/tex]Where k is the scale factor and (a,b) are the coordinates of the center of dilation.
By applying this formula to the actual coordinates we obtain:
[tex]\begin{gathered} (2,-1)\to(2(2-(-1))+(-1),2(-1-1)+1)\to(5,-3) \\ (-3,-1)\to(2(-3-(-1))+(-1),2(-1-1)+1)\to(-5,-3) \\ (-1,-3)\to(2(-1-(-1))+(-1),2(-3-1)+1)\to(-1,-7) \\ (2,-3)\to(2(2-(-1))+(-1),2(-3-1)+1)\to(5,-7) \end{gathered}[/tex]If we place these coordinates in the coordinate plane we obtain:
The answer is option B.
Answer:
B .
Step-by-step explanation:
Got the answer right.
write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the graph of the given equations(0,0); y = -6x+3y =
To find the equation of the line we need a point and the slope. We have the point but we need to find the slope, to do this we need to remember that two lines are perpendicular if and only if their slopes fullfils:
[tex]m_1m_2=-1[/tex]Now, the slope of the line given is -6, this comes from the fact that the line is written in the form y=mx+b, hence comparing both equation we conclude that.
Pluggin this value into the condition above we have:
[tex]\begin{gathered} -6m_1=-1 \\ m_1=\frac{-1}{-6} \\ m_1=\frac{1}{6} \end{gathered}[/tex]Therefore the slope of the line we are looking for is 1/6. The equation of a line is given as:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values of the slope and the point we have:
[tex]\begin{gathered} y-0=\frac{1}{6}(x-0) \\ y=\frac{1}{6}x \end{gathered}[/tex]Therefore the equation we are looking for is:
[tex]y=\frac{1}{6}x[/tex](x + y)² – 3zz when X = -2, y = -4, and z = 5.
-39
Explanation
[tex]\begin{gathered} \mleft(x+y\mright)^2-3zz \\ \end{gathered}[/tex]Step 1
let
x=-2
y=-4
z=5
Step 2
Now, replace those values in the expression
[tex]\begin{gathered} (x+y)^2-3zz \\ (-2+(-4))^2-3\cdot5\cdot5 \\ (-2-4)^2-75 \\ (-6)^2-75 \\ 36-75 \\ -39 \end{gathered}[/tex]I hope this helps you
If y varies inversely as x and y=−97 when x=28, find y if x=36. (Round off your answer to the nearest hundredth.)
For this problem, we were informed that two variables "x" and "y" vary inversely to each other. We were also informed about one data point on the relation between the two (28, -97). From this information, we need to determine the value of "y" when "x" is equal to 36.
We can write the expression between two variables that vary inversely according to a constant, K, as shown below:
[tex]\begin{gathered} y\cdot x=k \\ y=\frac{k}{x} \end{gathered}[/tex]We can find the value of k by applying the known datapoint.
[tex]\begin{gathered} -97=\frac{k}{28} \\ k=-97\cdot28 \\ k=2716 \end{gathered}[/tex]The full expression is:
[tex]y=\frac{2716}{x}[/tex]Now we can apply the value of "x" to calculate the desired "y".
[tex]y=\frac{2716}{36}=75.44[/tex]The value of "y" is 75.44, when "x" is 36
Please help on average rate of change!
The average rate of change on the interval [-1, 2] is 1/3.
How to get the average rate of change?For any function f(x), we define the average rate of change on an interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
In this case, the function is graphed, and the interval is [-1, 2]
On the graph we can see that:
f(-1) = -3
and
f(2) = -2
Replacing these we will get:
r = ( f(2) - f(-1))/(2 - (-1))
r = (-2 + 3)/(3) = 1/3
The average rate of change is 1/3.
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four times a number increased by 2 is less than -24
Four times a number increased by 2 is less than -24
The number (x)
4x +2 < -24
_________________
Solving
4x +2 < -24
4x < -24 -2
4x < -26
x<-26/4
x < -6.5
__________________
Answer
x < -6.5
the five number summary for a set of data is given in the picture.what is the interquartile range of the set of data?
ANSWER
[tex]IQR=13[/tex]EXPLANATION
The interquartile range can be found by finding the difference between the first quartile, Q1, and the third quartile, Q3.
That is:
[tex]IQR=Q3-Q1[/tex]Therefore, the interquartile range is:
[tex]\begin{gathered} IQR=81-68 \\ IQR=13 \end{gathered}[/tex][tex]2x ^{2} - 6x + 10 = 0[/tex]solve by completing the square
We know that we can use the quadratic equation
Using this we have
[tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot2\cdot10}}{2\cdot2}=\frac{6\pm\sqrt[]{36-80}}{4} \\ =\frac{6\pm\sqrt[]{-44}}{4}=\frac{6\pm\sqrt[]{4\cdot-11}}{4}=\frac{6\pm2\cdot\sqrt[]{-11}}{4} \\ =2\cdot(\frac{3\pm\sqrt[]{-11}}{4})=\frac{3\pm\sqrt[]{-11}}{2}=\frac{3\pm\sqrt[]{11}i}{2} \\ =\frac{3}{2}\pm\frac{\sqrt[]{11}}{2}i \end{gathered}[/tex]So the answer is B)
Need help with homework
Domain interval are the interval for the x - values on the linear graph
Therefore the domain intervals from the attached graph is
[tex]-3\leq x\leq4[/tex]ActiveApplying the Triangle Inequality Theoremin triangle ABC, AB measures 25 cm and AC measures 35 cm.The inequalitycentimeters.
Using the Triangle inequality:
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