Mutually exclusive events:
Two events are mutually exclusive if they cannot occur at the same time.
There are 52 cards in a deck of cards.
n(s)=52.
Let A be event of getting jack.
n(A)=4.
So, Probability of getting jack is,
Let B be event of getting 4
n(B)=4.
So, Probability of getting 4 is,
[tex]\begin{gathered} P(B)=\frac{n(B)}{n(s)} \\ =\frac{4}{52} \end{gathered}[/tex]These two events do not occur at same time.
Therefore the events are mutually exclusive.
[tex]P(A\cap B)=0[/tex]To find the probability of getting jack or 4
[tex]P(\text{A }\cup\text{B)}=P(A)+P(B)-P(A\cap B)[/tex]hence,
[tex]\begin{gathered} P(\text{A }\cup\text{B)}=\frac{4}{52}+\frac{4}{52}-0 \\ =\frac{8}{52} \\ =\frac{2}{13} \end{gathered}[/tex]The probability of getting jack or 4 is,
[tex]\frac{2}{13}[/tex]solve for theta. Enter answer only round to the tenth
ANSWER:
[tex]\theta=62.73\text{\degree}[/tex]STEP-BY-STEP EXPLANATION:
We can calculate the value of the angle by means of the trigonometric ratio sine which is the following
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{ hypotenuse}} \\ \text{opposite = 24} \\ \text{hypotenuse = 27} \end{gathered}[/tex]Replacing and solving for the angle:
[tex]\begin{gathered} \sin \theta=\frac{24}{27} \\ \theta=\arcsin (\frac{24}{27}) \\ \theta=62.73\text{\degree} \end{gathered}[/tex]18. What is the value of f(-2) for the function f(x) = 2(3Y"?A12fca=acze33B118С.29D. 18
Given the function:
[tex]f(x)=2(3)^x[/tex]To find f(-2), substitute x for -2 in the function.
[tex]f(-2)=2(3)^{-2}[/tex]Solving further using law of indicies, we have:
[tex]\begin{gathered} f(-2)\text{ = }\frac{2}{3^2} \\ \\ f(-2)\text{ = }\frac{2}{9} \end{gathered}[/tex]ANSWER:
[tex]\frac{2}{9}[/tex]order the fallowing numbers from least to greatest -3, -3.12, 1 1/2
Solution:
Consider the following numbers:
[tex]-3[/tex][tex]-3.12[/tex]and the mixed number:
[tex]1\frac{1}{2}=\frac{(2\text{ x 1)+1}}{2}=\frac{3}{2}\text{ =}1.5[/tex]now, applying the usual order of the real numbers, we have that:
[tex]-3,12<-3<1.5[/tex]then, the order of the given numbers from least to greatest is:
[tex]-3.12[/tex][tex]-3[/tex][tex]1\frac{1}{2}[/tex]what is a solution to the inequality below [tex] \sqrt{x} \ \textgreater \ 6[/tex]
Answer:
C. x > 36
Explanation:
Taking the square of both sides gives
[tex](\sqrt[]{x})^2=6^2[/tex][tex]x>36[/tex]Therefore, looking at the answer choice, we see that choice C is the correct one.
1 point The following expression represents monthly growth. What is the yearly rate of growth? (1.04)^m
(1.04)^m
m= Months
One year has 12 months_
(1.04)^12 = 1.60
0.60 = yearly rate of growth
Define Miller for the perimeter P of a rectangle with length L and width W is p equals 2L + 2W. which of the following is the formula for the length of a rectangle in terms of the perimeter and width.a.l equals B- W / 2 b.l equals b + W / 2 c.l equals P -2 W / 2 d.l equals p + 2 W / 2
P = 2L + 2W ok
2L = P - 2W
L = (P - 2W)/2 This is the correct answer
I think it's letter C
Problem 2.
4x - 4 > 12
4x > 12 + 4
4x > 16
x > 16/4
x > 4 This is the correct choice
Hello I need help with this problem for my home work here’s a picture
The Solution:
Given:
We are required to find the equivalent of the given expression.
Simplifying the given expression, we get:
[tex]4x^2\sqrt{5x^4}\cdot3\sqrt{5x^8}=4x^2\times x^2\sqrt{5}\times3x^4\sqrt{5}[/tex][tex]=4x^2\times x^2\times3x^4\times\sqrt{5}\times\sqrt{5}=4x^4\times3x^4\times5=60x^8[/tex]Therefore, the correct answer is [option B]
A school wants to put a bond in the next election, they call this bond Measure K. Before puttingthe bond on the ballot, they want to see how much support they would have from voters in thecounty. They select a random sample of voters in the county, and find a 90% confidence intervalfor the proportion of voters in this county who would vote yes. In order to do this, they neededto use:(Multiple choice)O 1 proportion (z) confidence intervalO 1 proportion (2) hypothesis testO 2 proportion (z) confidence intervalO 2 proportion (2) hypothesis test
A school wants to put a bond in the next election, they call this bond Measure K.
They select a random sample of voters in the county and find a 90% confidence interval for the proportion of voters in this county who would vote yes.
Recall that a hypothesis test is used when we want to test an assertion or a claim.
For the given case, there is no assertion or any claim so this is definitely not a hypothesis test.
This is in fact a confidence interval since we are interested in the proportion of voters in this county who would vote yes.
The confidence interval would give us a fair estimate of the true population proportion of voters in this county who would vote yes.
Now coming to whether is it a 1 proportion or 2 proportion confidence interval.
Notice that there is only 1 proportion for the given case that is the proportion of voters in this county who would vote yes.
Therefore, the need to use "1 proportion (z) confidence interval"
Passing through (-2, 8) and PERPENDICULAR to y = 2x + 5
the equation of the line is,
y = 2x + 5
the slope of the line is m = 2
the slope of the line perpendicular to y = 2x + 5 is ,
m = -1/2
it is passing through (-2,8)
so the equation of the line is
[tex]y-8=(-\frac{1}{2})(x-(-2))[/tex][tex]\begin{gathered} y-8=-\frac{1}{2}x-1 \\ y=-\frac{1}{2}x+7 \end{gathered}[/tex]thus the equation of the line is,
y = -1/2 x + 7
what would the correlation coefficient -0.86 represent in the context of the situation?
Here, the table and scatter plot show the relationship between the number of missing assignment and the student's grade.
The correlation coefficient shows the relationship between the number of missing assignments and the student's grade.
To find the correlation coefficient, we have:
Make a straight line to connect the points on the graph
The correlation coefficient r, = -0.86
ANSWER:
-0.
this is 50 points help me out k
Answer: It is 45
Step-by-step explanation:
you have 5 four and the number is 4
How can I solve this?x=AD=AB= 5X-4DB=x+1
AD = AB + DB
AD = (5x - 4) + (x+1)
= 5x - 4 + x + 1
= 5x + x - 4 + 1
AD = 6x - 3
Given the image, if AB is a semicircle and DB = 70 degrees, what is the measure of ACD?
Hi can you please help me with this problem?The shape is shown below What is the area of the triangle below (in square units)?
ANSWER:
28 square inches
STEP-BY-STEP EXPLANATION:
Given:
Base = 7 inches
Height = 8 inches
We can calculate the area with the help of the triangle area formula, which is as follows:
[tex]A=\frac{1}{2}b\cdot h[/tex]We replacing:
[tex]\begin{gathered} A=\frac{1}{2}\cdot7\cdot8 \\ A=28 \end{gathered}[/tex]The area is 28 square inches.
What is the area of the circle if CY= 5.4 mm
Given
The diameter is given XY = 5.4 mm.
Explanation
To determine the area of circle,
Use the area of circle formula.
[tex]A=\pi(r)^2[/tex]Find the radius, using the relation between diameter and radius.
[tex]d=2r[/tex]Substitute the diameter in the relation.
[tex]\begin{gathered} 5.4=2r \\ r=2.7mm \end{gathered}[/tex]Now substitute the radius in the area of circle formula.
[tex]\begin{gathered} A=(2.7)^2\pi \\ A=7.29\pi mm^2 \end{gathered}[/tex]Answer
Hence the area of circle is
[tex]7.29\pi mm^2[/tex]The correct option is C.
Part A: A landscape service charges costumers a one-time fee and an hourly rate of $15. For 3 hours of work m, it charges $75 Write the equation in point-slope formHow much does the landscape service charge for 20 hours
The hourly rate is the slope m, and we're given the point (3,75)
Now, using the point-slope form:
[tex]y-75=15(x-3)[/tex]Now, let's put it in the slope-intercept form (clear y):
[tex]\begin{gathered} y-75=15x-45 \\ \rightarrow y=15x+30 \end{gathered}[/tex]For 20 hours of service,
[tex]\begin{gathered} y=15(20)+30 \\ \rightarrow y=330 \end{gathered}[/tex]The service would charge $330
find the new price after the markup given. round to the nearest cent if necessary. $145 marked up 175%
Answer:
Explanation:
Given that the initial/cost price is;
[tex]\text{ \$145}[/tex]It was then marked up 175%.
The new price can be calculated using the formula;
[tex]\begin{gathered} S=C+r(C) \\ S=(1+r)C \\ \text{where;} \\ S=\text{ new price} \\ C=\text{ cost price} \\ r=\text{markup percent in fraction} \end{gathered}[/tex]Given;
[tex]\begin{gathered} C=\text{ \$145} \\ r=\frac{175\text{\%}}{100\text{\%}} \\ r=1.75 \end{gathered}[/tex]substituting:
[tex]\begin{gathered} S=(1+r)C \\ S=(1+1.75)\times\text{ \$145} \\ S=2.75\times\text{ \$145} \\ S=\text{ \$398.75} \end{gathered}[/tex]Therefore, the new price is;
[tex]undefined[/tex]For a standard normal distribution, find:P(Z > -1.79)Express the probability as a decimal rounded to 4 decimalplaces.
Given the probability:
[tex]P(Z>-1.79)[/tex]To find this probability, you have to use the tables for the standard normal distribution. These tables show the accumulated probability for the Z-distribution, this means that you can find the probability up to a determined Z-value. To find the probability above a determined Z-value you have to use the complementary probability, that is:
[tex]P(Z>-1.79)=1-P(Z\leq-1.79)[/tex]- First, use the Z-table to find the accumulated probability until Z=-1.79, the Z-value is negative, so you have to use the left entry of the table:
In the first column, you will find the first two digits of the Z-value, and in the first two, you will find the third digit of the Z-value, and in the body of the table, all accumulated probabilities are listed.
Cross the corresponding row and column to find the accumulated probability:
Then the accumulated probability until -1.79 is:
[tex]P(Z\leq-1.79)=0.0367[/tex]Now that you found the accumulated probability, you can use the complement to find the probability above -1.79
[tex]\begin{gathered} P(Z>-1.79)=1-P(Z\leq-1.79) \\ P(Z>-1.79)=1-0.0367 \\ P(Z>-1.79)=0.9633 \end{gathered}[/tex]I need help with this practice problem solving The subject is pre trigonometry
Answer:
[tex]\theta=\frac{2\pi}{3}+\pi\cdot n[/tex]Step-by-step explanation:
Find the general solution for:
[tex]\begin{gathered} 3\cot \theta=-\sqrt[]{3} \\ \text{ Divide both sides by 3} \\ \cot \theta=-\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Now, for the general solution, it is known that for
[tex]\begin{gathered} \cot (\frac{\pi}{6})=\sqrt[]{3} \\ \text{Then,} \\ \theta=\frac{2\pi}{3}+\pi\cdot n \end{gathered}[/tex]find the equivalent expression for x^1/2
We want to find the equivalent expression for
[tex]x^{\frac{1}{2}}[/tex]Read as: x to the power of half
The equivalent expression for this is
[tex]\sqrt[]{x}[/tex][tex]x^{\frac{1}{2}}\text{ and }\sqrt[]{x}\text{ both have the same meaning}[/tex]help with more than 1 question pls and ty if nkt i will report u its not fair
SOLUTION
9.
[tex]\begin{gathered} (x+10)^2\text{ = ( x + 10 ) ( x + 10 )} \\ =x^2\text{ + 10 x + 10x + 100} \\ =x^2\text{ + 20 x + 100} \end{gathered}[/tex]10.
[tex]\begin{gathered} (x-10)^2\text{ = ( x - 10 ) ( x - 10 )} \\ =x^2\text{ -10 x - 10 x + 100} \\ =x^2\text{ - 20 x + 100} \end{gathered}[/tex]11. ( x + 10 ) ( x - 10 ) ( Difference of two squares)
[tex]\begin{gathered} x^2\text{ - 10 x + 10 x - 100} \\ =x^2\text{ - 100} \end{gathered}[/tex]At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans X that a
randomly selected loan agent closes on a randomly selected day has the probability distribution below.
4
5 6
P(x) 0.05 0.10 0.22 0.30 0.18 0.12 0.03
X
1
2
3
At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let Y represent the amount of money made by a randomly selected loan
agent on a randomly selected day.
Which is the mean of X?
Which is the mean of Y?
V
Which is the standard deviation of X?
7
which is the standard deviation of Y
The mean of X is E(X)=$3.94
The mean of Y is E(Y)=$347
The standard deviation of X is $1.4129
The standard deviation of Y is $220.645
What is meant by mean and standard deviation?The mean is the set of two or more numbers' mathematical average. It is possible to calculate two different types of means: the arithmetic mean and the geometric mean. Add the numbers in a set together and divide by the total number of numbers in the set to find the arithmetic mean.
Standard deviation, which is the square root of the means of the squared deviations from the arithmetic mean, is also known as root-mean square deviation. To quantify the risks associated with an investment instrument, standard deviation is used in finance.
The computation is shown below:
Y = a +bX
where,
Y = money earned by a randomly chosen
a = $150
b = $50
X = number of loan
Now,
E(X) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)
=$3.94
E(X) =$3.94
Therefore, mean of X is $3.94
Now,
E(y) = $150 + ($50 × 3.94)
= $347
E(y) =$347
Therefore, mean of Y is $347
Variance=∑[tex]P_{i}[/tex]([tex]X_{i}[/tex]-μ)
=0.43218+0.37636+0.194392+0.00108+0.202248+0.509232+0.280908
=1.9964
Standard deviation=√variance
=√1.9964
=1.4129
Therefore, the standard deviation of X is $1.4129
Y=a+bX
Y=$150+($50×1.4129)
Y=$220.645
Therefore, the standard deviation of X is $220.645
To know more about standard deviation and mean, visit:
https://brainly.com/question/28108712
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Charlie is saving money to buy a game. So far he has saved $20, which is one-fourth of the total cost of the game. how much does the game cost?
Let 'x' represent the cost of the game.
Therefore, one-fourth of the total cost of the game is
[tex]\begin{gathered} \frac{1}{4}\text{ of x=20} \\ \frac{1}{4}x=20 \end{gathered}[/tex]Evaluate for x
[tex]x=20\times4=80[/tex]Hence, the total cost of the game is $80.
3.Which equation does not describe the line? Place the red X on the one that does not belong x y 10 y = 2x + 4 ce 6 4, y + 0 = 2(x + 2) 2 10 -8 -6 -4 2 0 2+ 2 4 6 8 10 y + 4 = 2(x + 0) 4+ 6+ 8+ y - 4 = 2(x + 0) 107
step 1
Find the equation of the graph
Find the slope
take the points
(-2,0) and (0,4)
m=(4-0)/(0+2)
m-4/2
m=2
step 2
Find the equation of the line in point slope form
point (-2,0) and m=2 ------> y-0=2(x+2)
point (0,4) and m=2 ------> y-4=2(x-0)
Find the equation in slope intercept form
y=mx+b
we have
m=2
b=4 (given)
y=2x+4
therefore
Find the area of each circle. Round to the nearest tenth.Only 1 and 2
Explanation
The area a circle can be expressed in two forms;
[tex]\begin{gathered} \text{Area}=\pi r^2 \\ \text{Area}=\pi(\frac{d}{2})^2 \\ \end{gathered}[/tex]Where r and d are the radius and the diameter of the circle.
Therefore;
For number 1, r =21 yards,
[tex]\text{Area}=\pi\times21^2=1385.4\text{square yards}[/tex]Answer: 1385.4 square yards
For number 2, d= 0.4 km
[tex]\text{Area}=\pi\times(\frac{0.4}{2})^2=\pi\times0.2^2=0.1km^2[/tex]Answer:0.1 square kilometres
Triangle ABC has vertices A(1,3), B(2,5), and C(5,3). What are the coordinates of B after the translation described by the rule T(1,4)?B =
Answer:
B' (3, 9)
Explanation:
Given the coordinates of vertices of a triangle A(1,3), B(2,5), and C(5,3), if the triangle is translated by T(1, 4), the coordinates of the new triangle will be expressed as:
A' = (1, 4) + A(1, 3)
A' = (1+1, 4+3)
A' = (2, 7)
B' = (1, 4) + B(2, 5)
B' = (1+2, 4+5)
B' = (3, 9)
C' = (1, 4) + C(5, 3)
C' = (1+5, 4+3)
C' = (6, 7)
From the calculation above, it can be seen that the coordinates of B after translation is B' (3, 9)
Instructions: For the given polynomial, select eachstatement that applies regarding end behavior.
Solution:
Given:
[tex]f(x)=-x^4-21x^2-2x+3[/tex]To get the end behaviour of the polynomial, we plot the function using a graphing calculator and see how it behaves.
The function is graphed as shown in the image below,
From the image above, the vertex of the curve shows a rise towards the left.
Hence, the end behaviour is that it rises to the left.
assume the unit population density of a state is approximately 104 people per mi2. if this state has 196,352 square miles, what is the population of the state? people
Given:
The unit population density of a state is 104 people per mi².
Also, the state has 196,352mi².
Therefore, the population of the state will be the multiplication of the unit population density and the square miles of the state.
Hence,
[tex]\frac{104people}{miles^2^{}}\times196352miles^2=20,420,608people[/tex]Therefore, the population of the state is 20,420,608 people.
27. The following chart represent the cost, Cd), in dollars, of a pizza in relation to its diameter, d, in inches. What is the average rate of change in cost from an 8 in to a 16 in pizza. d Cd) 8 2.51 103.93 125.65 147.70 16 10.05
The average rate of change is the ratio of the absolute change in one quantity divided by the absolute change in another quantity. Usually, the first one is dependent on the second one.
An 8 in pizza costs $2.51.
A 16 in pizza costs $10.05.
The absolute change in the cost is:
[tex]10.05-2.51=7.54[/tex]The absolute change in the diameter is:
[tex]16-8=8[/tex]Then, the average rate of change of the cost with respect to the diameter is:
[tex]\frac{7.54}{8}=0.9425[/tex]Therefore, to the nearest hundredth, the average rate of change in the cost from an 8in to a 16 in pizza, is:
[tex]0.94[/tex]Find the least common multiple of these two expressions. 12x^2w^6v^8 and 8x^5w^3
Given
[tex]12x^2w^6v^8\text{ }and\text{ }8x^5w^3[/tex]To find:
The Least Common Multiple of the above expressions.
Explanation:
It is given that,
[tex]12x^2w^6v^8\text{ }and\text{ }8x^5w^3[/tex]That implies,
[tex]\begin{gathered} 12x^2w^6v^8=4\cdot3\cdot x^2\cdot w^3\cdot w^3\cdot v^8 \\ 8x^5w^3=4\cdot2\cdot x^2\cdot x^3\cdot w^3 \\ \therefore LCM=4\cdot3\cdot2\cdot x^2\cdot x^3\cdot w^3\cdot w^3\cdot v^8 \\ =24x^5w^6v^8 \end{gathered}[/tex]Hence, the Least Common Multiple of the given expressions is,
[tex]LCM=24x^5w^6v^8[/tex]