In the game of roulette, a player can place a $99 bet on the number 3333 and have a startfraction 1 over 38 endfraction 1 38 probability of winning. if the metal ball lands on 3333, the player gets to keep the $99 paid to play the game and the player is awarded an additional $315315. otherwise, the player is awarded nothing and the casino takes the player's $99. what is the expected value of the game to the player? if you played the game 1000 times, how much would you expect to lose? note that the expected value is the amount, on average, one would expect to gain or lose each game.
Use basic identities to simplify the expression. sin^2θ + tan^2θ + cos^2θ
A tree grows 1 3/4 feet per year. How long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?
What is the solution to the equation below? Log6 4x^2-log6x-2
The logarithmic equation is solved to find x to be equal to 9
How to solve the equation
To solve the equation, we can use logarithmic properties to simplify and solve for x
[tex]\(\log_6(4x^2) - \log_6(x) = 2\)[/tex]
[tex]log_6\left(\frac{4x^2}{x}\right) = 2[/tex]
[tex]log_6(4x) = 2[/tex]
6²= 4x
36 = 4x
x = 9
The solution to the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\) is \(x = 9\).[/tex]
To solve the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\)[/tex], you can use the properties of logarithms.
First, apply the quotient rule of logarithms to combine the two logarithms:
[tex]\[ \log_6\left(\frac{4x^2}{x}\right) = 2 \][/tex]
Simplify the expression inside the logarithm:
[tex]\[ \log_6(4x) = 2 \][/tex]
Now, rewrite this equation in exponential form:
[tex]\[ 6^2 = 4x \]\[ 36 = 4x \][/tex]
Now, solve for x:
[tex]\[ x = \frac{36}{4} \]\[ x = 9 \][/tex]
So, the solution to the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\) is \(x = 9\).[/tex]
Students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.
Approximately what percent of students in the sample were male?
Round your answer to the nearest percent.
%
Preference Male Female TOTAL
Prefers dogs 36 20 56
Prefers cats 10 26 36
No preference 2 6 8
TOTAL 48 52 100
To find the percentage of students in the sample who were male, divide the total number of male students by the total number of students and multiply by 100.
Explanation:To find the percentage of students in the sample who were male, we need to look at the total number of male students and divide it by the total number of students in the sample. From the given two-way table, we can see that the total number of male students is 48. The total number of students in the sample is 100. To find the percentage, we can divide 48 by 100 and multiply by 100 to get:
Percentage of male students = (48/100) * 100 = 48%
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Answer:
36%
Step-by-step explanation:
How will the circumference of the circle change if it is dilated by a scale factor of 4?
The circumference will be 4 times greater than the original.
The circumference will be 16 times greater than the original.
The circumference will be 1/4 the original.
The circumference will be1/16 the original.
Answer:
The circumference will be [tex]4[/tex] times greater than the original
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
where
r is the radius of the circle
In this problem we have
The radius of the original circle is
[tex]r1=16\ cm[/tex]
The circumference of the original circle is equal to
[tex]C1=2\pi (16)=32\pi\ cm[/tex]
If the circumference is dilated by a scale factor of [tex]4[/tex]
then
the radius of the dilated circle will be
[tex]r2=4*16=64\ cm[/tex]
and the circumference of the dilated circle will be
[tex]C2=2\pi (64)=128\pi\ cm[/tex]
so
[tex]C2=4C1[/tex]
therefore
The circumference will be [tex]4[/tex] times greater than the original
You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.
Which answer is correct
diagonal is square root of A^2+b^2
so C is the correct answer
A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=140-8t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
The time would be 2.71 seconds after the ball is thrown does it hit the ground.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s.
The ball's height h (in feet) after t seconds is given by the following.
⇒ h = 140-8t - 16t²
h = 0 at the ground.
We divide both sides of the equation by (-8) to yield:
⇒ 0 = 2t² + t - 17.5
where a = 2, b= 1, c = -17
[tex]t = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\t = \dfrac{-1\pm\sqrt{2^2-4\times2\times-17.5}}{2\times2}[/tex]
t = [-1 ± √141] / (4)
t = 2.71 and -3.21
For this problem, time can only be positive, so ignore the negative solution.
Therefore, the time would be 2.71 seconds after the ball is thrown does it hit the ground.
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Michelle found a new violin on sale at 30% off. how much would she pay the cashier if it originally sells for $250 in a city that had no sales tax
100%-30% = 70%
70%=0.70
250*0.70 = 175
she would pay $175
Which shows 54^2 − 46^2 being evaluated using the difference of squares method?
54^2 − 46^2 = (2916 + 2116)(2916 − 2116) = 4,025,600
54^2 − 46^2 = (54 + 46)(54 − 46) = (100)(8) = 800
54^2 − 46^2 = 2916 − 2116 = 800
54^2 − 46^2 = (54 − 46)^2 = 8^2 = 64
A carpenter trims a triangular peak of a house with three 7-ft pieces of molding. The carpenter uses 21 ft of molding to trim a second triangular peak. Are the two triangles formed congruent? Explain.
The two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent.
Explanation:To determine if the two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent, we can use the concept of the Side-Angle-Side (SAS) congruence criterion.
In the first case, the carpenter uses three 7-ft pieces of molding to trim the first triangular peak. This means that each side of the triangle is 7 feet long.
In the second case, the carpenter uses 21 ft of molding to trim the second triangular peak. Since the total length of molding used is 21 ft, we know that each side of the triangle is still 7 feet long.
So, in both cases, the triangles are formed by sides of the same length, which is 7 feet, and they have a common angle at the peak of the house.
This satisfies the SAS congruence criterion, which states that if two triangles have two sides of equal length and the included angle is the same, then the triangles are congruent.
Therefore, the two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent.
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What number is 7 units to the left of -1?
What is the factorization of 2x²+4x+2
A. (2x+2)(x+2)
B. (2x+1)(x+2)
C. (2x+1)(x+1)
D. (2x+2)(x+1)
150 centimeters is equivalent to
Which expression will produce an answer with the fewest significant figures?
a.15.4 - 8.1
b.54.5 30.7
c.4350 - 2210
d.18.8 - 6.5?
Which expression is equivalent to (m^5n/pq^2)^4
Answer
Find the expression is equivalent to
[tex](\frac{m^{5}n}{pq^{2}})^{4}[/tex]
To prove
As the expression is given in the question as follow .
[tex]=(\frac{m^{5}n}{pq^{2}})^{4}[/tex]
By using the exponent properties of the raise a power to a power
[tex](x^{a})^{b} = x^{ab}[/tex]
than the above expression becomes
[tex]=\frac{(m^{5}n)^{4}}{(pq^{2})^{4}}\\ =\frac{(m^{5})^{4}n^{4}}{p^{4}(q^{2})^{4}}[/tex]
[tex]=\frac{m^{20}n^{4}}{p^{4}q^{8}}[/tex]
Thus the expression is equivalent to
[tex]=(\frac{m^{20}n^{4}}{p^{4}q^{8}})[/tex]
Help asap plz ill give a gold medal. the label on cars antifreeze claims to protect the car between -30celsius and 130celsius. to convert Celsius temperature Fahrenheit temperature, the formula is, c=5/9(F-32). Write an solve and inequality to determine the Fahrenheit temperature range at which antifreeze protects the car.
A quick-loan company charges an 18% fee on any loan that is paid up to one week late. A woman borrowed $400 and paid the loan back 3 days late. What is the total she has to pay, including any fee?
Is the coordinate (1, 2) a solution of the system below?
x + 2y = 5
y = x + 1
A. Yes
B. No
If the inflation rate increases faster than their income, people will most likely:
A. use a higher proportion of their incomes on basic needs
B. spend a lower proportion of their incomes on basic needs
C. get more goods and services for less money
D. obtain less goods and services for less money
If the inflation rate increases faster than their income, people will most likely use a higher proportion of their incomes on basic needs
What is inflation rate?Inflation is the rate of increase in prices over a given period of time. Inflation is typically a broad measure, such as the overall increase in prices or the increase in the cost of living in a country.
According to the question
If the inflation rate increases faster than their income, people will most likely:
As
inflation rate increases means increase in prices of goods and services over a given period of time.
i.e
People will use a higher proportion of their incomes on basic needs .
Hence, If the inflation rate increases faster than their income, people will most likely use a higher proportion of their incomes on basic needs.
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In the diagram, ∠ABC = 90°. What is the radius of the circle?
A. 5.7 in
B. 16.5 in
C. 24.6 in
D. 12.3 in
D. 12.3 in
Explanation and solution;We are give that ∠ABC = 90°; therefore a line from point A to point C is the diameter, this is because a diameter subtends an right angle to the circumference of the circle. Therefore; triangle ABC is a right-angled triangle, thus AC is the hypotenuse.Using the Pythagoras theorem;
AC² = AB² + BC²
= 22.1² + 10.9²
= 607.22
AC = √ 607.22
= 24.64
But, since AC is the diameter and the radius is half of the diameter, then
Radius = 24.64/2
= 12.32
≈ 12.3 (to 1 decimal place)
A 31-in. television has a 31 in. diagonal and a 18 in. width. what is the height of the 31-in. television?
Use the the factor theorem to determine wether the first polynomial is a factor of the second. X-3; 2x^2-4x+30
(02.01 LC)
Figure ABCD is transformed to figure A′B′C′D′:
Which angle in Figure A′B′C′D′ is equal to Angle CDA.?
Angle D prime A prime B prime.
Angle A prime B prime C prime.
Angle B prime C prime D prime.
Angle C prime D prime A prime.
Answer:
I think it is Angle B prime C prime D prime
Step-by-step explanation:
A'B'C'D' is a translation so they are congruent.So the figure B'C'D' is congruent or equal to BCD. Please let me know if i'm right
Need help on #30 and 31 thanks!!
how do you find the inverse of a 2x2 matrix
To find the inverse of a 2x2 matrix, calculate the determinant (ad-bc), then swap the diagonal elements, change the signs of the off-diagonal elements, and multiply each by the reciprocal of the determinant.
Explanation:To find the inverse of a 2x2 matrix, you must follow a specific procedure. Given a 2x2 matrix A:
\( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \)
The inverse of matrix A, denoted as \( A^{-1} \), is calculated using the formula:
[tex]\( A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \)[/tex]
Here, \( ad - bc \) is called the determinant of matrix A. For the inverse to exist, the determinant must not be zero. To calculate the inverse, you compute the determinant \( (ad - bc) \), then swap the elements of the diagonal positions (a and d), change the signs of the off-diagonal elements (b and c), and then multiply each element by \( \frac{1}{ad - bc} \).
For example, if you have a matrix:
[tex]\( A = \begin{bmatrix} 4 & 7 \\ 2 & 6 \end{bmatrix} \)[/tex]
The determinant is [tex]\( 4\cdot6 - 7\cdot2 = 24 - 14 = 10 \).[/tex]
The inverse of A is:
[tex]\( A^{-1} = \frac{1}{10} \begin{bmatrix} 6 & -7 \\ -2 & 4 \end{bmatrix} = \begin{bmatrix} 0.6 & -0.7 \\ -0.2 & 0.4 \end{bmatrix} \)[/tex]
The sum of twice a number and a larger number is 145. The difference between the numbers is 55. Let x represent the smaller number and y represent the larger number. Which equations represent the situation? Check all that apply.
A. x-y=55
B. 2(x+y)=145
C. 2x+y=145
D. y-x=55
E. y=x+55
The area of a rectangular plot 24 feet long and 16 feet wide will be doubled by adding an equal distance to each side of the plot. What is the distance added to each side?
24*16 = 384
384*2 = 768
24+d * 16+d =768
384 + 40d+d^2 = 768
d^2 + 40d-384 =0
(d+48) (d-8) = 0
d=-48, d=8 can't use a negative number so d = 8
check:
24+8=32, 16+8=24, 32x 24 = 768
so 8 feet is added to each side
Which theorem could Chelsea use to show the measure of angle KPR is equal to the measure of angle QRL?