The Probability that at least one of the cards drawn is 3 is 0.3412 .
In the question ,
it is given that ,
number of cards drawn from the deck [tex]=[/tex] 5 .
total cards in the deck is [tex]=[/tex] 52 .
number of "3" cards in the deck = 4
number of cards that are not "3" = 48 .
Number of ways to draw cards that are not 3 = ⁴⁸C₅
Total number of ways to draw 5 cards from the deck = ⁵²C₅
the probability that card dawn is not 3 = ⁴⁸C₅/⁵²C₅
as the value of ⁴⁸C₅ = 1712304 and ⁵²C₅ = 2598960
= 1712304/2598960
= 0.65885
So , the probability that at least one card is 3 = 1 - (probability that no card is 3)
= 1 - 0.65885
= 0.34115
≈ 0.3412
Therefore , The Probability that at least one of the cards drawn is 3 is 0.3412 .
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The 3rd term of a a G.P is 18 and the 7th term is 32/9. Find the G.P
The G.P. of a term is 256/243.
To find out the G.P. for the 3rd term:
Let us consider the 1st term to be 'a'.
So, [tex]ar^{2}=18[/tex] ....... Equation (1)
Also [tex]ar^{6} = \frac{32}{9}[/tex] ..... Equation (2)
Dividing (2) by (1), we get,
[tex]\frac{ar^{6}}{ar^{2}} = \frac{32}{162}[/tex]
[tex]r^{4}[/tex] = 16/81.
r = 2/3.
Putting r in equation (1) than we will get
a = 81/2.
So, 10th term = [tex]ar^{9}[/tex]
= (81/2) ×(512/19683)
= 256/243.
Hence the answer is the G.P. of a term is 256/243.
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This graph shows the height in inches, h, of a bamboo plant t months after it had been planted
4.1 Write an equation that describes the relationship between t and h.
4.2 After how many months will the Bamboo plant be 66 inches tall?
The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
A linear function is a function that varies linearly with respect to the changing variable.
4.1)
The linear equation is given as y = mx + c
Here, m is the slope while c is the y-intercept.
Given line has a y-intercept of 12.
Slope m = (12 - 24)/(0 - 4) = 3
Thus, h = 3t + 12
4.2)
Time is taken to bamboo to 66 inches tall,
66 = 3t + 12
3t = 54
t = 3 months.
Hence "The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months".
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Solve all 3 and maybe I will give brainlest
PLEASE HELP, NEEDED ASAP
Answer:
a) x=5
b) x=4
Step-by-step explanation:
4x-3=2x+7
-2x. -2x
2x-3=7
+3. +3
2x=10
x=5
2x+6=7x-14
-2x. -2x
6=5x-14
+14. +14
20=5x
/5. /5
4=x
Hopes this helps please mark brainliest
Point K is located at (−2,−5) on the coordinate plane. Point K is reflected over the y-axis to create point K'
. Point K'
is then reflected over the x-axis to create point K
′′
. What ordered pair describes the location of K''?
′′
?
After the two reflections, the coordinates are:
k'' = (2, 5)
What is the coordinate pair of k''?We start with the point K located at (-2, -5), and first, we apply a reflection over the y-axis.
It will only change the sign of the x-value, then we will get the new point:
k' = (- (-2), -5) = (2, -5)
And now we apply a reflection over the x-axis, this will only change the sign of the y-value,then we will get:
k'' = (2, -(-5)) = (2, 5)
These are the coordinates after the two reflections.
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If i toss a fair coin five times and the outcomes are ttttt, then the probability that tails appears on the next toss is.
The probability that tails appears on the next toss is 0.5
Given,
In the question:
If I toss a fair coin five times and the outcomes are TTTTT,
To find the probability that tails appears on the next toss is.
Now, According to the question:
The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.
A sequence of five fair coin flips has a sample space that contains all potential outcomes. [tex]2^3[/tex] {H, T} is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .
The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH} or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5
Hence, the probability that tails appears on the next toss is 0.5
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8. Angles x and y are located in the first quadrant
such that sin x=5/3 and cos y=5/13
a) Determine an exact value for cosx.
b) Determine an exact value for siny.
sin y =12/13 but can't find cos x as sin x can't exceed from 1.
It can be solved by using identities of trigonometry.
What are the trigonometric identities?
These are the equivalent ways to define trigonometric functions.
Basic identities are:
sin²x + cos²x = 1
1 + tan²x = sec²x
1 + cot²x = cosec²x
For cos x:
cos²x = 1 - sin²x
= 1 - (5/3)²
= 1- (25/9)
= -16/9
i.e. not possible
For sin y:
sin²y = 1 - cos²y
= 1 - (5/13)²
= 1 - 25/169
= 144/169
So, sin y = ±(12/13)
but as mentioned x and y are in 1st quadrant ,
so, sin y = 12/13.
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19) Over the past 4 hours the temperature fell 37.5°F. On average, how much did the temperature fall per hour?
Answer:
if you don't mind is there a starting number or a chart so i can calculate and solve this for you!
The sum 691 + 208 is closest to the sum
A. 600 + 200
B. 700 + 200
C. 700 + 300
D. 900 + 200
Answer:
B. 700+200
Step-by-step explanation:
691+208=899
A. 600+200=700
B.700+200=900
C.700+300=1000
D.900+200=1100
B is closest to 899
Answer:
700+200
Step-by-step explanation:
we round these numbers to the closest hundreds by looking at the tenth place
5 or more we round up
4 or less we let it rest and round down
691 since it is 9 in the tenths place we round up to 700
208 since the tenths place is 0 we round down to get 200
700+200 is the answer hopes this helps please mark brainliest
at gumdrops galore candy store, miguel and his sister each fill a bag with gumdrops. miguel's bag of black gumdrops weighs 3 8 of a pound. miguel pays for both his gumdrops and his sister's red gumdrops. in all, miguel buys 7 8 of a pound of gumdrops. he wants to know how much his sister's red gumdrops weigh. use an equation to find the weight of his sister's red gumdrops. to write a fraction, use a slash ( / ) to separate the numerator and denominator.
Miguel's sister's red gumdrops weigh 0.5 pounds.
Formulate based on the conditions stated: [tex]\frac{3}{8} + x = \frac{7}{8}[/tex]
Unknown terms should be moved to the left side of the equation: [tex]x = \frac{7}{8} - \frac{3}{8}[/tex]
Numerators written over common denominator: [tex]x = \frac{7-3}{8}[/tex]
Determine the total or difference: [tex]x = \frac{4}{8}[/tex]
Remove the connecting element: [tex]x = \frac{1}{2}[/tex]
get the outcome: or x = 0.5 or 50%
A fraction is a mathematical symbol representing any quantity of equal parts, and it also represents a portion of a whole. In common English, the word "fraction" is used to describe the quantity of parts of a particular size. Fractions speed up and simplify calculations by making it easier to divide and evaluate numbers.
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Jo flips a coin {h, t}; then rolls a 6-sided die {1, 2, 3, 4, 5, 6}. How many possible outcomes are in the sample space of this experiment?.
The possible outcomes in the sample space of this experiment are
{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}
Jo flips a coin sample space for a coin = {h, t}
and rolls a 6-sided die sample space for a die = {1,2,3,4,5,6}
at a time coin is tossed and the die is rolled
the possible outcomes in the sample space of this experiment are
{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}
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what is 10 + 10 i need some help
Answer:20
Step-by-step explanation: my man
Answer:
20
Step-by-step explanation:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10
+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10
= 20
which of the following is most likely to generalize to its population of interest? a random sample of 6 a stratified random sample of 120 a convenience sample of 12,000 a quota sample of 1,200
The most likely to generalize to it's population of interest is a stratified random sample of 120
a stratified random sample 120
Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members’ shared attributes or characteristics, such as income or educational attainment. Stratified random sampling has numerous applications and benefits, such as studying population demographics and life expectancy.
Stratified random sampling is also called proportional random sampling or quota random sampling.Stratified random sampling allows researchers to obtain a sample population that best represents the entire population being studied.Sampling involves statistical inference made using a subset of a population.Stratified random sampling is done by dividing the entire population into homogeneous groups called strata.Proportional stratified random sampling involves taking random samples from stratified groups, in proportion to the population. In disproportionate sampling, the strata are not proportional to the occurrence of the population.To learn more about stratified random sampling:
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Write the equation of the line that passes through the points (3, -8) and(9, 9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Find the value of a that makes m||n
The value of x that makes m║n is 40°
Line of transverse on parallel lines:In geometry, the line that intersects two straight lines at distinct points is known as a transversal.
Corresponding angles:The angles that are formed when two parallel lines are intersected by a third line i.e a transversal are corresponding angles.
Note:
Two corresponding angles are formed by a transversal with two parallel lines that are equal
Here we have
The angle made by the intersecting line with line m is 120°
And the angle made by the same line with line n is 3x°
Let us assume that m║n
From above observations
The given angle are corresponding angles
=> 3x° = 120°
=> x° = 40°
Therefore,
The value of x that makes m║n is 40°
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Express using exponents and simplify any numerical coefficients: 4 · 4 · 4 · b · b · c · c · c
The expression can be represented in terms of exponent as 4³ b² c³ if the expression is 4 · 4 · 4 · b · b · c · c · c.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that:
The expression is:
= 4 · 4 · 4 · b · b · c · c · c
By using the properties of exponent:
= 4³ b² c³
4³ = 64
= 64b² c³
Thus, the expression can be represented in terms of exponent as 4³ b² c³ if the expression is 4 · 4 · 4 · b · b · c · c · c.
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1. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the pair of triangles?
The pair of triangles can be proved to be congruent using the ASA postulate of congruency.
In the two triangles , let the first right angled triangle be ABC and the second right angled triangle be DEF.
In ΔABC and ΔDEF
∠ABC = 90° and ∠DEF = 90°
∠ACB = ∠DFE
therefore by using the angle sum property of the triangle we can say that:
∠CAB = ∠FDE
Therefore in the pair of triangles: ΔABC and ΔDEF we have :
∠ACB = ∠DFE
∠CAB = ∠FDE
AC = DF is given which is also the common side to both the angles.
Hence we can say
ΔABC ≅ ΔDEF ( By angle-side -angle postulate of congruency)
Therefore the two triangles are congruent by the ASA postulate of congruency.
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question is in the pic .
The set of ordered pairs that represent dilation factor of -3 is
c. A' (-3, -18) B' (-18, -18) C' (-3, -6)
How to find the coordinates of the imageDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
From the graph the coordinates are read and following the given transformation rule we have
preimage image
A (1, 3) → (2 * -3, 4 * -3) → A' (-3, -8)
B (6, 6) → (4 * -3, 4 * -3) → B' (-18, -18)
C (1, 6) → (3 * -3, 2 * -3) → C' (-3, -6)
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PLEASE HELPPPPP ASAPPPP I NEED THIS MATH DONE! WILL GIVE BRAINLIST
Answer: __________________________________________
3x + 9
Answer: 3x + 9
Step-by-step explanation:
cos²x + 2 cosx - 3=0
The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .
In the question ,
it is given that ,
the quadratic equation is cos²x + 2 cosx - 3 = 0 ,
let cosx = a ,
So , the equation becomes , a² + 2a - 3 = 0
writing the factors using the splitting the middle term method ,
we get ,
a² [tex]+[/tex] 3a -a - 3 = 0
a(a + 3) -1(a [tex]+[/tex] 3) = 0
(a - 1)(a [tex]+[/tex] 3) = 0
which means a - 1 = 0 or a + 3 = 0
a [tex]=[/tex] 1 or a [tex]=[/tex] -3 ,
Substituting a = cosx , we get
cosx [tex]=[/tex] 1 or cosx [tex]=[/tex] -3 ,
Therefore , The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .
The given question is incomplete , the complete question is
Solve the given quadratic equation for Cosx , cos²x + 2 cosx - 3 = 0 .
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Kelly, Beth, Ann, and Tabitha were asked to draw a model to explain the following problem: Britt had 0.7 of a pan of brownies left. She covered 0.3 of them with chocolate icing. What part of the pan of leftover brownies now has icing? Indicate each diagram that shows this multiplication.
The proportion of the pan of leftover brownies that now has icing is of 0.21 = 21%.
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations to find the desired amounts in whichever context of the problem.
In the context of this problem, these amounts are given as follows:
Amount of the pan left: 0.7.Amount of the pan that was covered in icing: 0.3 of the remaining 0.7.Hence the part of the pan of leftover brownies that now has icing is obtained by the multiplication presented as follows:
0.7 x 0.3 = 0.21.
It can be interpreted by the multiplication of 7 and 3 = 21, and then the result moves two decimal places to the left as each factor of the multiplication has one decimal digit.
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suppose someone pays you 100 if you draw 3 cards from a standar deck of 52 and all the cards are clubs. what should you pay for the chance to win if it is a fair game
$ 1.31 should pay for the chance to win if it is a fair game.
Probability is simply how likely something is to happen.
Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
It is a fair game if what we gain equals what we stake.
There are 13 clubs in a standard deck of 52 cards.
Probability of 3 clubs = 13C3 / 52C3 = 286/22100 = 0.01294
For a fair game,
$100(0.01294) = x(1-0.01294)
Solving for x,
1.294 = x(0.98706)
x = 1.31
$ 1.31 should pay for the chance to win if it is a fair game.
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[tex]3x-8\geq 7[/tex]
Answer:
x ≥ 5
Step-by-step explanation:
3x - 8 ≥ 7 ( add 8 to both sides )
3x ≥ 15 ( divide both sides by 3 )
x ≥ 5
which statement can you use to conclude that quadrilateral xyzw is a parallelogram
The statement can you use to conclude that quadrilateral xyzw is a parallelogram
The statement to conclude that quadrilateral XYZW is a parallelogram is
XY = WZ and XW = YZ
Quadrilateral :
A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.
Parallelogram :
A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other , where the pair of parallel sides are equal in length.
So we can conclude that :
XY is parallel to WZ and XW is parallel to YZ .
so ,
XY = WZ and XW = YZ is the conclusion .
Hence , the answer is XW = YZ and XY = WZ
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you are synthesizing a chip composed of random logic with an average activity factor of 0.1. you are using a standard cell process with an average switching capacitance of 450 pf/mm2 . estimate the dynamic power consumption of your chip if it has an area of 70 mm2 and runs at 450 mhz at vdd
The dynamic power consumption of your chip if it has an area of 70 mm² and runs at 450 MHz at vdd = 0.9V is 1.08 W.
It is given that,
The average activity factor = 0.1
The Average switching capacity = 450 pF/mm²
We know that,
p = aCV²f
putting the values in the above equation:
= 0.1× (450e⁻¹² × 70) × (0.9)² × 450e⁶
= 1.08 W
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the equation for line p can be written as y = -1/2x+8. Line q, which is perpendicular to line p, includes the point (4,7). what is the equation of line q
Answer:
y = 2m -1
Step-by-step explanation:
y = mx + b is the slope intercept form of a line.
Perpendicular slopes are opposite reciprocals of each other. That means that you flip the fraction and take the opposite sign. The slope will be 2.
Now us the slope, the x value and the y value from the give point to find the y-intecept (b)
Slope = 2 (m)
y = 7 from the point (4,7)
x = 4 from th point (4,7)
y = mx + b
7 = 2(4) + b
7 = 8 + b Subtract 8 from both sides
-1 = b
y = 2x - 1
Answer:
Step-by-step explanation:
y = 2x - 1
See #17
Given that RQ=TQ, Angle QSR=(9a+48) and Angle QST=(6a+50), find Angle QST
Answer:
54°
Step-by-step explanation:
We know that the triangles are congruent by HL, meaning that [tex]m\angle QSR=m\angle QST[/tex].
[tex]9a+48=6a+50 \\ \\ 3a=2 \\ \\ \implies m\angle QST=2(2)+50=54^{\circ}[/tex]
Hello! Can someone please help me. I am in trouble, hope ypu help me guys, with complete answer! THANK YOU
Answer:
[tex]\textsf{1.} \quad (x-1)^2=12(y+2)[/tex]
See attachment 1.
2. See attachment 2.
Step-by-step explanation:
Question 1Given values:
Vertex: (1, -2)Focus: (1, 1)As the x-value of the vertex and focus is the same, the parabola has a vertical axis of symmetry.
The focus is always on the inside of the parabola.
Since p represents the distance from the vertex to the focus, and the distance from the vertex to the focus is 1 - (-2) = 3, then p = 3.
If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards. Therefore, as p > 0, the parabola opens upwards.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a parabola}\\(with a vertical axis of symmetry)\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k+p)$\\ \phantom{ww}$\bullet$ Directrix: \; $y=(k-p)$\\ \phantom{ww}$\bullet$ Axis of symmetry: \; $x=h$\\\end{minipage}}[/tex]
Therefore:
h = 1k = -2p = 3Substitute the values into the formula:
[tex]\implies (x-h)^2=4p(y-k)[/tex]
[tex]\implies (x-1)^2=4\cdot 3(y-(-2))[/tex]
[tex]\implies (x-1)^2=12(y+2)[/tex]
See attachment 1 for the graph of the parabola.
Question 2Given equation of a parabola:
[tex](y-4)^2=8(x+2)[/tex]
As the y-variable is contained within the squared part of the equation, the parabola has a horizontal axis of symmetry.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a parabola}\\(with a horizontal axis of symmetry)\\\\$(y-k)^2=4p(x-h)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h+p,k)$\\ \phantom{ww}$\bullet$ Directrix: \; $x=(h-p)$\\ \phantom{ww}$\bullet$ Axis of symmetry: \; $y=k$\\\end{minipage}}[/tex]
Therefore:
h = -2k = 44p = 8 ⇒ p = 2If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left. Therefore, as p > 0, the parabola opens to the right.
Find the y-intercepts of the graph by substituting x = 0 into the equation:
[tex]\implies (y-4)^2=8(0+2)[/tex]
[tex]\implies (y-4)^2=16[/tex]
[tex]\implies y-4=\pm4[/tex]
[tex]\implies y=4\pm4[/tex]
[tex]\implies y=0, y=8[/tex]
To sketch the graph of the parabola, plot:
Vertex = (-2, 4)Focus = (0, 4)Axis of symmetry: y = 4y-intercepts: (0, 0) and (0, 8)Draw a curve through the vertex and y-intercepts, opening to the right.
Use the axis of symmetry to ensure the curve is symmetric.
See attachment 2 for the graph of the parabola.
In a study of cell phone usage and brain hemispheric dominance, an internet survey was e-mailed to subjects randomly selected from an online group involved with ears. There were surveys returned. Use a 0. 01 significance level to test the claim that the return rate is less than 20%. Use the p-value method and use the normal distribution as an approximation to the binomial distribution.
The statistics z is -1.878 and the p value is 0.0302
Given,
Number of random sample selected, n = 6967
Number of surveys returned, x = 1331
Estimated proportion of return rate;
p = 1331/6967 = 0.192
Significance level, ∝ = 0.01
z would represent the statistic
We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:
Null hypothesis, p₀ ≥ 0.2
Alternative hypothesis, p₀ < 0.2
The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)
That is,
z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878
Using the alternative hypothesis and the following probability, we can now get the p value:
p value = p(z < - 1.878) = 0.0302
We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.
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3
What is the area of the composite figure?
12.5cm
20cm
500
490.62
245.31
745.31
25cm
4
27
Answer: 745.31 cm²
Total area of the figure can be obtained by adding area of the semi circle and rectangle.
The radius of the semi circle is given as 12.5cm and it's area is equal to (πr²)/2
I hope you understand It's simple!