We start by saying that the deck has 52 cards, in which they have 4 aces (one for each suit).
We are also taking about drawing cards wthout replacement.
Then, for the first draw, we have 4 in 52 chances of drawing an ace.
For the second draw, as one ace is taken out of the deck of cards, there is a chance of 4-1=3 out of 52-1=51 of drawing an ace.
This can be generalized for the 4 draws as:
[tex]P=\frac{4}{52}\cdot\frac{3}{51}\cdot\frac{2}{50}\cdot\frac{1}{49}=\frac{24}{6,497,400}=3.7\cdot10^{-6}[/tex]where P is the probability of drawing 4 aces in 4 draws.
There is a probability of 3.7 * 10^(-6) = 0.0000037 = 0.00037% of drawing 4 cards from a standard deck and all 4 being aces.
In what quadrant of the complex plane is -10 + 23i - (20 - 171)
Simplify the expression -10+23i-(20-17i) implies,
[tex]-30+40i[/tex]The point (-30,40) lies in second quadrant.
Thus, the answer is second quadrant.
Indicate which property is illustrated in Step 6.Step 19 + 11x - 9 - 4x + 2=9 + (11x - 9) - 4x + 2Step 2=9 + (-9 + 11x) - 4x + 2Step 3=[9 + (-9)] + (11x - 4x) + 2Step 4=0 + (11x - 4x) + 2Step 5=(11x - 4x) + 2Step 6=(11 - 4)x + 2Step 7=7x + 2 A. additive inverse B. commutative C. associative D. distributive
step 6
(11 - 4)x + 2
the answer is option D.
distributive
5 A carpenter charges $720 for 18 hours of work. She charges the same amount of money foreach hour of work.Which table shows the relationship between the amount of time the carpenter works andamount of money she charges?theACarpenter's ChargesсCarpenter's ChargesAmountAmount ofAmountChargedTime WorkedCharged(dollars)(hours)(dollars)80375512571759225Carpenter's ChargesAmountCharged(dollars)720720720720Amount ofTime Worked(hours)2416062408320Carpenter's ChargesAmountCharged(dollars)720738756774Amount ofTime Worked(hours)19202122DAmount ofTime Worked(hours)14151617
Given:
A carpenter charges for 18 hours=$720.
Find:
We have to find the table which represents correct relationship between hours and charges.
Explanation:
A carpenter charges for 18 hours=$720.
A carpenter charges for 1 hour = 720/18 = $40.
Therefore, the charges of the carpenter for each hour is $40.
So, option A is correct option.
6. A right triangle has legs of 4 and 5. What is the hypotenuse? Show your work.
Given:
The leg of 4 and 5
Find-:
The value of the hypotenuse
Explanation-:
The right triangle is:
Let the Hypotenuse is "x."
Use Pythagores theorm is:
[tex]\text{ Hypotenuse}^2=(\text{ Leg}_1)^2+(\text{ Leg}_2)^2[/tex]So the value of "x" is:
[tex]\begin{gathered} x^2=4^2+5^2 \\ \\ x^2=16+25 \\ \\ x^2=41 \\ \\ x=\sqrt{41} \end{gathered}[/tex]So value of hypotenuse is:
[tex]\begin{gathered} =\sqrt{41} \\ \\ \approx6.403 \end{gathered}[/tex]Given a sphere with a diameter of 6.2 cm, find its volume to the nearest wholeknumberA. 998 cmB. 125 cmC. 39 cmD. 70 cm
The volume of a sphere of radius r is given by the following expression:
[tex]\frac{4}{3}\pi\cdot r^3[/tex]In this case the radius is equal to 6.2 cm so the volume of this sphere is:
[tex]\frac{4}{3}\pi\cdot6.2^3=\frac{4}{3}\pi\cdot238.328=998.3[/tex]If we round this to the nearest whole number we obtain 998 cm³. Then the answer is option A.
What is the equation of a line that passes through the point (8, -4) and is parrallel to the line 6x + 2y = 9
The equation of a line that passes through the point (8, -4) and is parallel to the line 6x + 2y = 9 is 3x+y-20=0.
6x + 2y - 9 = 0
2y = -6x + 9
divide by 2 on both sides
y = -3x + 9/2
slope m = -3 and c = 9/2.
Line equation through point(8, -4) is y-y1 = m(x-x1)
y - (-4) = -3(x-8)
y+4=-3x+24
3x+y-20=0.
Therefore the equation of a line that passes through the point (8, -4) and is parallel to the line 6x + 2y = 9 is 3x+y-20=0.
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Write a transformation of a quadratic function with a vertical stretch by a factor of 2, followed by a horizontal shift of 3 units to the left and 5 units down.show workkkk!!!
The standard form of a quadratic function presents the function in the form
[tex]f(x)=a(x-h)^2+k[/tex]where (h, k) is the vertex.
The standard form is useful for determining how the graph is transformed from the graph of y = x^2. The figure below is the graph of this basic function.
You can represent a horizontal (left, right) shift of the graph of
by adding or subtracting a constant, h, to the variable x, before squaring. Here h = -3
[tex]y=(x+3)^2[/tex]The magnitude of a indicates the stretch of the graph. a = 2
[tex]y=2(x+3)^2[/tex]Find the first five terms of the sequence
defined recursively as follows: t₁ = 1,
tn = 3(t(n-1)), n≠1, n is a natural number.
Answer:
1, 3, 9, 27, 81
Step-by-step explanation:
using the recursive rule
[tex]t_{n}[/tex] = 3 [tex]t_{n-1}[/tex] with t₁ = 1 , then
t₂ = 3 × t₁ = 3 × 1 = 3
t₃ = 3 × t₂ = 3 × 3 = 9
t₄ = 3 × t₃ = 3 × 9 = 27
t₅ = 3 × t₄ = 3 × 27 = 81
the first 5 terms are 1, 3, 9, 27, 81
Use the Venn diagram shown to answer the question below.Which regions represent set B?
Answer
From the image attached, we can see that the regions in set B include
II
III
V
VI
Explanation
We are provided with the Venn Diagram for this question and asked to list the region spanned by set B.
For that, we will look at the circle representing the set B and easily list out the regions that exist in this circle.
From the image attached, we can see that the regions in set B include
II
III
V
VI
Hope this Helps!!!
What is the area of this triangle? A=bh254 cm²90 cm²108 m²216 m²
Given:
A triangle with sides base 9 cm , height 12 cm and hypotenuse 15 cm.
Required:
What is the area of triangle?
Explanation:
The area of triangle is
[tex]A=\frac{1}{2}\times base\times height[/tex]We have base = 9 cm and height = 12 cm.
Now,
[tex]\begin{gathered} A=\frac{1}{2}\times9\times12 \\ A=54\text{ cm}^2 \end{gathered}[/tex]Answer:
Option A is correct.
Which of the statements below is true for the following set of numbers? 20, 15, 50, 85, 75, 60A. The range is 70 and the midrange is 35 B.the range is 70 and the midrange is 50C. The range is 85 and the midrange is 55D.the range and the midrange are equal
B
1) Firstly, we need to orderly write this sequence of numbers:
[tex]15,20,50,60,75,85[/tex]2) Then we need to calculate the Range of this Data Set, by subtracting from the highest values the least one:
[tex]R=85-15=70[/tex]2.2) The Midrange is the average between the Highest Value and the Least value on this Data Set:
[tex]M=\frac{85+15}{2}=50[/tex]3) Thus the answer is B
Hello not homework just review not worth any points question 9
We were given:
[tex]\begin{gathered} 74Dyani's age is not an even number. That means that:[tex]\begin{gathered} d=13\text{ or }15\text{ or }17 \\ \text{Dyani's age is the median} \\ \Rightarrow d=15 \\ \\ d=15 \end{gathered}[/tex]Dyani's age is halfway between Rachel & Shannon's:
[tex]\begin{gathered} d=\frac{r+s}{2} \\ 2d=c \\ 2(15)=r+s \\ 30=r+s \\ r+s=30 \\ \text{From the age set},\text{ the possible age of Rachel \& Shannon is 17 \& 13} \\ We\text{ were told that:} \\ sWe were given the inequality:[tex]\begin{gathered} sTherefore, the age of the girls are listed below:Shannon is 13 years old,
Mercedes is 14 years old
Dyani is 15 years old
Aisha is 16 years old
Rachel is 17 years old
Which of the following is an infinite series?A) 3, –6, 12, –24, 48B) 2 − 6 + 18 − 54 + . . .C) 3, 13, 23, 33, . . .D) 4 + 8 + 16 + 32
SOLUTION
An infinite series is the sum of an indefinitely many numbers related in a given way. That is the addition of such number is continuos. So our answer should be between
B) 2 − 6 + 18 − 54 + . . . and
C) 3, 13, 23, 33, . . .
But, looking at both, C) is a sequence showing ordered list of numbers.
Hence B) is a showing series showing sum of a list of numbers or showing multiplication pattern.
Therefore, the correct answer is option B.
Recall that the formula for an area of a circle is A=πr^2 Find the radius of a circle whose area is 300 square meters. Give a decimal approximation rounded to 2 decimal places.raduis=_______meters
Given:
a.) Area of circle = 300 m²
Let's determine its radius,
[tex]\text{ Area = }\pi\text{r}^2[/tex][tex]\text{ }\pi r^2\text{ = Area}[/tex][tex]\text{ r}^2\text{ = }\frac{300}{3.1416}\text{ ; }\pi\text{ }\approx\text{ 3.1416}[/tex][tex]\text{ r = }\sqrt{\frac{300}{3.1416}}[/tex][tex]\text{ r = 9.77203881243 }\approx\text{ 9.77 m}[/tex]Therefore, the radius of the circle is approximately 9.77 m
What is the coefficient and the constant of 5x+2-3x^2
Factor -1 out of the expression:
[tex]-1(3x^2-5x-2)[/tex]the coefficient of x² is 3 and the constant term is -2. The product of 3 and -2 is -6. The factors of -6 which sum to -5 are 1 and -6. Therefore:
[tex]undefined[/tex]Un gerente compró un total de 21 tazas de café y llaveros. Cada taza de café cuesta $8,50 y cada llavero cuesta $2,75. Si el gerente gastó un total de $132.50, ¿cuántas tazas de café compró el gerente?
Usemos la variable x para representar el número de tazas e y para el número de llaveros.
Si el número de artículos es 21, tenemos:
[tex]x+y=21[/tex]Si el costo total es 132.5, tenemos:
[tex]8.5x+2.75y=132.5[/tex]De la primera ecuación, podemos escribir:
[tex]y=21-x[/tex]Usando este valor de y en la segunda ecuación:
[tex]\begin{gathered} 8.5x+2.75(21-x)=132.5 \\ 8.5x+57.75-2.75x=132.5 \\ 5.75x=74.75 \\ x=13 \end{gathered}[/tex]Entonces la cantidad de tazas compradas es 13.
Find the value of x. 984 (149-x) 128 2x+4)
You have a pentagon. In order to determine the value of x for the given expression, of the measure of the angles, take into account that the sum of the interior angles of a pentagon is 540°.
Then, by using the given expressions you have:
(98) + (149 - x) + (2x + 4) + (114) + (128) = 540
To solve for x, proceed as follow:
(98) + (149 - x) + (2x + 4) + (114) + (128) = 540 eliminate parenthesis
98 + 149 - x + 2x + 4 + 114 + 128 = 540 simplify like terms left side
493 + x = 540 subtract 493 both sides
x = 540 - 493
x = 47
Hence, the value of x is x = 47
An ice cream cone costs $3 plus 6% sales tax. How many ice creamcones can be purchased for $24270908
We know that
• Each ice cream costs $3.
,• Sales tax is 6%.
,• The total amount of money is $24.
Let's find the unit price including sales tax.
[tex]3+0.06(3)=3+0.18=3.18[/tex]So, each ice cream costs $3.18 with sales tax included. Now, we divide $242 by this price to get the total number of ice creams we can buy
[tex]\frac{24}{3.18}=7.5[/tex]Therefore, we can buy 7 ice creams.which one of these must be a correct congruence statement
Answer:
C. AB ≅ DE
Explanation:
If triangles ABC and DEF are similar, then the following holds:
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Likewise, the similar sides are:
[tex]\begin{gathered} AB\cong DE \\ AC\cong DF \\ BC\cong EF \end{gathered}[/tex]The correct choice is C.
Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.)
Solution
The given function is
[tex]f(x)=4x^3[/tex]With given interval
[tex]\lbrack1,2\rbrack[/tex]The function is differentiable on the open interval (1,2) and it is continuous on the closed interval [1,2]
Therefore mean value theorem can be used
Calculating the c value iit follows:
[tex]f^{\prime}(c)=\frac{f(2)-f(1)}{2-1}[/tex]This gives
[tex]\begin{gathered} f^{\prime}(c)=\frac{4(2)^3-4(1)^3}{1} \\ f^{\prime}(c)=\frac{32-4}{1} \\ f^{\prime}(c)=28 \end{gathered}[/tex]Differentiating the given function gives:
[tex]f^{\prime}(x)=12x^2[/tex]Equate f'(c) and f'(x)
This gives
[tex]x^2=\frac{28}{12}[/tex]Solve the equation for x
[tex]\begin{gathered} x^2=\frac{28}{12} \\ x^2=\frac{7}{3} \\ x=\pm\sqrt{\frac{7}{3}} \\ x=\sqrt{\frac{7}{3}},x=-\sqrt{\frac{7}{3}} \end{gathered}[/tex]Therefore the values of c are
[tex]\sqrt{\frac{7}{3}},-\sqrt{\frac{7}{3}}[/tex]balanced equation question for lrwctoce
Letter B is the correct answer.
2 Al 2
3 Ni 3
6 Br 6
The other equatins are unbalanced
need help with this
x=19 * sin(40)
x = 12.21
1) Since we have a right triangle and the opposite leg to angle 40º, then we can write the following trig ratio
[tex]\begin{gathered} \sin (40)=\frac{x}{19} \\ x=19\cdot\sin (40) \\ x=12.21296 \\ x\approx12.21 \end{gathered}[/tex]2) Then the equation for that is x= 19*sin(40) and the value of that leg is approximately 12.21 units
i need help with math Will u
The value of 'w' for the two parallel lines are cut by the transversal is 52.
What is meant by the supplementary angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two perspectives are known as supplements. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, so unless Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary.For the given question
Two parallel lines are cut by the transversal.
Then,
w + (3w -28) = 180 (same side exterior angle of the traversal are supplementary)
Solve the equation;
4w - 28 = 180
4w = 208
w = 208/4
w = 52
Thus, the value of 'w' for the two parallel lines are cut by the transversal is 52.
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Graph y-12=4(x-(-3))
The graph of the equation can be given as
What is an equation of the line how to graph the equation?
An equation is an expression between two variables With an equality sign. Usually an equation of the line can be given as y= mx + c, Where x is independent and y is dependent and c is y-intercept. as the value of x changes the value of y also changes.
We are given an equation y-12 = 4(x-(-3))
We first simplify the equation
we get y -12 = 4(x+3)
Multiplying 4 inside the bracket we get,
y-12= 4x+12
Adding 12 on both sides to get slope intercept form.
y=4x+24
The slope of the line is 4 and y-intercept is 24.
Now we can plot the given equation.
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What is the location of the vertex on the parabola defined by f(x) = 2x2 + 14x + 11 and in what direction does the parabola open?
Vertex of a parabola
The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved.
The given function is,
[tex]f(x)=2x^2+14x+11[/tex]We will apply graphical method to obtain the solution to the vertex of the parabola
From the graph above, the vertex of the parabola is (- 3.5, - 13.5) which can also be represented into fraction as
[tex](-\frac{7}{2},-\frac{27}{2})[/tex]And finally, the parabola opens upward.
Hence, the correct option is Option 2.
Result is Result isRational IrrationalReason(a) 34 +O(Choose one)12(b)4+ -21(Choose one)17(c) ſo6 x 23(Choose one)13(d)8 x(Choose one)19
Firstly, rational numbers are numbers that can be express in the form of a ratio.
[tex]\begin{gathered} \frac{x}{y} \\ \text{where} \\ y\ne0 \end{gathered}[/tex]Irrational numbers are numbers that cannot be express in the form of a fraction. These numbers are non-terminating. Therefore,
a.
[tex]\begin{gathered} 34+\sqrt[]{7}=34+\sqrt[]{7} \\ 34\text{ is a rational number as it can be express in fraction} \\ \sqrt[]{7}\text{ is an irrational number. The square root of 7 is non-terminating.} \\ \text{The sum of a rational and an irrational number will }always\text{ be an irrational number} \end{gathered}[/tex]b.
[tex]\begin{gathered} \frac{12}{17}+\frac{4}{21}=\frac{252+68}{357}=\frac{320}{357}(rational) \\ \text{The sum of 2 rational numbers }produces\text{ a rational number.} \\ \text{Notice that the individual numbers can be express in fractions. This makes them rational.} \end{gathered}[/tex]c.
[tex]\begin{gathered} \sqrt[]{6}\times23=23\sqrt[]{6} \\ The\text{ product of the irrational number(}\sqrt[]{6}\text{) and rational number(23) will result in an irrational number.} \end{gathered}[/tex]d.
[tex]\begin{gathered} 8\times\frac{13}{19}=\frac{104}{19} \\ 8\text{ is rational number} \\ \frac{13}{19}\text{ is a rational number because it can be express in fraction.} \\ \text{The product of the 2 rational number will produce a rational number (}\frac{104}{19}\text{)} \end{gathered}[/tex]the graph to the right represents the cost of a taxi where X is distance in miles and y is cost $10 what conclusion can you make? A. the taxi will stop every two miles B. The taxi cost $2 per mile C. The taxi will stop after 5 miles D. The taxi cost $2 just to get into attacks
Explanation
Step 1
the graph to the right represents the cost of a taxi where X is the distance in miles and y is the cost.
if the cost is $10m it means,exist a x, that satisfies
[tex]f(x)=10[/tex]look for the y value = 10 in the graph
Step 2
down vertically for to find the x value
The Super Discount store is having a sale and all the clearance items are %40 off. Which of the following are correct ways to find the price of an item that is $25.00 normally ?
The normal price is $25, we need to find the 40% of $25.
40% = 0.4
So if we multiply $25 by 0.4
An item is regularly priced at $95. It is on sale for 60% off the regular price. How much (in dollars) is discounted from the regularprice?
We have to find the 60% of $95. Doing so, we have:
60/100*$95
0.6*$95 (Dividing)
$57 (Multiplying)
The discount is $57
What is the length of BC to the nearest 10th of a centimeter
Step 1: sketch out the right angled triangle
Step 2: calculate the value BC
To calculate the value of BC we will use the trigonometric ratio
[tex]\begin{gathered} \sin \theta=\frac{opp}{hyp} \\ \text{where,} \\ \text{opp}=BC \\ \text{Hyp}=6.2\operatorname{cm} \\ \theta=32^0 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \sin 32^0=\frac{BC}{6.2} \\ BC=6.2\times\sin 32^0 \\ BC=6.2\times0.5299 \\ BC=3.2854\operatorname{cm} \\ \text{appro}\xi\text{mately to the nearest tenth we will have} \\ BC=3.3\operatorname{cm} \end{gathered}[/tex]Hence,
The value of BC =3.3cm