The probability of selecting an ace or a heart when one card is drawn from 52 cards is 1/52.
Given that there are 52 cards in which there are 13 cards each for spades,clubs,hearts and diamonds.
We are required to find the probability of getting an ace or a heart when one card is drawn from 52 cards.
Probability is basically the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative. The probability can be calculated through following formula:
Probability=Number of items/total number of items.
Number of hearts=13
Number of ace=4
Probability of getting an ace or a heart when one card is drawn=P(X=heart)*P(X=ace)
=13/52 * 4/52
=52/(52*52)
=1/52
Hence the probability of getting an ace or heart when one card is drawn from standard deck of cards is 1/52.
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Help pls i cant answer and i need to get them right
The expression has 2 factors, and the second factor has 2 terms.
How many factors has the expression?We can write an expression of N factors as:
[tex]y = A_1*A_2*...*A_n[/tex]
Here, the expression is:
4*(8x + 5)
This expression has 2 factors, which are:
4 and (8x + 5)
Now, if we look at the only factor 8x + 5, we have two terms (the terms are the parts that are added), the terms are:
8x and 5.
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Write the equation for a parabola with a focus at (-4,8) and a directrix at x=-6
x= ?
The equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).
What is the equation for a parabola with a focus at (-4,8) and a directrix at x = -6?Given that x = -6, it means the directrix is horizontal.
Equation of parabola that opens left or write is expressed as;
( y - k )² = 4p( x - h )
Given that;
Focus: ( -4, 8 )Directrix: y = -6First, we find the vertex.
The vertex( h, k ) is halfway between the directrix and the focus.
Hence, x coordinate of the vertex is;
x = ( x coordinate of focus + directrix ) / 2
x = ( -4 + (-6) ) / 2
x = -10/2
x = -5
y coordinate of the vertex will be the same as that of the focus.
y = 8
Hence vertex will be;
( -5, 8 )
Next, we find the distance p from the focus to the vertex and from the vertex to the directrix.
Subtract x coordinate of vertex from x coordinate of focus.
p = -4 - ( -5 )
p = -4 + 5
p = 1
Now, we substitute these values into the equation.
( y - k )² = 4p( x - h )
( y - (8) )² = 4(1)( x - (-5) )
( y - 8)² = 4( x +5 )
Therefore, the equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).
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Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.
y = 7.5x
y = 5.5x + 10
1. Substitute: 7.5x = 5.5x + 10
How many classes could Anna take so that the total cost for the month would be the same?
classes
What is the total monthly cost when it is the same for both gyms?
The number of classes Anna can take so the total cost for the month will be the same is 5.
The monthly cost would be $37.50.
When would the total cost be the same?When the monthly cost is equal, both equations would be equal: 7.5x = 5.5x + 10
In order to determine the value of x, take the following steps:
Combine similar terms: 7.5x - 5.5x = 10 Add similar terms: 2x = 10 Divide both sides by 2 : 10 /2 = 5Monthly cost when the cost is the same: 7.5 x 5 = $37.50
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Answer:
5 classes
37.50
Step-by-step explanation:
got it right on edge
PLEASE CAN SOMEONE HELP!!!!!! ASAP
Answer:
C
Step-by-step explanation:
Express functions as a ratio: put one in the numerator and the other in the denominator
[tex]\frac{12- \frac{2}{3}t}{3-\frac{1}{8}t }[/tex]
We want to get rid of the fractions which would mean multiplying top and bottom by 3 and 8. (Remember to multiply both terms). The answer would result in C.
Solve the right triangle. Round decimals to the nearest tenth
Answer:
j = 19.6
k = 25.9
J = 49°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.
AnalysisThe given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Tan = Opposite/Adjacent ⇒ Adjacent = Opposite/Tan
Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.
ApplicationHypotenuse = Opposite/Sin
IJ = 17/sin(41°) ≈ 25.9
Adjacent = Opposite/Tan
IK = 17/tan(41°) ≈ 19.6
Angle J = 90° -41° = 49°
In summary, ...
j = 19.6
k = 25.9
J = 49°
1. The accompanying table shows the number of movie theaters showing a popular film and the film's weekly gross earnings, in millions of dollars. Use the table to answer the questions 1), 2).
Number of Theaters (x)
443
456
493
530
569
657
723
1,054
Gross Earnings (y)
(millions of dollars)
2.57
2.65
3.73
4.05
4.76
4.79
5.15
9.63
1). Write the linear regression equation for this set of data, rounding values to five decimal places. Using this linear regression equation, find the approximate gross earnings, in millions of dollars, generated by 610 theaters. Round your answer to two decimal places.
2). Find the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.
2. A real estate agent plans to compare the price of a cottage, y, in a town on the seashore to the number of blocks, x, the cottage is from the beach. The accompanying table shoes a random sample of sales and location data. Write a linear regression equation that relates the price of a cottage to it's distance from the beach. Use the equation to predict the price of a cottage, to the nearest dollar, located three blocks from the beach.
Number of Blocks
from the Beach
(x) Price of a Cottage
(y)
5 $132,000
0 $310,000
4 $204,000
2 $238,000
1 $275,000
7 $60,800
3. The table below represents a chart kept by a pediatrician tracking the circumference of babies heads at various months of age.
Age
(in months) Circumference
(in cm)
1 35.8
2 36.6
5 38.5
6 39.1
4 38.9
13 40.1
7 39.1
15 40.3
10 39.9
2 36.8
18 40.6
1). Determine the regression model that best fits the data, rounding all values to the nearest thousandth. Then predict the size of a baby's head at 24 months old. Round your answer to the nearest tenth.
2). The pediatrician measured a newborns head and found the circumference to be 35.1cm. Can he add the pair (0, 35.1) to the data set to calculate a new regression? Justify your answer.
The regression equation of this group of data is given as ŷ = 0.0108X - 1.98123.
How to solve for the amount generated by the theaterŷ = 0.0108X - 1.98123
x = 610
= 0.0108*610 - 1.98123
= 4.61 million dollars
2. the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.
7.65= 0.0108x-1.98123
take like terms
x = 892
2. correlation coefficient of X and Y is r = -0.987
This shows a negative relationship
b)Linear Regression Equation =
Y = 313309 - 34740x
c) Y = 313309 - 34740x
Y = 313309 - 34740 * 3
209089
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The voice onset time (vot) for the sound /da/ is 17 ms, and the vot for the sound /ta/ is 91 msec. When a computer produces a sound with a vot of 65 ms, listeners are likely to report hearing?
The the /ta/ sound is the sound which listeners are likely to report hearing. The option B is correct option.
According to the statement
we have given that the The voice onset time (vot) for the sound /da/ is 17 ms, and the vot for the sound /ta/ is 91 msec. and we have to find the sound which listeners are likely to report hearing.
So, For this purpose, we know that the
Traffic announcement (TA) refers to the broadcasting of a specific type of traffic report on the Radio Data System. It is generally used by motorists, to assist with route planning, and for the avoidance of traffic congestion.
And according to this and the voice onset time is
The brief instant that elapses between the initial movement of the speech organs as one begins to articulate a voiced speech sound and the vibration of the vocal cord.
And according to this
the /ta/ sound is the sound which is the like by the listeners are likely to report hearing.
So, The the /ta/ sound is the sound which listeners are likely to report hearing. The option B is correct option.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
The voice onset time (VOT) for the sound /da/ is 17 ms, and the VOT for the sound /ta/ is 91 msec. When a computer produces a sound with a VOT of 65 msec, listeners are likely to report hearing
a. the /da/ sound
b. the /ta/ sound
c. the /ja/ sound
d. a combination of /ta/ and /da/
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A box is to constructed with a rectangular base and a height of 5cm. if the rectangular base must have a perimeter of 28cm, which quadratic equation best models the volume of the box ? a. y=5(28-8)(x) b.y=5(28-2x)(x) c. y=5(14-x)(x) d. y=5(14-2x)(x)
y=5(14-x)(x) quadratic equation best models the volume of the box .
What is volume of cuboid?
Perimeter is the distance around the outside of a shape. Area measures the space inside a shape. The volume of a cuboid is found by multiplying the length by the breadth by the height.Perimeter = 2(width + length) =28
Let x=width of base, then length of base = (28/2)-x = 14-x
Volume of box = length*width*height
=x(14-x)*5 ⇒ 5x(14-x)(x)
Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .
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The marked price of an article is rs 10000 . If he discounted rate and VAT rate are equal and the price with VAT is 9900 find the vat rate .
The rate of VAT is 10%.
In the question, we are asked to find the VAT rate, given that the market price of an article is Rs. 10000, the rate of discount and the rate of VAT are equal, and the price after VAT is Rs. 9900.
We assume the rate of discount and the rate of VAT to be r%.
Thus, discount = r% of Rs. 10000 = Rs. r/100 * 10000 = Rs. 100r.
Thus, the price after discount = Rs. 10000 - 100r = Rs. 100(100 - r)
Then, VAT = r% of (Rs. 100(100 - r)) = Rs. r/100 * 100(100 - r) = Rs. r(100 - r).
Thus, the price after VAT = Rs. 100(100 - r) + Rs. r(100 - r) = Rs. (100 + r)(100 - r).
The price after VAT is given to be Rs. 9900.
Thus, (100 + r)(100 - r) = 9900,
or, 100² - r² = 9900,
or, r² = 100² - 9900,
or, r² = 10000 - 9900 = 100,
or, r = ±√100 = ±10.
Since r is the rate of VAT, it cannot be negative, making r = 10.
Thus, the rate of VAT is 10%.
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#14
quick answer pls :)
Answer:
35.56
Step-by-step explanation:
Let f(x) = (x − 3)−2. find all values of c in (1, 4) such that f(4) − f(1) = f '(c)(4 − 1). (enter your answers as a comma-separated list. if an answer does not exist, enter dne. ) c =
If the function is [tex](x-3)^{-2}[/tex] and f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.
Given function is [tex](x-3)^{-2}[/tex] and f(4) − f(1) = f '(c)(4 − 1).
In this question we have to apply the mean value theorem, which says that given a secant line between points A and B, there is at least a point C that belongs to the curve and the derivative of that curve exists.
We begin by calculating f(2) and f(5):
f(2)=[tex](2-3)^{-2}[/tex]
f(2)=1
f(5)=[tex](5-3)^{-2}[/tex]
f(5)=1
And the slope of the function:
[tex]f^{1}[/tex](x)=[tex]f(5)-f(2)/(5-2)[/tex]
[tex]f^{1}[/tex](c)=0
Now,
[tex]f^{1} (x)=-2*(x-3)^{-3}[/tex]
=-2[tex](x-3)^{-3}[/tex]
=0
-2 is not equal to 0. So there is not any answer.
Hence if the function is [tex](x-3)^{-2}[/tex] and f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.
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Select the correct answer.
Based on the construction shown, what is the next step in the process of constructing parallel line CD?
A.
Using the same compass width that created the first arc, repeat the arc centered at point B.
B.
Using the same compass width that created the first arc, repeat the arc centered at point C.
C. Set the compass width to the distance between point E and where the arc crosses line AB.
D.Set the compass width to be where the arc intersects lines ECand EB.
The next step in the process of constructing parallel line CD is C. Set the compass width to the distance between point E and where the arc crosses line AB.
How to illustrate the information?It's important to draw a line parellel to line AB. Then, on should set compasses' width to the distance where the lower arc crosses the two lines.
After that, it's vital to move the compasses to where the upper arc crosses the transverse.
In conclusion, the correct option is C.
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Answer:
The answer is A
Step-by-step explanation:
PLEASE HELP ME! THE QUESTION IS DOWN BELOW PLEASE PLEASE HELP ME
The given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.
What is an expression?An expression can be defined as a type of mathematical equation which is used to show the relationship that is existing between two or more variables and numerical quantities (integers).
In this exercise, you're required to fully simplify the given expression in the lowest terms. Thus, we would simplify the given expression completely by collecting like terms and performing the necessary arithmetic operations (addition and subtraction) as follows:
Collecting like terms, we have:
8h - 5h + 3w + 2w
Subtracting and adding the like terms respectively, we have:
3h + 5w.
In conclusion, we can logically deduce that the given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.
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Complete Question:
Fully simplify 8h + 2w - 5h + 3w.
Need help!!!!!!! Please help me out
Answer:
x = 10°
Step-by-step explanation:
If the two lines are parallel then the two marked angles will be equal.
8x = 2x + 60
Subtract 2x to combine like terms.
6x = 60
Divide by 6.
x = 10
A radioactive material has a half life of 10 years. What is the fraction of the initial isotope is left after 60 years
Answer:
1/64
Step-by-step explanation:
10 = ½
20 = ¼
30 = ⅛
40 = 1/16
50 = 1/32
60 = 1/64
Answer:
0.015625 left.
Step-by-step explanation:
If we start with say 100g of the material, in 10 years there is 100 * 1/2 =
50g left ( = 0.5 left).
In 20 years there is 100*(1/2)^2 = 25 g left.
In n*10 years there is 100(1/2)^2 g
So in 60 years there is 100(1/2)^6 = 1.5625 g left
This is 1.5625 %
= 0.015625 of the origin material left.
Select all the types of quadrilaterals that describe DEFG.
A parallelogram D trapezoid
B rhombus E rectangle
C square
_________ DEFG maps out Xavier’s running route. If he does one complete loop, how far does he
run? (Each unit represents 1 mile) Round answer to the nearest whole mile. Show work below.
The quadrilaterals that describe DEFG include parallelogram, rhombus, and square
What is a quadrilateral?It should be noted that a quadrilateral simply means a close shape and a polygon that has four sides.
In this case, the quadrilaterals that describe DEFG include parallelogram, rhombus, and square. In a parallelogram, it should be noted that the sides are parallel to each other.
Therefore, the quadrilaterals that describe DEFG include parallelogram, rhombus, and square.
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If u=(-5,3) and v=(-15,25) with an angle theta between the vectors, are u and v parallel or orthogonal? Explain
Answer:
Option (2)
Step-by-step explanation:
[tex]\mathbf{u} \cdot \mathbf{v}=(-5)(-15)+(3)(-25)=0[/tex]
So, the vectors are orthogonal.
How do I get my answer
Confused about this question
Answer:
17.1
Step-by-step explanation:
Plug in -1 for x, this gets you -4.
Solve 2^-4 and get .0625.
Add .0625 to 17 and get 17.0625.
The question says answer to the nearest tenth so you round the 6 up to a 1 giving you 17.1
- What is the area of the figure below? Use 3.14
for T.
7 cm
22 cm
18 cm
Answer: [tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]
Step-by-step explanation:
PART I: Find the area of the triangleGiven information
[tex]Height=7~cm[/tex]
[tex]Base=18~cm[/tex]
Given formula
[tex]A=b\times h\times\dfrac{1}{2}[/tex]
[tex]A=Area\\b=base\\h=height\\[/tex]
Substitute values into the formula
[tex]A=(7)\times (18)\times\dfrac{1}{2}[/tex]
Simplify by multiplication
[tex]A=(7)\times 9[/tex]
[tex]A=63~cm^2[/tex]
PART II: Find the area of the rectangleGiven information
[tex]Height = 18~cm[/tex]
[tex]Base=22~cm[/tex]
Given formula
[tex]A=b\times h[/tex]
[tex]A=Area\\b=base\\h=height\\[/tex]
Substitute values into the formula
[tex]A=(22)\times (18)[/tex]
Simplify by multiplication
[tex]A=396~cm^2[/tex]
PART III: Find the area of the half-circleGiven information
Diameter = 18 cm
Given formula
[tex]A=(\dfrac{d}{2} )^2\times \pi \div2[/tex]
[tex]A=Area\\d=diameter[/tex]
Substitute values into the formula
[tex]A=(\dfrac{18}{2} )^2\times (3.14) \div2[/tex]
Simplify the fraction
[tex]A=(9 )^2\times (3.14) \div2[/tex]
Simplify the exponents
[tex]A=81\times (3.14) \div2[/tex]
Simplify by multiplication
[tex]A=254.34\div2[/tex]
Simplify by division
[tex]A=127.17~cm^2[/tex]
PART IV: Find the total areaGiven formula
[tex]Total~area=Triangle+Rectangle+circle~(half)[/tex]
Substitute values into the formula
[tex]Total~area=(63)+(396)+(127.17)[/tex]
Simplify by addition
[tex]Total~area=459+(127.17)[/tex]
[tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Given these facts, determine how many cans of paint you would need to buy to paint 2 walls.
1st wall: 20 ft. x 8ft.
2nd wall: 40ft. x 8ft.
1 can will cover 200 square feet of wall.
Answer:
3 cans
Step-by-step explanation:
A = lw
a = 20 x 8 = 160[tex]ft^{2}[/tex]
a = 40 x 8 = 320 [tex]ft^{2}[/tex]
Together this is 480 [tex]ft^{2}[/tex]
I would need 3 cans.
What is the congruence correspondence, if any, that will prove the given triangles congruent?
Answer:
The answer is option A SAS.We have a side,an angle and the last side.If this helps please mark me BRAINLIEST
Combine like terms to create an equivalent expression. 1.3b 7.8-3.2b1.3b 7.8−3.2b
The simplified equivalent expression exists -1.9b + 7.8.
What is equivalent expression?An equivalent expression exists an expression that contain the same value or worth as another expression, but does not look the same.
Combine the coefficient of the term b, we get
1.3b + 7.8–3.2b
= (1.3−3.2)⋅b + 7.8
simplifying the equation, we get
= (- 1.9) +b + 7.8
= −1.9b + 7.8
The simplified equivalent expression exists -1.9b + 7.8.
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does someone mind helping me with this? Thank you!
Which function has a domain of x>5 and a range of y≤3?
Oy=√x-5+3
Oy=√x+5-3
O y=-√x-5+3
O y = -√x+5-3
The correct option is the third one.
y = -√(x - 5) + 3
Which function has a domain of x>5 and a range of y≤3?Remember that a square root can only be evaluated in values equal or larger than zero.
So, if we want the domain to be x > 5, then we must have:
√(x - 5)
Now we also want the range to be equal or smaller than 3, then we should have a constant term equal to 3, and a negative coefficient before the square root, then we get:
y = -√(x - 5) + 3
So the correct option is the third one.
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Geometry: complete this proof (ASAP!!!! It’s urgent)
Answer:
1. Given.
2. Reflexive Property of Congruence.
3. Alternate Interior Angles Theorem.
4. SAS
5. <4 ~= <2
6. Converse of Alternate Interior Angles Theorem.
2. A football team plays 28 games and wins 4 out of every 7 games played. No match ended in a draw. (b) Calculate the win - loss ratio of this football team. ( I know the answer is 4:3 but I don't know the way work )TY.
Answer:4:3
Step-by-step explanation: We can first calculate the wins. 24/7 is 4 and 4x4 = 16. So, they won 16 games and lost the rest. 28-16 = 12. 16:12 is equal to 4:3.
Find the surface area of the prism
Area of the base = 60 inches²
Height of the prism = 4 inches
perimeter of the base = 34 inches
Surface area of the rectangular prism = 256 inches²
How to find the surface area of a rectangular prism?The surface area of a rectangular prism can be calculated as follows;
area of the base = B = 12 × 5 = 60 inches²
Height of the prism = 4 inches
Perimeter of the base is the sum of the whole side of the base of the rectangular prism.
Therefore,
perimeter of the base = 12 + 12 + 5 + 5 = 34 inches
Surface area of the rectangular prism = 2B + ph
where
B = base areap = perimeter of the baseh =height of the rectangular prismTherefore,
Surface area of the rectangular prism = 2(60) + 34(4)
Surface area of the rectangular prism = 120 + 136
Surface area of the rectangular prism = 256 inches²
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A fourth-degree polynomial with a leading coefficient of 1 has gone through several transformations, including a vertical compression by a scale factor of 1/3 and a reflection across the x-axis. Two of the zero polynomials are -i and 3i.
Find a y-intercept of this polynomial, if it exists
The y-intercept of the resulting polynomial is equal to - 3.
How to derive a fourth-degree polynomial generated by rigid transformations
Herein we assume that the other two zeros of the polynomial are i and - i 3, otherwise the polynomial will have at least a complex number as coefficient of the expression. This is because we need to find values from a Cartesian plan, whose ordered pairs are real numbers.
Initially, we have the following expression by algebra properties:
f(x) = (x + i) · (x - i) · (x + i 3) · (x - i 3)
f(x) = (x² + 1) · (x² + 9)
f(x) = x⁴ + 10 · x² + 9
Then, we proceed to use the two rigid transformations described in the statement. Please notice that rigid transformations are transformations applied on polynomials such that Euclidean distance is conserved:
Vertical compression
f'(x) = (1 / 3) · f(x)
f'(x) = (1 / 3) · (x⁴ + 10 · x² + 9)
f'(x) = (1 / 3) · x⁴ + (10 / 3) · x² + 3
Reflection across the x-axis
g(x) = - f'(x)
g(x) = - (1 / 3) · x⁴ - (10 / 3) · x² - 3
The y-intercept is found for x = 0:
g(0) = - (1 / 3) · 0⁴ - (10 / 3) · 0² - 3
g(0) = - 3
The y-intercept of the resulting polynomial is equal to - 3.
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Which values below belong in this table? Select all that apply.
Answer:
16, 32, and 64
Step-by-step explanation:
We can see that this is an exponential function, since y multiplies by 2 every time x increases by 1. So the values of y are basically just powers of 2, because the equation of the table is y=2^x.