Step-by-step explanation:
it does not say what the card deck consists of, and how many cards of what type there are.
so, I assume a standard playing card set of 52 cards (no jokers) with 4 suits of
Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K
in that ranking of value.
so there are 4 cards of each of the 13 different types.
a card with a number greater than 9 means a 10, a J, a Q, or a K.
so, in total there are 4×4 = 16 such cards in the deck.
a card with a number less than 4 means an Ace, a 2, or a 3.
so, in total there are 4×3 = 12 such cards in the deck.
to get a number greater than 9 and a number less than 4 is a combination of the first card being greater than 9 and the 2 card being less than 4 OR the first card being less than 4 and the second card being greater than 9.
an "and" operation (without overlap) we represent by a multiplication, and an "or" operation (without overlap) by an addition.
remember, a probability is always
"desired cases / total possible cases".
so, the probability to draw a first card greater than 9 is
16/52 = 4/13
the probability to draw a second card greater than 9 (after a first card less than 4) is
16/51
because we still have all the large cards, but one of the smaller ones is now gone.
the probability to draw a first card less than 4 is
12/52 = 3/13
the probability to draw a second card less than 4 (after a first card greater than 9) is
12/51.
so, the complete probability of the scenario is
4/13 × 12/51 + 3/13 × 16/51 = 48/663 + 48/663 = 96/663 =
= 32/221 = 0.14479638...
if my assumptions about the cards are wrong, please adapt the numbers accordingly. but the basic structure of the calculation is the same.
If a satellite can travel 200ft per second, how many hours will it take the satellite to travel 10,000 miles?
Let's examine what the problem gives us:
Distance ⇒ 10000 milesTime ⇒ 200 ftWhat does the problem want:
⇒ time (in hours)
Must find the relationship between distance, speed, and time:
⇒ Distance = Speed * Time
⇒ [tex]Time = \frac{Distance}{Speed}[/tex]
Let's convert some units:
We want the time in hours and distance in miles, but we have speed in feet per sec, and we want miles per hour⇒ let's convert
⇒ [tex]\frac{200_.ft}{1_.s}*\frac{3600_.s}{1_.hr}*\frac{1_.mi}{5280_.ft}=136.36_. mi/hr[/tex]
Now let's solve:
[tex]Time = \frac{Distance}{Speed}=\frac{10000_.mi}{136.36.mi/hr} =73.33_.hrs[/tex]
Answer: 73.33 hrs (estimated)
Jesse measured a farm and made a scale drawing. The scale of the drawing was 1 centimeter = 4 meters. If the actual width of the goat pen is 8 meters, how many centimeters wide is the goat pen in the drawing?
Rewrite the equation below so that it does not have fractions:
3/4x - 2 = 5/12
Do not use decimals in your answer.
Answer:
Equation = [tex]\frac{3}{4}[/tex] x - 2 = [tex]\frac{5}{12}[/tex]
First: [tex]\frac{3}{4}[/tex] x = [tex]\frac{5}{12}[/tex] + 2
Then: [tex]\frac{3}{4}[/tex] x = [tex]\frac{29}{12}[/tex]
Answer: x = [tex]\frac{29}{9}[/tex] —> 9x = 29
—-
Have a nice day!!
What is the approximate value of X?! Help ASAP please
Triangles are similar
x/5=12/1313x=60x=60/13x=4.615x=4.62Option E
Answer:
Both of the triangles are similar but they look like they have been rotated a bit. Sides x is similar to 12 and side 5 (the hypotenuse) is similar to 13. Therefore we can just set up an equation and cross-multiply.
[tex]\frac{x}{5} = \frac{12}{13}[/tex]
[tex](x * 13) = (5 * 12)[/tex]
[tex]13x = 60[/tex]
Divide 12 from both sides
[tex]13x/13 = 60/13[/tex]
[tex]x=4.615[/tex]
Best option would be Option E, 4.62
What is the value of the rational expression below when xis equal to 4?
x-12/x-8
Answer:
= -7
Step-by-step explanation:
given x = 4
12/4 = 3
4 - 3 - 8 = -7
If xy + 1/(xy) = 2 , then what does (x^2)(y^2) + 1/((x^2)(y^2)) = ?
Show all work.
Show any graphical support.
Explain what happened with both the math work and the graph(s).
Think about what happened.
Would it happen with more terms or the next function in the sequence?
Why or why not? Explain.
The value of the expression will be [tex](xy)^2+\dfrac{1}{(xy)^2}=2[/tex]
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
The value of the expression is [tex]xy+\dfrac{1}{xy}=2[/tex]
So we need to find [tex](xy)^2+\dfrac{1}{(xy)^2}=?[/tex]
The value of the expression will be calculated as:-
[tex]xy+\dfrac{1}{xy}=2[/tex]
Squaring the above equation.
[tex](xy)^2+\dfrac{1}{(xy^2)}+2\times (xy)^2\times \dfrac{1}{(xy^2)}=4[/tex]
[tex](xy)^2+\dfrac{1}{(xy^2)}=2[/tex]
Again squaring the above expression.
[tex](xy)^4+\dfrac{1}{(xy^4)}+2\times (xy)^4\times \dfrac{1}{(xy^4)}=4[/tex]
[tex](xy)^4+\dfrac{1}{(xy^4)}=2[/tex]
Hence the value of the expression will be [tex](xy)^2+\dfrac{1}{(xy)^2}=2[/tex]
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Find the factor of each ff.
8t²-16t-4
Answer:
For me, this quadratic expression can simply be factored by 4 because all the values divide by four. so:
[tex]4( {2}t^{2} - 4t - 1)[/tex]
Step-by-step explanation:
Just factor it by 4
Answer:
4(2t^2 - 4t - 1)
Step-by-step explanation:
8t²-16t-4
= 4(2t^2 - 4t - 1)
2t^2 - 4t - 1 is prime so there are no more factors.
Find the factor of each ff.
49x²-63x+7
Answer:
7(7x²-9x +1)
Step-by-step explanation:
49x²-63x+7
7(7x²-9x +1)
Someone pls help fast!
Answer:
decreasing and linear
Step-by-step explanation:
it just is
Answer:
Decreasing, linear
Step-by-step explanation:
you are going -4 every time
i need this answer as fast and soon as possible
Answer:
1.732
Step-by-step explanation:
The first three terms of an arithmetic progression are 2x, x+4, 2x - 7 respectively.
a. Find the value of x
b. Find the three terms
(6 m
c. What is the common difference?
Answer:
a) x = 7.5
b) 15, 11.5, 8
c) -3.5
Step-by-step explanation:
As there is a common difference between consecutive terms of an arithmetic progression, then:
[tex]a_3-a_2=a_2-a_1[/tex]
Given:
[tex]a_1=2x[/tex][tex]a_2=x+4[/tex][tex]a_3=2x-7[/tex]Therefore:
[tex]\implies a_3-a_2=a_2-a_1[/tex]
[tex]\implies (2x-7)-(x+4)=(x+4)-2x[/tex]
[tex]\implies 2x-7-x-4=x+4-2x[/tex]
[tex]\implies x-11=-x+4[/tex]
[tex]\implies 2x=15[/tex]
[tex]\implies x=7.5[/tex]
Inputting the found value of x into the term expressions to find the three terms of the arithmetic progression:
[tex]a_1=2(7.5)=15[/tex][tex]a_2=(7.5)+4=11.5[/tex][tex]a_3=2(7.5)-7=8[/tex]The common difference (d) is the difference between each consecutive term. To find the common difference, subtract one term from the next term:
[tex]\implies d=a_3-a_2= 8 - 11.5 = -3.5[/tex]
[tex]\implies d=a_2-a_1= 11.5-15 = -3.5[/tex]
Therefore, the common difference is -3.5
15. Chris can run at a constant speed of 12 km/h. How long will it take him to run from
his home to the park, a distance of 0.8 km?
Remember to check that your answer is reasonable.
Answer:
Step-by-step explanation
1= 12
.8 of 1 = 48
so it should only take him 48 minutes since hes not taking a full hour but 0.8 is two of from an hour
Two lines intersect at a point, forming angle 1, angle 2, angle 3, and angle 4.
Angle 1 and angle 3 are vertical angles.
Angle 2 and angle 4 are vertical angles.
m angle1 = 70
What is the measure of angle 2?
O 20°
O 70°
O 90°
O 110°
Determine which expressions represent purely real numbers and which expressions represent non-real complex numbers. -i^2+i^3 7-5i √ 6 0+9i √(-5)^2 -12 2 -7i^2
purely real number
non-real complex number
Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.
What are Purely real numbers and Non-real complex numbers?Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.
The given expressions can be simplified in the following manner,
[tex]-i^2+i^3 = -(\sqrt{-1})^2+(\sqrt{-1} \times \sqrt{-1} \times \sqrt{-1}) = 1 -i[/tex] 7-5i [tex]\sqrt{-6} = \sqrt{-1 \times 6} = \sqrt{-1} \times \sqrt{6} = 0+ i\sqrt{6}[/tex]i⁶ = (i²)³ = (-1)³ = -1 = -1 +0i0+9i [tex](\sqrt{-5})^2 = (\sqrt{-1 \times 5})^2 = -1 \times 5 = -5+0i[/tex] -12 = -12+0i[tex]2 -7i^2 = 2-7(-1) = 2+7 = 9+0i[/tex]Purely real numbers (a+0i)
-1 +0i-5+0i-12+0i9+0iNon-real complex number (0+bi)
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Answer:
Step-by-step explanation:
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what is the slope of the line
Answer:
Step-by-step explanation:
(0, 2) (2, 0)
(0-2)/(2-0)= -2/2= -1
y - 2 = -(x - 0)
y - 2 = -x + 0
y = -x + 2
Which is a coeffecient
Answer:
B is a coefficient
Step-by-step explanation:
Coefficient of 2O2 is 2.
B = 2
Urgent help!!!
Write equation in slope intercept form.
1.25 (25) = 31.25
The equation in slope intercept form is,[tex]31.25 = 1.25 \times 25 +0[/tex]. The given equation is obtained by comparing the standard equation of the straight line.
What is a slope of a straight line?
A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The given equation is;
1.25 (25) = 31.25
31.25=1.25 (25)
The standard equation of the slope intercept form. is;
[tex]\rm y = mx +x[/tex]
On comparing the given equation with the above equation, we get;
y=31.25
m=1.25
x=25
c=0
The equation in slope intercept form is;
[tex]31.25 = 1.25 \times 25 +0[/tex]
Hence, the above equation is the slope intercept form.
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ASAP WILL GIVE BRAINLIEST!
Given: AB CD and AB || CD
Prove: ABCD is a parallelogram
The missing parts of the given table are
∠1 ≅ ∠4 → Alternate interior angles Theorem
DB ≅ DB → Reflexive property
ΔDAB ≅ ΔBCD → SAS (Side Angle Side)
Proving a quadrilateral is a parallelogramFrom the question, we are to complete the table to prove that ABCD is a parallelogram
The Alternate interior angles theorem states that when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. That is, they are equal.The reflexive property of congruence states that an angle, line segment, or shape is always congruent to itselfThe missing parts in the table can be completed as shown below
∠1 ≅ ∠4 → Alternate interior angles Theorem
DB ≅ DB → Reflexive property
ΔDAB ≅ ΔBCD → SAS (Side Angle Side)
Hence, the missing parts of the given table are
∠1 ≅ ∠4 → Alternate interior angles Theorem
DB ≅ DB → Reflexive property
ΔDAB ≅ ΔBCD → SAS (Side Angle Side)
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.
Help please I don’t get this one
Answer:
[tex]P = 8\pi[/tex]
Step-by-step explanation:
To solve this problem, we must calculate the circumference of one circle and multiply it by two because there are 2 circles (4 halves), that make up the perimeter.
We know the diameter is 4m, thus, the circumference of one circle (two halves) is:
[tex]C_1 = \pi d\\C_1 = \pi 4[/tex]
To get the total perimeter (circumference) multiply the result by 2:
[tex]C = C \times 2\\C = 4\pi \times 2\\C = 8\pi[/tex]
how many ways can 3 city council members from a list of 20 candidates be selected
A 2-pack of movie tickets costs $17.24. What is the unit price
Answer:
As the two pack of ticket cost 17.24. Mean that the unit or the price of one pack will be half of it which is
8.62
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
Ella conducted a survey to find out the amount of time high schoolers spend surfing the Internet. From the data collected, the range of time spent was 1 hour. What does this range say about the data?
All the students surveyed spend exactly 1 hour surfing the Internet.
All the students surveyed spend an average of 1 hour surfing the Internet.
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour.
The quotient between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour.
The statement third “the difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour” is correct.
What is range?It is defined as the difference between the maximum value in the data set to the minimum value in the data set.
As we know, the difference between the greatest and lowest values, called the range.
According to this response, the range is 1 hour, which is the difference between the most and least amount of time spent surfing the Internet. This is based on the term “Range.”
Thus, the statement third “the difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour” is correct.
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Answer:
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour!
Step-by-step explanation:
In order to select new board members, the French club held an election. 25% of the 84 members of the club voted. How many members voted?
Answer: 21 people voted
Step-by-step explanation:
an easy way to do this is simply multiply 84 * 0.25.
This gives you [tex]\frac{1}{4}[/tex] of the original amount
in this case 84×0.25 = 21
This means that 21 people voted
Margot has 8 kilograms of apples.how many liters Of apple juice can Margot make. How do l do this?????
Answer:
so about 4?
Step-by-step explanation:
1 kilogram = 1,000 grams
2 kilograms = 2 times 1,000 which equals 2,000 grams
2,000 grams makes one liter
uhh this is just an educated guess...
covert this rational number to its decimal form and round to the nearest thousandth. 7/9
Answer:
0.778 to the nearest thousandth.
Step-by-step explanation:
Dividing 7 by 9:
9) 7.000000
0.7777777 .... <-- quotient
So it is 0.778 to the nearest thousandth.
A circular tabletop has a circumference of 94.2 inches. What is its approximate area?
Answer:
1st choice : 706.5 square inches
Step-by-step explanation:
circumference is pi times diameter
divide 94.2 by pi to get diameter = 29.9847912785
diameter 29.9847912785 divided by 2 is
14.9923956393 which is the radius
area is pi times radius times radius again
pi times 14.9923956393 times 14.9923956393 =
706.141834613
2. Mary has saved $160 of the $250 she needs for rent.
She takes home $6 an hour from her part-time job.
Mary works the same number of hours each day for 3
days. How many hours does Mary have to work each
day to take home enough money to pay the balance
of her rent?
F. 3 hours
G.
4 hours
H.
5 hours
J.
6 hours
K
7 hours
Answer:
H - 5 hours
Step-by-step explanation:
We can setup an equation to solve the question.
Let [tex]h[/tex] be the number of hours Mary must work.
[tex]250 = 160 + 3(6h)[/tex]
250 - the amount of money Mary needs
160 - the amount of money Mary has saved already
3 - How many days she works
6h - How much she gets paid per day
[tex]250 = 160 + 3(6h)\\90 = 3(6h)\\90=18h\\5=h[/tex]
This means Mary must work 5 hours each day to pay her rent.
now bsf yall know........
Answer:
24 - 14.4b
Step-by-step explanation:
What is the mean absolute deviation.
Answer:
1.56 rounded 1.6
Step-by-step explanation:
MAD (Mean Absolute Value):
step 1: Find the mean of the data
formula: sum of the data set / total number of terms
sum of the data set: 4 + 9 + 4 + 5 + 3 = 24
total number of terms: there is 5 numbers in the data set
mean = 24 / 5
mean = 4.8
step 2: Find the distance between each data and mean.
3, 4, 4, 5, 9
Distance between 3 and 4.8 is 1.8 (4.8 - 3 = 1.8)
Distance between 4 and 4.8 is 0.8 (4.8 - 4 = 0.8)
Distance between 4 and 4.8 is 0.8 (4.8 - 4 = 0.8)
Distance between 5 and 4.8 is -0.2 (4.8 - 5 = -0.2)
Distance between 9 and 4.8 is -4.2 (4.8 - 9 = -4.2)
step 3: take the absolute value of any negative numbers
|-0.2| and |-4.2| is 0.2 and 4.2
step 4: add all the distances
1.8 + 0.8 + 0.8 + 0.2 + 4.2 = 7.8
step 5: divided it by the number of data
7.8 / 5 = 1.56
Let me know if you have any questions !
The following table gives the statements and justifications for solving the equation 4(x - 7) + 14 =
3x - 9.
Which of the following gives the justification steps in the correct order?
Answer:
From top to bottom:
Simplify
Combine like terms
Subtract 3x from both sides
Add 14 on both sides
Step-by-step explanation:
Hope this helps
