The probability that no two consecutive heads will occur is 13/32.
What is probability?It should be noted that probability simply means the likelihood of the occurence of an event based on chance.
In this case, the fair coin is tossed 5 times and we simony want it find the probability that no two consecutive heads will occur.
This will be:
Let n be the number of strings of h
Let t be the length n with two adjacent H's.
Therefore, the probability will be:
= (8+5)/2^5
= 13/32
In conclusion, the probability that no two consecutive heads will occur is 13/32.
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David has kept track of his family’s grocery bills for the past 10 weeks, as shown in the table.
Week 1 2 3 4 5 6 7 8 9 10
Bill ($) 92 106 129 115 100 84 110 156 98 87
Would you choose to use a histogram, a circle graph, or a line graph to display the data? Explain your choice. Then make a display.
The preferred choice would be a line graph (drawn in the figure attached) for displaying the data.
Why a line graph is the preferred option here?
For displaying the data of David's family's grocery bills for the past 10 weeks, a line graph is the most preferable choice since it would display the data's trend for us. This is similar to how we would notice times when there were huge costs.Another reason for choosing a line graph is that it is very easy to comprehend. It is simple to observe how the data are related and how they have changed.What is a line graph?
An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.
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Help ASAP will give 20 points!!!!!
use six unit multipliers to convert 33 cubic feet to cubic centimeters
Converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters
How to determine the conversionIt is important to note that conversion of units requires the appropriate equivalent values
For
I cubic foot is equivalent to 28316. 8 cubic centimeters
But we were given
33 cubic feet for the conversion
If 1 cubic foot = 28316. 8 cubic centimeters
Then 33 cubic feet = x
Cross multiply, we get
x = 28316. 8 × 33
x = 934454. 4 cubic centimeters
Thus, converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters
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If the ratio of areas of two similar solids is 25:36, what is the linear ratio.
Answer: Hi here go your answer is
25 divides by 36 is 0.69444 or 0.69
Step-by-step explanation:
A hat contains slips of paper with the letters A-Z printed on them. If you draw one at random, what is the probability that you will get a vowel?
The probability of selecting a vowel from the hat that contains slips of paper with the letters A-Z printed on them is 5/26
What is probability?Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events
How to determine the probability?The given parameters are:
Letters = A - Z
Vowels = A, E, I, O and U
The above means that the number of letters and vowels are
n(Letters) = 26
n(Vowel)
The probability of selecting a vowel from the hat that contains slips of paper with the letters A-Z printed on them is
P(Vowel) = n(Vowel)/n(Letters)
Substitute the known values in the above equation
P(Vowel) = 5/26
Hence, the probability of selecting a vowel from the hat that contains slips of paper with the letters A-Z printed on them is 5/26
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2. 2x+6y=6
-x-3y = -3
Solution(s):
PLEASE HELP SOLVE FOR X AND Y
Answer:
x = 0, y = 1
Step-by-step explanation:
2x + 6y = 6 → (1)
x - 3y = - 3 ( add 3y to both sides )
x = 3y - 3 → (2)
substitute x = 3y - 3 into (1)
2(3y - 3) + 6y = 6 ← distribute parenthesis and simplify left side
6y - 6 + 6y = 6
12y - 6 = 6 ( add 6 to both sides )
12y = 12 ( divide both sides by 12 )
y = 1
substitute y = 1 into (2)
x = 3(1) - 3 = 3 - 3 = 0
solution is x = 0 , y = 1
What is the shape of the graph of the function?
h(t)=0.6\cdot 3.2^th(t)=0.6⋅3.2
t
The graph of a function f exists the set of all points in the plane of the form (x, f(x)).
What is the graph of a function?
The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could even describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists as a special case of the graph of an equation.
Given: [tex]h(t)=0.6\cdot 3.2^t[/tex]
Substitute the values in the function, we get
t = -2, h(t) = 0.05859375
t = -1, h(t) = 0.1875
t = 0, h(t) = 0.6
t = 1, h(t) = 1.92
t = 2, h(t) = 6.144
t = 3, h(t) = 19.6608
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James has $0.50 more than his brother John. The sum of their money is $2.50. how much money does John have
Answer:
Step-by-step explanation:
John has $1.25
James has $1.75
i think
Answer:
$1.00
Step-by-step explanation:
James has $0.50 more than John.
When they put their money together, they have a combined total of $2.50.
[tex]2.50-0.50=2.00[/tex]
[tex]2.00\div2=1.00[/tex]
[tex]1.00+1.50=2.50[/tex]
[tex]=2.50[/tex]
John has one dollar.
Hope this helps.
Complete the following tasks for this equation: b/7.8= -2.15.
1. give an estimate for the solution. be sure to explain how you arrived at the estimate, either by showing an equation or in words.
2. solve the equation. show or explain your work.
3. compared to your estimate, is your answer reasonable? explain your answer in complete sentences.
Answer:
Step-by-step explanation:
Factors
A term in multiplication for an entire variety by which a bigger complete quantity may be dividedA divisor is an integer that evenly divides a range without leaving the restFactorization is the decomposition of an item right into a product of other objectsInteger factorization, the manner of breaking down a composite quantity into smaller non-trivial divisorsA coefficient, a multiplicative thing in an expression, usually more than a fewThe act of forming a component institution or quotient ring in summary algebraA von Neumann algebra, with a trivial centerFactor (graph principle), a spanning subgraphAny finite contiguous sub-sequence of a word in a group concept(b)/(7.8)=-2.15
Multiply each term in the equation by 7.8.
(b)/(7.8)*7.8=-2.15*7.8
Cancel the common factor of (1)/(7.8).
1b=-2.15*7.8
Multiply -2.15 by 7.8 to get -16.77.
1b=-16.77
Divide each term in the equation by 1.
(1b)/(1)=-(16.77)/(1)
Cancel the common factor of 1.
b=-(16.77)/(1)
Divide -16.77 by 1 to get -16.77.
b=-16.77
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How much work is performed lifting in order to lift a 50.0 kg block 7.00 meters? Use g=9.81 m/s^2
The work done in lifting the block is 3430 J
Calculating workFrom the question, we are to determine the work done in lifting the block
Using the formula,
Work done = mgh
Where m is the mass
g is the acceleration due to gravity
and h is the height
From the question,
m = 50.0 kg
g = 9.81 m/s²
h = 7.00 m
Putting the parameters into the formula,
Work done = 50.0 ×9.8 × 7.00
Work done = 3430 J
Hence, the work done in lifting the block is 3430 J
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When a large cake is cut into piece that each weighs 3 ounces, it yields 120 pieces. How many pieces would the cake yield if it were cut into 2- ounce pieces instead
when the cake is cut into [tex]2[/tex] ounce pieces instead of [tex]3[/tex] pieces it yields [tex]180[/tex] pieces.
How to find large cake pieces ?
Given in the question when cake cuts into piece that each weight is [tex]3[/tex] ounce it yields [tex]120[/tex]
So original large cake weight is
[tex]w=120*3\\\\w=360[/tex]
So we can find cake pieces when cake cuts into weight [tex]2[/tex] each piece
[tex]pieces=\frac{360}{2}\\=180[/tex]
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Can someone help me please
Answer:
[tex]the \: answer \: is \: choice \: b \: \frac{ - 2 \sin(x) }{1 + \cos(x) } [/tex]
will give you an explanation if you want tag me on comment.
Below is the market for funnel cakes at a small community fair.
a) what is the equilibrium price and quantity of the funnel cakes?
b) What is the total consumer spending on funnel cakes at the equilibrium point?
c) Calculate the producer surplus and consumer surplus at equilibrium. Show your work.
d) What would be the result if the suppliers charged $6? Explain.
e) Cheese pretzels are substitute good for funnel cakes at the same fair. Draw a correctly labeled graph of the market for cheese pretzels. Shade the area of consumer surplus.
f) A large number of new guests enter the fair. Illustrate the effect of this change on the same graph from part E.
g) does the consumer surplus increase, decrease, or stay the same as a result of the change from part F? Explain.
h) A new cheese pretzel stand opens at the same fair. On a new graph, illustrate the market for cheese pretzels at this fair before and after the new stand opened.
i) if the large number of new guests entering the fair happened at the same time that the new cheese pretzel stand open how would the equilibrium price and quantity for cheese pretzels change? Explain.
From the graph given, the equilibrium price and quantities are given respectively as;
Price = $5Quantity = 6 units of funnel cakes.What is the total consumer spending on funnel cakes at the equilibrium point?The total consumer spending(TCS) is achieved by finding the product of the price and the quantities at the equilibrium point.
Hence,
TCS = 5 * 6
= 60
A) The producer surplus is the area of the triangle shaded yellow in the attached image.
Recall that he area of triangle is:
1/2 b * h
b = 4
h = 6
Hence Area of the RA-Triangle (Producer Surplus) =
1/2 * 4 * 6
= 12
B) The Consumer surplus is the area of the triangle shaded Green in the attached image.
Recall that the area of triangle is:
1/2 b * h
b = 4
h = 6
Hence Area of the RA-Triangle (Consumer Surplus) =
1/2 * 4 * 6
= 12
What would be the result if the suppliers charged $6?
If the suppliers charged $6, then the quantity demanded would drop to 4 units of funnel cakes. It is demonstrated graphically. Recall that the law of demand and supply indicates that when prices goes up, demand comes down and vice versa.
Graph II illustrates what would happen if a large number of guests entered the fair. It would result to a right-ward shift in the demand curve.
Does the consumer surplus increase, decrease, or stay the same as a result of the change from part F?Yes, there is an increase in the consumer surplus. Now there are more consumers hence the total amount they are willing to pay as an aggregate sum has increased from what was.
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Please someone help me with question a) and b). I’ve been having so much trouble with these types of questions. The booklet says that the answers are a) 134degrees and b) 14.3km. I just don’t get how to get there. Thank you!
The bearing to take is 134 degrees and the shortest distance is 14.3 km
The bearing it would takeThe attached diagram represents a labelled version of the ship movement
The angle at Q is
Q = 180 - 155 + 90 + 120 - 90
This gives
Q = 145
The distance PR is calculated as:
PR^2 =PQ^2 + QR^2 - 2 * PQ * QR * cos(Q)
This gives
PR^2 = 9^2 + 6^2 - 2 * 9 * 6 * cos(145)
Evaluate
PR^2 = 205.46
Take the square root
PR = 14.3 km
The angle at P is then calculated as:
QR/sin(P) = PR/sin(Q)
This gives
6/sin(P) = 14.3/sin(145)
Evaluate the quotient
6/sin(P) = 24.93
Make sin(P) the subject
sin(P) = 6/24.93
Divide
sin(P) = 0.2407
Take the arc sin of both sides
P = 14
The bearing is then calculated as:
Bearing = P + 120
This gives
Bearing = 14 + 120
Evaluate
Bearing = 134
Hence, the bearing to take is 134 degrees
The shortest distanceIn (a), we have
PR = 14.3 km
This represents the shortest distance
Hence, the shortest distance is 14.3 km
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Help me:-
Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y) =
Answer:
20 + 4y
Step-by-step explanation:
The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).
PQ has endpoints P(0, 0) and Q(8, 4). Find the coordinates of the midpoint of PQ
O
O
O
(4,4)
(2,4)
(4,2)
The functions f(x) and g(x) are shown on the graph.
f(x) = log(x)
g(x)
6
Using fix), what is the equation that represents gix)?
A) g(x) = log5(x) - 3
B) g(x) = log5(x) + 3
C) g(x) = log5(x-3)
D) g(x) = log5(x+3)
Using translation concepts, the equation of g(x) is:
D) [tex]\log_5{x + 3}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, g(x) is a shift left of 3 units of [tex]f(x) = \log_5{x}[/tex], hence:
[tex]g(x) = f(x + 3) = \log_5{x + 3}[/tex], which means that option D is correct.
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Expand (1 + root 2) (3 - root 2)
Give your answer in the form a+b root 2 where a and b are integers.
Answer:
1+2√2
a = 1 b= 2
See the attached page, I've shown the calculation over there.
Select the statement that describes the expression 5 + (3 x 6) − 4. 5 times the sum of 3 and 6, then subtract 4 Add 5 to the product of 3 and 6, then subtract 4 Add 5 to the product of 3 and 6, then add 4 Add 5 to the quotient of 3 and 6, then subtract 4
Answer: Add 5 to the product of 3 and 6, then subtract 4
Step-by-step explanation:
We will use the order of operations. Looking at 5 + (3 x 6) − 4, we would:
[1] Multiply 3 x 6
[2] Add 5 to that product
[3] Subtract 4 from that value
This means the answer to your question is:
Add 5 to the product of 3 and 6, then subtract 4
Answer: B
i DiD tHe TeSt
Given f(x) = x² + 3x -3 and g(z) = 2x, find f(g(x)).
Solution
First, we need to decide which function will go inside which. Since
our function reads "f of g of z", we know that we are going to
substitute the function for g(x) into every a spot in the f(x)
function.
f(g(x))=(x
)²+3(x
)-3
Next, perform normal order of operations for each term. (Hint:
(2x)² = (2x)(2x))
f(g(x)) = 4
²+3
2-3
Let's look at how this example would be different if it was
performed in the opposite order. Given f(x) = x² + 3x - 3 and
g(x)=2x, find g(f(x)).
In this case, we'll need to plug the whole function for f(x) into the
input (2) spot in the g(x) function.
g(f(x)) = 4
(x² + 3x - 3)
Then we'll distribute to each term.
g(f(x)) = 4(x²)+2(3x)-3 3
Simplify to get the final answer.
The composition of the functions f(x) and g(x) gives the equation:
[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]
How to get the composition of functions?Here we want to get the composition of the two functions:
[tex]f(x) = x^2 + 3x - 3\\\\g(x) = 2x[/tex]
f(x) is a quadratic and g(x) is a linear equation.
Now we want to get the composition:
[tex]f(g(x))[/tex]
This means that we need to evaluate function f(x) in g(x), so we can replace all the "x" in the function f(x) by the notation "g(x)"
[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3[/tex]
Now we replace all the "g(x)" by the actual function g(x) = 2x, we wll get:
[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3 = (2x)^2 + 3*(2x) - 3[/tex]
finally, we can simplify this to get the composition, which is a quadratic function just like f(x).
[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]
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If 15 actuators have failed today, what is the probability that a) at least 10 are repairable? b) from 3 to 8 are repairable? c) exactly 5 are repairable?
The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.
According to the statement
we have given that If 15 actuators have failed and we have to find the probabilities on some conditions.
we know that the formula of probabilities is
probability = possible outcomes / total outcomes
So,
at least 10 are repairable = 1 - (10 are not repairable)at least 10 are repairable = 1 - 10/15
at least 10 are repairable = (15 - 10)/15
at least 10 are repairable = (5)/15
at least 10 are repairable = 1/3
from 3 to 8 are repairable = 3/15 *8/15from 3 to 8 are repairable = 1/5 *8/15
exactly 5 are repairable = 5/15exactly 5 are repairable = 1/3
These are the probabilities of the given conditions.
So, The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.
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The volume of a rectangular box is 1.0 ft3. what is the length if the width is 1.0 ft and the height is 1.5 ft?
The length of the rectangular box is 0.67 feet
How to determine the length of the box?The given parameters are:
Length = ??
Width = 1.0 ft
Height = 1.5 ft
Volume = 1.0 ft^3
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
1 = Length * 1 * 1.5
Evaluate the product
1 = Length * 1.5
Divide both sides by 1.5
Length = 0.67
Hence, the length of the rectangular box is 0.67 feet
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What is the domain of the function graphed below?
X<7
x≤7
-2
all real numbers
Answer:
x < 7
Step-by-step explanation:
The domain encompasses all the "x" values (or inputs) of a function.
The arrow on the left line symbolizes that the function continues into the negative region for infinity. As such, this eliminates option C.
Closed dots are points whose "x" values are included in the function. Open-dots are on points whose "x" values are not included in the function. Although the open-dot on the left line at x = -1 generally means it is not included in the function, the closed dot on the right line overrides this. Therefore, x = -1 is in the domain. The value x = 7 is not within the domain of the function due to the open-dot. This eliminates option B and option D.
With this said, the domain of the function is x < 7.
Miguel is making pudding. The recipe yields
6 servings and calls for 2
cups of milk. How
many cups of milk will Miguel need for 18
servings of pudding?
Using the given recipe, he will need 6 cups of milk to make 18 servings.
How many cups of milk will Miguel need for 18 servings of pudding?We know that the recipe for 6 servings, calls for 2 cups of milk.
Miguel wants to do 18 servings, Then he needs to use the recipe:
18 = x*6
Solving the linear equation for x:
x = 18/6 = 3
So he needs to use his recipe 3 times.
And we know that for 6 servings he needs 2 cups of milk, then for 18 he needs:
3*(2 cups) = 6 cups of milk.
Using the given recipe, he will need 6 cups of milk to make 18 servings.
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Use the drop-down menus to complete each equation so the statement about its solution is true. CLEAR CHECK No Solutions 3x 9 4x x
The complete equation so that the statement is true is 3x+9+4x+x= 8x + 1
How to complete the equation?The equation is given as:
3x+9+4x+x=
Represent the blank with y
So, we have:
3x + 9 + 4x + x = y
Evaluate the like terms
8x + 9 = y
For the equation to have no solution the value of y and 8x + 9 must not be equal.
Take for instance
y = 8x + 1
So, we have:
8x + 9 = 8x + 1
Subtract 8x from both sides
9 = 1
The above equation is false because 1 and 9 are not equal
Hence, the complete equation so that the statement is true is 3x+9+4x+x= 8x + 1
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Complete question
Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions
3x+9+4x+x=
Please help me fast
What is the equation of this graph
Answer-4,5
Step-by-step explanation:
the population of happy land is 15.8 happys per acre exactly 553 happys live in happy land. how many acres is happyland
Answer:
35 acres.
Step-by-step explanation:
Proportions:
15. 8 ⇒ 1 acre
553 ⇒ P acres
P = 553*1/15.8
P = 35 acres
Ava bought 7.73 pounds of fruit for a class party. the class ate 3.59 pounds of the fruit. how much fruit is left?
Ava bought [tex]7.73[/tex] pounds of fruit for a class party , class ate [tex]3.59[/tex] pounds fruits then [tex]4.14[/tex] pounds fruit left after party.
How can we find how much fruit is left after party ?
Ava bought [tex]=7.73[/tex] pounds fruit
ate by class [tex]=3.59[/tex] pounds fruit
fruit left after party [tex]= total fruit -fruit ate by class[/tex]
[tex]= 7.73-3.59\\=4.14[/tex]
So [tex]4.14[/tex] pound fruit is left .
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d) Arrange 8/9,7/18,10/16 in ascending order of magnitude
8/9 = 0.888888....
7/18 = 0.388888888889
10/16 = 0.625
Ascending order - means going up, smallest to largest. (Imagine climbing a ladder, where you start of low, then, go higher up the ladder.)
Thus, answer is 7/18, 10/16, 8/9
Hope this helps!
A softball pitcher has a 0.507 probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that more than 8 of them are strikes
8/25 is the probability that more than 8 of them are strikes.
Lets simplify the problem,
We are given that a softball pitcher has a 0.507 probability of throwing a strike for each pitch. Also, the softball pitcher throws 15 pitches.
The above situation can be represented through Binomial distribution;
P(X = r) = 0,1,2,3,,.....
where, n = number of trials (samples) taken = 15 pitches
r = number of success = more than 8
p = probability of success which in our question is probability of
Throwing a strike for each pitch = 0.507
LET X = Number of strikes
So, it means X ~ n = 15, p = 0.507
So, Probability that more than 8 of them are strikes = P(X > 8)
P(X > 8) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)
After putting the values in it we get,
P = 0.323
P= 8/25 approx
8/25 is the probability that more than 8 of them are strikes.
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What is the simplified form of startroot 100 x superscript 36 baseline endroot ?
The simplified form of the expression is [tex]10 x^{18}[/tex].
What are indices in maths?
An index, or a power, is the small floating number that goes next to a number or letter.The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.The given expression is [tex]\sqrt{100x^{36} }[/tex]
Applying the rule, [tex]\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}[/tex]
Now, [tex]\sqrt{100} \sqrt{x^{36} }[/tex]
Simplifying, we get;
[tex]10\sqrt{x^{36} }[/tex]
Applying the exponent rule, [tex]a^{bc} = (a^{b} )^{c}[/tex]
We get
[tex]10 \sqrt{(x^{18} })^{2}[/tex]
[tex]10 x^{18}[/tex]
Therefore, the simplified form of the expression is [tex]10 x^{18}[/tex].
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Answer:
10 x 18
Step-by-step explanation: