Answer:
Hence, the probability of Tim Duncan making all of his next 8 free throw attempts is:
[tex](\dfrac{18}{25})^8=0.0722204136[/tex]
Step-by-step explanation:
As the probability of one free throw does not depend on the any other i.e. the probability of each throw is independent.
Hence, the probability of making all of his next 8 free throw is calculated as:
Probability of next 8 free throw=Probability of first free throw×probability o f second free throw×··················× Probability of 8th free throw.
i.e. it is given by:
[tex]Probability=\dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\\\\\\Probability=(\dfrac{72}{100})^8\\\\Probability=(\dfrac{18}{25})^8[/tex]
Hence, the probability is:
[tex](\dfrac{18}{25})^8=0.0722204136[/tex]
We have that the he probability of Tim Duncan making all of his next 8 free throw attempts is mathematically given as
[tex]P=0.72^8[/tex]
From the question we are told
Tim Duncan is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 72% of the time. What is the probability of Tim Duncan making all of his next 8 free throw attempts?ArithmeticGenerally the equation for the binomial probability is mathematically given as
[tex]P=\frac{n!}{X!(n-X)!}*p^X*(1-p)^{n-X}\\\\Therefore\\\\ P=\frac{8!}{8!(8-8)!}*0.72^8*(1-0.72)^{0}[/tex]
[tex]P=0.72^8[/tex]
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Leo spent the same amount of time working on each of 5 different weight machines and then spent 2/3 of an hour on the treadmill. If he spent a total of 1 3/4 hours at the gym, which shows the correct equation and solution for x, the number of hours Leo spent at each of the weight machines?
Let's break this down. We know that there are 5 weight machines, and Leo spent an equal amount of time on all of them. Since we don't know how long he spent on each, we'll use x. Our equation so far is 5x. Then, we know that he spent 2/3 hour on the treadmill, which we will just add to the 5x. So, now our equation is 5x + 2/3. Lastly, we know that the total time Leo spent at the gym is 1 3/4 hours, which we set the last equation equal to. Our final equation is 5x + 2/3 = 1 3/4. Then, all we have to do is solve for x. What we can do to make this easier is to change all of the fractions into numbers. After changing everything, here is our equation: 5x + 40 = 105. Then, we will subtract 40 from each side and divide both sides by 5. Therefore, Leo spent 13 minutes on each weight machine.
ANSWER:
A) 5x + 2/3 = 1 3/4 ; Leo spent 13 minutes at each machine
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Final answer:
Solving for the time Leo spent on each weight machine involves setting up an equation based on the total gym time and subtracting the time spent on the treadmill, resulting in Leo spending about 13 minutes at each weight machine.
Explanation:
To solve for the amount of time Leo spent at each weight machine, we need to set up an equation based on the total time spent at the gym. First, we know that Leo spent 2/3 of an hour on the treadmill. With a total gym time of 1 3/4 hours (which is the same as 7/4 hours), we can subtract the treadmill time to find the time spent on the weight machines. Thus, the equation can be set up as follows:
5x + 2/3 = 7/4
To solve for x, the hours Leo spent at each weight machine, follow these steps:
Subtract 2/3 from both sides of the equation: 5x = 7/4 - 2/3
Find a common denominator for the fractions and subtract: 5x = 21/12 - 8/12
Simplify the right side: 5x = 13/12
Divide both sides by 5 to solve for x: x = 13/60 hours
This means Leo spent 13/60 hours, or about 13 minutes, at each of the 5 weight machines.
Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until Tommy and Zach are 8 miles apart?
Zach=2 hours Tommy= 3 1/2 hours
(14y) exponent of 4 simplify plz help
Jacob wants to use an elevator to carry identical packages having the same weight. Each package weighs 3 pounds and Jacob weighs 99 pounds. If the elevator can carry a maximum of 300 pounds at a time, which inequality shows the maximum number of packages, n, that Jacob can carry with himself in the elevator if he is the only passenger?
Answer:
The required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].
Step-by-step explanation:
Consider the provided information.
Each package weighs 3 pounds and Jacob weighs 99 pounds.
let n is the maximum number of package that Jacob can carry with himself in the elevator.
Thus, the total weight of Jacob while having n packages on the elevator is:
[tex]3n+99[/tex]
The elevator can carry a maximum of 300 pounds at a time, therefore.
[tex]3n+99\leq 300[/tex]
Now, subtract 99 from both sides and divide the obtained inequality with 3.
[tex]3n+99-99\leq 300-99[/tex]
[tex]3n\leq 201[/tex]
[tex]\frac{3n}{3}\leq \frac{201}{3}[/tex]
[tex]n\leq 67[/tex]
Thus, the Jacob can carry maximum 67 packages.
Hence, the required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].
common ratio of fraction in geometric sequence?
5/12,-1/6,1/15,-2/75,4/375
The common ratio between each pair of terms in the given geometric sequence of fractions is -2/5.
Explanation:A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. To find the common ratio in a geometric sequence of fractions, we divide each term by the previous term. Let's calculate the common ratios for the given sequence:
Common ratio between 5/12 and -1/6 = (-1/6) / (5/12) = -1/6 * 12/5 = -2/5Common ratio between -1/6 and 1/15 = (1/15) / (-1/6) = 1/15 * (-6/1) = -2/5Common ratio between 1/15 and -2/75 = (-2/75) / (1/15) = -2/75 * 15/1 = -2/5Common ratio between -2/75 and 4/375 = (4/375) / (-2/75) = 4/375 * (-75/2) = -2/5As we can see, the common ratio between each pair of terms in the given geometric sequence of fractions is -2/5.
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55 divided by 2044 i need help for my summer packets
Final answer:
To divide 55 by 2044, use long division. The quotient is 0.027.
Explanation:
To divide 55 by 2044, you can use long division. Here is the step-by-step process:
Start by dividing 55 by the first digit of 2044, which is 2. The quotient is 27 and the remainder is 1.Bring down the next digit of 2044, which is 0.Divide 10 by 2044. The quotient is 0 and the remainder is 10.Bring down the next digit of 2044, which is 4.Divide 104 by 2044. The quotient is 0 and the remainder is 104.Bring down the next digit of 2044, which is 4.Divide 1044 by 2044. The quotient is 0 and the remainder is 1044.At this point, you have reached the end of the division process. The final quotient is 0.027 and there is no remainder. Therefore, 55 divided by 2044 is approximately 0.027.
the radius of the circle is πcm. the base of the triangle is πcm . the area of the circle equals the area of the triangle. what is the height of the triangle
is 113,724 divisible by 3,5,6,or9
Write the relatioship between the values of the given digits
The 6s in 6,600
NEED HELP FAST!
13.
(08.06 LC)
Variable g is 8 more than variable w. Variable g is also 2 less than w. Which pair of equations best models the relationship between g and w? (1 point)
g= 8w
g = w + 2
w = g + 8
w = g – 2
w = 8g
w = g + 2
g= w + 8
g = w – 2
The two equations are:
g= w +8
g= w +2
^_^
Which line has the following intercepts?
x intercept = (3/7, 0)
y intercept = (0, -1.2)
A) 7x+6y = 3
B) 7x-6y = 3
C) 7x+6y = (-3)
D) 7x-6y = (-3)
What is 14/28 in simplest form?
Plz someone help me
A regulation soccer goal net is 24 ft wide by 8 ft high. A soccer net for children is 6 ft wide. If the manufacturer wishes to keep the children's soccer net to scale, how tall should the children's net be? What is the scale factor? (round answer to two decimal places)
To maintain the scale of a children's soccer net to that of a regulation net, the height should be 2 feet, given that the child-size net is 6 feet wide. The scale factor used is 0.25.
Explanation:The question asks us to find the scaled dimensions for a children's soccer net based on the dimensions of a regulation soccer goal net. The original dimensions are 24 ft in width and 8 ft in height. If a children's soccer net is 6 ft wide and we want to keep the same scale, we need to calculate the height of the net in proportion to the regulation net's dimensions.
Height Calculation:
The scale factor is the ratio of the width of the children's net to the width of the regulation net. To find the height of the children's net, we multiply the height of the regulation net by the scale factor:
Scale Factor = Width of Children's Net / Width of Regulation Net
Scale Factor = 6 ft / 24 ft = 0.25
Height of Children's Net = Scale Factor × Height of Regulation Net
Height of Children's Net = 0.25 × 8 ft = 2 ft
Therefore, to maintain the scale, the height of the children's soccer net should be 2 feet, and the scale factor is 0.25.
which of the following is an example of a common topic.
A) anyone can be brave.
B) freedom takes sacrifice.
C) the box was broken.
D) bravery.
Answer:
D. Bravery
Step-by-step explanation:
Bravery is a general topic.
Multiply (4+I)(1-5i)
Answer:
9 - 19i
Step-by-step explanation:
How to work with negative exponents
Final answer:
Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. When multiplying or dividing with negative exponents, add or subtract them accordingly. In scientific notation, divide the coefficients and subtract the exponents to divide numbers.
Explanation:
Working with negative exponents is an essential skill in mathematics, where a negative exponent indicates the inverse or reciprocal of the base raised to the corresponding positive exponent. For example, 2-1 equals 1/2, which means that we are finding the reciprocal of 2. In operations involving exponents, such as multiplication and division, we follow certain rules with negative exponents:
When multiplying numbers, add the exponents (negative exponents included).
When dividing numbers, subtract the exponents (again, include negative exponents).
To convert a negative exponent into a positive one, take the reciprocal of the base with the corresponding positive exponent.
Here's an example of division in scientific notation: 106 ÷ 103 = 10(6-3) = 103. If you need to divide two numbers using scientific notation, you divide the coefficients and subtract the exponents.
Remember, a number like 3-4 is equivalent to 1/34, or 1 divided by 3 multiplied by itself four times. In general, negative exponents flip the base to the denominator, signifying a division rather than multiplication.
A street that is 351ft long is covered in snow. City workers are using a snowplow to clear the street. The snowplow has tires that are 3.5ft in diameter. How many times does a tire have to turn in traveling the length of the street?
What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)?
characteristics of the graph of the absolute value parent function
A skydiver is falling at about q42 feet per second.How many feet per minute is she falling?
How much is 1 foot line of quarters worth
a quarter is 1.75 mm thick
1 mm = 0.0393701 inches
0.0393701/12 = 25.4 mm per inch
25.4/1.75 = 14.5 quarters per inch
14.5 x 12 = 174 quarters per foot
174 x 0.25 = 43.50
$43.50 for a foot of quarters
Is 7.6 repeating greater or less than square root 55
compare the values of the underlined digets 6035 and 530 the digit is 3
I dont understamd this problem please help------!
A work crew has a new pump and an old pump. The new pump can fill a tank in 5 hours, and the old pump can fill the same tank in 7 hours. Write and solve and equation for the time it will take both pumps to fill one tank of the pumps are used together.
I REALY NEED HELP!
In kite ABCD, m∠ACD=82°. What is m∠DCE?
1.)41°
2.)82°
3.)90°
4.)98°
Answer:
(A)41°.
Step-by-step explanation:
We know that in Kite, the diagonals are the angle bisectors, therefore
In Kite ABCD, m∠ACD=82°, thus
[tex]m{\angle}DCE=\frac{1}{2}m{\angle}ACD[/tex]
Substituting the given value, we have
⇒[tex]m{\angle}DCE=\frac{1}{2}(82^{\circ})[/tex]
⇒[tex]m{\angle}DCE=41^{\circ}[/tex]
Therefore, the measure of m∠DCE is 41°.
Hence, option A is correct.
Part A: If (72)x = 1, what is the value of x? Explain your answer.
Part B: If (70)x = 1, what are the possible values of x? Explain your answer.
The solution of the equation 72x = 1 is 1/72 and 70x = 1 is 1/70.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
72x = 1
Simplify the equation, then the value of x will be
72x = 1
x = 1/72
The equation is given below.
70x = 1
Simplify the equation, then the value of x will be
70x = 1
x = 1/70
Then the solution of the equation 72x = 1 is 1/72 and 70x = 1 is 1/70.
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Triangle PQR is formed by the three squares A, B, and C:
Which statement best explains the relationship between the sides of triangle PQR?
(PQ)2 + (QR)2 = (PR)2, because 9 + 16 = 25
PQ + QR = PR, because 9 + 16 = 25
(PQ)2 + (QR)2 = (PR)2, because 52 + 32 = 42
PQ + QR = PR, because 52 + 32 = 42
Answer:
A.[tex]PR^2=PQ^2+QR^2[/tex]
Because [tex]25=9+16[/tex]
Step-by-step explanation:
We are given that
Area of square A=[tex]9[/tex] square units
Are of square B=[tex]16[/tex] square units
Area of square C=[tex]25[/tex] square units
We have to find the relationship between sides of triangle PQR.
Side of square=[tex]\sqrt{Area\;of\;square}[/tex]
Using the formula
Side of square A=[tex]\sqrt{9}[/tex]=3 units
Side of square B=[tex]\sqrt{16}=4[/tex] units
Side of square C=[tex]\sqrt{25}=5[/tex] units
Pythagoras theorem
[tex](hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2[/tex]
Using Pythagoras theorem
[tex]PR^2=PQ^2+QR^2[/tex]
[tex]5^2=3^2+4^2[/tex]
[tex]25=9+16[/tex]
Option A is true
How many 2/3- cup servings are in 6 cups of yogurt
Answer: The required number of servings in 6 cups of yogurt is 9.
Step-by-step explanation: We are given to find the number of [tex]\dfrac{2}{3}[/tex] cup servings in 6 cups of yogurt.
We will be using the UNITARY method to solve the given problem.
We have
Number of servings in [tex]\dfrac{2}{3}[/tex] cups of yogurt = 1.
So, the number of servings in 1 cup of yogurt will be
[tex]\dfrac{1}{\frac{2}{3}}=\dfrac{3}{2}.[/tex]
Therefore, the number of servings in 6 cups of yogurt is given by
[tex]\dfrac{3}{2}\times6=9.[/tex]
Thus, the required number of servings in 6 cups of yogurt is 9.
Cd tower is shaped like a cylinder and holds CDs in a diameter of 4.7 inches . If the cd tower is 12 inches tall what is the volume in cubic inches. Use 3.14 for pi. Round your answer to the nearest hundredth