The coefficient of the second term in the expansion of the binomial (4x + 3y)3
twice a number and 5 more is 100
Suppose a and b give the population of two states where a>b . Compare the expressions and tell which of the given pair is greater or if the expression are equal.
b/a+b and 0.5
What is the GCF of 12 and 20
Answer:
It is 4.
Step-by-step explanation:
It said so in my classes.
a patio is in the shape of a regular octagon. the sides have length 5m. Calculate the area of the patio
here is the solution.
Round the answer as needed.
Paige pays $532 per month for 5 years for a car. she made a down payment of $3,700.00. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?
⦁ The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 ⦁ What is the expected value for each choice? ⦁ Should he pass the ball or take the shot himself? Explain
Answer:
The given data is
Pr(xi)=0.3*0.70
The expected value =0.90
Where as we calculated the probability=0.96
As 0.96>0.9
So he should pass the ball as probability is greater.
A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. (1 point)
The equation of the parabola with the given dimensions and vertex at the origin is y = -4x^2.
Finding the Equation of a Parabola
To find the equation of a parabola with a vertex at the origin and given dimensions, we can use the standard form of a parabolic equation, which is y = ax^2. In this case, since the parabola opens downward and the vertex is at the origin (0,0), the equation will have the form y = -ax^2. The value of 'a' can be determined using the dimensions provided for the parabola, which are a width of 42 feet (meaning that the points (21,0) and (-21,0) are on the parabola) and a height of 84 feet (the y-coordinate at the vertex).
Since the point (21, 0) lies on the parabola, substituting it into the equation y=-ax^2 gives us 0 = -a(21)^2, which leads us to find that a = -84/(21)^2. Substituting the value of 'a' back into the equation gives us the final equation of the parabola: y = -84/(21)^2
x^2.
The equation of the parabola is: [tex]\[ y = -\frac{2}{21}x^2 + 42 \][/tex] .
To find the equation of the parabola with its vertex at the origin, we can use the standard form of a parabolic equation, which is [tex]\( y = ax^2 \).[/tex]
Given that the parabola opens downwards, we know that a must be negative. To determine the value of ( a ), we need to find a point on the parabola.
We're given the dimensions of the arch: 84 feet high and 42 feet wide at the base. Since the arch is symmetrical, the highest point is at the midpoint of the base, which is ( x = 0 ). At this point,( y = 84 ).
So, substituting the coordinates of this point into the equation, we get:
[tex]\[ 84 = a \times 0^2 \][/tex]
This simplifies to ( 84 = 0 ), which doesn't give us any useful information. Instead, we need to consider another point on the parabola.
Since the arch is symmetric, we can choose a point where ( x = 21 ) (half of the width of the base), and ( y = 0 ).
Substituting these coordinates into the equation, we get:
[tex]\[ 0 = a \times (21)^2 \][/tex]
0 = 441a
Dividing both sides by 441, we find ( a = 0 ). However, this seems incorrect, as it would mean the arch is just a straight line, which it isn't. This suggests that our choice of coordinates may not be correct.
Let's reconsider. The midpoint of the base is x = 0, but the highest point might not be there. Instead, let's choose a point where ( x = 0 ) and ( y = 42 ), as this is the highest point of the arch.
Substituting these coordinates into the equation, we get:
[tex]\[ 42 = a \times 0^2 \][/tex]
42 = 0
This also doesn't give us useful information. It seems we might have approached this problem incorrectly. Let's try a different strategy.
Since we know the arch is a parabolic shape, and the parabola opens downwards, we can write its equation in the form:
[tex]\[ y = ax^2 + c \][/tex]
To find the values of a and c , we need two points on the parabola. We already have one: the highest point of the arch, which is at x = 0 and (y = 42 ).
Now, we need to find another point. Since the arch is symmetric, we can use any point along the base. Let's choose the point where x = 21 , which is half of the width of the base. At this point, y = 0 .
Substituting these points into the equation, we get:
[tex]\[ 42 = a \times 0^2 + c \][/tex]
[tex]\[ 0 = a \times 21^2 + c \][/tex]
The first equation simplifies to ( c = 42 ).
Substituting this value of ( c ) into the second equation, we get:
[tex]\[ 0 = a \times 21^2 + 42 \][/tex]
Solving for a :
[tex]\[ a \times 441 = -42 \][/tex]
[tex]\[ a = \frac{-42}{441} \][/tex]
[tex]\[ a = -\frac{2}{21} \][/tex]
So, the equation of the parabola is:
[tex]\[ y = -\frac{2}{21}x^2 + 42 \][/tex]
0.8 is 10 times as great as which decimal
A random sample of 12 graduates of a certain secretarial school typed an average of 79.3 words per minute with a standard deviation of 7.8 words per minute. assuming a normal distribution for the number of words typed per minute, find a 95% confidence interval for the average number of words typed by all graduates of this school.
To find the 95% confidence interval for the average number of words typed, use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size).
Explanation:To find the 95% confidence interval for the average number of words typed by all graduates of the secretarial school, we can use the formula:
Confidence Interval = sample mean ± (critical value) * (standard deviation / square root of sample size)
Plugging in the given values, we have:
Confidence Interval = 79.3 ± (1.96) * (7.8 / √12)
Simplifying, the 95% confidence interval is approximately 75.6 to 83.0 words per minute.
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A new restaurant is to contain two-seat tables and four-seat tables. Fire codes limit the restaurant's maximum occupancy to 72 customers. If the owners have hired enough servers to handle 22 tables of customers, how many of each kind of table should they purchase?
To adhere to the fire code and server capacity, the restaurant should ideally buy 18 four-seat tables and 4 two-seat tables. This results in a total of 22 tables and maximizes seating capacity at 72.
Explanation:This problem can be solved using a system of linear equations. Let's denote the number of two-seat tables as T and the number of four-seat tables as F.
From the information given, we can establish two equations:
The total number of tables must not exceed 22, so T + F ≤ 22The total number of seats cannot exceed 72, so 2T + 4F ≤ 72To figure out how many of each type of table they should purchase, we need to solve this system of equations.
The goal is to maximize the number of customers (seats) while not exceeding the limits on tables and seats. So, a possible solution to maximize seating would be to have 18 four-seat tables (F = 18) and 4 two-seat tables (T = 4). This gives a total of 22 tables and 72 seats.
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A roof rises 9 feet for every 12 feet of run. What is the slope of the roof?
Since slope, m, is defined as the rise/run; then m = 9/12
simplify m = 3/4
Blue shaded 20 squares on his hundreds grid. Becca shaded 30 squares on her hundreds grid. Write two decimals greater than Luke decimal in less than Bekkas decimal
Given a mean of 8 and a standard deviation of 0.7, what is the z-score of the value 9 rounded to the nearest tenth?
Answer: The z-score of the value 9 rounded to the nearest tenth = 1.4
Step-by-step explanation:
Given: Mean [tex]\mu=8[/tex]
Standard deviation [tex]\sigma=0.7[/tex]
The given random value x= 9
Now, the formula to calculate the z score is given by:-
[tex]z=\dfrac{x-\mu}{\sigma}\\\\\Rightarrow\ z=\dfrac{9-8}{0.7}\\\\\Rightarrow\ z=1.42857142857\approx1.4[/tex]
Hence, the z-score of the value 9 rounded to the nearest tenth = 1.4
What is the relationship between the 6s in the number 7,664?
Answer:
10s
100s
Step-by-step explanation:
One of the 6s are in the 10th digit position
the other one is in the 100th digit position
In one day,Annie traveled 5 times the sum of the number of hours Brian traveled and 2. Together they traveled 20 hours.Find the number of hours each person traveled.
Solve p=10a+3b for a.
A local hamburger shop sold a combined total of 436 hamburger and cheeseburgers on Friday. There were 64 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Friday?
64 fewer cheeseburgers were sold than hamburgers. The total number of hamburgers sold on Friday was 250.
Use the concept of subtraction defined as:
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that,
Total number of hamburgers and cheeseburgers sold on Friday: 436.
The number of cheeseburgers sold was 64 fewer than the number of hamburgers.
The objective is to find the number of hamburgers sold on Friday.
To find out how many hamburgers were sold on Friday,
Set up a system of equations.
Let's denote the number of hamburgers as 'H' and the number of cheeseburgers as 'C'.
From the given information,
The total number of hamburgers and cheeseburgers sold is 436,
So write the equation,
H + C = 436.
Since there were 64 fewer cheeseburgers sold than hamburgers,
Which can be written as C = H - 64.
Now substitute the second equation into the first equation and solve for H:
H + (H - 64) = 436
Combine like terms,
2H - 64 = 436
Add 64 to both sides,
2H = 500.
Divide both sides by 2,
H = 250.
Hence,
250 hamburgers were sold on Friday.
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You've decided you want a plant for your room. At the gardening store, there are 4 different kinds of plants (tulip, fern, cactus, and ficus) and 4 different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).
If you randomly pick the plant and the pot, what is the probability that you'll end up with a tulip in a plastic pot?
The lengths of the sides of a triangle are 4,5,6 can the triangle still be a right triangle
No. We can use the pythagorean theorem to prove this.The equation being a2 + b2 = c2. We then use two of the least of the three numbers, which are 4 and 5, to substitute for “a” and “b”. We get a value for “c” which is 6.4, rounded off to the nearest tenth. This value is greater than 6. Note that this is a very logical way of solving the problem since a greater number for “a” and “b” would lead a greater value for “c”
Simple interest formula: P=Irt
Solve for t
The value of t in the simple interest formula P = Irt is t = P / (Ir).
To solve the simple interest formula P = Irt for t, we need to isolate the variable t on one side of the equation.
The formula can be rearranged as follows:
P = Irt
First, divide both sides of the equation by I:
P/I = rt
Next, divide both sides of the equation by r:
(P/I) / r = t
Simplifying further:
t = P / (Ir)
Therefore, the value of t in the simple interest formula P = Irt is t = P / (Ir).
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How do you write an equation that shows an estimate of each answer for 503+69
To estimate the sum of 503 and 69, one could round the numbers to the nearest tens or hundreds and then add the rounded numbers together. For example, rounding to the nearest tens would result in the equation 500 + 70 = 570.
Explanation:The question asks for a method to write an equation that would allow them to estimate the sum of 503 and 69. This is more related to the concept of rounding numbers. We can estimate this sum by rounding these numbers to the nearest tens or hundreds, and then adding those rounded numbers together.
For example, if you round to the nearest tens, 503 can be rounded down to 500 and 69 can be rounded up to 70. Adding these rounded numbers together gives 500 + 70 = 570. Therefore, one possible equation could be: 500 + 70 = 570, which is a fairly close estimate of the original sum, 503 + 69.
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How do you write 2/100000 as a decimal?
The fraction 2/100000 written in form of a decimal is 0.00002
Given the fraction 2/100000, we are to express this fraction as a decimal
The fraction can also be expressed as;
2/100000 = 2 * 1/00000
2/100000 = 2 * 0.00001
2/100000 = 0.00002
Hence the fraction 2/100000 written in form of a decimal is 0.00002
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The physician ordered Polymox (amoxicillin) oral suspension 20 mg/kg/day in divided doses every 8 hours for a child who weights 66 pounds. Convert pounds to kilograms and then calculate the prescribed dosage. ______ mg every _____ hours
Suppose we are flipping a fair coin (i.e., probability of heads = 0.5 and probability of tails = 0.5). further, suppose we consider the result of heads to be a success. what is the standard deviation of the binomial distribution if we flip the coin 5 times?
Dr. Blumen invested $5,000 part of it was invested in bonds at a rate of 6% in the rest was invested in a money market at the rate of 7.5% if the annual interest of is 337.50 how much did she invest in bonds
The nutritional chart on the side of a box of a cereal states that there are 93 calories in a three fourths 3/4 cup serving. How many calories are in 5 cups of the cereal?
Find the surface area of a cylinder with a diameter of 2 and an altitude of 16
Find all numbers for which the rational expression is undefined z^2+6/z^2-7z-8
Write the fractions in order from smallest to largest. 7/10, 3/20,22/25, 2/25