Find an equation of the sphere with points p such that the distance from p to a(−3, 6, 4) is twice the distance from p to b(5, 3, −2).
Thirty-five states in a country have four-star hotels. Assume the country has 50 states. (a) What fraction of the states can claim at least one four-star hotel? (b) How many states do not have a four-star hotel? (c) Write the fraction of states without a four-star hotel.
a. The fraction of states with a four-star hotel ........ (Simplify your answer.)
The fraction of states with at least one four-star hotel is 7/10, 15 states do not have a four-star hotel, and the fraction of states without a four-star hotel is 3/10.
Answer to Student's Question
(a) To find the fraction of states with at least one four-star hotel, we divide the number of states with a four-star hotel by the total number of states. Therefore, the fraction is 35/50, which simplifies to 7/10.
(b) To determine how many states do not have a four-star hotel, we subtract the number of states with a four-star hotel from the total number of states: 50 - 35 = 15. So, there are 15 states without a four-star hotel.
(c) Finally, the fraction of states without a four-star hotel is the number of states without such hotels divided by the total number of states. This is 15/50, which can be simplified to 3/10.
An arithmetic sequence with a thrid term of 8 and constant difference of 5
Only individuals over the age of 60 need to create an estate plan? True or False
Answer: False
Step-by-step explanation: People of any age over 21 need to complete an estate plan or a will. If you don't complete an estate plan or a will, anything you have could be left to the government. Regardless of your age or income, you always want to have a plan to distribute your money should you die unexpectedly.
Whats the rule for this pattern, 3,1.5,0,-1.5,-3
Final answer:
The rule for the pattern 3, 1.5, 0, -1.5, -3 is to subtract 1.5 from the previous term in the sequence.
Explanation:
The rule for the number pattern 3, 1.5, 0, -1.5, -3 is subtracting 1.5 from the previous number each time. To identify this, observe the difference between consecutive terms:
From 3 to 1.5 we subtract 1.5 (3 - 1.5 = 1.5).
From 1.5 to 0 subtract 1.5 (1.5 - 1.5 = 0).
From 0 to -1.5 subtract 1.5 (0 - 1.5 = -1.5).
And from -1.5 to -3, again subtract 1.5 (-1.5 - 1.5 = -3).
This pattern consistently decreases by 1.5, and it can be continued indefinitely by keeping this rule in mind.
what is 3(7x-6)<-81?
In winter, the price of apples suddenly went up by \$0.75$0.75dollar sign, 0, point, 75 per pound. Sam bought 333 pounds of apples at the new price for a total of \$5.88$5.88dollar sign, 5, point, 88.
Write an equation to determine the original price per pound (p)(p)left parenthesis, p, right parenthesis.
Your formula would be 3(p+0.75)=5.88
Because you have 3 pounds and 0.75 for each.
Solving the equation by distributing, you will get P=1.21
Hope this helps!
The equation will be 3 (p + 0.75) = 5.88. Then the original price per pound p will be 1.21.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
In winter, the price of apples suddenly went up by a $0.75 dollar sign per pound. Sam bought 3 pounds of apples at the new price for a total of $5.88 dollar sign.
The original price per pound p will be
3 (p + 0.75) = 5.88
p + 0.75 = 1.96
p = 1.96 - 0.75
p = 1.21
The equation will be 3 (p + 0.75) = 5.88. Then the original price per pound p will be 1.21.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
what is the measure of an angle that turns through 1/12 of a circle
The measure of an angle that turns through 1/12 of a circle is 30 degree.
What is Angle?A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.
We know the complete is 360 degree.
Then, to turn 1/12 of circle
= 360 x 1/2
= 360 / 12
= 30 degree
Thus, the measure of angle is 30 degree.
Learn more about Angle here:
https://brainly.com/question/28451077
#SPJ3
A soccer player runs 1 5/6 miles during the first half of a match and 2 1/2 miles during the second half. How many miles does he run during the match in total?
Find the inverse of f(x)= -x + 3
What is the distributive property of 60 - 50?
Natalia is making gift bags for her son's birthday party. Each bag costs $3.24 to make and she needs to make 15 bags. How much will the 15 bags cost?
A.) $48.60
B.) $47.40
C.) $486.00
D.) $4.74
Answer:
48.60
Step-by-step explanation:
The answer is $48.60 you just have to multiply the amount of bags times the cost of each bag to get your amount so
15 x 3.24 =48.60
Is it possible for two different numbers, when squared, to give the same result? What does this result tell you about solving an equation when the variable is squared? How many solutions will an equation like this have? Will there always be the same number of solutions for any equation with a squared variable? Explain.
x + y = 12
x - y = 10
What is the value of the x-determinant for the system shown?
(A.) -22
(B.) -12
(C.) -2
Final answer:
The value of the x-determinant for the system of equations is (C) -2, which is found by evaluating the determinant of the system's coefficient matrix.
Explanation:
To find the x-determinant for the system of equations given below:
x - y = 10
We can set up the coefficient matrix for these equations:
Matrix [A] =
| 1 1 |
| 1 -1 |
The determinant of this matrix is calculated by multiplying the diagonal elements and then subtracting the product of the off-diagonal elements. Hence, the determinant (det A) = (1)(-1) - (1)(1) = -1 - 1 = -2.
Therefore, the value of the x-determinant is (C) -2.
The square root of 2.25 is
A.15
B.1.5
C.0.15
D.irrational
How many ways are there to separate these 10 people into two groups, if no group can have less than 2 people?
Which expression is equivalent to x6 – 9?
Answer:
(x3)2 – 32
Step-by-step explanation:
Stan and hilda can mow the lawn in 35 min if they work together. if hilda works twice as fast as stan, how long would it take stan to mow the lawn alone?
The Hamptons family has a fish tank holding 10,450 ml of water. The water is leaking at a rate of 270 ml per minute. Define the input and output in the given scenario
The input is any variable which goes into the system. In this case there is no input.
While the output is any variable going out of the system. In this case the output is the amount of water which leaked out.
Answer:
The number of minutes represents input and remaining water represents output.
Step-by-step explanation:
Given,
The original quantity of the water in the tank = 10,450 ml,
Also, the quantity of the water leaked per minute = 270 ml,
Thus, the quantity water leaked in x minutes = 270x
∵ Remaining water in the tank ( say y ) = Original water - leaked water
⇒ y = 10450 - 270x,
Which is the equation that shows the given scenario.
In this equation, x represents the input value and y represents the output value,
Hence, the number of minutes represents input and remaining water represents output.
I thought of a number, multiplied it by 2 1/2 , divided the result by 1 1 /5 , subtracted 7/18 from it, and got 1 5/6 . What was my number?
The student's original number was 1 3/45. This was obtained by reversing the processes described in the problem and applying them to the final number.
Explanation:
To solve this problem, we basically need to reverse the operations given in the problem and perform them on the final answer 1 5/6. Let's start:
Add 7/18 to 1 5/6. The sum is 2. Multiply 2 by 1 1/5. The product is 2 2/5. Finally, divide 2 2/5 by 2 1/2. The quotient, which is the number the student originally thought of, is 48/45 or 1 3/45.
So the student's original number was 1 3/45.
Learn more about Reverse Operations here:
https://brainly.com/question/35361856
#SPJ12
The Kendal Company manufactures automobile engine parts. Running the manufacturing operations requires 12 watts (units of electricity per hour). The amount of electricity required to run the manufacturing operations and lighting the facility is given by y = 12x + 24, where x is the number of hours of manufacturing and y is the amount of electricity expended. How much electricity is used on a day when no parts are manufactured? (x 0, y 0)
Answer:
The answer is 24 watts.
Step-by-step explanation:
Running the manufacturing operations requires 12 watts (units of electricity per hour).
The amount of electricity required to run the manufacturing operations and lighting the facility is given by [tex]y=12x+24[/tex]
Here x is the number of hours of manufacturing and y is the amount of electricity expended.
When there are no parts manufactured, then x = 0
[tex]y=12(0)+24[/tex] = 24.
???????????????????????????
Grandpa Schmidt is 75 years old this is nine years less than seven times the age of Junior submit how old is Junior
Find an equation of a linear function given h(1)=6 and h(4)=-3
We can rewrite this in the form of h (t):
at t = 1, h = 6
at t = 4, h = -3
The linear equation is in the form of:
h = mt + b
where m is the slope and b is the h-intercept
So calculating for the slope m:
m = [-3 – 6] / (4 – 1)
m = (-9) / 3
m = -3
So,
h = -3t + b
Solving for b by plugging in any pair:
6 = -3(1) + b
b = 9
Therefore:
h = -3t + 9
The store keeper sold 9 1/4 yards from a piece of material containing 53 yards. How much was left in the original piece?
At the half ime show, a marching band marched in formation. the lead drummer started at a point with coordinates (–2, –5) and moved 3 steps up and 1 step right.
a. write a rule to describe the translation.
b. what were the coordinates of the drummer's final position?
Which pair of angles are interior angles?
A. 1 and 8
B. 3 and 6
C. 3 and 4
D. 3 and 5
3 & 5 are the interior angles
Answer is D
About 36,100,000 households in the U.S. have cats and about 43,300,000 households have dogs. About how may more households dogs and cats
how would you translate this into an equation
"one less than the product of number and 3 is 5 more than the number itself "
If r = x, y, z and r0 = x0, y0, z0 , describe the set of all points (x, y, z) such that |r − r0| = 5.
We are concern about the vector (x-x0, y-y0, z-z0) equaling to 5.
This happens when √(x-x0)^2 + (y-y0)^2 + (z-z0)^2 = 5
Square both side:
(x-x0)^2 + (y-y0)^2 + (z-z0)^2 = 25 , a sphere
Which you will recognize as a circle of radius one centered at (x0, y0, z0)
Answer:
Point [tex]\left ( x,y,z\right )[/tex] represents a sphere
Step-by-step explanation:
Take [tex]r=\left ( x,y,z \right )\,,\,r_0=\left ( x_0,y_0,z_0 \right )[/tex]
We need to describe the set of all points (x, y, z) such that [tex]\left | r-r_0 \right |=5[/tex]
Solution :
For [tex]r-r_0=\left ( x,y,z \right )-\left ( x_0,y_0,z_0 \right )[/tex], we will subtract the respective elements .
[tex]r-r_0=\left ( x,y,z \right )-\left ( x_0,y_0,z_0 \right )=\left ( x-x_0,y-y_0,z-z_0 \right )[/tex]
Therefore, [tex]\left | r-r_0 \right |=\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}[/tex]
As [tex]\left | r-r_0 \right |=5[/tex], we get
[tex]\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}=5[/tex]
On squaring both sides, we get
[tex]\left ( \sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2} \right )^2=5^2\\(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=25[/tex]
The general equation of a sphere is (x - a)² + (y - b)² + (z - c)² = r², where (a, b, c) denotes the center of the sphere and r represents the radius .
So, [tex](x-x_0)^2+(y-y_0)^2+(z-z_0)^2=25[/tex] represents a sphere with center as [tex]\left ( x_0,y_0,z_0 \right )[/tex] and radius equal to 5 units