There are 50 dimes in a roll of dimes, 40 nickels in a roll of nickels, and 40 quarters in a roll of quarters. Rob has 12 rolls of coins with a total value of $70.00. He has 3 more rolls of nickels than dimes. How many rolls of each coin does he have?
Find the coordinates of the point (x,y,z)(x,y,z) on the plane z=2x+3y+3z=2x+3y+3 which is closest to the origin.
To find the point closest to the origin on the plane with equation z = 2x + 3y + 3, an offset vector from the origin to a point on the plane is used. This vector's dot product with the plane's normal vector should be zero, since the shortest path to the plane will be perpendicular to it. This creates a system of equations that can be solved for x, y, and z.
Explanation:To find the closest point (x, y, z) on the given plane to the origin in three-dimensional Cartesian axes, we can start by creating an offset vector from the origin to an arbitrary point on the plane. Let's use the equation of the plane, z = 2x + 3y + 3. Let's presume a point P(x, y, z) on this plane. The vector to this point from the origin is (x, y, z - 3).
Because we want the shortest distance to the origin, the dot product of this vector and the normal vector to the plane (2, 3, -1) should be zero, because the shortest path to the plane will be perpendicular to it. So, the formula for the dot product gives us:
2*x + 3*y - (z - 3) = 0
This simplifies to:
2x + 3y - z + 3 = 0
Which combined with the equation of the plane (z = 2x + 3y + 3), provides a system of equations that can be solved using methods like Gaussian elimination or substitution.
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Draw a number line and show all numbers that are between 1 and 20 and have exactly 4 factors
(or visualize, make it somewhat close to being a number line)
(work with a number line all positives, 1 being smallest, 20 being biggest.
Numbers which have exactly 4 factors between 1 and 20 are 6, 8, 10, 14, 15 represented on number line.
Define factor ?
" In mathematics factor is a number by which when we divides another number remainder is zero."
According to the question,
Factors of all the numbers between 1 and 20
2, 3, 5, 7, 11, 13, 17, 19 are prime number , so they have only two factors.
4 = 1, 2, 4
6 = 1, 2, 3, 6
8 = 1, 2, 4, 8
9 = 1, 3, 9
10 = 1, 2, 5, 10
12 = 1, 2, 3, 4, 6, 12
14 = 1, 2, 7, 14
15 = 1, 3, 5, 15
16 = 1, 2, 4, 8, 16
18 = 1, 2, 3, 6, 9, 18
Hence, we conclude that numbers which have exactly 4 factors between 1 and 20 are 6, 8, 10, 14, 15.
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what statement about this figure is true-- i know its one of the last two but they both seem right to me
Find the average rate of change of the function
8 students can ride in each van. How many vans are needed for 29 students?
There is the need for 4 vans.
To determine how many vans are needed for 29 students, with each van able to transport 8 students, we can use division and then round up, since you can't have a fraction of a van. We divide 29 students by 8 students per van, which gives us 3.625. Since we can't have 0.625 of a van, we need to round up to the next whole number to ensure all students have a seat. That means we need 4 vans to transport 29 students.
Divide the total number of students by the number of students each van can hold: 29 / 8 = 3.625.
Round this number up to the nearest whole number, because you need whole vans: This gives us 4.
Thus, you need 4 vans to transport 29 students.
What is 2/7 = 2x what would be the answer
There are different ways to think about the meaning of speed.
Which description correctly completes this sentence?
Speed is ________________________.
A.time traveled times distance traveled
B.time traveled divided by distance traveled
C.the number of hours it takes to travel a certain distance
D.the distance traveled divided by the time it takes to travel that distance
30 POINTS
Answer:
D
Step-by-step explanation:
A square pyramid has a base length of 6 inches and a height of 8 inches. What is the volume of this pyramid? Enter your answer in the box. in³
Final answer:
The volume of the square pyramid with a base length of 6 inches and a height of 8 inches is 96 cubic inches.
Explanation:
To find the volume of a square pyramid, you can use the formula V = (1/3) × base area × height, where the base area is the area of the square base. Since the base length is 6 inches, the area of the base is 6 in. × 6 in. = 36 in.². The height of the pyramid is 8 inches. So, the volume of the pyramid can be calculated as follows:
V = (1/3) × 36 in.² × 8 in. = 96 in.³
Therefore, the volume of the square pyramid is 96 cubic inches.
A group of 30 bikers went on a trip. some rode bicycles and the others rode tandems. if the total number of bicycles and tandems was 23, how many tandems were used?
Point E is located at (2, −3) and point F is located at (−2, −1). Find the y value for the point that is 3 over 4 the distance from point E to point F.
A. -2.5
B. -4.5
C. -3.5
D. -1.5
lars has been approved for$420,000, 20-year mortgage with an APR of 5.125%.What is his monthly payment ? How much interest would he expect to pay on the loan in one month?How much of the monthly payment will go towards the principal?
Answer:
Monthly Payment = $2,286.85
Interest on first month payment = $1,793.75
Principal value on first month payment = $493.10
Step-by-step explanation:
lars has been approved for $420,000 for loan.
Time for loan = 20-years
APR (Annual Rate of interest ) = 5.125%
We need to find monthly payment. First month interest and First month principle.
Formula for loan:
[tex]p=\dfrac{PV\cdot \frac{r}{n}}{1-(1+\frac{r}{n})^{-nt}}[/tex]
Where,
p is monthly payment.
PV = Loan Amount (PV=$420,000)
R = Rate of interest (R=0.05125)
t = Loan period ( t=30)
n = Mode of payment (n=12)
Substitute the value into formula and solve for p
[tex]p=\dfrac{420000\cdot \frac{0.05125}{12}}{1-(1+\frac{0.05125}{12})^{-12\cdot 30}}[/tex]
p=$2,286.85
Thus, Monthly Payment =$2,286.85
Interest for first month [tex]=420000\times \dfrac{0.05125}{12}=1793.75[/tex]
Interest pay on the loan in on month = $1,793.75
Principle value on first month payment = 2286.85 - 1793.75 = $493.10
The monthly payment will go towards the principal is $493.10
Tom weighs 168.5 pounds. His son weighs 33.7 pounds. How many times as much as his son does Tom weigh
Jake ate 1/6 of the cookies at the valentines party. If he ate 5 cookies, how many cookies were there in all?
Ella used 1/4 yard of red ribbon. Fill in each box with a number from the list to show equivalent fractions for 1/4
Answer:
To find fractions equivalent to a given fraction, the process of amplifying the numerator and the denominator of that fraction must be performed. Specifically, each element is amplified by multiplying it by a positive integer. Thus, fractions equivalent to 1/4 are:
(1x2) / (4x2) = 2/8
(1x3) / (4x3) = 3/12
(1x4) / (4x4) = 4/16
(1x5) / (4x5) = 5/20
(1x6) / (4x6) = 6/24 ... Successively.
Step-by-step explanation:
plez help What is the value of y in the equation 4 + y = −3?
7
1
−1
−7
PLEASE HELP WILL GIVE BRAINLIEST!!! What is the y-intercept of f(x)=(1/2)^x
Try this explanation:
'y-interception' means x=0.
If x=0, then y=1.
answer: (0;1)
What is the answer to my math problem from my school for homework today?
what are the roots of the equation?
x^2+24=14x
enter answers in the boxes
A math teacher assigns 3 projects. She gives the students 5 project options to choose from. How many different groups of projects can the students choose from?
In a group of 25 factory workers, 20 are low-risk and five are high-risk. two of the 25 factory workers are randomly selected without replacement. calculate the probability that exactly one of the two selected factory workers is low-risk.
What are the slope and the y intercept of the graph of the liner function shown on the grid
A car traveled at an average rate of 51 miles per hour on one highway. It then traveled at an average rate of 71 miles per hour on a second highway. If the car traveled a total of 508 miles in 8 hours, how many miles were driven on the first highway?
Which of these distance measures would you most likely find on a walking tour map of downtown Paris, using the metric system?
A. Kilo feet
B. Millimeters
C. Centimeters
D. Meters
Answer:meters
Step-by-step explanation:
reuben deposits $700 into an account that pays simple interest at a rate if 5% per year. How much interest will he be paid in the first 3 years.
Reuben deposits $700 at a 5% annual interest rate for 3 years, using the simple interest formula, he will earn $105 in interest over that period.
Explanation:The question deals with calculating the simple interest Reuben will receive by depositing $700 into an account at a 5% annual interest rate over 3 years. To calculate simple interest, the formula used is Interest = Principal × Rate × Time. In this scenario, the principal (P) is $700, the rate (R) of interest per year is 5% or 0.05 when expressed as a decimal, and the time (T) is 3 years.
Substituting these values into the formula provides us with: Interest = $700 × 0.05 × 3. Simplifying this gives us: Interest = $105.
Therefore, Reuben will be paid $105 in interest over the first 3 years.
The base of a 6-inch long ice cream cone with a diameter of 2 inches, is cut 0.25 inches from the base. This cut creates two shapes, one is a cone, and the other one resembles a cylinder since it was cut so close to the base. What is the BEST estimate for the volume of the shape that resembles a cylinder?
The third side of an isosceles triangle is 2 inches shorter than each of the other two sides. if the perimeter of this triangle is 67 inches find the length of each side.
How many extraneous solutions does the equation below have? 9 over n squared +1 =n+3 over 4? 0 1 2 3
Answer:
Option 1 - There is no extraneous solution i.e. 0.
Step-by-step explanation:
Given : Expression [tex]\frac{9}{n^2+1}=\frac{n+3}{4}[/tex]
To find : How many extraneous solutions does the equation have ?
Solution :
First we solve to expression to determine the extraneous solution,
[tex]\frac{9}{n^2+1}=\frac{n+3}{4}[/tex]
Cross multiply,
[tex]9\times 4=(n+3)(n^2+1)[/tex]
[tex]36=n^3+n+3n^2+3[/tex]
[tex]n^3+3n^2+n-33=0[/tex]
An extraneous solution is defined as a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.
The equation form is a cubic function so it has 3 solutions.
Therefore, There is no extraneous solution.
Write an equation or inequality that best represents each statement below
6 times a number, x, is at least 22
Last week,you finished level 2 of a video gamr in 32 minutes. Today, you finish level 2 in 28 minutes. What is your percent change