Mr. Rr the Rreliable Rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting from the moment he is turned on. (For example, he does his first jumping jack $42$ seconds after he is turned on.)
How many times during the first $15$ minutes after activation will Mr. Rr whistle and do a jumping jack at the same instant?
Answer:
7 times during the first 15 minutes
Step-by-step explanation:
Remember that
[tex]1\ min=60\ sec[/tex]
so
[tex]15\ min=15(60)=900\ sec[/tex]
Decompose the numbers 18 and 42 in prime factors
we know that
[tex]18=(2)(3^2)[/tex]
[tex]42=(2)(3)(7)[/tex]
Find the least common multiple (LCM)
The LCM is
[tex](2)(3^2)(7)=126\ sec[/tex]
we need to find all multiples of 126 that are less than or equal 900.
[tex]126*1=126\ sec\\126*2=252\ sec\\126*3=378\ sec\\126*4=504\ sec\\126*5=630\ sec\\126*6=756\ sec\\126*7=882\ sec[/tex]
therefore
7 times during the first 15 minutes
Help me please!!!!!!
Find S8 for the geometric series 3 + -6 + 12 + -24 +…
the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].
To find the sum [tex]\( S_8 \)[/tex] of the geometric series [tex]\( 3 - 6 + 12 - 24 + \ldots \)[/tex], we need to determine the common ratio [tex](\( r \))[/tex] and the first term [tex](\( a \)).[/tex]
The general form of a geometric series is [tex]\( a + ar + ar^2 + \ldots + ar^{n-1} \)[/tex], where:
- [tex]\( a \)[/tex] is the first term,
- [tex]\( r \)[/tex] is the common ratio,
- [tex]\( n \)[/tex] is the number of terms.
In our series:
- [tex]\( a = 3 \)[/tex] (the first term),
- To find the common ratio [tex](\( r \))[/tex], we can divide any term by its preceding term:
- [tex]\( \frac{-6}{3} = -2 \)[/tex]
- [tex]\( \frac{12}{-6} = -2 \)[/tex]
- [tex]\( \frac{-24}{12} = -2 \)[/tex]
So, [tex]\( r = -2 \)[/tex].
Now, [tex]\( S_n \)[/tex], the sum of the first [tex]\( n \)[/tex] terms of a geometric series, is given by the formula:
[tex]\[ S_n = \frac{a(1 - r^n)}{1 - r} \][/tex]
Substituting the values of [tex]\( a \), \( r \)[/tex], and [tex]\( n = 8 \)[/tex], we get:
[tex]\[ S_8 = \frac{3(1 - (-2)^8)}{1 - (-2)} \][/tex]
[tex]\[ S_8 = \frac{3(1 - 256)}{1 + 2} \][/tex]
[tex]\[ S_8 = \frac{3(-255)}{3} \][/tex]
[tex]\[ S_8 = -255 \][/tex]
So, the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].
The state of wyoming has roughly the shape of a rectangle that is 3.6 x 102 miles long and 2.8 x 102 miles high. what is the approximate area of wyoming? hint: the area of a rectangle is product of its length and width.
Assuming a regularly shaped rectangle, the formula for the area is given as:
A = L * W
where L and W are the length and width respectively
A = 3.6 x 10^2 miles * 2.8 x 10^2 miles
A = 100,800 square miles
or
A = 10.08 x 10^2 miles
Answer: The area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Step-by-step explanation:
The shape of wyoming is rectangular with length , [tex]L=3.6\times 10^{2}\, miles[/tex]
and height , [tex]H=2.8\times 10^{2}\, miles[/tex]
Area of rectangle , [tex]A=L\times W[/tex]
=> [tex]A=(3.6\times 10^{2})\times (2.8\times 10^{2})\, miles^{2}[/tex]
=>[tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Thus the area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)
1. A grocer mixes two grades of coffee which sell for 70 cents and 80 cents per pound, respectively. How much of each must he take to make a mixture of 80 pounds which he can sell for 76 cents per pound?
2. How many quarts of pure alcohol must be added to 40 quarts of a mixture that is 35% alcohol to make a mixture that will be 48% alcohol?
3. If a container contains a mixture of 5 gallons of white paint and 11 gallons of brown paint, how much white paint must be added to the container so that the new mixture will be two-thirds white paint?
4. Can the sum of three consecutive odd integers be (a) 25? (b) 45?
5. A tank can be filled in 9 hours by one pipe alone, in 12 hours by a second pipe alone, and can be drained when full, by a third pipe, in 15 hours. How long would it take to fill the tank if it is empty, and if all pipes are in operations?
You will be charged 12.5% interest on a loan of $678. how much interest will you pay on the loan?
It is given in the question that
You will be charged 12.5% interest on a loan of $678.
So to find the interest, we have to find 12.5% of 678. And 12.5% = 0.125
So we have to find the value of 0.125 of 678.
[tex]0.125*678 = 84.75[/tex]
Therefore the interest that you will have to pay on loan is $84.75 .
What is the graph of the function f(x) = the quantity of 3 x squared plus 2 x plus 10, all over x plus 3
A) a graph is shown with a vertical asymptote at x = -3 increasing from negative infinity to just under -35 and then decreasing back to negative infinity as well as decreasing to just under five and increasing to infinity
B) graph with vertical asymptote of x equals 3, and oblique asymptote of y equals x minus 1
C) graph with vertical asymptote of x equals 3, and oblique asymptote of y equals negative x minus 1
D) graph with vertical asymptote of x equals negative 3, and oblique asymptote of y equals negative x minus 1
What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? Their is 10 marbles total, 2 yellow, 3 pink, and 5 blue
Final answer:
The probability of drawing two yellow marbles in succession without replacement from a bag of 10 marbles, where 2 are yellow, is 1/45.
Explanation:
The student is asking about the probability of drawing two yellow marbles successively without replacement from a bag containing a total of 10 marbles with different colors. To solve this problem, we use conditional probability. The probability of drawing the first yellow marble is 2 out of 10 since there are 2 yellow marbles among 10 total marbles. This can be written as P(Y1) = 2/10 or 1/5. After the first yellow marble is drawn, there is only 1 yellow left among 9 total marbles, so the probability of drawing a second yellow marble is P(Y2|Y1) = 1/9.
The two events are dependent since the outcome of the first draw affects the second draw. Therefore, to find the overall probability of both events happening, we multiply their probabilities: P(Y1 and Y2) = P(Y1) × P(Y2|Y1) = (1/5) × (1/9) = 1/45. So, the probability of drawing two yellow marbles successively without replacement is 1/45.
If the lengths of two of the possible sides of a right triangle measure 4 root 15 and 7 root 6 what is the smallest possible length of the third side
Help please:((((((((((((((((
Answer:
B. The amount spent on grapes compared with the weight of the purchase.
Step-by-step explanation:
Grapes are usually sold at some dollar amount per pound. That dollar amount is the "rate of change," and it is generally constant.
___
In the case of pizza delivery or bus ridership, it is hard to imagine what the "rate of change" might be, as the relationship is probably not a function.
Which of the following is the sum of the polynomials 5x2 - 4x + 1 and -3x2 + x - 3 ?
2x2 + 3x + 2
8x2 - 5x - 2
2x2 - 3x - 2
-8x2 - 3x - 2
Solve the inequality -2x is less than or equal to 3x + 1 is less than or equal to 10
What is 78% written as a decimal
What is the equation of the following line? Be sure to scroll down first to see all answer options.
Answer:
Option C. is the correct option.
Step-by-step explanation:
Equation of line is represented as y = mx + c
where m = slope of the line
c = y - intercept
Since line is passing through origin (0, 0) and a point (6, 2)
Therefore y intercept of the line will be 0.
c = 0
Slope of the line [tex]m=\frac{y-y'}{x-x'}[/tex]
[tex]m=\frac{2-0}{6-0}[/tex]
[tex]m=\frac{2}{3}[/tex]
So the equation will be
[tex]y=\frac{1}{3}x[/tex]
Therefore, option C. is the answer.
Decide if the situation involvesâ permutations, combinations, or neither. explain your reasoning.
What is the area of a rectangle with a length of 15 feet and a width of 9 feet?
Final answer:
The area of a rectangle with a length of 15 feet and a width of 9 feet is 135 square feet.
Explanation:
The area of a rectangle can be found by multiplying its length and width.
In this case, the length is 15 feet and the width is 9 feet.
To find the area, multiply 15 feet by 9 feet:
Area = 15 feet x 9 feet = 135 square feet
Therefore, the area of the rectangle is 135 square feet.
find the magnitude of 6+2i
Final answer:
The magnitude of 6 + 2i is 2√10.
Explanation:
To find the magnitude of the complex number 6 + 2i, we can use the Pythagorean theorem. The magnitude, or absolute value, of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 6 and the imaginary part is 2. So the magnitude is:
|6 + 2i| = √(6^2 + 2^2) = √(36 + 4) = √40 = 2√10
Therefore, the magnitude of 6 + 2i is 2√10.
Find all solutions in the interval [0, 2π). 7 tan3x - 21 tan x = 0
Given a polynomial f(x), if (x + 7) is a factor, what else must be true?
f(0)=7
f(0)=-7
f(7)=0
f(-7)=0
Answer:
f(-7)=0 that is option 4th is correct.
Step-by-step explanation:
If we have given any polynomial then its factor means that value is giving zero of that polynomial
And opposite sign of factor is the zero of the polynomial
For example:
x+a is factor of any polynomial f(x) then f(-a)=0
Similarly, If x+7 is a factor of any polynomial then f(-7)=0
Hence, option 4th is correct.
Solve for x and y: 28x-49y=35 and 4x-7y=5
What is a variable?
a.
A variable is an unknown number or value represented by a letter
c.
A variable represents a change in value
b.
A variable always represents the total amount
d.
A variable is always represented by the letter x
Please select the best answer from the choices provided
Let $AB = 6$, $BC = 8$, and $AC = 10$. What is the area of the circumcircle of $\triangle ABC$ minus the area of the incircle of $\triangle ABC$?
Max is in a control tower at a small airport. He is located 50 feet above the ground when he spots a small plane on the runway at an angle of depression of 27. What is the distance of the plane from the base of the tower? Round to the nearest foot. A. 25 feet B. 110 feet C. 56 feet D. 98 feet
The distance of the plane from the base of the tower is:
Option: D
D. 98 feet
Step-by-step explanation:Let x denotes the distance of the plane from the base of the tower.
Now, in the right angled triangle we will need to use trignometric identity corresponding to 63°.
Based on the figure we have:
[tex]\tan 63=\dfrac{x}{50}\\\\\\x=50\times \tan 63[/tex]
[tex]x=50\times 1.9626\\\\\\x=98.13\ feet[/tex]
which to the nearest feet is:
98 feet
Drag the tiles to the correct boxes to complete the pairs. Match the numerical expressions to their simplified forms.
Drag the tiles to the correct boxes to complete the pairs. Match the numerical expressions to their simplified forms
Tiles:
A).
(P^5) ^1/4
---------------
(P^-3 Q^-4)
B).
(P^2Q^7) ^1/2
----------
(Q^4)
C).
(P^6Q^3/2)^1/3
D).
(PQ^3)^1/2
--------------
(PQ)^-1/2
Pairs:
1.)
P^2Q^1/2
2.)
PQ^2
3.)
P^2Q
4.)
PQ^3/2
in the diagram which pair of angles are corresponding angles
Answer:
Option C is correct .i.e., ∠3 and ∠7
Step-by-step explanation:
Corresponding angles are the angles that are at the same corner at each Point of Intersection.i.e., if first angle is at the top left corner of one intersection then the angle at the other intersection is also at the top left.
From Given Figure,
Following are pairs of corresponding angles,
∠1 and ∠5
∠2 and ∠6
∠4 and ∠8
∠3 and ∠7
Therefore, Option C is correct .i.e., ∠3 and ∠7
Grace is standing 14 feet from a lighthouse and Kelly is standing 12 feet from Grace. The angle that Grace looks up to see the top of the lighthouse is 45°. The angle that Kelly looks up to see the top of the lighthouse is y°. Find the height, h, of the lighthouse. Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse. To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations
Find the possible value or values of n in the quadratic equation 2n2 – 7n + 6 = 0
Answer:
[tex]n=\frac{3}{2},\,\,n=2[/tex].
Step-by-step explanation:
The equation you have is a quadratic equation because the polynomial [tex]2n^{2}-7n+6[/tex] has degree 2. One of the methods available to solve kind of equations is to factorize the polynomial on the left hand side. To factorize you can do the following:
(1) [tex]2n^2-7n+6[/tex]. The given polinomial
(2) [tex]\frac{2\times(2n^2-7n+6)}{2}=\frac{(2n)^{2}-7(2n)+12}{2}[/tex]. Multiply and divide by 2, because it is the coeficient of [tex]n^{2}[/tex]
(3) [tex]\frac{(2n)^{2}-7(2n)+12}{2}=\frac{(2n-\_\_)(2n-\_\_)}{2}[/tex]. Separate the polynomial in two factors, each one with [tex]2n[/tex] as a first term. The sign in the first factor is equal to the sign in the second term of the polynomial, that is to say, [tex]-7n[/tex]. The sign in the second factor is the sign of the second term multiplied by the sign of the third term, that is to say [tex](-)\times(+)=(-)[/tex] . In the blanks you should select two numbers whose sum is 7 and whose product is 12. Those numbers must be 3 and 4.
(4)The polynomial factorized is [tex]\frac{(2n-4)(2n-3)}{2}[/tex]
(5)Use the common factor in the numerator to cancel the number 2 in the denominator to obtain [tex](n-2)(2n-3)[/tex]
Then the given equation can be written as:
[tex]{(2n-3)(n-2)=0[/tex]
The product of two expression equals zero if and only if one of the expression is zero. From here we have that
[tex]2n-3=0[/tex] or [tex]n-2=0[/tex]
From the first equality we obtain that [tex]n=\frac{3}{2}[/tex]. From the second equality we obtain that [tex]n=2[/tex].
please help , show your steps , thanks
5 + 2*SQRT(x) = 15
subtract 5 from each side
2*SQRT(x) = 10
(2*SQRT(x))^2 =10^2
2^2 *x = 100
4x=100
x=400/4
x = 25
Help which is the correct function
Arrange the functions in ascending order, starting with the function that eventually has the lowest value and ending with the function that eventually has the greatest value.
2x+5
2^x+3
2^x+10
2x
x²+2
x²
PLEASE HELP 20 POINTS PROVIDED