A) In standard form, the length of time the light is on is [tex]2.67 \times 10^{-2} \text{ seconds}[/tex]
B) As a decimal, the length of time the light is on is [tex]0.0267 \text{ seconds}[/tex]
Step 1: Understanding the conversion
1 microsecond ([tex]\mu s[/tex]) is equal to [tex]10^{-6}[/tex] seconds.Therefore, 26700 microseconds is equal to [tex]26700 \times 10^{-6}[/tex] seconds.Step 2: Converting microseconds to seconds
First, let's calculate the time in seconds as a decimal:
[tex]26700 \times 10^{-6} = 0.0267[/tex]
Step 3: Converting seconds to standard form
Standard form (also known as scientific notation) expresses numbers as a product of a number between 1 and 10 and a power of 10.
Here, [tex]0.0267[/tex] can be written as:
[tex]2.67 \times 10^{-2}[/tex]
Given that x is a whole number, Niram conjectured that x3>x2 .
What value is a counterexample to Niram's conjecture?
(a) −2
(b) 1/10
(c) 1
(d) 5
Answer:
The answer is 1.
Step-by-step explanation:
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What is the length of segment NS?
1 unit
2 units
4 units
6 units
Answer:
Option C. 4 units
Step-by-step explanation:
As we know median of a triangle intersect each other at a point in the ratio of 2.01.
Therefore, in Δ QNL,
[tex]\frac{NS}{SR}[/tex] = [tex]\frac{2}{1}[/tex]
[tex]\frac{(7x-3)}{(5x-3)}[/tex] = [tex]\frac{2}{1}[/tex]
By cross multiplication
(7x - 3) = 2(5x -3)
7x - 3 = 10x - 6
6 - 3 = 10x - 7x
3 = 3x
x = 1
Now length of NS
= (7x - 3)
= (7 × 1 - 3)
= (7 - 3)
= 4 units
Option C. 4 units is the answer.
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Students observed that their teacher's desk plant looked wilted on Monday morning compared to how it looked at the end of the day on Friday. Some students hypothesized that a warmer room temperature over the weekend caused the plant to wilt. Other students hypothesized that the lack of light caused the plant to wilt. Both hypotheses are valuable because they
A.) are reasonable and testable ---- (My answer)
B.) compare independent variables
C.) compare light and temperature
D.) are the only possible explanations.
Why does a negative times a negative equal a positive proof?
Temperatures in the Gobi desert reach -40 F in the winter and 90 F in the summer. Find the range of the temperatures
add the 2 numbers together
40 + 90 = 130 degree range
A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?
a
(x − 4)2 + (y − 4)2 = 16
b
x2 + y2 = 16
c
(x + 4)2 + (y + 4)2 = 16
d
x2 + y2 = 4
e
(x − 4)2 + (y − 4)2 = 4
The equation of the circle is: is (x - 4)² + (y - 4)² = 16 Option A
How the equation of the circle was derivedTo find the equation of a circle tangent to the x-axis at (4, 0) and tangent to the y-axis at (0, 4)
Let's use the general form of the equation for a circle:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.
The center of the circle is (4, 4) because it's tangent to both the x-axis and y-axis at 4.
The radius can be found by the distance from the center to the point (4, 0) (which is on the x-axis):
r = √((4 - 4)² + (0 - 4)²) = √(0 + 16) = √16 = 4
So the equation of the circle is:
(x - 4)² + (y - 4)² = 4²
(x - 4)² + (y - 4)²= 16
The correct option is: a) (x - 4)² + (y - 4)² = 16
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The perimeter of a rectangular pig pen is 310 ft. The length is 15 ft greater than the width. Find the width
In dividing an irregular shape into polygons it is permissible for the polygons to overlap
In his free time, Gary spends 8 hours per week on the Internet and 10 hours per week playing video games. If Gary has five hours of free time per day, approximately what percent of his free time is spent on the Internet and playing video games?
Answer:
He spent a total of 22.85+28.57 = 51.42 % of his free time o internet and videogames.
Step-by-step explanation:
If Gary has 5 hours of free time per day, he has 5*7=35 hours of free time per week.
Now, in the case of internet:
[tex]\frac{35h}{8h}= \frac{100}{x}[/tex]
[tex]x= \frac{8*100}{35}[/tex]
x= 22.85% spent on internet.
In the case of videogames:
[tex]\frac{35h}{10h}= \frac{100}{x}[/tex]
[tex]x= \frac{10*100}{35}[/tex]
x= 28.57% spent on internet.
Michael is riding his bicycle. He rides at a speed of 8 kilometers per hour for 12.8 kilometers. For how many hours does he ride?
Please help with the tennis court one.
Answer:
Length = 78 feet
Width = 36 feet
Step-by-step explanation:
Pedro has $50. He wants to go to Disney World after 12 weeks saving weekly . The trip will cost him $530 for the long weekend. How much does he need to save every week ?
Subtract. Your answer should be a polynomial in standard form. (-9g^4+3g^2h+1) -(6g^4-3g^2h+h)
Which of the following expressions is equivalent to 6m - 10?
2(3m + 5)
-2(5 - 3m)
2(3m - 10)
What is meant by the term financial planning?
Find the number of real number solutions for the equation. x2 – 4x + 4 = 0
The quadratic equation x^2 - 4x + 4 = 0 has one real number solution, x = 2, which is a repeated solution since the discriminant of the equation is zero.
To determine the number of real number solutions for the equation x2
- 4x + 4 = 0, we can use the discriminant method. The discriminant D of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac. For our equation, a = 1, b = -4, and c = 4.
Calculating the discriminant gives us D = (-4)2 - 4(1)(4) = 16 - 16 = 0. Since the discriminant is equal to zero, it indicates that there is exactly one real number solution, which means the quadratic has a perfect square trinomial, or the two real solutions are identical.
In this case, the solution to the equation can be found by factoring the quadratic as (x - 2)2 = 0, which implies that x = 2. Therefore, the equation x2 - 4x + 4 = 0 has one real solution, x = 2, which is repeated.
The banner over the finish line of a running race is 400. Centimeters long and 85 centimeters high. What is the area over the banner?
In a study, a group of ten-year-old boys are fed doughnuts every morning for a week and then weighed to see how much weight they gained. which factor is the dependent variable?
In the stated experiment, the weight gain of the ten-year-old boys is the dependent variable. It is expected to change based on the consumption of doughnuts, which is the independent variable.
Explanation:
In the study described, where a group of ten-year-old boys are fed doughnuts every morning for a week and then weighed to see how much weight they gained, the dependent variable is the weight gain of the boys. The dependent variable is the outcome that is measured in an experiment or study. It is the factor that is expected to change as a result of changes to the independent variable, which in this case is the eating of doughnuts.
The dependent variable depends on the independent variable. For example, if the independent variable is the number of doughnuts eaten, the dependent variable (body weight) would likely change in response to the number of doughnuts consumed.
To illustrate this further, if we were to create a graph with the number of doughnuts eaten (independent variable) on the x-axis and the weight gained (dependent variable) on the y-axis, we could see if there is an exponential relationship or a different kind of correlation between these two variables. By understanding the dependent and independent variables, we can better interpret the results of studies and experiments.
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The sum of the ages of ruth and her mother is 77 years. the difference in their ages is 27 years. how old is each?
Which of these facts is used to prove that triangle ptr is similar to triangle qts? (1 point)?
solve y=x^2+2 for x.
In a certain region the number of highway accidents increased by 20% over a four years. How many accidents were in the 2006 if there was 5120 in 2002? hint when the percent increases if you want the original 100% plus the additional 20%
find the coordinates of G if f(1, 3.5) is the midpoint of Line GJ and J has coordinates (6, -2).
Bruce wants to make sure that each tiger at the zoo has 1,000 square feet of space. He wants to write an equation to represent the relationship between the number of tigers, t, and the number of square feet of space, f. Based on this information, answer these questions. Write an equation to represent the relationship between the number of tigers, t, and the total number of square feet of space, f, if each tiger has 1,000 square feet of space.
Answer:
The equation that represents the relationship between the number of tigers and the total number of square feet of space is f = 1,000t.
Step-by-step explanation:
Name one particular solution to 5x-(x+2)>-5(1+x)+3
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3/x-1-5*x/x+2-(1/4)=0
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
5.2 Adding up the two equivalent fractions
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using x as the denominator :
7.1 Pull out like factors :
3 - 6x = -3 • (2x - 1)
7.2 Adding up the two equivalent fractions
8.1 Find the Least Common Multiple
The left denominator is : x
The right denominator is : 4
Least Common Multiple:
4x
8.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 4
Right_M = L.C.M / R_Deno = x
8.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
8.4 Adding up the two equivalent fractions
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
Now, on the left hand side, the 4x cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
12-17x = 0
9.2 Solve : -17x+12 = 0
Subtract 12 from both sides of the equation :
-17x = -12
Multiply both sides of the equation by (-1) : 17x = 12
Divide both sides of the equation by 17:
x = 12/17 = 0.706
The inequality 5x-(x+2)>-5(1+x)+3 simplifies to x>5/9 after combining like terms and isolating x. Therefore, any x greater than 5/9 is a solution, including x=1, which satisfies the inequality.
To find a particular solution to the inequality 5x-(x+2)>-5(1+x)+3, we first simplify both sides of the inequality:
5x - x - 2 > -5 - 5x + 3
This further simplifies to:
4x - 2 > -5x + 3
Next, we add 5x to both sides and add 2 to both sides to get:
9x > 5
Now, we divide both sides by 9 to isolate x:
x > 5/9
Therefore, any x greater than 5/9 is a particular solution to the original inequality. For example, x=1 is such a solution, as it satisfies the inequality:
5(1) - ((1)+2) > -5(1+(1)) + 3
That simplifies to:
5 - 3 > -5(2) + 3
2 > -10 + 3
2 > -7, which is true, thus confirming x=1 is a solution.
A computer and printer cost a total of $908. The cost of the computer is three times the cost of the printer. Find the cost of each item.
Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
Answer:
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
Step-by-step explanation:
{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} is not a function because 1 have two different images.
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} is not a function because -2 have two different images.
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)} is not a function because -3 have two different images.
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} is a function because all x values has one only image value.
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Write an equation, in the slope intercept form, of the line with an x-intercept at (3 , 0) and a y-intercept at (0 , -5).
Hello : let A(3,0) B(0,-5)
the slope is : (YB - YA)/(XB -XA)
(-5-0)/(0-3) = 5/3
At what point on the curve x = t 3, y = 3t, z = t 4 is the normal plane parallel to the plane 6x + 6y − 8z = 1?
The coordinates of the point are x=3 / 4, y = 3 / 4, and z = 3 for the plane.
What is a plane?A plane is a two-dimensional Euclidean surface that extends indefinitely in mathematics. A plane is the two-dimensional equivalent of a point, a line, and space.
Given that the points are x = 3t, y = 3t and z = 4t. The equation of the plane is 6x + 6y -8z = 1.
Substitute the value of x,y, and z in the equation and solve for the value of 't'.
6x + 6y -8z = 1.
6 x 3t + 6 x 3t - 8 x 4t = 1
18t + 18t - 32t = 1
4t = 1
t = 1 / 4
The coordinates will be calculated as,
x = 3t = 3 x 1 / 4= 3 / 4
y = 3t = 3 x 1 / 4= 3 / 4
z = 4t = 4 x 3 / 4 = 3
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