The correct answer is option c i.e. the value of the function decreases as x approaches positive infinity.
The function g(x) = -4 log(x – 8) has the following features:
a. The domain is x > 8, because the expression x - 8 must be greater than 0 for the logarithm to be defined. Therefore, x must be greater than 8, so the domain is x > 8.
b. is incorrect because the range of the function is y < 0, not y > -8.
c. The value of the function decreases as x approaches positive infinity. As x gets larger and larger, the expression x - 8 gets larger and larger, so log(x - 8) gets larger and larger, approaching infinity. Multiplying by -4 makes the function more and more negative, so the value of the function decreases as x approaches positive infinity.
d. The value of the function does not increase as x approaches positive infinity, because as we just explained, the value of the function actually decreases as x approaches positive infinity. Therefore, option d is not correct.
Therefore, the correct answer is option c
Learn more about Functions here
https://brainly.com/question/20199690
#SPJ4
LA and LB are vertical angles. If mLA=(x+21)° and mLB=(4x-30)°, the find then measure of LB
Answer:
38 degrees
Step-by-step explanation:
Vertical angles are congruent(equal measures), so mLA = mLB
STEP 1:
Let's use some simple substitution.
mLA = mLB
mLA = x+21, mLB = 4x-30
You plug these two in and get:
x+21 = 4x-30
This is your equation.
STEP 2:
Let's solve our equation!
x+21 = 4x-30
(add 30 to both sides)
x+51 = 4x
(subtract x from both sides)
51 = 3x
(switch order for comprehension)
3x = 51
(divide both sides by 3)
x = 17
Ta-da! You get the measure of x = 17 degrees.
STEP 3:
Let's plug in our value of x to get the value of LB.
mLB = 4x - 30
mLB = 4(17) - 30
mLB = 68 - 30
mLB = 38
This is your answer.
HELP DUE TOMORROW!!!
The equation of the attached graph is
y = 1 cos (1x) + 0 How to write the equation of the graphThe equation is written by the general formula
y = A cos (Bx + C) + D
where:
A = amplitude.
B = 2π/T
where T = period
C = phase shift.
D = vertical shift.
A = amplitude
A = (maximum - minimum) / 2
Using the graph,
maximum = 1
minimum = -1
A = [1 - (-1)] / 2 = 2/2 = 1
B = 2π/T
where T = 2π
B = 2π/(2π) = 1
C = phase shift = 0
D = vertical shift
D = 1 - 1 = 0
substituting results to
y = 1 cos (1x + 0) + 0
this is written as
y = 1 cos (1x) + 0
y = cos (x)
Learn more about trigonometry graph at:
https://brainly.com/question/24329125
#SPJ1
Grams of
Peanuts
Grams of
Raisins
14
4
21
6
35
10
Enter the number of grams of peanuts in a bag for every 1 gram of raisins.
For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.
To find the number of grams of peanuts for every 1 gram of raisins, you need to set up a ratio and solve for the missing value.
1. Set up the ratio: grams of peanuts / grams of raisins.
2. You are given three sets of values: (14, 4), (21, 6), and (35, 10).
For the first set (14, 4):
3. Calculate the ratio: 14 grams of peanuts / 4 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
For the second set (21, 6):
4. Calculate the ratio: 21 grams of peanuts / 6 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
For the third set (35, 10):
5. Calculate the ratio: 35 grams of peanuts / 10 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
Your answer: For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.
Learn more about ratio,
https://brainly.com/question/2328454
#SPJ11
determine whether the function f(x) = a^x-a^(-x)+sinx is even or odd.
To determine whether the function f(x) = a^x-a^(-x)+sinx is even or odd, we need to check if it satisfies the properties of even and odd functions.
An even function is a function that satisfies the property f(x) = f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the y-axis, we get the same graph.
An odd function is a function that satisfies the property f(x) = -f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the origin (both x and y-axis), we get the same graph.
Let's start by checking whether f(x) is even:
f(-x) = a^(-x)-a^(x)+sin(-x) (since sin(-x) = -sin(x))
= -a^x+a^(-x)-sin(x)
Comparing f(-x) with f(x), we can see that f(-x) = -f(x) only when sin(x) = 0.
This means that f(x) is an even function only when sin(x) = 0, which occurs when x = nπ (where n is an integer).
Now, let's check whether f(x) is odd:
f(-x) = a^(-x)-a^(x)+sin(-x) (since sin(-x) = -sin(x))
= -a^x+a^(-x)-sin(x)
Comparing f(-x) with -f(x), we can see that f(-x) = -f(x) only when a^x = -a^x, which is not possible for any real value of a.
Therefore, f(x) is neither an even nor an odd function.
To determine whether the function f(x) = a^x - a^(-x) + sin(x) is even or odd, we can evaluate f(-x) and compare it to f(x).
An even function satisfies the condition f(-x) = f(x), while an odd function satisfies the condition f(-x) = -f(x).
Let's evaluate f(-x):
f(-x) = a^(-x) - a^(-(-x)) + sin(-x)
f(-x) = a^(-x) - a^x - sin(x)
Now, let's compare f(-x) to f(x):
f(-x) ≠ f(x) because f(x) = a^x - a^(-x) + sin(x)
f(-x) ≠ -f(x) because -f(x) = -a^x + a^(-x) - sin(x)
Since f(-x) is neither equal to f(x) nor -f(x), the function f(x) = a^x - a^(-x) + sin(x) is neither even nor odd.
Learn more about graphs here: brainly.com/question/17267403
#SPJ11
How much paint will you need to paint all sides of the box shown below? 4m 13m 4m 4m 11m
To paint all sides of the box, you would need approximately 344 square meters of paint.
To calculate the amount of paint needed to paint all sides of the box, we first need to find the total surface area of the box.
The box has five sides: top, bottom, front, back, and two sides.
Given the dimensions:
Top: 4m x 13m
Bottom: 4m x 13m
Front: 4m x 4m
Back: 4m x 4m
Sides (2): 4m x 11m.
To calculate the surface area, we sum the areas of all the sides:
Surface Area = (4m x 13m) + (4m x 13m) + (4m x 4m) + (4m x 4m) + (4m x 11m) + (4m x 11m)
Surface Area = 52m² + 52m² + 16m² + 16m² + 44m² + 44m²
Surface Area = 224m² + 32m² + 88m²
Surface Area = 344m²
For similar question on surface area.
https://brainly.com/question/27812847
#SPJ11
Ink pens and pencils are substitutes. If demand of pen falls,what happens to demand, supply, quantity
Pen demand decrease reduces pen price, quantity supplied; increases pencil demand, price, and quantity supplied as a substitute.
How do pen demand changes affect supply?If the demand for ink pens falls, this would likely result in a decrease in the demand for pens and an increase in the demand for pencils, since they are substitutes.
As a result, the price of pens would likely fall, as producers try to entice buyers to purchase pens over pencils. This decrease in the price of pens would, in turn, lead to a decrease in the quantity supplied of pens, as producers shift their focus to producing other goods that are more in demand.
However, the quantity demanded of pencils would increase, leading to an increase in the price of pencils and an increase in the quantity supplied of pencils. Ultimately, the market for ink pens and pencils would adjust to reflect the changes in demand, resulting in changes in both price and quantity.
Learn more about demand
brainly.com/question/29703449
#SPJ11
the line whose equation is 3x-5y=4 is dilated by a scale factor of 5/3 centered at the origin. Which statement is correct?
The correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]y= (\frac{5}{3} )x[/tex] centered at the origin, and the equation of the dilated line is y= (\frac{5}{3} )x
When a line is dilated by a scale factor of k centered at the origin, the equation of the dilated line is given by y = kx, if the original line passes through the origin. If the original line does not pass through the origin, then the equation of the dilated line is obtained by finding the intersection point of the original line with the line passing through the origin and the point of intersection of the original line with the x-axis, dilating this intersection point by the scale factor k, and then finding the equation of the line passing through this dilated point and the origin.
In this case, the equation of the original line is 3x - 5y = 4. To find the intersection point of this line with the x-axis, we set y = 0 and solve for x:
3x - 5(0) = 4
3x = 4
[tex]x = \frac{4}{3}[/tex]
Therefore, the intersection point of the original line with the x-axis is (4/3, 0). Dilating this point by a scale factor of 5/3 centered at the origin, we obtain the dilated point:
[tex](\frac{5}{3} ) (\frac{4}{3},0) = (\frac{20}{9},0)[/tex]
The equation of the dilated line passing through this point and the origin is given by [tex]y= (\frac{5}{3} )x[/tex]. Therefore, the correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]\frac{5}{3}[/tex] centered at the origin, and the equation of the dilated line is [tex]y= (\frac{5}{3} )x[/tex]."
To know more about "Dilated line" refer here:
https://brainly.com/question/30241444#
#SPJ11
The berry-picking boxes at bingo berry farm have square bottoms that are 8 centimeters on each side. mateo fills his box with raspberries to a height of 6 centimeters. what is the volume of raspberries in mateo's box?
The volume of raspberries in Mateo's box is 384 cubic centimeters.
To calculate the volume of raspberries in Mateo's box, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length and width are both 8 centimeters, as the box has a square bottom. The height is 6 centimeters, as Mateo fills the box to that height with raspberries.
So, the volume of raspberries in Mateo's box is:
Volume = length x width x height
Volume = 8 cm x 8 cm x 6 cm
Volume = 384 cubic centimeters
Therefore, the volume of raspberries in Mateo's box is 384 cubic centimeters. This calculation assumes that the raspberries are tightly packed in the box, without any gaps or air pockets. In reality, the actual volume of raspberries may be slightly less than this, depending on how they are arranged in the box. Nonetheless, this calculation provides a reasonable estimate of the amount of raspberries that Mateo is able to pick and fit in the box.
Know more about volume here:
https://brainly.com/question/1578538
#SPJ11
Select all the correct answers.
Isosceles trapezoid ABCD is shown.
Which three statements are correct?
In the given Isosceles trapezoid ABCD, the following three statements are correct:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths. Non-parallel sides on isosceles trapezoids have the same lengths. Hence, AD ≅ BC
A triangle with two equal sides is said to be isosceles. The two angles facing the two equal sides are also equal. Hence, ∠ADC ≅ ∠BCD.
The diagonals of the isosceles trapezoid are also equal. Hence, AC ≅ BD.
Thus, three correct statements in the given question are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
To learn more on isosceles trapezoid click on:
https://brainly.com/question/29964121
#SPJ1
Which shows 71. 38 in word form? O A seventy-one thirty-eighths O B. Seventy-one and thirty eighths O c. Seventy-one and thirty-eight tenths D. Seventy-one and thirty-eight hundredths E seventy-one and thirty-eight thousands
The number 71.38 can be written in word form as "seventy-one and thirty-eight hundredths." The correct answer is option D.
In decimal notation, the number 71.38 can be broken down into its whole number and decimal parts. The whole number part is 71, and the decimal part is 0.38.
In a decimal number, the digits to the right of the decimal point represent fractions of a whole. Each digit to the right of the decimal point has a place value that is a power of 10.
In word form, the decimal part 0.38 is read as "thirty-eight hundredths." Therefore, when combined with the whole number 71, the correct word form is "Seventy-one and thirty-eight hundredths."
Therefore option D is the correct answer.
Learn more about the whole number:
https://brainly.com/question/9879870
#SPJ11
66. Which value of m makes the inequality true?
A. 4
B. 5
3m-4 < 11
C. 6
D. 7
Answer:
The answer to the question provided is choice A, 4.
The value of m which makes the inequality true is, 4
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 3m - 4 < 11
Now,. We can simplify as;
⇒ 3m - 4 < 11
⇒ 3m < 11 + 4
⇒ 3m < 15
⇒ m < 5
Thus, The value of m which makes the inequality true is, 4
Learn more about the inequality visit:
https://brainly.com/question/25944814
#SPJ2
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
a = 8. 0 in.
b = 13. 7 in.
c = 16. 7 in.
A = 26. 4°, B = 54. 5°, C = 99. 1°
A = 28. 4°, B = 54. 5°, C = 97. 1°
A = 30. 4°, B = 52. 5°, C = 97. 1°
No triangle satisfies the given conditions
The missing parts of the triangle are:
Angle A ≈ 28.4°Angle B ≈ 52.5°Angle C ≈ 99.1°How to find the missing parts of the triangle?To find the missing parts of the triangle, we can use the Law of Sines and Law of Cosines.
First, we can use the Law of Cosines to find angle A:
cos(A) = (b² + c² - a²) / (2bc)
cos(A) = (13.7² + 16.7² - 8²) / (2 * 13.7 * 16.7)
cos(A) = 0.773
A = [tex]cos^-^1^(^0^.^7^7^3^)[/tex]
A ≈ 28.4°
Next, we can use the fact that the sum of the angles in a triangle is 180° to find angles B and C:
B = 180° - A - C
B = 180° - 28.4° - 99.1°
B ≈ 52.5°
C = 180° - A - B
C = 180° - 28.4° - 52.5°
C ≈ 99.1°
Therefore, the missing parts of the triangle are:
Angle A ≈ 28.4°Angle B ≈ 52.5°Angle C ≈ 99.1°Learn more about triangle
brainly.com/question/2773823
#SPJ11
Find the measure of the question marked arc (view photo )
The arc angle indicated with ? is derived as 230° using the angle between intersecting tangents.
What is an angle between intersecting tangentsThe angle between two tangent lines which intersect at a point is 180 degrees minus the measure of the arc between the two points of tangency.
angle G = 180° - arc angle HF
arc angle HF = 180° - 50°
arc angle HF = 130°
so the arc angle indicated with ? is;
? = 360° - 130°
? = 230°
Therefore, using the angle between the intersecting tangents, the arc angle indicated with ? is 230°.
Read more about tangents here:https://brainly.com/question/9132922
#SPJ1
5. this prism has a right triangle for a base. the volume of the prism is 54 cubic units.
what is the value of h?
The value of h is 6 units.
The volume of the prism is given by the formula V = 1/3 x (base area) x height. Since the base of the prism is a right triangle, the area of the base is given by A = 1/2 x base x height of the triangle. Therefore, the volume of the prism can be written as V = 1/3 x 1/2 x base x height of the triangle x height of the prism.
Simplifying this expression, we get V = 1/6 x base x height^2. Given that the volume of the prism is 54 cubic units, and substituting the value of the base which is not given as per the formula we get, 54 = 1/6 x base x h^2. Solving for h, we get h = 6 units. Therefore, the value of h is 6 units.
For more questions like Triangle click the link below:
https://brainly.com/question/2773823
#SPJ11
If a+b=3 and ab=4 find the value of a3+b3
Answer:
-9
Step-by-step explanation:
Recall the following relationships about the sum of cubes and a square binomial:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The second factor on the right hand side of equation 1 looks similar to the right hand side of equation 2, but differs slightly.
Carefully choosing to subtract 3ab from both sides of the equation 2, and Combining like terms yields...
[tex](a+b)^2-3ab=a^2-ab+b^2[/tex]
This now matches the second factor on the right hand side of the first equation. So, with substitution, the first equation becomes:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]
Note that all of the parts on the right hand side of the equation are given in the question:
a+b=3 and ab=4
With some substitution and simplification
[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]
[tex]=(3)((3)^2-3(4))[/tex]
[tex]=(3)(9-3(4))[/tex]
[tex]=(3)(9-12)[/tex]
[tex]=(3)(-3)[/tex]
[tex]=-9[/tex]
What is the main conflict in the story? Responses The people want to travel around. The people want to travel around. The people have trouble finding food. The people have trouble finding food. The babies have trouble going to sleep. The babies have trouble going to sleep. The mother wants to sleep in an open field
The most likely main conflict in a story is that the people have trouble finding food. The Option B is correct.
What is the main conflict in the given story?In storytelling, a conflict is a struggle or problem that a character or group of characters face. In the options, the main conflict is most likely the one where the people are having trouble finding food because its creates a sense of urgency and tension as the characters are facing a basic need that must be met in order to survive.
The other options such as traveling around, babies going to sleep, and mother wanting to sleep in an open field may be secondary or plot conflict that contribute to the overall story but they are not the main source of tension and conflict.
Read more about story conflict
brainly.com/question/1909141
#SPJ4
Consider the following planes. 5x - 3y + z = 2, 3x + y - 5z = 4 Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)) = Find the angle between the planes. (Round your answer to one decimal place.)
the cross product of the normal vectors of the planes will give you the direction vector of the line.
(5,−3,1)×(3,1,−5)=(14,28,14)
Which we can scale down to (1,2,1)
Now we need a point on the line. By inspection we can see that (1,1,0) lies in both planes.
Sometimes it it not that easy. But it is usually pretty easy to find a point in at least one plane and then travel along some line in that plane until we intersect the line in question.
Vector form of the line L:(x,y,z)=(1,2,1)t+(1,1,0)
In parametric form x=t+1,y=2t+1,z=t
The parametric equations are (x(t), y(t), z(t)) = (17/34 + 11t/34, 22/34 - 5t/34, 57/34 + 7t/34), where t is a parameter. The angle between the planes is 93.7 degrees.
To find the line of intersection of the planes, we can set the two equations equal to each other and solve for x, y, and z in terms of a parameter t. We can begin by eliminating one variable, say z.
From the first equation, we have z = 2 - 5x + 3y, and substituting this into the second equation gives 3x + y - 5(2 - 5x + 3y) = 4. Simplifying this equation, we get 22x - 14y - 23 = 0. Solving for y in terms of x, we get y = (22/14)x - (23/14).
Substituting this into the first equation and solving for z, we get z = (17/14)x + (57/14). Therefore, we have x = (17/22) + (11/22)t, y = (22/14) - (5/14)t, and z = (17/14)x + (57/14) + (7/22)t. These are the parametric equations for the line of intersection of the planes.
To find the angle between the planes, we can find the angle between their normal vectors.
The normal vector to the plane 5x - 3y + z = 2 is (5, -3, 1), and the normal vector to the plane 3x + y - 5z = 4 is (3, 1, -5). Using the dot product formula, we have cosθ = (5)(3) + (-3)(1) + (1)(-5) / sqrt(5² + (-3)² + 1²) sqrt(3² + 1² + (-5)²), which simplifies to cosθ = -19/34.
Taking the inverse cosine of this value, we get θ = 93.7 degrees, rounded to one decimal place. Therefore, the angle between the planes is approximately 93.7 degrees.
To know more about parametric equation, refer here:
https://brainly.com/question/29187193#
#SPJ11
Bob earns $60,000 a year at an accounting firm. Each year, he receives a raise. Bob
has determined that the probability that he receives a 10% raise is 0. 7, the probability that he earns
a 3% raise is 0. 2, and the probability that he earns a 2% raise is 0. 1.
A competing company has offered Bob a similar position for $65,000 a year. Bob wonders if he
should take the new job or take his chances with his current job. SHOW ALL WORK!
A) Find the mathematical expectation of the dollar amount of his raise at his current job
The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680. Therefore, Bob should take the new job at the competing company.
To find the mathematical expectation of the dollar amount of Bob's raise at his current accounting firm, we'll first calculate the expected raise percentages using the given probabilities. Then, we will multiply those percentages by his current salary to determine the expected dollar amount.
A) Step 1: Calculate the expected raise percentages using probabilities
- 10% raise with a probability of 0.7: (0.1 * 0.7) = 0.07
- 3% raise with a probability of 0.2: (0.03 * 0.2) = 0.006
- 2% raise with a probability of 0.1: (0.02 * 0.1) = 0.002
Step 2: Add up the expected raise percentages
0.07 + 0.006 + 0.002 = 0.078
Step 3: Multiply the expected raise percentage by Bob's current salary
Expected dollar amount of raise = $60,000 * 0.078 = $4,680
The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680.
To know more about accounting firm, visit:
https://brainly.com/question/28364190#
#SPJ11
Americans consume on average 32. 3 lbs of cheese per year with a standard deviation of 8. 7 lbs. Assume that the amount of cheese consumed each year by an American is normally distributed. An American in the middle 70% of cheese consumption consumes per year how much cheese?
An American in the middle 70% of cheese consumption consumes per year between 23.252 and 41.348 lbs of cheese.
To find the amount of cheese consumed by an American in the middle 70%, we need to find the range of values that contain the middle 70% of the distribution.
First, we need to find the z-scores corresponding to the lower and upper boundaries of the middle 70% of the distribution. We can use the standard normal distribution for this, by converting the raw score of 32.3 lbs to a z-score:
z = (x - μ) / σ = (32.3 - 32.3) / 8.7 = 0
The z-score for the mean is zero, which means the mean is the midpoint of the normal distribution.
Next, we need to find the z-scores that correspond to the lower and upper boundaries of the middle 70% of the distribution. We can use the standard normal distribution table or calculator to find the z-scores. For a middle 70% range, the z-scores are approximately -1.04 and 1.04.
Finally, we can use the z-scores and the formula z = (x - μ) / σ to find the corresponding values of x, which represent the range of cheese consumption that contains the middle 70% of the distribution:
Lower boundary: z = -1.04
-1.04 = (x - 32.3) / 8.7
x - 32.3 = -9.048
x = 23.252 lbs
Upper boundary: z = 1.04
1.04 = (x - 32.3) / 8.7
x - 32.3 = 9.048
x = 41.348 lbs
Learn more about normal distribution at https://brainly.com/question/29509087
#SPJ11
Tamekia and Marsha mow lawns during the summer to earn money. Tamekia determined that she can earn between $6. 00 and $6. 25 per hour. Marsha estimates that she earns between $7. 50 and $8. 00 per hour. About how much more money will Marsha earn than Tamekia if they each work 22 hours?
If they each work 22 hours, Marsha will earn about $35.75 more than Tamekia.
To compare how much more money Marsha will earn than Tamekia, we can use the averages of their respective hourly rates and then multiply by the number of hours worked.
Tamekia's average hourly rate: ($6.00 + $6.25) / 2 = $6.125
Marsha's average hourly rate: ($7.50 + $8.00) / 2 = $7.75
Now, we'll multiply their average hourly rates by the number of hours worked, which is 22 hours.
Tamekia's total earnings: $6.125 x 22 = $134.75
Marsha's total earnings: $7.75 x 22 = $170.50
Finally, we'll subtract Tamekia's earnings from Marsha's earnings to find the difference:
$170.50 - $134.75 = $35.75
So, Marsha will earn about $35.75 more than Tamekia if they each work 22 hours.
More on earnings: https://brainly.com/question/9330111
#SPJ11
Marsha will earn $38.50 more than Tamekia if they each work 22 hours.
8x + 19 -28 + 8x
what is the solution?
A water tank is filled with a hose. The table shows the number of gallions of water in the tank compared to the number of minutes the tank was
being filed The line of best for this data is g = 9m-0. 17
Minutes (m) 13 27 33 60
Gallons (3) 120 241 294 542
Approximately how much water was in the tank after 45 minutes of being filled?
O A 388 gallons
OB 405 gallons
O c 407 gallons
D. $18 gallons
Based on the given data, the line of best fit equation is g = 9m - 0.17, where "g" represents the number of gallons of water in the tank and "m" represents the number of minutes the tank was being filled.
To find the approximate number of gallons of water in the tank after 45 minutes of being filled, we need to substitute "m=45" in the equation and solve for "g".
g = 9(45) - 0.17
g = 405.83
Therefore, approximately 405 gallons of water would be in the tank after 45 minutes of being filled. The closest option to this answer is option B, which states 405 gallons. Therefore, option B is the correct answer.
To know more about gallons of water refer here
https://brainly.com/question/29196597#
#SPJ11
Skyler has 4 1/3 hours until she needs to go to bed she watches a movie for 2 2/9 hours how much time does she have left
Step-by-step explanation:
just convert the 1/3 and times 3 to both it's numerator and denominator.
once you have the same denominator as the other mixed number, you can start to minus.
Answer:
2 1/9 hrs
Step-by-step explanation:
4 1/3 = 13/3 = 39/9
2 2/9 = 20/9
39/9 - 20/9 = 19/9 = 2 1/9 hrs
or,
(4 - 2) + (3/9 - 2/9) = 2 1/9 hrs
Find the length of the curve. y = ∫√25sin^2t - 1 dt, 0 < x < т/2
I apologize, but there seems to be some confusion in your question. The function given, y = ∫√25sin^2t - 1 dt, is not a curve but rather an indefinite integral expression. In order to find the length of a curve, we need a function defined explicitly in terms of x (or y) and its bounds. Could you please provide more information or clarify your question?
To find the length of the curve given by y = ∫√(25sin^2(t) - 1) dt from 0 to π/2, we need to calculate the definite integral.
First, let's set up the integral:
Length = ∫√(25sin^2(t) - 1) dt, with bounds from 0 to π/2
Unfortunately, this integral cannot be solved analytically using elementary functions. You will need to use a numerical method, such as the Trapezoidal Rule or Simpson's Rule, to approximate the value of the integral, and thus find the length of the curve.
Learn more about Trapezoidal Rule here: brainly.com/question/30514442
#SPJ11
when rounding to the nearest hundred what is the greatest whole number that rounds to 500?
Answer:
499
Step-by-step explanation:
A tree farm has begun to harvest a section of trees that was planted a number of years ago. the table shows the number of trees remaining for each of 8 years of harvesting.
a) find the regression equation for the relationship between time and trees remaining. (round values for a and b to two decimal places.)
b) the owners of the farm intend to stop harvesting when only 1000 trees remain. during which year will this occur?
The owners of the farm will stop harvesting when only 1000 trees remain during the fifth year of harvesting.
a) To get the regression equation for the relationship between time and trees remaining, we need to use linear regression. We can use the data given in the table to create a scatterplot and then find the line of best fit. Using a calculator or Excel, we can find that the regression equation is:
Trees remaining = 1177.38 - 36.25(time)
where "Trees remaining" is the number of trees remaining and "time" is the number of years since harvesting began.
b) To find during which year the owners of the farm will stop harvesting when only 1000 trees remain, we can substitute "1000" for "Trees remaining" in the regression equation and solve for "time":
1000 = 1177.38 - 36.25(time)
Solving for "time", we get:
time = (1177.38 - 1000) / 36.25
time ≈ 4.89 years
Therefore, the owners of the farm will stop harvesting when only 1000 trees remain during the fifth year of harvesting.
Learn more about regression equation here, https://brainly.com/question/25987747
#SPJ11
Find the equation of the line that
is perpendicular to y = -8x + 2
and contains the point (-4,1).
Help
=
y = (?)X +
X
8
Enter the correct symbol, + or -, that
belongs in the green box
The equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).
To find the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1), first, determine the slope of the given line. The slope is -8. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the new line will be 1/8.
Now, use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point (-4, 1). Plug in the values: y - 1 = (1/8)(x - (-4)).
Simplify the equation: y - 1 = (1/8)(x + 4). Distribute the 1/8: y - 1 = (1/8)x + (1/2). Finally, add 1 to both sides: y = (1/8)x + (1/2) + 1.
So, the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).
To know more about perpendicular, refer here:
https://brainly.com/question/18271653#
#SPJ11
Tickets for the school basketball game cost $4 each. Spencer plans to
make a table relating the number of people (x) to the money made from
ticket sales (y).
What is the most appropriate domain for Spencer's table?
A.
all integers
B.
all rational numbers
C.
all real numbers
D
all whole numbers
The most appropriate domain for Spencer's table would be D. all whole numbers.
To explain this, let's first understand the terms involved. In this context, the domain refers to the set of possible input values (x) for the function, which in this case, represents the number of people attending the school basketball game.
Option A, all integers, includes negative numbers, which are not suitable as you cannot have a negative number of people. Option B, all rational numbers, comprises fractions, which are also not applicable because you cannot have a fraction of a person attending the game. Option C, all real numbers, consists of all numbers including irrational numbers like π, which are not relevant in this context as well.
Option D, all whole numbers, represents the most suitable domain as it includes all non-negative integers (0, 1, 2, 3, ...). This set accurately represents the possible number of people attending the game, since you can have zero or a whole number of people attending but not negative or fractional values.
Therefore, Spencer should use whole numbers as the domain for his table to relate the number of people (x) to the money made from ticket sales (y).
To know more about domain, refer to the link below:
https://brainly.com/question/29281112#
#SPJ11
Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth.
1. The probability that the point chosen is in the triangle is 0.1 (nearest tenth)
2. The probability that the point is in the square is 0.2( nearest tenth)
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty for an event is 1 which is equivalent to 100%.
Probability = sample space / total outcome
total outcome is the area of rectangle , which is
A = l× w
= 12 × 8
= 96
area of the rectangle = 1/2 bh
= 1/2 × 4 × 5
= 2 × 5
= 10
Area of the square = 4×4
= 16
1. Probability the the point will be in the triangle= 10/96 = 5/48
= 0.1( nearest tenth)
2. probability the the point will be in the square =
16/96 = 1/6
= 0.2 ( nearest tenth)
learn more about probability from
https://brainly.com/question/24756209
#SPJ1
A store has 25 VCRs in stock, but 2 of these are defective. What is the probability
that the second person to buy a VCR gets a defective one and the first
customer's VCR was not defective? Round your answer to the nearest
thousandth. *
. 083
. 0736
. 077
. 08
A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.
The probability that the first customer's VCR is not defective is 23/25, as there are 23 working VCRs out of the total 25.
Since one VCR has already been sold, there are 24 VCRs left and 1 defective VCR. Thus, the probability that the second customer gets a defective VCR is 1/24.
To find the probability that both events occur, we multiply the individual probabilities:
P = (23/25) x (1/24)
P = 0.077 or 0.0778 when rounded to the nearest thousandth.
Therefore, A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.
To know more about probability refer here:
https://brainly.com/question/30446665
#SPJ11
