The biologist was checking the condition for inference that (d) the observations within each sample are close to independent.
This is concluded from the fact that the biologist was checking if the product of sample size and the proportion of deer with chronic wasting disease in each sample was greater than or equal to 10. This is a commonly used rule of thumb to ensure that each sample has enough data to provide meaningful information about the population, and it is based on the idea that the sample size should be large enough such that the expected number of success (deer with chronic wasting disease) is at least 10 and the expected number of failures (deer without chronic wasting disease) is at least 10.
This helps to ensure that the observations within each sample are close to independent, as the sample proportions are unlikely to be greatly influenced by any individual deer in the sample.
Correct Question :
A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in northern colorado. to estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. the biologist checked for the following:
(200)(0.06)≥10
(200)(0.94)≥10
(197)(0.086)≥10
(197)(0.914)≥10
Which of the following conditions for inference was the biologist checking?
a. The population of deer within each region is approximately normal.
b. It is reasonable to generalize from the samples to the populations.
c. The samples are independent of each other.
d. The observations within each sample are close to independent.
e. The sampling distribution of the difference in sample proportions is approximately normal.
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Melanie is given two hours to complete a science test that has two sections. If she takes forty-three minutes to complete the first section, how many minutes does she have remaining on the second section?
Type a numerical answer only no words, symbols, or variables.
She have 1 hour 17 minutes remaining for the second section.
what is total time ?
Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.
Given:
Total time : two hours
Time taken to complete the first section = forty-three minutes
Now , minutes she have remaining on the second section
= Total time - Time taken to complete the first section
= 2 hours - 43 minutes
= 1 hour 17 minutes
Hence , she have 1 hour 17 minutes remaining for the second section.
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a wheel for a wheel of winning game makes one revolution in 4 seconds. What is their unit rate in terms of minutes
It will take 15 revolutions per minute.
What is the unit rate?
An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Here, we have
Given: a wheel for a wheel of winning game makes one revolution in 4 seconds.
Take a time for 1 revolution = 4 seconds
Assume that the unit rate in terms of revolutions per minute is x.
1 rev/4 second = x rev/60 second
4x = 60
x = 15
Hence, it will take 15 revolutions per minute.
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PLEASE ONLY ANSWER IF YOU KNOW
The value of AB in the triangle is 2.5 cm and the value of x in the triangle is 10 units
How to determine the value of ABFrom the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following equivalent ratio
AB : 4 = 10 : 16
Express as fraction
So, we have
AB/4 = 10/16
This gives
AB = 4 * 10/16
Evaluate
AB = 2.5
How to determine the value of xHere, we understand that the line bisects the angle BAC
This means that
x = 20 - x
So, we have
2x = 20
Divide
x = 10
Hence, the value is 10
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FIND THE LENGTH OF arc AB
thanks
Answer: D, 9.4
Step-by-step explanation:
(pi*2*12) *45/360 = 9.4
Answer:
9.4 is correct
Step-by-step explanation:
C=2πr = 2x3.14x12=75.36
arc AB=(45/360)x75.36=9.42
There are 96 birds at the Parkdale Zoo. of the birds are penguins. How many penguins are at Parkdale Zoo?
The number of penguins at the zoo is 48.
How many penguins are at the zoo?Percentage is a measure of frequency that determines the value of a number as an amount out of hundred. The sign that is used to represent percentage is %. In order to convert a number to percentage, multiply by 100.
Number of penguins = percentage of penguins x number of birds
50% x 96
(50/100) x 96 =
0.5 x 96 = 48
Here is the complete question:
There are 96 birds at the Parkdale Zoo. 50% of the birds are penguins. How many penguins are at Parkdale Zoo?
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An equation is shown below.
4.3(3.4z-19.2) = 5.3z + 10.7-2.4z
Which of the following statements describes a step that can be used to solve the equation for ?
O Subtract 4.32 from both sides of the equation.
O Add 10.7 to both sides of the equation.
O Divide both sides of the equation by 4.3.
O Multiply both sides of the equation by 10.7.
Answer:z=4663/586
Step-by-step explanation:
An object is launched at 19. 6 meters per second (m/s) from a 58. 8-meter tall platform.
The item reached its highest point at 78.4 meters by quadratic form of equation.
Suppose a quadratic form of equation has the following form
y=a[tex](x-h)^2[/tex] + k
Once in vertex form, it is said to be. It is so named because the vertex point (peak point) lies on the graph of this equation (h,k)
Using the data shown above, we can determine that
-4.9[tex]t^2[/tex] + 19.6 t + 58.8 = 0
The equation will naturally be converted to vertex form after the square is finished:
where h is the amount of time needed to reach a height of k.
Next, square the half of the linear term and add it to both sides.
-4.9([tex]t^2[/tex]-4t)=-58.8
-4.9([tex]t^2[/tex]-4t+4)=-58.8-19.6
-4.9([tex](t-2)^2[/tex])=-78.4
s(t)=-4.9([tex](t-2)^2[/tex])+78.4
As can be seen, the vertex is (2,78.4).
The maximum height is 78.4m.
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Question: An object is launched at 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is s(t)=−4.9[tex]t^2[/tex]+19.6t+58.8. What is the maximum height of the object?
A bag contains only pink sweets, white sweets, green sweets and red sweets.
The table gives each of the probabilities that, when a sweet is taken at random from
the bag, the sweet will be green or the sweet will be red.
Answer:
Below
Step-by-step explanation:
Since : .35 x = 28 Given ( where x = total sweets)
x = 80 sweets total
28 are red ( given ) then 02. * 80 = green = 16
80 - 28 - 16 = 36 remaining
and are divided between pink : white in ratio of 2:1
pink are 2 out of (2+1) = 2/3
2/3 * 36 remaining = 24 pink
then 12 are white
Step 2 Use the answers from Step 1 to find the total distance Sonja's ball traveled during her warm
up. Show your work (4 points)
I need help on the whole page if anyone knows the answer to this
Answer: step 1:
wickets 2 and 9, (16,18) and (15,43) = 25.02ft
wickets 9 and 8, (15, 43) and (37,65) = 31.11 ft
wickets 8 and 5, (37, 65) and (63,39) = 36.7 ft
wickets 5 and 3, (63, 39) and (41, 17) = 31.11 ft
wickets 3 and 2, (41, 17) and (16, 18) = 25.02 ft
Find any points of discontinuity for the rational function. y=(x+3)(x-5)(x+7)/(x+1)(x+4)
Points of discontinuity for the rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4) are x = -1 and x = -4.
A rational function is a function that can be expressed as the ratio of two polynomial functions. In the case of the given rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4), the numerator is a polynomial of degree 3, and the denominator is a polynomial of degree 2.
To find any points of discontinuity for a rational function, we need to determine where the denominator is equal to zero. Division by zero is undefined, so any value of x that makes the denominator equal to zero will be a point of discontinuity for the function.
In this case, we set the denominator (x+1)(x+4) equal to zero and solve for x:
(x+1)(x+4) = 0
This equation is true if either (x+1) = 0 or (x+4) = 0. So we have two solutions:
x+1 = 0 or x+4 = 0
x = -1 or x = -4
These values of x make the denominator of the function equal to zero, which means that the function is undefined at these points. These points are known as vertical asymptotes of the function, since the function approaches infinity as x approaches these points from either side.
It's important to note that the numerator of the function does not affect the points of discontinuity, since it is always defined for any value of x. Therefore, the points of discontinuity only depend on the denominator of the function.
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You are on a team of architects. You are charged with building a scale-model replica of one section of a new roller coaster before construction gets underway.
Certain reinforcement cables and struts are required to make the roller coaster sturdier. The goal for this project is for your team to determine where to place these cables or struts. The mathematical models for these reinforcements are known.
Your team must provide both algebraic and graphical evidence for your conclusions regarding the location of the cables.
Directions:
The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.
1. Write the equation that models the height of the roller coaster.
The circle equation is x² + y² = r²
Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is x2 + y2 = r2. (10 points)
The roller coaster's leg is 30 feet above the ground, as stated.
⇒ r = 30
⇒x² + y² = 30²
⇒x² + y² = 900
Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root. (10 points)
Roller coaster height equation: - x2 + y2 = 900
As we know, x² + y² = 900
⇒y² = 900 - x²
⇒y = √900 - x²
2. Graph the model of the roller coaster using the graphing calculator. Take a screenshot of your graph and paste the image below, or sketch a graph by hand. (5 points)
Model 1: One plan to secure the roller coaster is to use a chain fastened to two beams equidistant from the axis of symmetry of the roller coaster, as shown in the graph below:
You need to determine where to place the beams so that the chains are fastened to the rollercoaster at a height of 25 feet.
3. Write the equation you would need to solve to find the horizontal distance each beam is from the origin. (10 points)
To find the horizontal distance, we use the equation: x = 30^2-25^2
4. Algebraically solve the equation you found in step 3. Round your answer to the nearest hundredth. (10 points)
The horizontal distance is 16.58 feet
How to determine the equation:
The height is given as: 25 feet.
The roller coaster's length is 30 feet.
Use h to represent horizontal distance.
Given that the roller coaster represents the hypotenuse side length, the following equation can be used to calculate h
In step 3, we have: 30^2-25^2
This gives
Take the roots of both sides to get our answer
5. Explain where to place the two beams. (10 points)
The beam should be placed 8 feet from the center.
The struts are y = √(x + 8) and y = √(x − 4).
The struts are 2 feet apart at the location of the beam: √(x + 8) − √(x − 4) = 2
Solving:
√(x + 8) = 2 + √(x − 4)
x + 8 = 4 + 4√(x − 4) + x − 4
8 = 4√(x − 4)
2 = √(x − 4)
x − 4 = 4
x = 8
Model 2: Another plan to secure the roller coaster involves using a cable and strut. Using the center of the half-circle as the origin, the concrete strut can be modeled by the equation and the mathematical model for the cable is. The cable and the strut will intersect.
6. Graph the cable and the strut on the model of the roller coaster using the graphing calculator. Take a screenshot of your graph and paste the image below, or sketch a graph by hand. (5 points)
7. Algebraically find the point where the cable and the strut intersect. Interpret your answer. (10 points)
root 2x+8=x-8
2x+8=x^2-16x+64
-x^2+18x-56=0
x^2-18x+56=0
x(x-4)-14(x-4)=0
(X-4)(x-14)=0
x=4 ,x=14
x=14
Model 3: Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region. Again, using the center of the half-circle as the origin, the struts are modeled by the equations and. A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart.
8. Graph the two struts on the model of the roller coaster. Take a screenshot of your graph and paste the image below, or sketch a graph by hand. (5 points)
Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart.
9. Algebraically determine the x -value of where the beam should be placed. (15 points)
10. Explain where to place the beam. (10 points)
Step 1: Equation for Roller Coaster Height.
The general form for the equation of a circle at the origin is:
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Equation of a Circle (at origin):}}\\\\x^2+y^2=r^2\\\\\bullet \ \text{where 'r' is the radius of the circle}\end{array}\right}[/tex]
It is given that the height of the roller coaster is 30 feet. Thus, r = 30. Plug this into the equation above and solve for 'y.'
[tex]\Longrightarrow x^2+y^2=(30)^2\\\\\\\\\Longrightarrow x^2+y^2=900\\\\\\\\\therefore \boxed{\boxed{y=\sqrt{900-x^2} }}[/tex]
Step 2: Graph of Roller Coaster Model.
Refer to the attached image(s).
Step 3: Equation for Horizontal Distance of Beams.
Going back to the equation we got in step (1), we can solve for the variable ‘x.’
[tex]\Longrightarrow y=\sqrt{900-x^2}\\\\\\\\\therefore \boxed{\boxed{x=\pm\sqrt{900-y^2}}}[/tex]
Step 4: Algebraic Solution for Beam Placement.
Given a height, y = 25 ft. We can plug this into the equation above and solve for 'x.'
[tex]\Longrightarrow x=\pm\sqrt{900-(25)^2}\\\\\\\\\Longrightarrow x=\pm\sqrt{275}\\\\\\\\\Longrightarrow x=\pm5\sqrt{11}\\\\\\\\\therefore \boxed{\boxed{x\approx\pm16.58 \ ft}}[/tex]
Step 5: Placement of Beams.
The beams should be placed 16.58 feet from either side of the origin.
Step 6: Graph of Cable and Strut.
Refer to the attached image(s).
Step 7: Algebraic Intersection of Cable and Strut.
To find the point of intersection, set the two given equations (from model 2) equal to each other and solve for 'x.'
[tex]y=\sqrt{2x+8} \ \text{and} \ y=x-8\\ \\\\\\\Longrightarrow \sqrt{2x+8}=x-8 \\\\\\\\\Longrightarrow 2x+8=(x-8)^2 \\\\\\\\\Longrightarrow 2x+8=x^2-16x+64\\\\\\\\\Longrightarrow x^2-18x+56=0\\\\\\\\\Longrightarrow (x-14)(x-4)=0\\\\\\\\\therefore x=\{14,-4\}[/tex]
In order to determine which value of 'x' is correct we must verify the solution.
When x = 14:
[tex]\Longrightarrow 2(14)+8=(14-8)^2\\\\\\\\\Longrightarrow 36=36 \checkmark[/tex]
When x = -4:
[tex]\Longrightarrow 2(-4)+8=(-4-8)^2\\\\\\\\\Longrightarrow 0\neq 144[/tex]
Thus, the correct x-value is 14. Plug this into either given equations and solve for 'y.'
[tex]\Longrightarrow y =x-8\\\\\\\\\Longrightarrow y =14-8\\\\\\\\\therefore y=6[/tex]
Thus, the point of intersection is (14, 6).
Step 8: Graph of Two Struts.
Refer to the attached image(s).
Step 9: Algebraic Solution for Beam Placement.
To find the x-value of the beam placement, you need to find the point where the two strut equations are 2 feet apart. Set up an equation using the given functions and solve for 'x.'
[tex]\Longrightarrow y=\sqrt{x+8}-\sqrt{x-4}; \ y=2\\\\\\\\\Longrightarrow 2=\sqrt{x+8}-\sqrt{x-4}\\\\\\\\\Longrightarrow 2+\sqrt{x-4}=\sqrt{x+8}\\\\\\\\\Longrightarrow 4\sqrt{x-4}+x=x+8\\\\\\\\\Longrightarrow 4\sqrt{x-4}=8\\\\\\\\\Longrightarrow \sqrt{x-4}=2\\\\\\\\\Longrightarrow x-4=4\\\\\\\\\therefore \boxed{\boxed{x=8}}[/tex]
Step 10: Placement of Beam.
The beams will need to be placed 8 feet from either side of the origin.
Pixflix online video charges $5.95 to view a movie. Movie Prime video service charges $150 per year membership and $3.95 per movie. Assuming Minda views the same number of movies each month, what is the fewest number of movies per month Minda must view to make Movie Prime the better deal?
Minda must view 76 movies to make Movie Prime the better deal
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let, The number of movies be 'x' and from the given information the two equations can be formed as,
5.95x and 150 + 3.95x.
And to make Movie Prime the better deal,
150 + 3.95x < 5.95x.
2x > 150.
x > 75.
So, Minda must watch greater than 75 movies.
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(3b + 3)(-b² - 2b + 2)
solve the following systems of equations by graphing y=2x-4
y=-1/2x+6
Answer:
(4,4)
By using a graphing we can see that the lines intersect at (4,4).
therefore, 4 is the solution
don't forget to say thanks
What does it mean by the nearest cent?
Answer:
Rounding to the nearest cent implies approximating a money amount to two decimals (which represent the number of cents), applying the following rules: If the third decimal digit is lower than 5, we leave the second decimal digit as it is. E.g., $4.563 ≈ $4.56.
My age 2 years ago plus my age 2 years from now equals 24. How old am I
Answer:
= 6 years old.
Step-by-step explanation:
Let your age 2 year ago be = x
= 2x
again
Let your age 2 years from now be x
= 2x
therefore
= 2x +2x = 24
= 4x = 24
= 4x/4 = 24/4
= x = 6
therefore you're 6 years old.
The table shows the world birth rates y number of births ler thousands people) in r years since 1960
Identify an equation that models the birth rate as a function of the number years since 1960
An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35. Thus, option 3 is correct.
What do you mean by equation?It represents a relationship between variables and constants and is used to describe the behavior of a function or system. Equations can be linear or nonlinear and can have one or multiple variables. They can be used to solve real-world problems, such as finding the slope of a line, calculating distances, or determining the minimum or maximum value of a function. Equations are also used in advanced mathematical disciplines, such as calculus, algebra, and geometry.
When x = 0, y-intercept = 35.4 ≈ 35
And when x increases, the value of y decreases, so slope is negative
From the given options
There is only two negative slope equation but only one with y-intercept = 35. i.e.
y = -0.3x + 35
Thus, An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35.
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Drag each tile to the correct box. Not all tiles will be used.
Order the steps for bisecting line segment AB using a reflective device.
A
Place the reflective device anywhere on
the segment.
Move the reflective device around on the
paper until the reflection of point A
coincides with point B.
Place the reflective device on Point A.
Place the reflective device on Point B.
Draw the line of reflection using the edge
of the reflective device as a guide.
The correct steps for bisecting line segment AB using a reflective device is given below:
Place the reflective device on Point A.Move the reflective device around on the paper until the reflection of point A coincides with point B.Draw the line of reflection using the edge of the reflective device as a guide.What is Bisecting a line?Cutting a line exactly in half is known as bisecting it. Due to the fact that the line you are drawing will be at a right angle to the initial line, it is also sometimes referred to as creating a perpendicular bisector.
A compass, pencil, and ruler are required.
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PLEASE HELP AS FAST AS POSSIBLE
Answer:
l is parallel to m and u is parallel to t
Step-by-step explanation:
Parallel line means that never meet each other
A B What is the converse of the following statement? "If I studied for it, then I did well on the exam." "If I did well on the exam, then I studied for it." "If I did not do well on the exam, then I did not study for it."
Answer:
A
I believe because p→q
q→p
Step-by-step answer please, thanks! :)
The amount of money you'll have at the end of 5 years is $4,060.
How to calculate the simple interest and future value?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 3,500 × 3.2/100 × 5
S.I = 3,500 × 0.03.2 × 5
S.I = $560.
Next, we would calculate the future value as follows;
Future value, A = S.I + P
Future value, A = $560 + $3,500
Future value, A = $4,060.
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Please answer these for 100 points
The area of a trapezoid with the given parallel sides and height is 4x+8 square units. Therefore, option B is the correct answer.
What is area of the trapezoid?The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (b₁+b₂)×h.
where (A) is the area of a trapezoid, 'b₁' and 'b₂' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between b₁ and b₂).
1) Given that, b₁=x-3, b₂=x+7 and the height=4
Now, area of a trapezoid = 1/2 (x-3+x+7)×4
= 2×(2x+4)
= 4x+8 square units
Hence, option B is the correct answer.
2) The given polynomials are -3x²-7x+9 and -5x²+6x-4.
Here, sum = -3x²-7x+9+(-5x²+6x-4)
= -3x²-7x+9-5x²+6x-4
= -8x²-x+5
Hence, option 1 is the correct answer.
Therefore, the area of a trapezoid is 4x+8 square units.
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9) Before hibernation, a bear weighs 990 pounds. Its weight decreases by 32% during hibernation. How much does the bear weigh when it comes out of hibernation? Show your work.
The weight of the bear after hibernation is 673.2 pounds
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Before hibernation, a bear weighs 990 pounds.
Its weight decreases by 32% during hibernation.
We need to find how much the bear weigh when it comes out of hibernation.
Lets find what is 32% of 990
32/100×990
0.32×990
316.8
Now let us subtract 316.8 from 990 pounds, to find the weight after hibernation.
990-316.8
673.2
Hence, 673.2 pounds is the weight of the bear after hibernation.
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In a company, 70% of the workers are. If 1170 people work for the company who aren't women, how many workers are there in all?
The number of workers in the company is given as follows:
3900 workers.
How to obtain the number of workers in the company?The number of workers in the company is obtained applying the proportions in the context of the problem.
From the problem, we have that:
70% of the workers are women.1170 of the workers are not women.Hence 30% of the workers is equivalent to 1170, hence the number of workers in the company is obtained as follows:
0.3x = 1170
x = 1170/0.3
x = 3900 workers.
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Help with this PLEASE!!
Answer:
x = 24°
Step-by-step explanation:
See the attached worksheet. Let a and b stand for the two unknown angales as shown on the worksheet. Since the sum of angles across a straight line is 180°, we can express the two angles as:
a = 180°-x, and
b = 180° - 111° or b = 69°
The sum of the interior angles of a quadrilateral is 360°. Set the four angles equal to 360° and solve for x.
x = 24°
What is the percent composition of water in the compound magnesium sulfate heptahydrate, MgDO4•7H2O?
A. 7.3%
B. 24.8%
C. 48.8%
D. 51.2%
Answer:51. 2%
Step-by-step explanation:
24+32+(16×4)+7(2+16)=24+32+64+126=246
26g of Epsom salt contains 126g of water of crystallisation.Hence, 100g of Epsom salt contains 100×126/246The % of H2O in MgSO4.7H2O=
Python formats all floating point numbers to two decimal places when outputting using the print statement O True O False 1 pts >> Question 9 The if statement causes one or more statements to execute only when a Boolean expression is true. O True O False
Python formats all floating point numbers to two decimal places when outputting using the print statement. (FALSE)
The if statement causes one or more statements to execute only when a Boolean expression is true. ( TRUE)
What are Floating Points?Floating point is a number format that can be used to represent a large or small value.
In writing this number is done by writing it in exponential form, so that the number has a base number, the exponential number and the base number.
The following is writing scientific notation in floating point. example in decimal numbers
261,000,000,000 written 2.61 x 10¹¹
0.000000000261 is written 2.61 x 10^-10
The Floating point representation itself has two parts, namely the mantissa part and the exponent part. The mantissa determines the digits, while the exponent determines the value of how many powers the mantissa is, as follows:
±S * B±E
S = Significant also called mantissa
E = Exponent
B = Base
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Determine the interval(s) on which the given function is increasing.
Polynomial going up from the left and passing through the point negative 1 comma 0 and going to a relative maximum at the point 0 comma 5 and then going down to a relative minimum at the point 1 comma 4 and then going up to the right
(–∞, –1) ∪ (1,∞)
(–1, ∞)
(–∞, 0) ∪ (1, ∞)
(0, 1)
The intervals on which the function is increasing is (0, 1). Option D
What is a polynomial?A polynomial is a type of mathematical expression that has variables that are raised to whole number powers.
Since the factors of 5 are 1 and 5, we'll try to factor the polynomial by assuming that (x-1) and (x-5) are factors.
The product of (x-1) and (x-5) is (x² - 6x + 5), which is the polynomial we're given.
⇒ (x² - 6x + 5) is the factored form of the polynomial.
A polynomial is increasing on the intervals where it's greater than zero. So we just need to look at the sign of (x² - 6x + 5) for values between 1 and 5.
For values between 1 and 5, the function is always positive, so it's increasing on the interval (1, 5). Therefore, the increasing interval is (1, 5).
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Thomas won $16,000 on a game show, and he put all of the money in a checking account (which does not give interest). Each month, he takes $400 out of the account for "spending" money.
The equation that describes this situation is M=16000−400t
, where t
is the time in months since opening the account, and M
is the amount of money left in the account.
In how many months will Thomas empty the account (which means that there will be no money left)?
It will take Thomas 40 months to empty the account if he continues to take out $400 each month of $16,000.
To find out how many months it will take for Thomas to empty the account, we need to set M to 0 and solve for t. This will give us the number of months it will take for Thomas to spend all of the $16,000 he won on the game show. The equation we need to solve is:
0 = 16000 - 400t
First, we'll isolate the variable t on one side of the equation by adding 400t to both sides:
400t = 1600
Next, we'll divide both sides of the equation by 400 to get the value of t:
t = 16000/400
Simplifying the right side of the equation gives us:
t = 40
So, it will take Thomas 40 months to empty the account if he continues to take out $400 each month for spending money.
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The ratio of staff to guests at the gala was 3 to 5. There were a total of 576 people in the ballroom. How many guests were at the gala?
360 guests were at the gala
How to determine how many guests were at the gala?Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.
Since the ratio of staff to guests at the gala was 3 to 5.
Let S and G represent the number of staff and guests respectively. From the given information, we can write:
S/G = 3/5
S + G = 576
Thus, S = 576 - G
Put S = 576 - G in S/G = 3/5 and solve for G. That is:
(576 - G)/G = 3/5
3G = 5(576 - G)
3G = 2880 - 5G
3G + 5G = 2880
8G = 2880
G = 2880/8
G = 360
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