Answers
The equation to the given graph is y= (1/2) * 2ˣ. So correct option is B.
Describe Parabola?A parabola is a type of curve that results from the intersection of a cone with a plane that is parallel to one of its sides. It is a conic section, which means it is a geometric shape that can be formed by cutting a cone with a plane.
The shape of a parabola is similar to that of a U-shaped curve, but it is symmetric around a vertical line called the axis of symmetry. The point where the axis of symmetry intersects the parabola is called the vertex.
The equation of a parabola can be written in different forms, but the most common form is:
y = ax^2 + bx + c
where "a", "b", and "c" are constants that determine the shape, position, and orientation of the parabola. If "a" is positive, the parabola opens upward, and if "a" is negative, it opens downward.
We can observe that the given graph passes through the points (-1,1), (0,2), (1,4), (2,8). This suggests that the graph is a parabola that opens upwards.
We can use the general form of a quadratic equation to write the equation of the parabola in the form y = ax² + bx + c, where a, b, and c are constants. Since the parabola opens upwards, we know that the coefficient of the x² term is positive.
To find the values of a, b, and c, we can substitute the coordinates of the given points into the equation and solve the resulting system of equations.
Using the point (-1,1), we get:
1 = a(-1)² + b(-1) + c
1 = a - b + c
Using the point (0,2), we get:
2 = a(0)² + b(0) + c
2 = c
Using the point (1,4), we get:
4 = a(1)² + b(1) + c
4 = a + b + c
Using the point (2,8), we get:
8 = a(2)² + b(2) + c
8 = 4a + 2b + c
Substituting c = 2 from the second equation into the third and fourth equations, we get:
4 = a + b + 2
8 = 4a + 2b + 2
Simplifying these equations, we get:
a + b = 2
2a + b = 3
Solving for a and b, we get:
a = 1
b = 1
Therefore, the equation of the parabola is y = x² + x + 2.
To check which of the given options matches this equation, we can simplify the equation:
y = x² + x + 2
y = (x + 1/2)² + 7/4
This shows that the given parabola is a vertical shift of the standard parabola y = x² by 7/4 units upward.
Out of the given options, the only equation that matches this form is option B, y = (1/2) * 2ˣ. Therefore, the answer is B) y= (1/2) * 2ˣ.
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Related Questions
question 4 when is the mean of the sampling distribution of means equal to the mean of the population from which the samples were drawn?
Answers
The mean of the sampling distribution of means will be equal to the mean of the population from which the samples were drawn when the sampling distribution is unbiased.
The unbiased sampling distribution of means is one in which the sample means are drawn such that their average equals the population mean. Therefore, an unbiased sample should be representative of the population mean.The sampling distribution is a statistical term that refers to the probability distribution of a given random sample of size n that is taken from the population's larger dataset.
The distribution of the statistics collected from different samples is known as the sampling distribution. The mean of the sampling distribution is equal to the population mean. Sampling distribution provides insight into the sample data's variation, which can be used to make population inferences.
The mean of the sampling distribution of means is also known as the expected value of the sampling distribution. It is the mean of the population, which is equal to the mean of the sampling distribution of means. If the sample means are unbiased, the mean of the sampling distribution of means equals the population mean. The central limit theorem states that, as the sample size increases, the sampling distribution of means approaches a normal distribution with a mean equal to the population mean.
The mean of the sampling distribution is a critical statistic in inferential statistics because it aids in determining the statistical significance of the sample. If the sample mean is significantly different from the population mean, the results of the test can be used to reject or accept the null hypothesis.
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The ratio of boys to girls is 3:2, if the total number of children in the class is 35, how many boys are there?
PLSSS HELPP NOWW!!!!!
Answers
Answer:
21 boys
Step-by-step explanation:
girls 3+3=6+3=9+3=12+3=15+3=18+3=21
boys 2+2+2=6+2=8+2=10+2=12+2=14
3times 7=21
2 times 7 equals 14
so 21+14=35
If the dartboard has a diameter of 14 inches and each number occupies 1/20 of the board, how much space does a single number occupy in square inches?
Answers
Answer:
Step-by-step explanation:
If the dartboard has a diameter of 14 inches, then the radius is 7 inches. The area of the dartboard is given by the formula for the area of a circle: A = pi x r^2, where pi is approximately 3.14 and r is the radius.
A = 3.14 x 7^2 = 153.86 square inches (rounded to two decimal places)
Each number occupies 1/20 of the board, so we need to divide the total area by 20 to get the area occupied by a single number:
153.86 / 20 = 7.69 square inches (rounded to two decimal places)
Therefore, a single number occupies approximately 7.69 square inches of space on the dartboard.
if £24=500rubles how many £ are in 648rubles
Answers
The answer is 31.10.
Based on the given conditions, formulate: 648 * 24 / 500 Cross out the common factor:dfrac162 * 2412.
~£31=648rubles
648/20,8333
why is it that you can buy a double cheese burger for 99 cents and you can't even get a head of broccoli for 99 cents
Answers
A double cheeseburger costs less than a head of broccoli due to lower ingredient costs, a more efficient manufacturing process and some more reasons which are listed below:
Firstly, cheeseburgers are typically made with cheaper ingredients, such as pre-made patties, processed cheese, and pre-made buns. The manufacturing process is also more streamlined and efficient, which further reduces cost. Additionally, the demand for cheeseburgers is typically higher than that for broccoli, which helps to keep prices low.
On the other hand, broccoli requires more labor to harvest and process. It also requires more storage space, which drives up costs. The demand for broccoli is typically lower than for cheeseburgers, which also keeps prices higher.
Additionally, broccoli is more labor-intensive and requires more storage space, which further drives up its cost.
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Determine the maximum cubic centimeters this container will hold
A. 24 cubic cm
B. 75.36 cubic cm
C. 77.87 cubic cm
D. 311.49 cubic cm
Answers
Answer:
D
Step-by-step explanation:
Volume: π*[tex]r^{2} *h[/tex]= π*[tex]4^{2}[/tex]*6.2=311.49
its special angles, please show work
Answers
Answer:
H=25
I=36
Step-by-step explanation:
In QRS, s = 3.1 cm, m 10th of a centimeter.
Answers
The value of q according to the given triangle measures is 3 cm.
What is Sine Rule for Traingles?
For any general triangle ABC with 3 angles A, B, and C and 3 sides a, b, and c corresponding to their opposite angle, the formula of sine is always fulfilled :
[tex]\frac{a}{sin A} = \frac{b}{sin B} =\frac{c}{sin C}[/tex]
Here, we are given that :
s i.e. Side QR = 3.1 cm
Angle Q = 62 degree
Angle R = 114 degree
Firstly we need to find the third angle S using the sum of triangle angles property :
[tex]AngleQ + AngleR + AngleS = 180\\[/tex]
[tex]Angle S = 180 - 114 - 62[/tex]
[tex]= 180 - 176[/tex]
[tex]= 4[/tex]
Now, we apply the sine formula for angles Q and S :
[tex]\frac{q}{sinQ} = \frac{s}{sinS}[/tex]
[tex]q = (sinQ) * s / (sinS)[/tex]
[tex]= ( 3.1 * sin(62)) / sin(4)[/tex]
[tex]= ( 3.1 * (-0.739)) / (-0.756)[/tex]
[tex]= 3.03[/tex]
Hence, the length of side RS i.e. q to its nearest 10th is 3 cm.
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A chain fits tightly around two gears as shown. The distance between the centers of the gears is 32 inches. The radius of the larger gear is 19 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale.
Answers
Answer:
The answer to your problem is, C.
Step-by-step explanation:
From the given figure it is noticed that the radius of a circle is 11 inches and the centers of two circles are 20 inches apart. The length of the direct common tangent between both circles is 19 inches.
If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is
[tex]L = \sqrt{d^{2} - (r_{1} - r_{2} )^{2} }[/tex]
[tex]19 = \sqrt{20^{2} - (11-r_{2} )^{2} }[/tex]
Next, Square both sides.
[tex]361 = 400 - ( 11 - r_{2} )[/tex]
[tex]( 11 - r_{2} )^{2} = 400 - 361[/tex]
[tex]( 11 - r_{2} )^{2} = 39[/tex]
Change the square root both sides.
[tex]11-r = \sqrt{39}[/tex]
[tex]11- 6.245 = r[/tex]
[tex]4.775 = r[/tex]
[tex]R = 4.8ish[/tex]
Therefore the radius of second circle is 4.8 inches
Thus the answer to your problem is, C.
Does anybody know the answer to this question?
Answers
The perimeter of isosceles triangle PRQ is 24.65 units.
The lengths of its three sides and add them up. We can use the distance formula to find the length of each side.
Distance formula: The distance d between two points (x1, y1) and (x2, y2) is given by:
d = [tex]sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
Using this formula, we can find the lengths of the sides PR, RQ, and PQ.
PR = [tex]sqrt((-1 - (-7))^2 + (4 - (-1))^2) = sqrt(36 + 25) = sqrt(61)[/tex]
RQ =[tex]sqrt((3 - (-1))^2 + (-1 - 4)^2) = sqrt(16 + 25) = sqrt(41)[/tex]
PQ = [tex]sqrt((3 - (-7))^2 + (-1 - (-1))^2) = sqrt(100) = 10[/tex]
Therefore, the perimeter of triangle PRQ is:
PR + RQ + PQ = [tex]sqrt(61) + sqrt(41) + 10 ≈ 24.65[/tex] (rounded to two decimal places)
So, the perimeter of triangle PRQ is approximately 24.65 units.
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You have been keeping track of the outside temperature for a class project.
At noon, the temperature was 80°F
.
At 5:00
p.m., the temperature was 64°F
.
What was the percent change between the temperature at noon and the temperature at 5:00
p.m.?
Answers
Answer:
20%
Step-by-step explanation:
80 - 64 = 16
16 ÷ 80 = 0.2
0.2 × 100 = 20%
Can someone pls help me (you are the best)
Answers
The answer is x=6x +2
Cydni is working with some algebra tiles at her desk. She makes groups that look like this:
A:
x + 1 + 1 + 1 + x + 1 + 1 + 1 + x + 1 + 1 + 1
B:
3x + 9
C:
3(x + 9)
D:
3(x + 3)
E:
x + 2x + 3(x + 2)
F:
x3 + 13
(Please answer quickly!!)
Answers
Answer:
B. 3x+9
hope this helped
21 x 8 ÷ 12 as a equivalent ratio?
Answers
Answer:
There are many options, like:
14/1 or 28/2...
Step-by-step explanation:
First write the system:
(21 x 8) / 12
Then simplify the brackets:
(168) / 12
= 14
Then you can put 14 over 1 as an example of proportionality:
14/1 : (21 x 8) / 12
Or multiply it by 2, 3 etc.:
42/3 : (21 x 8) / 12.
Find the value of x in the figure below
Answers
Consequently, x is 70 degrees as a consequence. The supplied diagram labels the angles of the triangle ABC as 40°, 70°, and x.
what is triangle ?Three straight lines that meet at three different locations to create a triangle, a two-dimensional geometric shape. Triangles have three sides and three vertices, which are the three places where those three lines intersect. Triangles can be categorised based on the dimensions of their angles and side lengths. . In contrast, a triangle with three equal sides and three equal angles of 60 degrees is called an equilateral triangle. The sides and angles of a scalene triangle are not identical.
given
The angles of the triangle ABC are labelled in the provided figure as 40°, 70°, and x. We can use the knowledge that the sum of a triangle's angles is 180° to find x.
As a result, we have:
x + 40° + 70° = 180°
The left half of the equation is simplified as follows:
x + 110° = 180°
110° from both edges subtracted:
x = 70°
Consequently, x is 70 degrees as a consequence. The supplied diagram labels the angles of the triangle ABC as 40°, 70°, and x.
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A company manufactures and sells DVD's. Here are the equations they use in connection with their business.Number of DVD's sold each day: n(x) = xSelling price for each DVD: p(x) = 8.5 - 0.02xDaily fixed costs: f(x) = 210Daily variable costs: v(x) = 2xFind the following functions.a. Revenue = R(x) = the product of the number of DVD's sold each day and the selling price of each DVD.b. Cost = C(x) = the sum of the fixed costs and the variable costs.c. Profit = P(x) = the difference between revenue and cost.d. Average cost = C (x) C¯(x) = the quotient of cost and the number of DVD's sold each day.
Answers
The Average cost, after calculations, comes up to 210/x + 2.
To find the following functions such as Revenue, Cost, Profit and Average cost, we have given the equations as below:
Number of DVD's sold each day: n(x) = x
Selling price for each DVD: p(x) = 8.5 - 0.02x Daily fixed costs: f(x) = 210 Daily variable costs: v(x) = 2x
To Find the following functions:
a. Revenue = R(x) = the product of the number of DVD's sold each day and the selling price of each DVD.
b. Cost = C(x) = the sum of the fixed costs and the variable costs.
c. Profit = P(x) = the difference between revenue and cost
d. Average cost = C (x) C¯(x) = the quotient of cost and the number of DVD's sold each day.
Number of DVD's sold each day: n(x) = x
Selling price for each DVD: p(x) = 8.5 - 0.02x Daily fixed costs: f(x) = 210 Daily variable costs: v(x) = 2x
a. Revenue = R(x) = the product of the number of DVD's sold each day and the selling price of each DVD.R(x) = n(x) × p(x) = x × (8.5 - 0.02x) = 8.5x - 0.02x2
b. Cost = C(x) = the sum of the fixed costs and the variable costs.C(x) = f(x) + v(x) = 210 + 2x = 2x + 210
c. Profit = P(x) = the difference between revenue and cost.P(x) = R(x) - C(x) = 8.5x - 0.02x2 - (2x + 210) = -0.02x2 + 6.5x
d. Average cost = C(x)C¯(x) = the quotient of cost and the number of DVD's sold each day. C¯(x) = C(x) / x = (210 + 2x)/x = 210/x + 2
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A team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use? A. A one-sample t-interval for a sample mean B. A one-sample t-interval for a population mean C. A one-sample z-interval for a population proportion D. A two-sample t-interval for a difference between means E. A two-sample z-interval for a difference between proportions
Answers
The correct inference procedure for the ecologists to use is A. A one-sample t-interval for a sample mean.
This is because they are trying to estimate the average number of eggs per nest for all robins in the region, so they will need to use a one-sample t-interval for a sample mean to draw inferences about the population.
Ecologists will choose a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. The correct inference procedure for the ecologists to use is A. A one-sample t-interval for a sample mean.
What is a t-interval for a sample mean?A t-interval for a sample mean is a type of confidence interval that estimates the unknown population parameter, μ, based on the data in a random sample. The t-distribution is used to estimate the population parameter because the population standard deviation is not known.
The following is an illustration of the method of calculating a confidence interval for the mean using a t-distribution:If a sample of n observations is drawn from a normal population, the mean x of the sample is normally distributed with the following properties:Mean: μx = μ.Standard deviation: σx = σ/√n.
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can sombody help me
Simplify. (4k2−12)−(6k2−3k−10)
Answers
Answer:
n
Step-by-step explanation:
n
Answer: -2k^2+3k-2
Step-by-step explanation:
distribute
add
combine like terms
rearrange
adult men have an average height of 69.0 inches with a standard deviation of 2.8 inches. find the height of a man with a z-score of . round your answer to one decimal place.
Answers
The height of a man with a z-score of 0 is 69 inches.
The average height of adult men = 69.0 inches, Standard deviation of adult men = 2.8 inches to find the Z-score the following formula is used:
z = (x- μ)/σ where z is the z-score, x is the value to be standardized, μ is mean and σ is the standard deviation.
To find the height of a man with a z-score of Standardized value(z) = 0
z = (x - μ)/σ
0 = (x - 69)/2.8
x = 69 + 0 (2.8)
x = 69 inches.
Therefore, the height of a man with a z-score of 0 is 69 inches.
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a probability density function, or pdf, tells you how likely a sampled random variable is to occur with a certain value. for the chi-squared distribution, the pdf is
Answers
The probability density function (PDF) of a chi-squared distribution is used to describe the probability of a certain outcome occurring when a continuous random variable is sampled. The PDF is a mathematical formula that gives the probability of a given value of the random variable, x, occurring. It is typically expressed as f(x).
The chi-squared distribution is a type of continuous probability distribution that is used to describe the sum of the squares of multiple normally distributed random variables. Its PDF is represented as:
f(x) = 1/2k/2π-1/2 * xk/2-1 * e-x/2
Where x is the value of the chi-squared random variable and k is the number of degrees of freedom.
The PDF of the chi-squared distribution is used to calculate the probability of a particular outcome. It is used in hypothesis testing to determine the probability that a given set of data fits a certain distribution. It is also used to estimate the confidence intervals of parameters in various models.
The chi-squared distribution is widely used in statistical applications, such as testing for goodness of fit, tests for independence, tests for homogeneity, and tests for normality. It is also used in the analysis of variance, analysis of covariance, regression analysis, and other advanced statistical techniques.
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in the past year, 13% of businesses have eliminated jobs. if 5 businesses are selected at random, find the probability that at least 3 have eliminated jobs during the last year. round your answer to at least three decimal places. do not round your intermediate calculations.
Answers
The probability that at least 3 out of 5 businesses have eliminated jobs in the past year is 0.0556.
To find the probability that at least 3 out of 5 businesses have eliminated jobs, we can use the binomial probability formula:
P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)
where X is the number of businesses out of 5 that have eliminated jobs, and P(X = k) is the probability of exactly k businesses out of 5 eliminating jobs.
Using the binomial probability formula, we can calculate the probabilities for each possible value of X:
P(X = 3) = (5 choose 3) x (0.13)³ x (0.87)² = 0.0519
P(X = 4) = (5 choose 4) x (0.13)⁴ x (0.87)¹ = 0.0036
P(X = 5) = (5 choose 5) x (0.13)⁵ x (0.87)⁰ = 0.0001
where (n choose k) represents the number of ways to choose k items from a set of n items, and can be calculated using the formula:
(n choose k) = n! / (k! * (n - k)!)
where n! represents the factorial of n.
Now we can add up these probabilities to get the probability of at least 3 out of 5 businesses having eliminated jobs:
P(X >= 3) = 0.0519 + 0.0036 + 0.0001 = 0.0556
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Brainly what is the volume of a cylinder with a base radius 3 and height 6
Answers
Answer:
about 169.65
Step-by-step explanation:
The formula for the volume of a cylinder is [tex]\pi r^2h[/tex].
All you have to do is plug the numbers in.
[tex]V=\pi (3)^2(6)[/tex]
Then use a calculator to evaluate.
The volume of the cylinder is approximately 169.56 cubic units.
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius of the base, and h is the height.
Substituting the given values, we get:
V = π(3)^2(6)
V = π(9)(6)
V = 54π
Therefore, the volume of the cylinder is 54π cubic units. If you need an approximate numerical value, you can use the approximation 3.14 for π and calculate:
V ≈ 54 x 3.14
V ≈ 169.56
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The correct question is :
What is the volume of a cylinder with a base radius of 3 units and height of 6 units?
if you have to choose a complete meal from one of 3 meats, one of 4 vegetables, and one of 7 desserts, how many different choices are there? question 17 options:
Answers
3 meats x 4 vegetables x 7 desserts = 84 choices.
There are 84 different choices for a complete meal from the given options. To calculate this, use the formula: number of choices
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what is the measure of angle 1 in degrees?
Answers
Answer:
39°
Step-by-step explanation:
angles are alternate exterior angles making them congruent
for example:
The prices of petrol in a British and an American
petrol station are shown below.
The conversion rate is $1 = £0.80
What is the price of 1 litre of petrol in the cheaper
petrol station?
Give your answer in pounds (£).
British petrol station
£13.20 for 12 litres
of petrol
American petrol station
$17 for 20 litres
of petrol
Answers
The price of 1 liter of petrol at the cheaper petrol station is £0.68.
What is the conversion rate?
Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. Your conversion rate would be 5%, for instance, if you had 50 conversions out of 1,000 interactions, as 50 divided by 1,000 equals 5%.
Here, we have
Given: The prices of petrol in a British and an American petrol station are shown below. The conversion rate is $1 = £0.80.
We have to find the price of 1 liter of petrol in the cheaper petrol station.
$1 = £0.80
= £13.20×($1/£0.80)
= $16.5
For British petrol station
12 liter of petrol = $16.5
1 liter = $16.5/12
1 liter = $1.375
For American petrol station
20 liters of petrol = $17
1 liter = $17/20
1 liter = $0.85
The price of cheaper petrol from American petrol stations = $0.85× (£0.80/$1)
= £0.68
Hence, the price of 1 liter of petrol at the cheaper petrol station is £0.68.
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QUIZ:
Square Roots and Cube Roots to Solve Equations
Question
The volume of a cube can be found using the equation V = s³, where V is the volume and s is the measure of one side of the cube.
Match the equation for how to solve for the side length of a cube to its description.
Drag the equation to the box to match the description.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A cube has a volume of 2560 in³.
Answers
Answer:
Step-by-step explanation:
2560
Which equation can be used to find x, the measure of angle M in AAMP?
A = 180 +95 + 54
B x = 180 - 95 + 54
C x = 180- 149
D x = (95 +54) - 180
Answers
the correct equation to find x, the measure of angle M in AAMP is: [tex]x = 149[/tex]. Thus, option C is correct.
What is the equation for measure of angle?To find the value of x, we need to know the angles of triangle AMP.
Assuming that AAMP is a quadrilateral, we know that the sum of its angles is [tex]360[/tex] degrees.
Thus, we can write:
Angle AMP + Angle M + Angle A [tex]= 360[/tex]
We know that Angle AMP is [tex]180 - 95 - 54 = 31[/tex] degrees (since the sum of the angles in triangle AMB is 180 degrees, and we are given that Angle BAM = 95 degrees and Angle ABM = 54 degrees).
Substituting this value and the given value of Angle A (which is 180 degrees) into the equation above, we can solve for Angle M:
[tex]31 + Angle M + 180 = 360[/tex]
Angle [tex]M = 149[/tex] degrees
Therefore, the correct equation to find x, the measure of angle M in AAMP is: [tex]x = 149[/tex]
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a bag contains a collection of distinguishable marbles. the bag has two red marbles, four green ones, one lavender one, six yellows, and five orange marbles. hint [see example 7.] how many sets of four marbles include exactly two green marbles? (note that this means there must be two other non-green marbles as well).
Answers
Therefore, the total number of sets of four marbles, including exactly two green marbles, is 720.
The given bag contains a total of [tex](2+4+1+6+5)=18[/tex] marbles.
There are two possibilities of selecting two green marbles and the other two marbles in a set, as shown below;GG -- NN (No Green Marbles)GG -- RR (No Green Marbles)GG -- YY (No Green Marbles)GG -- OO (No Green Marbles)GG -- GL (Lavender)GG -- RG (Red)GG -- OG (Orange)
The first two options have no green marbles; thus, they are eliminated. We can select non-green marbles in C(16,2) = 120 ways, then multiply by C(4,2) = 6 to choose two green marbles out of four.So, the total number of such sets is
[tex]120 × 6 = <<120*6=720>>720.[/tex]
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Each yoga mat measures 2.2 ft by 6.3 ft. What is the area in square feet of each yoga mat?
Answers
2.2 x 6.3 = 13.86 square feet
i really dont understand this please help me out
Answers
Answer: D
Step-by-step explanation: It is going up in a strait trend line, making it where it has no relation ship unless very closely examined.