The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.
How to interpret the equation of the parabola?To obtain the graph of a quadratic function, these three features have to be obtained from the function's definition:
- The x-intercepts, which are the roots of the function.
- The y-intercept, which is the value of y when the function crosses the y-axis.
- The vertex, which is the turning point of the function.
- The function for this problem is defined as follows:
y = 1.5x² + 4x - 2.
Hence the numeric values of the coefficients are listed as follows:
a = 1.5, b = 4, c = -2.
Inserting these coefficients into a calculator, the x-intercepts of the function are given as follows:
x = -3.09 -> hence the function passes through point (-3.09, 0).
x = 0.43 -> hence the function passes through point (0.43, 0).
The y-intercept of the function is given by coefficient c = -2, hence the function also passes through point (0, -2).
The x-coordinate of the vertex is given as follows:
x = -b/2a = -4/3 = -1.33.
Hence the y-coordinate of the vertex is:
y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.
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Missing Information
The problem asks for the graph of the following function:
y = 1.5x² + 4x - 2.
Yesterday, between noon and midnight, the temperature dropped by 28.4°F. If the temperature was -1.9°F at midnight, what was it at noon?
Answer:
n= 26.5
Step-by-step explanation:
Comment
You need some sort of formula for this question. But you more or less have to invent it.
Formula
Temperature midnight = noon - temperature drop
Givens
temperature drop = 28.4
temperature midnight = -1.9
Temperature noon = x
Solution
-1.9 = x - 28.4 Add 28.4 to both sides
-1.9 + 28.4 = x-28.4+28.4 Combine
Answer
26.5 = x
The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?
Click pic to see whole problem
Answer:
Step-by-step explanation:
Solving systems of equations gives the points of intersection when the equations are graphed.
The answer is 3.
The tyre of a car wheel has an outer diameter of 30 cm . How many times will the wheel rotate on a journey of 5 km
Answer:
5305.1647 times
Step-by-step explanation:
The Circumference of a circle : πd
d = diameter of circle = 30 cm
Circumference of wheel = π * 30cm = 94.247779 cm
1km to cm
1km = 100000cm
5 km = 500000 cm
Hence, number of times wheel rotate on a 5km journey :
500000 cm / 94.247779 cm
= 5305.1647 times
a car has a initial velocity of 20 ms-1 for the first 4 second of its motion it accelerates at 2.5ms-2. for the next t seconds it travels at a constant velocity if vms-1 the car then decelerates to rest. find v
The velocity, vms-1 has a numerical value of 30 m/s from the information provided in the question.
Now we have to use the formula;
v = u + at
Where;
v = final velocity
u = initial velocity
a = acceleration
t = time taken
Given that;
v = ?
u = 20 ms-1
t = 4 s
a = 2.5ms-2
If we substitute the values;
v = 20 ms-1 + (2.5ms-2 × 4 s)
v = 30 m/s
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The constant velocity (V) of the car as it decelerates to rest is 2.222 m/s.
Given the following data:
Initial velocity = 20 m/sInitial time = 4 secondsAcceleration = 2.5 \(m/s^2\)Total time = 40 secondsTo determine the constant velocity (V) of the car:
First of all, we would calculate the distance traveled by the car within the first 4 seconds of its motion by using the second equation of motion;
\(S = ut + \frac{1}{2} at^2\\\\S=20(4)+\frac{1}{2} \times 2.5 \times 4^2\\\\S=80+20\)
S = 100 meters.
Next, we would calculate the distance traveled after the first 4 seconds of its motion by using the third equation of motion;
Note: Final velocity is equal to zero since the car decelerated to rest.
\(V^2 =u^2 -2aS\\\\0^2 =20^2-2(2.5)S\\\\5S=400\\\\S=\frac{400}{5}\)
S = 80 meters.
Now, we can find the constant velocity (V) of the car:
Time = \(40-4=\) 36 seconds.
\(Velocity = \frac{distance }{time} \\\\Velocity = \frac{80 }{36}\)
Velocity = 2.222 m/s
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The purchased cost of a 5-m3 stainless steel tank in 1995 was $10,900. The 2-m-diameter tank is cylindrical with a flat top and bottom. If the entire outer surface of the tank is to be covered with 0.05-m-thickness of magnesia block, estimate the current total cost for the installed and insulated tank. The 1995 cost for the 0.05-m-thick magnesia block was $40 per square meter while the labor for installing the insulation was $95 per square meter.
The estimated current total cost for the installed and insulated tank is $12,065.73.
The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:
surface_area = 2 * pi * r * h + 2 * pi * r^2
where:
r is the radius of the cylinder
h is the height of the cylinder
In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:
surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586
The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:
surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293
The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:
cost = 6.806032934459293 * (40 + 95) = $1,165.73
The original cost of the tank was $10,900, so the total cost of the insulated tank is:
cost = 10900 + 1165.73 = $12,065.73
Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.
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During the first 100 days, the school book store sold a total of 1,344
pennants. There were 384 pennants left unsold. How many pennants did the
book store have at the beginning of the school year?
Answer:
1,728
Step-by-step explanation:
a tomato has a mass of 100 grams the mass of the ant is 4.0x10x^{3} gram the of the tomato is how much greater than the mass of the ant
Note that if a tomato has a mass of 100 grams and the mass of the ant is 4.0x10⁻³gram, then the mass of the tomato is 25,000 times greater than the mass of the ant.
What is the justification for the above result?The expression for finding the extent to which the Mass of the tomato is greater than that of the ant is given as follows:
100/4.0x10⁻³
= [100 x 10³] / 4.0x10⁻³ x 10³
= 100,000/4
= 25,000
Therefore, the tomato is 25,000 times the mass of the ant.
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Answer:yes 2.5* 10-2
Step-by-step explanation:
Help? I will give brain list + 5 star rating and like on the profile
Answer:
7. Jamal and Steve finished the same amount of homework
8. 8/12 and 4/6
Hope this helps =]
solve and check each equation below
2x+50=3x
Answer:
x=50
Step-by-step explanation:
for x = 50, the equation 2x + 50 = 3x holds true
What is an equation?
An equation is a statement indicating that the values of two mathematical expressions are equal (indicated by the sign =). For example -
2x + 3 = 5
ax + c = 9
Given is the following equation to solve -
2x + 50 = 3x
We have -
2x + 50 = 3x
On solving for [x], we can write -
3x - 2x = 50
x = 50
Therefore, for x = 50, the equation 2x + 50 = 3x holds true.
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What is the shape of the base of a pentagonal right prism?
A. octagon
B. hexagon
C. pentagon
D. rectangle
Answer:c
Step-by-step explanation:
Answer:
C) Pentagon
Step-by-step explanation:
Find x:
(Round the answer to the nearest tenth if there is a decimal)
Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)
Use tangent:
tan x = 8/15
x = arctan (8/15)
x = 28.1° (rounded)
Step-by-step explanation:
the area of a square garage is 121 square feet. will it fit a car that measures 13 feet long? explain
Answer:
It won't because the area is length times height. So 11 x 11. So some of the car will be hanging out of the garage.
Step-by-step explanation:
The table shows the total distance that Myra runs over different time periods.
A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0.0, 0.4, 0.8, 1.2, 1.6.
Distance is increasing with a speed of 0.2 Miles/Min
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Time in Minutes Distance in Miles
0 0.0
2 0.4
4 0.8
6 1.2
8 1.6
Here, Myra’s distance is increasing as time increase with a constant Speed.
Now, In every 2 mins distance traveled = 0.4 Miles
Hence, In every 1 min Distance traveled = 0.4/2 = 0.2 Miles/Min
Thus, Distance is increasing with a speed of 0.2 Miles/Min.
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If you start with the equation x-6, what equation do you have when you add 3 to both sides
develop a plot of the residuals against the independent variable x. do the assumptions about the error terms seem to be satisfied? the plot suggests a generally horizontal band of residual points indicating that the error term assumptions are not satisfied. the plot suggests curvature in the residuals indicating that the error term assumptions are not satisfied. the plot suggests a generally horizontal band of residual points indicating that the error term assumptions are satisfied. the plot suggests a funnel pattern in the residuals indicating that the error term assumptions are not satisfied. the plot suggests curvature in the residuals indicating that the error term assumptions are satisfied.
To develop a plot of the residuals against the independent variable x, you would first calculate the residuals by subtracting the predicted values from the actual values of the dependent variable.
Then, you would plot the residuals on the y-axis and the independent variable x on the x-axis.
If the plot suggests a generally horizontal band of residual points, this indicates that the error term assumptions are not satisfied. This is because a horizontal band suggests that the variance of the residuals is constant across all values of x, which violates the assumption of homoscedasticity (equal variance of the error terms).
If the plot suggests curvature in the residuals, this also indicates that the error term assumptions are not satisfied. This is because curvature suggests that the variance of the residuals changes across different values of x, violating the assumption of homoscedasticity.
If the plot suggests a funnel pattern in the residuals, this also indicates that the error term assumptions are not satisfied. This is because a funnel pattern suggests that the variance of the residuals increases or decreases as the values of x increase, violating the assumption of homoscedasticity.
However, if the plot suggests a generally horizontal band of residual points and there is no curvature or funnel pattern, this indicates that the error term assumptions are satisfied. It is important to assess the plot of residuals against the independent variable x to ensure that the error term assumptions are met and the results of the analysis are valid.
To develop a plot of the residuals against the independent variable x and evaluate whether the error term assumptions are satisfied, follow these steps:
1. Collect the data for the independent variable x and the corresponding residuals.
2. Create a scatter plot with the independent variable x on the x-axis and the residuals on the y-axis.
3. Analyze the plot to identify any patterns or trends.
Based on your provided descriptions, the following conclusions can be drawn:
a) If the plot suggests a generally horizontal band of residual points, this indicates that the error term assumptions are satisfied, as it shows that the errors are randomly distributed and have constant variance.
b) If the plot suggests curvature in the residuals or a funnel pattern, this indicates that the error term assumptions are not satisfied. These patterns may suggest nonlinearity, heteroskedasticity, or other issues with the underlying model, which violate the assumptions of constant variance and independence of errors.
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I NEED HELP RIGHT NOW ! PLEASE HURRY UP ASAP
Answer:
D.
Step-by-step explanation:
Using a Table to Multiply Multivariable Polynomials What is the product of 6x – y and 2x – y + 2? 8x2 – 4xy + 12x + y2 – 2y 12x2 – 8xy + 12x + y2 – 2y 8x2 + 4xy + 4x + y2 – 2y 12x2 + 8xy + 4x + y2 + 2y
Answer: B.
\(12x^{2}\) \(-8xy + 12x + y^2 - 2y\)
Step-by-step explanation:
i just took the assignment
I need help with the bottom part I know the top parr
A probability that can be deducted through logical reasoning before an experiment is performed is what type of probability?"
A probability that can be deducted through logical reasoning before an experiment is performed is Theoretical probability.
What is Theoretical probability?Theoretical probability is based on what is expected to happen, or a theory, using reasoning. It is based on knowledge and mathematics. An experiment is not conducted to find theoretical probability.
How to calculate Theoretical probability?The formula to calculate the theoretical probability of event A happening is:
P(A) = number of desired outcomes / total number of possible outcomes
For example, the theoretical probability that a dice lands on “2” after one roll can be calculated as:
P(land on 2) = (only one way the dice can land on 2) / (six possible sides the dice can land on) = 1/6
Thus, A probability that can be deducted through logical reasoning before an experiment is performed is Theoretical probability.
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c) For any set S of propositional sentences and any propositional sen- tence A, a maximal subset of S that doesn't entail A is any set X of propositional sentences that satisfies all the following three conditions: 1. X CS 2. X# A 3. For any Y CS: if X C Y and Y & X then Y EA Let p, q, r, s be propositional variables and let Si = {-r, s, ((-- Vq) + p),q}. Write down all the maximal subsets of Sį that don't entail p. Justify your answer using truth-tables or otherwise. [6]
The maximal subsets of Si that don't entail p are {-r}, {s}, and {-r, s}.
How to find the maximal subsets of Sį that don't entail p.To determine the maximal subsets of Si that don't entail p, we need to check each subset of Si and see if it satisfies the three conditions given.
Let's analyze each subset of Si and check if it satisfies the conditions:
Subset 1: {-r}
This subset satisfies all the conditions since it is a subset of Si, does not contain p, and for any other subset Y that contains this subset, Y does not entail p. Therefore, {-r} is a maximal subset that doesn't entail p.
Subset 2: {s}
This subset satisfies all the conditions since it is a subset of Si, does not contain p, and for any other subset Y that contains this subset, Y does not entail p. Therefore, {s} is a maximal subset that doesn't entail p.
Subset 3: {-r, s}
This subset satisfies all the conditions since it is a subset of Si, does not contain p, and for any other subset Y that contains this subset, Y does not entail p. Therefore, {-r, s} is a maximal subset that doesn't entail p.
Subset 4: {-r, ((-- Vq) + p)}
This subset satisfies condition 1 and 2, but it does not satisfy condition 3. If we consider the subset {((-- Vq) + p)}, it contains Subset 4, but it does entail p. Therefore, Subset 4 is not a maximal subset that doesn't entail p.
Subset 5: {-r, q}
This subset satisfies condition 1 and 2, but it does not satisfy condition 3. If we consider the subset {q}, it contains Subset 5, but it does entail p. Therefore, Subset 5 is not a maximal subset that doesn't entail p.
Subset 6: {s, ((-- Vq) + p)}
This subset satisfies condition 1 and 2, but it does not satisfy condition 3. If we consider the subset {((-- Vq) + p)}, it contains Subset 6, but it does entail p. Therefore, Subset 6 is not a maximal subset that doesn't entail p.
Therefore, the maximal subsets of Si that don't entail p are {-r}, {s}, and {-r, s}.
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please help me answer this question
thanks
Answer:
-10,-6,-4,3,7
Step-by-step explanation:
This is because -10 is less than -6,-6 is less than -4,-4 is less than 3 and followed by 7 and vice versa for descending other
Slope of a line with one point at (2,1) and another at (5,3)
Answer:
Step by step in image below. Hope this helps
Step-by-step explanation:
Determine whether the improper integral \( \int_{0}^{2} x^{2} \ln x d x \) is convergent or divergent.
The improper integral \(\int_{0}^{2} x^{2} \ln x d x\) is convergent.
The given integral is as follows:
\($$\int_{0}^{2} x^{2}\ln x dx$$\)
In order to determine whether the improper integral is convergent or divergent, we use integration by parts and calculate the following:
\($$\int_{0}^{2} x^{2}\ln x dx = \lim_{t \rightarrow 0} \int_{t}^{2} x^{2} \ln x dx$$\\$$= \lim_{t \rightarrow 0} \Biggl(\left[x^{2}\cdot\frac{\ln x}{3}\right]_{t}^{2/3}-\frac{2}{3}\int_{t}^{2/3}x\ln x dx\Biggr)+\int_{2/3}^{2} x^{2} \ln x dx$$\\$$= \lim_{t \rightarrow 0} \Biggl(\frac{4}{9}(\ln2-2\ln3)-\frac{2}{3}\int_{t}^{2/3}x\ln x dx\Biggr)+\int_{2/3}^{2} x^{2} \ln x dx$$\)
Now, we have to determine the value of $$\int_{0}^{2/3} x\ln x dx$$
We use integration by parts here as well:
\($$\int_{0}^{2/3} x\ln x dx = \left[\frac{x^{2}}{2}\ln x \right]_{0}^{2/3} - \int_{0}^{2/3} \frac{x}{2} dx$$\\$$=-\frac{1}{4}\cdot\frac{8}{27}\\=-\frac{1}{27}$$\)
Putting this value back into the initial integral equation, we get:
\($$\int_{0}^{2} x^{2}\ln x dx = \frac{4}{9}(\ln2-2\ln3)-\frac{2}{3}\cdot\frac{-1}{27}+\int_{2/3}^{2} x^{2} \ln x dx$$\\$$= \frac{4}{9}(\ln2-2\ln3)+\frac{2}{81}+\int_{2/3}^{2} x^{2} \ln x dx$$\)
Since the integral on the right side of the equation is finite, the improper integral is convergent.
Answer: Therefore, the improper integral\(\(\int_{0}^{2} x^{2} \ln x d x\)\) is convergent.
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The integral is convergent. Thus, the value of the improper integral is:\[\int_{0}^{2} x^2\ln x \; dx = \frac{8}{3}\ln 2 - \frac{8}{27}\]
The given integral is given below:
\(\[\int_{0}^{2}x^2\ln x \; dx\]\)
To determine whether the integral is convergent or divergent, we need to apply integration by parts, where:
\(\[u=\ln x\] \[dv=x^2 \; dx\]\[du = \frac{1}{x} \; dx\] \[v = \frac{1}{3} x^3\]\)
By applying the formula of integration by parts, we get:
\(\[\int_{0}^{2} x^2\ln x \; dx = \frac{1}{3} \left[x^3 \ln x\right]_0^2-\frac{1}{3}\int_{0}^{2}x^3\frac{1}{x} \; dx\]\[= \frac{1}{3}\left[2^3 \ln 2\right] - \frac{1}{3} \int_{0}^{2} x^2 \; dx\]\[= \frac{8}{3}\ln 2 - \frac{1}{3} \left[\frac{1}{3} x^3\right]_0^2\]\[= \frac{8}{3}\ln 2 - \frac{8}{27}\]\)
Now, let's determine whether the integral is convergent or divergent. As the integrand is continuous on the interval \([0,2]\), it is integrable on this interval.
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number of boys and girls are in the class are in the ratio of 7 : 5 the number of boys is 8 more than the number of girls what is a total class strength?
Answer:
Step-by-step explanation:
Given ratio of boys and girls in the class =7:5
No of boys is 8more than the girls
So
Let no of boys in the class =7x
No of girls in the class=5x
7x=5x+8
2x=8
X=8/2
X=4.
Total strength =no of boys + no of girls
=7x+5x
=7×4+5×4
= 28+20
=48.
Total strength in the class is 48.
Answer:
Total class strength = 48
Step-by-step explanation:
Boys : Girls = 7 : 5
Number of boys = 7x
Number of girls = 5x
7x - 5x = 8
2x = 8
x = 8/2
x = 4
Total strength = 7x + 5x = 12x = 12*4 = 48
Q1 - Multiplying one equation
Work these simultaneous equations out
on paper and write down your answers.
p
4p + 2q = 28
13p + 69 = 88
9 =
3s + 4t = 31
S =o
88 + 8t = 72
t =
a =
4a + 3b = 45
16a + 4b = 124
b =
5m + 6n = 61
m =
15m + 4n = 99
n =
Answer:
p = 4
q = 6
s = 5
t = 4
a = 6
b = 7
m = 5
n = 6
The sides of the base of a right square pyramid are 10 feet long. The slant height is 15 feet. When the side lengths of the base and the slant height are both multiplied by a factor of 4, by what factor is the surface area multiplied?
The surface area is multiplied by a factor of 16
How to determine the factor of the surface area?The dimensions are given as:
Base = 10 feetSlant height = 15 feetFactor, k = 4The factor of the surface area is calculated as:
Surface area = Factor^2
So, we have:
Surface area = 4^2
Evaluate
Surface area = 16
Hence, the surface area is multiplied by a factor of 16
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16
Step-by-step explanation:
what happens to the mean for a trait in a population during directional selection what is being selected for?
When a population is subjected to directional selection over time, the traits that are selected for will remain stable while the traits that are selected against will disappear.
Evolution is the study of how populations change over time. Most traits have multiple genes controlling their structure, function, appearance, and other characteristics. Single genes only very infrequently control a trait.
As a result, most traits have a tendency to be continuous in nature and to have a wide range of values. One side of these values will be picked against during directional selection, while the other side will be selected in favor of. Look at the illustration of a lemur's fur color below.
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Deborah had 3 1/4 yards of ribbon she used 3/8 of a yard for a project how much ribbon does she have left
Find the total
price of a $14.00
shirt including the
7% sales tax?
Answer:
$14.98
Step-by-step explanation: Literally just use a sales tax calculator...
In Spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how many hours they had exercised in the past 24 hours.For the 39 randomly selected upperclassmen, the sample mean was 0.76 and sample standard deviation was 0.75.For the 35 randomly selected underclassmen, the sample mean was 0.60 and the sample standard deviation was 0.73.What is the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen?
The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.
In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us
0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16
Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.
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