Answer:
25
Step-by-step explanation:
The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.
The graph shows f of x equals x squared minus 3, which is an upward-opening parabola with a vertex at 0 commas negative 3 and a point at negative 1 comma negative 2, and a point at 1 comma negative 2. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 commas 2 and a point at negative 1 comma 1, and a point at 1 comma 1.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y ≤ x^2 – 3
y > –x^2 + 2
The solution set to the given system of inequalities is represented by the shaded region under the curve of f(x) = x^2 – 3 (including the points on the curve) and above the curve of g(x) = –x^2 + 2 (excluding the points on the curve). The overlapping region between these shaded areas represents the solution set to the system.
To graph the solution set to the system of inequalities y ≤ x^2 – 3 and y > –x^2 + 2, we can modify the graphs of f(x) = x^2 – 3 and g(x) = –x^2 + 2 accordingly. Here's how:
For the inequality y ≤ x^2 – 3:
The original graph of f(x) = x^2 – 3 is an upward-opening parabola with a vertex at (0, -3).
To graph y ≤ x^2 – 3, we need to shade the region below or on the parabola. This includes all points on the parabola itself.
Therefore, we shade the area under the curve of the original graph of f(x) and include the points on the curve.
For the inequality y > –x^2 + 2:
The original graph of g(x) = –x^2 + 2 is a downward-opening parabola with a vertex at (0, 2).
To graph y > –x^2 + 2, we need to shade the region above the parabola. This excludes all points on the parabola itself.
Therefore, we shade the area above the curve of the original graph of g(x) but exclude the points on the curve.
By modifying the graphs of f(x) and g(x) according to these shading instructions, we can graphically represent the solution set to the system of inequalities.
The solution set can be identified by observing the overlapping region or the intersection between the shaded area under the curve of f(x) and the shaded area above the curve of g(x). The points within this overlapping region satisfy both inequalities simultaneously.
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Two sides of a right triangle have lengths of 78 inches and 30 inches. The third side is not the hypotenuse. How long is the third side ?
Answer:
the answer is 72 inches
Step-by-step explanation:
a²+b²=c²
a²+900=6084
a²=5184
a=72
Find the percent of change. Round to the nearest tenth of a percent if necessary.
1/4 to 1/2
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Answer:
100%
Step-by-step explanation:
The percentage change can be computed from ...
pct change = ((new value)/(old value) -1) × 100%
= ((1/2)/(1/4) -1) × 100%
= (2 -1) × 100%
= 100%
The increase by 1/4 from 1/4 to 1/2 is an increase of 100%.
Max used a base ten blocks to solve the division problem 9.15 divided by 3.
Which set of blocks shows the quotient for 9.15 divided by3?
A. 3 Ones,5 Tenths,0 Hundredths
B. 5 ones, 0 tenths, 3 hundredths
C. 0 ones, 3 tenths, hundredths
D 3 ones, 0 tenths, 5 hundredths
Answer:
D 3 ones, 0 tenths, 5 hundredths
Step-by-step explanation:
9.15 divided by 3.
915/3 = 305
Then, moving the decimal point two units to the left, we have 3.05.
The last number before the decimal point is called ones, which means that we have 3 ones.
The first number after the decimal point is called tenths, which means that we have 0 tenths.
The second number after the decimal point is called hundredths, which means that we have 5 hundredths.
The correct answer is given by option D.
A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Let x represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket.
Help on this one please
Answer:
74.2
Step-by-step explanation:
First think of a whole circle. The area of a circle is pi*r^2., which is 81 pi. Then the fraction of the circle is 105/360. Times this by 81 pi and you get about 74.2 and that is the answer.
By the way, can you follow me? Thanks!
The area of a rectangle is 56 square inches the rectangle is 8 inches long how wide is the retangle
Answer:
7 inches
Step-by-step explanation:
56/8=7
Area/length=width
The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.05x2 − 7x + 300
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
0.6 899.58
0.8 899.52
1 899.50
1.2 899.52
1.4 899.58
Based on the given information, determine which company has a lower minimum and find the minimum value.
f(x) at (1, 899.50)
g(x) at (70, 55)
f(x) at (70, 55)
g(x) at (1, 899.50)
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Answer:
(c) f(x) at (70, 55)
Step-by-step explanation:
The point (70, 55) is not on g(x), which increases from a minimum of 899.5. Obviously, 55 is less than 899.5, so f(x) at (70, 55) has a lower minimum.
Answer:
f(x) at (70, 55)
Step-by-step explanation:
I got it right on the test
D. If the scale factor for the dilation of the figure is 0.9, then the dilation is an enlargement
Answer:
Option C.
Step-by-step explanation:
Suppose that we have a point (x, y)
If we do a dilation with a center in the origin of scale factor K, then the new coordinates of our point will be:
(k*x, k*y)
If k > 1, we have an elargement.
if 0 < k < 1, we have the opposite case.
Now, suppose that one random vertex of the preimage is A (a, b)
Then after we do the dilation, the new coordinate of this vertex will be:
A' = (k*a, k*b) (this is, the original coordinates multiplied by the scale factor)
And this will happen for all points actually, so particularly the corresponding coordinates of the vertices of the image are the vertices of the preimage multiplied by the scale factor.
Then the correct option is C
What is the equation of the circle shown in the graph?
6 9 12 36
Which is a greater fraction 2/5 or 1
1 is greater that 2/5
1>2/5
Answer:
1 is a whole number (an integer) and 2/5 is a proper fraction
find he prodct
4(-2)
Answer:
-8
Step-by-step explanation:
four times two equals eight, positive times negative equals negative, so -8
Answer:
-8
Step-by-step explanation:
4(-2)=4×(-2)=-8 I Know The Answer Is Correct I Am Sure.
A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a medical examination during the past year. An interval estimate of the proportion p with a margin of error of 0.06 0.06 and 99% 99 % confidence is required.
Answer:
The minimum sample size required is 461.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
An interval estimate of the proportion p with a margin of error of 0.06. What is the minimum sample size required?
The minimum sample size required is n, which is found when M = 0.06.
We don't have an estimate for the true proportion, which means that we use [tex]\pi = 0.5[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.06 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.06\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.06}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.06})^2[/tex]
[tex]n = 460.5[/tex]
Rounding up
The minimum sample size required is 461.
Marking as brainiest
Each student in a class recorded how many books they read during the
summer. Here is a box plot that summarizes their data. What is the Range
of the data?
. 8
10 1 18
number of books
Your answer
This is a required question
Need answer please !!
the volume of a solid triangular prism is 726 cubic centimeters. its height is 12 centimeters and its bases are congruent right isosceles triangles. find the lengths of the equal sides of each base.
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Answer:
11 cm
Step-by-step explanation:
The volume of the prism is given by the formula ...
V = Bh
where B is the area of the triangular base, and h is the height.
Filling in the given information, we find the area of the triangular base to be ...
726 cm³ = B(12 cm)
B = 726 cm³/(12 cm) = 60.5 cm²
The area of an isosceles right triangle is half the area of a square with the same side lengths:
B = 1/2s²
60.5 = 1/2s²
s = √(2(60.5)) = √121 = 11
The length of each of the equal sides of the base is 11 cm.
What is the area of a rectangle whose length is 4 2/3 cm and width is 8 cm?
Answer: 37 1/3 cm
Step-by-step explanation:
Area = Length times width
4 2/3 times 8 = 37 1/3
You want to install a 3 yd wide walk around a circular swimming pool. The diameter of the pool is 16 yd. What is
the area of the walk? Use 3.14 for it.
The area of the walk is approximately
What is the mode of the set of data points given below? 1 15 12 6 12 9 12 3 6 12 15 9 15 12 15
Answer:
the mode is 12
Step-by-step explanation:
Arrange the numbers in order : 1 , 3, 6, 6, 9, 9, 12, 12, 12, 12, 12, 15, 15, 15, 15
Then count how many numbers that appears the most, so the number that appears the most is 12, therefore, the mode in the data set is 12 .
Decide if each statement about the expression 7t + 15-23 is true or false?
Answer:
7t -8 true
Step-by-step explanation:
whos ur celeb crush I need to know mines is the actor of wanda
Answer:
Same!!!!!!!!!!!
Step-by-step explanation:
Answer:
mines Matthew Mercer i dont know if he counts as a celeb cuz he is a famous voice actor
An online furniture store sells chairs for $150 each and tables for $450 each. Every day, the store can ship a maximum of 16 pieces of furniture and must sell at least $3900 worth of chairs and tables. If xx represents the number of tables sold and yy represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
Required inequalities:
x + y ≤ 16150x + 450y ≥ 3900The graph is attached.
The darker triangle is the solution region.
The solution examples:
(1, 15), (4,12), (5, 10), (11, 5)The first number is chairs, the second number is tablesQuadrilateral WXYZ has a length of five, six, seven, and eight. A new quadrilateral is created, using a scale factor of 1.2. Which of the following are stylings of the new quadrilateral?
Choose all that apply:
10
8.4
9.6
6
7.2
5
PLEASE HELP I Got 5 minutes
Answer:
10
8.4
5
Step-by-step explanation:
Help me please ASAP I need help
Answer:
Are you looking for the perimeter? if so it would be 34 yards
Step-by-step explanation:
Which of the following is the radical expression of2 times d to the seven tenths power? (2 points)
a
seventh root of 2 d to the tenth power
b
tenth root of 2 d to the seventh power
c
2 times the tenth root of d to the seventh power
d
2 times the seventh root of d to the tenth power
Direct mail advisors send notifications to thousands of potential customers in the hope that summer by the company's product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and send it to 1060 people randomly selected from their mailing list of over 200,000 people. They get orders from 110 of those people.
A) Create a confidence interval for the percentage of people to company contracts
who may buy something
Create a 90% confidence interval for the percentage of people the company contacts who may buy something.
Answer:
CI = (8.84%, 11.92%)
We are 90% Confident that the percentage of people the company contacts who may buy something is between 8.84% and 11.92%.
Step-by-step explanation:
We are given;
n = 1060
x = 110
Confidence level = 90%
Sample proportion; p^ = x/n = 110/1060
p^ = 0.1038
DF = n - 1 = 1060 - 1 = 1059
From the table attached, the critical value for a confidence level of 90% at a DF greater than 1000 is 1.645
Formula for CI is;
CI = p^ ± t√(p^(1 - p^)/n)
CI = 0.1038 ± 1.645√(0.1038(1 - 0.1038)/1060)
CI = 0.1038 ± 0.0154
CI = (0.0884, 0.1192) or
CI = (8.84%, 11.92%)
Thus, we are 90% Confident that the percentage of people the company contacts who may buy something is between 8.84% and 11.92%.
Can you answer (a,b)?
Answer:
a) 11.283 dollars
b) 1.435 hour
Step-by-step explanation:
1 kilo watt of electricity used for 1 hour
Charges of electricity per unit = $0.05224
Laura uses 5 heaters to warm her house. The electricity consumed by each use 1800 wats or 1.8 kilo wats
a) Charges in one day = 5 heaters * 1.8 kilo wats per hour * 24 hour* $0.05224 per kilowats per hour
= 11.283 dollars
b) 75 wat light bulb consumes 0.075 kilo wats per hour
Charge per kilowat per hour = $0.05224
In order to cost 1 $, the 75 wat bulb need to be on for 1.435 hour
draw the graph of the equation:
x+6y=0
please annotate a graph or say the coordinates (for ex: (0, 6))
Answer:
Step-by-step explanation:
NEED HELP ASAP WILL GIVE BRAINLIEST REAL ANSWERS ONLY PLZ REPORT LINKS OR PEOPLE ANSWERING FOR POINTS
Answer:
B
Step-by-step explanation:
Trust
Question 4
1p
Given the chart below, calculate the number of days one
could expect to have off due to hurricanes. Round to the nearest
day (enter your answer as a number only, you don't need to write "days" at the
end)
Number of Hurricane Days Each School Year
1
2
3
4
0
5
6
7
Days:
Chances of
having that
many days oft:
03
02
0.25
0.2
0.02
0.01
0.01
0.01
Answer:
2
Step-by-step explanation:
Given
See attachment for chart
Required
Number of off days
To do this, we simply calculate the expected value of the chart.
This is calculated as:
[tex]E(x) = \sum x * f[/tex]
Where
x = days
f = chances
So, we have:
[tex]E(x) = 0* 0.3 + 1 *0.2 + 2 * 0.25 + 3 * 0.2 + 4 * 0.02 + 5 * 0.01 + 6 * 0.01 + 7 * 0.01[/tex]
[tex]E(x) = 1.56[/tex]
[tex]E(x) \approx 2[/tex]