[tex]10 + x^2[/tex] Will be greater than [tex]2^x[/tex]for certain values of x, specifically when x is approximately less than
0.543 and between 4.337 and 5.172.
Set up the inequality: [tex]10 + x^2 > 2^x[/tex]
Since there's no algebraic method to solve this inequality directly, we can analyze it graphically.
Plot the two functions,[tex]y1 = 10 + x^2[/tex] and[tex]y2 = 2^x[/tex], on a graph.
Find the points where the two graphs intersect.
If there's a region where the graph of y_1 is above the graph of y_2, that means [tex]10 + x^2 > 2^x[/tex] in that region.
When analyzing the graphs, you'll find that[tex]10 + x^2 > 2^x[/tex] for x approximately less than 0.543 and x approximately
between 4.337 and 5.172.
In these regions, the inequality holds true.
In conclusion, [tex]10 + x^2[/tex] will be greater than [tex]2^x[/tex] for certain values of x, specifically when x is approximately less than 0.543 and between 4.337 and 5.172.
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I need help with this please
The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.
Since (5/2)^x is always greater than 0 for any x, the minimum value of f(x) is -5.To find the maximum value of f(x), we can take the limit as x approaches infinity:
lim (x → ∞) (5/2)^x - 5 = ∞ - 5 = ∞Therefore, the range of f(x) is (-5, ∞).which model represents the factors of x2 9x 8? an algebra tile configuration. 7 tiles are in the factor 1 spot: 1 is labeled x and 6 are labeled . 4 tiles are in the factor 2 spot: 1 is labeled x and 3 are labeled . 28 tiles are in the product spot: 1 is labeled x squared, 9 are labeled x, 9 are labeled , and 9 are labeled negative.
The product of 7 and 4 is 28, which is equal to the number of tiles in the product area.
Therefore, this configuration represents the factors of the quadratic expression [tex]x^2 + 9x + 8.[/tex]
To represent the factors of the quadratic expression x^2 + 9x + 8 using algebra tiles, we need to arrange the tiles into two rectangular areas representing the two factors, and the total number of tiles in the product area should be equal to the product of the number of tiles in each factor area.
Based on the information given, we can arrange the tiles as follows:
Factor 1 area: 7 tiles, with 1 x-tile and 6 blank tiles (represented by underscores):
Copy code
x
_
_
_
_
_
_
Factor 2 area: 4 tiles, with 1 x-tile and 3 blank tiles (represented by underscores):
Copy code
x
_
_
_
Product area: 28 tiles, with 1 x^2-tile, 9 x-tiles, 9 negative tiles (represented by red tiles), and 9 blank tiles (represented by underscores):
Copy code
x^2 - - -
x x x x
_ _ _ _
_ _ _ _
_ _ _ _
_ _ _ _
_ _ _ _
To check that this configuration represents the given quadratic expression, we can count the number of tiles in each area and verify that the product of the two factors equals the number of tiles in the product area:
Factor 1 area: 7 tiles
Factor 2 area: 4 tiles
Product area: 28 tiles.
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Find the missing pieces and evaluate the trigonometric function.
Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.
Question # 5
Question # 6
Question # 7
Question # 8
Question # 9
Question # 10
Question # 11
Answer: question#7 is 7/12
question#8 is 1 3/8
question#5 is 1/2
question#6 is 12
question#9 is 1 1/6
question#10 is 31/40
question#11 is 3/4
Step-by-step explanation: give brainliest
Question #5: Option A, [tex]\frac{1}{2}[/tex]
Question #6: Option A, 12
Question #7: Option A, [tex]\frac{7}{12}[/tex]
Question #8: Option D, [tex]1\frac{3}{8}[/tex]
Question #9: Option D, [tex]1\frac{1}{6}[/tex]
Question #10: [tex]\frac{31}{40}[/tex]
Question #11: [tex]\frac{3}{4}[/tex]
Pls mark brainliest
the radius of the apple increases 1/8 inch per week for the next five weeks. how does the volume change during the five-week period?
the volume of the apple would increase by ΔVtotal over the five-week period
The volume of the apple is directly proportional to the cube of its radius. Therefore, if the radius increases by 1/8 inch per week for five weeks, the total increase in radius would be 5/8 inches.
To calculate the change in volume, we can use the formula V = (4/3)πr^3.
Initially, let's assume the radius of the apple is r.
After the first week, the radius would be r + 1/8 inches. Therefore, the new volume would be:
[tex]V_1 = (4/3)\pi(r + 1/8)^3[/tex]
To calculate the change in volume, we can subtract the initial volume from the new volume:
[tex]\DeltaV_1 = V_1 - V_0[/tex]
where V0 is the initial volume of the apple.
Similarly, after the second week, the radius would be r + 2/8 inches, and the new volume would be:
[tex]V2 = (4/3)\pi(r + 2/8)^3[/tex]
The change in volume after the second week would be:
ΔV2 = V2 - V1
We can repeat this process for the remaining three weeks and find the total change in volume by adding all the individual changes:
ΔVtotal = ΔV1 + ΔV2 + ΔV3 + ΔV4 + ΔV5
By simplifying this equation, we get:
[tex]\Delta V_{total }= (4/3) \pi r^3[(r + 1/8)^3 + (r + 2/8)^3 + (r + 3/8)^3 + (r + 4/8)^3 + (r + 5/8)^3 - 5r^3][/tex]
Therefore, the volume of the apple would increase by ΔVtotal over the five-week period.
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The volume of the apple will increase by [tex](4/3)π[(r0 + 5/8)^3 - r0^3][/tex] during the five-week period.
Assuming that the apple is a perfect sphere, we can use the formula for the volume of a sphere:
[tex]V = (4/3)πr^3[/tex]
where V is the volume of the sphere and r is the radius of the sphere.
Let's start by finding the initial volume of the apple. We are not given the initial radius, so let's assume it to be r0.
[tex]V0 = (4/3)πr0^3[/tex]
After one week, the radius increases by 1/8 inch, so the new radius is r1 = r0 + 1/8. The new volume is:
[tex]V1 = (4/3)π(r0 + 1/8)^3[/tex]
After two weeks, the radius increases by another 1/8 inch, so the new radius is r2 = r0 + 2/8. The new volume is:
[tex]V2 = (4/3)π(r0 + 2/8)^3[/tex]
Similarly, after three weeks, the new radius is r3 = r0 + 3/8 and the new volume is:
[tex]V3 = (4/3)π(r0 + 3/8)^3[/tex]
After four weeks, the new radius is r4 = r0 + 4/8 and the new volume is:
[tex]V4 = (4/3)π(r0 + 4/8)^3[/tex]
Finally, after five weeks, the new radius is r5 = r0 + 5/8 and the new volume is:
[tex]V5 = (4/3)π(r0 + 5/8)^3[/tex]
To find how the volume changes during the five-week period, we need to subtract the initial volume from the final volume:
ΔV = V5 - V0
[tex]ΔV = (4/3)π(r0 + 5/8)^3 - (4/3)πr0^3[/tex]
Simplifying this expression, we get:
[tex]ΔV = (4/3)π[(r0 + 5/8)^3 - r0^3][/tex]
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This table contains equivalent ratios between x and y
——————-
x
1
3
7
——————-
y
5
15
25
35
The missing values in the table that contains the equivalent ratios between X and Y would be = 5
What is an equivalent ratio?An equivalent ratio is defined as the constant that exists between two different numbers when compared.
The figures in the table is as follows:
X= 1 3 ? 7
y = 5 15 25 35
If X = 1 when y = 5, X= ? when y= 25
That is;
1 =5
?= 25
? = 25/5 = 5
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Which parent function is represented by the table? A √x) = x² B. f(x) = |x| C. f(x) = x. D. f(x) = 2^x
The parent function which is represented by the given table as required in the task content is; Choice B. f(x) = |x|.
Which answer choice represents the parent function of the table?It follows from the task content that the parent function which is represented by the table is to be determined.
On this note, by observation of the function; the values of y represent the positive version of x.
Consequently, it follows that the table represents the absolute value function.
Therefore, Choice B; f(x) = |x| is correct.
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For what value of x is the rational expression below equal to zero? x-4/x-6 A. -6 B. 4 C. -4 D. 6
!!!!!!I NEED THIS ASAP!!!!!
Find x,y, and z
Thus, the values of x,y, and z for the similar triangles are obtained:
Part A: y = 6.70; z = 13.41 and x = 6.
Part B: z = 17.88 ; y = 35.77 and x = 32.
Explain about the similarity of the triangle:Congruent triangles and similar triangles are two distinct but closely related concepts. There are two different kinds of similar triangle problems: those that ask you to determine whether a set of triangles is similar and those that ask you to determine the angles and side length of similar triangles that are missing.
Part A: using similarity of the triangle, taking the ratios of corresponding side.
y/15 = x/z = 3/y
Consider
y/15 = 3/y
y² = 15*3
y² = 45
y = 6.70
Now,
applying Pythagorean theorem:
y² = 3² + x²
x² = y² - 3²
x² = 45 - 9
x² = 36
x = 6
And,
z² = 12² + x²
z² = 144 + 36
z² = 180
z = 13.41
Part B:using similarity of the triangle, taking the ratios of corresponding side.
z/(x + 8) = 16/y = 8/x ... eq 1
applying Pythagorean theorem:
z² = 16² + 8²
z² = 256 + 64
z² = 320
z = 17.88
Now, from eq 1
z² = 8(8 +x)
320 = 64 + 8x
8x = 320 - 64
x = 256/8
x = 32
Now,
applying Pythagorean theorem:
y² = 16² + x²
y² = 256 + 32²
y² = 1280
y = 35.77
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which of the following descriptive measures may be calculated when data has been grouped into class intervals in a frequency distribution? a. the mean for grouped data. b. all of these measures can be computed. c. the variance for grouped data. d. the standard deviation for grouped data.
The mean for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution. (Option A)
When data has been grouped into class intervals, it is not possible to calculate the exact mean of the data. Instead, we use the midpoint of each class interval as a representative value for that interval. Then, we calculate the weighted average of these midpoints to find the mean for grouped data.
Options C and D, the variance and standard deviation, respectively, cannot be directly computed from grouped data. However, we can estimate them using the assumed normal distribution of the data within each class interval and the mean for grouped data.
Therefore, the correct answer is option A: the mean for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution.
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the ratio of toddlers to infants at a day care center is 7 to 3. if twelve more infants join the day care to change the ratio to 7 to 5, how many toddlers are there at this day care center?
In order to change the ratio of toddlers to infants from 7 to 3 to 7 to 5, with an increase of 12 more infants, the number of toddlers in the daycare center has to be 42
Let the coefficient of the ratio be x
Therefore, before the addition of the 12 infants
the number of toddlers = 7x
number of infants = 3x
After the addition of 12 infants
the number of toddlers = 7x
the number of infants = 3x+12
According to the question, new ratio = 7 : 5
[tex]\frac{7x}{3x+12}=\frac{7}{5}[/tex]
5(7x) = 7(3x+12)
35x = 21x + 84
35x - 21x = 84
14x = 84
x = 6
Therefore, the original number of infants = 3 * 6 = 18
the number of toddlers = 7x = 7 * 6 = 42
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If twelve more infants join the day care to change the ratio to 7 to 5, then 126 toddlers are there at this day care center.
Let's first set up the initial ratio using variables: let T represent the number of toddlers and I represent the number of infants. The ratio of toddlers to infants is 7 to 3, so we can write:
T/I = 7/3
To solve for the actual number of toddlers and infants, we need more information. We are told that twelve more infants join the day care, so the new number of infants is I + 12. The new ratio is 7 to 5, so we can write:
T / (I + 12) = 7/5
Now we have two equations with two unknowns, so we can solve for T. First, we can use the initial ratio to solve for I in terms of T:
T/I = 7/3
3T = 7I
I = (3/7)T
Now we can substitute this expression for I into the second equation:
T / (I + 12) = 7/5
T / ((3/7)T + 12) = 7/5
Multiplying both sides by ((3/7)T + 12) gives:
T * (7/5) = ((3/7)T + 12) * (7/5)
Simplifying:
21T / 35 + 84 / 5 = 49T / 35
84 / 5 = 28T / 35
Solving for T:
T = (84/5) * (35/28)
T = 126
Therefore, there are 126 toddlers at this day care center.
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(15 POINTS) HELP ASAP TY!!
How are solving systems of two linear equations or inequalities and solving systems of two quadratic equations or inequalities alike? How are they different?
Find the length of each segment.
12. AB and AC
Applying the Angle Bisector Theorem, the length of the segments are:
AB = 15; AC = 20.
What is the Angle Bisector Theorem?The Angle Bisector Theorem states that in a triangle, if a line segment bisects an angle of the triangle and intersects the opposite side, then it divides that side into two segments that are proportional to the lengths of the other two sides of the triangle.
Therefore, we would have the following equation based on the angle bisector theorem:
5y/8 = 4y - 1 / 6
Cross multiply:
8(4y - 1) = 6(5y)
32y - 8 = 30y
32y - 30y = 8
2y = 8
y = 4
AB = 4y - 1 = 4(4) - 1 = 15
AC = 5y = 5(4) = 20
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Add. Express your answer in simplest form. 2/5 + 5/6
A. 1/3
B. 7/11
C. 7/30
D. 1 7/30
Answer:
d. 1 7/30...............
Answer:
D
Step-by-step explanation:
2/5 + 5/6
Make the denominator same
(2×6)/30 + (5×5)/30
12+25/30
37/30
1 7/30
A pyrotechnician plans for two fireworks to explode together at the same height in the air. They travel at speeds shown below. Firework B is launched 0.25 s before
Firework A. How many seconds after Firework B launches will both fireworks explode?
Firework A: 300 ft/s
Firework B: 280 ft/s
Both fireworks will explode seconds after
Firework B launches.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
The fireworks will explode after 1.125 seconds of launching Firework B.
How to find when the fireworks will explode?Distance = Speed × time
Let time = t
Firework A:
[tex]D(t) = 360t - - - (1)[/tex]
Firework B:
[tex]D(t) = 280(0.25) + 280t[/tex]
[tex]D(t) = 70 + 280t - - - (2)[/tex]
Equate 1 and 2 :
[tex]360t = 280t + 70[/tex]
Collection of like terms
[tex]360t - 280t = 70[/tex]
[tex]80t = 70[/tex]
[tex]t = 70/80[/tex]
[tex]t = 0.875 seconds[/tex]
[tex]0.875 + 0.25 = 1.125 seconds[/tex]
Therefore, the fireworks will explode after 1.125 seconds of launching Firework B.
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write in expanded form
2d with an exponent of -5
The expanded form of 2d with an exponent of -5 is 32d⁵
How to solve exponents?2d with an exponent of -5
[tex] {(2d)}^{ - 5} [/tex]
[tex] = \frac{1}{ {(2d)}^{5} } [/tex]
expand
[tex] = \frac{1}{2d \times2d \times2d \times2d \times2d } [/tex]
[tex] = {32d}^{5} [/tex]
Therefore, 2d with an exponent of -5 is 32d⁵
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Y+5=2(x+1) what is the x and y intercepts
Answer: x-intercept is (3/2, 0), y-intercept is (0, -3)
Step-by-step explanation:
Can someone help me with this?
The value of angle G is 31⁰.
The value of line GF is 5.
The value of X is 13.
The value of Y is 2.
What is the value of angle G?The value of angle G is calculated as follows;
4x + 7 = 5x - 6
4x - 5x = - 6 - 7
-x = -13
x = 13
Angle H = angle F = 4x + 7
= 4(13) + 7
= 59⁰
Angle G = ¹/₂ (180 - 2x59)
Angle G = ¹/₂(180 - 118)
Angle G = 31⁰
The value of Y is calculated as follows;
y + 3 = 2y + 1
y - 2y = 1 - 3
-y = -2
y = 2
GF = 2y + 1
GF = 2x2 + 1 = 5
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In a triangle PQR,the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively.
Thus, the in a triangle PQR, with the sides PQ, QR and PR formed a right angled triangle.
Explain about the Pythagorean theorem:If we know the lengths of two of the sides of a right triangle, we can apply the Pythagorean theorem to determine the third side.
According to the Pythagorean theorem, the hypotenuse squared equals the total of the squared legs. The vertical and horizontal sides, which make a 90° angle, are the legs of a right triangle. The longest side, or hypotenuse, is located on the other side of the right angle.Given data:
Triangle :PQR, PQ = 15 inQR = 20 inand PR = 25 inIN right triangle, the longest side is called the hypotenuse.
So,
hypotenuse H = 25
Now using Pythagorean theorem:
(PR)² = (PQ)² + (QR)²
(25)² = (20)² + (15)²
625 = 400 + 225
625 = 625
LHS = RHS
Thus, the in a triangle PQR, with the sides PQ, QR and PR formed a right angled traingle.
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Complete question:
In a triangle PQR,the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively. prove that triangle PQR, is the right traingle.
discuss possible sources of measurement error in this experiment. are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.
The "possible-sources" of in the measurement error of an experiment are Instrument error, Human error, sampling error and environmental factors, these sources "may" or "may-not" be enough to account for the percent differences calculated from the data.
There are several possible sources of "measurement-error" in an experiment which affect the accuracy and precision of the results.
These sources include instrument error, human error, environmental factors, and sampling error.
(i) "Instrument-Error" : is defined as inaccuracies in the measuring instruments used in the experiment. This include issues such as calibration errors, sensitivity of the instruments.
(ii) "Human-Error" can arise from mistakes made by experimenters during data collection or analysis, such as misreading measurements or recording data incorrectly.
(iii) "Environmental-Factors", such as temperature, humidity, or electromagnetic interference, can also cause error into experiment if they affect performance of measuring instruments.
(iv) "Sampling-Error" occur when a subset of the population is used for the experiment, and the results are generalized to the entire population.
Depending on the magnitude of these sources of error, they may or may not be enough to account for the percent differences calculated from the data.
If the measurement errors are small and within an acceptable range for the experiment, they may not significantly impact the results.
If the errors are large or systematic, they can introduce significant bias into the data and affect the percent differences calculated.
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The given question is incomplete, the complete question is
Discuss the possible sources of measurement error in an experiment. Are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.
Solve for X. I don’t know how to solve
The value of x is approximately 10.57 and the value of y is approximately 15.25.
Describe Chords?In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.
The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.
In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:
105 + (7y + 1) + (7x + 1) + (4y + 14) = 180
Simplifying and solving for x and y, we get:
7x + 4y + 122 = 180
7x + 4y = 58 ......(1)
Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:
105 + (4y + 14) = 180 ......(2)
(7y + 1) + (7x + 1) = 180 ......(3)
Simplifying and solving for y in equation (2), we get:
4y + 119 = 180
4y = 61
y = 15.25
Substituting this value of y in equation (3) and solving for x, we get:
(7x + 1) + (7*15.25 + 1) = 180
7x + 106 = 180
7x = 74
x = 10.57
Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.
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Zain's current credit card balance is $9,160.00 with a minimum payment of $325.00. Over the next month he spends $1,098.00. If the APR is 18.99% (billed monthly), what will the new balance be, including interest?
Answer: To find the new balance including interest, we need to take into account the interest charged on the current balance and the new purchase.
First, let's calculate the interest charged on the current balance. The monthly interest rate is 18.99% / 12 = 1.5825%.
The interest charged on the current balance is therefore:
interest on current balance = 0.015825 * 9160.00 = 144.98
So the total balance including interest for the current month is:
current balance including interest = 9160.00 + 144.98 = 9304.98
Next, let's calculate the interest charged on the new purchase of $1,098.00. The interest charged on the new purchase is:
interest on new purchase = 0.015825 * 1098.00 = 17.39
So the total balance including interest for the new purchase is:
new balance including interest = 1098.00 + 17.39 = 1115.39
Finally, we add the current balance including interest and the new balance including interest to get the total balance including interest:
total balance including interest = current balance including interest + new balance including interest
total balance including interest = 9304.98 + 1115.39
total balance including interest = 10420.37
Therefore, the new balance including interest is $10,420.37.
Step-by-step explanation:
PLEASE HELP WITH THIS IF YOU NNED MORE INFO TELL ME
The proof that Proven AB ≅ CD and BC ≅ DA is given below.
What is a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel.
The Proof: given ABCD is a parallelogram
In parallelogram ABCD, compare triangles ABC and CDA. In these triangles (See attached image)
AC = CA (common side)
∠BAC = ∠DCA (alternate interior angles)
∠BCA = ∠DAC (alternate interior angles)
Hence by the Angle-Side- Angle postulate, both the triangles are congruent and the corresponding sides are equal.
Therefore we have AB = CD, and BC = AD.
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HELPP PLS ILL MARK U BRAINLIST
Maybe 9/12? I counted the amount of times 6 or 9 shows up on the graph. :D. Hope that helps.
Ten seventh graders and 15 eighth graders were selected for the elite choir ensemble.
a. Write the ratio of seventh graders to eighth graders who were selected for the
elite choir.
b. Write the ratio of seventh graders to total students who were selected for the
elite choir.
c. Write the ratio of eighth graders to total students who were selected for the elite
choir.
Answer:
Your answer should be A
a pollster is going to sample a number of voters in a large city and construct a 95% confidence interval for the proportion who support the incumbent candidate for mayor. find a sample size so that the margin of error will be no larger than 0.05
The surveyor must test at the slightest 385 voters within the expansive city to build a 95% certainty interim for the extent who bolster the occupant candidate with an edge of blunder no bigger than 0.05.
To discover the test measure required to attain an edge of mistake of no more than 0.05 for a 95% certainty interim, able to utilize the taking after equation:
n = (z[tex]^{2}[/tex] * p * q) / E[tex]^{2}[/tex]
where:
n is the test estimate
z is the z-score related to the specified level of certainty (in this case, 95% corresponds to a z-score of 1.96)
E is the specified edge of blunder (in this case, 0.05)
Substituting the given values, we get:
n = (1.96[tex]^{2}[/tex] * 0.5 * 0.5) / 0.05[tex]^{2}[/tex]
n = 384.16
thus, we get a test measure of 385.
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help asap its for my practice grade and i dont know it
Answer:
The answer for anle X is 66°
Step-by-step explanation:
Base angles of an isosceles triangle are equal
<x=<y
<x+<y+<w=180
let<x=X
Remember <X=<Y
X+X+48=180
2X+48=180
2X=180-48
2X=132
divide both sides by 2
X=66°
<X=X
<X=66°
8.G.B.6
The better definition of squares is
A number multiplied by itself.
What is square?
In mathematics, a square is a number that is obtained by multiplying a number by itself. It is also a geometric shape with four equal sides and four right angles. The area of a square is calculated by multiplying the length of one of its sides by itself. The formula for calculating the area of a square is A = s^2, where A is the area and s is the length of one side.
Squares have many important applications in mathematics, including in algebra, geometry, trigonometry, and calculus. They are used in the Pythagorean theorem, which relates to the sides of a right triangle, and they are used to represent variables in algebraic equations. Squares are also important in geometry, where they are used to construct geometric shapes and to calculate their areas and perimeters.
The better definition of squares is:
A number multiplied by itself.
In mathematics, a square refers to the product of a number multiplied by itself. For example, the square of 4 is 16, because 4 multiplied by 4 equals 16. Squares have a variety of important applications in mathematics, including in geometry, algebra, and calculus.
While a result that has been proved to be true is sometimes referred to as a "square" in certain contexts, it is not the primary definition of the term. Similarly, a triangle with a right angle is referred to as a "right triangle" or a "right-angled triangle," but not a square.
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write a function that computes your test statistic. it should take a table with two columns, totchol (total serum cholesterol) and anychd (whether or not the person had coronary heart disease), and compute the test statistic you described above.
The function computes the test statistic for the relationship between total serum cholesterol and coronary heart disease, given a table with two columns: "totchol" and "anychd".
The function in Python that computes the test statistic:
import pandas as pd
import numpy as np
from scipy.stats import t
def compute_test_statistic(data):
"""
Compute the test statistic for the relationship between total serum cholesterol and coronary heart disease.
Parameters:
-----------
data: pandas.DataFrame
A DataFrame with two columns: "totchol" (total serum cholesterol) and "anychd" (whether or not the person had coronary heart disease)
Returns:
--------
float
The test statistic
"""
# Compute the mean total serum cholesterol for each group (with and without coronary heart disease)
group_means = data.groupby("anychd").mean()["totchol"].values
# Compute the standard deviation of the total serum cholesterol for each group
group_std = data.groupby("anychd").std(ddof=1)["totchol"].values
# Compute the sample size for each group
group_n = data.groupby("anychd").count()["totchol"].values
# Compute the pooled standard error
pooled_se = np.sqrt(np.sum((group_n - 1) * group_std ** 2) / np.sum(group_n - 2))
# Compute the t-value
t_value = (group_means[1] - group_means[0]) / (pooled_se * np.sqrt(1/group_n[0] + 1/group_n[1]))
# Compute the degrees of freedom
df = np.sum(group_n) - 2
# Compute the p-value (two-sided test)
p_value = 2 * t.cdf(-np.abs(t_value), df)
# Return the test statistic
return t_value
This function assumes that the input table is in the form of a pandas DataFrame, with columns "totchol" and "anychd".
It uses the groupby method to split the data into two groups based on the "anychd" column, and then computes the mean, standard deviation, and sample size for each group. It then uses these values to compute the test statistic using the formula given in the prompt.
Finally, it uses the t.cdf function from the scipy.stats module to compute the p-value for a two-sided test.
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40 decreased by m is 21
Answer:
40-m=21
40-40-m=21-40
m=21-40
m=-19