The critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).
What is Critical value ?
In statistics, a critical value is a threshold value that is used to determine whether to reject or fail to reject the null hypothesis in a statistical test. It is typically based on the significance level of the test, which is the probability of rejecting the null hypothesis when it is actually true.
To find the critical value for a 90% confidence interval with n = 5, we need to use a t-distribution with (n-1) degrees of freedom.
Using a t-distribution table or a calculator, we can find the critical value with a 90% confidence level and 4 degrees of freedom (n-1 = 5-1 = 4) to be approximately 2.132.
Therefore, the critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).
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Mrs. Davis had 6 bowls of flour for a group project. The line plot below shows the fraction of a cup of flour that was left in each bowl after the project.
By summing all the fractions that was left, we have 3 cups of flour left. The correct option is (B).
Understanding Simple Line PlotThe "x" represents the quantity while the fractions represents the value.
To get the cups of flour left, we first multiply the number of "x" with the fraction and then add the resulting fractions together.
Cups left = 1 (1/8) + 1(3/8) + 2(1/2) + 2(3/4)
= 1/8 + 3/8 + 1 + 3/2
Find the LCM
= [tex]\frac{1 + 3 + 8 + 12}{8}[/tex]
= 24/8
Cups left = 3 cups
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Parametric Functions
Answer:
Step-by-step explanation:
it think it 23 becasue u add
1 divide it by 2
What are the x-intercepts of the function f(x)= 4x^2-36 over x-9?
Therefore , the solution of the given problem of function comes out to be f(x) = (4x² - 36)/(x - 9) has -3 and 3 as its x-intercepts.
Describe function.On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
Setting the y-value (or output) of a function to zero and then solving for the corresponding x-values will allow us to determine the x-intercepts of the function.
The function in this instance is f(x) = (4x² - 36)/(x - 9)
=> 4x² - 36 = 0
To make the equation simpler, we can factor out a 4:
=> 4(x² - 9) = 0
We can factor further based on the difference of squares we now have:
=> 4(x + 3)(x - 3) = 0
We may determine the x-values where the function crosses the x-axis by setting each element to zero:
=> x + 3 = 0 or x - 3 = 0
To find x, solve for:
=> x = -3 or x = 3
The function f(x) = (4x² - 36)/(x - 9) has -3 and 3 as its x-intercepts.
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Please help me with this
Answer: 1st option
explanation: The ones that are crossed out include 1 whole number and 7 1/8 pieces. this is equal to 1 and 7/8. Then there is 3 whole 1 pieces so the answer is the 1st option
What is the value of y in the solution to the system of equations shown?
y = 3x − 1
y = −x − 5
Answer:{y,x}={-4,-1}
Step-by-step explanation:
PLEASE FIND THE AREA
Answer:
50 cm
Step-by-step explanation:
To solve this answer you can find the area of the small triangle, and multiply it by 2 to get the area of the top part.
Then you can find the area of one of the bigger triangles and multiply it by 2.
Please could I get brainiest? I'm trying to get to the Expert level.
You start at (2, -1). You move left 4 units. Where do you end?
Answer:
(-2, -1)
Step-by-step explanation:
You want the point that is 4 units left of (2, -1).
X-coordinateThe x-coordinate of an (x, y) coordinate pair tells you the number of units to the right of the x=0 point. It increases for points farther right, and decreases for points farther left.
Moving left 4 units decreases the x-coordinate by 4 units. The x-coordinate of 2 becomes ...
2 -4 = -2
The coordinates of the moved point are (-2, -1).
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see attachment
3(3m+N)
Answer:
Step-by-step explanation:
Divide and state the quotient in simplest form.
The quotient of the two fractions is (x - 5) / (x - 4).
Option D is the correct answer.
We have,
To divide two fractions, we can multiply the first fraction by the reciprocal of the second fraction.
In this case, that means we need to multiply:
(x² - 2x - 15) / (x + 2) x (x + 2) / (x² - x - 12)
Notice that the (x + 2) terms in the numerator and denominator of the first fraction cancel out with the denominator of the second fraction, so we can simplify before multiplying:
(x² - 2x - 15) / 1 x 1 / (x² - x - 12)
Now we can multiply the numerators and the denominators separately:
(x² - 2x - 15) / (x² - x - 12)
To simplify further, we can factor both the numerator and the denominator:
(x - 5)(x + 3) / (x - 4)(x + 3)
Notice that the (x + 3) terms in the numerator and denominator cancel out, leaving:
(x - 5) / (x - 4)
Therefore,
The quotient of the two fractions is (x - 5) / (x - 4).
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Which of the following accurately graphs the points listed in the table above?
Answer:
Correct ANSWER IS A
Step-by-step explanation:
For each coordinate pair (r,θ) listed in the table, first identify the ray on the graph created by the angle θ. On this ray, plot a point a distance of r from the pole.
2. Find g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3
A. 9
B.8
C.329
d. 536
D.536
The value of the function g(f(-4)) = 536. Option D
How to determine the valueFrom the information given, we have that the functions are;
f(x)= 4x+5
g(x) = 4x^2 -5x - 3
To determine the composite function, g(f(-4)), we need to first determine the value of the function f(x) at -4
Now, substitute the value, we have;
f(-4) = 4(-4) + 5
expand the bracket, we get;
f(-4) = - 16 + 5
Add the values
f(-4) = -11
Now, substitute the value in the function g(x), we have that;
g(f(-4)) = 4(-11)² - 5(-11) - 3
find the square and expand the bracket
g(f(-4)) =484 + 55 - 3
Subtract the values, we have;
g(f(-4)) = 536
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what is pi * 12 * 2
Answer: 3.14 x 12 x 2
= 75.36
Step-by-step explanation:
The length of a particular animals pregnancies are approximately normally distributed, with a mean of 272 days and a standard deviation of 12 days.
A) what is the proportion of pregnancies that lasts more than 278 days?
B) what is the proportion of pregnancies lasts between 257 and 275 days?
C) what is the probability that a randomly selected pregnancy lasts no more than 266 days?
D) a “very preterm” baby is one whose gestation period is less than 242 days. Are very preterm babies unusual?
Answer:
To answer these, we can use the standard normal distribution & z-scores. A z-score represents the number of standard deviations a value is from the mean. The formula to calculate a z-score is: z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.
A) To find the proportion of pregnancies that last more than 278 days, we first calculate the z-score for 278 days: z = (278 - 272) / 12 = 0.5. Using a standard normal distribution table, we find that the proportion of values above a z-score of 0.5 is approximately 0.3085. So, about 30.85% of pregnancies last more than 278 days.
B) To find the proportion of pregnancies that last between 257 and 275 days, we first calculate the z-scores for both values: z1 = (257 - 272) / 12 = -1.25 and z2 = (275 - 272) / 12 = 0.25. Using a standard normal distribution table, we find that the proportion of values between z-scores of -1.25 and 0.25 is approximately 0.3944. So, about 39.44% of pregnancies last between 257 and 275 days.
C) To find the probability that a randomly selected pregnancy lasts no more than 266 days, we first calculate the z-score for 266 days: z = (266 - 272) / 12 = -0.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -0.5 is approximately 0.3085. So, there is about a 30.85% chance that a randomly selected pregnancy lasts no more than 266 days.
D) To determine if very preterm babies are unusual, we first calculate the z-score for 242 days: z = (242 - 272) / 12 = -2.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -2.5 is approximately 0.0062. Since this value is less than 0.05, we can conclude that very preterm babies are unusual.
If the profit function for a product is
P(x) = 2400x + 105x^2 − x^3 − 167,000
dollars, selling how many items, x, will produce a maximum profit?
x = items
Selling 80 items will produce maximum profit if the profit function is [tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex].
What is the value of x that produces maximum profit?To find value of x that produces maximum profit, we must get critical points of the profit function and determine which one corresponds to a maximum.
The profit function is given as:
[tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex]
Taking the derivative of P(x) with respect to x, we get:
[tex]P'(x) = 2400 + 210x - 3x^2[/tex]
Setting P'(x) equal to zero and solving for x, we get:
[tex]0 = 2400 + 210x - 3x^2\\3x^2 - 210x - 2400 = 0\\x^2 - 70x - 800 = 0\\(x - 80)(x + 10) = 0[/tex]
Here, the critical points are x = 80 and x = -10.
To determine one that corresponds to a maximum, we can use the second derivative test. Taking the derivative of P'(x), we get:
[tex]P''(x) = 210 - 6x[/tex]
Evaluating P''(80), we get:
[tex]P''(80) = 210 - 6(80)\\P''(80) = 210 - 420\\P''(80) = -330[/tex]
Since P''(80) is negative, the critical point x = 80 corresponds to a maximum. So, selling 80 items will produce maximum profit.
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helpppppppp pleaseeeeee
Adding -4(row 1) to row 3 in the matrix will produce: 0, -9, 2, and 12 respectively.
What is the row of a matrixA rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.
row 1 of the given matrix are: 1, 2, 1, and -5, multiplying -4(row1) will gives;
-4 × 1 = -4
-4 × 2 = -8
-4 × 1 = -4
-4 × -5 = 20
-4(row 1) + row 3 will result to:
-4 + 4 = 0
-8 + (-1) = -9
-4 + 6 = 2
20 + (-8) = 12
Therefore, adding -4(row 1) to row 3 in the matrix will produce: 0, -9, 2, and 12 respectively.
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The volume of a suitcase is 8,556 Cubic
inches. It is 32 inches long and 15.5
inches high. Write an equation to
represent the width. Then find the width
of the suitcase.
To find the width of the suitcase, we need to use the formula for the volume of a rectangular prism:
Volume = Length × Width × Height
Given the volume of the suitcase as 8,556 cubic inches, the length as 32 inches, and the height as 15.5 inches, we can write the equation:
8556 = 32 × w × 15.5
Simplifying this equation, we can divide both sides by the product of 32 and 15.5:
8556 ÷ (32 × 15.5) = w
Solving for w, we get:
w ≈ 16.50 inches
Therefore, the width of the suitcase is approximately 16.50 inches.
Suppose that the function is defined, for all real numbers, as follows.
The graph of the function "g", which is defined for all "real-numbers" is shown below.
The function "g" which is defined for all "real-numbers" is represented as :
g(x) = {2 if x<0,
{-1 if x=0
{-3 if x>0
this function means that, for every input-value, which is less than 0, the output will be always 2,
For the input-value "0", the output-value will be = -1;
For all the input-value which are greater than "1", the out will be always "-3",
So, from the above information, the graph is plotted below,
The red-line represents "2 if x<0", the green line represents "-3 if x>0".
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Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is µg =0. Compute the value of the t test statistics. Round intermediate
calculations to four decimal places as needed and final answers to three decimal places as needed.
x 9 6 7 5 12
y 6 8 3 6 7
A.t= 2.890
B.t= 1.292
C. t=0.578
D. t=0.415
Answer: To compute the t-test statistic for the paired sample data, we need to first calculate the sample mean difference and the sample standard deviation of the differences. Then we can use the formula:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the standard error of the mean difference is calculated as:
standard error = sample standard deviation / sqrt(sample size)
Let's first calculate the sample mean difference:
x 9 6 7 5 12
y 6 8 3 6 7
The differences between each pair of x and y values are:
(9-6), (6-8), (7-3), (5-6), (12-7) = 3, -2, 4, -1, 5
The sample mean difference is the average of these differences:
sample mean difference = (3 - 2 + 4 - 1 + 5) / 5 = 1.8
Next, we need to calculate the sample standard deviation of the differences. To do this, we first calculate the deviations of each difference from the sample mean difference:
(3 - 1.8), (-2 - 1.8), (4 - 1.8), (-1 - 1.8), (5 - 1.8) = 1.2, -3.8, 2.2, -2.8, 3.2
The sample standard deviation of the differences is the square root of the sum of the squared deviations divided by (n-1):
sample standard deviation = sqrt[(1.2^2 + (-3.8)^2 + 2.2^2 + (-2.8)^2 + 3.2^2) / 4] = 3.153
Finally, we can calculate the t-test statistic:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the hypothesized mean difference is 0, and the standard error of the mean difference is:
standard error = sample standard deviation / sqrt(sample size) = 3.153 / sqrt(5) = 1.410
Substituting the values, we get:
t = (1.8 - 0) / 1.410 = 1.277
Rounding the final answer to three decimal places, we get:
t = 1.277
Therefore, the correct option is B. t = 1.292.
solve for x and y (Hint: is this a right triangle?)
(30° angle and 5 on the opposite side if anyone couldn’t see)
Answer: c=10, b=5 root 3
Step-by-step explanation:
it is a 30-60-90 triangle (use sum of angles in a triangle theorem.)
5 is the leg oppoiste to the 30 degree, so it is half of the hypotenuse, which is c, so c=10
then just use pythagorean theorem and 100-25=75 so answer is root 75 simplified to 5 root 3
Rotate 180 degrees about the origin
The rotation transformation of the quadrilateral IJKL, to obtain the quadrilateral I'J'K'L', are; I'(-2, 3), J'(0, -2), K'(-2, -3), L'(-3, 1)
What is a rotation transformation?A rotation transformation is one in which the coordinates of a geometric figure are rotated about a point.
The coordinates of the vertex points on the figure are;
J(0, 2), K(2, 3), L(3, -1), and I(2, -3)
The coordinates of the point (x, y) following a rotation of 180° about the origin are (-x, -y)
Therefore, the coordinates of the image of the figure J(0, 2), K(2, 3), L(3, -1), and I(2, -3), following a rotation about the origin are;
J(0, 2) ⇒ J'(0, -2)
K(2, 3) ⇒ K'(-2, -3)
L(3, -1) ⇒ L'(-3, 1)
I(2, -3) ⇒ I'(-2, 3)
Therefore, we get;
The coordinates of the image are; I'(-2, 3), J'(0, -2), K'(-2, -3), L'(-3, 1)
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Express the following probability as a simplified fraction and as a decimal.
If one person is selected from the population described in the table, find the probability that the person
I need done asap I have 1 min
Write the standard form of the following polynomial.
(2x-3)²-3(x-2)(x+4)-7
X² ? X+ ?
Please help. This is geometry
∠WTA and ∠HTC are vertical angles. Thus, they are equal.
As WA || HC, that means ∠AWT and ∠THC are alternate interior angles and are equal. Additionally, ∠WAT and ∠TCH are also alternate interior angles and are equal.
∠WTA = ∠HTC, ∠AWT = ∠THC, and ∠WAT = ∠TCH
Since both triangles have the same angle measurements, they are similar.
i need the answer for this +explanation it had me confused
Answer:
The surface area of the square pyramid is 18 km².
Step-by-step Explanation:
What is the surface area of a square pyramid with a slant height?
The surface area of a square pyramid with a slant height can be determined by the product of the base perimeter with the slant height divided by two.
Mathematically, it can be expressed as:
Surface Area S.A = P × l/2
where;
Side length (a) = 3
Base perimeter (P) = 4a = 4(3) = 12km
Slant length (l) = 3 km
Surface Area (S.A) = 12 × (3/2)
Surface Area (S.A) = 12 x 1.5 = 18 km²
Therefore, the surface area of the same pyramid is 18 square km.
[tex]\sf SA_{Pyramid} =\boxed{\sf 27km^{2}}.[/tex]
Step-by-step explanation:We're asked to calculate the surface area (SA) of a pyramid. Surface area of a tridimensional shape isn't more than calculating the area of all of its "faces" and then adding them all together. Some of these tridimensional shapes already have equations that provide a direct calculation of this parameters, without the need to add together the area of the different parts of the shape.
There's a developed formula for directly calculating the surface area of square pyramids, but in this case it is easier to just calculate the individual areas of each face and add them all together.
1. Calculate the area of the base.This is pretty easy to calculate, as the base forms the shape of a square. Therefore, multiplying the length and width of this square will give us that area:
[tex]\sf A_{Base} =lw=3km*3km=\boxed{\sf 9km^{2}} .[/tex]
Check attached image 1 to see where we got these values from.
2. Calculate the area of one triangular face.So these faces form the sape of a triangle. Therefore, mul;tiplying their lengh by width and then dividing by 2 should give us the area.
[tex]\sf A=\dfrac{lw}{2} =\dfrac{(3km)(3km)}{2}=4.5km^{2}.[/tex]
Check attached image 2 to see where we got these values from.
This is the area of an individual triangular face of the pyramid, but we have a total of 4 faces. Hence, let's multiply this area by 4 to find the total area of all triangular faces:
[tex]4.5km^{2} *4=\boxed{\sf 18km^{2}}.[/tex]
3. Calculate the total surface area.So the total surface area, as stated at the beginning of this answer, is given by the addition of all individual areas from all the faces of the shape, so let's do just that:
[tex]\sf SA_{Pyramid} =9km^{2} +18km^{2}=\boxed{\sf 27km^{2}}.[/tex]
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2. Four friends have stamps, as described below.
• Samir has 60 stamps.
•Lisa has 24 times as many stamps as Samir.
Kwame has 443 stamps.
To the nearest whole number, what is the mean of the
Jake has 159 fewer stamps than Kwame.
number of stamps for these four friends?
Answer:
All of them have a combined of 2,227 Stamps
Mean: 2014
PLEASE HURRY
Let
u = 4i - j v = 3i + j w = i + 3j
Find the specified scalar.
u(v + w)
The specified scalar is 12 as the result of u(v + w) is 12i + 12j.
The provided vectors are given to be u = 4i - j v = 3i + j w = i + 3j. First, we need to find the vector v + w,
v + w = (3i + j) + (i + 3j)
v + w = 4i + 4j
Now, we can find dot product, u(v + w),
u(v + w) = u(4i + 4j)
u(v + w) = 4ui + 4uj
Substituting the given values of u, we get,
u(v + w) = 4(4i - j)i + 4(4i - j)j
u(v + w) = 16i - 4j + 16j - 4i
Simplifying, we get,
u(v + w) = 12i + 12j
Therefore, the specified scalar is 12.
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help struggling pealse if do brainliest!
Based on the data in the table, if Colin draws a marble 336 times, he predicts a yellow marble will be drawn roughly 63 times, but probably not exactly 63 times.
Based on the data in the table, if Colin draws a marble 216 times, he predicts a white marble will be drawn roughly 2 times that a purple marble will be drawn.
What is the number of times the yellow marble can be drawn?If Colin draws a marble x times, he predicts a yellow marble will be drawn roughly 63 times.
The number of times = 63 / 3/16)
The number of times = 336 times.
If Colin draws a marble 216 times,
Number of times he can draw a white marble = 216 * 1/4
Number of times he can draw a white marble = 54 times
Number of times he can draw a purple marble = 216 * 1/6
Number of times he can draw a purple marble = 36 times
The number of times a white marble can be drawn more than a purple marble = 54/36 or 1.5 times more
The number of times a white marble can be drawn more than a purple marble is approximately two times.
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Solve for the missing side using c =
Answer:
c=12.04
Explanation:
You can use the formula given: c=√a^2+b^2
c=√8^2+9^2=√64+81=√145=12.04
Use the graph to find f(2)
Pleaaaaaaase answer ASAP
Answer:
f(2) = 3
Step-by-step explanation:
At f(2) we can notice that there is 2 y-values (one is an open circle and another is a closed circle)
But, an open circle means that the function is not defined at that point
But a closed circle means that it is defined
So we ignore the open circle and the closed circle is 3
So f(2) = 3