Therefore , the solution of the given problem of test statistics comes out to be the p-value is 0.00052.
What is the test statistic?The Z-statistic, which demonstrates that the ordinary normal balanced hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the results show that you got a 2.5 R t. (also referred as a Z-value). The p-value for this Z-value is 0.0124.
Here,
(a) State the null hypothesis [tex]H_{0}[/tex] and the alternative hypothesis H1.
The null hypothesis (H0) is that the population mean sodium level for healthy adults is equal to the textbook value of 141 Eq per liter of blood.
[tex]H_{0}[/tex] : μ = 141
The alternative hypothesis (H1) is that the population mean sodium level for healthy adults differs from the textbook value.
H1: μ ≠ 141
(b) Determine the type of test statistic to use.
Since the sample size is greater than 30 and the population standard deviation is known, we can use a z-test to test the hypothesis.
(c) Find the value of the test statistic. (Round to three or more decimal places.)
The test statistic is calculated as:
z = (x'- μ) / (σ / √n)
Where x' is the sample mean, μ is the population mean under the null hypothesis, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get:
z = (149 - 141) / (13 / √21) = 3.464
Therefore, the value of the test statistic is 3.464.
(d) Find the p-value. (Round to three or more decimal places.)
Since this is a two-tailed test, we need to find the area under the normal curve beyond 3.464 in both directions. Using a standard normal table or calculator, we find that the area beyond 3.464 is 0.00026 in one direction. So, the p-value is:
p-value = 2 * 0.00026 = 0.00052
Therefore, the p-value is 0.00052.
(e) Can we conclude that the population mean adult sodium level differs from that given in the textbook?
Since the p-value (0.00052) is less than the level of significance (0.01), we can reject the null hypothesis and conclude that the population mean adult sodium level differs from that given in the textbook at the 0.01 level of significance.
Answer: Yes, we can conclude that the population mean adult sodium level
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What is the probability of rolling a number greater than or equal to 2 on a standard six-sided die? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.
The probability of getting a number greater than or equal to 2 is 0.8333( 3 decimal place)
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/ total possible outcome
The total outcome on a standard six-sided die is 6
The sample space of getting a number greater or equal to 2 is 2,3,4,5,6 = 5
Therefore the probability of getting a number greater or equal to 2 is = 5/6
= 0.833 ( 3 decimal place)
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For the following exercises, find the measure of the angle between the three-dimensional vectors a and b. Express the answer in radians rounded to two decimal places, if it is not possible to express it exactly 135. a = (3. -1,2), b = (1,-1,-2) 136. a = (0,-1, -3), b = (2,3,-1)
The angle between the 3D vectors a = (3, -1, 2) and b = (1, -1, -2) is 2.23 radians. The angle between a = (0, -1, -3) and b = (2, 3, -1) is 2.43 radians.
The angle between two vectors a and b in three-dimensional space can be found using the dot product formula:
cos(θ) = (a * b) / (||a|| * ||b||)
Where ||a|| and ||b|| represent the magnitude (length) of vectors a and b, respectively, and "*" represents the dot product of the two vectors. The dot product is given by:
a * b = a1 * b1 + a2 * b2 + a3 * b3
Where a1, a2, and a3 are the components of vector a, and b1, b2, and b3 are the components of vector b. The angle θ is then calculated using the inverse cosine function:
θ = arccos(cos(θ))
Finally, the angle θ is expressed in radians.
For the first problem, we have:
a = (3, -1, 2)
b = (1, -1, -2)
So, we have:
a * b = 3 * 1 + (-1) * (-1) + 2 * (-2) = 3 - 1 - 4 = -2
||a|| = [tex]\sqrt{(3^2 + (-1)^2 + 2^2)} = \sqrt{(14)}[/tex]
||b|| = [tex]\sqrt{(1^2 + (-1)^2 + (-2)^2) }= \sqrt{(6)}[/tex]
cos(θ) = [tex](-2) / (\sqrt{(14)} * \sqrt{(6)} ) = -\sqrt{(2)} / \sqrt{(21)[/tex]
θ = arccos[tex](-\sqrt{(2)} / \sqrt{(21)})[/tex] = 2.23 radians (rounded to two decimal places)
For the second problem, we have:
a = (0, -1, -3)
b = (2, 3, -1)
So, we have:
a * b = 0 * 2 + (-1) * 3 + (-3) * (-1) = -3
||a|| = [tex]\sqrt{(0^2 + (-1)^2 + (-3)^2)} = \sqrt{(10)}[/tex]
||b|| = [tex]\sqrt{(2^2 + 3^2 + (-1)^2)} = \sqrt{(14)}[/tex]
cos(θ) = [tex]-3 / (\sqrt{(10)} * \sqrt{(14)}) = -3 / \sqrt{(140)}[/tex]
θ = arccos[tex](-3 / \sqrt{(140)})[/tex] = 2.43 radians (rounded to two decimal places)
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Pls help I need this quick thx :D
The steps followed by Nikki are correct. Hence, option 1 is the correct answer.
How to construct parallel line to a given line and passing through a given point?Using a ruler and compass, perform the following procedures to create a line from an exterior point that is parallel to the other line:
Given: A point P that sits outside of line segment AB and line segment AB
to create a line that runs through point P and is parallel to line AB.
Select any point X and connect it to point P on the line segment AB.
Draw an arc with X as the center and any reasonable radius, cutting the line segments PX and AB at points M and N, respectively.
Draw an arc EF with P as the center and the same radius as in the previous step, cutting the line segment PX at point Q.
Draw an arc with Q as the center and the same radius as previously, cutting the arc EF at R.
To create the line segment CD, join R and P.
The necessary parallel to the line segment AB that goes through the point P is the line segment CD.
According to the steps of construction we determine that the steps of construction of Nikki are correct.
Hence, option 1 is the correct answer.
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The cost of tuition at a state college is $8,500 and is increasing by 3% each year. what is the cost of the tuition after 6 years?
Answer: $51,000
Step-by-step explanation:
At first, I multiplied 8,500 times 3 then the outcome I got was 25,500 so now I'm going to try multiplying 8,500 times 6 which equals 51,000 but I'm sorry if I got the answer wrong
Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem?a. 10X1+5X2−2X3≥20b. X1−2X22≤100c. 5X1+3≥25d. X1+0.5X2≤30e. 6X1+2X2∗X3≥10
The constraints that are not linear or cannot be included as a constraint in a linear programming problem are b. X1−2X2²≤100.
What is linear constraint?A linear constraint in linear programming occurs when linear components are added or subtracted and the resulting expression must either rise, decrease, or be exactly equal to a right-hand side value.
A constraint is referred to as linear if all of its terms are of the first order.
We know that the degree of the linear constraint is one, hence the constraint that does not have a degree of one is not a linear constraint.
Thus, option b X1−2X2²≤100 has a degree of two and it cannot be used as constraint in a linear programming problem.
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50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 which of the following histograms is the best representation of the data?
The best way to represent histograms is by decreasing to increasing order.
The mean is the arithmetic mean and is calculated by adding a group of numbers and dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
Given the values:
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45
We have that:
(22+24+28+28+30+31+31+32+32+35+36+37+38+41+42+42+44+44+45+46+46+47+47+49+50)/25=37.88.
The average age that a large construction company wants to know is 38.
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Rewrite vertex form y = 3(x + 5)2 − 11 into standard form.
The standard form is y= 3x^2+114+30x.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given;
y = 3(x + 5)^2 − 11
y= 3(x^2+25+10x)-11
y= 3x^2+125+30x-11
y= 3x^2+114+30x
Therefore, the equation will be y= 3x^2+114+30x
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Which of the following integrals represents the area of the region bounded by the curves, y = -3x^(1/2), y = x - 4, and y = 0, in terms of x?a. ∫(4, 0) (-3 √x) dx + ∫(5, 4) (x - 4) dxb. ∫(4, 0) -3 √x dx c. ∫(1, 0) 3√x dx + ∫(4, 1) (-x + 4) dxd. ∫(2, 0) 3√x dx + ∫(4, 2) (-x + 4) dxe. ∫(1, 0) (-3√x) dx + ∫(4, 1) (-x + 4) dx
12. aj is 10 and the difference is 6, find the numbers. b) A number is greater than another number by 3. If their sum is 33, find the numbers.
The value of the two numbers in b is 15 and 18
How to solve for the numbersTo get the values we would have to set up an equation system
Such that we would have:
the smaller number is given as c
Then the bigger number is given as c + 3
The equation would be
c + c + 3 = 33
then
2c = 33 - 3
2c = 30
From here we would have to divide both sides of the equation by 2
2c / 2 = 30 / 2
c = 15
33 - 15 = 18
Hence the numbers are given as 15 and 18
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PLEASE HELP MY HW IS LATE
The following information can be extracted from the system of triangles ABC and DEF:
Case A: 3 / 5 = y / z
Case D: m ∠ C = m ∠ F
Case E: Δ ABC ~ Δ DEF
How to interpret a system of two similar triangles
In this problem we find a representation of a system with two similar triangles, that is, two triangles with two congruent internal angles and proportional sides. Then, the following relationships are derived below:
m ∠ A = m ∠ D
m ∠ B = m ∠ E
m ∠ C = m ∠ F
AB / DE = BC / EF = AC / DF
6 / 10 = y / z = x / w
3 / 5 = y / z = x / w
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what percent is represented by the region that is shaded?
the answer is not 333% or 333.33% or 333.3%
466.66%? Theres four whole circles and one that is two thirds. Unless 466.66% is correct, can you give more info?
40 EASY POINTS!
Answer all of them with examples of how you got the answer for 40 points :)
1. store A sells at cheaper rate.
2. Runner B tun at faster rate.
3. Submarine 2 will reach at depth of -1056 feet at faster rate.
4. Kira collected 18.33 points in one hour.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
1. Store A: y= 0.40 x
so, the unit rate is 0.40.
Store B:
the cots of 3 pound carrot= 20.16
and, the cost of 48 ounce carrot = 20.16
and, cost per ounce= 20.16 /48= 0.42
so, the unit rate is 0.42.
Thus, store A sells at cheaper rate.
2. The unit rate rate of runner A
= 54/4.5
= 12
and, the unit rate of runner B
= 275/20
= 13.75
Thus, Runner B tun at faster rate.
3. Submarine 1 descends at rate of 22 feet.
and Submarine 2 descends at rate of = 480/20 = 24 feet.
Thus, Submarine 2 will reach at depth of -1056 feet at faster rate.
4. Jess collected 18 points in one hour.
and, Kira collected 18.33 points in one hour.
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I'm fifty years old it's a discreet or continuous variable justify the answer
I'm fifty years old the sentence is a discrete variable and not continuous variable as age is counted in concrete numbers and it does not involve complex numbers.
What is discrete and continuous data?Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted. Complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.
Numerical information that is continuous refers to the unspecified number of measurements that could be made between two realistic sites.
Despite the fact that these numbers are frequently gathered via accurate measurements, they are not necessarily neat and orderly as those in discrete data. Measuring a specific issue repeatedly enables us to establish a defined range, within which we can predictably gather more data.
I'm fifty years old the sentence is a discrete variable as age is counted in concrete numbers and it does not involve complex numbers.
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how much is 0.15% of 12000 ?
Answer:
0.15% of 12000 is equal to 18.
Step-by-step explanation:
To calculate 0.15% of 12000, we first convert 0.15% to a decimal. To do this, we divide 0.15 by 100:
0.15 ÷ 100 = 0.0015
Next, we multiply this decimal by 12000:
0.0015 × 12000 = 18
So, 0.15% of 12000 is equal to 18.
If the interval size is decreased from $200 to $100, which of the following must remain the same on the newhistogram?a) The height of the bars will decrease.b) The total number of bars will decrease. c) The width of the bars will increase. d) Each bar will represent more data items than before.
If the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.
How is this determined?The height of the bars will decrease if the interval sizes in a histogram are reduced while the scale remains constant. When the intervals are compressed,
For a particular set of data, there will be more histogram bars, but fewer data points will make up each interval. Reducing the interval size will also reduce the height of the histogram's bars because the height of the bars represents the number of items in each interval.
Hence, if the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.
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Explain how to rewrite the function shown in order to determine the transformation of the parent function. Then, describe the transformation of the graph compared to the parent function. y=3sqaure root-8x-4
The parent function of the function f(x) = 3√(-8x - 4) will be h(x) = √x.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
f(x) = 3√(-8x - 4)
Simplify the function, then we have
f(x) = 3√(-8x - 4)
f(x) = 6√- (2x + 1)
Divide the equation by 6, then we have
g(x) = √(-2x - 1)
Replace -(2x + 1) with x, then we have
h(x) = √x
The parent function of the function f(x) = 3√(-8x - 4) will be h(x) = √x.
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Answer:
Rewrite the equation by factoring –8 from the radicand and taking the cube root to get –2 in front of the radical symbol.
The graph is reflected over the x-axis.
The graph is also reflected over the y-axis.
The graph is vertically stretched by a factor of 2.
The graph is translated ½ unit to the left.
Step-by-step explanation: All possible answers for edge
Fill in the missing number.
80% of
= 240,000
Answer:
The missing number is 300,000.
Step-by-step explanation:
To find the missing number, we can set up an equation based on the information given. If 80% of a number is equal to 240,000, we can write:
0.80x = 240,000
To find x, we can divide both sides of the equation by 0.80:
x = 240,000 / 0.80 = 300,000
So, the missing number is 300,000.
13. Kenny sets up his own waving business. He charges $2 each time he waves graciously at someone, and $3 each time he waves vigorously with zeal. Smiles cost extra. All the waving causes tendonitis in his elbow and he must pay a $150 bill for his doctor's visit. If he completed 125 gracious waves and 300 10 vigorous waves, how much money did he make?
Answer: Kenny made 125 * $2 = $250 from 125 gracious waves.
He made 300 * $3 = $900 from 300 vigorous waves.
So, he made a total of $250 + $900 = $1150.
After paying the doctor bill, he has $1150 - $150 = $1000 left.
Step-by-step explanation:
The amount of money that Kenny made after completing the number of gracious waves and vigorous waves would be = $1000.
How to calculate the total amount of money made by Kenny?The amount that Kenny charges for gracious waves= $2
The amount of money that he charges for vigorous wave = $3.
The total number of completed gracious waves = 125
The amount made for gracious waves = 2× 125 = $250
The total number of completed vigorous waves = 300
The amount made for vigorous waves = 3×300 = $900
The total amount made in both waves = 250+900= $1,150
The bill to be payed to doctor = $150
The amount left = 1,150- 150 = $ 1000
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∠A=8x+74
∘
start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 8, x, plus, 74, degrees, end color #11accd
∠
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=
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6
∘
∠B=2x+56
∘
start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, 2, x, plus, 56, degrees, end color #28ae7b
Encuentra el valor de
�
xx y luego la medida de
∠
�
∠Bstart color #1fab54, angle, B, end color #1fab54:
what do you mean by
∠B=2x+56
∘
start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, 2, x, plus, 56, degrees, end color #28ae7b
Encuentra el valor de
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∠Bstart color #1fab54, angle, B, end color #1fab54:
SOMEONE HELPPPPP MEEEEEE PLEASE
Answer:
a.) (1,4), (-2,3), (0,4)
b.) (4,1), (3,-2), (4,0)
Step-by-step explanation:
a. When we want to find the reflection over the Y axis, that means the X coordinate signs reflect. For A, it says (-1,4). To reflect it, we reflect the X coordinate, so now it's (1,4) instead. You'll do that to the other two.
b. When rotating, you would switch the numbers of the coordinates and switch the sign of X. For the first one (-1,4), we'll switch it to (1,4). Not we'll switch the numbers around to make it (4,1). You'll do that for the other two
Combine the like terms to create an equivalent expression. 9+a−5b−2
FIND MULTIPLICITY AND ZEROS OF THE GRAPH!
Answer: The Zeros Are(in order) -3,-2,-1,1, 1.5 ALL have a multiplicity of 1.
Step-by-step explanation: Since the 0's cross the graph and don't "bounce" on the x-axis, they're all for a multiplicity of 1.
A container holds 6 pounds of peanuts. How many ounces of peanuts are in the container? (1 pound = 16 ounces)
12 ounces
16 ounces
54 ounces
96 ounces
Step-by-step explanation:
Good Afternoon! Your Answer would be 96!
16 x 6 = 96
How do we find this answer?
16 + 16 = 32
And 32 would be 16 twice!
32 + 32 = 64
And 64 would be 16 four times!
So now time to get the answer, 64 + 32 = 96.
Have An Amazing day.
ANSWER ASAP IM BEGGING BRO
Part A: slope = 1
Part B: slope = 1
Part C: Slope values becomes equal.
What is slope?Slope, An evaluation of a line's inclination with respect to the horizontal using numbers. The slope of any line, ray, or line segment in analytical geometry is defined as the proportion of the vertically to the horizontally distance between the two points on the line ("slope equals rise over run").
As we know,
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Part A:
(x₁ , y₁) = (0, -4)
(x₂, y₂) = (-2, 2)
m = (2 - 4) / (-2 - 0)
m = -2 / -2
m = 1
Part B:
(x₁ , y₁) = (0, -4)
(x₂, y₂) = (-4, 1)
m = (-4 - 0) / ((-4 - 0)
m = -4 / -4
m = 1
Part C:
As we pick different points to calculate slope for Part A and Part B, conclude that slope values are equal. It means that lines are parallel to each other and they have different y-intercepts.
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Find the value of x of the triangle below
Angles in a triangle add to 180 degrees
make a little equation for that
58 + 42 + x = 180
simplify
100 + x = 180
x = 180 - 100
x = 80
Hope this helps,
- Jeron :- )
A is the correct of the circle. The diagram is not drawn to scale.
If m
Answer:
Four thousand two hundred and
Step-by-step explanation:
Mr. Abott washed 3 8 of his laundry. His son washed 1 3 of it. Who washed more laundry? How much of the laundry still needs to be washed?
To help restart the economy growth, government is offering simple interest loans to small business at a rate 1.5%.
Say, you obtain one of these loans of $90,000 for 5 years. Determine the amount of money you must repay the government after 5 years.
Answer:
96750
Step-by-step explanation:
s.i=p×r×t
=90000×5×15/10 all divided by 100
9000×5×15 divided by 100
=90×5×15
=6750
amount=s.i+principal
=6750+90000
=96750
find the value of x and please show process!
Angles BAE and FAC are straight angles. What angle relationship best describes angles BAC and EAF?
Adjacent angles
Complementary angles
Supplementary angles
Vertical angles
Answer: Vertical Angles
Step-by-step explanation:
Took The test!
Angles BAC and EAF are vertically opposite angles .
Given,
Angles BAE and FAC are straight angles.
Here,
∠BAC + ∠FAC = 180° (Linear pair angles).
Now ,
∠BAC and ∠EFA are vertically opposite to each other .
Thus,
∠BAC = ∠EFA.
Thus these angles are vertically opposite angles and are equal .
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