Eudora ran from her home to her secret laboratory at an average speed of
12
km/h
12 km/h12, start text, space, k, m, slash, h, end text. She then took one of her jetpacks and flew to her school at an average speed of
76
km/h
76 km/h76, start text, space, k, m, slash, h, end text. Eudora traveled a total distance of
120
120120 kilometers, and the entire trip took
2
22 hours.
How long did Eudora spend running, and how long did she spend flying using her jetpack?
Eudora spent 0 hours running and 2 hours flying using her jetpack.
Let's use the formula: time = distance / speed.
Let x be the time Eudora spent running and y be the time she spent flying using her jetpack.
From the problem, we know that:
Eudora ran at an average speed of 12 km/h, so she covered a distance of 12x kilometers while running.
Eudora flew at an average speed of 76 km/h, so she covered a distance of 76y kilometers while flying.
The total distance she traveled was 120 kilometers, so: 12x + 76y = 120.
The entire trip took 2 hours, so: x + y = 2.
We can use the second equation to solve for x: x = 2 - y.
Substituting into the first equation, we get: 12(2 - y) + 76y = 120.
Simplifying the equation, we get: 152 - 64y = 120.
Solving for y, we get: y = 2 hours.
Substituting into x = 2 - y, we get: x = 0 hours.
Therefore, Eudora spent 0 hours running and 2 hours flying using her jetpack.
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Complete question:
Eudora ran from her home to her secret laboratory at an average speed of 12 km/h. She then took one of her jetpacks and flew to her school at an average speed of 76 km/h. Eudora traveled a total distance of 120 kilometers, and the entire trip took 2 hours.
How long did Eudora spend running, and how long did she spend flying using her jetpack?
i need to graph y=-1/4x+6
Answer:y intercept is 6 slope is -1/4
Step-by-step explanation:
to graph it in y=mx+b form b is the y intercpt and where you start the graph and m is the slope is [tex]-\frac{1}{4}[/tex] the you go to the right 4 and up one to graph the line
Need help with this problem 1
By the given definition of matrix A, the value of the matrix A⁻¹ is [tex]\left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right][/tex] and it is true that AA⁻¹ = I₃.
Calcuting the matrix A⁻¹Given that
[tex]A = \left[\begin{array}{ccc}1&0&2\\1&1&0\\1&0&1\end{array}\right][/tex]
To find the inverse of A, we can use the following formula:
A⁻¹ = (1/|A|) adj(A)
where |A| is the determinant of A and adj(A) is the adjugate matrix of A.
First, let's calculate the determinant of A:
|A| = 1(1×1 - 0×0) - 0(1×0 - 0×1) + 2(1×0 - 1×1)
|A| = -1
Next, we need to find the adjugate matrix of A.
To do this, we need to find the matrix of cofactors of A, then take its transpose:
[tex]C = \left[\begin{array}{ccc}1&-2&0&0&1&0&-1&2&1\end{array}\right]\\[/tex]
adj(A) = [tex]C^T = \left[\begin{array}{ccc}1&0&-1&-2&1&2&0&0&1\end{array}\right][/tex]
Now we can calculate A⁻¹ using the formula:
A⁻¹ = (1/|A|) adj(A)
So, we have
[tex]A^{-1} = (-1) \left[\begin{array}{ccc}1&0&-1&-2&1&2&0&0&1\end{array}\right] = \left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right][/tex]
Checking whether AA⁻¹ = I₃Finally, we can check whether AA⁻¹ = I₃ using
[tex]A^{-1}A = \left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right] \left[\begin{array}{ccc}1&0&2&1&1&0&1&0&1\end{array}\right] = \left[\begin{array}{ccc}1&0&0&0&1&0&0&0&1\end{array}\right] = I_3[/tex]
Therefore, we have found the inverse of A and verified that AA⁻¹ = I₃.
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A rainwater tank has a diameter of 160 cm and a height of 190 cm. The tank is half full. The water is used at a rate of 25,5 litres per day. In how many days will the tank run dry, assuming that no rain falls in that time?
It will run dry after 141.7 days.
In how many days will the tank run dry?The rainwater tank has a diameter of 160 cm and a height of 190 cm, then its volume is:
V = 3.14*(180cm)*(160cm/2)² = 3,617,280 cm³
We know that 1 L = 1000 cm³
then:
3,617,280 cm³ = 3,617.280 L
The water is used at a rate of 25,5 litres per day, so after x days there is:
W = 3,617.280 - 25.5*x liters
It is zero when:
0 = 3,617.280 - 25.5*x
x = 3,617.280/25.5
x = 141.7 days.
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Find the equilibrium level of national income in the basic Keynesian macroeconomic model
Y=c+I
C= 40+ 0.5y
I= 200
Therefore, the equilibrium level of national income in this basic Keynesian macroeconomic model is 480.
What is sum?In mathematics, the sum is the result of adding two or more numbers or quantities together. The symbol used to represent a sum is the capital Greek letter sigma (∑), which stands for "sum up."
by the question.
In the basic Keynesian macroeconomic model, equilibrium occurs when national income (Y) equals total spending in the economy. Therefore, we can set Y equal to the sum of consumption (C) and investment (I), as follows:
Y = C + I
Substituting the given consumption and investment functions into this equation, we get:
Y = (40 + 0.5Y) + 200
Simplifying and rearranging, we get:
Y - 0.5Y = 240
0.5Y = 240
Y = 480
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A payday loan is made for four weeks, where the amount of interest owed per $100
borrowed is $10
. If you borrow $800
for four weeks, how much do you owe at the end of the four weeks?
Consider the given function.
ƒ(1): =
5,
I < -2
3, -2 <=<0
0,
0 <=<2
> 2
-3,
Which graph represents the given function?
Help
Please …….
Zxrxrxrdrdrxxtxtcvyhnin
The box-and-whisker plot shows that the dataset has a median of approximately 5.5 and is relatively symmetric, with the middle 50% of the data falling between approximately 4 and 7.
The box-and-whisker plot offers a visual summary of the distribution of the given dataset. The following is one way to understand the plot:
The median, which is the midway number when the data is organised from least to largest, is shown by the line inside the box. The median in this situation is roughly 5.5.
The box's bottom edge corresponds to the first quartile (Q1) and its top edge to the third quartile, and it represents the middle 50% of the data (Q3). The interquartile range is the space between Q1 and Q3 (IQR). In this instance, Q1 is roughly 4 and Q3 is roughly 7, hence the IQR is roughly 3.
The whiskers reach from the box's boundaries to the dataset's lowest and largest values that aren't regarded as outliers. Although there are many different definitions of an outlier, it is generally accepted that any number that is more than 1.5 times the IQR below Q1 or above Q3 qualifies as an outlier. There aren't any anomalies in this circumstance.
Individual data points outside the box and whiskers are shown as dots above and below the whiskers. There are no such data points in this situation.
Hence, the box-and-whisker plot reveals that the dataset is very symmetrical and has a median of about 5.5, with the middle 50% of the data ranging between roughly 4 and 7.
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i’m confused on this
The value of the side x is 8. 4
How to determine the value of the variableIt is important to note that the Pythagorean theorem states that the square of the longest leg of a triangle, is equal to the sum of the squares of the other two sides, that is, the opposite and adjacent sides.
The formula is expressed as;
a² = b² + c²
From the information shown in the diagram, we have that;
Hypotenuse side = 21
Adjacent side = 12. 6
Opposite side = 2(x)
Substitute the values
x² = 21² - 12.6²
find the squares
x² = 441 - 158. 76
subtract the values
x = 16. 8
But, we have that this value is the diameter but x as shown is the radius.
Radius, x = 16. 8 /2 = 8. 4
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15. Find the value of x that makes the
quadrilateral a parallelogram.
6x-8
4x
If the value of x is 4, the quadrilateral meets all the requirements of a parallelogram and will be a parallelogram.
What is a quadrilateral?A quadrilateral is a four-sided shape with straight line segments as its sides. It is a two-dimensional shape with four angles, each measuring 90°. Quadrilaterals can be categorized into different shapes such as squares, rectangles, parallelograms, trapezoids, rhombuses, and kites.
A parallelogram is a four-sided shape with opposite sides parallel and equal in length. To find the value of x that makes the quadrilateral a parallelogram, we need to use the property of a parallelogram, which states that the opposite sides of a parallelogram are equal in length.
Therefore, we need to equate the opposite sides of the quadrilateral: 6x-8=4x. After solving this equation, we get x=4. Thus, the value of x that makes the quadrilateral a parallelogram is 4.
In order for a quadrilateral to be a parallelogram, opposite sides must be parallel. Using this property, we can set the opposite sides equal to each other and solve for x.
[tex]$2x + 5 = 3x - 2$[/tex]
Simplifying this equation, we get:
[tex]$x = 7$[/tex]
Therefore, if [tex]$x=7$[/tex], the quadrilateral is a parallelogram.
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Find each measurement indicated using Law Of Sines. Round your answers to the nearest tenth.
answer 4 -8
Using Law of sines, the missing angles are:
4) ∠B = 45.74°
6) ∠C = 21.02°
8) ∠A = 60.84°
How to use the Law of Sines?The law of sines is a rule for solving the lengths and angles of triangles and it states that:
a/sin A = b/sin B = c/sin C
4) Using law of sines, we have:
8/sin B = 11/ sin 80
(8/11) sin 80 = sin B
sin B = 0.7162
B = sin⁻¹0.7162
∠B = 45.74°
6) Using law of sines, we have:
13/sin C = 32/sin 62
sin C = (13/32) sin 62
sin C = 0.3587
C = sin⁻¹0.3587
C = 21.02°
8) Using law of sines, we have:
30/sin 104 = 27/sin A
sin A = (27/30) sin 104
sin A = 0.8733
A = sin⁻¹0.8733
A = 60.84°
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203,433 rounded to the nearest ten thousand
Step-by-step explanation:
203,433 rounded to the nearest ten thousand is 200,000.
Which relationships describe angles 1 and 2?
Select each correct answer.
A. supplementary angles
B. complementary angles
C. vertical angles
D. adjacent angles
The relationship which describe angles 1 and 2 is supplementary angles.
The correct answer choice is option A.
What are supplementary angles?Supplementary angles are angles in which the sum of their measure is equal to 180°.
Based on this, angles 1 and 2 are supplementary because they both add up to 180°.
Complementary angles are two angles which add up to 90 degrees.
Vertical angles are angles opposite each other when two angles intersect.
Adjacent angles are angles which have a common side and common vertex.
Hence, angles 1 and 2 are supplementary.
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a) What is the height of the container if it’s a cylinder with a radius of 3cm?
b) If the container from Part A is filled with coffee and coffee costs $0.02 per cubic centimeter, what is the cost of coffee?
a. The Vοlume = 198 cm³ and height = 7, if it’s a cylinder with a radius οf 3cm.
b. The cοst οf cοffee is $3.96 when $0.02 per cubic centimetre.
What is the fοrmula fοr the vοlume οf the cylinder?The fοrmula fοr the vοlume οf a cylinder is
V = πr²h,
where V is the vοlume, r is the radius, and h is the height.
a) Tο find the height οf the cylinder, we need tο knοw the vοlume οf the cοntainer and the radius. The fοrmula fοr the vοlume οf a cylinder is:
V = πr²h
[tex]$\mathrm{\frac{V }{ h}} = \pi r\² }[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{22}{7} \times 3 \times 3}[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{22}{7} \times 3 \times 3}[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{198}{7}[/tex]
Thus, Vοlume = 198 cm³ and height = 7
b) If the cοntainer frοm is filled with cοffee and cοffee cοsts $0.02 per cubic centimetre, Then the cοst οf cοffee
= $0.02 × 198 cm³
= $3.96
Thus, The Vοlume = 198 cm³ and height = 7, if it’s a cylinder with a radius οf 3cm.
The cοst οf cοffee is $3.96 when $0.02 per cubic centimetre.
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Write a polynomial of least degree with real coefficients and with the root -20-7i. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answer:
Step-by-step explanation:
Logically, if a polynomial of real coefficients has a complex root, it’s conjugate is a root as well. That means if -20-7i is a root, -20+7i is also a root. Also, since we’re dealing with minimal degree, we wish to construct a quadratic expression with such roots. To do this, we can use Vieta’s formulas, which relates the trinomial coefficients with its roots. The two roots added together is -b/a in ax^2 + bx + c, and the two roots multiplied together is c/a. The two roots added together is -40. The two roots multiplied together is 449. So, our quadratic expression is x^2+40x+449
CAN SOMEONE HELP WITH THIS QUESTION?✨
The rate of change of the angle of elevation is 0.00011 rad/ft, for that we have to know the elevation.
What is Elevation?The height above or below a specified(predefined) reference point, most frequently a reference geoid, which is a mathematical representation (expression) of the Earth's sea level as an equipotential gravitational surface, determines(defines) a location's elevation.
The angle of elevation of the camera is, Θ= [tex]tan^-^1(\frac{x}{2000} )[/tex]
The distance between the camera and the launching pad is, b= 2000 ft
The distance between the camera and the racket is, h = 4255 ft
To find the rate of change of the angle of elevation of the camera, we need to differentiate the function of that angle.
Θ= [tex]tan^-^1(\frac{x}{2000} )[/tex]
Differentiating function with respect to x we have,
[tex]\frac{d}{dx}[/tex] Θ=[tex]\frac{d}{dx} tan^-^1(\frac{x}{2000} )[/tex]
Θ'=[tex]\frac{1}{1+\frac{x^2}{2000^2} }[/tex][tex]*\frac{1}{2000}[/tex]
[tex]\frac{1}{2000+\frac{x^2}{2000} }[/tex] (Equation 1)
[tex]h^2=b^2+p^2[/tex]
[tex]4255^2+2000^2+x^2[/tex]
Θ=[tex]\frac{1}{2000+\frac{14105025}{2000} }[/tex]
≈ 0.00011 rad/ft.
Thus, the rate of change of the angle of elevation is 0.00011 rad/ft.
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23841.0596 in standard form
Answer:
23841.0596 in standard form is 2.38410596 x 10^4.
Step-by-step explanation:
Answer:
2.38410596 x 10^4
Step-by-step explanation:
pls brainlist
describe javiers works by ritting an divison equationthat includes a fraction
thats part a the real question jevier drew a model to determine how many fifths are in 6 wholes
After addressing the issue at hand, we can state that Javier's model equation predicts that there are 30 fifths in 6 wholes.
What is equation?A mathematical statement known as an equation demonstrates the equivalence of two expressions when they are joined by the equals sign ('='). As an illustration, 2x - 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' joins the two expressions together. An equation is a mathematical formula with two algebraic expressions on either side of the equal sign (=). It shows how the left and right formulas have an equivalent relationship. In any formula, L.H.S. = R.H.S. (left side = right side).
To describe Javier's work, one division equation with a fraction might be written as follows:
6 ÷ (1/5) =
How many fifths are there in six wholes? is the equation that illustrates the question Javier was attempting to answer. In order to answer this equation, we must divide 6 by the fraction 1/5, which is equivalent to multiplying 6 by 1/5's inverse, or 5/1:
6 ÷ (1/5) = 6 × (5/1) = 30
Javier's model predicts that there are 30 fifths in 6 wholes.
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Write the six trig functions for the following
SOH CAH TOA
Please and thank you
The six trig functions are:
(1) Figure 1, sin θ = 1/√5
(2) Figure 1, cos θ = 2/√5
(3) Figure 1, tan θ = 1/2
(4) Figure 2, sin θ = 3/√13
(5) Figure 2, cos θ = 2/√13
(6) Figure 2, tan θ = 3/2
What is a trig function?Trig function (short for "trigonometric function") is a mathematical function that relates the angles of a right triangle to the lengths of its sides. The main trig functions are sine (sin), cosine (cos), and tangent (tan).
The trig functions are abbreviated using SOH CAH TOA.
SOH : sin θ = opposite / hypotheses
CAH: cos θ = adjacent / hypothenuse
TOA : tan θ = opposite / adjacent
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Rewrite in the simplest form 7(−8f−2)+10(−5f+7)
Answer:
-106f+56
Step-by-step explanation:
7(-8f-2)= -56f-14
10(-5f+7)= -50f+70
-56f-14. +. 50f+70
=-106f+56
Answer:
-2(53f-28)
Step-by-step explanation:
Distribute7(−8f−2)+10(−5f+7)
7x-8f=-56f 7x-2=-14
10x-5f=-50f 10x7=70
-56f-14+-50f+70 Adding a negative to something means to subtract. Like right here at -14 + -50 is the same as -14 - 50
2. Add the numbers
-56f-14+-50f+70 -14+70=56
-56f+56-50f
3. Combine like terms
-56f+56-50f -56+ -50= -106
-106f +56
4. Common Factor
-106f + 56
-2(53f-28)
simplify the polynomial
The polynomial after simplification is obtained as [tex]5 x^{2}[/tex] + 9x + 3.
What is simplification?
In mathematics, reducing an expression, fraction, or problem to a simpler form is referred to as simplification. With calculations and solution, the problem is made simple. Make something simpler by simplifying it.
We are given a polynomial as
5x - 5 + [tex]11 x^{2}[/tex] + 4x - [tex]6 x^{2}[/tex] + 8
Now, in order to simplify the given polynomial, we will combine the like terms of the polynomial.
On combining the like terms, we get
[tex]5 x^{2}[/tex] + 9x + 3
Hence, the polynomial after simplification is obtained as [tex]5 x^{2}[/tex] + 9x + 3.
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•Taylorann Johnson 3/6/23 3td pero For each parabola, label all parts on the curve. Circle if it is a max or a min. Fill in the points or lines. 1 Name 1. y = x² Opens up or down? Positive Vertex (0.0) Max/Min Axis of Symmetry: x=__ y-intercept (,0) x-intercept(s) or the zeros ( ) [ Parabola Review Domain: (0₁2) Range: (1,8)
For the given parabola, the parts on the curve should be labeled as follows;
The parabola with the equation y = x² opens up.The vertex of the parabola are (0, 0).The max/min value are equal to (0, 0).The axis of symmetry is x = 0.The y-intercept is equal to (0, 0).The x-intercept or the zeros is (0, 0).The domain is equal to (-∞, ∞).The range is equal to (0, ∞).How to calculate the vertex and axis of symmetry of a quadratic function?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using the following mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = y = x², we have the following:
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(0)/2(1)
Axis of symmetry, Xmax = 0/1 = 0.
Vertex (h, k) = (0, 0).
In conclusion, the domain of this quadratic function f(x) = y = x² are all the x-values that are located on the x-axis of the graph, which include {-∞, ∞} or all real numbers.
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What is the volume of this rectangular prism?
A)40 cu in
B)120 cu in
C)22cu in
D)84 cu in
Answer: B (120 in^3)
Step-by-step explanation: W * L *H = V
Length * Width * Height = Volume
You can multiply the LWH in any order.
Height = 4
Length = 10
Width = 3
Remember, anything multiplied by ten is just the product (answer) with a zero added to the end. Example: 4 * 3 = 12; 12 * 10 = 120
Another Example: 15 * 2 = 30; 30 * 10 = 300
4 * 10 = 40
40 * 3 = 120
Therefore, 120 is your answer.
Hope this helps!
Answer:
The answer to your problem is, 120 cu in
Step-by-step explanation:
In order to find the volume of the cube there is only one thing that you need to do which is pretty simple just follow these steps:
Multiply, l * w * h ( * = multiply )
By following the formula up above you can find the volume of a rectagular prism which is:
4 x 10 = 40
3 x 40 = 120.
Thus the answer to you problem is, 120 cu in
Which sequence of transformations results in figures that are similar but not congruent
Answer:
When two shapes are similar but not congruent, the sequence of steps showing the similarity usually has a single dilation and then the rest of the steps are rigid transformations. The dilation can come at any time.
Step-by-step explanation:
When two shapes are similar but not congruent, the sequence of steps showing the similarity usually has a single dilation and then the rest of the steps are rigid transformations. The dilation can come at any time.
Converting Standard Form-Slope Intercept Form
Solve for y.
Step 1: Move the x term to the other
side by performing the opposite
operation to BOTH sides.
-7x+y=-17
+ [?];
+7x
Therefore , the solution of the given problem of slope comes out to be y = 7x - 17 is the equation in slope-intercept form.
Explain slope.A line's steepness is determined by its slope. In gradient-based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).
Here,
Given :
=> -7x + y = -17
7x both faces together
=> -7x + 7x + y = 7x - 17
Condense: y = 7x - 17
So,
=> y = 7x - 17 is the equation in slope-intercept form.
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what is the meaning of the following statement?
The proposition states that if the multiplication operation in a set is commutative and associative, then the product of any sequence of elements in the set, arranged according to any permutation of the sequence, will be the same as the product of the elements arranged in their original sequence.
What is associative multiplication and permutation?Associative multiplication refers to a property of multiplication where the order of performing the multiplication does not affect the final result. In other words, if we have three elements a, b, and c, then (a x b) x c is equal to a x (b x c).
Permutation refers to the rearrangement of a set of elements in a specific order. In mathematics, a permutation of a set of n elements is a bijective function from the set of integers {1,2, ..., n} to itself. In other words, a permutation is a way of rearranging the elements of a set in a specific order by swapping them around.
In the context of the given proposition, the associative property of multiplication ensures that the order of multiplication of elements in the product Xσ(1) Xσ(2) ... Xσ(n) can be rearranged without changing the final result. The proposition states that no matter how we permute the order of multiplication of elements, the final product will be the same, provided that the multiplication operation is both commutative and associative.
In other words, if we have a set of elements X1, X2, ..., Xn, and we multiply them together using a commutative and associative multiplication operation, then no matter how we permute the elements (i.e., rearrange them in a different order), the result of the multiplication will be the same.
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Select from the drop-down menu to correctly complete each comparison 4.408
The prοduct οf the matrices is nοt the identity matrix. Therefοre, X and A nοt inverses οf each οther.
What is an identity matrix?An identity matrix is a square matrix in which all the elements οf principal diagοnals are οne, and all οther elements are zerοs. It is denοted by the nοtatiοn “In” οr simply “I”. Any matrix will yield a matrix as a result of being multiplied by the identity matrix.
The identity matrix is a matrix having entry οne in its diagοnal and rest οf the entries are zerο.
[tex]X.A = \left[\begin{array}{cc}2&-1\\6&-4\\\end{array}\right] \left[\begin{array}{cc}1/2&1/4&\\-2&-1/2&\end{array}\right][/tex]
[tex]X.A = \left[\begin{array}{cc}3&1\\11&7/2\end{array}\right][/tex]
Hence, The prοduct of the matrices is not the identity matrix. Therefοre, X and A not inverses of each other.
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The complete question is in the attached image.
A bakery sells chocolate cupcakes and mocha cupcakes. One day it sold 162 chocolate and 138 mocha. What percent of the cupcakes sold that day were chocolate?
N=6, p=0.3, x<4
P(x<4) =
Answer:
Step-by-step explanation:
To find P(x<4), we need to use the cumulative distribution function (CDF) of the binomial distribution.
For N = 6 and p = 0.3, the probability mass function (PMF) is:
P(X = k) = (6 choose k) * 0.3^k * 0.7^(6-k)
where (6 choose k) is the binomial coefficient.
Using this formula, we can find the probabilities for each value of X less than 4:
P(X = 0) = (6 choose 0) * 0.3^0 * 0.7^6 ≈ 0.1176
P(X = 1) = (6 choose 1) * 0.3^1 * 0.7^5 ≈ 0.3025
P(X = 2) = (6 choose 2) * 0.3^2 * 0.7^4 ≈ 0.3241
P(X = 3) = (6 choose 3) * 0.3^3 * 0.7^3 ≈ 0.1852
Therefore, P(x<4) is the sum of these probabilities:
P(x<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) ≈ 0.9294
So the probability of getting less than 4 successes in 6 trials with a success probability of 0.3 is approximately 0.9294.
Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is lower than that of the general population.
(a) State the hypotheses that we can use to consider this question.
(b) Carry out the hypothesis test in (a) using the critical-value method with a significance level of .05, and summarize your findings.
(c) What is the p-value for the test conducted in (b)?
(d) The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the standard deviation from the low-income group is lower than that of the general population. State the hypotheses that we can use to answer this question.
(e) Carry out the test in (d) and report the p-value with an α level of .05, and summarize your findings.
Answer:
The null hypothesis is that the mean daily iron intake of the low-income group is equal to or greater than the general population, and the alternative hypothesis is that the mean daily iron intake of the low-income group is less than that of the general population.
H0: μ >= 14.44
Ha: μ < 14.44
(b) We can use a one-tailed t-test to test this hypothesis. With a sample size of 51, degrees of freedom of 50, a sample mean of 12.50, a population mean of 14.44, and a standard deviation of 4.75, we can calculate the t-statistic as follows:
t = (12.50 - 14.44) / (4.75 / sqrt(51)) = -3.16
Using a t-distribution table with 50 degrees of freedom and a significance level of .05, the critical value is -1.677. Since the calculated t-statistic is less than the critical value, we reject the null hypothesis.
Therefore, we can conclude that the mean daily iron intake among the low-income group is significantly lower than that of the general population at a significance level of .05.
(c) The p-value for this test is the probability of obtaining a t-value of -3.16 or more extreme assuming the null hypothesis is true. Using a t-distribution table with 50 degrees of freedom, we find the p-value to be less than .005.
(d) The null hypothesis is that the standard deviation of the low-income group is equal to or greater than that of the general population, and the alternative hypothesis is that the standard deviation of the low-income group is less than that of the general population.
H0: σ >= 5.56
Ha: σ < 5.56
(e) We can use a chi-square test to test this hypothesis. With a sample size of 51, degrees of freedom of 50, and a sample standard deviation of 4.75, we can calculate the chi-square statistic as follows:
chi-square = (n - 1) * s^2 / σ^2 = 50 * 4.75^2 / 5.56^2 = 39.70
Using a chi-square distribution table with 50 degrees of freedom and a significance level of .05, the critical value is 68.67. Since the calculated chi-square statistic is less than the critical value, we fail to reject the null hypothesis.
Therefore, we do not have sufficient evidence to conclude that the standard deviation of daily iron intake among the low-income group is significantly lower than that of the general population at a significance level of .05.