The given in this problem are:
99% confidence level
N = 61
Mean = 2.0 kg
Standard deviation = 4.8
Z value for a 9% confidence interval is 2.576
Confidence Interval = mean ± Z s/ sqrt n
= 2.0 ± 2.576(4.8/sqrt 61)
=2.0 ± 2.576 (0.6145770236779006736364371988794)
= 2.0 ± 1.5832
= 0.4168 < x < 3.5832
The difference between the roots of the quadratic equation x2+x+c=0 is 6. Find c.
To solve this question:
First, we compare with the standard quadratic equation to find a, b and c.Then, we apply Bhaskara to find the roots, as function of c.Then, since the difference is 6, we use this to find c.Doing this, we get that: [tex]c = -\frac{35}{4}[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
x²+x+c=0
Comparing with the standard second order equation, which is:
[tex]ax^2 + bx + c = 0[/tex]
We get that:
[tex]a = 1, b = 1[/tex]
Finding the roots:
[tex]\Delta = b^{2} - 4ac = 1^2 - 4(1)(c) = 1 - 4c[/tex]
[tex]x_{1} = \frac{-1 + \sqrt{1 - 4c}}{2}[/tex]
[tex]x_{2} = \frac{-1 - \sqrt{1 - 4c}}{2}[/tex]
Difference of 6
Thus:
[tex]x_1 - x_2 = 6[/tex]
[tex]\frac{-1 + \sqrt{1 - 4c}}{2} - \frac{-1 - \sqrt{1 - 4c}}{2} = 6[/tex]
[tex]-\frac{1}{2} + \frac{\sqrt{1 - 4c}}{2} + \frac{1}{2} + \frac{\sqrt{1 - 4c}}{2} = 6[/tex]
[tex]\frac{2\sqrt{1 - 4c}}{2} = 6[/tex]
[tex]\sqrt{1 - 4c} = 6[/tex]
[tex](\sqrt{1 - 4c})^2 = 6^2[/tex]
[tex]1 - 4c = 36[/tex]
[tex]-4c = 35[/tex]
[tex]4c = -35[/tex]
[tex]c = -\frac{35}{4}[/tex]
Thus, [tex]c = -\frac{35}{4}[/tex] is the value.
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Write the slope-intercept form of the equation for the line.
A. y= -3x - 1
B. y= 1/3x - 1
C. y= 3x - 1
D. y= 1/3x + 1
(Picture is shown below)
a law clerk has earned more than $20000 since being hired (it's a math inequality problem)
How many terms are there in a geometric series if the first term is 7, the common ratio is 2, and the sum of the series is 105?
Hint: (image attached below) r ≠ 1, where a1 is the first term and r is the common ratio.
OPTIONS
A) n = 3
B) n = 4
C) n = 5
D) n = 6
Answer:
the answer would be B. N=4
Which killed the greatest number of American soldiers during the Spanish-American war?
A) yellow fever
B) invasion of Puerto Rico
C) battle of Manila Bay
D) battle of San Juan Hill
In a country where prices are rising quickly, bread that now costs $1.39 will cost 2.4 times as much next year. How much will the bread cost next year? (Round your answer to the nearest cent
The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of gasoline is 5:18. There are 36 gallons of gasoline. How many ounces of oil are there?
16 ounces
10 ounces
129.6 ounces
2.5 ounces
The amount of oil, in ounces, in the fuel mix can be found using a proportion with the given ratio and the amount of gasoline.
Explanation:To find the number of ounces of oil, we need to use the given ratio and the amount of gasoline. The ratio of oil to gasoline is 5:18, meaning that for every 5 ounces of oil, there are 18 gallons of gasoline. Since we know that there are 36 gallons of gasoline, we can set up a proportion to find the number of ounces of oil:
5 ounces / 18 gallons = x ounces / 36 gallons
Cross multiplying, we get:
18x = 5 * 36
Simplifying further:
18x = 180
Dividing both sides by 18, we get:
x = 10 ounces
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A triangular table has angles with measures in the ratio 7:9:4. What is the measure of the smallest angle?
The measure of an exterior angle of a regular polygon is 72 degrees. Find the measure of an interior angle.
Which statement describes the graph of an odd function
A. The graph is symmetric about the line Y equals X
B. The graph is symmetric about the X axis
C. The graph is symmetric about the line X equals zero
D. The graph is symmetric about the origin
The correct description is about graph of an odd function is;
''The graph is symmetric about the origin''.
Option D is true.
What is odd function?
The function is said to an odd function if it satisfy the condition;
⇒ f (-x) = - f (x)
Given that;
The function is an odd function.
Now,
Since, The odd function is rotate by the figure 180 degree then it will remains same.
So, The graph of an odd function is symmetric about the origin.
Thus, The correct description is about graph of an odd function is;
''The graph is symmetric about the origin''.
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Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value. G(x) = 2 sin (x-π) F(x) = 3x^2 + 12x + 16
The minimum of G(x) is -2 and of F(x) is 4 So, G(x) has the smallest minimum y-value.
The function G(x) is a sine function. The sine function, sin(x), has a range of -1 to 1. The minimum value of sin(x) is -1. Since G(x) = 2 sin(x - π), we multiply the minimum value of sin(x) by 2.
The minimum value of sin(x - π) is:
sin(x - π) = -1
Thus, the minimum value of G(x) is:
2 * (-1) = -2
To find the minimum value of a quadratic function, we use the vertex formula, x = -b / 2a. For F(x), a = 3, b = 12, and c = 16.
The x-coordinate of the vertex is:
x = -12 / (2 * 3) = -12 / 6 = -2
Substitute x = -2 into the function to find the minimum y-value:
F(-2) = 3(-2)² + 12(-2) + 16
F(-2) = 3(4) - 24 + 16 = 12 - 24 + 16 = 4
solve y + w - 3/4z = 0 for z
The expression solved for z is:
z = (4/3)*(y + w)
How to solve the expression for z?
Here we have the expression:
y + w - 3/4z = 0
And we want to solve it for z, which means that we need to isolate z on one side of the expression.
If we add (3/4)z in both sides we get:
y + w = (3/4)z
Now if we multiply both sides by (4/3).
(4/3)*(y + w) = (4/4)*(3/4)z = z
Then we got:
z = (4/3)*(y + w).
Thus, the expression is solved for z.
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The length of a rectangle is 2 cm longer than its width. if the perimeter of the rectangle is 36 cm , find its area.
The area of the rectangle is 80 square cm.
Explanation:To find the area of a rectangle, we need to know the length and width. Let's denote the width of the rectangle as 'w'. As given, the length of the rectangle is 2 cm longer than its width, so the length can be represented as 'w + 2'.
The perimeter of a rectangle is the sum of all four sides. In this case, it is given as 36 cm. Using the formula for the perimeter of a rectangle, we can set up the equation:
2(w + w + 2) = 36
Simplifying the equation:
4w + 4 = 36
4w = 32
w = 8
Substituting the value of 'w' back into the expression for length:
Length = 8 + 2 = 10
The area of a rectangle is given by the formula: area = length × width. So, the area of this rectangle is:
Area = 10 × 8 = 80 square cm
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Write the number 2174 to the nearest hundred
#12 if measure of angle 1 = 19x +1 and measure of angle 5 = 15x +13 then measure of angle 1 =? X=?
Devon and his friends bought strawberry wafers for $3 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $30 to buy a total of 22 packets of wafers of the two varieties.
Part A: Write a system of equations that can be solved to find the number of packets of strawberry wafers and the number of packets of chocolate wafers that Devon and his friends bought at the carnival. Define the variables used in the equations. (5 points)
Part B: How many packets of chocolate wafers and strawberry wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)
A)
S = Strawberry wafer packets
c = chocolate wafer packets
s +c = 22
3.00s +1.00c = 30.00
B)
s + c = 22
s = 22-c
3.00(22-c) + 1.00c = 30.00
66.00 - 3.00c +1.00c = 30.00
66.00 -2.00c =30.00
-2.00c = -36.00
c = -36.00 / -2.00 = 18
18 packets of chocolate wafers
4 packets of strawberry wafers
Name a line segment that is perpendicular to Line AC
a.) Segment AE
b.) Segment BF
c.) Segment HD
d.) Not enough information
what is 3 divided by 18.6
3 divided by 18.6 is 0.16129032258
What is division?Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.
Given expression,
3 divided by 18.6
To find the number :
We take division of 3 by 18.6.
3/18.6
= 0.16129032258
Therefore, the value is 0.16129032258
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Distributive property to simplify 39x5
what are the Answer choices
One positive integer is 6 less than twice another. the sum of their squares is 569. find the integers.
Find the slope of the line passing through points q(8, 7) and p(4, 1).
Hi there! :)
Step-by-step explanation:
[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{1-7}{4-8}=\frac{-6}{-4}=\frac{-6/2}{-4/2}=\frac{-3}{-2}=\frac{3}{2}[/tex]
Slope is 3/2.
Final answer is 3/2.
Hope this helps!
Thanks!
Have a nice day! :)
:D
For any distribution, what is the z-score corresponding to the median? 0 1 n cannot be determined from the information given
find sin x if cos x= 2/3 and x is in quadrant 4
write an equation in slope intercept form, passes through (-1,-10), parallel to y=7
An equation in slope intercept form, passes through (-1,-10), parallel to y=7 is y = -10 .
What is slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The slope of a line is the measure of the steepness and the direction of the line.
What is standard form of slope for line and point ?The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
According to the question
An equation in slope intercept form,
passes through (-1,-10), parallel to y = 7
now,
When line is y = 7
that means , x = 0
and it is also a horizontal line , i.e slope (m) = 0
As, Parallel lines have same slope .
By using slope intercept formula for (-1,-10)
y = mx + b
substituting the value
-10 = 0 + b
b = -10
Therefore, putting values in general equation of slope intercept for any point
y = mx + b
y = -10
Hence, an equation in slope intercept form, passes through (-1,-10), parallel to y=7 is y = -10 .
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if tan(145) = -1/1.43 , what is tan(-125) A. -1.43, B. 1.43, C. 1/1.43, D. -1/1.43
Answer:
B. 1.43
Step-by-step explanation:
Because tan (180-θ)=-tan θ
[tex]tan (145) = tan (180 -35)= -tan 35 = -\frac{1}{1.43}\\tan 35 =\frac{1}{1.43}[/tex]
Because tan (90+θ) = -cot θ
tan (-125) can be written as:
[tex] tan(-125)=-tan (125) = - tan (90+35) = cot 35[/tex]
tan θ x cot θ =1
⇒tan 35 x cot 35 = 1
⇒[tex]\frac{1}{1.43} \times cot 35 =1 \\ cot 35 = 1.43[/tex]
⇒[tex] tan(-125)= cot 35 = 1.43[/tex]
What is the 1st term when 3x3 − 7x + 6x4 − 2x2 is arranged in descending order?
3x3
−7x
6x4
−2x2
A turtle walked 1/8 of a mile in 1/2 of an hour. How many miles will he turtle walk in one hour?
if 8y-8=24, find the value of 2y
A kitten grows from 5oz at birth to 3lb 5oz at 6 months (find the rate of change)
I need to know this answer ?
combine all the like terms
4x^3 + 2x^2
then you have -6x-6x which = -12x and -10+4 = -6
so it becomes 4x^3+2x^2-12x-6
Answer is A