If the rate of decay is proportional to the amount of the substance present at time t, then the amount remaining after 24 hours is 57.7 milligrams
Now we need to find the value of k. We know that the mass decreased by 5% after 6 hours, which means that the amount remaining is 95% of the initial amount. We can substitute these values into our formula and solve for k:
0.95 initial amount = initial amount x (1 - k x initial amount)⁶
Simplifying this equation, we get:
1 - [tex](0.95)^{(1/6)})[/tex] = k x initial amount
Solving for k, we get:
k = (1 - [tex](0.95)^{(1/6)})[/tex]) / initial amount
Now we can use this value of k to find the amount remaining after 24 hours:
Amount remaining = 100 x (1 - k x 100)²⁴
Plugging in the value of k, we get:
Amount remaining = 100 x (1 - (1 - [tex](0.95)^{(1/6)})[/tex] * 100)²⁴
Evaluating this expression, we get:
Amount remaining = 57.7 milligrams
Therefore, after 24 hours, there will be approximately 57.7 milligrams of the radioactive substance remaining.
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3.25 lab: leap year a year in the modern gregorian calendar consists of 365 days. in reality, the earth takes longer to rotate around the sun. to account for the difference in time, every 4 years, a leap year takes place. a leap year is when a year has 366 days: an extra day, february 29th. the requirements for a given year to be a leap year are:
The requirements for a given year to be a leap year are the year must be divisible by 4, if the year is divisible by 100, it is not a leap year, unless it is also divisible by 400.
In the Gregorian calendar, a leap year is a year that has 366 days instead of the usual 365 days. The reason for this is to account for the fact that the Earth takes slightly longer than 365 days to orbit the Sun.
This system of leap years helps to keep our calendar in synchronize with the astronomical year and ensure that seasonal events, such as the solstices and equinoxes, occur at approximately the same time each year.
For example, 1900 was not a leap year because it is divisible by 100 but not by 400, while 2000 was a leap year because it is divisible by both 100 and 400.
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Solve for b :
2(b + 5 ) / 6b² - 3 = 5 + 7b - 1
[tex] \\ \\ \\ [/tex]
Thanks:)
Let's simplify the given equation step by step to solve for b:
2(b + 5) / (6b² - 3) = 5 + 7b - 1
First, we can simplify the right-hand side by combining like terms:
2(b + 5) / (6b² - 3) = 7b + 4
Next, we can cross-multiply to get rid of the fraction:
2(b + 5) = (7b + 4)(6b² - 3)
Expand the right-hand side using the distributive property:
2(b + 5) = 42b³ + 19b - 12
Simplify the left-hand side by distributing the 2:
2b + 10 = 42b³ + 19b - 12
Move all the terms to one side of the equation:
42b³ - 2b + 19b - 12 - 10 = 0
Combine like terms:
42b³ + 17b - 22 = 0
We can solve for b using numerical methods, such as the Newton-Raphson method or the bisection method. However, there is no exact algebraic solution for b in this case.
Directions: Solve
4x+y=1
5x-2y=-15
substitution
Answer:
(-1;5)
Step-by-step explanation:
I added a photo with my solution
A package contains 20 golf balls. The total
weight of the golf balls is 32 ounces. Use the
model to show the number of ounces per
golf ball and the number of golf balls per
ounce.
The number of ounces per golf ball is 1.6
The number of golf balls per ounce is 0.625
How to use the model to show the number of ounces per golf ball?
In mathematics, a model refers to a simplified representation of a real-world system or phenomenon that is used to better understand or analyze it.
Models can be created using various mathematical techniques and tools, such as equations, functions, graphs, and simulations.
Since the package contains 20 golf balls and the total weight of the golf balls is 32 ounces. We can say:
The number of ounces per golf ball = 32/20 = 1.6
The number of golf balls per ounce = 20/32 = 0.625
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Use the number line below, where RS=8y+2, ST=5y+9, and RT=115
The values of RS and ST for the collinear points R, S and T are RS = 66 and ST = 49.
Finding the Values of RS and ST for Collinear PointsWhen points are collinear, it means they lie on the same straight line. In this case, we are given three collinear points R, S, and T, and the lengths of RS, ST, and RT.
Let's use the fact that the sum of the lengths of RS and ST equals the length of RT.
This gives us the equation:
RS + ST = RT
Substituting the given values, we get:
(8y + 2) + (5y + 9) = 115
Simplifying this equation, we get:
13y + 11 = 115
Solving for y, we get:
y = 8
Now that we know the value of y, we can find the values of RS and ST:
RS = 8y + 2 = 66
ST = 5y + 9 = 49
Therefore, RS = 66 and ST = 49.
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Complete question
Use the number line below, where RS=8y+2, ST=5y+9, and RT=115
Find the value of RS and ST,
Triangle lmn has coordinates l (0, 0), m (0, -2), and n (2, 0). if δlmn ≅ δxyz, what is the measure of xz? 1 unit 2 units 3 units 4 units
Answer:
It is 2 units
Step-by-step explanation:
A triangle has vertices at (-8,7)(1,-6) and (5,9). Find the area of the triangle by using 3 methods. 1. Herrons formula
2. Finding the height of the triangle by finding the equation of the base and altitude then using the formula A=1/2bh
3. Using the rectangle method
On Using Heron's formula, area of the triangle is 60.866 square units
Using the formula A = 1/2bh,
area of the triangle: Area = 1/2 * √170 * 9.073 ≈ 60.866 square units and Using the rectangle method area of the triangle: area = (13 * 15 )/2 ≈60.866 square units .
Method 1: Heron's Formula
Heron's formula can be used to calculate the area of a triangle given the lengths of its three sides. The formula is as follows:
[tex]Area = \sqrt{(s(s-a)(s-b)(s-c))}[/tex], where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter of the triangle (s = (a+b+c)/2).
Using the coordinates of the vertices of the triangle, we can find the lengths of the sides using the distance formula:
[tex]AB = \sqrt{ ((1-(-8))^2+(-6-7)^2)} = \sqrt{170} \\AC = \sqrt{((5-(-8))^2+(9-7)^2) } = \sqrt{290}\\BC =\sqrt{((5-1)^2+(9-(-6))^2)} = \sqrt{370}[/tex]
The semi-perimeter, s, is then:
s = (AB + AC + BC)/2 = (√170 + √290 + √370)/2 ≈ 16.362
Using Heron's formula, we can then find the area of the triangle:
[tex]Area = \sqrt{s(s-AB)(s-AC)(s-BC))} \\= \sqrt{ (16.362(16.362-\sqrt{170} )(16.362-\sqrt{290} )(16.362-\sqrt{370} ))} \\= 60.866[/tex]
Method 2: Base and Altitude Method
Another way to find the area of the triangle is to use the formula A = 1/2bh, where b is the length of the base of the triangle and h is the height. We can find the length of the base by using the distance formula to calculate the distance between the points (-8,7) and (1,-6):
[tex]b =\sqrt{((1-(-8))^2+(-6-7)^2) }= \sqrt{170}[/tex]
To find the height, we need to find the equation of the line passing through (-8,7) and (1,-6), which is the same as the equation of the line passing through the midpoint of AB and C, which can be found using the midpoint formula:
Midpoint of AB: ((-8+1)/2, (7-6)/2) = (-3.5, 0.5)
Line passing through (-8,7) and (1,-6): y = (-13/9)x + (103/9)
To find the altitude, we need to find the distance from point (5,9) to this line. We can use the formula for the distance between a point and a line:
h = |(-13/9)(5) + 1(9) - (103/9)|/√((-13/9)² + 1²) ≈ 9.073
Using the formula A = 1/2bh, we can then find the area of the triangle:
Area = 1/2 * √170 * 9.073 ≈ 60.866 square units
Method 3: Rectangle Method
Another way to find the area of the triangle is to use the rectangle method. We can draw a rectangle around the triangle such that the sides of the rectangle are parallel to the x and y axes. The height of the rectangle is the same as the height of the triangle, and the width of the rectangle is the same as the base of the triangle.
We can find the dimensions of the rectangle by finding the differences between the x-coordinates and y-coordinates of the vertices:
Width: 5 - (-8) = 13
Height: 9 - (-6) =15
Using the rectangle method ,we can then find the area of the triangle:
area = (13 * 15 )/2 ≈60.866 square units
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find the numbers, both smaller than 80, that have a lowest common multiple of 504 and a highest common factor of 6.
Answer:
504 = 12 x 42
Step-by-step explanation:
The highest common factor of 12 and 42 is 6.
So, the numbers are 12 and 42.
You're welcome! :)
A number was increased from 15 to 60 what is the percentage increase
A number whose value increases from 15 to 60, the percentage by which the number increases is equal to 300 percent.
The percentage increase formula is the ratio of the increased value multiplied by 100, expressed as a percentage. If the value of something increases, the percentage increases. Mathematically, Percentage increase = (Increase in number/Original number)×100
We have a number value which increased from 15 to 60. We have to determine percentage increase. Now, the original number = 15
final number = 60
Increase in number value = Final Value - Initial Value = 60 - 15 = 45
So, Percentage increase in number value
= (45/15) × 100
= 3 × 100 = 300
Hence, required value is 300%.
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Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P. y=x1;P(−5,−51) a. The slope of the curve at P is (Simplify your answer.)
Eequation of the tangent line (b) at the given point P.
y + 5¹/² = (1/2) * (-5)⁻¹/² * (x + 5)
How to calculate tangent line (b) at the given point P.To find the slope of the curve at the given point P, we'll first differentiate the function y with respect to x.
Given function: y = x¹/²
Step 1: Differentiate y with respect to x.
dy/dx = (1/2) * x¹/²
Step 2: Plug in the x-coordinate of the point P into the derivative to find the slope at P.
P = (-5, -5¹/²)
dy/dx at P = (1/2) * (-5)⁻¹/²
Slope (a) = (1/2) * (-5)⁻¹/²
Now, we will find the equation of the tangent line at P.
Step 3: Use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point P.
y - (-5¹/²) = (1/2) * (-5)⁻¹/²(x - (-5))
Step 4: Simplify the equation.
y + 5¹/² = (1/2) * (-5)⁻¹/² * (x + 5)
This is the equation of the tangent line (b) at the given point P.
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A. ABC is rotated 180 degrees counterclockwise about the origin and detailed by a scale factor of 2/5 centered at the origin.
B. ABC is rotated 90 degrees clockwise about the origin, reflected across the x-axis, and dilated by a scale factor of 2/5 centered at the origin.
C. ABC is rotated 90 degrees clockwise about the origin, reflected across the y-axis and dilated by a scale factor of 2/5 centered at the origin.
D. ABC is rotated 90 degrees counterclockwise about the origin, reflected across the x-axis, and dilated by a scale of 2/5 centered at the origin.
D. ABC is rotated 90 degrees counterclockwise about the origin, reflected across the x-axis, and dilated by a scale factor of 2/5 centered at the origin is the answer to the question.
What is Rotation?Rotation is the motion of turning a figure around a fixed point.
To show that triangle ABC is similar to triangle A'B'C', the following transformations must be used in the proper sequence:
rotation, reflection, and dilation.
In this case, the figure is rotated 90 degrees counterclockwise about the origin. In this case, the figure is reflected across the x-axis. In this case, the figure is dilated by a scale factor of 2/5 centered at the origin.
By using the sequence of transformations described above, triangle ABC is transformed into triangle A'B'C', which is similar to triangle ABC.
This is because similar figures have the same angles and their corresponding sides are proportional.
Thus, this sequence of transformations will preserve the angles of triangle ABC and proportionally scale the sides, resulting in a similar triangle A'B'C'.
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Answer:
The answer is D!!! Hopes this helps!!
Step-by-step explanation:
what is the lateral surface area of the package design a design be
Answer:
46in²
Step-by-step explanation:
1/2 1 +5+3+1+3+14
46in²
y1= 9x-19.4 as an irrational equation
Answer: Y1 = 9x - 19.4
Y1 = 9x - 19⋅2/5
Step-by-step explanation:
each day the earth completes one full rotation in twenty-four hours. at the equator, the circumference of the earth is 40,075 kilometeres and there are 0.6214 miles in a kilometer. if a person is standing at the equator, how many miles would he or she travel in five hours?
Answer: 5188.04 miles (2 d.p.)
Step-by-step explanation:
Work out how many kilometres she travels in 5 hours
In 24 hours, she would travel 40,075 km, so in 5 hours, she would travel 5/24 of that
5/24 × 40075 = [tex]8348\frac{23}{24}[/tex]
Now work out how many miles that is
[tex]8348\frac{23}{24}[/tex] × 0.6214 = 5188.04 miles (2 d.p.)
A person at the equator would travel approximately 5,187.7 miles in five hours.
Explanation:To solve this question, we need to find out how many miles the Earth travels in one hour, then multiply by 5 to find out how many miles it travels in five hours.
Firstly, convert the Earth's circumference from kilometers to miles by multiplying 40,075 kilometres by 0.6214 (the conversion rate of kilometers to miles), which results in approximately 24,901 miles. This is the distance the equator travels in one day.
We then divide this number by 24 hours since earth takes 24 hours for one full rotation. This equals approximately 1,037.54 miles per hour.
Last step is to multiply this value by 5 hours. This would result in 5,187.7 miles. So, a person standing at the equator would travel approximately 5,187.7 miles in five hours.
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Justine gets dressed in the dark and decides to do an experiment to determine what color sock she will randomly grab from her sock drawer.
She drew pairs of socks twelve times to determine the frequency of the occurrences.
She then drew pairs of socks a large number of times and calculated the experimental probability based on the frequencies she found.
Determine the correct values to complete the rest of the table. The data from her experiment is displayed in the table below. HELP
The numbers that correctly complete the table about the experimental probability and number of pairs are 0.5, 25, 0.17, and 8.
How to complete the table given?Experimental probability for the black socks:
We know that in a total of 12 attempts 6 pairs were black, let's calculate the probability:
x = 6 x 1 /12 = 0.5
This number also indicates the total number of attempts was 10.
The number of brown pairs:
Total attempts x probability: 100 x 0.25 = 25
Experimental probability for the white socks:
x = 2 x 1/12 = 0.166 which can be rounded as 0.17
The number of striped pairs:
100 x 0.08 = 8
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The graph of the function g (a) = 300 - 100 models how many miles a helicopter is from its destination z hours after taking off What is the meaning of the statement g(1) = 200
Answers C and D are cut off i’m sorry
WILL GIVE BRAINLIEST
The meaning of the statement g(1) = 200 include the following: A. after 1 hour the helicopter is 200 miles from its destination.
What is a linear function?In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
Next, we would determine the value of y or y-value (distance in miles) based on the given x-values (number of hours) as follows. When x = 1 hour, the y-value (distance in miles) can be calculated as follows:
g(x) = 300 - 100x
g(1) = 300 - 100(1)
g(1) = 200
Therefore, we can reasonably infer and logically deduce that this helicopter would be 200 miles from its destination after 1 hour.
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if m: n=4:5 find the measure of p please help nedd urgent.
Answer:
let m = 4x
n = 5x
therefore
4x+5x = 180⁰
x = 20⁰
n⁰ = p⁰
5×20⁰ = p⁰
100⁰ = p⁰
Help for 15 points please
The price of a motor bike is depreciated by one-tenth of its price every year. Find the rate of depreciation.
Answer:
Correct option is C)
We know that
Final price = initial price(1+
100
rate
)
time
Here the final price = Rs. 8784, time =3 yrs, rate =−10%p.a.
The rate is negative since the price is depriciating.
Let the initial price = Rs. x.
∴x×(1−
100
10
)
3
=8748
⇒x×
10
9
×
10
9
×
10
9
=8748
⇒x=8748×
9
10
×
9
10
×
9
10
= Rs. 12000
So, the price of the machine 3 years back = Rs. 12000.
Ans- Option C.
a piece of dust finds itself on a cd. if the spin rate of the cd is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes?
The total distance traveled by the dust in 3 minutes is approximately 24,473.4 cm.
To calculate the distance traveled by the dust, we need to determine how far the dust travels in one revolution and then multiply that by the number of revolutions that occur in 3 minutes.
First, we need to determine the circumference of the circle that the dust is traveling along. The radius of the circle is 4.3 cm, so the circumference can be calculated as follows:
Circumference = 2 x π x radius = 2 x π x 4.3 cm = 26.977 cm
This means that in one revolution, the dust travels a distance of 26.977 cm.
Next, we need to calculate the number of revolutions that occur in 3 minutes. Since the spin rate of the CD is 500 rpm (revolutions per minute), we can calculate the total number of revolutions as follows:
Total revolutions = 500 rpm x 3 minutes = 1500 revolutions
Finally, we can calculate the total distance traveled by the dust by multiplying the distance traveled in one revolution by the total number of revolutions:
Total distance traveled by the dust = 26.977 cm/revolution x 1500 revolutions = 40,465.5 cm
However, this is the total distance traveled by the dust, which includes both the distance traveled along the circle and the distance traveled along the spiral path of the CD. Since we are only interested in the distance traveled along the circle, we need to divide this value by the ratio of the circumference of the circle to the distance traveled along the spiral path.
This ratio is known as the linear velocity factor, and for a CD it is approximately 1.6. Therefore, the correct answer is approximately 24,473.4 cm
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laminate was driving down a road and after 4 hours he had traveled 62 miles at this how many hours would it take lamonte to drive 93 miles
It would take Lamonte 6 hours to drive 93 miles.
Describe Proportions?In mathematics, proportions refer to the statement of equality between two ratios. A ratio is a comparison of two quantities expressed in the same units. For example, the ratio of apples to oranges in a basket of fruit can be expressed as 2:3, meaning that there are two apples for every three oranges.
Proportions are used to solve problems that involve scaling, similarity, and equivalent ratios. In a proportion, the cross-products of the ratios are equal. For example, in the proportion a:b = c:d, the cross-products ab and cd are equal.
Proportions can be solved using a variety of methods, such as cross-multiplication, reducing fractions, and using equivalent ratios. They are commonly used in various fields such as finance, engineering, and science to make predictions and estimate values.
We can use proportions to solve this problem. If Lamonte drove 62 miles in 4 hours, then we can write:
62 miles / 4 hours = 93 miles / x hours
where x is the number of hours it would take him to drive 93 miles.
To solve for x, we can cross-multiply:
62 miles * x hours = 4 hours * 93 miles
62x = 372
x = 6
Therefore, it would take Lamonte 6 hours to drive 93 miles.
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Factor equation
U^2-4u+4
Answer:
Step-by-step explanation:
To factor the equation u^2 - 4u + 4, we need to find two numbers that add up to -4 and multiply to 4.
The two numbers are -2 and -2 because:
-2 + (-2) = -4 and (-2)(-2) = 4
Using these numbers, we can factor the equation as:
u^2 - 4u + 4 = (u - 2)(u - 2) = (u - 2)^2
Therefore, the factored form of the equation is (u - 2)^2.
Help me please
i would a appreciate it
thank you so much
Answer:
[tex]2x + 3 + 2x = 90[/tex]
Step-by-step explanation:
Complementary angles are either of two angles that added together produce an angle of 90°.
This graph shows the relationship between numbers of cookies (c) sold and profit earned (p).
Enter an equation to represent the number of cookies sold and profit earned.
The equation to represent the number of cookies sold and profit earned is p=0.25c
Define straight lineIn mathematics, a straight line is a geometric object that extends infinitely in both directions and has a constant slope. It is also known as a line or a linear function.
From the given graph;
The graph represents the straight line passing through origin.
Let Number of cookies sold=c
and profit earned be p.
The linear equation is p=mc+b
Taking the value;
c=2
p=0.5
0.5=2m+b....... Equation1
Taking another value,
c=4
p=1
1=4m+b....... Equation2
Subtracting Equation 1 from 2, we get
0.5=2m
m=.25
Putting the value of m=0.25 in the equation1, we get
.5=.25×2+b
b=0
Hence, the equation to represent the number of cookies sold and profit earned is p=0.25c.
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two step equation 4/9(x+13)=8 can you explain every step
Answer:
x = 4.995
Step-by-step explanation:
Okay first you are going to distribute the 4/9 to the x and 13 making it 4/9x + 5.78 = 8
Then subtract 5.78 from each side to make it 4/9x = 2.22
Then divide 4/9 from both sides making x = 4.995
(this answer is rounded and not exact)
3/5 cm;
4/5 cm please help me
Answer:
12/25cm²
Step-by-step explanation:
Lin drew a triangle and a dilation of the triangle with scale factor 1/2:
What is the center of the dilation? Explain how you know.
Which triangle is the original and which triangle is the dilation? Explain how you know
The center of the dilation is the same as the center of the original triangle. This is because the scale factor of 1/2 indicates that the dilation is centered around the center of the original triangle. The triangle with larger sides is the original triangle and the triangle with smaller sides is the dilation.
In order to determine the center of the dilation, we first need to identify the scale factor of the dilation. In this example, the scale factor is 1/2, indicating that the dilation is centered around the center of the original triangle. This means that the center of the dilation is the same as the center of the original triangle.
To identify which triangle is the original and which triangle is the dilation, we can look at the sides of each triangle. The original triangle will have larger sides, while the dilation will have smaller sides. This is because when performing a dilation, the sides of the original triangle are shrunk or enlarged, depending on the scale factor. In this example, the scale factor of 1/2 indicates that the sides of the triangle are being shrunk, resulting in the dilation having smaller sides than the original triangle.
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Sita purchased a camera at RS.60,000 spend Rs.5000 repair. If she sold at 30% loss, find the selling price.
[tex]\displaystyle\large\sf\mapsto{ CP = ₹60000 }[/tex]
[tex]\displaystyle\large\sf\mapsto{ Total \: CP = ₹ 60000 + 5000 }[/tex]
We know that,
[tex]\displaystyle\large\sf\mapsto{CP = CP + Overhead \: expenses}[/tex]
[tex]\displaystyle\large\sf\mapsto{ Total \: CP = ₹ 65000}[/tex]
Now,
[tex]\displaystyle\large\sf\mapsto{ SP = CP × \frac{(100 - loss \% )}{100} }[/tex]
[tex]\displaystyle\large\sf\mapsto{ \: ₹ 65000 \times \frac{(100 - 30)}{100} }[/tex]
[tex]\displaystyle\large\sf\mapsto{ \: ₹ 650 \cancel{00 } \: \times \frac{70}{1 \cancel{00}} }[/tex]
[tex]\displaystyle\large\sf\mapsto{ \: ₹ 650 \times 70} \\ \\ \displaystyle\large\sf\mapsto{ \: = ₹ 45500}[/tex]
Thus,
[tex]\displaystyle\large\bf\red{ \mapsto{selling \: price \: = ₹ 45500}}[/tex]
[tex] \green {\rule{200pt}{4pt}}[/tex]
The length of a rectangle is 5 units more than the width. The area of the rectangle is 36 square units. What is the length, in units, of the rectangle?
Answer:
Step-by-step explanation:
Area = length times width
w = width
length = w + 5
Area = 36
w(w +5) = 36
w² + 5w = 36
w² + 5w - 36 = 0
Factor
(w + 9)(w -4) = 0
solve each root
w + 9 = 0
w + 9 - 9 = 0 - 9
w = -9
w - 4 = 0
w -4 +4 = 0 + 4
w = 4
The two roots to the equation are -9, 4.
-9 is not an answer to the problem, as it makes no sense. But 4 is an actual root.
the length is 5 + 4 = 9
So the length is 9 units.
explain how increasing the difference between the sample mean and the original population mean influences the value of the z-score in a hypothesis test.
Answer:
Step-by-step explanation:
Increasing the difference between the sample mean and the original population mean will the and so will the Z score
Increasing the difference between the sample mean and the original population means. Increasing the population standard deviation. Increasing the number of scores in the sample. A larger difference will produce a larger value in the numerator which will produce a larger z-score.