Answer:
To add mixed numbers, we need to add the whole numbers separately and fractions separately.
Starting with the whole numbers, we have:
9 1/2 − 3 7/8 + 4 4/5 − 1 1/2
= (9 + 4) − (3 + 1) + (4/5 − 1/2) + (1/8 − 7/8) (grouping the terms)
= 10 − 4 + (8/10 − 5/10) + (−6/8) (converting fractions to have a common denominator)
= 6 + 3/10 − 3/4 (simplifying fractions and adding whole numbers)
= 5 7/20 (expressing the result as a mixed number in simplest form)
Therefore, the value of the expression is 5 7/20.
True or false? the solution  Who’s system of equation is the point or points with a graph crosses the X axis 
answer: false
explanation: i took the test and got it right
As a result, the spot or points where the graph crosses the x-axis is not always the solution of a system of equations.
what is solution ?A solution in mathematics is the response to an issue or equation that meets specific requirements. The context of the issue or equation determines the kind of solution. For instance, in mathematics, the value of the variable(s) that makes an equation true is known as the solution. For instance, the answer to the equation 2x + 5 = 9 is x = 2, since the equation can be solved with x = 2.
given
False.
The values of the variables that fulfill every equation in a system of equations are represented by the system's solution.
A unique solution to a system of equations corresponds to the spot in the Cartesian plane where the equations' graphs intersect. This spot could be on the x-axis or not.
The graphs of the equations will be coincident or parallel lines that do not intersect and do not span the x-axis if a system of equations has an infinite number of solutions.
As a result, the spot or points where the graph crosses the x-axis is not always the solution of a system of equations.
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What is the effective interest rate of a simple discount note for $3,500 at a bank discount rate of 11%, for 24 months?
The effective interest rate of the simple discount note is 6%.
The effective interest rate (EIR) of a simple discount note can be calculated using the following formula:
EIR = (Discount ÷ Face Value) x (360 ÷ t)
Where Discount is the difference between the face value and the discounted value, t is the time in days from the issuance of the note until its maturity, and 360 is the number of days in a year used for interest rate calculations.
In this case, the face value is $3,500, the bank discount rate is 11%, and the time to maturity is 24 months or 720 days.
Discounted value = Face value x (1 - Bank discount rate x t ÷ 360)
Discounted value = $3,500 x (1 - 0.11 x 720 ÷ 360)
Discounted value = $3,080
Therefore, the discount is $420 ($3,500 - $3,080).
Using the formula for EIR, we get:
EIR = ($420 ÷ $3,500) x (360 ÷ 720)
EIR = 0.06 or 6%
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Linear or non-linear?
What is the length of side x?
Given:-
A right angled triangle with two angles 60° and 30° is given to us.Length of two shorter sides is x and √10 .To find:-
The value of x .Answer:-
Here since the given triangle is a right angled triangle, we may use the trigonometric ratios . We can see that perpendicular and base are involved in this question whose measures are "x" and "√10" respectively with respect to 60° angle. So here we may use the ratio of tangent as , in any right angled triangle,
[tex]\implies\tan\theta =\dfrac{p}{b} \\[/tex]
and here p = x , and b = √10 . So on substituting the respective values, we have;
[tex]\implies \tan\theta = \dfrac{x}{\sqrt{10}} \\[/tex]
Also the angle here is 60° , so that;
[tex]\implies\tan60^o =\dfrac{x}{\sqrt10} \\[/tex]
The value tan60° is √3 , so we have;
[tex]\implies \sqrt3 =\dfrac{x}{\sqrt10}\\[/tex]
[tex]\implies x =\sqrt{10}\cdot \sqrt{3}\\[/tex]
[tex]\implies x =\sqrt{10\cdot 3} \\[/tex]
[tex]\implies x =\sqrt{30} \\[/tex]
The value of √30 is approximately 5.48 , so that;
[tex]\implies \underline{\underline{\red{\quad x = 5.48\quad }}} \\[/tex]
Therefore the value of x is approximately 5.48 .
Answer:
The length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
Step-by-step explanation:
From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.
A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:
b is the shortest side opposite the 30° angle.b√3 is the side opposite the 60° angle.2b is the longest side (hypotenuse) opposite the right angle.We have been given the side opposite the 30° angle, so:
[tex]\implies b=\sqrt{10}[/tex]
The side labelled "x" is the side opposite the 60° angle, so:
[tex]\implies x=b\sqrt{3}[/tex]
Substitute the found value of b into the equation for x:
[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]
[tex]\implies x=\sqrt{10 \cdot3}[/tex]
[tex]\implies x=\sqrt{30}[/tex]
Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
[tex]\hrulefill[/tex]
We can also calculate the length of side x using the tangent trigonometric ratio:
[tex]\boxed{\tan \theta=\sf \dfrac{O}{A}}[/tex]
where:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.From inspection of the given right triangle:
θ = 30°O = √(10)A = xSubstitute these values into the formula:
[tex]\implies \tan 30^{\circ}=\dfrac{\sqrt{10}}{x}[/tex]
[tex]\implies \dfrac{\sqrt{3}}{3}=\dfrac{\sqrt{10}}{x}[/tex]
[tex]\implies x\sqrt{3}=3\sqrt{10}[/tex]
[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}[/tex]
Rationalise the denominator by multiplying the numerator and denominator by √3:
[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}\cdot \dfrac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac{3\sqrt{10}\sqrt{3}}{3}[/tex]
[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]
[tex]\implies x=\sqrt{10\cdot3}[/tex]
[tex]\implies x=\sqrt{30}[/tex]
Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
The perimeter of a rectangular garden is 30 ft. The length is 3 ft more than the width. Find the length and the width of the garden.
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
in our case
length = width + 3
and
2×length + 2×width = 30
using the first equation in the second :
2×(width + 3) + 2×width = 30
width + 3 + width = 15
2×width + 3 = 15
2×width = 12
width = 12/2 = 6 ft
length = width + 3 = 6 + 3 = 9 ft
How do you write y = 6 in slope intercept form
Draw a conclusion based upon true statements (i) and (ii).
(i) If two triangles are congruent, then they are similar.
(ii) △ ABC is not similar to △ DEF
Based οn the true statements (i) and (ii), we can cοnclude that △ ABC is nοt cοngruent tο △ DEF.
Statement (i) tells us that if twο triangles are cοngruent, then they are similar. This means that cοngruence implies similarity. Hοwever, statement (ii) tells us that △ ABC is nοt similar tο △ DEF. This means that there is nο similarity between the twο triangles.
Therefοre, we cannοt cοnclude that the twο triangles are cοngruent, because cοngruence implies similarity and we have been given that there is nο similarity between them. In οther wοrds, the fact that △ ABC is nοt similar tο △ DEF means that we cannοt cοnclude anything abοut their cοngruence, because we dο nοt have enοugh infοrmatiοn tο determine whether they are cοngruent οr nοt.
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What is the center and radius of a circle with the following equation
Answer:
Center: (1, -3); radius: 2
Step-by-step explanation:
(x - h)² + (y - k)² = r²
(x - 1)² + (y + 3)² = 4
(x - 1)² + (y - (-3))² = 2²
Center: (1, -3); radius: 2
Orlando and Nancy are scuba diving. Orlando is at an elevation of -60 feet, and he is descending at a rate of 8 feet per minute. Nancy is at an elevation of -35 feet and she is descending at a rate of 12 feet each minute. The variable t represents the time in minutes. After how many minutes will Orlando and Nancy be at the same elevation? At what elevation will they be at that time?
Answer:
Orlando and Nancy will be at an elevation of -110 when they are at the same elevation.
Step-by-step explanation:
We can set up an equation to find the time it takes for Orlando and Nancy to be at the same elevation
We will use the variable T to represent the time in minutes
Orlando's elevation : -60 + 8t
Nancy's elevation : -35 + 12t
We will solve for t to see at what time the elevations were equal
-60 + 8t = -35 + 12t
-60 + 35 = 12t - 8t
-25 = 4t
4t = -25
t = -6.25
This means that both will be at the same elevation 6.25 minutes before Orlando goes down
To find the elevation they will be at that time, we will plug -6.25 into either expression.
-60 + 8t = -60 + 8(-6.25) = -110
Orlando and Nancy will be at an elevation of -110 when they are at the same elevation.
5/12x6/15=30/180
How do I simplify?
Answer:
0.167
Step-by-step explanation:
if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6
technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167
that should end up being your answer if i did the math right
Answer:
Step-by-step explanation:
5/12 * 6/15 =30/180
1/6=1/6
which is true, Right-hand side is equal to left-hand side
Which of the following values of x makes this inequality true? Circle all that apply
5 + x > 5
A.1/2
B. -10
C. -5
D. 0.000003
E. 1.5
Answer:
A. 1/2
D. 0.000003
E. 1.5
Step-by-step explanation:
The inequality 5 + x > 5 can be simplified as follows:
5 + x > 5
x > 5 - 5
x > 0
Parts of similar triangles
Find x
In Δ PRQ, The value of the missing variable x is 4.8.
What is the triangle area formula?Calculating the area οf a triangle. Use the fοrmula area = 1/2 * base * height tο calculate the area οf a triangle. Select a side tο serve as the base and calculate the triangle's height frοm that pοint.
Cοrrespοnding sides in similar triangles are prοpοrtiοnal. As a result, using the infοrmatiοn prοvided, we can calculate the fοllοwing prοpοrtiοn:
As Δ PQS ≅ Δ PRQ
Then according to CPCT
PQ ≅ PR
and
PS ≅ PQ
Then we have
7 ≅ 5+ x
5 ≅ 7
Then
[tex]$ \frac{7}{5 + x} = \frac{5}{7}[/tex]
Cross multiply
[tex]$ \frac{7}{5 + x} = \frac{5}{7}[/tex]
7 × 7 = 5(5+ x)
49 = 25 + 5x
49 - 25 = 5x
24 = 5x
x = 24/5
x = 4.8
Thus, In Δ PRQ, The value of the missing variable x is 4.8.
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Complete question:
Parts of similar triangle are given as the Δ PQS ≅ Δ PRQ. Find the value of x.
The following data indicate the scores of some students in a competition. Which a box plot represents the data?
100 points!!!!!
The correct answer to the given question is graph D
How to solveGiven a set of data points, we are tasked with identifying the correct box plot representation.
We begin by arranging the data in ascending order, which gives us 12, 17, 21, 23, 24, 28, and 29 points.
Next, we use the properties of a box plot to eliminate incorrect representations.
The left end of the whisker should correspond to the smallest data point, and the right end to the largest.
Among the given graphs, only one satisfies this condition.
The middle point is identified as the fourth data point, which is 23.
Finally, we determine the lower and upper lines of the box to be 17 and 28, respectively.
The only graph that satisfies all conditions is graph D.
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Natalie invests $2,000 into a savings account
which earns 11% per year. In 20 years, how
much will Natalie's investment be worth if
interest is compounded monthly? Round to the
nearest dollar.
Answer:
We can use the formula for compound interest to find the future value (FV) of Natalie's investment:
FV = P * (1 + r/n)^(n*t)
Where:
P is the principal amount (the initial investment), which is $2,000 in this case
r is the annual interest rate as a decimal, which is 11% or 0.11
n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly
t is the number of years, which is 20
Substituting the values into the formula, we get:
FV =
2
,
000
∗
(
1
+
0.11
/
12
)
(
12
∗
20
)
�
�
=
2,000 * (1.00917)^240
FV = $18,255.74
Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.
Answer:
$17,870
Step-by-step explanation:
You must use the formula for compound interest.
A = P(1 + r/n)^nt
I suggest you look it up at some point so that you can do these more easily in the future!
John drives to work each morning, and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John’s drive to work will take between 36 and 40 minutes?
The probability that John's drive to work will take between 36 and 40 minutes is 0.3413.
What is Probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.
Using the normal distribution, the probability of John's drive taking between 36 and 40 minutes can be calculated using the standard normal distribution table. The formula for calculating the probability is: P(x<X<y) = P(y) - P(x).
For the given problem, the lower boundary is 36 minutes and the upper boundary is 40 minutes. Using the standard normal distribution table, the probability of John's drive taking between 36 and 40 minutes can be calculated by subtracting the probability of 36 minutes from the probability of 40 minutes. This gives us a probability of 0.3413.
Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3413.
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The probability that John's drive to work will take between 36 and 40 minutes is 0.3829.
What is Probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.
The probability that John's drive to work will take between 36 and 40 minutes can be calculated using a normal distribution table. The mean of the distribution is µ = 38 minutes, and the standard deviation is σ = 5 minutes.
To calculate the probability, we need to convert the given range (36 minutes to 40 minutes) into standard normal scores. This is done by subtracting the mean (µ = 38 minutes) from the lower bound (36 minutes) and then dividing by the standard deviation (σ = 5 minutes). The result is a standard normal score of -0.4. The same calculation is carried out for the upper bound (40 minutes) and the result is a standard normal score of 0.4.
Using a normal distribution table, we can then determine the probability that John's drive to work will take between 36 and 40 minutes. This probability is equal to the area under the normal curve between the two standard normal scores of -0.4 and 0.4. The result is a probability of 0.3829.
Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3829.
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What is the equation of the line thatt is parallel to the given line and passes through the point (12,-2)?
We want to write it in slope-intercept form:
y = mx + (b' = -12m - 2).
What is the parallel and perpendicular line equation?The slope of parallel lines is the same. The slopes of perpendicular lines are opposite reciprocals. To put it another way, if m=ab, then m=ba. To find the equation of a line, first determine the slope using the given information.
We can use the fact that parallel lines have the same slope to find the equation of a line that is parallel to a given line and passes through a given point.
Assume that the given line has the equation y = mx + b, where m represents the slope and b represents the y-intercept.
The slope of the line we are looking for is m because it is parallel to the given line. Because we don't know what the y-intercept of this line is, let's call it b'.
We now have two pieces of information regarding the new line:
It has the same slope as the given line (m).
It runs through the point (12,-2).
We can use this data to calculate the equation of the new line:
To begin, we can use the point-slope form of a line equation:
y - y1 = m(x - x1) (x - x1)
(x1, y1) denotes the point (12,-2) and m denotes the slope of the given line.
Substituting known values:
y - (-2) = m(x - 12) (x - 12)
Simplifying:
y + 2 = mx - 12m
We must now calculate the value of b' that makes this equation true for any point on the line. Because b' is the line's y-intercept, we can set x = 0 and solve for y:
y + 2 = m(0) - 12m
y = -12m - 2
As a result, the equation of the line parallel to the given line and passing through the point (12,-2) is:
y = mx - 12m - 2
Alternatively, we can write it in slope-intercept form:
y = mx + (b' = -12m - 2).
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For what values of a are the following expressions true?
|a+5|=a+5
|a+5|=-5-a
Hello,can yall help me with this
The area of Jade's rectangular wall is equal to 11⅓ yd² expressed as a mixed fraction
How to evaluate for the area of the rectangular wallGiven the formula for calculating area of rectangle as A = bh
b = 4¼ yd
h = 2⅔
so we can calculate the area of the rectangular wall as follows:
4¼ yd × 2⅔ yd
expressing the values of b and h as improper fractions;
17/4 yd × 8/3 yd
by simplification;
34/3 yd²
34/3 expressed as a mixed number is 11⅓.
Therefore, the area of Jade's rectangular wall is equal to 11⅓ yd² expressed as a mixed fraction.
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A triangle has sides with lengths of 8 meters, 15 meters, and 17 meters. Is it a right triangle?
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
From the given side lengths, let a = 8, b = 15, c = 17 (c cannot be less than a or b)
[tex]a^2 + b^2 = (8)^2 + (15)^2[/tex]
[tex]a^2 + b^2 = 64 + 225 = 289[/tex]
[tex]c^2 = (17)^2 = 289[/tex]
[tex]a^2 + b^2 = c^2 \ (289 = 289)[/tex]
Therefore, a Triangle with side lengths of 8, 15 and 17 is a Right Triangle
Note: Since the side lengths are positive integers and the GCF(8, 15, 17) = 1, they are a primitive Pythagorean Triple.
logos to shop that sells two models of Radio 1 cost 3 times as much as the other in the to cost £72 wants to know the cost of the cheaper one if they're cheaper radio cost x pounds form an equation and X what should Laura's answer be
Laura's answer should be: The cost of the cheaper radio is £18.
What is equations ?
An equation is a statement that two expressions are equal. It typically involves one or more variables (represented by letters) and mathematical operations such as addition, subtraction, multiplication, and division.
Let's call the cost of the cheaper radio "x". Then, according to the problem, the cost of the more expensive radio is 3x.
We know that the total cost for both radios is £72, so we can set up an equation:
x + 3x = 72
Simplifying the equation, we get:
4x = 7
Dividing both sides by 4, we get:
x = 18
Therefore, the cost of the cheaper radio is £18.
Therefore, Laura's answer should be: The cost of the cheaper radio is £18.
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The diagram below represents how rock is affected when water enters cracks in rock, freezes, and becomes ice.
Which geologic process is represented in the diagram?
Answer: Physical weathering, more specifically, ice wedging
Step-by-step explanation:
:D
4) It has been known that 18% of victims of financial fraud know the perpetrator of the fraud
personally. If a sample of 156 people were victims of fraud, what is the mean number of those
victims that know the perpetrator of the fraud personally?
Answer:
If 18% of victims of financial fraud know the perpetrator of the fraud personally, and a sample of 156 people were victims of fraud, we can find the mean number of those victims that know the perpetrator by multiplying the sample size by the percentage. Therefore, the mean number of victims that know the perpetrator is 156 x 0.18 = 28.08. However, since we cannot have a fraction of a person, we can round the answer to the nearest whole number. Therefore, the mean number of victims that know the perpetrator is 28.
Your tank has a volume of 10 L at the surface (1 atm pressure). You reach a depth of 66 ft. What is the
pressure? What is the volume?
the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.
EquationsTo find the pressure at a depth of 66 ft in a liquid, we can use the formula:
pressure = density x gravity x depth
Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².
First, we need to convert 66 ft to meters:
66 ft x 0.3048 m/ft = 20.1168 m
Then, we can find the pressure at this depth:
pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa
To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.
We can rearrange this equation to solve for V₂:
V₂ = (P₁ x V₁) / P₂
Substituting the values, we get:
V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L
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Find the average rate of change of g(x) = 3x² + 3 on the interval [ - 9, 4].
Answer:
-15
Step-by-step explanation:
You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].
Average rate of changeThe average rate of change is defined as ...
AROC(g) = (g(b) -g(a))/(b -a)
We can evaluate this directly, or we can simplify it a bit first.
AROC = ((3b² +3) -(3a² +3))/(b -a)
= (3b² -3a²)/(b -a)
= 3(b -a)(b +a)/(b -a)
= 3(b +a)
Interval [-9, 4]The AROC on the interval [a, b] = [-9, 4] is then ...
AROC = 3(4 +(-9)) = 3(-5)
AROC = -15
__
Additional comment
In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
Step-by-step explanation:
Let x be the measure of the first angle.
According to the problem, we know that:
The sum of the angles of the triangle is 180: x + y + z = 180
The sum of the second and third angles is five times the measure of the first angle: y + z = 5x
The third angle is 16 more than the second: z = y + 16
We can substitute the third equation into the second equation to get:
y + (y + 16) = 5x
Simplifying this equation, we get:
2y + 16 = 5x
We can rearrange this equation to get:
y = (5/2)x - 8
Now we can substitute this equation and the equation z = y + 16 into the first equation to get:
x + (5/2)x - 8 + (5/2)x + 8 = 180
Simplifying this equation, we get:
6x = 360
Dividing both sides by 6, we get:
x = 60
Now we can use this value of x to find y and z:
y = (5/2)x - 8 = (5/2)(60) - 8 = 58
z = y + 16 = 58 + 16 = 74
Therefore, the measures of the three angles are x = 60, y = 58, and z = 74.
The accompanying table shows the results from a test for a certain disease. Find the probability of selecting a subject with a negative test result, given that the subject has the disease. What would be an unfavorable consequence of this error?
The individual actually had the disease
Yes
No
Positive
320
9
Negative
12
1160
Question content area bottom
Part 1
The probability is enter your response here.
(Round to three decimal places as needed.)
The probability to three decimal places is 0.036 and the unfavorable consequence of this result will be that the patients who tested negative will not be treated and as such will spread the disease.
How to solve the probabilityTo find the probability of an event, we often use divide the total number of possible results by the total results. In this case, we are told to find the total number of persons who tested negative for the disease by the total number of positive cases. 320 + 12 persons tested positive for the disease. The sum is 332.
The total number of negative cases recorded from this sum is 12. Thus, the probability will be 12/332 = 0.036. An unfavorable consequence of this error will be that the subjects who tested negative will not be treated and can thus spread the disease.
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I need help with my iready assignment
Answer: Cone is correct just switch cylinder and sphere.
Step-by-step explanation:
Answer: Switch the formula for the cylinder for the sphere. the formula for the cone is right
Step-by-step explanation:
Bruno bought a used car for $8,500 and had to pay 7.0% sales tax.
How much tax did he pay?
Answer:
Step-by-step explanation:
$8,500 -7.0%= $7,905
$8,500 - $7,905 = $595
another bank offers a different savings rate. if an account with $400 earns interest of $6, how much interest is earned by an account with $1800?
Answer:
$27
Step-by-step explanation:
$400 earns $6
$6÷$400= 0.015% interest
$1800 * 0.015% = $27
A capsule of paracetamol is made of a cylinder and a hemisphere at each end. The total length of the capsule is 20 mm and the width is 6 mm.
Calculate:
(a) What is the length of the cylinder? (b) Find the volume of the cylinder, to 3 significant figures
(c) Find the volume of the two hemispheres
(d) What is the total volume of the capsule?
Answer:
Step-by-step explanation:
To solve this problem, we can use the following formulae for the volume of a cylinder and a hemisphere:
Volume of a cylinder = πr²h
Volume of a hemisphere = 2/3πr³/2
where r is the radius of the cylinder or hemisphere, and h is the height of the cylinder.
(a) To find the length of the cylinder, we can subtract the combined length of the two hemispheres from the total length of the capsule:
Length of cylinder = Total length of capsule - 2 × radius of hemisphere
Length of cylinder = 20 mm - 2 × 3 mm (radius of hemisphere)
Length of cylinder = 14 mm
(b) To find the volume of the cylinder, we need to know the radius and height. Since the width of the capsule is given as 6 mm, and we know that the cylinder runs the full length of the capsule, we can use the following formula to find the radius of the cylinder:
Width = 2 × radius of hemisphere + diameter of cylinder
6 mm = 2 × 3 mm + diameter of cylinder
Diameter of cylinder = 6 mm
Radius of cylinder = 3 mm
Now we can use the formula for the volume of a cylinder to find the volume of the cylinder:
Volume of cylinder = πr²h
Volume of cylinder = π(3 mm)² × 14 mm
Volume of cylinder ≈ 395.8 mm³ (to 3 significant figures)
(c) The radius of each hemisphere is 3 mm (since they have the same radius as the cylinder), so we can use the formula for the volume of a hemisphere to find the volume of each hemisphere:
Volume of hemisphere = 2/3πr³/2
Volume of hemisphere = 2/3π(3 mm)³/2
Volume of hemisphere ≈ 56.55 mm³ (to 3 significant figures)
(d) To find the total volume of the capsule, we can add the volumes of the cylinder and the two hemispheres:
Total volume of capsule = Volume of cylinder + 2 × Volume of hemisphere
Total volume of capsule ≈ 509.9 mm³ (to 3 significant figures)
Therefore, the length of the cylinder is 14 mm, the volume of the cylinder is approximately 395.8 mm³, the volume of each hemisphere is approximately 56.55 mm³, and the total volume of the capsule is approximately 509.9 mm³.