Answer:
0.8343
Step-by-step explanation:
From the question, we have the following values:
Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75
Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25
P = 0.25
n = number of random variables = 9
The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:
P < 4 = P ≤ 3
n = 9
P(x) = n!/(n - x)! x! × p^x × q^(n - x)
x = 3
p = 0.25
q = 0.75
P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)
P(x) =0.8343
The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.
Given information:
75% of the vehicles passing through a checkpoint are from within the state.
So, the probability that the vehicle is from within the state is 0.75.
The probability that the vehicle is from outside the state will be 1-0.75=0.25.
Now, let x be the random variable. So, the value of n=9. and x<4
It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.
So, [tex]x< 4[/tex], p=0.25 and q=0.75.
So, the required probability can be calculated as,
[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]
Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.
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A bus averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle to travel 155 miles, then what is the speed of each?
Answer:
The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour
Step-by-step explanation:
Represent the bus average speed with x and the motorcycle average speed with y
Given
[tex]x = y + 2[/tex]
Distance covered by bus = 165 miles
Distance covered by motorcycle in same time = 155 miles
Required
Determine the speed of each
Average Speed is calculated as;
[tex]Average\ Speed = \frac{Distance}{Time}[/tex]
Since the two are measured with the same time, represent time with T
For the bus
[tex]Average\ Speed = \frac{Distance}{Time}[/tex] becomes
[tex]x = \frac{165}{T}[/tex]
Make T the subject of formula
[tex]T = \frac{165}{x}[/tex]
For the motorcycle
[tex]y = \frac{155}{T}[/tex]
Make T the subject of formula
[tex]T = \frac{155}{y}[/tex]
Since, T = T; we have that
[tex]\frac{165}{x} = \frac{155}{y}[/tex]
Cross Multiply
[tex]165y = 155x[/tex]
Substitute [tex]x = y + 2[/tex]
[tex]165y = 155(y+2)[/tex]
Open Bracket
[tex]165y = 155y - 310[/tex]
Collect Like Terms
[tex]165y - 155y = 310[/tex]
[tex]10y = 310[/tex]
Divide both sides by 10
[tex]y = 31[/tex]
Recall that [tex]x = y + 2[/tex]
[tex]x = 31 +2[/tex]
[tex]x = 33[/tex]
Hence;
The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour
i will give brainliest and 5 stars if you help ASAP
Answer:
£39.20
Step-by-step explanation:
→ Identify which ratio goes to each person
2 : 1 : 5
2 = Paul
1 = Colin
5 = Brian
→ Divide the total tip by the total sum of the ratio's
£78.40 ÷ ( 2 + 1 + 5 ) ⇔ £78.40 ÷ 8 = £9.80
→ Now we know one part is equal to £9.80 we multiply this number by each of the associated ratio's
Paul = £9.80 × 2 ⇔ £19.60
Colin = £9.80 × 1 ⇔ £9.80
Brian = £9.80 × 5 ⇔ £49
→ Minus Brian's tip against Colin's tip
£49 - £9.80 = £39.20
Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (ß) error used to measure?
Answer:
Alpha (α) is used to measure the error for decisions concerning true null hypotheses, while beta (ß) is used to measure error for decisions concerning false null hypotheses.
Step-by-step explanation:
Suppose we have events X and Y.
1. If it is said that X equals Y, when X is actually not equal to Y, α is used in this case, the null hypotheses.
2. If X is said to not be equal to Y, when X is actually equal to Y, β is used in this case, the false null hypotheses.
Luke owns a trucking company. For every truck that goes out, Luke must pay the driver $17 per hour of driving and also has an expense of $1.75 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 40 miles per hour and Luke's total expenses for the driver, gas and truck maintenance were $522. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.
Answer:
17h+1.75m=522 m=40h
Step-by-step explanation:
Let h= {the number of hours the driver drove}
Let m= the number of miles driven
The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:
17h+1.75m=522
17h+1.75m=522
Since the driver drove an avearge of 40 miles per hour, if the driver drove hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:
m=40h
m=40h
Write System of Equations:
17h+1.75m= 522
m=40h
The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
The following are the different costs of the truck that Luke must be pay while running a truck:
Luke must pay the driver $17 per hour of driving.A truck has an expense of $1.75 per mile driven for gas and maintenance.Let ' x ' be the total time of driving a truck in hours.
and ' y ' be the total mile distance that is covered by the truck.
Therefore, the system of the equation for the overall running cost for a truck is given below.
[tex]\rm{Cost}=17x+1.75y[/tex]
Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.
Thus,
The total distance traveled by truck is 40x.
That is,
[tex]y=40x[/tex]
Substitute the values and solve them further.
[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]
Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
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Using the digits 0-9, at most only one time each, fill in the boxes to
Answer:
2 * 3 + 4 * 5 = 26
5 * 7 + 1 * 8 = 43
Step-by-step explanation:
Given
_ * _ + _ * _ = _ _
Required
Fill in the boxes with digits 0 to 9
From the question we understand that the result must be two digits i.e. _ _
To solve this, we'll make use of trial by error method:
Fill the first two boxes wit 2 and 3: _ * _ becomes 2 * 3
Fill the next two boxes with 4 and 5: _ * _ becomes 4 * 5
So,we have
2 * 3 + 4 * 5
6 + 20
26
Hence, the first combination is 2 * 3 + 4 * 5 = 26
Another possible combination is:
Fill the first two boxes wit 5 and 7: _ * _ becomes 5 * 7
Fill the next two boxes with 1 and 8: _ * _ becomes 1 * 8
So,we have
5 * 7 + 1 * 8
35 + 8
43
Hence, another combination is 5 * 7 + 1 * 8 = 43
Note that; there are more possible combinations
Line A passes through the point (-1,2). Which of the
following CANNOT be the equation of line A?
A y=1 - 2
B
y = x +1
C
X = -1
D y=x+3
Answer:
b
Step-by-step explanation:
y = x + 1
The correct answer is (B). The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the "m" in front of the "x" variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn't give us y = 2 is (B).
Option B is correct.
Given:
Line A passes through the point [tex](-1,2)[/tex].
To find:
Which of the given equations cannot be the equation of line A.
Solution:
If Line A passes through the point [tex](-1,2)[/tex], it means the equation of Line A must be satisfied by the point
In option A, consider the given equation is:
[tex]y=1-x[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=1-(-1)[/tex]
[tex]2=1+1[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=1-x[/tex] can be the equation of line A.
Similarly, check for the other options.
In option B,
[tex]y=x+1[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+1[/tex]
[tex]2=0[/tex]
This statement is false. So, [tex]y=x+1[/tex] cannot be the equation of line A.
In option C,
[tex]x=-1[/tex]
It is a vertical line and it passes through the point [tex](-1,2)[/tex] because the x-coordinate is [tex]-1[/tex]. So, [tex]x=-1[/tex] can be the equation of line A.
In option D,
[tex]y=x+3[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+3[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=x+3[/tex] can be the equation of line A.
Therefore, the correct option is B.
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In a genetics experiment on peas, one sample of offspring contained green peas and yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of that was expected? 350 127 3 4 The probability of getting a green pea is approximately . (Type an integer or decimal rounded to three decimal places as needed.) Is this probability reasonably close to ? Choose the correct answer below. 3 4 A. No, it is not reasonably close. B. Yes, it is reasonably close.
Complete Question
In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?
Answer:
The probability is [tex]P(g) =0.72[/tex]
Yes the result is reasonably close
Step-by-step explanation:
From the question we are told that
The number of of green peas is [tex]g = 436[/tex]
The number of yellow peas is [tex]y = 171[/tex]
The sample size is [tex]n = 171 + 436 = 607[/tex]
The probability of getting an offspring pea that is green is mathematically represented as
[tex]P(g) = \frac{g}{n}[/tex]
[tex]P(g) = \frac{436}{607}[/tex]
[tex]P(g) =0.72[/tex]
Comparing [tex]P(g) =0.72[/tex] to [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close
If the item regularly cost d dollars and is discounted 12percent which of the following represents discount price dollar
Answer:
-12
Step-by-step explanation:
Find the missing side or angle.
Round to the nearest tenth.
Answer:
65.8
Step-by-step explanation:
Use the sin formula
100/sin (28) = x/ sin (18)
(sin (18) (100))/ sin (28) = x
x = 65.8223
x = 65.8
Answer:
65.8
Step-by-step explanation:
Accellus Correct
Someone help again:/
What is the best way you learn math?
Answer:
to provide interest in the subject
As per my experience,I used to hate math and always scored less marks,the moment I was going to high school I realized the importance of math towards the future, see you'll find maths in nearly all subjects like the 3 sciences, economics, geography, business e.t.c
Why did you write this question at first?, just take some free time and think about it,the only best way to learn maths is to take maths positively as the best and most valuable subject,if you want to ace math you have to race it, challenge math like you'd challenge anyone to a game, practice math if it's your weakest point, practice is very much needed to skill maths and never be shy to ask your teachers whether you are studying online/offline. You'll need to get the shy behaviour out of you whether you like /don't like your teacher or your an average student.
Concentrate while learning math, whether there's noise in you background or not, Nothing can stop you in excelling math if you have full concentration, positiveness and the "will" to do so.
if you're next to your exams then just one thing, Start now!!
hope this helps!
In a small town 68% of the people owned television 72% on radio and 12% owned neither television nor radio (1)represent the information on a Veen diagram.
(2)what percentage of the population owned television.
Answer:
See attachment for Venn diagram
Percentage of only TV owners is 16%
Step-by-step explanation:
Given
[tex]TV\ Owners = 68\%[/tex]
[tex]Radio\ Owners = 72\%[/tex]
[tex]None = 12\%[/tex]
Required
Represent with a Venn Diagram
What percentage owned television
From the Venn Diagram and In sets theory; we have that
Total = (TV Owners - Radio and TV Owners) + (Radio Owner - Radio and TV Owners) + Radio and TV Owners + None
Represent Radio and TV Owners with y
[tex]Total = (TV\ Owners - y) + (Radio\ Owner - y) + y + None[/tex]
Substitute 68% for TV Owners, 72% for Radio Owners, 12& for None:
[tex]Total = 68\% - y + 72\%- y + y + 12\%[/tex]
Collect Like Terms
[tex]Total = 68\% + 72\%+ 12\%- y + y - y[/tex]
[tex]Total = 152\% - y[/tex]
In Sets, Total represents 100%; So, we have
[tex]100\% = 152\% - y[/tex]
Make y the subject of formula
[tex]y = 152\% - 100\%[/tex]
[tex]y = 52\%[/tex]
The percentage of only TV owners is calculated by subtracting y from TV owners
[tex]\%P = 68\% - 52\%[/tex]
[tex]\%P = 16\%[/tex]
Answer:
The answer is 90%
Step-by-step explanation:
A circle has center (3, -5) and the point (-1, -8) lies on the circumference of the circle. What is the equation of the circle in Standard Form?
Answer:
[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]
Step-by-step explanation:
First find the radius
Which is the distance between the 2 points.
Radius =5
The answer in the standad form is above.
The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25
The standard equation of a circle is given as:
(x - a)² + (y - b)² = r²
where (a, b) is the center of the circle and r is the radius of the circle.
Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:
[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]
hence:
(x - 3)² + (y - (-5))² = 5²
(x - 3)² + (y + 5)² = 25
The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25
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What is the difference between a consistent and inconsistent system of equations?
Answer:
A consistent of equations has at least one solution,and an inconsistent system has no solution, watch an example of analyzing a system to see if its consistent or inconsistent.
Answer: see below
Step-by-step explanation:
Consider the standard form of a linear equation in Slope-Intercept form:
y = mx + b where
m is the slopeb is the y-interceptA CONSISTENT system of equations is where the equations have different slopes OR the same slope and y-intercept.
This results in the lines crossing so they have at least one solution.
An INCONSISTENT system of equations is where the equations have the same slope but different y-intercepts.
This results in parallel lines so they have no solutions.
paul worked 50 hours last week. if he earns $10 per hour plus time-and-a-half for any hours worked beyond 40 in a week, how much did he earn last week?
Answer: 4150
Step-by-step explanation:
You take the 50, becuse the amount earned increases once you surpass 40 you do 40 x 10 and that = 4000 then you take the remaining 10 and times that by 15 (becuse after 40 it is 1.5 of what you where earning before you hit 40 hours and half of ten is 5 so you do 10 plus 5 and times that by 10) then add both numbers together and you have 4150! Hope that helped!
savanah solved the equation 3+4 multiplied by the absolute value of x/2+3=11 for one solution. her work is shown below. what is the other solution to the given absolute value equation: savanah's solution was x= -2
Answer:
-10Step-by-step explanation:
Given the equation solved by savanah expressed as [tex]3+4|\frac{x}{2} + 3| = 11[/tex], IF she solved for one of the solution and got x = -2, we are to solve for the other value of x.
Note that the expression in modulus can be expressed as a positive expression and negative expression.
For the positive value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]\frac{x}{2} + 3[/tex], the expression becomes;
[tex]3+4(\frac{x}{2} + 3) = 11[/tex]
On simplification;
[tex]3+4(\frac{x}{2} + 3) = 11\\\\3 + 4(\frac{x}{2} )+4(3) = 11\\\\3 + \frac{4x}{2}+ 12 = 11\\\\3 + 2x+12 = 11\\\\2x+15 = 11\\\\Subtract \ 15 \ from \ both \ sides\\\\2x+15-15 = 11-15\\\\2x = -4\\\\x = -2[/tex]
For the negative value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]-(\frac{x}{2} + 3)[/tex], the expression becomes;
[tex]3+4[-(\frac{x}{2} + 3)] = 11[/tex]
On simplifying;
[tex]3+4[-(\frac{x}{2} + 3)] = 11\\\\3+4(-\frac{x}{2} - 3)= 11\\\\3-4(\frac{x}{2}) -12 = 11\\\\3 - \frac{4x}{2} - 12 = 11\\\\3 - 2x-12 = 11\\\\-2x-9 = 11\\\\add \ 9 \ to \ both \ sides\\\\-2x-9+9 = 11+9\\-2x = 20\\\\x = -20/2\\\\x = -10[/tex]
Hence her other solution of x is -10
Based on the image, which list of 3 points are collinear?
Answer:
Collinear occurs when the two points has the same gradient,
So, for this question any line that forms by any three points would be collinear.
Hence, EBF,DGC,MGN,BGA are all collinears
Step-by-step explanation:
4. Identify the means and the extremes in each of the following proportions.
a. 4 : 24 = 2 : 12
b. 24/6 = 164
c. 4:8 = 8:16
d. 650 = 3/25
Answer:
a) Means: 24 and 2; Extremes: 4 and 12
b) Means: 6 and 16; Extremes: 24 and 4
c) Means: 8 and 8; Extremes: 4 and 16
d) Means: 50 and 3; Extremes: 6 and 25
Step-by-step explanation:
The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:
a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.
The Means are the values that appear in the middle of the one line expression, that is: b and c.
Recall as well that the proportion can also be written with fractions:
a : b = c : d is the same as: a / b = c / d
so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.
What is the solution of the system of equations?
y = -3x + 7
y = 2x - 8
Answer:
x = 3, y = -2
Step-by-step explanation:
Since y=y
then, -3x +7 = 2x-8
7+8 = 3x+2x
15 = 5x
x=3
substitute
y = 2(3) - 8
y = -2
Hope that helped!!! k
Answer:
y = -2
x = 3
Step-by-step explanation:
Solve using elimination
1. Rearrange the equations to make it easier to solve
y = -3x + 7 → 3x + y = 7
y = 2x - 8 → 2x - y = 8
2. Multiply the equations to have a matching coefficient
2(3x + y = 7) = 6x + 2y = 14
3(2x - y = 8) = 6x - 3y = 24
3. Subtract
6x + 2y = 14
- 6x - 3y = 24
0 + 5y = -10
4. Solve for y
5y = -10
y = -2
5. Substitute y in any equation to solve for x
-2 = -3x + 7
-3x = -9
x = 3
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 6 3/4" by 4 1/2" on the drawing, how large is the bedroom? Please Help! (No other information was given.)
1 inch = four 1/4’s
1 inch = 4 feet
6 X 4 = 24 feet
3/4 inches = 3 feet.
6 3/4 inches = 27 feet
4 x 4 = 16
1/2 inch = 2 feet
4 1/2 inches = 18 feet
Room is 27 feet x 18 feet
p-value problem. Suppose the director of manufacturing at a clothing factory needs to determine wheteher a new machine is producing a particulcar type of cloth according to the manufacturer s specification which indicate that the cloth should have mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds. THe p value for this hypothesis testing scenario is
Answer:
The P-Value is 0.07186
Step-by-step explanation:
GIven that :
Mean = 70
standard deviation = 3.5
sample size n = 49
sample mean = 69.1
The null hypothesis and the alternative hypothesis can be computed as follows;
[tex]H_o : \mu = 70 \\ \\ H_1 : \mu \neq 70[/tex]
The standard z score formula can be expressed as follows;
[tex]\mathtt{z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]
[tex]\mathtt{z = \dfrac{69.1 - 70}{\dfrac{3.5}{\sqrt{49}}}}[/tex]
[tex]\mathtt{z = \dfrac{-0.9}{\dfrac{3.5}{7}}}[/tex]
z = -1.8
Since the test is two tailed and using the Level of significance = 0.05
P- value = 2 × P( Z< - 1.8)
From normal tables
P- value = 2 × (0.03593)
The P-Value is 0.07186
Hakim is making a mosaic
from square tiles. The area he
needs to fill measures 150 mm
by 180 mm. The tiles have side
lengths of 4, 6 or 8mm and are
too small to cut. Which tiles
should Hakim use?
Step-by-step explanation:
check the tile whose side length is divisible by both 150 and180 in such a way that you don't get decimal points
150÷4=37.5 so that is impossible
150÷8=18.75 so that is also impossible
150÷6=25 180÷6=30
so the six sided tile is applicable
Suppose a triangle has two sides of length 33 amd 37, and that the angle between these two sides is 120°. What is the length of the third side of the triangle
Answer:
c = 60.65 cm
Step-by-step explanation:
Given that,
The two sides of a triangle are 33 cm and 37 cm.
The angle between these two sides is 120°.
We need to find the length of the third side of the triangle. Let c is the third side. Using cosine rule,
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
a = 33 cm, b = 37 cm and C is 120°
So,
[tex]c^2=(33)^2+(37)^2-2\times 33\times 37\cos (120)\\\\c=60.65\ cm[/tex]
So, the length of the third side of the triangle is 60.65 cm.
The length and width of a rectangle are measured as 58 cm and 45 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
Error in calculated area = [tex]\pm 10.3 cm^2[/tex]
Step-by-step explanation:
x = 58 cm
y = 45 cm
A = x*y
delta A
= delta (x*y)
= y delta x + x delta y (neglecting small qty delta x * delta y = 0.01)
= 45(0.1) + 58(0.1)
= 103(0.1)
= 10.3 cm^2
Please answer asap this person made a mistake what is the error and correct solution to this problem
Answer:
6
Step-by-step explanation:
Hello, please consider the following.
[tex](4+x)^2=4^2+2\cdot 4\cdot x+x^2=16+\boxed{8}x+x^2\\\\\text{ ... and not ...}\\\\16+\boxed{4}x+x^2[/tex]
So the correct equation becomes.
[tex]x^2+64=16+8x+x^2\\\\8x=64-16=48\\\\\text{ we divide by 8 both sides of the equation.}\\\\x=\dfrac{45}{8}=6[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
Error : The expression ( 4 + x )² was expanded incorrectly.
Correct Solution : x = 6
Step-by-step explanation:
The planning of the solution is correct, by Pythagorean Theorem you can say that PQ² + QO² = PO², and hence through substitution x² + 8² = ( 4 + x )². Let's look into the calculations.
PQ² + QO² = PO²,
x² + 8² = ( 4 + x )²,
x² + 8² = 16 + 8x + x²,
64 = 16 + 8x,
48 = 8x,
x = 48 / 8 = 6, x = 6
As you can see, the only error in the calculations was expanding the expression ( 4 + x )². ( 4 + x )² = 4² + 2 [tex]*[/tex] 4 [tex]*[/tex] x + x² = 4² + 8x + x² = 16 + 8x + x², not 16 + 4x + x².
15. What is the next number in this series?
6, 11, 9, 14, 12,
a. 17
b. 10
C. 18
d. 16
Answer:
a. 17
Step-by-step explanation:
The pattern is add 5 then subtract 2
The radius of a sphere is measured as 7 centimeters, with a possible error of 0.025 centimeter.
Required:
a. Use differentials to approximate the possible propagated error, in cm3, in computing the volume of the sphere.
b. Use differentials to approximate the possible propagated error in computing the surface area of the sphere.
c. Approximate the percent errors in parts (a) and (b).
Answer:
a) dV(s) = 15,386 cm³
b) dS(s) = 4,396 cm²
c) dV(s)/V(s) = 1,07 % and dS(s)/ S(s) = 0,71 %
Step-by-step explanation:
a) The volume of the sphere is
V(s) = (4/3)*π*x³ where x is the radius
Taking derivatives on both sides of the equation we get:
dV(s)/ dr = 4*π*x² or
dV(s) = 4*π*x² *dr
the possible propagated error in cm³ in computing the volume of the sphere is:
dV(s) = 4*3,14*(7)²*(0,025)
dV(s) = 15,386 cm³
b) Surface area of the sphere is:
V(s) = (4/3)*π*x³
dV(s) /dx = S(s) = 4*π*x³
And
dS(s) /dx = 8*π*x
dS(s) = 8*π*x*dx
dS(s) = 8*3,14*7*(0,025)
dS(s) = 4,396 cm²
c) The approximates errors in a and b are:
V(s) = (4/3)*π*x³ then
V(s) = (4/3)*3,14*(7)³
V(s) = 1436,03 cm³
And the possible propagated error in volume is from a) is
dV(s) = 15,386 cm³
dV(s)/V(s) = [15,386 cm³/1436,03 cm³]* 100
dV(s)/V(s) = 1,07 %
And for case b)
dS(s) = 4,396 cm²
And the surface area of the sphere is:
S(s) = 4*π*x³ ⇒ S(s) = 4*3,14*(7)² ⇒ S(s) = 615,44 cm²
dS(s) = 4,396 cm²
dS(s)/ S(s) = [ 4,396 cm²/615,44 cm² ] * 100
dS(s)/ S(s) = 0,71
What is the value of 1/3x-3/4 when x =1/4
Answer:
The value of 1/3x-3/4 when x=1/4 is 0.08333 repeated.
Step-by-step explanation:
A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. The player scored 17 times. She scored 3 more 2-point field goals than 1-point free throws. The system of equations below represents the situation, where x is the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. x + y + z = 17 x + 2y + 3z = 33 y – x = 3
Answer:
No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4
Step-by-step explanation:
Equations : x + y + z = 17 [ Total times taken to score ]
1x + 2y + 3z = 33 [ Total Score ]
Also, y = x + 3
Putting the value of 'y' in both equations :
x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14 (i)
1x + 2 (x + 3) + 3z = 33 → x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)
Solving these equations :
From (i), z = 14 - 2x
Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27
42 - 3x = 27 → 3x = 15 → x = 5
y = x + 3 = 5 + 3 → y = 8
z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4
Answer:
4
Step-by-step explanation:
Solve for x: the quantity of x plus 4 over 3 = 2.
Answer:
x =2
Step-by-step explanation:
(x+4) /3 = 2
Multiply each side by 3
(x+4) /3 *3= 2*3
x+4 = 6
Subtract 4
x+4-4 = 6-4
x =2
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▹ Answer
x = 2
▹ Step-by-Step Explanation
[tex]\frac{x + 4}{3} = 2\\\\3 * 2 = 6\\\\x + 4 = 6\\\\x = 2[/tex]
Hope this helps!
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