The speed of the boat in still water is 12 mph, and the speed of the current is 9 mph.
Let's denote the speed of the boat in still water as ( b ) and the speed of the current as ( c ).
Downstream Trip:
The speed of the boat relative to the water is ( b + c ), and the distance is 210 miles.
Therefore, the time taken downstream is:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{210}{b + c} \][/tex]
Given that this trip took 10 hours, we have:
[tex]\[ 10 = \frac{210}{b + c} \][/tex]
Upstream Trip:
The speed of the boat relative to the water is ( b - c ), and the distance is again 210 miles.
Therefore, the time taken upstream is:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{210}{b - c} \][/tex]
Given that this trip took 70 hours, we have:
[tex]\[ 70 = \frac{210}{b - c} \][/tex]
Now, we have a system of two equations with two variables:
[tex]\[ 10 = \frac{210}{b + c} \][/tex]
[tex]\[ 70 = \frac{210}{b - c} \][/tex]
Solving this system of equations will give us the values of ( b ) and ( c ), which represent the speed of the boat in still water and the speed of the current, respectively. Let's solve it:
From the first equation:
[tex]\[ b + c = \frac{210}{10} = 21 \][/tex]
From the second equation:
[tex]\[ b - c = \frac{210}{70} = 3 \][/tex]
Adding the two equations:
(b + c) + (b - c) = 21 + 3
2b = 24
b = 12
Substituting ( b = 12 ) into ( b + c = 21 ):
12 + c = 21
c = 21 - 12
c = 9
So, the speed of the boat in still water is 12 mph, and the speed of the current is 9 mph.
Which pair of numbers is relatively prime?
A. 12 and 54
B. 9 and 21
C. 21 and 39
D. 15 and 49
Answer:
D. 15 and 49
Step-by-step explanation:
Numbers are relatively prime if the only positive integer that divides both of them is 1.
A. 12 and 54
both 12 and 54 can be divided by 3
12/3 =4 54/3 = 18
B. 9 and 21
both 9 and 21 can be divided by 3
9/3 =3 and 21/3 = 7
C. 21 and 39
both 21 and 39 can be divided by 3
21/3 =7 and 39/3 = 13
D. 15 and 49
13 is 3*5 and 49 is 7*7
This is relatively prime
Which sequence matches the recursive formula? an=2an-1+5, where a1=5. A) 5,10,15,20 B) 5,15,35,75. C)5,15,25,35. D) 5,20,35,40
The recursive formula
[tex] a_n = 2a_{n-1}+5 [/tex]
means that, to compute the next value, you have to double the previous one and then add 5.
So, we start with 5. To get the second term, we double it and add five, so we have
[tex] a_2 = 2\cdot 5+5 = 10+5 = 15 [/tex]
Next, we will double 15 and add 5:
[tex] a_3 = 2\cdot 15 + 5 = 30+5 = 35 [/tex]
So, the answer is B, because it's the only option starting with 5,15,35.
Just to check, let's compute the last step:
[tex] a_4 = 2\cdot 35 + 5 = 70+5 = 75 [/tex]
Which confirms option B
Four Ice Skaters participate in an ice skating competition. The table shows their scores. Who has the highest score?
Natasha 75.03
Taylor 75.39
Rowena 74.98
Suki 75.3
Answer:
Your answer is Taylor
Step-by-step explanation:
Answer:
Taylor
Step-by-step explanation:
her answer is 0.09 greater then suki who is 2nd biggest
plz mark brainliest
If P(3,2) and Q(7,10) are the endpoints of the diameter of a circle, what is the area of the circle in square units?
To find the area of a circle given its diameter's endpoints, determine the diameter length, radius, and then calculate the circle's area using the radius.
Explanation:The area of a circle can be found using the distance formula between two points representing the diameter's endpoints. Given points P(3,2) and Q(7,10), the diameter length is calculated as sqrt((7-3)^2 + (10-2)^2) = sqrt(4^2 + 8^2) = sqrt(16+64) = sqrt(80).
Knowing that the radius is half the diameter, the radius, r = sqrt(80)/2 = 4*sqrt(5).
Finally, the area of the circle is A = pi*r^2 = pi*(4*sqrt(5))^2 = 80*pi square units.
Is the simplified form of 2 square root of 3 ⋅ square root of 12 rational?
Yes
No
Answer:
It is rational
Step-by-step explanation:
2 * sqrt(3) * sqrt(12)
2 * sqrt(3) sqrt(4) * sqrt(3)
2 sqrt(3) 2 sqrt(3)
4 sqrt(3)^2
4 *3
12
simplify
[tex]( \frac{ {h}^{12} }{ {h}^{4} } ) {}^{3} [/tex]
Plz help! and explain how you got the answer
Answer:
[tex]h^{24}[/tex]
Step-by-step explanation:
[tex](\frac{h^{12}}{h^4})^3\\ (h^8)^3\\h^{24}[/tex]
When dividing two exponents (of the same bases) you subtract the exponents. When there is an exponent to an exponent, you multiply the to exponents.
[tex]\left(\dfrac{h^{12}}{h^4}\right)^3\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\left(h^{12-4}\right)^3=\left(h^8\right)^3\\\\\text{use}\ (a^n)^m=a^{n\cdot m}\\\\=h^{8\cdot3}=h^{24}\\\\Answer:\ \boxed{\left(\dfrac{h^{12}}{h^4}\right)^3=h^{24}}[/tex]
Can you help me graph this equation?
A graph is attached
Step-by-step explanation:The equation is in slope-intercept form:
... y = mx + b
Here, the value of m (the slope) is 1/2, and the value of b (the y-intercept) is -3.
This means that point (0, -3) is a point on the graph. This point is on the y-axis, 3 units below the x-axis.
Slope is sometimes referred to as "rise over run." The slope of 1/2 means the line will rise 1 unit for each 2 units to the right. That is, for some point (x, y) on the ine, another point will be found at (x+2, y+1).
Given a point at (0, -3), another point will be (0, -3) +(2, 1) = (2, -2), and another point will be (2, -2) +(2, 1) = (4, -1).
You can plot as many points as you like, then draw the line through them.
Suppose that a six-sided die is "loaded" so that any particular even-numbered face is three times as likely to be observed as any particular odd-numbered face. (a) what are the probabilities of the six simple events? (hint: denote these events by o1,..., o6. then p(o1) = p, p(o2) = 3p, p(o3) = p,..., p(o6)= 3p. now use a condition on the sum of these probabilities to determine p. answer as an exact fraction or round your answers to three decimal places.)
Answer:
p = 1/12 = p(o1) = p(o3) = p(o5)
3p = 1/4 = p(o2) = p(o4) = p(o6)
Step-by-step explanation:
p(o1) +p(o2) +... +p(o6) = 1 . . . . the condition on the sum of probabilities
... p +3p +p +3p +p +3p = 1 . . . . substitute values
... 12p = 1 . . . . simplify
... p = 1/12 . . . . divide by 12
Then ...
... 3p = 3/12 = 1/4
Final answer:
The probabilities of rolling each face of a loaded six-sided die, where even numbers are three times more likely than odd numbers, are 1/9 for odd numbers (1, 3, 5) and 1/3 for even numbers (2, 4, 6), satisfying the condition that the total probability sums to 1.
Explanation:
The student is dealing with a probability question involving a "loaded" die. To find the probabilities for each face of the die, we assign a variable p to represent the probability of rolling an odd-numbered face and 3p for an even-numbered face. The sum of all probabilities must equal 1 because one of the outcomes must occur when the die is rolled. We can set up the following equation: p + 3p + p + 3p + p + 3p = 1.
Combining like terms gives us 9p = 1, so p = 1/9. Thus, the probabilities of rolling each face are as follows:
P(Odd) = 1/9 for faces 1, 3, and 5P(Even) = 3/9 or 1/3 for faces 2, 4, and 6This system satisfies the condition that all probabilities sum to 1, making it the correct distribution for this loaded die.
What is the solution to the equation below? Log6 4x^2-log6x=2
Combine the left hand side, then write both sides as powers of 6:
[tex]\log_64x^2-\log_6x=\log_6\dfrac{4x^2}x=2\implies6^{\log_6\frac{4x^2}x}=6^2[/tex]
[tex]\implies\dfrac{4x^2}x=36[/tex]
[tex]\implies x^2=9x[/tex]
[tex]\implies x^2-9x=x(x-9)=0[/tex]
[tex]\implies x=0,x=9[/tex]
However, for any base [tex]b[/tex], [tex]\log_bx[/tex] is undefined if [tex]x=0[/tex], so the only solution is [tex]x=9[/tex].
Answer:
D. x=9
Step-by-step explanation:
The measure of one of the angles formed by two parallel lines and a transversal is 45°. Is it possible for the measure of any of the other seven angles to be equal to 55°? Explain.
Answer: No
Step-by-step explanation:
Three of the other angles are 45°. The other four are 180° - 45°, which is not 55°. At the intersection of two lines, opposite angles are equal and adjacent angles are complementary, so two adjacent angles add to 180°. Adding a parallel line gives four more angles identical to the first four.
Given: ∆AFD, m ∠F = 90°
AD = 14, m ∠D = 30°
Find: Area of ∆AFD
I need an answer asap thanks
We have the triangle 30° - 60° - 90°.
The sides are in proportion: 2 : √3 : 1
(look at the picture).
[tex]2a=14[/tex] divide both sides by 2
[tex]a=7[/tex]
[tex]a\sqrt3=7\sqrt3[/tex]
The area of a trinagle AFD:
[tex]A_{\Delta}=\dfrac{1}{2}(7)(7\sqrt3)=\boxed{\dfrac{49\sqrt3}{2}}[/tex]
The area of a triangle ADF is 42.46 square units.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, in ∆ADF, m∠F=90°, AD = 14 and m∠D=30°
We know that, sinθ= Perpendicular/Hypotenuse
Now, sin A=FD/AD
sin60°=FD/14
⇒ √3/2 = FD/14
⇒ FD=7√3
sin30°=FA/AD
⇒ 1/2 =FA/14
⇒ FA=7
We know that, area of a triangle is 1/2 ×Base×Height
Area of ∆ADF
= 1/2 ×FD×FA
= 1/2×7√3×7
= 42.46 square units
Therefore, the area of a triangle ADF is 42.46 square units.
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Aaron want to buy sod for his backyard. What is the amount of area he will need to cover?
Measurements in picture
(I know the square's area but not the triangle's)
Answer:
(16 + 8√3) in²
Step-by-step explanation:
The ratio of side dimensions for a 30°-60°-90° triangle are 1 : √3 : 2. If we call the horizontal dimension of the triangle its base, then its height (vertical dimension) will be √3×4 in. Of course the area of the triangle is ...
... A = (1/2)bh = (1/2)(4 in)(4√3 in) = 8√3 in²
The total sod area is the sum of the square area (16 in²) and the triangle area, so is ...
... area to cover = (16 +8√3) in²
_____
Comment on problem dimensions
The area involved here is not much larger than the size of your hand. It would make more sense for the dimensions to be in feet or yards or meters, rather than inches.
Answer: 29.9 in.
Step-by-step explanation:
16+(8*√3)
Simplify 3 square root of 5 end root minus 2 square root of 7 end root plus the square root of 45 end root minus square root of 28
2 square root of 12
2 square root of 2
6 square root of 5 end root minus 4 square root of 7
6 square root of 10 end root minus 4 square root of 14
Answer:
6 square root of 5 end root minus 4 square root of 7
Step-by-step explanation:
[tex]3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}=3\sqrt{5}-2\sqrt{7}+\sqrt{3^2\cdot 5}-\sqrt{2^2\cdot 7}\\\\=(3+3)\sqrt{5}+(-2-2)\sqrt{7}=6\sqrt{5}-4\sqrt{7}[/tex]
_____
Comment on the answer form
In symbols, parentheses are preferred for grouping:
... 6√(5) -4√7
or
... 6(√5)-4√7
As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.
Answer:
Answer:
6 square root of 5 end root minus 4 square root of 7
Step-by-step explanation:
_____
Comment on the answer form
In symbols, parentheses are preferred for grouping:
... 6√(5) -4√7
or
... 6(√5)-4√7
As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.
why is 3 * 1/10 less than 3*10
Multiplying 3 by a smaller number gives a smaller product.
1/10 is smaller than 10, so 3·(1/10) is smaller than 3·10.
Question: Which of the following represents the equation of a line that is parallel to the line r shown in the graph?
Answer:
B
Step-by-step explanation:
• Parallel lines have equal slopes
calculate the slope m of the given line using the gradient formula and compare to the slope of the equations given
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (1,1) ← 2 points on the line
m = [tex]\frac{1+1}{1+1}[/tex] = 1 ← slope of graph
consider the slope of the given equations
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
(A)
y = 2x + 1 has slope = 2 → not parallel
(B)
x - y = - 3 ( subtract x from both sides )
- y = - x - 3 ( multiply through by - 1 )
y = x + 3 with slope = 1 → thus parallel to graph
(C)
x + y = 2 ( subtract x from both sides )
y = - x + 2 with slope = - 1 → not parallel
(D)
y = - x + 1 with slope = - 1 → not parallel
An equation of a line that is parallel to the line r shown in the graph include the following: B. x - y = -3.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope for this line by using these points (1, 1) and (0, 0);
[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope (m) = (0 - 1)/(0 - 1)
Slope (m) = 1
For the line to be parallel to the line r, it must have the same slope as line r. At data point (0, 0) and a slope of 1, an equation for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = m(x - x_1)[/tex]
y - 0 = 1(x - 0)
y = x
Based on the answer options, we have;
y = 2x + 1 ⇒ slope is 2 (not parallel).
x - y = -3
y = x + 3 ⇒ slope is 1 (parallel).
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Ramona went to a theme park during spring break. She was there for 7 hours and rode 14 rides. At what rate did Ramona ride rides in rides per hour?
Final answer:
Ramona rode rides at a rate of 2 rides per hour during her visit to the theme park.
Explanation:
Ramona's Rate of Riding Rides:
Rate = Number of rides ÷ Number of hours
Rate = 14 rides ÷ 7 hours
Rate = 2 rides per hour
A point on the rim of a wheel moves with speed of 200 feet per second. Find the angular velocity of the point if the diameter of the wheel is 8 feet.
The angular velocity of the point is found this way:
w = v/r
w = 200/(8/2) <--the two is from 2 * Pi * r
w = 50 rad/sec.
Answer: 50 rad/sec.
fullness; live
The measure of an angle is three more than twice its supplement. What is the measure of the angle?
Answer: the angle is 1°+n×120°
1°, 121°, 241°
Step-by-step explanation:
Angles are taken modulo 360°, so 363° = 3°.
Angle plus supplement gives 180°.
Let a be angle, s be supplement of a.
So s = 180-a. Given a = 3 + 2s
a = 3 + 2(180 - a)
a = 3 + 360 - 2a = 363 - 2a
3a = 363° or 3° or 723°
a = 121° or 1° or 241°
a = 1°
s = 179°
2s = 358°
2s+3 = 361° = 1° (modulo 360)
a = 121°
s = 180-121 = 59°
2s = 118°
2s + 3 = 121°, as required.
a = 241°
s = 360+180-241 = 540-241 = 299
2s = 598
2s + 3 = 601 = 241 (modulo 360)
Which table contains a set of non-linear ordered pairs?
Answer:
The table A contains a set of non-linear ordered pairs.
Step-by-step explanation:
To answer this question we have to recall what is the meaning of a linear ordered pair. As you can see, in every table there are 4 values for x, and 4 values for y. In every case, the set of values for x are
[tex]x=\{0, 1, 2, 3\}[/tex]
but in every table, the values for y varies. Now, the key is to calculate the variation of these values, and in order to have a linear relation between x and y, the variation must be the same quantity for every y value that depend of each x value.
For example, in table B, the variation is +3, as from the first y value to the second, 3 is added... and this +3 variation must be the same for each new value of y (and as you can see, 4+3 is 7, 7+3 is 10, 10+3 is 13).
Keeping this in mind, the variation in table C is -2, and the variation in table D is +1, so tables B, C and D contains sets of linear ordered pairs.
To answer the question, we just have to realise that table A has differents variations in the values of y, and this means that it contains a set of non-linear ordered pairs, wich is the correct answer to the question.
Consider the following loan. Complete parts (a)-(c) below.
An individual borrowed $84,000 at an APR of 6%, which will be paid off with monthly payments of $587 for 21 years.
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
The amount borrowed is $
the annual interest rate is
the number of payments per year is
, the loan term is 21 years,
and the payment amount is $
The amount borrowed is $84,000. The annual interest rate is 6%. There are 12 payments per year for 21 years at a monthly payment amount of $587.
Explanation:The question pertains to the fundamentals of loan calculation. Let us identify the components asked:
The amount borrowed, as clearly stated, is $84,000.The annual interest rate, also known as the APR (Annual Percentage Rate), is 6%Since it was mentioned that payments are set to be monthly, the number of payments per year is 12.The loan term, the length of time given to repay the loan, is indicated as 21 years.The payment amount, which is the monthly payment the borrower must make, is $587.Learn more about Loan Calculation here:https://brainly.com/question/28244942
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In the loan scenario, the person borrowed $84,000 at an annual interest rate of 6%. They will make 12 payments of $587 each year for a term of 21 years.
Explanation:In the provided loan scenario, the following key components can be identified:
The amount borrowed - This is the initial amount that is provided to the individual. In this case, it is $84,000.The annual interest rate - This is the percentage of the loan amount that is charged as interest each year. Here, it is 6%.The number of payments per year - As the payments are made monthly, there are 12 payments in a year.The loan term - This is the period over which the loan will be repaid. In this scenario, it is 21 years.The payment amount - This is the amount that is paid each month towards the loan. It amounts to $587 per month in the given context.Learn more about Loan Terms here:https://brainly.com/question/29755394
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Find the missing values for the exponential function represented by the table below.
x y
-2 4
-1 6
0 9
1 ?
2 ?
a. -13.5 -20.25
b. -13.5 20.25
c. 6 4
d. 13.5 20.25
Answer: D
Answer:
d. 13.5, 20.25
Step-by-step explanation:
An exponential function is monotonic and does not change sign. On this basis alone, the first three choices can be eliminated.
The common ratio is 6/4 = 3/2.
The term in the sequence after 9 is 9·(3/2) = 27/2 = 13.5.
The term in the sequence after 27/2 is (27/2)·(3/2) = 81/4 = 20.25.
Final answer:
The missing values for the exponential function table with an increasing common factor of 1.5 are 13.5 for x=1 and 20.25 for x=2, making the correct answer Option D.
Explanation:
The student's question pertains to finding the missing values for the exponential function represented by the table with given x and y values. Given the nature of an exponential function, we expect that as x increases by 1, the value of y is multiplied by the same factor each time. We can observe this behavior in the initial y-values: 4, 6, and 9. To find this constant multiplier, we can divide 6 by 4 and 9 by 6, which both give us 1.5. This constant factor, which we'll call base of the exponential function, indicates that for every increase of 1 in x, the value of y is multiplied by 1.5.
To find the missing y-values for x=1 and x=2, we just continue multiplying by the base 1.5. Thus, when x=1:
y = 9 × 1.5 = 13.5
When x=2:
y = 13.5 × 1.5 = 20.25
Hence, the completed table should read as follows:
x=-2, y=4
x=-1, y=6
x=0, y=9
x=1, y=13.5
x=2, y=20.25
The correct answer is therefore Option D: 13.5, 20.25.
i will give the brainliest thank you
Answer:
option 2
Step-by-step explanation:
in the given triangle,
tan45° = 8/x
=> 1 = 8/x
=>x = 8
for y,
cos45° = 8/y
=>1/√2 = 8/y
=>y = 8√2
Answer:
x=8, [tex]y=8 \sqrt2[/tex]
Step-by-step explanation:
Consider the given right triangle,
As, [tex]\tan \Theta = \frac{Perpendicular}{Base}[/tex]
Consider [tex]\tan 45^{\circ}=\frac{x}{8}[/tex]
[tex]1=\frac{x}{8}[/tex]
So, x=8
As, [tex]\sin \Theta = \frac{Perpendicular}{Hypotenuse}[/tex]
Consider [tex]\sin 45^{\circ}=\frac{8}{y}[/tex]
[tex]\frac{1}{\sqrt2}=\frac{8}{y}[/tex]
So, [tex]y=8 \sqrt2[/tex]
Therefore, x = 8 and [tex]y=8 \sqrt2[/tex]
26.4w = 285.12. What is the width (w) of this rectangle? 10.8 units 11.0 units 258.7 units 7527.2 units
Answer:
10.8 units
Step-by-step explanation:
As the equation represents the area of a rectangle
i.e.
length * width = Area
Now area is 285.12 units square
while length is 26.4
and width is represented by w
now putting in the formula it will become
26.4 * w = 285.12
dividing both sides by 26.4
[tex]\frac{26.4w}{26.4}=\frac{285.12}{26.4}[/tex]
this will become
w = 10.8 units
Which is the required width of the Rectangle
so answer is 10.8 units
Sarah and her brother are 6 years apart. Right now, the ratio of their ages is 3:4. How old are both of them right now?
Sarah: 18
Brother: 24
Step-by-step explanation:The difference in ratio units is 4-3 =1. The difference in years is 6, so 1 ratio unit stands for 6 years.
Multiplying by 6, we have ...
... Sarah : Brother = 3·6 : 4·6 = 18 : 24
Sarah is 18; her brother is 24.
someone help pleaseeesee
Answer:
A. 36°
Step-by-step explanation:
Same-length chords subtend same-measure arcs. Arc YZ has the same measure as its central angle (∠YOZ) and the same measure as arc XY (36°).
the measure of angle YOZ is 36°, which corresponds to option A. Therefore, the correct answer is option b.
The measure of an angle formed by two chords in a circle is half the measure of the arc intercepted by the angle.
If chord XY is congruent to chord YZ, it means that the arcs intercepted by these chords are also congruent.
So, if the measure of arc XY is "x" degrees, then the measure of arc YZ is also "x" degrees.
Now, the angle YOZ is formed by these two congruent arcs. Therefore, the measure of angle YOZ is half the measure of the arcs XY and YZ.
Angle YOZ = 0.5 * (x + x) = 0.5 * 2x = x degrees.
Now, if you're given the measure of arc XY (or YZ), you can substitute that value into the formula to find the measure of angle YOZ.
The answer choices you provided are in degrees, so the correct answer is A. 36°, assuming you have the measure of the arc XY (or YZ) in the problem.
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“Camilla makes and sells jewelry. She has 8,160 silver beads and 2,880 black beads to make necklaces. Each necklace will contain 85 silver beads and 30 black beads. How many necklaces can she make?” ^^ please help and show work, due in 10 minutes
96 necklaces
Step-by-step explanation:To find out how many necklaces Camilla can make, we need to see how many times the required number of beads "goes into" the available number of beads.
Silver: 8160/85 = 96
Black: 2880/30 = 96
Camilla has enough beads to make 96 necklaces.
_____
Comment on this answer
Obviously, if one of the quotients is smaller than the other, Camilla can only make as many necklaces as are supported by the constraining resource.
Even if she had 3000 black beads (way more than 2880), she could still only make 96 necklaces (for example) because she would run out of silver beads making that 96th necklace. (There would be 120 black beads left over in that scenario.)
The least absolute deviation line equation for the data in the table is m = 0.1x + 2.9
What is the sum of the absolute deviations?
Answer:
24.5
Step-by-step explanation:
A calculator or spreadsheet is good for doing this sort of computation.
_____
You add up the magnitudes of the differences between the given y-value and the corresponding value you get from the equation. For the first couple of points, these values are ...
... |3 - (0.1·1 +2.9)| = 0
... |2.5 -(0.1·6 +2.9)| = |2.5 -3.5| = 1
The computation proceeds like this for the remaining 6 points, and the numbers added. The result is 24.5.
if point p is 3/8 of the distance from a to b, then point p partitions the directed line segment into what ratio from a to b? a. 3:11 b. 8:11 c. 3:5 d. 5:3
Answer:
b
Step-by-step explanation:
Final answer:
Point P divides the distance from A to B into a ratio of 3:5, with P being 3/8 of the way from A to B. The correct option is c.
Explanation:
If point P is 3/8 of the distance from A to B, we can understand this situation by imagining the entire distance from A to B as being divided into 8 equal parts, and point P lies at the end of the third part when moving from A to B. Since P is 3 parts away from A, it leaves the remaining 5 parts to reach B. This sets up a partition of the segment into two parts: one from A to P and the other from P to B. The ratio of these distances is the number of parts from A to P to the number of parts from P to B. Therefore, the ratio of AP to PB is 3:5. Option c is accurate.
At a high school with 800 students, 80% of the students ride the school bus. if 20 students are selected randomly (without replacement) and we let x = the number of students in the sample who ride the bus, what is the probability that at least one of the students doesn't ride the bus?
Answer:
0.9885 (98.85%)
Step-by-step explanation:
Since sample is less than 10% of the population, we can use binomial distribution to approximate the probability.
So we want to calculate P( X < 20 ).
We can calculate the probability of complement event P( X = 20 ).
Use binomial formula b(x; n, p) = C( n, x ) p^(x) (1-p)^(n-x)
b( 20; 20, 0.8 )
= C( 20, 20 ) (0.8)^(20) (0.2)^0
= (0.8)^20 ≈ 0.0115
So since P( X < 20 ) = 1 - P( X = 20 ), we have
P( X < 20 ) ≈ 1 - 0.0115 = 0.9885
The required value of probability for the given sample is given as 0.9885.
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Total number of students are given as 800.
The probability of students riding the school bus is 80% = 0.8.
Then, probability of students not riding the school bus is 1 - 0.8 = 0.2.
The probability of finding at least one student out of 20 not riding the bus is given as,
1 - P(All of the students ride bus)
It can be solved using binomial distribution as follows,
⇒ 1 - ²⁰C₂₀(0.8)²⁰(0.2)⁰
⇒ 1 - 0.0115 = 0.9885
Hence, the probability that at least one of the students doesn't ride the bus is given as 0.9885.
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i need help on finding the orthocenter of a triangle, i got the x right, x=6 but I got the Y value wrong, it's supposed to be y=4 but i got y=8 as my answer. the question is find the coordinates of the orthocenter of Triangle ABC with vertices A(2,6), B(8,6), and C(6,2). what i did to find the Y value was find the slope of BC then use that value and the coordinates of A and substituted them into an equation y-6=1/2(x-2), i solved it and got y = 1/2x+5. i then substituted my x value that i previously found into it to find Y , y=1/2(6)+5 . i got 8 as the Y value but it's wrong, can someone tell me what i missed?
Answer:
See the attached
Step-by-step explanation:
When in doubt, draw a diagram.
The orthocenter of this acute triangle will be within its bounds. That should tell you right away that the y-coordinate of it will not be 8, but must be between 2 and 6.
The line perpendicular to BC through A must have a y-intercept greater than the y-coordinate of A, so cannot be 5. Whatever it is, the y-coordinate of the orthocenter will be less, so again, your answer fails the reasonableness test.
The perpendicular line to BC through A is ...
... y = (-1/2)(x -2) +6 = -x/2 +7 . . . . . . looks like you had a sign error in (-1/2)(-2)
The intersection of that line and x=6 is ...
... y = -6/2 +7 = 4