two cars start moving from the same point. one travels south at 60 miles per hour. the other car travels west at 25 miles per hour. at what rate is the distance between the cars increasing 2 hours later?
The distance between the cars increasing 2 hours later is 65mph
Let’s say, the velocity in the west is x, the velocity in the south is y, and the distance between them is s at any time t. Since the west and south directions are perpendicular to each other, this will be for a right-angled triangle.
So, we have [tex]x^2 + y^2 = s^2[/tex] --------------(1)
(please note all of them are changing as t increases.)
So, x=u×t and y=v×t,
so using (1), we can write
[tex][(u\times t)^2 + (v\times t)^2] = s^2[/tex]
[tex]s= \sqrt{(u^2 + v^2)}* t[/tex]
Using the value of u and v,
get [tex]\sqrt{(u^2 + v^2)}[/tex]= 65
So, s= 65 t
ds/dt = 65 mph
There fore the distance between the cars increasing 2 hours later is 65mph
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Solve this equation please :)
The ratio of BE/BC is 1:3.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
In triangle ABC, the ratio of FA and CF is 1:2.
Since, the point G is the midpoint of BF,
Implies that G divides BF in ratio 1:1.
By using mass point geometry,
The ratio of BE/BC=1:3
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1. Jorge used 2 7/8 packs of pencils in the first 1/3
of the year. At what rate is Jorge using
pencils
Answer:
Jorge is using pencils at a rate of 6 packs a year or a rate of 2 packs every four months.
Step-by-step explanation:
1/3 of a year is four months so that would be 2 packs every four months and if you multiply that by three you’d get 12 month, or one year, and 6 packs of pencils.
What is the slope, m, of the following linear equation? y=x-6
Answer:
1
Step-by-step explanation:
because the 1 is actually invisible
its called invisible math
y=mx+b
Questions 1-4: The number of classes (X) a student takes in a given semester follows the following probability distribution: X 0 1 2 3 4 5 PIX) 0.4 0.25 0.15 0.08 0.02 ??? 1. What is the probability they take 5 classes? 2. What is the probability they take at least one class? 3. What is the probability a student will take 2 or 3 classes in a semester? 4. What is the expected number of classes a student will take in a given semester? (show your work on this one, and a screenshot of how you worked it out on the calculator or excel).
The probability to take 5 classes is 0.1, while the probability to take at least one class is 0.6, the probability to take 2 or 3 classes is 0.23 and the expectation of the distribution is 1.37.
The distribution given is
X PIX)
0 0.4
1 0.25
2 0.15
3 0.08
4 0.02
5 ???
1.
We know that the sum of all the probabilities in a probability distribution is always equal to 1.
Let the probability of X = 5 be p
Hence,
0.4 + 0.25 + 0.15 + 0.08 + 0.02 + p = 1
or, 0.9 + p = 1
or, p = 1 - 0.9
or, p = 0.1
Hence the probability to take 5 classes is 0.1.
2.
We need to find P(X ≥ 1)
= 1 - P(X = 0)
From the distribution we know that P(X = 0) is 0.4
Therefore, P(X ≥ 1)
= 1 - 0.4
= 0.6
Hence, the probability to take at least one class is 0.6
3.
The probability to take 2 or 3 classes in a semester
= P( X = 2) + P(X = 3)
= 0.15 + 0.08
= 0.23
4.
The expectation of any distribution
= ∑xp(x)
where,
x is the random variable
p(x) is the probability of the random variable
Therefore,
E(X) = 0 X 0.4 + 1 X 0.25 + 2 X 0.15 + 3 X 0.08 + 4 X 0.02 + 5 X 0.1
= 0 + 0.25 + 0.30+ 0.24 + 0.08 + 0.50
= 1.37
Therefore the expectation is 1.37
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an engineer designed a valve that will regulate water pressure on an automobile engine. the engineer designed the valve such that it would produce a mean pressure of 5.7 pounds/square inch. it is believed that the valve performs above the specifications. the valve was tested on 12 engines and the mean pressure was 5.9 pounds/square inch with a variance of 0.81. a level of significance of 0.1 will be used. assume the population distribution is approximately normal. determine the decision rule for rejecting the null hypothesis. round your answer to three decimal places.
the decision rule for rejecting the null hypothesis is, to reject H₀ if t > 1.363.
Right-tailed test: H0µ = k H1:>k P-value = P(z>z x) This indicates the probability of obtaining a test statistic as high as or higher than z x. If the P-value is less than α, we reject H0(null hypothesis) and conclude that the data are statistically significant at the level α. We do not reject H0 if the P-value is greater than α.
H0: µ = 5.3 , H1: µ> 5.3
it is a right-tailed test
n = 12
α = 0.10
therefore the decision rule for rejecting the null hypothesis is, Reject H0 if t> 1.363.
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10 PIONTS ANSWER PLEZ IT IS NOW DUE!!!!!!
15. A triangle pattern is shown below.
Figure Perimeter
1 triangle 24
2 triangles 30
3 triangles 36
Which equation relates the number of triangles in the figure (n) to the perimeter of the figure (P)?
(1 point)
P = 6n + 18
P = 9n + 6
P = 6n + 9
P = 9n + 12
The equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.
We are given:
The perimeter of the 1 triangle = 24
The perimeter of the 2 triangle = 30
The perimeter of the 3 triangle = 36
As we can see in the given figures two sides with lengths of 9 are fixed and the side with a length of 6 is varying.
So, we can write this as,
P = 6n + 18, where n = number of triangles.
Now, check the equation formed by substituting the values;
Substitute n = 1, and we get;
P = 6(1) + 18
P = 6 +18
P = 24 True.
Substitute n = 2, and we get;
P = 6(2) + 18
P = 12 +18
P = 30 True.
Substitute n = 3, and we get;
P = 6(3) + 18
P = 18 + 18
P = 36, true.
So, it is true for all the figures.
Thus, the equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.
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Write an equation of
the line that passes
through (7, 10) and
is perpendicular to the
line y =
x-9.
Equation:
2
Equation of the line that passes through (7, 10) and is perpendicular to the line y =x-9 is y = -x+17.
Given equation, y = x-9
Slope = m = 1
Slope of line perpendicular to given line = -1/m
= -1/1
= -1
Let the equation of line be y = mx + c
Passes through A(7,10)
10 = -1(7) + c
10 = -7 + c
c = 10 + 7
= 17
Hence, equation is y = -x+17
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Juan is 12. His father put $2000 into his bank account. The account
gained interest at a rate of 2.3% per year, compounded bi-monthly.
Assuming no more money was deposited and none was withdrawn, how
much money will be in the account when Juan turns 18? Round to the
nearest cents.
A=P
n
A accumulated amount
P = principal
r = interest rate
n = compounding per period
t = number of periods
Amount of money present in Juan's account when she is 18 years old is $2,284.73
When Juan is 12 years old ;
Given P = principal = $ 2000
r = interest rate = 2.3 %
t = number of periods = 2
To start, multiplying R percent by 100 gives us 2.3%/100, or 0.023 each year.
Simply converting time into years, 2 months divided by 12 months each year equals 0.166667 years.
How to resolve our equation
A = 2000(1 + (0.023 × 0.166667)) = 2007.666682
A = $2,007.67
Simple interest on a principal of $2,000.00 at a rate of 2.3% annually for 0.166667 years (2 months)
Juan when she is 18 years old
time = 18 - 12 = 6 years
rate = 2.3 %
Principal = $2,007.67
Accrued money = A = $2,284.73
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Quadrilateral ABCD is inscribed in this circle.
What iS the measure of LA?
Enter your answer in the box.
The measure of ∠A is 106°.
Quadrilateral ABCD is inscribed in this circle.
To find out the measure of LA:
We are given that, 'Quadrilateral ABCD is inscribed in the circle'.
So, we get that,
'ABCD is a cyclic quadrilateral' that is The sum of the opposite interior angles is 180°.
Thus, we have,
∠A +∠C = 180°
i.e. ∠A + 74° = 180°
i.e. ∠A = 180° - 74°
i.e. ∠A = 106°
Thus, the measure of ∠A is 106°.
Hence the answer is the measure of ∠A is 106°.
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Rewrite the following equation in slope-intercept form.
y + 6 = 9(x − 8)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
3. Here is a balanced hanger diagram.
What is the weight of a square if a triangle weighs 4 grams?
Explain your reasoning.
Answer:bgvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvddddddddddddddddddddddddddd
Step-by-step explanation:
Answer:
Step-by-step explanation:
well it will be 16 because a square has 4 sides so you multiply by the grams that would be 4. 4*4= 16
f/4 + 6 ≤ 7 what is the answer
Answer:
f ≤ 4
Step-by-step explanation:
f/4 + 6 ≤ 7
f/4 ≤ 7 - 6
f/4 ≤ 1
f ≤ 4
Answer:
F<4
________
________
Newton and Descartes have a $50.00 gift card to a pet store.
Newton's total is $18.95 and Descartes's total is $24.38. How much
money do they have left on their gift card?
the temperature was -20 degrees in the morning when Rae woke up. At dinner time, the temperature shows 35 degrees. What was the change in temperature from the time Rae woke up un dinner time? Draw a picture and write an equation to solve.
The change in temperature is 15°
How to find Change in temperature ?
If temperature rise then Change in temperature ,t₂ = t₁ + final temperature
If temperature dropped then Change in temperature ,t₂ = t₁ - final temperatureWe have given,
In morning, when Rae woke up the temperature is (t₁) = -20°
At dinner time, the temperature is = 35°
t₂ = t₁ + 35
t₂ = (-20) + 35
t₂ = 15°
Hence, the change in temperature is 15°
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Which equation represents a line that has a slope of One-third and passes through point (–2, 1)?
y = one-third x minus 1
y = one-third x + five-thirds
y = one-third x minus five-thirds
a blank CD can hold 80 minutes of music you have burned m minutes of music onto the cd which equation models the amount of time that is left on the cd
The equation that models the amount of time that is left on the cd is 80 - m.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, the blank CD can hold 80 minutes of music you have burned m minutes of music onto the cd. The time left will be:
= Total minutes - Time used
= 80 - m
This illustrates the equation.
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6.The percents of three types of tickets collected at the gate for a high school football game are shown.
a.Write the percents as decimals and as fractions.
b.There is one other type of ticket that is not shown. It is a ticket for a child under 5. What percent of the tickets were of this type?
The percentage of three types of tickets collected at the gate:
ai) student's ticket as a percent: 48%, as a fraction: 48/100, and as a decimal: 0.48.
aii)Adult's ticket as a percent:28%, as fraction:28/100, and as decimal: 0.28.
aiii) Senior's( 65 and older) ticket: 14%, as fraction:14/100 and as decimal: 0.14.
b)Tickets for children under 5years is: 10%, as fraction:10/100, and as decimal: 0.10.
what is percentage?
This is a number written as a ratio of a hundred or as a fraction of a hundred. it is represented with "%".
How to calculate the percentages:
.As a fraction: Write it as a ratio of a hundred.
ticket type for
i) students48% =48/100
ii)Adult 28%=28/100
iii)Senior's( 65 and older)14% =14/100
.As a decimal: Write it as a ratio of hundred then divide by hundred.
ticket type for:
i) students48% =48/100=0.48
ii)Adult 28%=28/100=0.28
iii)Senior's( 65 and older)14% =14/100=0.14
b)To calculate the percentage of tickets of children under 5 years:
Percent(% )means 100
Therefore,
100 - student ticket %- Adult's ticket % - Senior's( 65 and older) ticket%
100- 48 - 28 - 14 = 10%
Thus for children under 5 years,
i)As percent is:10%,
ii)as fraction:10/100
iii)decimal: 0.10.
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IIIIIIIIIII NEEEEEDDDDD HELPPPPP FASTTTTT!!!!!!!!!!!!! If a circle has a circumference of 60π, which equation shows the correct value for the radius, r?
we know that [tex]r[/tex]
area of the circle is equal to
A= [tex]\pi[/tex] × [tex]r^{2}[/tex]
solve for [tex]r[/tex]
[tex]r[/tex] = [tex]\sqrt{\frac{A}{\pi } }[/tex]
for A=60cm2
[tex]r[/tex] = [tex]\sqrt{\frac{60}{\pi } cm}[/tex]
we know that
[tex]\sqrt{60\\}[/tex] = [tex]\sqrt{2^{4} }[/tex] × 3 × 5
=2[tex]\sqrt{15}[/tex]
so,
[tex]\sqrt{\frac{60}{\pi } }[/tex] = 2 [tex]\sqrt{\frac{15}{\pi } }[/tex]
2[tex]\sqrt{\frac{15}{\pi } } = 2\frac{\sqrt{15} }{\pi }[/tex] × [tex]\frac{\sqrt{\pi } }{\sqrt{\pi } }[/tex]
= 2 [tex]\frac{\sqrt{15\pi } }{\pi }[/tex]cm
this means the answer is-
2 [tex]\frac{\sqrt{15\pi } }{\pi } cm[/tex]
10 points
Sup,
Use the order of operations to simplify this expression. Express your answer in the simplest form.
1/4 + 1/2 ÷ 3/8
Options
1
1 7/12
2
8/9
Have a great day answer Asap
Answer:
2
Step-by-step explanation:
1/4 + 1/2 ÷ 3/8
0.25 + 0.5 ÷ 3/8
0.25 + 1.33
= 1.58
approximately 2
how will coefficient of restitution change with angle of impact?
Kinematic parameters is the way by which coefficient of restitution change with angle of impact.
The ratio of a boulder's velocities or energy prior to and following its impact with the slope is represented by the coefficient of restitution, which is a dimensionless number. Different definitions of the coefficient of restitution have been put forth in earlier studies, but it has not been determined which definition is better suitable for predicting rockfall.
The determination of suitable values for the coefficients of restitution, which often change with the kinematic parameters and terrain conditions, is essential for the accuracy of a computer program modelling a rockfall trajectory. Using small-scale laboratory testing, the effects of the impact angle with regard to the slope on the coefficients of restitution have been identified and analyzed. to determine the validity of the current conclusion based on limited laboratory testing.
This study conducted a medium-scale laboratory test employing spherical limestone polyhedrons impacting concrete slabs to determine how the impact angle affects the coefficients of restitution when the test scale is changed. A 3D motion capture system measures the velocities before and after the collision during free fall tests. Several general laws apply when taking into account the impact angle's effect, regardless of the test scales and conditions, according to the results comparison between our test and the existing small-scale tests. The normal coefficient of restitution (Rn), the kinematic coefficient of restitution Rv, and the kinetic energy coefficient of restitution Re will all decrease as the impact angle increases.
In contrast, it will cause Rt's tangential coefficient of restitution to increase. The impact of the impact angle is significantly influenced by the rotation. The normal coefficient of restitution Rn and tangential coefficient of restitution Rt are always higher when more kinetic energy is converted to rotational energy.
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I could get these right but, Its being rude to
me so Im trying one more time to clarify.
Answer: The correct answer is the one that has 4 + 5 + 2 + 3.
(I didn't say which side it is in case you got confused but it's the one right above the speaker sign.)
Step-by-step explanation:
what is the anser for Latanya has a points card for a movie theater.
She receives 60 rewards points just for signing up.
She earns 9.5 points for each visit to the movie theater.
She needs 117 points for a free movie ticket.
How many visits must Latanya make to earn a free movie ticket?
If Latanya receives 60 rewards points just for signing up. She earns 9.5 points for each visit to the movie theater. She needs 117 points for a free movie ticket. Then 6 visits Latanya has to make to earn a free ticket.
What is slope intercept form of line?
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given that,
Latanya has 60 rewards points just for signing up.
For each visit to theatre she earns 9.5 points.
To get free ticket she needs 117 points.
We need to find how many visits she has to do to get free ticket.
We use Linear equation to solve this
Let y = total number of rewards points
x = number of visits to the movie theater
m=Points for each visit
y=mx+b
117=9.5x+60
Subtract 60 on both sides
117-60=9.5x
57=9.5x
x=6
Hence she has to make 6 visits to earn a free ticket.
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Answer:
6 x=6
Step-by-step explanation:
If Bruce can eat 2 1/2 bananas per day, how many bananas can Bruce can eat in 4 weeks?
The number of bananas Bruce can eat in 4 weeks is 70 bananas
Calculating numberFrom the question, we are to calculate the number of bananas Bruce can eat in 4 weeks.
From the given information,
Bruce can eat 2 1/2 bananas per day
First, we will determine the number of days there are in 4 weeks
NOTE: There are 7 days in 1 week
If there are 7 days in 1 week
Then,
There are 4 × 7 days in 4 weeks
4 × 7 = 28 days
That is, 4 weeks = 28 days
Now, we will determine the number of bananas Bruce can eat in 28 days
If Bruce can eat 2 1/2 bananas per day
Then,
Bruce can eat 28 × 2 1/2 bananas in 28 days
28 × 2 1/2 = 28 × 5/2
= 14 × 5
= 70
Hence, Bruce can eat 70 bananas in 4 weeks
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Answer:
70
Step-by-step explanation:
Bruse can eat 2 1/2 bananas in one day so:
1day=2 1/2bananas.
if 1wk=7days
4wks=x =28days
1day=2 1/2 bananas
28da
28×2 1/2
=28×5/2=70
answer=70bananas
–2.5x – 7.5 = x + 6.5
Answer:
Step-by-step explanation:
x=-4 that should be the answer i don't really know how too explain but i did this 2 years ago
Answer:
Step-by-step explanation:
18 feet:5 yards
Please helpppppppppppppp
Answer:
Foot: 18.416666666666668
Yard: 6.1388888888888892836
using traditional methods, it takes 11.8 hours to receive a basic driving license. a new license training method using computer aided instruction (cai) has been proposed. a researcher used the technique with 13 students and observed that they had a mean of 12.0 hours with a standard deviation of 1.9. a level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. assume the population distribution is approximately normal. find the value of the test statistic. round your answer to three decimal places.
The test statistics value is 0.380
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
For example: To find the standard deviation, you have to add up all the numbers in the data set, then divide by how many numbers there are, and that will get you your answer.
Formula:
t=(mean-time)/(standard deviation/√(number of students) )
=( 12 - 11.8) / (1.9 / √13 )
= 0.380
This is test statistics value.
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Marcus is selling t-shirts at the state fair. He brings 200 shirts to sell. He has long sleeved T-shirts and short sleeved t-shirts for sale. Obe the first day of the fair , he sells 1/2 of his long-sleeved t-shirts and 1/3 of his short sleeved t-shirts for a total of 80 t shirts sold. How many of each type of shirt did Marcus bring to the fair?
The number of each type of shirt that Marcus bring to the fair is 80 long-sleeved T-shirts and 120 short-sleeved T-shirts .
Let x =Number of long-sleeved T-shirts
Let y = Number of short-sleeved T-shirts
Hence,
x + y = 200
1/2x + 1/3y = 80
Using linear Combinations Method:
6[1/2x + 1/3y = 80]
x +y =200
3x + 2y =480
So,
-2(x +y = 200)
3x + 2y = 480
-2x -2y=-400
3x + 2y = 480
x = 80 (Long sleeved)
Solve for y
80 + y =200
y = 200 -80
y = 120 (Short sleeved)
Therefore he brought 80 and 120 T-shirts .
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Given that the point (-90, -56) is on the
terminal side of an angle, 0, find the exact
value of the following:
sin(0)=
cos(0)=
tan (0) =
csc(0)=
sec(0)=
cot (0)=
The value of sinθ = - 28/53, cosθ = - 45/53, tanθ = 28/45, cosecθ = -53/28, secθ = -53/45, cotθ = 45/28.
Given that:
The point (-90, -56) is on the terminal side of an angle, θ
Using Pythagoras' theorem,
Hypotenuse^2 = Perpendicular^2 + Base^2
Hypotenuse^2 = (-56)^2 + (-90)^2
Hypotenuse^2 = 3136 + 8100
Hypotenuse^2 = 11236
Hypotenuse = 106
The value of hypotenuse = 106
The exact value of the following is:
sinθ = Perpendicular/Hypotenuse = -56/106 = - 28/53
cosθ = Base/Hypotenuse = -90/106 = - 45/53
tanθ = Perpendicular/ Base = - 56/-90 = 28/45
cosecθ = 1/sinθ = -53/28
secθ = 1/cosθ = -53/45
cotθ = 1/tanθ = 45/28
Hence, we got all the values of θ.
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help me please...........................................................................................................................
The solution is
The Hypotenuse = FD
Side Opposite of ∠F = MD
Side Adjacent of ∠F = MF
Side Opposite of ∠D = MF
Side Adjacent of ∠D = MD
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
The triangle FMD and the ∠M is a right angle
So , ∠M = 90°
From the figure , we can deduce that
The Hypotenuse = FD
Side Opposite of ∠F = MD
Side Adjacent of ∠F = MF
Side Opposite of ∠D = MF
Side Adjacent of ∠D = MD
Hence , the required solution is based on trigonometric relations
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