The area of the trapezoid is 24 in.2.
True or false
Answer:
The answer is true
Step-by-step explanation:
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2
The equation r(t) = sin(4t)i + cos(4t)j, 0t≥0 describes the motion of a particle moving along the unit circle. Answer the following questions about the behavior of the particle.
a. Does the particle have constant speed? If so, what is its constant speed?
b. Is the particle's acceleration vector always orthogonal to its velocity vector?
c. Does the particle move clockwise or counterclockwise around the circle?
d. Does the particle begin at the point (1,0)?
Answer:
a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).
Step-by-step explanation:
a) Let is find first the velocity vector by differentiation:
[tex]\vec v = \frac{dr_{x}}{dt} i + \frac {dr_{y}}{dt} j[/tex]
[tex]\vec v = 4\cdot \cos 4t\, i - 4 \cdot \sin 4t \,j[/tex]
[tex]\vec v = 4 \cdot (\cos 4t \, i - \sin 4t\,j)[/tex]
Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:
[tex]\|\vec u \| = 1[/tex]
Then,
[tex]\| \vec u \| = \sqrt{\cos^{2} 4t + \sin^{2}4t }[/tex]
[tex]\| \vec u \| = \sqrt{1}[/tex]
[tex]\|\vec u \| = 1[/tex]
Hence, the particle has a constant speed of 4.
b) The acceleration vector is obtained by deriving the velocity vector.
[tex]\vec a = \frac{dv_{x}}{dt} i + \frac {dv_{y}}{dt} j[/tex]
[tex]\vec a = 16\cdot (-\sin 4t \,i -\cos 4t \,j)[/tex]
Velocity and acceleration are orthogonal to each other only if [tex]\vec v \bullet \vec a = 0[/tex]. Then,
[tex]\vec v \bullet \vec a = 64 \cdot (\cos 4t)\cdot (-\sin 4t) + 64 \cdot (-\sin 4t) \cdot (-\cos 4t)[/tex]
[tex]\vec v \bullet \vec a = -64\cdot \sin 4t\cdot \cos 4t + 64 \cdot \sin 4t \cdot \cos 4t[/tex]
[tex]\vec v \bullet \vec a = 0[/tex]
Which demonstrates the orthogonality between velocity and acceleration vectors.
c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is: [tex]t \geq 0[/tex]
And cosine decrease and sine increase inasmuch as t becomes bigger.
d) Let evaluate the vector in [tex]t = 0[/tex].
[tex]r(0) = \sin (4\cdot 0) \,i + \cos (4\cdot 0)\,j[/tex]
[tex]r(0) = 0\,i + 1 \,j[/tex]
False, the particle begin at the point (0,1).
Solve the system of equations y= x squared + 3x-6 and y=2x-6
Answer:
Slope = 4.000/2.000 = 2.000
x-intercept = 6/2 = 3
y-intercept = -6/1 = -6.00000
Step-by-step explanation:
Step by step solution :
Step 1 : Equation of a Straight Line
Graph of a Straight Line
Calculate the Y-Intercept
Calculate the X-Intercept
Calculate the Slope
Answer for y=2x-6 is below
Answer:
Slope = 4.000/2.000 = 2.000
x-intercept = 6/2 = 3
y-intercept = -6/1 = -6.00000
Hope this helps.
*I am greater than 80
*I am less than 90
*I am an even number
*My digits (of the mystery number) add up to 12
What’s my number
Answer:
Step-by-step explanation:
84?
8+4 is 12, and 84 is greater than 80, and less than 90
Answer:
84
Step-by-step explanation:
Which equation represents this number sentence?
Two less than one-fourth of a number is 10.
Answer:
[tex]\frac{1}{4} x-2=10[/tex]
Step-by-step explanation:
Let x be that number.
[tex]\frac{1}{4} x-2=10[/tex]
If you want to find the number..
[tex]\frac{1}{4} x=10+2[/tex]
[tex]0.25x=12[/tex]
[tex]x=12/0.25[/tex]
[tex]x=48[/tex]
Leap years are years in which February has 29 days instead of 28. The device of leap year was invented to keep the calendar in sync with the "True time of year" because a year has approximately 3651/4 days, but actually slightly less, most, but not all, years divisible by 4 have been made leap years. The rule that is used to keep the calendar in sync is:
Answer:
As you know, a year has around 365 + 1/4 days.
This means that in two years, we have:
365 + 356 + 1/4 + 1/4 = 730 + 1/2
and so on.
adding this up, when we have 4 years we have a full day extra, this is:
1460 + 1
When we divide 1461 by 4, we have 365 with a surpass of 1.
The rule used to keep the calendar in sync with this extra day is adding an extra day to each fourth year.
So each fourth year, we have an extra day in Februray (the Februray 29th), this is called a bisiest year.
The "math rule" used to know if a year is leap or not is:
if a year is not divisible by 4, then it is a common year
else if the year is not divisible by 100 then it is a leap year,
else if the year is not divisible by 400, then it is a common year
if not, the year is a leap year.
Where "year" represents the number of the year.
Use the Divergence Theorem to compute the net outward flux of the field F=<-2x,y,-2z> across the surface S, where S is the boundary of the tetrahedron in the first octant formed by the planex+y+z=2.
The net outward flux across the boundary of the tetrahedron is:___________.
The net outward flux across the boundary of the tetrahedron is: -4
What is the gradient of a function in a vector field?
The gradient of a function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z).
Given vector field:
F = ( -2x, y, - 2 z )
[tex]\mathbf{\nabla \cdot F = ( i \dfrac{\partial }{\partial x }+ j \dfrac{\partial}{\partial y} + k \dfrac{\partial}{\partial z}) \langle -2x, y, -2z \rangle}[/tex]
[tex]\mathbf{ \nabla \cdot F = ( \dfrac{\partial }{\partial x }(-2x)+ \dfrac{\partial}{\partial y}(y) + \dfrac{\partial}{\partial z}(-2z))}[/tex]
= -2 + 1 -2
= -3
According to divergence theorem;
Flux [tex]\mathbf{=\iiint _v \nabla \cdot (F) \ dv}[/tex]
x+y+z = 2; [tex]1^{st}[/tex] Octant
x from 0 to 2y from 0 to 2 -xz from 0 to 2-x-y[tex]= \int\limits^2_0 \int\limits^{2-x}_0 \int\limits^{2-x-y}_0 -3dzdydx[/tex]
[tex]=-3 \int\limits^2_0 \int\limits^{2-x}_0 (2-x-y)dy dx[/tex]
[tex]= -3 \int\limits^2_0[(2-x)y - \dfrac{y^2}{2}]^{2-x}__0 \ \ dx[/tex]
[tex]= -3 \int\limits^2_0(2-x)^2 - \dfrac{(2-x)^2}{2} dx[/tex]
[tex]= -3 \int\limits^2_0\dfrac{(2-x)^2}{2} dx = - \dfrac{3}{2} \int\limits^2_0(4-4x+x^2) dx[/tex]
[tex]=- \dfrac{3}{2}(4x-x^2 + \dfrac{x^3}{3})^2_0[/tex]
[tex]=- \dfrac{3}{2}(8-8+\dfrac{8}{3})[/tex]
[tex]=- \dfrac{3}{2}(\dfrac{8}{3})[/tex]
= -4
Therefore, we can conclude that the net outward flux across the boundary of the tetrahedron is: -4
Learn more about the gradient of a function here:
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A tree farming company is testing how many items customers purchase during their visits. Based on many results, the (partial) probability distribution below was determined for the discrete random variable X = number of pieces of information remembered (during a fixed time period). What is the missing probability P(X=6)? Note that the missing probability should be reported to the second decimal place.
Answer:
X probability = 0.02
Cumulative frequency at x ( 6 ) = 1
Step-by-step explanation:
X P ( X ) Cf ( X )
1 0.58 0.58
2 0.18 0.58 + 0.18 = 0.76
3 0.10 0.76 + 0.10 = 0.86
4 0.07 0.86 + 0.07 = 0.93
5 0.05 0.93 + 0.05 = 0.98
6 0.02 0.98 + 0.02 = 1
The risk of a child developing cancer is approx 3 in 1500. If there are approx 11,721,722 children, how many have cancer?
Answer:
Approximately 23,433 children will have cancer.
Step-by-step explanation:
3/1500 can be simplified to 1/500, which can also be written as 0.002. To find the number of children who have cancer, we do 11,721,722 * 0.002, which gives us 23,433.444 which we can round to 23,433.
السؤال الرابع
اب ج مثلث قائم الزاوية في ب ، فيه أب = 6 سم ،
ب ج= 8 سم . فجد قيمة جتاأ ؟
Answer:
10 cm
Step-by-step explanation:
نستخدم فيثاغورس
ٲب²+ب ج²=ج ٲ²
ج ٲ²= 6²+8²
ج ٲ²= 100
ج ٲ= 10 سم
Does anyone know this? I think its B? Am i correct?
Yes, B. Rising action is correct
What is
7 1/4 - 3 3/4 =?
Answer:
3 1/2
Step-by-step explanation:
7 1/4 - 3 3/4
Borrow 1 from the 7 in the form of 4/4
6 + 4/4 + 1/4 - 3 3/4
6 5/4 - 3 3/4
3 2/4
Simplify the fraction
3 1/2
Answer:
[tex]3 \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]7 \frac{1}{4} - 3 \frac{3}{4} \\ \frac{29}{4} - \frac{15}{4} \\ = \frac{14}{4} \\ = \frac{7}{2} \\ = 3.5 = 3 \frac{1}{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
100 points for brainiest
absurd answers WILL be recorded!
Please try!!!
Answer:
462cm^3
Step-by-step explanation:
Volume of a pyramid = 1/3 × base area × height
Now the base is a rectangle with sides 7cm and 18cm; area of base is;
7 × 18 = 126cm^2
Therefore volume =
1/3 × 126 × 11 = 42 × 11= 462cm^3
What’s the correct answer for this? Select all the ones that apply ?
Answer:
A and D
Step-by-step explanation:
Either rotate the dilated circle 180° about point C or Translate the dilated circle so that it's centre is at point B so that we come to know that the circles are similar
Add. Write your answer in simplest form. 7/10 + 1/4
Answer:
[tex] \frac{19}{20} [/tex]
Step-by-step explanation:
[tex] \frac{7}{10} + \frac{1}{4} \\ \frac{14 + 5}{20} \\ = \frac{19}{20} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Write an equation that would represent the following word problem: Billy buys one candy bar for $2 and 3 lollipops. If he spends $3.98 in total, how much is each lollipop? [USE x AS YOUR VARIABLE - DO NOT USE SPACES IN YOUR ANSWER]
A numerical measure of linear association between two variables is the
Answer:
Correlation Coefficient
Step-by-step explanation:
The correlation coefficient (r) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.
A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of
Answer:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
The statistic would be given by:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]
Step-by-step explanation:
Information given
[tex]n_1 = 60 [/tex] represent the sample size 1
[tex]n_2 =40[/tex] represent the sample size 2
[tex]s^2_1 = 8[/tex] represent the sample variance 1
[tex]s^2_2 = 10[/tex] represent the sample variance 2
The statistic to check the hypothesis is given by:
[tex]F=\frac{s^2_2}{s^2_1}[/tex]
Hypothesis to test
We want to test if the two variances are equal, so the system of hypothesis are:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
The statistic would be given by:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]
Rajeev walked 7/8 mile in 1/4 hour. what was his speed in miles per hour?
Answer:
V(speed)=3.5 mile per hour
Step-by-step explanation:
[tex]V=mile per hour[/tex]
[tex]V=\frac{7}{8}/ \frac{1}{4}[/tex]
[tex]V=\frac{7}{8}*\frac{4}{1}[/tex]
[tex]V=\frac{7}{8}*4[/tex]
[tex]V=3.5[/tex]
A research company desires to know the mean consumption of meat per week among people over age 29. A sample of 2092 people over age 29 was drawn and the mean meet consumption was 2.9 pounds. Assume that the standard deviation is known to be 1.4 pounds. Construct a 95% confidence interval for the mean consumption of meat among people over age 29. Round your answer to one decimal place.
Answer:
The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{1.4}{\sqrt{2092}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 0.1 = 2.8 pounds
The upper end of the interval is the sample mean added to M. So it is 2.9 + 0.1 = 3 pounds.
The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.
Answer:
[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]
[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]
The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=2.9[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma =1.4[/tex] represent the population standard deviation
n=2092 represent the sample size
Confidence interval
The confidence interval is given by:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence interval is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]z_{\alpha/2}=1.96[/tex]
Replacing the info we got:
[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]
[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]
The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]
What value of x is in the solution set of 3(x – 4) ≥ 5x + 2? –10 –5 5 10
Answer:I think it -5 wait lemme check answer again
The solution to the inequality will be greater than or equal to –5. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
3(x – 4) ≥ 5x – 2
Simplify the equation, then the solution to inequality will be
3(x – 4) ≥ 5x –2
3x – 12 ≥ 5x –2
5x – 3x ≤ – 12 + 2
2x ≤ – 10
x ≤ –5
The solution to the inequality will be greater than or equal to –5.
Then the correct option is B.
The correct equation is 3(x – 4) ≥ 5x – 2.
More about the inequality link is given below.
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One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 12 hours. How long will it take the pipe to fill the pool if the drain is left open?
Answer: 12 hours
Step-by-step explanation:
Let x = time it takes to fill the pool if the inlet pipe and drain pipe are both open
1/6 = portion of pool filled per hour by the inlet pipe
1/12 = portion of pool emptied per hour by the drain
1/x = portion of pool filled per hour if the inlet pipe and drain are both open
Then, 1/6 - 1/12 = 1/x
Multiply by the LCD, 12x, to obtain
2x - x = 12
x = 12 hours
The population of coyotes in the northwestern portion of Alabama is given by the formula p (t )equals (t squared plus 100 )ln (t plus 2 ), where t represents the time in years since 2000 (the year 2000 corresponds to t equals 0 ). Find the rate of change of the coyote population in 2002 (tequals2).
Answer:
The rate of change of the Coyote population in 2002 is 32
Step-by-step explanation:
Given the formula for the population of a Coyotes in the Northwestern portion of Alabama, we are to calculate rate of change of the Coyote population in the year 2002 where t = 2
The formula is given as;
P(t) = (t^2 + 100) ln (t + 2)
The rate of change refers to the first integral of the formula;
Thus we need to calculate this by the use of product formula;
The first differential of t^2 + 100 is 2t
while that of ln(t + 2) is 1/(t + 2)
P’(t) = 2t(ln (t+2)) + (t^2 + 100) (1/t+2)
Now, we substitute 2 for the value of t here.
P’(2) = 2(2)( ln (2 + 2) + (2^2 + 100)(1/(2+2))
P’(2) = 4 ln 4 + 104(1/4)
P’(2) = 4ln 4 + 26
P’(2) = 5.55 + 26 = 31.55 which is approximately 32
Please help i do not understand this one!
Answer:
B. [[0,4]
[-6,1]
[3,-4]]
Step-by-step explanation:
If you multiply the matrices, you get the answer.
10,25,35,45... What's the pattern?
Answer:
15
Step-by-step explanation:
The pattern is going by 15 because 10+15=25 and then continue going.
Answer:
15 is the answer
Step-by-step explanation:
The difference of a rational number and an irrational number is ____ an irrational number. Which word correctly fills in the blank to create a true statement?
A) sometimes
B) always
C) never
Answer:
a
Step-by-step explanation:
The difference between a rational number and an irrational number is always an irrational number. The correct option is B.
What is a rational and irrational number?A Rational Number is a number of the form p/q, p & q are integers, and q ≠ 0. An irrational number is all real numbers except rational numbers i.e. it is a non-repeating and non-terminating decimal number or it can not be expressed in a ratio of two integers.
Further, natural numbers can be rational numbers. Also, all repeating and terminating decimals are rational.
The difference between a rational number and an irrational number is always an irrational number. For example:
2 - √3 is always an irrational number where 2 is rational and √3 is an irrational number.
Hence addition and subtraction of rational and irrational numbers is always an irrational number.
To know more about an irrational number follow
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Which table represents a nonlinear function?
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 19, negative 11, negative 3, 5.
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries 15, 12, 9, 6.
Answer:
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.
Step-by-step explanation:
When the x-values are evenly spaced, a linear function will have evenly-space y-values.
In the first table, the y-differences are all +8.
In the second table, the y-differences are 0, 1.5, 1.5, so are not all the same.
In the third table, the y-differences are all -3.
The second table represents a non-linear function.
__
In the graph, you can see that the points from the second table (purple) are not on a straight line.
Answer:
B
Step-by-step explanation:
The arithmetic sequence a1 is defined by the formula:
a1 = 4
a1=ai-1 +11
Find the sum of the first 650 terms in the sequence.
Answer:
2,322,775
Step-by-step explanation:
Given a1 = 4 and ai =ai-1 +11
when i = 2
a2 = a2-1+11
a2 = a1+11
a2 = 4+11
a2 = 15
when i = 3
a3 = a2+11
a3 = 15+11
a3 = 26
The sequence formed by a1, a2, a3... is am arithmetic sequence as shown;
4, 15, 26...
Sum of nth term of an arithmetic sequence = n/2{2a+(n-1)d}
a is the first term = 4
d is the common difference = 15-4 = 26-15 = 11
n is the number of terms.
Since we are to find the sum of the first 650 terms in the sequence, n = 650
S650 = 650/2{2(4)+(650-1)11}
S650 = 325{8+(649)11}
S650 = 325(8+7,139)
S650 = 325×7147
S650 = 2,322,775
Pls show work ASAP
Multiplying polynomials
Answer:
Step-by-step explanation:
1. 6w*2v + 3*6w= 12vw + 18w
2. 7(-5v) - 7(8)= -35v - 56
3. 2x*(-2x) - 3(2x) = -4x^2 - 6x
4. -4*v - 4(1)= -4v - 4
5. 2n*6n + 2n + 2*6n + 2= 12n^2 + 14n + 2
6. 4n(2n) + 4n(6) + 2n + 6= 8n^2 + 26n + 6
7. x(6x) - 2x - 18x + 6 = 6x^2 - 20x + 6
8. 8p(6p) + 8p(2) - 2(6p) - 4 = 48p^2 + 16p - 12p - 4= 48p^2 + 4p - 4
9. 6p(5p) - 6p(8) + 8(5p) - 40= 30p^2 - 48p + 40p - 40= 30p^2 - 8p - 40
10. 3m(8m) + 3m(7) - 8m - 7 = 24m^2 + 21m - 8m - 7= 24m^2 + 13m - 7
11. 2a(8a) - 2a(5) - 8a + 5 = 16a^2 - 10a - 8a + 5 = 16a^2 - 18a + 5
12. 5n(5n) - 5n(5) + 6(5n) - 6(5)= 25n^2 - 25n + 30n - 30= 25n^2 + 5n - 30
13. 4p(4p) - 4p - 4p + 1 = 16p^2 - 8p +
14. 7x(5x) + 7x(6) -6(5x) - 6(6)= 35x^2 + 42x - 30x - 36= 35x^2 + 12x - 36
MIDDLE SCHOOL MATH BRAINLEIST AND 5 STARS AS SOON AS YOU ANSWER!!!!!!!! PLEASE HELP AND THANKS SO MUCH IM SUPER GRATEFUL!!!!!!!!!!!
Answer:
Bottom prism: 126*11=1386
Top Prism: 2*45=90
Total volume: 1386+90= 1746 cubic cm
