Answer:
Step-by-step explanation:
Displacement: d(t) = 2t^3 + 5t^2 - 3
Velocity: (d/dt)(2t^3 + 5t^2 - 3) = v(t) = 6t^2 + 10t
Acceleration: (d/dt)(d/dt)(6t^2 + 10t) = a(t) = 12t + 10
At time t = 4hr,
d(4) = [128 + 80 - 3] km = 205 km
v(4) = [96 + 40] km/hr = 136 km/hr
a(4) = [48 + 10] km per hour squared = 58 km over hours squared
Answer:
Step-by-step explanation:
hello,
for t = 4 hours
[tex]d(4)=24^3+54^2-3=2*64+5*80-3=128+80-3=205[/tex]
this is 205 km
d is differentiable and
[tex]d'(t)=6t^2+10t[/tex]
and
[tex]d'(4)=6*4^2+10*4=6*16+40=96+40=136[/tex]
this is 136 km/h
d' is differentiable and
[tex]d''(t)=12t+10[/tex]
and
[tex]d''(4)=12*4+10=48+10=58[/tex]
this is [tex]58 \ km/h^2[/tex]
A rectangular garden that measures 6 feet by 8 feet is roped off to form a
right triangle. What is the length of the rope?
Rope
6 ft
Answer:
10feet
Step-by-step explanation:
We solve this question, using Pythagoras Theorem to solve for the other side.
Pythagoras Theorem states that
c² = a² + b²
c = √(a² + b²)
In the question, a = 6 feet
b = 8 feet
c = length of the rope
c = √6² + 8²
c = √36 + 64
c = √100
c = 10 feet
The length of the rope is 10 feet
Help Please. It's maths, for HegartyMaths.
In order for the data in the table to represent a linear
function with a rate of change of +5, what must be the
value of a?
O a = 3
O a = 8
O a = 18
O a = 33
The table to represent a linear function with a rate of change of +5
So, m = 13 + 5 = 18
a = 18
What is linear function?The slope-intercept pattern of the linear function equation. As a result, it is written as f(x) = mx + b, where m denotes the slope and b the line's y-intercept.
The graph in the table shows a linear function.
The linear function's general equation is written as y = ax+b, where a is the slope and b is a constant.
Finding the linear function's equation by using the first and third points from the table
at x = 3 ⇒ y = 13 and at x = 5 ⇒ y = 23
13 = 3a+b → (1)
23 = 5a+b → (2)
solve (1) and (2) to find a and b
So, a = 5 and b = -2
∴ y = 5x - 2
After that by substitution with x = 4 int the equation of y
∴ y = 5*4-2 = 18
m= 18
Thus, option C is correct.
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Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in. H =210 + 33t How fast does the tree grow?
Answer:
The tree grows 33cm per year.
Step-by-step explanation:
Please help us with Plato: Select all the correct answers. Which vectors represent the reflection of the vector across the x-axis?
Answer:
<3, 7>
AND
[tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex]
Step-by-step explanation:
I did the plato
The vectors that represent the reflection of the vector across the x-axis are; <3, 7> and [tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex].
Explanation of how reflection across axis works?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.
If we study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
The vectors that represent the reflection of the vector across the x-axis are;
<3, 7> and [tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex].
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HELP NEEDED PLS HELP! THANK YOU Use the fundamental theorem of algebra to state all the possible roots of the function f(x)=2x^3+3x^2-4x-12 Can someone please show me how to do it
Answer:
x=2 (−∞,∞)
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x
Hope this helps (sorry if it's confusing)
Answer:
x = 1.71282
Step-by-step explanation:
2x^3+3x^2-4x-12
2 x³ + 3 x² - 4x - 12 = 0
x = 1.71282
see attachment.
STATS List below are the ages (years) of randomly selected race car drivers. Construct a 95% confidence interval estimate of the mean age of all race car drivers: ages 32, 40, 27, 36, 29, 28
Answer:
A 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].
Step-by-step explanation:
We are given below the ages (in years) of randomly selected race car drivers;
Ages: 32, 40, 27, 36, 29, 28.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean age = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{32+40+27+36+29+28}{6}[/tex] = 32 years
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 5.1 years
n = sample of car drivers = 6
[tex]\mu[/tex] = population mean age of all race car drivers
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.571 < [tex]t_5[/tex] < 2.571) = 0.95 {As the critical value of t at 5 degrees of
freedom are -2.571 & 2.571 with P = 2.5%}
P(-2.571 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.571) = 0.95
P( [tex]-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]32-2.571 \times {\frac{5.1}{\sqrt{6} } }[/tex] , [tex]32+2.571 \times {\frac{5.1}{\sqrt{6} } }[/tex] ]
= [26.65, 37.35]
Therefore, a 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].
Write the algebraic expression for each word problem. See if you can spot the trick problem that doesn’t need algebra!
Answer:
6) -7 + 10 = 3 (3 more; total number doesn't matter)
7) 50w + 20
8) c / 5
9) 5 + 2t
10) 4d + 2d
I didn't see the trick problem!
explain the words and the connections of population ,area, urban,and density
Answer:
Step-by-step explanation:
In this sense "area" refers to a geographical area in which people may or may not live; any "population" refers to the group of people living in a specific area. We might discuss the "population" of the "Los Angeles area," which refers to people living within the geographic boundaries of the City of Los Angeles.
"Urban" characterizes a given area where the land is thickly settled with human residents (as opposed to open, commercial or rural land). Most of the area within the boundaries of "Los Angeles" are "urban."
"Density" refers to "population density," defined as the number of people per square mile (or other measure of area); as an example we might refer to the population density of the City of Los Angeles, and that reasure might be in the area of "246,000 residents per square mile."
Answer:
Search the words up on google and it will explain better then me
Step-by-step explanation:
plz help me do this i will help u if i know
Answer:
77
Step-by-step explanation:
2+3+5+7+11+13+17+19=77
On two investments totaling $13,500, Peter lost 3% on one and earned 5 % on the other. If his net annual receipts were $319, how much was each investment?
During the recent recession, Bob's home value dropped to only $175,000. Since then the economy has turned around and the market is improving at a rate of 4.5% annually. At this rate, how much will Bob's home be worth 12 years after the market started improving? And what equation did you use?
Answer:
Bob's home will worth $296,779.25 after 12 years.
Equation used is [tex]FV = $175,000( 1 + 4.5/100)^(12)\\[/tex]
Step-by-step explanation:
Current value of Bob's house =[tex]FV = $175,000( 1 + 4.5/100)^12\\FV = $175,000( (100+ 4.5)/100)^12\\FV = $175,000( (104.5)/100)^12\\FV = $296,779.25[/tex]
market is improving at 4.5% annually.
This, means that the value of house gets appreciated by 4.5% each year from its previous year value.
This is a problem of compound interest formula
[tex]FV = PV(1+r/100)^n[/tex]
where PV is the present value of any thing
FV is the future value
r is the annual rate of interest
t is the time in number of year for which rate is applicable.
_____________________________________
Given
PV = $175,000.
r = 4.5%
t = 12 years
Value after 12 year will be given by
[tex]FV = $175,000( 1 + 4.5/100)^(12)\\FV = $175,000( (100+ 4.5)/100)^(12)\\FV = $175,000( (104.5)/100)^(12)\\FV = $296,779.25[/tex]
Thus, Bob's home will worth $296,779.25 after 12 years.
Equation used is [tex]FV = $175,000( 1 + 4.5/100)^(12)\\[/tex]
Need help finding the missing length to the attached triangle.
Answer:
65 units
Step-by-step explanation:
Let the length of the perpendicular dropped from the right angle to the hypotenuse be h units.
Now by geometric mean property:
[tex]h = \sqrt{144 \times 25} \\ h = 12 \times 5 \\ h = 60 \: units \\ Next \: by \: Pythagoras \: Theorem: \\ {x}^{2} = {h}^{2} + {25}^{2} \\ {x}^{2} = {60}^{2} + {25}^{2} \\ {x}^{2} = 3600 + 625 \\ {x}^{2} = 4225 \\ x = \sqrt{4225} \\ \huge \red{ \boxed{x = 65\: units }}[/tex]
Classify the following triangle. Check all that apply.
60
604
60°
A. Scalene
B. Right
O C. Acute
O D. Isosceles
E. Obtuse
F. Equilateral
Answer:
C. Acute
F. Equilateral
Step-by-step explanation:
Since all angles in the triangle are 60° (and less than 90°), it makes it an acute triangle.
Since all sides and angles are congruent to each other, respectively, we know that the triangle is equilateral.
Answer:
the actual answer is acute,equilateral,isosceles
The functions f(x) and g(x) are shown on the graph.
Rx) = x²
What is g(x)?
Please solve okay ty ty
Answer:
The answer is A.
Step-by-step explanation:
Ok, first let see with each point makes the inequality true. Remember that a point is made up of x and y in the form of (x , y).
Let's see if A suits this inequality. Replace the x in the inequality with 5 and the y with 1. The inequality should look like this: 5(1) - 8(5) [tex]\leq[/tex] 10. 5 times 1 is 5 and 8 times 5 is 40. 5 - 40 is -35. -35 is less than 10 so this true. So A is a solution.
NOTE THAT THE SIGN "[tex]\leq[/tex]" MEANS GREATER THAN OR LESS THAN SO YOU ONLY NEED TO MEET ONE CONDITION.
Let's see if B suits this inequality. Replace the x in the inequality with -3 and the y with 2. The inequality should look like this: 5(2) - 8(-3) [tex]\leq[/tex] 10. 5 times 2 is equal to 10 and -8 times -3 is equal to 24. Now the quation is this: 10 + 24 [tex]\leq[/tex] 10. 10 plus 24 is 34 and 34 IS NOT EQUAL OR LESS THAN 10. So B is not a solution.
Let's see if C suits this inequality. Replace the x in the inequality with 0 and the y with 4. The inequality should look like this: 5(4) - 8(0) [tex]\leq[/tex] 10. 5 times 4 is 20 and -8 times 0 is 0. 20 + 0 is 20 and 20 IS NOT LESS THAN OR EQUAL TO 10. So C is not a solution.
-1, -5
Let's see if D suits this inequality. Replace the x in the inequality with -1 and the y with -5. The inequality should look like this: 5(-5) - 8(-1) [tex]\leq[/tex] 10. 5 times -5 is -25 and -8 times -1 is 8. -25 plus 8 is -17 and -17 IS NOT LESS THAN OR EQUAL TO 10. So D is not a solution.
HOPE THAT HELPED!
Answer:
the answer is A
hope it helps
Find the Surface Area
Answer:
120 km squared.
Step-by-step explanation:
The shape shown has 5 sides: three rectangles and 2 triangles.
If you examine each triangle closely, they are 3-4-5 triangles. The area of one triangle is 3 * 4 * 1/2 = 12 * 1/2 = 12 / 2 = 6. Since there are two triangles, the total area of the triangles is 6 * 2 = 12 km squared.
The three rectangles have the same length, but their widths differ. They all have a side length of 9 km, but the largest rectangle has a width of 5 km, the medium has a width of 4 km, and the smallest has a width of 3 km.
So, the rectangles' areas added up will be (9 * 5) + (9 * 4) + (9 * 3) = 45 + 36 + 27 = 108 km squared.
And so, the total surface area is 12 km squared + 108 km squared, or 120 km squared.
Hope this helps!
PLEASE HELP!
What is the distance from Z= (16,−15) to the x-axis?
Answer:
15 units
Step-by-step explanation:
Distance from the x-axis is measured vertically, so you would look at the second number of the coordinates, the y value. Point Z is 15 units below the x-axis.
Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.
What is the axis?
An axis in mathematics is defined as a line that is used to make or mark measurements.
Here given that,
[tex]Z= (16,-15)[/tex] which is on the x-axis.
So,
The shortest distance between the coordinate [tex](16,-15)[/tex] and [tex](16,15)[/tex].
Now, applying the distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here,
[tex](x_1,y_1)=(16,0)\\(x_2,y_2)=(16,-15)[/tex]
Substituting these values in the formula
[tex]d=\sqrt{(16-16)^2+(-15-0)^2}\\\\d=\sqrt{(0)^2+(-15)^2}\\\\d=\sqrt{0+225}\\\\d=15[/tex]
Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.
To know more about the axis
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solve for x 3x+3+=12 1. 6 2. 5 3. 4 4. 3
Answer:
4.(3)
Step-by-step explanation:
3x+3 = 12
Subtract 3 to both sides.
3x = 9
Divide the left side by 3, then divide the right side by 3
x = 3
Answer:
Hi! your answer should be D. 3
Step-by-step explanation:
1. 3x+3=12
-3 -3
2. 3x=9
÷3 ÷3
3. x= 3
[So, your answer should be D. x=3]
Hope this helps!
give your answer as a mixed number
4 3/7 - 2 5/7
get brainliest urgent plz help
Answer:
[tex]1\frac{5}{7}[/tex]
Step-by-step explanation:
[tex]4\frac{3}{7} -2\frac{5}{7}[/tex]
Step 1. Simplify left side 4*7+3 , Right Side 2*7+5
[tex]=\frac{31}{7} -\frac{19}{7} = \frac{12}{7}[/tex]
Step 2. Re-write 12/7 as mixed number
[tex]\frac{12}{7} = 1\frac{5}{7}[/tex]
Jacob is painting the walls of his new tiny house. If 3⁄4 of a can of paint is enough to paint 1 / 8of the walls, how much paint does Jacob need to paint all of the walls?
Answer:
6 cans
Step-by-step explanation:
I used Improper Fractions to solve this question.
3/4 is enough to paint 1/8
Therefore we can multiply 3 by 8 to calculate how much paint is required for the whole wall.
3 * 8 = 24
24/4 = 6
plzzzzz answer this question about density mass and volume!!!!!!!!!
Answer:
13.896 kg
Step-by-step explanation:
You can find the mass of the bar by first finding the volume.
V = BH
where B = area of the base (the trapezium), and
H = height (distance trapezium between bases)
The area of a trapezium is
A = (b1 + b2)h/2
where b1 and b2 are the lengths of the bases of the trapezium (the parallel sides), and
h = the altitude of the trapezium (distance between the bases of the trapezium)
V = (b1 + b2)h/2 * H
V = (12 cm + 6 cm)(5 cm)/2 * 16 cm
V = 720 cm^3
The volume of the bar is 720 cm^3.
Now we use the density and the volume to find the mass.
density = mass/volume
mass = density * volume
mass = 19.3 g/cm^3 * 720 cm^3
mass = 13,896 g
Now we convert grams into kilograms.
1 kg = 1000 g
mass = 13,896 g * (1 kg)/(1000 g)
mass = 13.896 kg
Answer: 1.3896 kg
is this right? someone please help :)
Answer:
it should be yes. if there are no values for A and C then yes the answer is correct.
Answer:
2a + 2c = b
Step-by-step explanation:
a = 1/2 b -c
Add c to each side
a+c = 1/2 b- c+c
a+c = 1/2 b
Multiply each side by 2
2( a+c) = 2 * 1/2 b
2a + 2c = b
A hobbyist is making a toy sailboat. For the triangular sail, she wants the height h (in inches)
to be twice the length of the base b (in inches). Can the area of the sail be 10 inº?

Answer:
xx
Step-by-step explanation:
HELP. Analyze the diagram below and complete the instructions that follow. Find the exact value of tan 0.
Answer:
Using SohCahToa we know it will be opposite over adjacent, opposite being the side across from theta and adjacent being the side next to theta, Using Toa we know it will be opposite over adjacent so the answer will be 6/2sqrt5
If they wants you to simplify more than you cant have a sqrt on the bottom so to fix this you will multiply the top and bottom by sqrt5 leaving you with 6sqrt5/ 2*5 or 6sqrt5/15
hope this helped
Answer:
C. 3^5/5
Step-by-step explanation:
Help pleaseeeeeeeeeeeeeeeeeeeeeee
Answer:
The answer is 3 mark as brainliest
Step-by-step explanation:
3 *3-4*4+2*5
9-16+10
9-6=
3
Answer:
Hey there!
3a-4b+2c
3(3)-4(4)+2(5)
9-16+10
3
Your answer would be 3.
Hope this helps :)
Please may someone answer it,
WORTH 81 POINTS!!!
Answer:
[tex]\boxed{V = 1436.8 cm^3}[/tex]
Step-by-step explanation:
Volume of sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where r = 7 cm
Volume of Sphere = [tex]\frac{4}{3} (3.14)(7)^3[/tex]
V = [tex]\frac{4}{3} (3.14)(343)[/tex]
V = 4310/3
V = 1436.8 cm³
Answer:
1436.8 cm^3Solution,
Radius= 7 cm
Volume of sphere:
[tex] \frac{4}{3} \pi \: {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {7}^{3} \\ = \frac{4}{3} \times 3.14 \times 343 \\ = 1436.8 \: {cm}^{3} [/tex]
Hope this helps...
Good luck on your assignment...
can someone help me i cant understand with work
Answer:
Right now it would be
[tex]-40[/tex]
Since desend means down add -20 to -40
[tex]-40+(-20)=-60[/tex]
or
[tex]-40-20=-60[/tex]
Then is goes up 35, which is positive
[tex]-60+35=-25[/tex]
Therefore, the answer is -25
Hope this helps
Answer by
Fishylikeswater
Answer:
A. -25M
Step-by-step explanation:
The submarine starts at -40M underwater which then it descends ( goes down ) another -20M which added means it is now -60M underwater. It then rises 35M so you would then add -60M + 35M = -25M
Hope this helps :)
A recent survey found that 65% of high school students were currently enrolled in a math class,43% were currently enrolled in a science class,and 13% were enrolled in both a math and a science class. Suppose a high school student who is enrolled in a math class is selected at random. What is the probability that the student is also enrolled in a science class?
Answer: 0.20
Step-by-step explanation:
As per given :
P(student enrolled in a math class ) = 65% = 0.65
P( student enrolled in a science class) = 43%= 0.43
P( student enrolled in both ) = 13% = 0.13
Formula of conditional probability :
[tex]P(A|B)=\dfrac{P(A\text{ and }B)}{P(B)}[/tex]
Using the above formula,
The probability that the student is enrolled in a science class given that he is enrolled in maths class :
[tex]P(\text{science}|\text{math})=\dfrac{P(\text{science and maths})}{P(\text{math})}\\\\=\dfrac{0.13}{0.65}\\\\=\dfrac{13}{65}\\\\=\dfrac{1}{5}=0.20[/tex]
Hence, the probability that the student is also enrolled in a science class = 0.20 .
Find the common difference for the sequence shown.
56, 49, 42, 35, ...
0-12
0-7
07
To find the common difference, subtract all the numbers in order.
56 - 49 = 7
49 - 42 = 7
42 - 35 = 7
Therefore, common difference is 7.
Best of Luck!
Answer:
The answer is -7
(got this answer right on the lesson)
Step-by-step explanation: