Answer:
122 km/h
138 km/h
Step-by-step explanation:
distance = speed * time
One bus travels 16 km/h slower than the other
(s * 2) + (s - 16)2 = 520
2s + 2s - 32 = 520
4s = 552
s = 552/4
s = 138 km/h
s - 16 = 122 km/h
Answer the following.
A bag contains, 4, green balls 3 red balls, 6 yelow and 5 pink balls. A ball is
selected at random and not relased. The ball is green. What is the probably
of selecting another green be?
Express the answer as a frection |
Engress the answer as a decimal to three deomal places
ELess this answer as a percentage to the nearest Wacle number
Answer:
[tex]\frac{3}{17}, \\0.176, \\18\%[/tex]
Step-by-step explanation:
The area a total of 4+3+6+5=18 balls, consisting of:
4 green3 red6 yellow5 pinkAfter a green ball is selected (implied that it is not replaced or put back), there will be 17 balls total, consisting of:
3 green3 red6 yellow5 pinkTherefore, the probability of drawing another green one is:
[tex]\boxed{\frac{3}{17}=0.176=18\%}[/tex]
0,-2,-4,-6,-8,-10 nth term
Answer:
The nth term of this sequence is [tex]a_{n} = -2n + 2[/tex]
Step-by-step explanation:
In this sequence we keep adding -2 on to get the next term. This sequence is called an arithmetic sequence, a sequence that uses addition to keep increasing.
The formula for the nth term of an arithmetic sequence is
[tex]a_{n} = d[/tex] · [tex]n + a_{1} - d[/tex]
[tex]a_{1}[/tex] stands for the first term in the sequence, and [tex]d[/tex] stands for the difference between each number in the sequence.
[tex]a_{1} = 0[/tex] and [tex]d[/tex] = -2, so :
[tex]a_{n} = -2[/tex] · [tex]n + 0 - (-2)\\[/tex]
[tex]a_{n} = -2n + 2[/tex]
Therefore, to find the nth term in this sequence you would use the formula
[tex]a_{n} = -2n + 2[/tex]
8h+(-5.9d)-17+4d-3.4h = A simplified equation
Answer:
8h+(-5.9d)-17+4d-3.4h
8h-5.9d-17+4d-3.4h
group the like terms
8h-3.4h+4d-5.9d-17
4.6h-1.9d-17
Step-by-step explanation:
When a fair dice is thrown, what is the probability of getting a number greater than 4? (Reduce to simplest form)
Answer:
I searched the q and this is what I found
Step-by-step explanation:
Explanation: Number greater than 4 are 5 and 6 . So required probability is 26=13.
A cylinder of radius 12cm and height 9cm.
What is the mean of 43,69,48,37,85,57,95,102
The mean of 43,69,48,37,85,57,95,102 is 67
A furniture delivery truck leaves the store at 8 A.M. It travels 6 miles east, then 4 miles south, then 2 miles west and then 4 miles north.
At the end of this route, how far is the truck from the store?
Answer:
It's 4 miles East from the store.
Step-by-step explanation:
6 miles east - 2 miles west = 4 miles East
Displacement for north and south should cancel out since they are equal to each other.
What is the value of
[tex] \frac{ - 2(7 - 15)}{4} [/tex]
○-4
○-2
○2
○4
Answer:
4
Step-by-step explanation:
Based on your math expression:
7-15 = -8
-2*(-8) = 16
16 / 4 = 4
Answer:
4
Step-by-step explanation:
-2(7-15)
=-14+30
=16÷4
=4
Susan really loves the lemon-flavored Fruity Tooty candies, but there always seems to be a lot of grape-flavored candies in each bag. To determine whether this is because grape candies are so popular or because each bag contains fewer lemon candies, Susan randomly picks a Fruity Tooty candy from her bag, records its flavor, and places it back in the bag. Each bag contains a mixture of cherry, grape, apple, lemon, and orange flavors. Which statement about Susan's distribution of sample proportions is true?
a. The distribution of the count of picking a cherry candy cannot be modeled as approximately normal if Susan picks candies over 200 times.
b. The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times.
c. The sample proportion of drawing an orange candy is not a binomial distribution.
d. The distribution of lemon candy can be modeled as normal if Susan picks candies 10 times.
Option B, The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times
Step-by-step explanation:
The distribution of apple candies can be represented as normal curve and hence the sample proportion for this is true and can be drawn.
The rest other cases do not represent a normal distribution and hence it will not be easy to plot curve for these samples.
hence, option B is correct
Find the surface area of
the prism.
Answer:
[tex]\text{D. }464\:\mathrm{ft^2}[/tex]
Step-by-step explanation:
The surface area of the prism consists of four rectangles and two trapezoids. The sum of the areas of these polygons will give the total surface area of the prism:
Rectangle 1 (top base): [tex]12\cdot 14=168[/tex]
Rectangle 2 (bottom base): [tex]6\cdot 14 = 84[/tex]
Trapezoids 1 and 2 (lateral): [tex]2\cdot 9 \cdot 4=72[/tex]
Rectangles 3 and 4 (lateral): [tex]2\cdot 14\cdot 5=140[/tex]
Thus the total surface area is equal to
[tex]168+84+72+140=\boxed{\text{D. }464\:\mathrm{ft^2}}[/tex]
The sea ice area around the North Pole fluctuates between about 6 million square kilometers in September to 14 million square kilometers in March. Assuming sinusoidal fluctuation, during how many months are there less than 9 million square kilometers of sea ice?
Answer:
there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.
Step-by-step explanation:
Given the data in the question;
Let S(t) represent the amount sea ice around the North Pole in millions of square meters at a given time t,
t is the number of months since January.
Now, we use a cosine curve to model this scenario
Vertical shift will be;
D = ( 6 + 14 ) / 2 = 20 / 2
D = 10
Next is the Amplitude;
|A| = ( 6 - 14 ) / 2
|A| = 4
Now, the horizontal stretch factor will be;
B = 2π / 12
B = π/6
Hence;
S(t) = 4cos( π/6 × t ) + 10 ----------- let this be equation 1
Now we find when there will be less than 9 million square meters of sea ice;
S(t) = 9
so we have
9 = 4cos( π/6 × (t-2) ) + 10
9 - 10 = 4cos( π/6 × (t-2) )
-1 = 4cos( π/6 × (t-2) )
-1/4 = cos( π/6 × (t-2) )
so we have;
cos⁻¹( -1/4 ) = π/6 × (t₁-2) -------- let this be equation 2
2π - cos⁻¹( -1/4 ) = π/6 × (t₂-2) -------- let this be equation 3
so we solve equation 2 and 3
we have'
t₁ - t₂ = 6/π × ( 2π - cos⁻¹( -1/4 ) - cos⁻¹( -1/4 ) )
t₁ - t₂ = 6/π × ( 2π - 2cos⁻¹( -1/4 )
t₁ - t₂ = 6/π × ( π - cos⁻¹( -1/4 )
t₁ - t₂ = 6/π × ( π - 104.4775 )
t₁ - t₂ = 6/π × ( π - 104.4775 )
t₁ - t₂ = 5.035
therefore, there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.
A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for
Answer:
Perimeter: 18.28
Area: 22.28
Step-by-step explanation:
1. Approach
An easy method that can be used to solve the given problem is the partition the given figure into two smaller figures. One can divide this figure into a square and a semi-circle. After doing so, one can find the area of the semi-circle and the area of the square. Finally, one can add the two area together to find the final total area. To find the perimeter of the figure, one can add the lengths of three of the sides of the square and then one can add half of the circumference of the circle to the result. The final value will be the perimeter of the entire figure.
2. Find the circumference of the semi-circle
The circumference of a circle is the two-dimensional distance around the outer edge of a circle, in essence the length of the arc around a circle. The formula to find the circumference of a circle is as follows,
C = 2(pi)r
Since a semi-circle is half of a circle, the formula to find its circumference is the following,
C = (pi)
Where (pi) is the numerical value (3.1415) and (r) is the radius of the circle. By its definition, the radius of a circle is the distance from a point on the circle to the center of the circle. This value will always be half of the diameter, that is the distance from one end of the circle to the other, passing through the center of the circle. The radius of a circle is always half of the diameter, thus the radius of this semi-circle is (2). Substitute this into the formula and solve for the circumference;
C = (pi)r
C = (pi)2
C ~ 6.28
3. Find the area of the semi-circle
The formula to find the area of a circle is as follows,
A = (\pi)(r^2)
As explained earlier, a semi-circle is half of a circle, therefore, divide this formula by (2) to find the formula for the area of a semi-circle
A = ((pi)r^2)/(2)
The radius of this circle is (2), substitute this into the formula and solve for the area of a semi-circle;
A = ((pi)r^2)/(2)
A = ((pi)(2^2))/(2)
A = (pi)2
A = 6.28
4. Find the area and perimeter of the square,
The perimeter of a figure is the two-dimensional distance around the figure. Since the semi-circle is attached to one of the sides of a square, one only needs to add three sides of the square to find the perimeter of the square;
P = 4+4+4
P = 12
The area of a square can be found by multiplying the length by the width of the square.
A = l*w
Substitute,
A = 4*4
A=16
5. Find the area and the perimeter of the figure,
To find the perimeter of the figure, add the value of the circumference to the vlalue of the perimeter of the square;
A = C+P
A = 6.28+12
A = 18.28
To find the area of the figure, add the value of the area of the circle to the area of the square;
A = 6.28+16
A = 22.28
Two-fifths if one less than a number is less than three-fifths of one mira than than number. What numbers are in the solution set of this problem
A. X < -5
B. X > -5
C. X > -1
D. X < -1
Kelly collected $15, $15, $25, and $29 in the last four donations. What is the
mode of these donations?
A. $15
B.$20
C. No mode
Step-by-step explanation:
15 may be
HOPE IT HELP U ...
Answer:
A. $15 is the mode.
Step-by-step explanation:
In order to answer this question, we need to know the definition of mode. "The mode of a set of numbers is the number that occurs the most" Since out of the four numbers, the one that appears the most is $15, then $15 is the mode.
A team of researchers want to measure the distance covered while driving compared to a car's driving speed. Which statement is correct?
a. The speed of the car is a confounding variable.
b. The speed of the car is an explanatory variable.
c. The speed of the car is a response variable.
d. The speed of the car is a dependent variable.
Answer:
b. The speed of the car is an explanatory variable
Step-by-step explanation:
In the scenario above, the variable which the researcher intends to measure is the a distance covered by a car using the speed information available. The measured variable is the dependent variable as it outcome depends on the variable with which it is being measured, this is called the independent or explanatory variable.
Therefore, car speed is the explanatory or independent variable
Distance is the dependent, response or measured variable.
Find the
volume of the
composite solid
Answer:
253.5 ft³
Step-by-step explanation:
Volume of a pyramid = [tex] \frac{1}{3} [/tex]× base area × height
Volume of a prism = base area × height
Volume of the pyramid
= [tex] \frac{1}{3} [/tex]× (6×6.5÷2) × 9
= [tex] \frac{1}{3} [/tex]× 19.5 × 9
= 58.5 ft³
Volume of the prism
= (6×6.5÷2) × 10
= 195 ft³
Volume of the solid
= 58.5 + 195
= 253.5 ft³
Answer:
A
Step-by-step explanation:
the base is 19.5 feet squared
(6 * 6.5 / 2)
multiplied by 10 gives you 195 feet cubed for the lower solid
19.5 * 9 / 3
gives you 58.5 feet cubed for the upper solid
just add both volumes together
Find the radius of the sphere with the given volume.
Answer:
see below
Step-by-step explanation: 6 5 17 43
Volume of a sphere = 121.5 π mm³ Find r
Vol Sphere = (4π r³) / 3 solve for r
Vol Sphere × 3 = (4π r³)
(Vol Sphere × 3) / 4π = r³
∛((Vol Sphere × 3) / 4π) = r
∛((121.5 π mm³× 3) / 4π) = r the pi terms cancel
∛((121.5 mm³× 3) / 4) = r
∛((364.5 mm³) / 4) = r
∛((91.125 mm³) ) = r
4.5 = r
25 Points!!! Need to be Done Now Please. Priority
Use Newton's method to app a root of the equation 3x^7+2x^4+3=0
Let x1=1 be the initial approximation
Second approx. x2 is?
Third approx x3 is?
9514 1404 393
Answer:
x2 = .72413793x3 = .087249546Step-by-step explanation:
Modern graphing calculators have a derivative function available, so using a calculator to find the next value of x is pretty simple.
The Newton's Method iterator for finding the next approximation to the root (x') is ...
x' = x -f(x)/f'(x) . . . . . where f'(x) is the derivative of f(x).
The attachment shows the first 3 iterations (4 approximations). We observe that the starting point is pretty far from the root, and on the wrong side of some wiggles in the function, so convergence is pretty slow.
The desired approximations are shown above and in the table below.
__
Additional comment
To 12 significant figures, the only real root is −1.10305899649. When the calculator can interactively produce a next guess, you can type the next guess value into the iterator function even as it is showing you the next value. This lets you find the best-precision result as fast as you can type it.
For a calculator like a TI-84, the iterator function can make repeated use of "Ans" as an argument. It usually doesn't take more than 3 or 4 iterations to get a best-precision result, since the number of good decimal places is about doubled on each iteration. (Of course, you have to start with a better approximation than the one given in this problem.)
How does a pedometer help people reach their fitness goals?
A.
It measures calories burned throughout the day
B.
It usually doubles as an MP3 player and keeps people motivated.
C.
They help people reach their goals by counting the number of steps taken.
D.
They measure the number of lifts done during each exercise performed.
Answer:
C
Step-by-step explanation:
pedometers are devices that count the steps you take throughout the day. Seeing your daily step count can give you an idea of how active you are in a given day and give motivating feedback to help you achieve a daily step goal.
Answer:c i just took the test
Step-by-step explanation:
Paulette had two books One of the books weighed 7/8 pound and the other book weighed 2/3 pound If both books were put on sale how much will they weigh together
HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
The solution set to the absolute value is:
[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]
Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].
Step-by-step explanation:
From Mathematics, we know that absolute values are defined by the following characteristics:
1) For [tex]x \ge 0[/tex], [tex]|x| = x[/tex]
2) For [tex]x < 0[/tex], [tex]|x| = - x[/tex]
Then, if [tex]|x| = x[/tex], then the solution set to the absolute value is:
[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]
Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].
help plssssssssssssssssssssssssssssss
Answer:
285 mi
Step-by-step explanation:
We can see that for every gallon, Josh drives 30 more miles. This means that he will drive 30*9.5 mi.
30*9.5 = 285
Pls help luv y’a thx
Let f(x)= 6x^2+7x-4. Find:
a) f(3)
b) f(m)
c) f(x+1)
SHOW WORK PLEASE.
Answer: b) f(m)
Step-by-step explanation:
how can i solve the following
2(x + 3) = x - 4
Answer:
x=-10
Step-by-step explanation:
2(x+3)=x-4
2*x+2*3=x-4
2x+6=x-4
2x-x=-4-6
x=-10
Answer:
[tex]x = - 10[/tex]
Step-by-step explanation:
Let's solve:
[tex]2(x+3)=x−4[/tex]
Step 1: Simplify both sides of the equation.
[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]
Step 2: Subtract x from both sides.
[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]
Step 3: Subtract 6 from both sides.
[tex]x+6−6=−4−6 \\ x=−10[/tex]
Name two numbers that are 14 units from 2 on the number line
Answer:
12 and 12.5
Step-by-step explanation:
Find the volume of this figure
Answer:
A
Step-by-step explanation:
36*12*6+12*24*3=3456
Answer:
3456
Step-by-step explanation:
36*12*6 + 24*12*3
just add up the two volumes
A bicycle has a listed price of 593.98 before tax. If the sales tax rate is 9.5%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
the answer is in
Step-by-step explanation:
Madison and Aidan roll two number cubes. Which of the following rules will make the game fair?
Madison wins if a total of 5 is rolled. Aidan wins if a total of 10 is rolled.
Madison wins if a total of 8 is rolled. Aidan wins if a total of 6 is rolled.
Madison wins if a total of 9 is rolled. Aidan wins if a total of 7 is rolled.
Madison wins if a total of 2 is rolled. Aidan wins if a total of 11 is rolled.
Answer:
If I understand this right I think it would be 8 and 6?
Step-by-step explanation:
Sorry if this is wrong I'm really bad at math, please tell me if this is right.
Can you please answer these im really stuck!
Answer:
(My answers are not rounded!)
Problem A:
Area: 285 cm^2
Perimeter: 70 cm
Problem B:
Area: 30 m^2
Perimeter: 30 m
Problem C:
Area: 28 m^2
Perimeter: 24 m
Problem D:
Lateral Area: 150 in^2
2 (l + w) h
= 2 (11 + 4) 5
= 2(15)5
= 30(5)
= 150
Surface Area: 238 in^2
2 (lw + hl + hw)
2 (11 x 4 + 11 x 5 + 5 x 4)
= 2 ( 44 + 55 + 20)
= 2 (119)
= 238
Volume: 220 in^3
Length x width x height (rectangular prism)
use formula: 11 x 5 x 4 = 220
Problem E:
Area: 379.94 m^2
Formula: πr^2 (circle)
3.14(11^2)
= 3.14(121)
= 379.94
Circumference: 69.08 m
Formula: 2πr
= 2(3.14)11
= 6.28(11)
=69.08
Problem F:
Area: 49 m^2
length x width
7 x 7 = 49
Perimeter: 28 m
2 (l + w)
= 2 (7 + 7)
= 2(14)
= 28
Problem G:
Area: 1,056 cm^2
length x width
48 x 22 = 1,056
Perimeter: 140 cm
2 (l + w)
2 (48 + 22)
2(70)
=140
Problem H:
Lateral Area: 94.2 in^2
2πrh
= 2(3.14) x 1.5(10)
= 6.28 x 15
= 94.2
Surface Area: 108.33 in^2
2πrh+2πr2
=2(3.14) 1.5(10) + 2(3.14) 1.5^2
= 108.33
Volume: 70.65 in^3
πr2h
= 3.14(1.5^2) 10
= 3.14(2.25) 10
= (7.065) 10
= 70.65