Answer:
20 mph
Step-by-step explanation:
time = distance / speed
speed up stream = s - 4
speed down stream = s + 4
time up = time down
8 / (s - 4) = 12 / (s + 4)
cross multiply
8s + 32 = 12s - 48
subtract 8v from both sides
32 = 4s - 48
add 48 to both sides
80 = 4s
Divide both sides by 4
20 = s
20mph
Find the first partial derivatives of the function.
z = (6x + 2y)^9
dz/dx=
dz/dy=
If z = (6x + 2y)⁹, then the partial derivatives of z are
• with respect to x :
∂z/∂x = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂x
∂z/∂x = 9 (6x + 2y)⁸ • 6
∂z/∂x = 54 (6x + 2y)⁸
• with respect to y :
∂z/∂y = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂y
∂z/∂y = 9 (6x + 2y)⁸ • 2
∂z/∂y = 18 (6x + 2y)⁸
On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. Use central limit theorem to calculate
Using the normal distribution and the central limit theorem, it is found that there is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 62 mph, hence [tex]\mu = 62[/tex].Standard deviation of 5 mph, hence [tex]\sigma = 5[/tex].Sample of 50 cards, hence [tex]n = 50, s = \frac{5}{\sqrt{50}} = 0.7071[/tex]The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 1 subtracted by the p-value of Z when X = 66, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{66 - 62}{0.7071}[/tex]
[tex]Z = 5.66[/tex]
[tex]Z = 5.66[/tex] has a p-value of 1.
1 - 1 = 0.
There is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
A similar problem is given at https://brainly.com/question/24663213
10. The ordered pairs (1, 2), (2, 8), (3, 18), and (4, 32) represent a function. What is a rule that represents this function?
It also gives me these numbers:
a. 2x
b. 2x + 2
c. x^2
d. 2x^2
Answer:
d. 2x^2
Step-by-step explanation
y-3=1/2(x-7)
PLS HELP ME OUT GUYS
Answer:
X = -1
Step-by-step explanation:
y - 3 = 1/2 (x - 7)
x would equal -1.
Part F
Describe the shape of the graph.
∠a = 85°, what does ∠b equal?
Answer:
∠b = 95°
Step-by-step explanation:
Assuming these angles are Supplementary, it would look something like this:
/
∠b / ∠a
_______________/__________________
If this is true, and ∠a = 85°, then this means that ∠b must equal 95° because being supplementary angles means all angles add to 180°, so 180 - 85 = 95
Answer:
90° − 85° = 5°
Carly spent $150 on supplies and $125 on labor for her home. She could not spend more than $500 total. Which of these is a valid statement?
Answer:
she could spend up to $225 on more supplies
Step-by-step explanation:
the total amount of supplies and labor has to be less than or equal to $500. If she spent $150 and $125=$275 on supplies and labor, the equation would be 150+125+x≤ 500. Isolate x, to get x≤ $225. The value of x has to be less than or equal to $225.
Which algebraic expression is equivalent to this expression?
6(22 - 12) + 63
Help me please!!
The numerical value of this algebraic expression is 123
Step-by-step explanation:To solve this algebraic expression, we're going to subtract the numbers indicated in parentheses, and finally, we're going to multiply and add the numbers.
Resolution:[tex]\large \sf =6(22 - 12) + 63[/tex]
[tex]\large \sf =6(10) + 63[/tex]
[tex]\large \sf =60 + 63[/tex]
[tex]\boxed{\boxed{{\large \sf 123}}}[/tex]
Therefore, we can conclude that the numeric value of this expression will be 123
Find the general solution of the given differential equation x2 y’ -2xy = x4 + 3
[tex] \times 2 \: y \: - 2xy = \times 4 + 3 = \times - \frac{3}{4} \: y \: e \: r[/tex]
how do i rewrite -2/3x+2y=-7 in slope intercept form?
Answer:
y=1/3x-7/2
Step-by-step explanation:
First get the 2y by itself by adding 2/3x to both sides. Then subtract both sides by 2.
The ratio of boys to girls in the class is 4 to 5. If there are 18 boys and girls in the
class, how many of each are there?
Answer:
8 boys and 10 girls
Step-by-step explanation:
If the ratio is 4:5,
4x2 + 5x2 equal 8+10 =
18.
4:5=8:10
Answer:
8 boys
10 girls
Step-by-step explanation:
4:5
8:10
8+10=18
x divide3=8 solve equation for x
Answer:
x = 24
Step-by-step explanation:
x ÷ 3 = 8
you multiply both sides by three
so it cancels out 3 and 8 × 3 = 24
so your answer is 24
hope this helps
2. Jones has already taken 1 page of notes on his own, and he will take 2 pages during each hour of class. If after 4 hours, he had 9 pages of notes completed, at what rate did he complete the
note pages during those 4 hours?
O 2.25 pages per hour
O 2 pages per hour
O 2.5 pages per hour
0 4 pages per hour
Answer:
2.25
Step-by-step explanation:
if you did 4ph you would get 16 so no. if you did 2ph you would get 8 so no. if you did 2.5ph you would get 8.20 so no but if you did 2.25ph you would get 9 c:
Answer:
A) 2.25 pages per hourStep-by-step explanation:
Let the average rate is x.
We have:
1 + 4*2 = 4xSolve for x:
4x = 9 x = 9/4x = 2.25Correct choice is A
-8-8-6-2 4 12 22
What is the nth term rule of the quadratic sequence
Answer:
[tex]n^2 -3n - 6[/tex]
Step-by-step explanation:
Looking at the image attached, you must first work out the difference between each term. This is +0, +2, +4, +6, +8, +10 (shown in orange).
Because you now have a linear sequence, the difference is now the same each time. This is +2 (shown in blue).
Because the original sequence is a quadratic, you have to halve the second difference (the +2). This means that the value of [tex]n^2[/tex] is 1, so 1[tex]n^2[/tex] or just [tex]n^2[/tex] .
If you write out the values of [tex]n^2[/tex], you can work out how much more you need to add or take away. For example, take the first three terms in the sequence.
n = 1, 2, 3
x = -8, -8, -6
[tex]n^2[/tex] = 1, 4, 9
Work out the difference between [tex]n^2[/tex] and x:
1 - -8 = 9
4 - -8 = 12
9 - -6 = 15
This gives you yet another linear sequence, 9, 12, 15.
Working out the formula for this, the difference is 3 each time, so it is 3n. The first value of n is 1, so 3n is 1. The difference is 6, so the formula for this linear sequence is 3n + 6.
Because [tex]n^2[/tex] is greater than x, you need to take 3n + 6 away from [tex]n^2[/tex].
This gives [tex]n^2[/tex] - (3n+6), so the final answer is:
[tex]n^2[/tex] - 3n - 6.
how many ways can the letters a, b, c, d, e be arranged where d and e cannot be next to eachother
Answer:
Step-by-step explanation:
a
- The point A(8, – 7) is reflecteabver the origin and its image is point B. What are the coordinates of point B?
Answer: Definitely point A
Step-by-step explanation:
A recipe for 24 cookies requires112 cups of sugar. If Ben wants to make 36 cookies, how much sugar does he need?
Answer:
168 cups of sugar
Step-by-step explanation:
36 cookies require you to use what the recipes calls for plus one half.
112 divided by two is 56
112 + 56 = 168 cups
I hope that this helps!
For this case we have the following data:
24 cookies require 1 1/2 cups of sugar. To know the amount of sugar that is required to make 36 cookies, we make a rule of three:
24 -----------> 1 1/2
36 -----------> x
Where x represents the amount of sugar required to make 36 cookies.
Thus, cups of sugar are required to make 36 cookies.
evaluate (2/3)6 power
evaluate 2/3 evaluate 2/3 6th power
Answer:
64/729
Step-by-step explanation:
(2/3)^6 = (2^6)/(3^6) = 64/729
HELP PLS!! no links !!!
Answer:
the correct answer is b
Step-by-step explanation:
Like and give 5 star rating
From a club with 12 members, how many ways could you choose a committee of 5?
Step-by-step explanation:
that is 12 over 5
12! / (5! × (12-5)!) = 12×11×10×9×8/5×4×3×2 =
= 11×9×8 = 792
i need a lot of help from the smartest people now right now
Answer:
K) I, II, and III
Step-by-step explanation:
Given the quadratic equation in standard form, h = -at² + bt + c, where h is the height or the projectile of a baseball that changes over time, t. In the given quadratic equation, c represents the constant term. Altering the constant term, c, affects the h-intercept, the maximum value of h, and the t-intercept of the quadratic equation.
I. The h-interceptThe h-intercept is the value of the height, h, when t = 0. This means that setting t = 0 will leave you with the value of the constant term. In other words:
Set t = 0:
h = -at² + bt + c
h = -a(0)² + b(0) + c
h = -a(0) + 0 + c
h = 0 + c
h = c
Therefore, the value of the h-intercept is the value of c.
Hence, altering the value of c will also change the value of the h-intercept.
II. The maximum value of hThe maximum value of h occurs at the vertex, (t, h ). Changing the value of c affects the equation, especially the maximum value of h. To find the value of the t-coordinate of the vertex, use the following formula:
t = -b/2a
The value of the t-coordinate will then be substituted into the equation to find its corresponding h-coordinate. Thus, changing the value of c affects the corresponding h-coordinate of the vertex because you'll have to add the constant term into the rest of the terms within the equation. Therefore, altering the value of c affects the maximum value of h.
III. The t-interceptThe t-intercept is the point on the graph where it crosses the t-axis, and is also the value of t when h = 0. The t-intercept is the zero or the solution to the given equation. To find the t-intercept, set h = 0, and solve for the value of t. Solving for the value of t includes the addition of the constant term, c, with the rest of the terms in the equation. Therefore, altering the value of c also affects the t-intercept.
Therefore, the correct answer is Option K: I, II, and III.
True or false? The point (−5, 0) lies on the y-axis.
\well the answrnist that brcause if u think it guys up
Divide 2/3 by 1/5. Simplify your answer and write it as a mixed number.
Answer:
3.33
Step-by-step explanation:
3.33
mixed number= 3 1/3
Answer:
3 1/3
Step-by-step explanation:
[tex]\frac{\frac{2}{3}}{\frac{1}{5}}[/tex] =
[tex]\frac{2}{3} * \frac{5}{1} = \frac{10}{3}[/tex]
10/3 = 3 1/3
-Chetan K
A board 120 inches long is divided into 2 sections. If the ratio of the 2 sections is 3:5, what are the lengths of the sections?
15 inches, 105 inches
A
B
24 inches, 96 inches
C 40 inches, 80 inches
D 45 inches, 75 inches
Answer:
D 45 inches, 75 inches
Step-by-step explanation:
3:5 is 3 + 5 = 8 parts
one section is 3/8 of 120 = 45 inches
other section is 5/8 of 120 = 75 inches
D 45 inches, 75 inches
6.
Write the equation of the parabola in vertex form.
A. y = x2
B. y = 1/4x^2 + 1
C. y = 1/4x^2
D. y = 1/4( x - 2)^2 + 1
Answer: The answer is NOT Letter B
C. y = 1/4x^2
Step-by-step explanation: I used math.way
A. y = x^2 = Rewrite in vertex form and use this form to find the vertex ( h , k ) . ( 0 , 0 ) =Find the vertex form. y = x 2
B. y = 1/4x^2 + 1 = Rewrite in vertex form and use this form to find the vertex ( h , k ) . ( 0 , 1 ) =Find the vertex form. y = 1 /4 ⋅ ( x + 0 ) 2 + 1
C. y = 1/4x^2 = Rewrite in vertex form and use this form to find the vertex ( h , k ) . ( 0 , 0 ) =Find the vertex form. y = 1 /4 x 2
D. y = 1/4( x - 2)^2 + 1 = Rewrite in vertex form and use this form to find the vertex ( h , k ) . ( 2 , 1 ) = Already in vertex form. y = 1 /4 ( x − 2 ) 2 + 1
a line with slope -2 passes through the point (-2,3). What is the equation of the line?
Find the volume of a coffee can with r=7.5 cm, h= 16.8 cm, to the nearest cubic centimeter.
Answer:
V = 2968.8 cm³ or 2969 cm³
Step-by-step explanation:
Given the radius, r = 7.5 cm, of a cylindrical coffee can whose height, h = 16.8 cm:
We can find the volume of a cylinder by using the following formula:
V = πr²h
Substitute the given values into the formula:
r = 7.5 cm
h = 16.8 cm
V = πr²h
V = π(7.5)²(16.8)
V = π × 56.25 × 16.8
V = 2968.8 cm³ or 2969 cm³
Therefore, the volume of a coffee can is 2969 cm³.
What's the negative reciprocal of 5? Question 12 options: A) 1∕5 B) –5 C) –1∕5 D) 5
Answer:
[tex]\huge\boxed{C)\ -\dfrac{1}{5}}[/tex]
Step-by-step explanation:
The reciprocal of 5: [tex]\dfrac{1}{5}[/tex]
The negative reciprocal of 5: [tex]-\dfrac{1}{5}[/tex]
HELP PLS
Answer:
with what 0-0 are youy okay?
Step-by-step explanation:
Let g(x)=Intragal from 0 to x f(t) dt, where r is the function whos graph is shown.
Picture attached with question and graphs. As well as points needed
If
[tex]\displaystyle g(x) = \int_0^x f(t) \, dt[/tex]
then g(x) gives the signed area under f(x) over a given interval starting at 0.
In particular,
[tex]\displaystyle g(0) = \int_0^0 f(t) \, dt = 0[/tex]
since the integral of any function over a single point is zero;
[tex]\displaystyle g(4) = \int_0^4 f(t) \, dt = 8[/tex]
since the area under f(x) over the interval [0, 4] is a right triangle with length and height 4, hence area 1/2 • 4 • 4 = 8;
[tex]\displaystyle g(8) = \int_0^8 f(t) \, dt = 0[/tex]
since the area over [4, 8] is the same as the area over [0, 4], but on the opposite side of the t-axis;
[tex]\displaystyle g(12) = \int_0^{12} f(t) \, dt = -8[/tex]
since the area over [8, 12] is the same as over [4, 8], but doesn't get canceled;
[tex]\displaystyle g(16) = \int_0^{16} f(t) \, dt = 0[/tex]
since the area over [12, 16] is the same as over [0, 4], and all together these four triangle areas cancel to zero;
[tex]\displaystyle g(20) = \int_0^{20} f(t) \, dt = 24[/tex]
since the area over [16, 20] is a trapezoid with "bases" 4 and 8, and "height" 4, hence area (4 + 8)/2 • 4 = 24;
[tex]\displaystyle g(24) = \int_0^{24} f(t) \, dt = 64[/tex]
since the area over [20, 24] is yet another trapezoid, but with bases 8 and 12, and height 4, hence area (8 + 12)/2 • 4 = 40, which we add to the previous area.