first off, let's notice that "x" and "y" are encapsulating a function in terms of time or namely "t", and that dy/dt is decreasing at a rate of 3 cm/s, since the rate is decreasing, that makes the rate negative, thus is changing at -3 cm/s.
[tex]xy=12\implies \stackrel{product~rule}{\cfrac{dx}{dt}y~~ + ~~ x\cfrac{dy}{dt}}~~ = ~~0\implies \cfrac{dx}{dt}y~~ + ~~x(-3)~~ = ~~0 \\\\\\ \cfrac{dx}{dt}y=3x\implies \left. \cfrac{dx}{dt}=\cfrac{3x}{y} \right|_{(\stackrel{x}{4},\stackrel{y}{3})}\implies \cfrac{3(4)}{3}\implies 4[/tex]
-2/14=-6/4x what is the value of x
Step-by-step explanation:
-1/7 = -3/2x
1/7 = 3/2x
x = 1/7×2/3
= 2/21 :")
8. 1 hour 15 minutes
minutes
Answer:
1 hour and 15 minutes=75 mins.
Step-by-step explanation:
What is the volume of this cone? Use 3.14 for r and round your answer to the
nearest tenth.
In your answer, give the volume of the cone rounded to the nearest tenth, and then
explain how you calculated it. (Note: type out all of your work AND type out your
explanation for FULL credit.)
Answer:
39.5 in^3
Step-by-step explanation:
lol someone had the same question
The formula for a cone is (pi)(r^2)(h/3)
Since we have to use 3.14 for pi, we plug 3.14 in for pi:
(3.14)(r^2)(h/3)
The radius is 2 and the height is 8, so we plug in those numbers:
(3.14)(2^2)(8/3)
Simplify:
(3.14)(4)(2.666...)
Multiply:
(12.56)(2.666...) -> 39.49333...
Finally, we round 39.49333... to the tenths place:
39.5
Hope this helps :)
Find the volume of the shape
Answer:
i think. 8 times 12 = 96 times 20 = 1,920
13-28 Sketch the region enclosed by the given curves and find its area.
25. [tex]y=x^{4}, \quad y=2-|x|[/tex]
Answer:
Area (A) 0.0682
Step-by-step explanation:
The sketch for the region enclosed by the given curves can be found in the image attached below.
From the image below;
The two curves intersect in the area of tan 9x = 2 sin 9x
Recall that:
making x the subject; then:
The subdivision of the domain is in two intervals
where;
Area (A) =
Area (A) = 0.06818
Area (A) 0.0682
Given P(A) = 0.51, P(B) = 0.79, and P(A or B) = 0.66, are events A and B mutually exclusive?
Answer: No, the events are not mutually exclusive
Work Shown:
P(A and B) = P(A) + P(B) - P(A or B)
P(A and B) = 0.51 + 0.79 - 0.66
P(A and B) = 0.64
Since the result is not zero, this means the events are not mutually exclusive.
Mutually exclusive events are ones that cannot happen at the same time. Example: getting a "2" and a "3" on the same roll of a number cube.
What is the volume of this oblique cone?
(A) 4321 cm?
(B) 2881 cm3
(C) 3240 cm
(D) 1441 cm3
Answer:
Its D I did my math
Step-by-step explanation:
Answer:
D. I worked the math out.
180 divided by *blank* = 9
In 16 years' time Jim will be three times his current age. How old will Jim be in 4 years' time?
Answer:
12
Step-by-step explanation:
Jim's currect age is x.
In 16 years, JIm will be x + 16.
In 4 years, Jim will be x + 4.
x + 16 = 3x
-2x = -16
x = 8
x + 4 = 8 + 4 = 12
Help please i need this done!!
Answer:
True, True, True, False
Step-by-step explanation:
The maximum grain yield for corn is achieved by planting at a density of 37,000 plants per
acre. A farmer wants to maximize the yield for the field represented on the coordinate grid.
Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest
thousand, does the farmer need? (Hint: 1 acrt = 43,560 ft?)
у
500 fx
E
F
X
-500
0
500
G
-500
H
The farmer needs approximately
corn plants.
According to the question, there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
Determining the area of a trapezium?The trapezium is a 2 -dimensional plane shape with the area calculated as shown below:
The formula for calculating the area of a trapezoid is expressed as:
Area = 0.5(a + b)h
Given the following parameters
a = 500 ftSubstitute the given parameters
Area = 1/2 (500 + 900) * 800
Area = 1/2 (1400) * 800
Area = 560000 square feet
Since 1 acre is equivalent to 43560 square feet, hence the total acre required is expressed as:
Total acre = 560000/43560
Total acre = 12.856 acres
Also since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
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Problem 20 pls helps
Answer:
135
Step-by-step explanation:
[tex]d = 45t[/tex]
[tex]d(3) = 45( 3) = 45 \times 3 = 135[/tex]
[tex]d(3) = 135[/tex]
I HOPE IT HELPED YOU
Answer:
135
Step-by-step explanation:
sub 3 in place of t then times and it 135
The net of a rectangular prism is shown below. The surface area of each face is labeled.
(Picture Below)
Answer:
option A is correct.
Explanation:
Total Area of the prism: 8 + 48 + 8 + 24 + 24 + 48 = 160 ft²
Area of rectangular prism: 2(LW+HW+HL)
Option A
2(2*4+4*12+12*2)
2(8+48+24)
2(80)
160 ft²
areas of all 6 surfaces of the rectangular prism are given just add them up for finding Total surface area
TSA:-
24+8+8+48+48+242(24+48+8)2(80)160ft²A rectangle has a length of 11.8 centimeters and a width of 8.2 centimeters.
What is the area of this rectangle?
48.38 cm²
96.76 cm²
107.2 cm²
140.76 cm²
Answer:
96.76 cm²
Step-by-step explanation:
The area of a rectangle is the product of its length and width.
__
A = LW
A = (11.8 cm)(8.2 cm) = 96.76 cm²
Answer:
96.76 cm2
Step-by-step explanation:
The short-film festival at the county fair draws a large crowd of
moviegoers who enjoy the work of local filmmakers. Each year,
attendees vote for their favorite film in several categories, including
comedy, horror, and documentary. 65% of the 280 votes cast in the
comedy category were for Cat-urday Night Fever.
How many people voted for Cat-urday Night Fever as the best
comedy film shown at the festival?
The number of people who voted for Cat-urday Night Fever as the best comedy film is given by the equation A = 182 people
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of people who voted for the comedy film be = A
Now , the equation will be
The total number of people = 280 people
The percentage of people who voted for the best comedy film = 65 %
So , number of people who voted for the comedy film A = percentage of people who voted for the best comedy film x total number of people
Substituting the values in the equation , we get
Number of people who voted for the comedy film A = ( 65 / 100 ) x 280
On simplifying the equation , we get
Number of people who voted for the comedy film A = 0.65 x 280
Number of people who voted for the comedy film A = 182 people
Therefore , the value of A is 182 people
Hence , the number of people is 182 people
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What is the constant of proportionality for this relationship?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
and to get it, we only need two points off a line, hmmm let's use those two points in the picture below.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{4}}}\implies \cfrac{6}{4}\implies \cfrac{3}{2}[/tex]
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Since it's a right angled Triangle we can } \\ \textbf{ use Pythagoras theorem } [/tex]
[tex] \sf{Cos (29°) = \dfrac{b}{c}} [/tex][tex] \sf{Cos (29°) = \dfrac{b}{260}} [/tex][tex] \sf{b= 260\cdot Cos (29°) } [/tex][tex] \sf{b= 260\cdot 0.875 } [/tex][ [tex] \textsf{Cos(29°)= 0.875} [/tex] ]
[tex] \sf{b= 227.5 in }[/tex][tex] \textsf{I hope you understood the procedure} [/tex]
Find the slope-intercept equation
Please help me
Answer:
[tex]y = -\frac{1}{3}x + 5[/tex]
Step-by-step explanation:
To being, slope intercept form is the infamous y = mx + b form. In which, m is equal to the slope and b is equal to the y-intercept. (1) To solve this, begin by finding two points of the line. One easy point to find is when x = 0 as it intersects with the y-axis. Two points are: (0,5) and (-3,6). (2) Next, use the slope formula to solve for the slope. The slope formula is [tex]\frac{y2-y1}{x2-x1}[/tex]. Plug in the y and x values; [tex]\frac{6-5}{-3-0}[/tex]. Simpliify the fraction; [tex]\frac{1}{-3}[/tex] --> [tex]-\frac{1}{3}[/tex]. Therefore -1/3 is our slope. (3) To solve for b, the y-intercept, set up the slope-intercept equation with the newfound slope (y = -1/3x + b) and plug in a point for the y and x values. Doing this will isolate the b so you can solve for it.
6 = -1/3(-3) + b
6 = 1 + b
-1 -1
5 = b
Therefore the y-intercept (b) is 5. (4) The final step is to combine the information into the slope-intercept form; y = -1/3x + 5. Good luck!
Given that cos(theta) = 8/17 and that theta lies in Quadrant IV, what is the exact value of sin 2(theta)?
Answer: [tex]-\frac{240}{289}[/tex]
=========================================================
Explanation:
Use the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex] and plug in the fact that [tex]\cos(\theta) = \frac{8}{17}\\\\[/tex]
Isolating sine leads to [tex]\sin(\theta) = -\frac{15}{17}\\\\[/tex]. I'm skipping the steps here, but let me know if you need to see them.
The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.
Therefore,
[tex]\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\[/tex]
What is x?
If necessary, round to the nearest tenth (one decimal place)
Please help, Thank you!
Answer:
4/x-8=8/2
4/x-8=4
4=4(x-8)
4=4x-32
4+32=4x
36=4x
dividing through by 4
x=9
converting to the nearest tenth will be 9.0
therefore x=9.0
Can you guide me through the steps of finding the area of a circle?
Answer:
A=(3.14)r²
Step-by-step explanation:
First you find your radius if it is a diameter you divide it by 2
Second you multiply the radius by pi (π=3.14)
lastly you square your answer
hope this helps!
This is the graph of y=x² + 4x + 7.
-5
What is the range of this function?
A. x²-2
B. y≤ 3
OC. y23
D. All real numbers
10- ly
(-2,3)
x45
Answer:
C y≥3
Step-by-step explanation:
Range is the y values that a function can be ...this one can be as low as 3 and up to infinity
For each value of y, determine whether it is a solution to -2y+75-5.
Is it a solution?
Answer:
• No
• Yes
• Yes
• No
Step-by-step explanation:
To determine if the 4 given values of y are solutions to the inequality, start by solving the inequality. Solving an inequality is just like that of an equation, except that the direction of the sign changes when the inequality is divided by a negative number.
-2y +7≤ -5
Subtract 7 on both sides:
-2y≤ -5 -7
-2y≤ -12
Divide by -2 on both sides:
y≥ 6
This means that the solution can be 6 or greater than 6.
-10 and 3 are smaller than 6 and are not a solutions, while 7 and 6 satisfies the inequality and are therefore solutions.
_______
Alternatively, we can also substitute each value of y into the inequality and check if the value is less than or equal to -5.
Here's an example to check if -10 is a solution.
-2y +7≤ -5
When y= -10,
-2y +7
= -2(-10) +7
= 20 +7
= 27
Since 27 is greater than 5, it is not a solution to the inequality.
A movie theater sold 4 adult tickets for every 2 child tickets. The theater sold
32 adult tickets. How many tickets did it sell in all?
Adult tickets
Child tickets Total tickets
4
2
32
Answer:
Total amount of tickets is 48
Step-by-step explanation:
Step 1: Determine the amount of tickets they solid in all
We see that the movie theater has a ratio of 4 adult tickets for every children ticket which means that wen a child purchases a ticket there are 2 adult tickets that come along.
32 adult tickets / (2 adult tickets per child)
16 children tickets
Total tickets: 32 adult tickets + 16 children tickets = 48 tickets
Answer: Total amount of tickets is 48
A local gym conducted a survey to find the average number of hours per week people in the community spent exercising. Of the
300 people surveyed, 64% were men. Of all the people surveyed, 37% of people said they exercised 7 or more hours per week. Of all
the women surveyed, 75% said they spent less than 7 hours per week exercising.
Complete the two-way table to show the number of men or women in each category based on the given information.
Answer:
Men Women Total
Exercise less than 7 hours per week
Men:108
Women:81
Exercise 7 or more hours per week
Men:84
Women:27
Step-by-step explanation:
how do i solve this?
Please explain. I'm a bit confused
The table shows the amount of red paint that can be added to different amounts of white paint while making a custom paint color:
Which statement is true about the ratio of red paint to white paint in the paint color?
A) It is 1:16.
B) It is 16:1.
C) It is 5:1.
D) It is 1:5.
Answer:
D) It is 1:5.
Step-by-step explanation:
[tex] \frac{4}{20} = \frac{1}{5} [/tex]
A data set is normally distributed with a mean of 27 and a standard deviation of 3.5. Find the z-score for a value of 25, to the nearest hundredth.
Answer:
z score = .2843
Step-by-step explanation:
25 is 2 below 27
this is 2/3.5 = .5714 S.D. below mean
z-score . 2843
Here is a rule for generating a sequence; 3n+10 What is the 150th term of the sequence generate by this rule?
Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Topic - Arithmetic Progression ( AP )Given - a general term for a sequence.To find - the 150th term of the given sequenceso let's start ~
General term , [tex] A_{n} [/tex] = 3n + 10
let's consider certain values of n to get some information with us which will help us solve the problem further !
let's first consider , n = 1 ! then ,
[tex]3n + 10 = 3(1) + 10 \\ \dashrightarrow \: 13[/tex]
now , let's consider n = 2
[tex]3n + 10 = 3(2) + 10 = 6 + 10 \\ \dashrightarrow \: 16[/tex]
then , let's consider n = 3
[tex]3n + 10 = 3(3) + 10 = 9 + 10 \\ \dashrightarrow \: 19[/tex]
hence ,
now we've with us an AP which is as follows -
[tex]13 \: , \: 16 \: , \: 19 \: ......[/tex]
from this Arithmetic Progression ,
we can know that
a = first term = 13
d = common difference = 16 - 13 = 19 - 16 = 3
now ,
[tex]A _{n} = a + (n - 1)d \\ \implies \: A _{150} = 13 + (149)(3) \\ \implies \: A _{150} = 13 + 447 \\ \pink{\implies \: A _{150} = 460}[/tex]
hope helpful :D
In 1999 the average cost of a house
was £91,199. In 2022 the average cost
of a house is £278,123. Find the
percentage change and state if this is
an increase or decrease.
The percentage change is 204.96% and it was increasing
Our percent calculator uses this formula:
[tex]((y2-y1)/y1)*100[/tex] = your percentage change
(where [tex]y1=[/tex] start value and [tex]y2=[/tex] end value)
[tex]((278.123-91.199)/91.199)*100=204.96%[/tex]
Therefore, The percentage change is 204.96% and it was increasing
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