The question is about the mathematical modeling of a vineyard's grape production. As the number of vines increases, the individual yield of each vine decreases by 1%. An equation, such as P = 5000 - 50(n-500), is a possible mathematical model to represent this situation.
Explanation:This question appears to require a detailed understanding of mathematical modeling and percentage decrease concept. The problem presented describes the decrease in grape production per vine as the number of vines planted per acre increases. It's an example of an inverse relationship, when one variable increases the other variable decreases.
The initial production quantity is 10 lb of grapes per vine when there are 500 vines per acre. However, for every additional vine planted, there is a subsequent 1% drop per vine. This means that if 501 vines are planted, each vine then produces only 99% of 10 lbs, or 9.9 lbs, and so on.
To model this mathematically, an equation could possibly be P = 5000 - 50(n-500), where P is the production of grapes in pounds, and n is the number of vines. This formula might help to calculate the maximum yield that could be obtained according to the number of vines.
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Solve for x. 5x = -25
The correct Answer is: x= -5
It's me again ok so
Simplifying
5x = -25
Solving
5x = -25
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '5'.
x = -5
Simplifying
x = -5
BOOM
Use a composite figure to estimate the area of the figure. The grid has squares with side lengths of 1.5 cm.
Answer:
about [tex]49.1\ cm^{2}[/tex]
Step-by-step explanation:
The area of the composite figure is approximate to the area of the rectangle plus the area of the semicircle at the top of the rectangle plus the semicircle at the right of the rectangle
Find the area of the rectangle
[tex]A=(3*1.5)(4*1.5)=27\ cm^{2}[/tex]
Find the area of the semicircle at the top of the rectangle
[tex]A=\frac{1}{2}\pi (2*1.5)^{2}=4.5 \pi\ cm^{2}[/tex]
Find the area of the semicircle at the right of the rectangle
[tex]A=\frac{1}{2}\pi (1.5*1.5)^{2}=2.53 \pi\ cm^{2}[/tex]
The area of the composite figure is
[tex]27\ cm^{2}+4.5 \pi\ cm^{2}+2.53 \pi\ cm^{2}=(27+7.03 \pi)\ cm^{2}[/tex]
use [tex]\pi=3.14[/tex]
[tex](27+7.03(3.14))=49.1\ cm^{2}[/tex]
HELP! During the period 1998–2002, the number y (in millions) of juvenile books shipped to bookstores can be modeled by the equation y = -15x^2 + 64x + 360 where x is the number of years since 1998. During what year were there 400 million juvenile books shipped to bookstores?
Answer:
1999
Step-by-step explanation:
y=-15x^2+64x+360
y=-15(1)^2+64(1)+360
y=409
(y is in millions)
I hope this helps!
Determine which polynomial is a difference of two squares. a. X2 + 14 b. X2 ? 14 c. X2 + 49 d. X2 ? 49
Answer:
d. X^2 - 49
Step-by-step explanation:
I will assume that the question marks are minus signs.
Let's remember what does "difference of two squares" means:
The difference of two squares is a number multiplied by itself subtracted from another number multiplied by itself (the number multiplied by itself is called squared number).
In our options, the first number is always a squared number because it's X^2 = X * X.
We just have to analyze the second number.
First, let's notice that a. and c. can't be correct because we have a sum instead of a subtract.
We have left 14 and 49 to analyze:
14 = 7*2 (it's not a squared number)
49 = 7*7 (it's a squared number)
The answer is X*X - 7*7 = X^2 - 49
Find the best estimate for the volume of the prism by rounding before you calculate
Answer:
I need numbers to actually calculate the problem.
Step-by-step explanation:
Answer:36ft^3
Step-by-step explanation:
On a track and field team, 8% of the members run only long-distance, 32% compete only in field events, and 12% are sprinters only. Find the probability that a randomly chosen team member runs only long-distance or competes only in field events.
Answer:
0.40
Step-by-step explanation:
Members who run only long distance = 8%
So, probability that a member will run only long distance = P(A) = 0.08
Members who compete only in field events = 32%
So, probability that a member will compete only in field events = P(B) 0.32
Members who are sprinters = 12%
So, probability that a member is sprinter = P(C) 0.12
We have to calculate the probability that a randomly chosen team member runs only long-distance or competes only in field events. i.e we have to find P(A or B). Since these events cannot occur at the same time, we can write:
P(A or B) = P(A) + P(B)
Using the values, we get:
P(A or B) = 0.08 + 0.32 = 0.40
Thus, the probability that a randomly chosen team member runs only long-distance or competes only in field events is 0.40
The probability that a randomly chosen team member runs only long-distance or competes only in field events is 0.40.
1. To find the probability that a randomly chosen team member runs only long-distance or competes only in field events, we need to add the probabilities of these two mutually exclusive events.
2. Given:
Probability of running only long-distance: 8% or 0.08Probability of competing only in field events: 32% or 0.323. Since these events are mutually exclusive (they cannot happen at the same time), we simply add the probabilities:
P(long-distance or field events) = P(long-distance) + P(field events)
P(long-distance or field events) = 0.08 + 0.32 = 0.40
Therefore, the probability that a randomly chosen team member runs only long-distance or competes only in field events is 40% or 0.40.
A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s production and used them continuously until they failed to work. The life lengths of the batteries, in hours, until they failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, and 298. At the .05 level of significance, is there evidence to suggest that the mean life length of the batteries produced by this manufacturer is more than 400 hours? A. Yes, because the test value 1.257 is less than the critical value 1.782 B. No, because the test value 1.257 is greater than the critical value 1.115 C. No, because the p-value for this test is equal to .1164 D. Yes, because the test value 1.257 is less than the critical value 2.179 Reset Selection
Answer:
A:
Step-by-step explanation:
***I'm pretty sure A should read "NO, because the test value 1.257 is less than the critical value 1.782. Please check the wording of the problem***
H0 : μ ≤ 400
Ha : μ > 400 (claim)
Sample mean: 6,155/13
Sample standard deviation: √44422.4359
Critical test value: t > 1.782
t = (6,155/13 - 400)/[(√44422.4359)/√13] = 1.257
1.257 < 1.782 ; we fail to reject the null hypothesis
There is not enough evidence at the 5% level of significance to support the claim that the mean battery life is at least 400 hours.
A rectangular field has side lengths that measure 5/6 mile and 1/3 mile. What is the area of the field?
Team infinate demensions canoed 15 3/4 miles in 3 hours. What was their average rate of speed in miles per hour
Answer:
5.25 or 5 1/4 MPH
Step-by-step explanation:
1. convert 15 3/4 into a decimal = 15.75
2. divide the miles canoed (15.75) by the time (3)
15.75/3 = 5.25 MPH
Milk is being poured into a cylindrical pail at a constant rate of 8 cubic inches per second. The pail has a base radius of 5 inches and a height of 16 inches. At this rate, how many seconds will it take to fill the pail with milk? Use 3.14 for ? . Round your answer to the nearest second.
9514 1404 393
Answer:
157 seconds
Step-by-step explanation:
The volume of the pail is ...
V = πr^2·h
V = 3.14(5 in)^2(16 in) = 1256 in^3
At 8 in^3/s it will take ...
(1256 in^3)/(8 in^/s) = 157 s
to fill the pail.
It will take 157 seconds to fill the pail with milk.
How many times greater. Is the value of 8 in 18,272 than the value of 8 in 17,282
1,8272 --- 8,000
17,282 --- 80
8,000÷80=100 times greater
Final answer:
The value of 8 in the number 18,272 (8,000) is 100 times greater than its value in the number 17,282 (80).
Explanation:
The question is asking how many times the value of 8 in 18,272 is greater than the value of 8 in 17,282.
In the number 18,272, the 8 is in the thousands place, making it have a value of 8,000. In the number 17,282, the 8 is in the tens place, giving it a value of 80.
To determine how many times greater the value of 8 is in the first number compared to the second, divide the larger value by the smaller value: 8,000 ÷ 80 = 100.
Therefore, the value of 8 in 18,272 is 100 times greater than in 17,282.
WILL MARK BRAINLEST!! HELP ASAP
On your own paper, carefully plot the starting point and follow the directions to find a new point.
Start at (-4, -2) and find another point by moving both
i) up 3 and
ii) left 2
What are the coordinates of the new point?
Answer:
(-6, 1)
Step-by-step explanation:
We are given a point with the coordinates (-4, -2) and we are to plot this on a graph and then find another point by moving three units upwards and 2 units towards left.
If we move 3 units up from the point (-4, -2), we get (-4, 1).
Then from (-4, 1), we move 2 units towards left and we get the coordinates of this new point which are (-6, 1).
point A is locatee at (2,8) and point B is located at (8,5). what point partitions the directed line segment AB into a 1:3 ratio
Answer:
The point is (3.5 , 7.25)
Step-by-step explanation:
∵ A = (2 , 8) and B = (8 , 5)
∵ Let point P divides AB into a ratio 1:3
∵ [tex]x=\frac{m_{2}x_{1}+m_{1}x_{2}}{m_{1}+m_{2}}[/tex]
∵ [tex]y=\frac{m_{2}y_{1}+m_{1}y_{2}}{m_{1}+m_{2}}[/tex]
∴ x-coordinate of P = (2)(3) + (8)(1)/3 + 1 = (6 + 8)/4 = 3.5
∴ y-coordinate of P = (8)(3) + (5)(1)/1 + 3 = (24 + 5)/4 = 7.25
∴ P = (3.5 , 7.25)
The point that partitions the directed line segment AB into a 1:3 ratio is P(3.5, 7.25), calculated using the section formula.
To find the point that partitions the directed line segment AB into a 1:3 ratio, we use the section formula. The section formula for a point P(x, y) that divides the line segment connecting A(2, 8) to B(8, 5) in the ratio m:n is given by:
x = ([tex]m \times x2 + n \times x1[/tex]) / (m + n)
y = ([tex]m \times y2 + n \times y1[/tex]) / (m + n)
Given the ratio 1:3, the coordinates for point P can be calculated as follows:
x = ([tex]1 \times 8 + 3 \times 2[/tex]) / (1 + 3) = (8 + 6) / 4 = 14 / 4 = 3.5
y = ([tex]1 \times 5 + 3 \times 8[/tex]) / (1 + 3) = (5 + 24) / 4 = 29 / 4 = 7.25
Therefore, the point that divides the line segment AB in a 1:3 ratio is P(3.5, 7.25).
A train travels 16 miles in 20 minutes. At this rate, how ,any minutes will it take to travel 12 miles
Answer:
16 minutes
Step-by-step explanation:
Beatrice calculated the slope between two pairs of points.
She found that the slope between (-3, -2) and (1, 0) is 12.
She also found that the slope between (-2, -1) and (4, 2) is 12.
Beatrice concluded that all of these points are on the same line.
Use the drop-down menus to complete the statements about Beatrice's conclusion.
Beatrice is (correct/incorrect). All of these points (are/ are not) on the same line because the slope between (-2,-1) and (1,0) (is/ is not) equal to 1/2.
Answer:
Beatrice is incorrect. All of these points are not on the same line because the slope between (-2, -1) and (1, 0), which are coordinates from each of the pairs above, is not equivalent equal to 1/2
Step-by-step explanation:
The answer is: incorrect; are not; is not. Beatrice is incorrect. All of these points are not on the same line because the slopes between (-2,-1) and (1,0) is not equal to [tex]\frac{1}{2}[/tex].
Beatrice is incorrect. All of these points are not on the same line because the slope between (-2,-1) and (1,0) is not equal to 1/2.
Here’s a step-by-step explanation:
First, let’s verify Beatrice’s given slopes. The slope is calculated using the formula:[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex].
For points (-3,-2) and (1,0): [tex]y_2 = 0,\ y_1 =-2,\ x_2=1,\ x_1 = -3[/tex]. So:Since the slopes between these points vary, they do not lie on the same line. All three sets must have the same slope to be considered collinear.
Jackson buys a new Shirt. The shirt is 25% off the original price. Jackson pays a total of $11.34 for the shirt, which includes a sales tax of 8%. What is the original price, in dollars, of the shirt?
Answer:
$13.04 is the original price of the shirt
Step-by-step explanation:
As sales tax is 8% we will find the price of the shirt
11.34 * 8/100 = 0.91
11.34-0.91= 10.43
so, $10.43 is the price of the shirt after discount and excluding sales tax.
The original price of the shirt is:
10.43 * 25 /100 = 2.60
adding it to the price of shirt
10.43 + 2.61 = 13.04
Answer:
14 or 14.00
Step-by-step explanation:
If he is getting 25% off, that means that what he paid with 75% of the original cost. Don't forget that he also has to pay a percent tax so that is the same as multiplying by 1.08. (btw this is what it said the correct answer was after I get it wrong two times)
help asappp
Write the following equations in slope-intercept form. Remember to show all the work!!
x − 3y = 6
Write the following equations in Standard form. Remember to show all work!
y = −x − 3
Y = 1/2x - 5
Answer:
y = -x-3
x-y = -3
x - 2y = 10
Step-by-step explanation:
x − 3y = 6
Slope intercept form is y = mx +b
We need to solve for y
Subtract x from each side
x-x-3y = -x+6
-3y = -x +6
Divide each side by -3
-3y/-3 = -x/-3 +6/-3
y = 1/3 x -2
Standard form is Ax +By = C
y = -x-3
Add x to each side
x-y = -x+x-3
x-y = -3
y = 1/2x -5
We do not like fractions in standard form, so multiply by 2
2y = 2*1/2x -2*5
2y =x-10
Subtract x from each side
-x +2y = x-x-10
-x+2y = -10
We like to have the coefficient on x be positive
Multiply by -1
x - 2y = 10
Choose some numbers to compare to 55 use = and <,> WHAT NUMBERS COMPARE TO 55
There's literally unlimited answers but here are some simple ones.
5 x 11 = 55
55 = 55
55 > 54
1 < 55
3 x 2 < 55
To compare numbers to 55, choose numbers less than, greater than, or equal to 55 and use the appropriate comparison operator. Examples include 50 < 55 (less than), 55 = 55 (equal to), and 60 > 55 (greater than).
To compare numbers with 55 using the comparison operators >, <, and =, we must choose numbers that are either greater than, less than, or equal to 55. For example:
50 < 55 - Here, 50 is less than 55.55 = 55 - Here, 55 is equal to 55.60 > 55 - Here, 60 is greater than 55.When you are comparing numbers, always remember that a number is greater than another if it represents a larger quantity, and it is less than another if it represents a smaller quantity. The equal sign is used when the quantities are identical.
11 points each!!
Explain how to find the y-intercept of a graph.
Answer:
You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. The x coordinate will always be 0
Step-by-step explanation:
by seeing at which a point cuts y axis
(Q3) Which of the following functions decreases, going downwards from left to right?
Answer: third option
Step-by-step explanation:
By definition, for the function [tex]y=b^x[/tex] if 0<b<1 then the function decreases from left to right
Therefore, it cannot be the options 1 or the option 2.
As the function given in the third option of problem has a negative coefficient (which is -2) and b=0.3 (0<b<1)
[tex]y=-2*0.3^x[/tex]
Then, each ouput value wil be negative.
Therefore, you can conclude that the function [tex]y=-2*0.3^x[/tex] decreases and going downwards from left to right.
Answer:
The answer is B.
Step-by-step explanation:
got it right on edge.
5p/7 - 18 = - 43 help me please!
Answer:
-35
Step-by-step explanation:
[tex]5p/7-18=-43[/tex] ⇒ [tex]5p/7=-43+18[/tex] ⇒
[tex]7(5p/7=- 25)7[/tex] ⇒ [tex]5p=-175[/tex] ⇒
[tex]5p/5 = -175/5[/tex] ⇒ [tex]p = -35[/tex]
3 geometric solids that have circular cross sections
Answer:
The 3 geometric solids with circular cross sections are a sphere, a cone and a cylinder
Step-by-step explanation:
While a cone and a cylinder will not in every direction, if you slice them on a horizontal plane, they will have a circular cross section.
The sphere, cylinder, and cone are three-dimensional geometric solids with circular cross sections, existing in both solid and hollow forms, important in physics for understanding properties like moment of inertia and involvement in superelastic collisions.
Three geometric solids that possess circular cross sections are the sphere, cylinder, and cone. These shapes are known as three-dimensional solid figures. The sphere is a solid figure where all points on the surface are equidistant from the center, resulting in any cross-section through its center being a circle.
A cylinder is a solid with straight parallel sides and a circular or oval cross section. A cone has a flat circular base and tapers to a point called the apex or vertex, creating circular cross-sections when sliced parallel to the base.
In addition to fully solid forms, there are also hollow versions of these shapes, such as the hollow spherical shell, which still have circular cross sections. These solids can be involved in various physics concepts such as rotational dynamics and superelastic collisions. When analyzing the rotational motion or collision attributes of these solids, the shapes' geometrical and mass properties play a crucial role.
For instance, the moment of inertia of a solid sphere differs from that of a hollow spherical shell due to the distribution of mass within the object.
Find, picture provide below
Answer:
C. 2916
Step-by-step explanation:
The given limits is
[tex]\lim_{h \to 0} \frac{f(9+h)-f(9)}{h}[/tex]
if [tex]f(x)=x^4[/tex].
[tex]\Rightarrow f(9)=9^4=6561[/tex]
[tex]f(h+9)=(h+9)^4=h^4+36 h^3+486 h^2+2916 h+6561[/tex]
Our limit becomes;
[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= \lim_{h \to 0} \frac{h^4+36 h^3+486 h^2+2916 h+6561-6561}{h}[/tex]
This simplifies to;
[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= \lim_{h \to 0} \frac{h^4+36 h^3+486 h^2+2916 h}{h}[/tex]
[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= \lim_{h \to 0} h^3+36 h^2+486 h+2916 [/tex]
[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= (0)^3+36 (0)^2+486(0)+2916 [/tex]
[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= 2916 [/tex]
the correct choice is C.
The graph of f(x) = 7x is shifted 6 units to the right. What is the equation of the new graph?
A. g(x) = 7x + 6
B. g(x) = 7(x - 6)
C. g(x) = 7(x + 6)
D. g(x) = 7x - 6
the correct answer choice is B.
The equation of the graph for the function f(x) = 7x after being shifted 6 units to the right is g(x) = 7(x - 6), which is option B.
Explanation:When a graph of the form f(x) = mx is shifted horizontally, this is represented in the equation by manipulating the x variable within the function. A shift to the right by 6 units results in the input value being decreased by 6 before it is multiplied by the slope (in this case, 7). Therefore, the new equation reflecting a horizontal shift to the right is g(x) = 7(x - 6), which corresponds to option B.
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A florist has 40 tulips 32 roses 60 daisies and 50 petunias.Draw a line from each comparison to match it to the correct ratio
Answer:
Need to see the choices
Step-by-step explanation:
The table shows Zack's daily pay with respect to the hours he works.What is the rate of change of pay,y, with respect to hours, x?
Answer:
B.
Step-by-step explanation:
63/4= 15.75
The rate of change of pay with respect to hours is $15.75 per hour.
How to find the rate of change of pay?The rate of the change by calculated by dividing the total pay by the corresponding number of hours.
We can find the rate of change of pay with respect to hours as follows:The amount of money he earns is $63 in 4 hours.
Rate of change of pay = $110.25 - $63/7 - 4 per hour
= $15.75 per hour
This is consistent with the other values in the given table.
Rate of change of pay = $141.75 - $110.25/9 - 7 per hour
= $15.75 per hour
Therefore, we have found the rate of change of pay, y, with respect to hours, x to be $15.75 per hour. The correct answer is option B.
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Plz help me
WILL GIVE BRAINLIEST
Answer:
D 2x(3x+4) + 1(3x+4)
Step-by-step explanation:
(2x+1) (3x+4)
We need to FOIL
First 2x*3x = 6x^2
Outer 2x*4 = 8x
Inner 1*3x =3x
Last 1*4 =4
Add them together
6x^2 +8x+3x+4
Combine like terms
6x^2 +11x+4
This process is simply taking 2x (3x+4) and adding 1 (3x+4)
2x(3x+4) + 1(3x+4)
Laura is a songwriter. The table shows the number of songs she wrote in each of the past 5 months. Use the information in the table to create a probability distribution table.
Answer:
[tex]\begin{array}{ccccc}\text{January}&\text{February}&\text{March}&\text{April}&\text{May}\\\dfrac{3}{20}&\dfrac{5}{20}&\dfrac{2}{20}&\dfrac{8}{20}&\dfrac{2}{20}\end{array}[/tex]
Step-by-step explanation:
During 5 months Laura wrote
3+5+2+8+2=20 songs.
1. The probability that the song was written in January is [tex]\frac{3}{20}.[/tex]
2. The probability that the song was written in February is [tex]\frac{5}{20}.[/tex]
3. The probability that the song was written in March is [tex]\frac{2}{20}.[/tex]
4. The probability that the song was written in April is [tex]\frac{8}{20}.[/tex]
5. 1. The probability that the song was written in May is [tex]\frac{2}{20}.[/tex]
The probabolity distribution table:
[tex]\begin{array}{ccccc}\text{January}&\text{February}&\text{March}&\text{April}&\text{May}\\\dfrac{3}{20}&\dfrac{5}{20}&\dfrac{2}{20}&\dfrac{8}{20}&\dfrac{2}{20}\end{array}[/tex]
The radius of the circle is ✓2. The distance from the center to the chord is 1. If the measure of AB is 90°, the area of the shaded region is
Answer:
c. (π/2 -1) square units
Step-by-step explanation:
A segment that subtends an arc of θ in a circle of radius r has an area given by ...
A = (1/2)(θ -sin(θ))r² . . . . . where θ is in radians
In your figure, the radius is r = √2 and the angle is 90°, so θ = π/2. Then the area is ...
A = (1/2)(π/2 -sin(π/2))·(√2 units)²
A = (π/2 -1) units²
Kate packs snow into 5 identical jars. Each jar represents a different depth of snow. Kate then lets the snow in each jar completely melt. The table shows the height of the liquid in each jar as it relates to the original depth of snow in the jar.
Which statements are true about the relationship between the depth of the snow and the height of water in the jar after the snow is melted? Check all that apply.
The points on a graph representing the relationship lie on a line.
There is 0.4 inch of water to every 1 inch of snow.
A line through the points will pass through (0, 0).
The function relating snow depth to water depth is quadratic.
The data can be represented by f(x) = 0.2x.
Answer:
A, C, E
Step-by-step explanation:
From the table you can see that the water depth cahnges
[tex]0.8-0.4=1.2-0.8=1.6-1.2=2.0-1.6=0.4\ in[/tex]
for every
[tex]4-2=6-4=8-6=10-8=2\ in[/tex] of snow (option B is false).
This means that the function modelling this situation is linear function (option A is true and option D is false). Let the equation of this function be [tex]y=ax+b.[/tex] Then
[tex]0.4=2a+b,\\ \\0.8=4a+b.[/tex]
Subtract these two equations:
[tex]2a=0.8-0.4,\\ \\2a=0.4,\\ \\a=0.2.[/tex]
Hence,
[tex]b=0.4-2\cdot 0.2=0.[/tex]
The equation of the straight line (the graph of linear function) is [tex]y=0.2x.[/tex] (option E is true) This line passes through the point (0,0), because its coordinates satisfy the equation (option C is true).
Answer:
A and C
Step-by-step explanation:
Ok listen here. The guy from the other thing said ACE however thats so wrong that I can't explain how wrong that is. how is it wrong you might ask. Well if you can READ the question you know that you should select 2 options
second of all f(x)=0.2^x is saying that if x equals 2 then y is 0.2*0.2 which is 0.04 which is not the result.
I hope this helps more than whatever answer the other answer was. If not then you gotta figure it out yourself