Natalee's mistake is that she has written the function incorrectly. In her function, she has multiplied the starting number of bacteria, 100, by the growth rate, 40%, to get the final number of bacteria. However, this is not correct because a growth rate of 40% means that the number of bacteria increases by 40% of the starting number, not by 40 itself.
To write the correct function, we can use the fact that a growth rate of 40% means that the final number of bacteria is 1.4 times the starting number. Therefore, the correct function for this scenario is y = 1.4 * 100 = <<1.4*100=140>>140. This function shows that the number of bacteria increases to 140 after experiencing a 40% increase in growth.
Answer:
The actual function for this scenario would be:
y = 100 * 1.40
Step-by-step explanation:
Natalee's mistake was that she didn't add 1 to the value of the increase. When you multiply a number by 1 plus the percentage increase, you get the correct result. In this case, the correct function would be:
y = 100 * 1.40
This function will show a 40% increase in the number of bacteria, starting with 100 bacteria. When graphed, the y-values will not be extremely high.
if you have any question let me know!
Revert to the photo for the math question.
Thanks!
The volume of the crater is 64800000 m³
Calculating volume of the craterFrom the question, we are to determine the volume of the crater.
From the given information,
d = 2∛(V/0.3)
To determine the volume,
First, we will solve for V in the equation
d = 2∛(V/0.3)
Divide both sides by 2
d/2 = ∛(V/0.3)
Take the cube of both sides
(d/2)³ = V/0.3
Then,
V = 0.3(d/2)³
Now, substitute the value of the diameter
d = 1200m
Then,
V = 0.3(1200/2)³
V = 0.3(600)³
V = 64800000 m³
Hence, the volume is 64800000 m³
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A cubic polynomial function f is defined by. 3. 2. ( ) 4. f x x ax bx k where a, b, and k are constants
In a cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants and has a local minimum at x = -2 and a local maximum at x = 0, then values of a and b is 12 and 0 respectively. If integrate of f(x)dx = 32 from 0 to 1, then value of k is 27.
The given cubic polynomial function is
f(x) = 4x³ + ax² + bx + k
f'(x) = 12x² + 2ax + b
f''(x) = 24x + 2a
At local maximum f' = 0
f'(0) = 12×(0)² + 2a×(0) + b = 0
b = 0
At local minimum, f' = 0
That is f'(-2) = 0 and f''(-2) > 0
f'(-2) = 12×(-2)² + 2a×(-2) + b = 0
48 - 4a + b = 0
4a - b = 48
a = 12
Therefore, f(x) = 4x³ + 12x² + k
Integrate f(x)dx = 32 from 0 to 1, that is
∫₀¹ f(x)dx = 32
∫₀¹ (4x³ + 12x² + k) dx = 32
[ x⁴ + 4x³ + kx ]₀¹ = 32
(1⁴ - 0⁴) + 4(1³ - 0³) + k(1 - 0) = 32
1 + 4 + k = 32
k = 27
-- The question is incomplete, answering to the question below--
"A cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants. The function f has a local minimum at x = -2 and a local maximum at x = 0.
A. Find the values of a and b
B. If you integrate f(x)dx = 32 from 0 to 1, what is the value of k?"
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Clayton and Iri purchae admiion to a carnival plu a number of game ticket. Clayton purchaed 10 game ticket and pend $19. 50. Iri purchae 15 game ticket and pend $23. 25. Determine tye cot per game ticket
The combined cost per game ticket is $1.71
In this question we have been given Clayton and Iris purchase admission to a carnival plus a number of game tickets. Clayton purchased 10 game tickets and spend $19. 50.
Iris purchase 15 game tickets and spend $23. 25
We need to determine cost per game ticket.
The total cost of Clayton's game tickets is $19.50 for 10 tickets,
So, by unitary method the cost per ticket is:
= 19.5/10
= $1.95 per ticket.
The total cost of Iri's game tickets is $23.25 for 15 tickets
So, by unitary method the cost per ticket is:
= 23.25/15
= $1.55 per ticket.
The combined cost of all the game tickets is $19.50 + $23.25 = $42.75.
The total number of game tickets purchased is 10 tickets + 15 tickets = 25 tickets.
The combined cost per game ticket would be,
= 42.75 / 25
= $1.71 per ticket.
Therefore, the cost per game ticket = $1.71
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Which statement best explains
why the sum of the areas of the
two white squares in Figure 2 is
the same as the area of the white
Q
square in Figure 1?
Figure
Figure 2
The combined area of the four triangles is equal to the area of the large white
square.
In each triangle, the length of side a plus the length of side b equals the length
of side c. That means that a2 + b2 = c?.
In each figure the total area is equal and the area of the triangles is equal, se
the remaining white area in each figure must also De equal.
Answer:
This because the root cancel each other
Divide the rational expressions. Write your answer in its fully
factored form. Look at picture
Answer:
4m(m+7m) 8(2m+1)
________. x. ______
8(3m+2). 4m(5m-1)
(m+7m). (2m+1)
________. x. ______
(3m+2). (5m-1)
2m2 + 1m + 14m2 + 7m
__________________
15m2 -3m + 10m -2
16m2 + 8m
_________
15m2 + 7m - 2
8m (2m + 1)
__________
(5m - 1) (3m + 2)
J'(-7, -3) is the image of J after a translation along the vector <-5, 4>. What are the coordinates of J? Choose from the following:
(12,-1)
(-12, 1)
(-2,-7)
(2,7)
The coordinates of J are (-2, -7) , hence the correct option is C.
What is translation?
A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.The translated forms (or the image) seem to be an equivalent size because the original shape, indicating that they're congruent. They’ve merely shifted in one or additional directions.
Main body:
Given that, J’(-7, -3) is the image of J after translation (x, y) → (x - 5, y + 4)
We have, x-5 = -7
x = -2
And, y+4 = -3
y = -7
Hence, We get the coordinates of J are (-2, -7).
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if the sides of a square are increasing at a rate of 3 in/sec, at what rate is the area increasing when the edges are 10 in?
Answer:
Below
Step-by-step explanation:
Square area = s^2
ds/dt = 3
Area = s^2 Find the derivative with respect to t of both sides
area/dt = 2s ds/dt
= 2 (10)(3) = 60 in^2 per sec
for how many values of xx in the closed interval [1,11][1,11] does the instantaneous rate of change of ff at xx equal the average rate of change of ff over that interval?
The average rate of change of a function is said to be a measure of how much the function changed per unit The average rate of change is -100/11
The average rate of change of a function is said to be a measure of how much the function changed per unit, on average, over that interval. It is also said to be derived from the slope of the straight line connecting the interval's endpoints on the function's graph
f(x) over an interval [x1,x2] is given by:
average rate of change = change in y/change in x
= f(x2) − f(x1) / x2−x1
With f(x) = 1/x over [1, 11]
average rate of change = f(11) − f(1) / 11−1
average rate of change = (1/11 − 1) / 10
average rate of change = (−10/11 / 10
average rate of change = −100/11
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lana elf measured the width of 9 xmas presents the total width of all the presents was 135 inches if the presents were the same width ow wide was each present if all presents had different widths what is one possiility for the widths of 9 presents
15 inches is the width of each present.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Lana elf measured the width of 9 Christmas presents.
The total width of all the presents was 135 inches.
If the presents were all the same width then we need to find the width of each present.
w=width.
As given, 9w=135
Divide both sides by 9
w=135/9
w=15
Hence, 15 inches is the width of each present.
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the extent to which a reesearcher's sample is representative of the population that it was drawn from is called
The extent to which the researcher can refer that findings with a sample from which it was drawn is referred to as generalizability.
Generalizability refers to the ability to extrapolate study findings from a sample to the entire population. It also refers to the capacity to apply findings from one study to a similar environment in a different investigation.
Generalizability and transferability are two research traits that are related. When considering generalizability in research, there are two features or dimensions to consider: generalizability as it relates to the specific population on which the research is conducted, and generalizability on a global scale.
Such studies will be easier to generalize if the researcher uses adequate sampling approaches, sample sizes, and exact processes.
In general, a study has strong generalizability when the findings apply to a wide range of persons or situations. The study has weak generalizability if the results can only be applied to a subset of the population or in a very specific circumstance.
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tonya and jill each opened savings accounts. tonya started with $60 and deposited $20 each month. jill started with $20 and deposited $40 each month. if they continue to make deposits at the same rate, when will they have the same amount of money
The month they would have the same amount of money is 2 months.
When would they have the same amount of money?The linear equation that can be used to represent the total amount of money saved by each person is
Total amount saved = amount started with + (amount deposited per month x number of months)
Amount saved by Tonya = $60 + $20m
Amount saved by Jull = $20 + $40m
When they save the same amount of money, the two two above equations would be equal:
60 + 20m = 20 + 40m
In order to determine the value of m, take the following steps:
60 - 20 = 40m - 20m
40 = 20m
m = 40 / 20
m = 2
Substitute for m in the equation that represents the total amount of money saved by Tonya:
$60 + $20(2)
$60 + $40 = $100
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-10.5 + m/ 11.57 = -2.748
Solve for M
Answer: 89.69
Step-by-step explanation:
-10.5 + m/ 11.57 = -2.748
First, we add 10.5 on both sides
m/ 11.57 = 7.752
Then we multiply both sides by 11.57
m = 89.69064, or we can simplify it be 89.69
Use Descartes' Rule of Signs to identify the number of positive real roots and negative real roots for the polynomial function.
P(x)=xthree+5x2-3x+7 PLS HELP ME ILL MARK YOU BRAINLIEST 20 POINTS
Answer:
the number of positive real roots is one
the number of negative real roots is one
I not sure I was right
Step-by-step explanation:
[tex]x^{3} +5x^{2} -3x+7[/tex]
it changed the sign in the second to the third term，so,it was one root
[tex]-x^{3} +5x^{2} +3x+7[/tex]
Change the coefficients of odd items, and the signs of the first to second items change, so there is also a root.
Answer:
Maximum of 2 positive real rootsExactly 1 negative real rootStep-by-step explanation:
Descartes' Rule of Signs tells us the maximum number of positive and negative real roots in a polynomial function.
Positive root case
[tex]\begin{aligned}p(x)&=(x)^3+5(x)^2-3(x)+7\\ &=+x^3+5x^2-3x+7\end{aligned}[/tex]
Check the signs of the coefficients. As there are 2 sign changes, the maximum possible number of positive roots is 2.
However, as some pairs of roots may be complex, count down by two's to find the complete list of the possible number of roots.
So there may be as many as 2 real roots or there might also be no real roots (zero).
Negative root case
[tex]\begin{aligned}p(-x)&=(-x)^3+5(-x)^2-3(-x)+7\\&=-x^3+5x^2+3x+7\end{aligned}[/tex]
Check the signs of the coefficients. As there is one sign change, the maximum possible number of negative roots is 1. We can't count down by two's since this would give us a negative number. Therefore, there is exactly 1 negative root.
Note: There is one real negative root of the given function at x ≈ -5.74 and two complex roots at x = 0.37 + 1.04i and x = 0.37 - 1.04i.
5/6x-4=-2 PLease help thanks so much i hope yall have a good day
The value of x would be [tex]x=\frac{12}{5}[/tex].
What is Calculus?Calculus is a branch of mathematics that focuses on the study of change, or the rate of change of a given function. It involves the use of derivatives, integrals, and limits to solve problems in physics, engineering, economics, and other sciences. Calculus is used to describe the behavior of objects under changing conditions, such as velocity, acceleration, and force. It is also used to optimize systems and to solve equations involving functions of several variables. Calculus provides a powerful tool for analyzing and understanding the physical world.
[tex]\frac{5}{6} x-4=-2[/tex]
Now, combining [tex]\frac{5}{6}[/tex] and x we get
[tex]\frac{5x}{6} -4=-2[/tex]
So,
[tex]\frac{5x}{6} -4=-2\\\\\frac{5x}{6} =2\\\\x=\frac{12}{5}[/tex]
Hence, [tex]x=\frac{12}{5}[/tex].
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2. A computer technician charges
$75 for a consultation plus $35
per hour
Answer: y = 35x + 75
Step-by-step explanation:
Let x be the number of hours and y is the total cost
We will have the equation
y = 35x + 75
-3(2x - 4) = 18 help pleaseee
Answer:
x=−1Step-by-step explanation:
Steps for Solving Linear Equation
−3(2x−4)=18
Divide both sides by −3.
2x−4=
−3
18
Divide 18 by −3 to get −6.
2x−4=−6
Add 4 to both sides.
2x=−6+4
Add −6 and 4 to get −2.
2x=−2
Divide both sides by 2.
x=
2
−2
Divide −2 by 2 to get −1.
x=−1
Answer:
x= -1
Step-by-step explanation:
-3x (2x-4) 18
Distribute
-6x + 12 = 18
Subtract
-6x + 12-12 = 18 - 12
Simplify
-6x = 6
Divide
-6x/-6 = 6/-6
Simplify
x= -1
6d+5/1/3 Tell how many terms the expression has
Answer:
2 terms
Step-by-step explanation:
An algebraic expression may be composed of one or more terms. A term of an expression may be a constant, a variable, a product of more than two variables (xy), or a product of a variable and a constant.
Amy wants to save 500 to buy a TV. She saves each week. The amount, A (in dollars), that she still needs after W weeks is given by the following function . A(W)=500-19W Answer the following questions. (a) If Amy still needs 177 , how many weeks has she been saving?
Answer:
A(W)=500-19W
177W = 500 - 19W
177W + 19W = 500
196W = 500
W = 2.5
Therefore, Amny needs to save for 2.5 weeks
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The cable company has yearly projections for an increase in the cost of cable a customer must pay. The monthly increase is represented by x^2-16x+64=0x2
−16x+64=0, where x is the amount of increase in dollars per month. What will be the monthly increase for all of the cable customers?
The amount of monthly increase will be 8$
What is Quadratic Equation?
Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. x is an unknown variable, whereas a, b, and c are numerical coefficients.
Solution:
Given Equation is x² - 16x + 64 = 0
Using the formula method we will first find the discriminant
D = b² - 4ac
D = 256 - 256 = 0
x = -b +- √D / 2a
x = 16/2 = 8
x = 8
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I need help at math
Answer:
I) 70°
II) 120°
Step-by-step explanation:
In a regular polygon the sum of all its internal angles is equal to
180° × (n – 2)
where:
n = number of sides of the polygon
Urgent!!! Help guysss
Answer:
mandatory pay raises
Step-by-step explanation:
m/STM = 31x - 3
m/MTU = 20x + 5
m/STU = 155 degrees
Find m/MTU.
The Angle ∠MTU from the figure is 65°
What are Angles?The study of shapes and their measurements falls under the umbrella of geometry, a subfield of mathematics. It also emphasizes how the shapes are arranged in relation to one another and their spatial characteristics. We are aware that geometry is divided into 2D and 3D categories. All geometrical shapes are first created by the intersection of points, lines, rays, and plane surfaces. The distance measured between two lines is referred to as a "Angle" when the rays or lines converge at a single point.
Calculation:Given,
∠STM=31X-3;
∠MTU=20X+5;
∠STU=155°;
From the figure we can say that
∠STU= ∠STM+∠MTU;
⇒ 155=31x-3+20x+5;
⇒155=51x+2;
⇒x=3;
Now substitute x in ∠MTU;
⇒∠MTU=20(3)+5=65°
The Angle ∠MTU from the figure is 65°
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Marc wrote down a 5 digit number on a piece of paper. The number when rounded off to the nearest thousand was 12 000. What was the greatest possible number that he wrote?
Answer:
12499
Step-by-step explanation:
because if it would be 12500 it would round up to 13000.
Solve this equation. -108 = 6x for x
Answer: x = 18
Step-by-step explanation: If you do 108 divided by 6, you get 18.
I'm not sure whether this is what you wanted for an answer, but here.
Answer:
[tex] \sf \: x = - 18[/tex]
Step-by-step explanation:
Given equation,
→ -108 = 6x
Now the value of x will be,
→ -108 = 6x
→ 6x = -108
→ x = -108/6
→ [ x = -18 ]
Hence, the value of x is -18.
A shipping container will be used to
transport several 150-kilogram crates
across the country by rail. The greatest
weight that can be loaded into the
container is 27500 kilograms. Other
shipments weighing 6800 kilograms have
already been loaded into the container.
Write and solve an inequality which can
be used to determine x, the number of
150-kilogram crates that can be loaded
into the shipping container.
Answer:
x=138
Step-by-step explanation:
The question is a high school Mathematics problem. It involves using inequalities to solve a practical problem about a shipping container's weight limit. The answer found was that a maximum of 138 crates can be added to the container.
Explanation:In this Mathematics problem, we have a shipping container that can hold a maximum weight of 27500 kilograms and there are already shipments totaling 6800 kilograms inside. We want to find out how many 150-kilogram crates (let's call this number 'x') can be added to the container without exceeding the maximum allowable weight.
Firstly, we build an inequality. The total weight of the container should not exceed 27500 kilograms, so we have:
6800 (the weight of the already loaded shipments) + 150*x (the weight of the x crates) ≤ 27500
This simplifies to:
150*x ≤ 20700 (because 27500-6800=20700)
Finally, to solve the inequality for 'x', divide throughout by 150:
x ≤ 138 (because 20700/150=138)
So, 138 is the maximum number of 150-kilogram crates that can be loaded into the shipping container without violating the weight constraint.
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Each nack cot $0. 75 , and the amount wa charged to Dave’ account. What amount hould be on Dave’ account for nack lat month?
If Dave bought 5 packs of snacks, then the amount on Dave's account for snack last month should be $3.75.
Dave purchased 5 packs of snacks last month and the cost of each pack was $0.75. The total cost of the snacks was charged to Dave's account, so his account balance should reflect the total cost of the snacks. In this case, Dave purchased 5 packs of snacks, so the total cost would be $3.75 ($0.75 x 5). Therefore, Dave's account balance should show $3.75 for the snack purchases last month. This amount is the sum of the individual cost of each snack pack, multiplied by the number of packs Dave purchased. In this case, the amount on Dave's account for snack last month should be $3.75.
5 packs of snacks x $0.75 = $3.75
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What is the biggest misconception about you?*
I do not have any information about you or your beliefs, experiences, or actions.. I do not have the ability to make judgments or assumptions about you or any other individual, you should provide more context as well as fix the category your question is listed under, you might have better results.
Theresa is making accessories for the soccer team. She uses 759.56 inches of fabric on headbands for 31 players and 3 coaches. She also uses 267.53 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
The amount of fabric used on a headband and wristband for each player is $30.97.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
As per the given,
She uses 759.56 inches of fabric on headbands for 31 players and 3 coaches.
Per person = 759.56/(31 + 3) = $22.34
As per the given,
267.53 inches of fabric on wristbands for just the players.
Per player = 267.53/31 = $8.63
Total material of per player = $22.34 + $8.63
⇒ $30.97
Hence "Each player's wristband and headband cost $30.97 worth of cloth".
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Which of the following is not a criteria for the construction of triangle Class 7?
a)SSS
b) SAS
c) ASA
d) SSA
Answer:
D. SSA
Step-by-step explanation:
SSA doesn't work because it can produce 2 different triangles that wouldn't be congruent. The angle of the 3rd side without restriction could change, changing the size of the figure. The image attached can help you understand this.
a segmented bar chart was created showing the lunch preference by grade. what percent would the bar for 11th graders show for preferring hotdogs?
If the 11th graders prefer hotdogs at a rate of 70%, the bar for 11th graders would show 70% percentage.
A segmented bar chart is a graphical representation of data that is divided into different segments. It is typically used to compare different categories of data. In this case, the bar chart is used to compare the lunch preference of different grades. The bar for 11th graders would show the percentage of 11th graders who prefer hotdogs. If 70% percentage of 11th graders prefer hotdogs, then the bar for 11th graders would show 70%. The bar chart can also show the percentage of 11th graders who prefer other lunch options, such as sandwiches, salads, etc. This information can help school administrators to better understand the lunch preferences of their students and make informed decisions about what types of food to serve for school lunch.
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