.A bacteria culture grows at a rate of 20%
per minute. If the culture initially has 3,200
bacteria specimens, how many specimens
would be in the culture after 5 minutes?
The number of the specimens would be in the culture after 5 minutes will be 7,962.62.
What is an exponent?Consider the function:
y = a (1 + r) ˣ
Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.
A bacteria culture grows at a rate of 20% per minute.
If the culture initially has 3,200 bacteria specimens.
Then the equation will be
y = 3200 (1 + 0.2) ˣ
y = 3200 (1.20) ˣ
Then the number of the specimens would be in the culture after 5 minutes will be
y = 3200 (1.20)⁵
y = 7962.62
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What is the solution to the following system of equations? (1 point)
x − 3y = 5
2x + y = 10
(5, 0)
(0, 5)
(7, 0)
(0, 7)
Answer:
Step-by-step explanation:
Which expression is equivalent to
( 4^(1/3) × 4^(2/6) ) ^(3/4)
( ---------÷------------ )
( 4^(5/6) )
*All the numbers in the division problem are in parenthesis with the ^(3/4) on the outside.*
A: (1/4)^(3/66)
B: (1/4)^(-3/66)
C:(1/4)^(-1/11)
D: (1/4)^(1/11)
The simplified form of the expression is [tex]4^{-1/3}[/tex]
Indices and exponentsGiven the indices expression as shown;
[tex]\frac{(4^{1/3}\times 4^{2/6} )^{3/4}}{4^{5/6}}[/tex]
Applying the product and quotient law of indices
[tex]\frac{(4^{1/3+1/3})^{3/4}}{4^{5/6}}\\\frac{(4^{2/3})^{3/4}}{4^{5/6}}\\\frac{4^{1/2}}{4^{5/6}}\\[/tex]
Take the difference in the power to have:
4^(1/2 - 5/6)
4^(-2/6)
[tex]4^{-1/3}[/tex]
Hence the simplified form of the expression is [tex]4^{-1/3}[/tex]
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PLEASE HELP!!!!!! i will give brainiest!
Answer:
[tex]\sf B) \ y=-\dfrac{1}{5}x-4[/tex]
Explanation:
Equation: y = mx + b [where "m" is slope, "b" is y-intercept]
The y-intercept (b) is -4
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here take two points: (0, -4), (5, -5)
[tex]\sf slope \ (m) : \dfrac{-5-(-4)}{5-0} = -\dfrac{1}{5}[/tex]
[tex]\sf Hence \ equation : y = -\dfrac{1}{5} x -4[/tex]
What is the equation of a sine function with an amplitude of 2 and a period of 4π?
y = one-half sine (2 x)
y = one-half sine (4 pi x)
y = 2 sine (one-half x)
y = 2 sine (4 pi x)
The general equation
y=Asin(Bx)B is period and A is amplitude
A=2RearrAnge
y=2sinBxPeriod:-
2π/4π2/41/2So final equation
y=2sin(1/2x)Option C
what two numbers mutiples by -36 and adds to 5
Answer:
+ 9 and - 4
Step-by-step explanation:
9 × - 4 = - 36
9 + (- 4) = 9 - 4 = 5
Answer:
The two numbers are :
9 and -4
9 x -4 = -36
9 + (-4) = 5
Step-by-step explanation:
Hope It Helps!!!
Brian is drawing a scale diagram of a building. for every 10 m of the building he draws a line 5 cm long. Bryn thinks he is using a ratio of 2:1. Alun thinks Bryn is using a ratio of 200:1, is either of them correct? explain your answer
Answer:
200:1, Bryn is correct.
Step-by-step explanation:
Each 10 m is represented by a 5cm length on the diagram. We first note that 100 cm = 1 meter. 5 cm is (0.5 cm)*(1 meter/100 cm) =0.05 meters.
The 0.05 meters on the diagram represents 10 meters on the actual building. The ratio is (10 meters/0.05 meters) or 200:1. This is what Bryn believes is the ratio.
If m < 0 and b > 0, the graph of y = mx + b does not pass through which quadrant?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer: Quadrant III
Step-by-step explanation:
The slope is negative and the y-intercept is positive.
This means that it is impossible for both x and y to be negative, and thus it does not pass through Quadrant III
A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours
there will be 800 bacteria.
The population after t hours is 160 x (1.3797)^t.
What is the population after t hours?The first step is to determine the growth rate of the bacteria:
growth rate = (future population / initial population) ^(1/number of years) - 1
(800 / 160)^(1/5) - 1= 37.97
The exponential function : 160 x (1.3797)^t
Here is the complete question:
A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours
there will be 800 bacteria. Express the population after t hours as a function of t. population:
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what is the x intercept of the function
Step-by-step explanation:
0 = sqrt(x - 4) + 3 Set equation equal to 0
-3 = sqrt(x - 4). Subtract 3 from both sides
the principle square root will only output positive values, since if it every outputted a negative value it would not be a function since a function cannot have 2 outputs for the same input.
no x-intercept
What is the slope of the line that passes through the points (8,-8) and (5,-1)?
Hey there!
Answer :[tex] \sf{ \purple{ \boxed{\bold{m = - \dfrac{7}{3} }}}} [/tex]
[tex] \\ [/tex]
Explanation :We are given the points [tex] \sf{P_1(\overbrace{ \blue{8}}^{\blue{x_1}} ,\underbrace{\orange{-8}}_{ \orange{y_1}}) \: and \: P_2(\overbrace{ \green{5}}^{\green{x_2}} ,\underbrace{\red{-1}}_{\red{y_2} })} [/tex] . To find the slope [tex] \sf{\purple{m}} [/tex] of such a line, we use the slope formula which is the following:
[tex] \sf{ \purple{m} }= \dfrac{\Delta y}{\Delta x} = \dfrac{ \red{y_2} - \orange{y_1}}{ \green{x_2 }- \blue{x_1}} [/tex]
[tex] \\ [/tex]
⇢Now, by plugging in our values, we get :
[tex] \sf{ \purple{m}} = \dfrac{ \red{ - 1} - \orange{( - 8)}}{ \green{5} \: - \: \blue{8}} = \dfrac{ \: \: 7 \: }{ - 3 \: } \\ \\ \implies \sf{ \purple{ \boxed{m = - \dfrac{7}{3} }}}[/tex]
Therefore, the slope of the line is [tex] \sf{ \purple{ \boxed{m = - \dfrac{7}{3} }}} [/tex]
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the slope of a linear function that goes through (8,-8) and (5,-1)?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Formula utilised, here [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].
We utilise that formula because we have two points as our given information.
So, we
put in the values
[tex]\bf{\dfrac{-1-(-8)}{5-8}}[/tex] | subtract on top and bottom
[tex]\bf{\dfrac{-1+8}{-3}}[/tex] | simplify
[tex]\bf{\dfrac{7}{-3}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope=-\dfrac{7}{3}}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]
Please help me with this ASAP.
Kiran’s mother gets a restaurant bill for $25. She has a coupon for 15% off. After the discount is applied, she adds 20% as a tip.
What is the total after the discount and tip? Explain or show your reasoning.
Answer:
See below for both parts
Step-by-step explanation:
A)
Coupon Price:
$25 - 15% ($3.75) = $21.25
10% = 2.50
5% = 1.25
After taking the discount coupon off the final price is $21.25
B)
20% is given as a tip.
20% of $21.25 = $4.25
10% = 2.125
$21.25 + $4.25 = $25.50
Final price with tip is $25.50
The davidson family wants to expand its rectangular patio, which currently measures 15 ft by 12 ft. they want to extend the length and width the same amount to increase the total area of the patio by 160 ft2. which quadratic equation best models the situation? a = lw (15)(12) (x)(x) = (15)(12) 160 (15x)(12x) = (15)(12) 160 2(15 x) 2(12 x) = (15)(12) 160 (15 x)(12 x) = (15)(12) 160
Answer:
160
Step-Step Explaining:
So I Know This ⏩ ⏩
A grocery store had 38 employees but then they hired 4 more people. What is the percent change in their staff?
Answer:
+ 10.53 % change
Step-by-step explanation:
Percent change is 4 more people added to 38
4 / 38 * 100% = 10.53 %
Mike has a large amount of chocolate spheres, each chocolate sphere having a radius of 2 inches.
The value of the expression Z² + Q² is 4321
How to evaluate the expression?The radius of the chocolate spheres is given as:
r = 2
The maximum number of chocolates that can fit in a spherical capsule is calculated as:
Max = R³/r³
Where:
R represents the radius of the sphere.
For the spherical capsule whose radius is 8 inches, we have:
Z = 8³/2³
Evaluate
Z = 64
For the spherical capsule whose radius is 5 inches, we have:
Q = 5³/2³
Evaluate
Q = 15.625
Remove decimal
Q = 15
So, we have:
Z² + Q² = 64² + 15²
Evaluate the exponent
Z² + Q² = 4096 + 225
Evaluate the sum
Z² + Q² = 4321
Hence, the value of Z² + Q² is 4321
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En una clase hay 30 alumnos. Las 3/5 partes son chicas ¿Cuántas chicas hay?
Answer:
18
Step-by-step explanation:
30/5=6
6*3=18
There are 7 pieces of pie left over in the cafeteria. If 4 pieces are apple and 3
are cherry, what fraction of the remaining pieces are apple?
The function f represents the marketing team's expected number of user profiles after x months, when the domain is restricted to all real or hole
The standard equation of user will be y = 625x²+1250x+5000
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
A connection or statement involving one or more variables is called a function.
From the graph we can find following equation:
(0,5000) ----------- 5000 = [tex]\frac{1}{4(f-k)}(0-h)^2 +k[/tex]
(2,10000) ---------- 10000 = [tex]\frac{1}{4(f-k)}(2-h)^2 +k[/tex]
(4,20000) --------- 20000 = [tex]\frac{1}{4(f-k)}(4-h)^2 +k[/tex]
Solving the above three equations we will get following values:
h = -1
k = 4375
f = 10937501/2500
Hence the standard equation of user will be y = 625x²+1250x+5000
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Jithu is curating Christmas hampers for his neighbours.
A minimum of 6 cupcakes are to be included in a hamper box.
If he wants to pack 665 cupcakes evenly into hamper boxes, what could be the smallest number of cupcakes that can be included in one hamper box?
1 hamper box, curated by Jithu can be contained 5 cupcakes.
Calculation:The total amount of cupcakes =665 nos.
Jithu wants to create a gift box, each of which contains 6 cupcakes.
We have to see first, whether 665 could be equally distributed or not.
Hence, 665/6= 110.84 unit
It is seen that the number is in a fraction.so, It can be said that 665 cakes cannot be equally distributed to each gift pack carrying 6 cakes.
Hence, 110*6=660 cupcakes.
∴665-660= 5 cupcakes in one box
So, it is concluded that Jithu could be prepared 110 gift boxes containing 6 cakes each & 1 box containing 5 cupcakes.
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Rearrange x = 3g + 2 to make g the subject.
Answer:
g = [tex]\frac{x-2}{3}[/tex]
Step-by-step explanation:
x = 3g + 2 ( subtract 2 from both sides )
x - 2 = 3g ( divide both sides by 3 )
[tex]\frac{x-2}{3}[/tex] = g
Answer:
g = 1/3x - 2/3Step-by-step explanation:
x =3g + 2
3g + 2 = x
3g = x - 2
g = 1/3 x - 2/3
Answer: g = 1/3x - 2/3
From one vertex of an n-sided polygon 5 different diagonals can be drawn which one of the following pairs of numbers are the number of sides (n) and the sum of measures of all interior angles of this polygon?
The number of diagonals drawn from the vertex of the polygon of n sides is (n−3).
The correct option is C)
⇒ A diagonal is a segment that connects two non-consecutive vertices in a polygon.
⇒ The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides.
What is the polygon?
A polygon is a plane figure enclosed by line segments called sides. Polygon is a 2d shape.
Regular polygons contain equal side lengths.
⇒ Let n be the number sides in the polygon.
⇒ So, the number of diagonals drawn from the vertex of the polygon of n sides is (n−3).
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table shows the travelling time to work of 50 people.
Travelling time (t) in minutes
Frequency
0 < t < 10
5
10 < t < 20
15
20 < t < 30
13
30 < t < 40
10
40 < t < 50
Calculate an estimate of the mean travelling time.
An estimate of the mean travelling time will be 24.8 mins.
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Given;
Time > timemark > frequency
0 – 10 > 10/2 = 5 > 5
10 – 20 > (10+20)/2 = 15 > 15
20 – 30 > (20+30)/2 = 25 > 13
30 – 40 > (30+40)/2 = 35 > 10
40 – 50 > (40+50)/2 = 45 > 7
The mean time for the 50 people can be calculated as;
Mean = Summation of (mid-time x frequency) / total frequency
Mean = [5x5 + 15x15 + 25x13 + 35x10 + 45x7] / 50
Mean = [25 + 225 + 325 + 350 + 315] / 50
Mean = 1240 / 50
Mean = 24.8 mins
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Find (f + g)(x).
(f + g)(x) =
The value of (f + g)(x) is 2x + 8
Complete questionLet f(x) = 4x + 3 and g(x) = -2x + 5.
Find (f + g)(x).
How to evaluate the composite function?The functions are given as:
f(x) = 4x + 3
g(x) = -2x + 5
The composite function (f + g)(x) is calculated using
(f + g)(x) = f(x) + g(x)
Substitute known values
(f + g)(x)= 4x + 3 - 2x + 5
Evaluate the like terms
(f + g)(x)= 2x + 8
Hence, the value of (f + g)(x) is 2x + 8
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Solve the equation.
–3x + 1 + 10x = x + 4
x = x equals StartFraction one-half EndFraction
x = x equals StartFraction 5 Over 6 EndFraction
x = 12
x = 18
Answer:
x = 1/2
Step-by-step explanation:
-3x + 1 + 10x = x + 4 [given]7x + 1 = x + 4 [combine like terms]6x + 1 = 4 [subtract x from both sides]6x = 3 [subtract 1 from both sides]x = 1/2 [divide both sides by 6)Answer:x = 1/2
Step-by-step explanation: Just took the test on EDGE!!
Calcular la altura, h de un arbol sabiendo que, si nos situamos 8 metros de la base del tronco, vemos la parte superior de su copa en un angulo de 36.87*
Utilizando trigonometría, veremos que la altura del arbol es 6m.
¿Como obtener la altura del arbol?
Podemos visualizar la situación como un triangulo rectangulo.
La altura del arbol será el cateto opuesto al angulo de 36.87°.
La distancia a la base del tronco, que es 8 metros, será el cateto adjacente a dicho angulo.
Entonces, podemos usar la relacion:
tan(θ) = (cateto opuesto)/(cateto adjacente).
Reemplazando lo que conocemos, y definiendo:
altura = cateto opuesto = H.
tendremos:
tan(36.87°) = H/8m
Resolviendo para H:
H = tan(36.87°)*8m = 6m
Así, concluimos que la altura del arbol es 6m.
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Which of the following is equal to m
Answer: tan^-1 (c/a)
Step-by-step explanation: An angle C ∈ ℝ such that angle C > 0 can be defined by the trigonometric ratio Arctangent (or rather tan^-1) where side "c" divided by side "a" ≠ 0.
Which statement accurately describes the movement of an object under a translation vector (-3)? The object moves 2 units down and then 3 units The object moves 2 units to the right and then 3 units down. The object moves 2 units up and then 3 units to the left. D. The object moves 2 units to the left and then 3 units up. A. C.
The object moves 2 units to the left and then 3 units up.
Translation of vectorsTranslation is a transformation technique used to change the position of an object on the xy-plane.
Given the translation vector (-2, 3), this translation shows a movement of an object to the left by 2units and 3 units in the upward direction
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students were asked to chose their favorite season if 1/9 of the students chose spring and 3/9 chose summer what fraction chose either spring or summer
Answer:
4/9 of the students chose summer.
Step-by-step explanation:
Think about it this way. There are 9 students being asked what their favorite season is. 1 chose spring, 3 chose summer. Add those together, and you have 4 people that chose either spring or summer. That number goes on top of the fraction. The total amount of people that were asked goes on the bottom, which is 9.
What is the equation if the blue line?
Answer:15
Step-by-step explanation:
Start off using Java. As u progress you cant move over to C and the then transfer to python.
Please help! Multiply the following two numbers in scientific notation.
Answer:
d) 5.88×10^9
Step-by-step explanation:
Answer:
d) 5.88 × 10⁻⁹
Explanation:
[tex]\rightarrow \sf \left(1.2\cdot 10^7\right)\left(4.9\cdot 10^2\right)[/tex]
[tex]\sf apply \ exponent \ rule : a^b + a^c = a^{b + c}[/tex]
[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7}\cdot \:10^{2}[/tex]
[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7+2}[/tex]
[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^9[/tex]
[tex]\rightarrow \sf 5.88 \cdot \:10^9[/tex]
