Answer:
Step-by-step explanation:
The population of bacteria in the culture after 7 hours is approximately 883.
What is an exponential function?Several real-world phenomena, including population expansion, radioactive decay, compound interest, and the spread of diseases, are modeled using exponential functions. In calculus, where they are used to define the exponential and logarithmic functions—essential ideas in calculus and other fields of mathematics—they also play a significant role.
Using the formula [tex]P_t = P_0 \times 2^{\frac{t}{d}}[/tex], where P_t is the population after t hours, P₀ is the initial population, t is the time in hours and d is the doubling time, we can find the population of bacteria in the culture after 7 hours as follows:
Since the initial population is 470, we have P₀ = 470.
The doubling time is 8 hours, so we have d = 8.
Substituting these values into the formula, we get:
[tex]P_7 = 470 \times 2^{\frac{7}{8}}[/tex]
P₇≈ 882.77
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A line that includes the points ( – 8,9) and ( – 10,d) has a slope of 6. What is the value of d?
Answer:
The value of d is -3.
Step-by-step explanation:
We are given that a line that includes the two points (-8, 9) and (-10, d) have a slope of 6. We want to determine the value of d.
Recall that the formula for slope is:
[tex]\displaystyle m = \frac{\Delta y}{\Delta x}[/tex]
We know that the slope is 6. Substitute:
[tex]\displaystyle (6) = \frac{(d) - (9) }{(-10) - (-8)}[/tex]
Solve for d:
[tex]\displaystyle \begin{aligned} 6 & = \frac{d - 9}{-10 + 8} \\ \\ 6 & = \frac{d - 9}{-2} \\ \\ -12 & = d - 9 \\ \\ d & = -3 \end{aligned}[/tex]
In conclusion, the value of d is -3.
Simplify 5a×3×2b
Write down the answer, please.
[tex]5a \times 3 \times 2b \\ = (5 \times 3 \times 2)ab \\ = 30ab[/tex]
Answer:30 ab
Hope it helps
ray4918 here to help
Answer:
30ab
Step-by-step explanation:
Given expression,
→ 5a × 3 × 2b
Simplifying the expression,
→ 5a × 3 × 2b
→ (5 × 3)a × 2b
→ 15a × 2b
→ (15 × 2)ab
→ 30ab
Hence, the answer is 30ab.
30/40 in simple form
Answer:
The simplest form is 3/4
Step-by-step explanation:
Cancel the common factor of 30 and 40
Write the Fraction in Simplest Form Of 30/40
Area and perimeter for this rectangle
Answer:
perimeter = (8x + 3mm + 5mm) ×2
area = (8x + 3mm) × 5mm
Answer:
Perimeter: 48mm
Area: 95mm
Step-by-step explanation:
Perimeter=2(l+w)
2((8x+3)+5)
-8x=2(3+5)
-8x=2(8)
-8x=16
x=2
2((8(2)+3)+5)= 48
So the perimeter is 48mm
Area=wl
l=19mm
w=5mm
19*5=95mm
So the area is 95mm
I need to find y and z
for y-
24
45
27
135
for z-
135
98
82
90
Answer:
y = 27°z = 98°Step-by-step explanation:
The interior angle marked 5y is the supplement of the adjacent exterior angle marked 45°.
5y + 45° = 180°
5y = 135° . . . . . . . . subtract 45
y = 27° . . . . . . . . divide by 5
__
The sum of the interior angles of a pentagon is (5-2)(180°) = 540°.
90° +5y +z +82° +135° = 540°
Using y=27°, we can subtract 442° from both sides to get ...
z = 98°
_____
Additional comment
You might recognize that the downward-sloping diagonal sides of the figure are parallel, so z and 82° are consecutive interior angles, hence supplementary. This fact means you don't have to be concerned with the other three angles in the figure to find the value of z: 180° -82° = 98°.
5/7×0.25 equals 5/7÷ What to make the equation right?
4
Step-by-step explanation:
5/7 × 0.25 = 5/7 ÷ a
25/100 = 1/a
25a = 100
a = 100/25
a = 4
Given the function y = (x - 2)2 graphed below, which restriction of the domain will result in
the inverse being a function?
VIEW IMAGE FOR GRAPH!
A: y = (x - 2)^2 , x ≥ 1
B: y = (x - 2)^2 , x ≥ 2
C: y = (x - 2)^2 , x ≥ 0
D: y = (x - 2)^2 , x ≥ -2
The restriction of the domain of the function will be y = (x - 2)², x ≥ 2. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
Then the parabolic function is given below.
y = (x - 2)²
The restriction of the domain will result in the inverse being a function given as,
x - 2 ≥ 0
x ≥ 2
The restriction of the domain of the function will be y = (x - 2)², x ≥ 2. Then the correct option is B.
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please someone answer with an explanation if possible!
Answer:
download gauth math and scan it and will give u the answer
Answer:
C
Step-by-step explanation:
The y intercept is where the line first crosses the y axis, so it would be positive 2. The slope is negative because it's diagonally going the left way, and its 3 because from one point to another it's 3 down and 1. The formula for a slope is rise/run, in this case it would be 3/1 which is 3.
he total cost of 5 doughnuts and 6 cookies at a bakery is $11.95. The cost of each cookie is $0.95.
Select the equation and its solution that can be used to determine the cost, x, of 1 doughnut.
Answer:
x=1.25
Step-by-step explanation:
Answer:
($0.95 * 6) + (5x) = $11.95
The cost of one donut (x) = $1.25
Step-by-step explanation:
I hope this helps!
What is the image point of (9, -1) after the transformation T-4,-3 0 R270°?
Answer:
Given A point (9,-1) is first translated by rule T-4,3 : ( x,y ) goes ( x - 4 , y+ 3) followed by rotation of 270°
rule of rotation of 270° : ( x , y ) goes ( y,-x )
image of ( 9 , -1) after translation :
( 9 - 1) goes (-9,-1+3)=(-9,2)
then , image after rotation of 270° :
( -9,2 ) goes (2,9 p
hence , the image point of ( 9,-1 ) (9,-1)
after the transformation T-4,3 and rotation of 270°i is ( 2,9 ).
Step-by-step explanation:
hope it helps
PLEASE HELP!! Only answer if correct.
Answer:
top -55
bottom 325
Step-by-step explanation:
Simplify 10/16 to lowest terms and find and equivalent fraction that has a denominator of 32
The lowest terms of fraction are, 5/8
And, The equivalent fraction that has a denominator of 32 is,
⇒ 20 / 32
We have to given that,
To simplify fraction 10/16 to lowest terms and equivalent fraction that has a denominator of 32.
We have,
⇒ 10 / 16
⇒ 10 ÷ 2 / 16 ÷ 2
⇒ 5 / 8
Therefore, The lowest terms of fraction are, 5/8
And, Let the numerator of the fraction with denominator 32 is, x
Hence, It can be written as,
⇒ x / 32
Equivalent to 10/16,
⇒ 10/16 = x/32
⇒ 32 x 10 = 16x
⇒ 320 = 16x
⇒ x = 20
Therefore, The equivalent fraction that has a denominator of 32 is,
⇒ 20 / 32
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Which division problem is modeled in the image? A) 2 ÷ 6 = 3 B) 2 ÷ 3 = 6 C) 3 ÷ 2 = 6 D) 6 ÷ 3 = 2 the image has 3 circles an 2 stars in each circle
Answer:
b
Step-by-step explanation:
Answer:
its b
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue
graph?
GO) = ?
6
F(x) = x2
5
-5
G(x) =
A. G(X) = (x - 1)
B. G(X) = x2 + 1
C. G(x) = x2 - 1
D. G(X) = (x + 1)2
100 points !!!!
Answer:
D
Step-by-step explanation:
The graph G(x) is moved to the left by 1.
So it would be G(x) = (x+1)^2
The equation of the blue graph is,
⇒ g (x) = (x + 1)²
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The equation of the red graph is,
⇒ f (x) = (x)²
Since, The blue graph is shift 1 unit from red graph.
Hence, The equation of the blue graph is,
⇒ g (x) = (x + 1)²
Thus, The equation of the blue graph is,
⇒ g (x) = (x + 1)²
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One yard company charges $10x + $50 a month to mow and edge a lawn. A second company charges $8x + $60 a month to mow and edge a lawn. Each lawn company also offers additional services for an extra fee.
Let x represent the number of additional services.
Mr. Mead is comparing the two companies. How many additional services are needed for the two companies to be the same price?
I’m too lazy to do it
Answer: x=5
Step-by-step explanation:
What is the slope from a graph:
Rise/run = slope
hope this helps :)
Evaluate a1 (r)^n-1 for a1 = 2, r= 3, and n = 4.
A. 216
B. 18
C. 32
D. 54
Answer:
[tex]54[/tex]
Answer D is correct
Step-by-step explanation:
[tex]a_1 \: {r}^{n - 1} \\ 2 \times {3}^{4 - 1} \\ 2 \times {3}^{3} \\ 2 \times 3 \times 3 \times 3 \\ 2 \times 9 \times 3 \\ 2 \times 27 \\ = 54[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
=
angle E and angle F are supplementary. If mangleF =
(9x - 38)° and mangleF = (2x + 42), find mangleF
=
Answer:
jhhffffffffffffffffffffhfbrsjjssssssssssss
Step-by-step explanation:
Please help me I need to pass
Write the measure in degrees (pi)/4
Let's see
[tex]\\ \rm\longmapsto \pi/4[/tex]
[tex]\\ \rm\longmapsto \dfrac{\pi}{4}\times \dfrac{180}{\pi}[/tex]
[tex]\\ \rm\longmapsto \dfrac{180}{4}[/tex]
[tex]\\ \rm\longmapsto 45°[/tex]
The solution is: the measure in degrees (pi)/4 is 45°.
Here, we have,
given that,
we have to find the measure in degrees (pi)/4.
now, we know that,
Measure of an Angle in Degrees = 180°
Measure of an Angle in Radians is:
180° × (π/180°) = π = 3.14 Rad
so, we have,
π/4
= π/4 × (180°/π)
=180 /4
=45°
Hence, the measure in degrees (pi)/4 is 45°.
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1
2
3
4
5
10
50
Which function has an inverse that is a function?
Ob(x) = x2 + 3
Od(x) = -9
Om(x) = -7x
O p(x) = 1x1
Which function has an inverse that is a function?
Step-by-step explanation:
an equation is a function, if it delivers for every possible input value x exactly one result value y.
b(x) = y = x² + 3
y - 3 = x²
x = sqrt(y -3)
our formally correct
y = sqrt(x - 3)
that is actually NOT a function, as a square root delivers for most x values 2 y values : a positive and a negative value.
d(x) = -9
that means for every possible value of x the result is -9.
reversing this means that the input value of -9 has infinitely many possible results
that is NOT a function.
m(x) = y = -7x
x = -y/7
or formally correct
y = -x/7
that is a normal function. every possible value of x leads to exactly one value of y.
p(x) = y = 1x¹ = x
y = x is its own inverse function.
and this is, of course, a function. every possible value of x leads to exactly one value of y.
how long does a pregnancy last will give 100 points I'm in test
a 1day
b 1mounth
c 2weeks
d 1year
Answer: D is the answer
Step-by-step explanation:
And why are you asking this question? Are you a girl?
I need help I never got taught how to do this
Answer:
736cm²
Step-by-step explanation:
The surface area of a regular pyramid is equal to:
area of the square base + 1/2ps
where p is the perimeter of the base and
s is the height of the slant line of the pyramid.
In your drawing s = 15cm and the base has four equal lengths of 16cm
So first find the area of the base. Since this is a square, the area is just the
length x the width or 16cm x 16cm = 256cm²
(p) is the perimeter of the base. Find this by adding all four side of the bottom square together which is 16cm + 16cm + 16cm + 16cm or 4 x 16cm which is 64cm.
You already were given (s) which is the height of the slanted side from the base to the pointed top. The drawing gives you this as 15cm.
So plugging all this into the formula, you get:
Surface Area = Area of Base + 1/2 p s
= 256 cm² + [1/2 ( 64cm )(15cm)]
= 256 cm² + {1/2 ( 960 cm²)]
= 256 cm² + 480 cm²
= 736 cm²
1+1 ASAP PLEASE. Marking Brainliest.
Answer:
2...
Step-by-step explanation:
1 + 1 = 2
Solve for z:
32=12+4(z-1)
Answer:
6
Step-by-step explanation:
32 = 12 + 4 ( z - 1 )
32 - 12 = 4 ( z - 1 )
20 = 4 ( z - 1 )
20 / 4 = z - 1
5 = z - 1
z - 1 = 5
z = 5 + 1
z = 6
whats the greateats hundreds you can multiply by 6 to get close to but not go over 3236
Answer:
100
Step-by-step explanation:
6×100=600
600 might not be that much close to 3236 but it's not over 3236
Ken used 3/4 of his wrapping paper. If he used 12 feet how much wrapping paper did he use
Answer: If Ken used 12 feet of wrapping paper, 3/4 then he would have had 16 ft of wrapping paper before he started wrapping
Step-by-step explanation:
12 divided by 3 is 4 giving us the equation 4/4 equals 4 x 4
To Baker’s plus their contents have a mass of 180.4 g the total mass of the contents is 56.8 g each Baker has the same mess right and solve an equation to find the mass of one bigger
please help me asap and show your work
Answer:
A) = 5
B) = 3
C) = [tex]2\sqrt{3}[/tex]
D) = 2.2894
Step-by-step explanation:
A) [tex]x^2=25[/tex]
[tex]\sqrt{x^2} = \sqrt{25} \\x= 5[/tex]
5*5 = 25
B) [tex]x^3 = 27[/tex]
[tex]\sqrt[3]{x^3} = \sqrt[3]{27} \\x=3[/tex]
3*3*3 = 27
C) [tex]x^2 = 12\\[/tex]
[tex]\sqrt{x^2} = \sqrt{12} \\x=2\sqrt{3} \\[/tex]
[tex]2\sqrt{3}[/tex] * [tex]2\sqrt{3}[/tex] = 12
D) [tex]x^3 = 12[/tex]
[tex]\sqrt[3]{x^3} = \sqrt[3]{12} \\x=2.2894.....\\[/tex]
2.2894 * 2.2894 *2.2894 = 12
No exact solution
if i sell 329 ham sandwiches this week how many ham sandwiches did i sell each day this week.
Answer:
you would have sold 47 ham sandwiches each day of the weed
Answer:
Your answer would be 47 ham sandwiches.
Step-by-step explanation:
It is very simple you would just do 329/7=47