Answer:
1(2)^x
Step-by-step explanation:
(^x means x is an exponent.)
Since the experiment begins with a single cell, the initial value, A, is 1. The population increases by a factor of 2 every hour, so the growth factor, b, is 2. Substitute the values of A and b in the general form of an exponential expression to create the expression modeling the number of bacteria in the colony after x hours.
A(b)^x=1(2)^x
=2^x
The exponential expression to model the number of bacteria in a colony that begins with a single cell and doubles in size every hour is [tex]1 * 2^{x}[/tex].
What is exponential expression?Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor.
Let number of hours be x hours.
The bacterial count in the dish after x hours of growth is [tex]1 * 2^{x}[/tex].
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Solve each system of equations by substitution. 4y=3x+6 2y=x+8
Answer:
Step-by-step explanation:x=2y-8
4y=3.(2y-8)+6
4y=6y-24+6
4y-6y=-24+6
-2y=-18
Y=9
X=2Y-8
x=2.9-8=10
Dennis walks from (–5, –2) to (–5, 5) on the map. Which expression represents the distance that he walked? |-2| + |5| |-5 + 5| |-2| - |5| |-5| + |-5|
Answer:
|-2| + |5|
Step-by-step explanation:
Dennis walks from (–5, –2) to (–5, 5) on the map.
Point on the format (x,y). On the x-coordinate, he stayed at the same position, x = -5, so it does not enter the distance calculation.
On the y-coordinate, he went from -2 to 5, so the distance is of:
[tex]d = 5 - (-2) = 5 + 2 = |5| + |2| = |5| + |-2| = 7[/tex]
So the correct option is |-2| + |5|
=
SYSTEMS
Solving a value mixture problem using a system of linear...
Somel
A delivery truck is transporting boxes of two sizes: large and small. The combined welght of a large box and a small box is 85 pounds. The truck is transporting
70 large boxes and 50 small boxes. If the truck is carrying a total of 5350 pounds in boxes, how much does each type of box weigh?
9514 1404 393
Answer:
large: 55 lbsmall: 30 lbStep-by-step explanation:
Let x and y represent the weights of the large and small boxes, respectively. The problem statement gives rise to the system of equations ...
x + y = 85 . . . . . combined weight of a large and small box
70x +50y = 5350 . . . . combined weight of 70 large and 50 small boxes
We can subtract 50 times the first equation from the second to find the weight of a large box.
(70x +50y) -50(x +y) = (5350) -50(85)
20x = 1100 . . . . simplify
x = 55 . . . . . . . divide by 20
Using this in the first equation, we can find the weight of a small box.
55 +y = 85
y = 30 . . . . . . . subtract 55
A large box weighs 55 pounds; a small box weighs 30 pounds.
0.7(1.5 + y) = 3.5y - 1.47
Answer:
y = 0.9
Step-by-step explanation:
1.05 + 0.7y = 3.5y - 1.47
-3.5y + 0.7y = -1.47 - 1.05
-2.8y = -2.52
y = 9/10 = 0.9
Answer:
[tex]\textbf{HELLO!!}[/tex]
[tex]0.7\left(1.5+y\right)=3.5y-1.47[/tex]
[tex]1.05+0.7y=3.5y-1.47 \gets \textsl{Expand}[/tex]
[tex]1.05+0.7y-1.05=3.5y-1.47-1.05 \gets Subtract\; 1.05 \from\:both\:sides[/tex]
[tex]0.7y=3.5y-2.52[/tex]
[tex]0.7y-3.5y=3.5y-2.52-3.5y[/tex]
[tex]\mathrm{Subtract\:}3.5y\mathrm{\:from\:both\:sides} \nwarrow[/tex]
[tex]-2.8y=-2.52[/tex]
[tex]\frac{-2.8y}{-2.8}=\frac{-2.52}{-2.8} \hookleftarrow \mathrm{Divide\:both\:sides\:by\:}-2.8[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{y=0.9}}}}}[/tex]
[tex]\bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet[/tex]
[tex]\textbf{HOPE IT HELPS}[/tex]
[tex]\textbf{HAVE A GREAT DAY!!}[/tex]
I need help k please help gardinuhola
Answer:
Step-by-step explanation:
for circle
diameter = 26 cm
radius = diamtere/2
=26/2
=13 cm
area of circle = πr^2
=3.14^13^2
=3.14*169
=530.66 cm^2
=531 cm^2 (after round off )
area of square= l^2
=5.1^2
=26.01 mi^2
are of rectangle = l *b
=6*5.1
=30.6 m^2
area of triangle = base*height / 2
=9*6.4 / 2
=57.6 / 2
=28.8 yd^2
what percentage of the appies are yellow?
Answer:
20%
Step-by-step explanation:
6 out of 30. = 1/5 = multiply 5*20= 100 and 1*20= 100 so it is 20% of 100.
find the radius of this circle.
Answer:
r = 5 units
Step-by-step explanation:
Given:
Angle subtended at the centre (∅) in radians = 2π/3
Arc length (S) = 10π/3
radius (r) = ?
Required:
Radius (r)
Solution:
Formula for arc length given the central angle in radians is:
S = r∅
Make e the subject of the formula by dividing both sides by ∅
S/∅ = r∅/∅
r = S/∅
Plug in the values
r = (10π/3) / (2π/3)
Change the operation sign to multiplication and turn the fraction by your right upside down
r = 10π/3 × 3/2π
r = (10π × 3)/(3 × 2π)
Cross out terms that can divided each other
r = 5
6. Donna adds 400 ml (milliliters) of water to 100 ml of coffee. What percentage of Donna's drink is coffee?
9514 1404 393
Answer:
20%
Step-by-step explanation:
100 mL of the drink is coffee
The total amount of drink is 100 mL +400 mL = 500 mL. Then the fraction that is coffee is ...
coffee/total = (100 mL)/(500 mL) = 1/5 = 1/5 × 100% = 20%
20% of Donna's drink is coffee.
Tom went to bed at 8.30 pm and woke up at 6.15 am the next day . How long did he sleep ?
Answer:
tom sleep 14hour my ans lt might help you
Use the diagram shown to find 4 ÷ 1/3
Answer:
12
Step-by-step explanation:
Since there is no diagram. I will just tell you the answer. first convert into multiplcation keep everything but the 1/3. Change 1/3 into 3/1 (3). Multiply 4*3=12.
Sorry if I don't have a graph.
Hope this helps!
The C Train travels north at a rate of 80 miles per hour. The D Train travels east
at a rate of 150 miles per hour. How far apart will they be after 4 hours?
600
What is 3 log Subscript 2 Baseline x minus (log Subscript 2 Baseline 3 minus log Subscript 2 Baseline (x + 4)) written as a single logarithm?
log Subscript 2 Baseline left-bracket StartFraction x cubed Over (StartFraction 3 Over x + 4 EndFraction) EndFraction Right-bracket
log Subscript 2 Baseline (StartFraction 3 x cubed Over x + 4 EndFraction)
log Subscript 2 Baseline left-bracket (StartStartFraction x cubed Over 3 EndFraction) Over x + 4 EndEndFraction Right-bracket
log Subscript 2 Baseline (StartFraction x cubed Over 3 + (x + 4) EndFraction)
Answer:
A i think
Step-by-step explanation:
edge 2021
The simplified expression is - f(x) = [tex]log_{2} (\frac{x^{3} (x+4)}{3}})[/tex]
We have the following statement -
3 log Subscript 2 Baseline x minus (log Subscript 2 Baseline 3 minus log Subscript 2 Baseline (x + 4))
We have to convert it into Single logarithm.
What is Logarithm?Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
[tex]log_{b} (b^{x} ) = x[/tex]
According to the question, We can write the given statement in the mathematical form as follows -
f(x) = [tex]3\;log_{2} (x )-[log_{2} (3) -log_{2} (x+4)][/tex]
Using the property of logarithm -
log (A) - log(B) = log ([tex]\frac{A}{B}[/tex]), we get -
f(x) = [tex]3\;log_{2} (x )-log_{2} (\frac{3}{x+4} )[/tex]
Using the property of logarithm -
[tex]a\;log (b) = log(b^{a})[/tex]
f(x) = [tex]log_{2} (x^{3} )-log_{2} (\frac{3}{x+4} )[/tex]
f(x) = [tex]log_{2} (\frac{x^{3}}{\frac{3}{x+4}} )[/tex]
f(x) = [tex]log_{2} (\frac{x^{3} (x+4)}{3}})[/tex]
Hence, the simplified expression is - f(x) = [tex]log_{2} (\frac{x^{3} (x+4)}{3}})[/tex]
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Mr. Smith wants to know if he can fit 4 trapezoid tables like the one shown below into a room. What is the total area of 4 trapezoid tables? Answer without units. NUMBER ONLY!
Answer:
(1/2)(2)(5+3)
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
The area of a trapezoid is:
( a + b ) ÷ 2 x h
Where a & b are the bases, and h is the height.
Use formula with the given measurements:
(3 + 5) ÷ 2 x 2
= 8 ÷ 2 x 2
= 4 x 2
= 8
Hope this helps
For how many minutes did Lynn run at a greater speed
than Kael?
0 12
O 17
O 23
O 28
Answer:
D. ✔ 28
Step-by-step explanation:
E 2021
in a triangle the angle with the smallest measure is always the opposite the
Answer:
in a triangle, the angle with the smallest measure is always opposite the shortest side.
Step-by-step explanation:
The height of the saddle off horse above the base ofa carousel can be modeled 4t by the equation f-rr) : 12 sin ^ r 42, where I represents seconds after the ride started. I How much time does to take for the horse to complete one cycle of motion and return to its starting height. What is the maximum height and the minimum height of the horse's saddle above the base ofthe carousel
Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period. This is calculated using:
[tex]T = \frac{2\pi}{w}[/tex]
Where:
[tex]w =\frac{3\pi}{8}[/tex]
So, we have:
[tex]T = \frac{2\pi}{\frac{3\pi}{8}}[/tex]
[tex]T = \frac{2}{\frac{3}{8}}[/tex]
[tex]T = \frac{2*8}{3}[/tex]
[tex]T = \frac{16}{3}[/tex]
Solving (b): The maximum and the minimum height
To do this, we have:
[tex]-1 \le \sin(\theta) \le 1[/tex]
Which means:
[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]
So, the minimum is:
[tex]\sin(\frac{3\pi}{8}) =- 1[/tex]
And the maximum is:
[tex]\sin(\frac{3\pi}{8}) =1[/tex]
Recall that the height is:
[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]
So, the maximum and the minimum of are:
[tex]h_{min} =12 * -1 + 42[/tex]
[tex]h_{min} =30[/tex]
and
[tex]h_{max} =12*1+42[/tex]
[tex]h_{max} =54[/tex]
Explain how you can use fraction strips or number lines to show that three fourths and six eighths are equivalent. plsssssss
The solution is given below.
What is number line?A number line is a pictorial representation of numbers on a straight line. In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
here, we have,
Refer to the fraction strip to show 3/4 & 6/8 are same.
Also if you reduce 6/8 by dividing 2 to numerator & denominator…
it’s 3/4.
The solution is attached below.
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A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the following 95% confidence interval for the proportion of employees who prefer plan A: (0253.0553). Identify the point estimate for estimating the true proportion of employees who prefer that plan.
a. 0.403
b. 0.253
c. 0.553
d. 0.15
Answer:
a. 0.403
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
Confidence interval of (0.253,0.553)
The bounds are 0.253 and 0.553, so the point estimate is:
[tex]p = \frac{0.253 + 0.553}{2} = 0.403[/tex]
This means that the correct answer is given by option A.
Giving brainliest There are 12 inches in 1 foot. This is equivalent to 60 inches in 5 feet. Which proportions can be used to represent this? Check all that apply.
StartFraction 12 over 1 EndFraction = StartFraction 5 over 60 EndFraction
StartFraction 12 over 1 EndFraction = StartFraction 60 over 5 EndFraction
StartFraction 1 over 12 EndFraction = StartFraction 5 over 60 EndFraction
StartFraction 1 over 12 EndFraction = StartFraction 60 over 5 EndFraction
Answer:
12/1=60/5
1/12=60/5
Answer:
B and C
Step-by-step explanation:
15
Type the correct answer in each box. If necessary, round your answer(s) to the nearest hundredth.
The vertices of ABC are Al-2, 2), B6, 2), and 90, 8). The perimeter of ABC is
units, and its area is
square units.
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Answer:
perimeter: 22.81 unitsarea: 24 square unitsStep-by-step explanation:
The lengths of the sides can be found using the distance formula.
d = √((x2 -x1)^2 +(y2 -y1)^2)
AC = √((0 -(-2))^2 +(8 -2)^2) = √(4+36) = 2√10
BC = √((0 -6)^2 +(8 -2)^2) = √(36+36) = 6√2
The distance AB is the difference of the x-coordinates of the points: 6-(-2) = 8.
Then the perimeter is ...
P = a + b + c = 6√2 +2√10 +8 = 8.49 +6.32 +8 = 22.81 . . . units
__
The height of the triangle is the difference in y-values between vertex C and line AB: 8 -2 = 6. The area is given by the formula ...
A = 1/2bh
A = 1/2(8)(6) = 24 . . . square units
Help help help help help
Answer:
x2+y2−12x+4y−60=0
The center of the circle is point: C=(6,−2).
The radius of the circle is r=10.
The number 0.2 can be written as 2/10 so it is a rational number
Expand and simplify (b+6)(b-4)
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: {b}^{2} + 2b - 24}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
[tex] \: (b + 6)(b - 4)[/tex]
➼[tex] \: b \: (b - 4) + 6 \: (b - 4)[/tex]
➼[tex] \: {b}^{2} - 4b + 6b - 24[/tex]
Combining like terms, we have
➼[tex] \: {b}^{2} + 2b - 24[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
The coeffcient of determination is the ratio of the explained variation to the total variation. A. The coefficient of determination is the ratio of the unexplained variation to the total variation. B. The coefficient of determination is the ratio of the total variation to the unexplained variation. C. The coefficient of determination is the ratio of the total variation to the explained variation. D. The coefficient of determination is the ratio of the explained variation to the total variation. Choose the correct answer below. A. The coefficient of determination is a measure of how closely two variables vary together. B. The coefficient of determination is the percent of the variation that is unexplained. C. The coefficient of determination is the percent of variation of y that is explained by the relationship between x and y. D. The coefficient of determination is the percent of the predicted values that equal the actual data values. Choose the correct answer below. A. The value 1r is a measure of how closely two variables vary together. B. The value 1r is the percent of the predicted values that equal the actual data values. C. The value 1r is the percent of the variation that is unexplained. D. The value 1r is the percent of variation of y that is explained by the relationship between x and y.
Answer:
D. The coefficient of determination is the ratio of the explained variation to the total variation.
C. The coefficient of determination is the percent of variation of y that is explained by the relationship between x and y
Step-by-step explanation:
The Coefficient of determination is the ratio of the explained variation in y to the total variation in y.
Coefficient of determination, r² ;
r² = explained variation / total variation
The coefficient of determination is the proportion of variation in y (predicted value) which is due to the regression line ; Hence, it is the percent of variation of y that is explained by the relationship between x and y.
Solve each equation.
2p = 2 p = _____
q - 3 = 7 q = _____
Answer:
[tex]\textbf{HELLO!!}[/tex]
[tex]2p=2[/tex]
[tex]\frac{2p}{2}=\frac{2}{2}[/tex] [tex]\hookleftarrow \mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]=1[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{P=1}}}}}[/tex]
---------------------
[tex]q - 3 = 7[/tex]
[tex]q-3+3=7+3[/tex] [tex]\hookleftarrow \mathrm{Add\:}3\mathrm{\:to\:both\:sides}[/tex]
[tex]=10[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{q=10}}}}}[/tex]
-----------------------
[tex]\textbf{HOPE IT HELPS}[/tex]
[tex]\textbf{HAVE A GREAT DAY!!}[/tex]
how many terms are in this expression 8+(10-7)
Answer:
the perdom
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Which compound inequality could be represented by the graph?
–4 ≤ x ≤ 4
–2 ≤ x ≤ –1
x ≤ –1 or x ≥ 0
x ≤ 3 or x ≥ –1
Answer:
It is D.
Step-by-step explanation:
x ≤ 3 or x ≥ –1
Answer:
D) X <_ 3 or X _> -1
Whole Unit Test Review Answers:
1) D
2)D
3)B
4)C
5)D
6)A
7)B
8)C
9)A
10)B
11)D
12)D
13)B
14)B
15)D
(I got a 100%, and these were my answers, hope they help!)
(The pic below is a screenshot of the 100%, for reassurance)
Which is the graph of f(x) = 2 (4)?
5
40.4)
404)
4
(4,4)
3
3
3 2
2
2
2
(2.1)
6,2)
1
5 -4 -3 -2 -14
1
3
4
-5 4 -3 -2 -14
234
-5 6 -3 -2 -14
2
3
4
5
X
-2
-2
نا دیا
-3
-3
4
W4
-5
5
Tu
5
4
(
24)
Answer:
The Third one
Step-by-step explanation:
Your Welcome :)
Graph of the function is attached below.
Correct option is D.
What is exponential function?As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:
Definition of exponential function
In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0.
Given, exponential function
f(x) = (1/4)4ˣ
exponential function is defined for x∈R
Putting x = 0
f(0) = (1/4)4⁰
f(0) = 1/4
Point on curve is (0,1/4)
Putting x = 1
f(1) = (1/4)4¹
f(1) = (1/4)4
f(1) = 1
Point on curve is (1,1)
Putting x = 2
f(2) = (1/4)4²
f(2) = (1/4)16
f(2) = 4
Point on curve is (2,4)
Putting x = 3
f(3) = (1/4)4³
f(3) = (1/4)64
f(3) = 16
Point on curve is (3,16)
Point (0, 1/4), (1, 1), (2, 4), (3, 16) can be used to draw graph of the function.
Hence, graph of the function is drawn as follows.
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Annabelle is going to see a movie and is taking her 4 kids. Each movie ticket costs $and there are an assortment of snacks available to purchase for $3 each. How much total money would Annabelle have to pay for her family if she were to buy 6 snacks for everybody to share? How much would Annabelle have to pay if she bought x snacks for everybody to share?
Cost for 6 snacks:
Cost for x snacks:
Answer:
(a) $83 for 6 snacks
(b) [tex]y = 65 + 3x[/tex] --- for x snacks
Step-by-step explanation:
Given
Let:
[tex]n \to people[/tex]
[tex]ticket =\$13[/tex] --- per individual
[tex]snacks = \$3[/tex] --- per individual
Solving (a): Amount for 6 snacks
The amount paid (y) is:
[tex]y = ticket * n + snacks * 6[/tex] ---- because she bought 6 snacks
[tex]y = 13 * n + 3 * 6[/tex]
[tex]y = 13n + 18[/tex]
[tex]n = 5[/tex] ---- Annabelle and the 4 kids.
So:
[tex]y =13*5+18[/tex]
[tex]y =65+18[/tex]
[tex]y =83[/tex]
Solving (b): For x snacks
The amount paid (y) is:
[tex]y = ticket * n + snacks * x[/tex] ---- because she bought x snacks
[tex]y = 13* 5 + 3* x[/tex]
[tex]y = 65 + 3x[/tex]
Ivan runs a cake shop. Renting the
shop costs him $1600 per month,
and he makes a profit of $16 on each
cake he sells. Ivan wants a profit of at
least $2000 a month.