Answer:
Step-by-step explanation:
Suppose that at time [tex]t_0[/tex] we have x mold cells. We are told that after 12 minutes the amount present is double. That is a [tex]t= t_0+12[/tex] we have 2x cells. Then, at [tex]t = t_0+24[/tex] we have (2x)*2 = 4x. We can continue as follows
[tex]t: t_0+36[/tex] we have (4x)*2 = 8x.
[tex]t: t_0+48[/tex] we have (8x)*2 = 16x
[tex]t: t_0+60[/tex] (one hour later) we have (16x)*2 = 32x.
So after one hour from now we have 32x cells.
The no. of mold cells one hour from now will be 32[tex]x[/tex].
Given,
The number of mold cells doubles every 12 minutes.
Let at time [tex]t[/tex] we have x mold cells.
So, after 12 minutes, the no of molds at[tex],t_{12} =t+12[/tex] the no. of mold will be[tex]2x.[/tex]
After further 12 minutes at, [tex]t_{24} =t+24[/tex], the no. of mould will be [tex]4x[/tex].
After further 12 minutes at, [tex]t_{36} =t+36[/tex], the no. of mold will be [tex]8x[/tex].
After further 12 minutes at, [tex]t_{48} =t+48[/tex], the no. of mold will be [tex]16x.[/tex]
After further 12 minutes at, [tex]t_{60} =t+60[/tex], the no. of mold will be [tex]32x[/tex].
Hence the no. of mold cells one hour from now will be 32[tex]x[/tex].
For more details follow the link:
https://brainly.com/question/11897796
Write the expression as the logarithm of a single number or expression
4 In 2 +3 In 5
4 In 2 + 3 In 5-
(Simplify your answer.)
Answer:
ln(2000) = 7.601
Step-by-step explanation:
For this we need to know the rules of logarithms, specifically the product rule and the power rule. The product rule is simply ln(a*b) = ln(a) + ln(b). The power rule is simply ln(a^b) = b ln(a).
With these rules, let's begin to simplify the expression:
4 ln(2) + 3 ln(5)
= ln(2^4) + ln(5^3)
= ln(16) + ln(125)
= ln(16 * 125)
= ln(2000)
= 7.601
Hope this helps. Cheers.
A logarithm is a power to which a number must be raised in order to get some other number.
The value of the expression 4 log 2 + 3 log 5 as a single number is 3.30102.
What is a log?A logarithm is a power to which a number must be raised in order to get some other number.
Example:
log 10 = 1
log 100 = log 10² = 2 log 10 = 2 x 1 = 2
log 1000 = log 10³ = 3 log 10 = 3 x 1 = 3
log 0 = undefined
log 1 = 0
We have,
Some formulas for log:
log[tex]x^{n}[/tex] = n log x
log mn = log m + log n
Given,
4 log 2 + 3 log 5
= log [tex]2^{4}[/tex] + log [tex]5^{3}[/tex]
= log 16 + log 125
= log (16 x 125)
= log 2000
= 3.30102
Thus the value of the expression 4 log 2 + 3 log 5 as a single number is
3.30102.
Learn more about log here:
https://brainly.com/question/14407082
#SPJ2
use the substitution method to solve the system of equations. Choose the correct ordered pair y=3x 2x+3y=55
Answer:
(x,y) = (5,15)
Step-by-step explanation:
y = 3x
2x + 3y = 55
2x + 3(3x) = 55
2x + 9x = 55
11x = 55
x = 5
y = 3(5)
y = 15
What does 0 = 0 mean regarding the solution to the system?
Answer:
It means the left side of the equation equals the right side of the equation regardless of the value of the variables. The solution is all real numbers for each variable
Step-by-step explanation:
find the slope of a line that is perpendicular to the line y= - 1/3x+7
the slope of the line is 3
Which expression is equivalent to ? (2^1/2 times 2^3/4)^2
Answer: B or square root 2^5
Step-by-step explanation: I checked on my calculator
A local bottler, Fossil Cove, wants to ensure that an average of 16 ounces of beer is used to fill each bottle. Ben takes a random sample of 48 bottles and finds the average weight to be 15.8 ounces. Historically, the standard deviation has been 0.8 ounces.
Required:
a. Complete a hypothesis test (using the p-‐‐value approach). Interpret your results.
b. How would your answer change if instead of being given that the sample standard deviation was 0.8 ounces you were given the sample variance is 0.64?
Answer:
(a) The mean weight of beer used to fill each bottle is 16 ounces.
(b) The answer of part (a) would not change.
Step-by-step explanation:
A local bottler, Fossil Cove, wants to ensure that an average of 16 ounces of beer is used to fill each bottle.
Ben takes a random sample of n = 48 bottles and finds the average weight to be [tex]\bar x=[/tex] 15.8 ounces. Also it is known that the standard deviation is, σ = 0.8 ounces.
(a)
The hypothesis can be defined as follows:
H₀: The mean weight of beer used to fill each bottle is 16 ounces, i.e. μ = 16.
Hₐ: The mean weight of beer used to fill each bottle is not 16 ounces, i.e. μ ≠ 16.
Assume that the significance level of the test is, α = 0.05.
As the population standard deviation is provided, we will use a z-test for single mean.
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{15.8-16}{0.80/\sqrt{48}}\\\\=-1.732[/tex]
The test statistic value is -1.732.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the two-tailed test as follows:
[tex]p-value=2\cdot P(Z>-1.732)[/tex]
[tex]=2\times [1-P(Z<1.732)]\\\\=2\times [1-0.04182]\\\\=0.08364\\\\\approx 0.084[/tex]
*Use a z-table for the probability.
The p-value of the test is 0.084.
p-value = 0.084 > α = 0.05
The null hypothesis will not be rejected.
Thus, it can be concluded that the mean weight of beer used to fill each bottle is 16 ounces.
(b)
The standard deviation of a random variable is the square root of the variance.
[tex]SD=\sqrt{Variance}[/tex]
So, if the variance was 0.64, then the standard deviation will be:
[tex]SD=\sqrt{Variance}=\sqrt{0.64}=0.80[/tex]
Thus, the answer of part (a) would not change.
A firm just paid an annual dividend of $1.40 and increases that dividend by 2 percent each year. How do you find the price if the firm's stock at year 4 if the discount rate is 13 percent?
Answer:
14.05
Step-by-step explanation:
We have the following:
Current Dividend = D0 = $ 1.40
g = growth rate = 2%
r = discount rate = 13%
Dividend in Year 5
= D5 = D0 * (1 + g) ^ 5
= $ 1.40 * (1 + 2%) ^ 5
= $ 1.40 * (1.02) ^ 5
Firm Stock Price at the end of year 4 = Dividend in Year 5 / (r - g)
= $ 1.40 * (1.02) ^ 5 / (13% -2%)
= $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02)
Therefore, firm stock at the end of year 4 is
P4 = $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02) = 14.05
how do you slove 21 - 4d for d= 5
Divide (28x5 + 29x4 + 5x3 + 86x2 + 56x + 53) by (–4x – 7) using synthetic division.
Answer:
-7x⁴+5x³-10x²-4x-7 - 4/4x+7
Step-by-step explanation:
Given the division problem, (28x⁵ + 29x⁴ + 5x³ + 86x² + 56x + 53) by (–4x – 7), find the solution in the attachment below.
The polynomial of a function is expressed as P(x) = Q(x) + R(x)/D(x)
Q(x) is the quotient
R(x) is the remainder
D(x) is the divisor
Accordin gto the divsion, Q(x) = -7x⁴+5x³-10x²-4x-7
R(x) = 4
D(x) = -4x-7
Substituting this functions in the polynomial P(x);
P(x) = -7x⁴+5x³-10x²-4x-7 - 4/4x+7
Solve for x in the equation x squared + 11 x + 121/4 = 125/4.
Step-by-step explanation:
x² + 11x + 121/4 = 125/4
x² + 11x + 121/4 - 125/4 = 0
x² + 11x - 1 = 0
after that apply quadratic formula
x = ( -b + or - √b² - 4ac ) ÷ 2a
x = (-11 + or - √11² - 4×1×-1 ) ÷ 2×1
+ = 0.090169....
- = -11.090168.....
x = 0.090 or x = -11.09
PLESE HELPPP!!!!!!!!!!!!!!!!
Answer:
B. [tex]\frac{6}{2x^{2} - 5x}[/tex]
Step-by-step explanation:
The product of the ratioal expressions given above can be found as follows:
[tex] = \frac{2}{x} * \frac{3}{2x - 5} [/tex]
Multiply the denominators together, and the numerators together, separately to get a single expression
[tex] \frac{2(3)}{x(2x - 5)} [/tex]
[tex] = \frac{6}{x(2x) - x(5)} [/tex]
[tex]= \frac{6}{2x^{2} - 5x}[/tex]
The product of the expression [tex]\ = \frac{2}{x}*\frac{3}{2x - 5}[/tex] = [tex]\frac{6}{2x^{2} - 5x}[/tex]
The answer is B.
A triangle has an area of 900m^2 . If a parallelogram has the same height and base as the triangle, what is the area of the parallelogram?
Answer:
area = 1800 m²
Step-by-step explanation:
area of one triangle = 900 m²
if a parallelogram has the same height and base as the triangle, then that means the area or the two triangle and shaped as a parallelogram
is twice the area given.
area = 900 * 2
area = 1800 m²
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
DAC
A
Statements
Reasons
00
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answer:
See below
Step-by-step explanation:
Proof:
Statements | Reasons
AD ≅ BC | Given
AD ║ BC | Given
AC ≅ AC | Reflexive Property
∠DAC ≅ ∠ACB | If 2 || lines are cut by a trans., the | alternate interior ∠s are congruent.
ΔADC ≅ ΔBCA | S.A.S Postulate
BA ≅ DC | Corresponding sides of congruent Δs
So, quad. ABCD is a ║gm | If a quad. has its opposite sides
| congruent, the quad. is a parallelogram.
It is prove that given quadrilateral is a parallelogram.
Given that,AD ≅ BC and AD ║ BC
By reflexive property,AC ≅ AC
If two parallel lines are cut by a transversal. Then, alternate interior angles are congruent.So that, ∠DAC ≅ ∠ACB
By Side - angle - Side congruency rule,ΔADC ≅ ΔBCA
Since, the Corresponding sides of congruent triangles are congruent.So that, BA ≅ DC
Hence, opposite sides of given quadrilateral are equal. Therefore, given quadrilateral are parallelogram.
Learn more:
https://brainly.com/question/16702162
Change -2Y - X=-2 to the slope-intercept form of the equation of a line.
Answer:
y = -(1/2)x+1
Step-by-step explanation:
-2Y - X = -2
Add x to both sides:
-2Y = X - 2
Divide both sides by -2:
Y = -(1/2)x+1
You could also use the shortcuts:
For Ay+Bx=C, the slope is -B/A and the y-intercept is C/A.
Slope = -B/A = -(-1)/(-2) = 1/-2 = -(1/2)
Y-intercept = C/A = (-2)/(-2) = 1
y = mx + b ---> y = -(1/2)x + 1
Answer:
y = -1/2x +1
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
-2y -x = -2
Solve for y
Add x to each side
-2y = x-2
Divide by -2
-2y/2- = x/-2 -2/-2
y = -1/2x +1
What is the slope of the line
described by -4X + 2Y = 16?
A. -2
B. -4
C. 4
D. 2
E. 16
Answer: THe slope is 2
SO answer d
Step-by-step explanation:
-4X + 2Y = 16 add 4x to the other side so equation is
2y=16+4x divided by 2
y=8+2x
Here is a list of ages (years) of children in a room: 4, 3, 2, 10, 10, 6, 7 State the median.
Answer: 6
Step-by-step explanation:
Lets re- write the numbers in growing order.
2,3,4,6,7,10,10
The number that stays exactly in the middle of the the sequence is the median.
Number 6 stays in the middle. So 6 is the median
Answer
6Step by step explanation
Given data : 4 , 3 , 2 , 10 , 10 , 6 , 7
Arranging the data in ascending order, we have,
2 , 3 , 4 , 6 , 7 , 10 , 10
Here, n ( total number of items) = 7
Now, position of median:
[tex] {( \frac{n + 1}{2}) }^{th} [/tex] item
plug the value
[tex] = {( \frac{7 + 1}{2} )}^{th} [/tex] item
Add the numbers
[tex] =( { \frac{8}{2} )}^{th} [/tex] item
Divide
[tex] = {4}^{th} [/tex] item
i.e 4th item is the median
Median = 6
------------------------------------------------------------------------
Further more explanation:
Let's take another example:
please see the attached picture.
In the above series, the numbers are arranged in ascending order. Here, the fourth item 17 has three items before it and three items after it. So, 17 is the middle item in the series. 17 is called the median of the series.
Thus, Median is the value of the middle - most observation, when the data are arranged in ascending or descending order of magnitude.
Hope I helped..
Best regards!!
What are the x and y intercepts?
[tex]f(x) = \frac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)} [/tex]
Answer:
(a)The x-intercepts are 3, -4 and 1.
(b)f(x)=-0.5
Step-by-step explanation:
Given the function:
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}[/tex]
The x-intercepts occurs when y=0The y-intercepts occurs when x=0x-Intercepts
When y=f(x)=0
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}=0\\(x - 3)(x + 4)(x - 1)=0\\x - 3=0$ or $ x + 4=0 $ or $ x - 1=0\\x=3$ or $ -4$ or $ 1[/tex]
The x-intercepts are 3, -4 and 1.
y-intercepts
When x=0
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}\\f(x) = \dfrac{(0 - 3)(0 + 4)(0 - 1)}{(0 + 2)(0 - 12)}\\= \dfrac{(- 3)( 4)( - 1)}{( 2)( - 12)}\\= \dfrac{12}{-24}\\\\=-0.5[/tex]
The y-intercept is -0.5
Maya is choosing between several pay plans for her new job. If she usually has monthly sales of about $5,000, which plan would allow Maya to earn the most money in a month? Plan Monthly base salary Commission rate A $500 8% B $600 7% C $700 6% D $800 5% plan A plan B plan C plan D
Answer:
Well Plan D
Step-by-step explanation:
Answer:
plan D.
Step-by-step explanation:
2021 edge
46/100 46/1,000
which is greater
Answer:
46/100.
Step-by-step explanation:
46 / 100 = 0.46
46 / 1,000 = 0.046
0.046 < 0.46
So, 46/100 is greater than 46/1,000.
Hope this helps!
46/100 is greater because it equals 0.46 while 46/1000 would equal 0.046.
Mike can stitch 7 shirts in 42 hours
He can stitch 1 shirt in hours, and in 1 hour he can stitch of a shirt
Answer:
He stitched 1 shirt in 6 hours.
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Given Mike can stitch 7 shirts in 42 hours
No. of shirt stitch in one hour = total no of shirt stitch/total time taken
No. of shirt stitch in one hour = 7/42 = 1/6
Thus, he can stitch 1/6 of a shirt in one hour
Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7) = 42/6 = 6 hours.
Thus, he stitched 1 shirt in 6 hours.
Answer:
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Because he stitched 7 shirts in 42 hours
42/7 = 6
so 6 hours per shirt
In one hour:
1/6
Find the exact value of each expression, if it defined. ( if answer is undefined, enter undefined) tan (-1)
Answer:
[tex]tan(-1) \approx -0.02[/tex]
Step-by-step explanation:
The given expression is
[tex]tan(-1)[/tex]
The tangent of -1 is defined, it's around -0.02.
The tangent is a trigonometric function with a period of [tex]\pi[/tex], where each period is separated by a vertical asymptote which indicates that the function is not determined through all its domain, that's what the question refers to when it says "if is undefined, enter undefined".
However, at [tex]x=-1[/tex], the tangent is determined, that means, there's no asymptote on that coordinate, that's why it has a "determined value", which is -0.02 approximately.
[tex]tan(-1) \approx -0.02[/tex]
two boxes have the same volume. One box has a base that is 5 cm5\text{ cm}5 cm5, start text, space, c, m, end text by 5 cm5\text{ cm}5 cm5, start text, space, c, m, end text. The other box has a base that is 10 cm10\text{ cm}10 cm10, start text, space, c, m, end text by 10 cm10\text{ cm}10 cm10, start text, space, c, m, end text. How many times as tall is the box with the smaller base?
Answer:
The height of the box with the smaller base is 4 times that of the box with the larger base
Step-by-step explanation:
The volume of a box is the product of the base area and the height of the box, it is given as:
Volume = base area × height
For the smaller base box, it has a base of 5 cm by 5 cm, therefore the base area of the smaller base box = 5 cm × 5 cm = 25 cm². Let the height of the smaller base box be [tex]h_1[/tex]The volume of the small box = [tex]25*h_1[/tex]
For the larger base box, it has a base of 10 cm by 10 cm, therefore the base area of the larger base box = 10 cm × 10 cm = 100 cm². Let the height of the large base box be [tex]h_2[/tex]The volume of the larger base box = [tex]100*h_2[/tex]
Since both boxes have the same volume, therefore:
[tex]100*h_2[/tex] = [tex]25*h_1[/tex]
[tex]\frac{h_1}{h_2} =\frac{100}{25} \\\\\frac{h_1}{h_2}=4\\\\h_1=4h_2[/tex]
The height of the box with the smaller base is 4 times that of the box with the larger base
We can use the formula V=lwh to compare the volume in the two boxes.
First let's compare the volume of both boxes to see if they have the same height. To make it simple, let's use a height of 1 centimeter.
First the box with the smaller base.
V=lwh
V=5⋅5⋅1
V=25
Now the box with the larger base
V=lwh
V=10x10x1
V=100
We can set up an equation to find out how many times as tall the smaller box needs to be to have the same volume as the box with the larger base.
25·h=100
h=4
The boz with the smaller base is 4 times tall
hope it helped :)
The value of a car dropped from $7400 to $6800 over the last year. What percent decrease is this?
Answer:
8.1% decrease
Step by step
To find precentage decrease we use formula:
Percent decrease= original amount-new amount/original amount(100%)
percent decrease= 7,400-6,800/7,400(100%)=300/37=8.1%
6th grade math help me, please. :)
Step-by-step explanation:
Hello there!!
no need to be panic we will help you, alright.
look solution in picture ok...
sorry for cutting in middle.
Hope it helps...
Use the minimum and maximum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 14, max = 121, 8 classes
Answer:
The class width is [tex]C_w \approx 13[/tex]
Step-by-step explanation:
From the question we are told that
The upper class limits is [tex]max = 121[/tex]
The lower class limits is [tex]min = 14[/tex]
The number of classes is [tex]n = 8 \ classes[/tex]
The class width is mathematically represented as
[tex]C_w = \frac{max - min}{n }[/tex]
substituting values
[tex]C_w = \frac{121 - 14}{8 }[/tex]
[tex]C_w = 13.38[/tex]
[tex]C_w \approx 13[/tex]
Since
please help Find: ∠a ∠b ∠c
Answer:
A-40
B-140
C-140
Step-by-step explanation:
b and c are supplementary angles to angle 40.
Therefore 180-40= 140.
and opposite angles in a quadrilateral are congruent to each other.
Which type of graphs allows the reader to view the raw data values?
Answer:
bar graphs
Step-by-step explanation:
as in a bar graph, we don't do any calculations to graph on a paper,
so the data values, are taken RAW while graphing.
need help fast APR is an ____?
19] After increasing the price of an article by 20%. The price was GHC
3000.00. What was the original price?
Step-by-step explanation:
Let the original price be x
After increasing by 20% the price is 3000
Thus,
x + ( x × 20%) = 3000
x + 20x/100 = 3000
x + x/5 = 3000
(5x + x)/5 = 3000
6x/5 = 3000
x = 3000 * 5/6
x = 2500
Hope it helps :)
WILL GIVE YOU BRAINLIEST
Answer:
AB = 20 tan55°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )
20 tan55° = AB