Convert 90.1% to a fraction in simplest form

Answer:

A

Step-by-step explanation:

Answer: 60% of a certain species of tomato live after transplanting from pot to garden. Eli transplants 161616 of these tomato plants. Assume that the plants live independently of each other. Let T = the number of tomato plants that live.

Step-by-step explanation:

Answer:

  75%

Step-by-step explanation:

The scale factor the copier uses is the ratio of the copy size to the original size.

__

The student wants that ratio to be ...

  copy size / original size = (9 cm)/(12 cm) = 9/12 = 3/4 = 75%

The student should use a setting of 75% to get the copy he wants.

Based on the information, then the linear system is not consistent and doesn't have a unique, therefore, it's false.

If the rref of the coefficient matrix has a pivot in every column, it means that the coefficient matrix has full column rank. However, this does not necessarily mean that the linear system is consistent and has a unique solution.

Since the linear system has more equations than unknowns, there may be redundant equations or inconsistencies among the equations. Therefore, the consistency of the linear system cannot be determined solely based on the rank of the coefficient matrix.

Therefore, the statement is false.

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The given expression as a sine function is \(sin(\frac{\pi}{5} +\frac{\pi}{2} )\)

The given expression is:

\(sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )\)

Note that:

\(sin(A+B)=sinAcosB+cosAsinB\)

Applying the addition principle to the given expression, we have:

\(sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )=sin(\frac{\pi}{5} +\frac{\pi}{2} )\)

Therefore, the given expression as a sine function is \(sin(\frac{\pi}{5} +\frac{\pi}{2} )\)

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Answer: 49/9

Step-by-step explanation:

\(2=3\sqrt{4x}-12\\\\14=3\sqrt{4x}\\\\\frac{14}{3}=\sqrt{4x}\\\\4x=\frac{196}{9}\\\\x=\frac{196}{36}\\\\x=\frac{49}{9}\)

Answer:

+13

Step-by-step explanation:

-4-9 gives -13

when +13 is added to -13 , the expression becomes +13+(-13) =13-13=0

9514 1404 393

Answer:

  y = -3x

Step-by-step explanation:

The slope formula gives the slope of the segment between the given points.

  m = (y2 -y1)/(x2 -x1)

  m = (-3 -(-5))/(2 -(-4)) = 2/6 = 1/3

The slope of the perpendicular line is the opposite reciprocal of this, so is ...

  m' = -1/(1/3) = -3

A perpendicular line is ...

  y = -3x

Answer:

56 minutes

Step-by-step explanation:

We can use proportions to solve.

6 miles            8 miles

------------     = ------------------

42 minutes        x minutes

Using cross products.

6x = 42 *8

Divide each side by 6

x = 42/6 * 8

x = 7*8

x = 56

The unit rate is given as follows:

0.5 laps per minute.

The unit rate is obtained applying the proportions in the context of the problem.

The unit rate is desired in laps per minute, hence we must take a point, and divide the number of laps by the number of minutes.

In two minutes, one lap is completed, hence the unit rate is obtained as follows:

1/2 = 0.5 laps per minute.

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Answer:

y = 340e^0.0427276t ; 908

Step-by-step explanation:

Given that :

t = time in days since study began

Number of bacteria after 11 days = 544

y = number of bacteria at time t

Exponential growth model:

y = ae^rt

Where a = initial amount ; r = Growth rate

y = 544 ; t = 11 ; a = 340

544 = 340*e^11t

544/340 = e^11t

1.6 = e^11t

Take the In of both sides

In(1.6) = 11t

0.4700036 = 11t

t = 0.4700036 / 11

t = 0.0427276

y = 340e^0.0427276t

Number of bacteria after 23 days :

Using the formula above :

t = 23

y = 340e^0.0427276(23)

y = 340 * 2.6717529

y = 908.39600

y = 908

The required formula is \(y = 340e^{0.0427}\)

908 bacteria are there 23 days after the beginning of the study .

Given that,

A certain culture of bacteria has a population of 340.

The population grows according to a continuous exponential growth model. After 11 days, there are 544 bacteria.

We have to find,

Write a formula relating y tot. Use exact expressions to fill in the missing parts of the formula.

How many bacteria are there 23 days after the beginning of the study.

According to the question,

And let y be the number of bacteria at time,

t = time in days since study began

Number of bacteria after 11 days = 544

y = number of bacteria at time t

Then,

Exponential growth model:

\(y = a.e^{rt}\)

Where, a = initial amount ; r = Growth rate

y = 544 ; t = 11 ; a = 340

Then,

\(544 = 340.e^{11t}\\\\\dfrac{544}{340} = e^{11t}\\\\1.6 = e^{11t}\\\\Taking \ log \ on \ both \ sides,\\\\ln(1.6) = 11t\\\\0.47 = 11t \\\\t = \dfrac{0.47}{11}\\\\t = 0.0427\)

The required formula is \(y = 340e^{0.0427}\)

\(y = 340e^{0.0427}\)

Where, t = 23

\(y = 340e^{0.0427276(23)}\\\\y = 340 \times 2.6717529\\\\y = 908.39600\\\\y = 908\)

Therefore, 908 bacteria are there 23 days after the beginning of the study .

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Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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The leading coefficient of the expression is 1

From the question, we have the following parameters that can be used in our computation:

4x² + x4 -8 -5

When written in standard form, we have

x^4 + 4x^2 - 8 - 5

Evaluate the like terms

x^4 + 4x^2 - 13

The leading coeffiicient is the coefficient of the term with highest power

In this case, it is

Coefficient = 1

Hence, the value is 1

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The correct option C: A rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC.

For the given question;

In triangles ABC angle CAB is 47.

If the triangles ABC and ACD becomes congruent such that angle ACD corresponds to angles ABC.

Then, both angles will be equal.

For, this, a rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC is to be done.

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Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

<95141404393>

The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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The graph of the exponential function is on the image at the end.

Here we have the exponential equation:

W(x) = 2^(x - 1)

To graph any function, we should find some points on the function, and to find, them, we need to evaluate the function in some values of x.

if x = 0

W(0) = 2^(0 -1 ) = 0.5

if x = 1

W(0) = 2^(1 - 1) = 2^0 = 1

if x = 2

W(0) = 2^(2 - 1) = 2^1 = 2

So we got the points (0, 0.5), (1, 1), and (2, 2) (you can try to find more points).

Now we need to graph them on the coordinate plane and draw a curve that connects them (with the general form of an exponential function).

The graph can be seen in the image below.

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The parameters of the absolute value function g(x) = -|2x| + 5 are given as follows:

The standard definition of the absolute value function is given as follows:

f(x) = a|bx + c| + d.

The meaning of each parameter is given as follows:

In this problem, the function is defined as follows:

g(x) = −|2x| + 5.

Compared with the standard absolute value function, the values of these parameters are given as follows:

a = -1, b = 2, c = 0, d = 5.

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Answer:

x^2+6x-15

Step-by-step explanation:

(3x^2+2x-8)-(2x^2-4x+7)

=3x^2+2x-8-2x^2+4x-7

=x^2+6x-15

Question:

Identify the sets that contain 2 as an element. (Check all that apply.)

\(A.\ \{2, 3, 4, 5, ...\}\)

\(B.\ \{0, 1, 4, 9, ...\}\)

\(C.\ \{2, \{2\} \}\)

\(D.\ \{\{2\}, \{\{2\}\}\}\)

\(E.\ \{\{2\}, \{2, \{2\}\}\}\)

\(F.\ \{\{\{2\}\}\}\)

Answer:

\(A.\ \{2, 3, 4, 5, ...\}\)

\(C.\ \{2, \{2\} \}\)

Step-by-step explanation:

Required

For which of the options is 2 an element

\(A.\ \{2, 3, 4, 5, ...\}\)

The elements of this set starts from 2, then 3 and continues as thus.

Hence: 2 is an element

\(B.\ \{0, 1, 4, 9, ...\}\)

From the given elements in the above set, 2 is not listed.

Hence: 2 is not an element of this set

\(C.\ \{2, \{2\} \}\)

Here, 2 is listed as an element, 2 is also listed as a subset.

Since 2 is listed as an element, then 2 is an element of the set.

\(D.\ \{\{2\}, \{\{2\}\}\}\)

Here, 2 is listed as a subset of {2} and also as a subset of subset of {{2}}.

Since 2 is not listed as an element itself, then 2 is not an element of the set.

\(E.\ \{\{2\}, \{2, \{2\}\}\}\)

Here, 2 is listed as a subset of {2} and also as a subset of subset of {2,{2}}. This set only contains subsets, i.e. 2 is not listed as a direct element of the set.

Hence: 2 is not an element of the set

\(F.\ \{\{\{2\}\}\}\)

Here, 2 is listed as a subset of subset of {{2}}. This set only contains subsets, i.e. 2 is not listed as a direct element of the set.

Hence: 2 is not an element of the set

Answer:

how

Step-by-step explanation:

Answer:

67 cookies

Step-by-step explanation:

When packaging in groups of 4, the possible number of cookies is x = (4n+3). The possible values are:

7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71...

When packaging in groups of 5, the possible number of cookies is x = (5n+2). The possible values are:

7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77...

When packaging in groups of 7, the possible number of cookies is x = (7n+4). The possible values are:

11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95...

The least value that appears on all three possibilities is 67, therefore the least number of cookies that Mohan could have is 67.

0.7745 is the probability that a randomly selected college student will take between 4.0 and 6.5 minutes to find a parking lot in the library lot.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Given

Mean, μ = 5.5 minutes

Standard Deviation, σ = 1 minute

We are given that the distribution of length of time is a bell-shaped distribution that is a normal distribution.

z(score) = (x -  μ)/σ

P(college student will take between 4.0 and 6.5 minutes)

= P(4.0 ≤ x ≤ 6.5)

=  P((4.0 - 5.5)/1 ≤ z ≤ (6.5 - 5.5)/1)

= P(-1.5 ≤ z ≤ 1)

= P(z ≤ 1) - P(z < - 1.5)

= 0.8413 - 0.0668

= 0.7745 = 77.45%

Hence, 0.7745 is the probability that a randomly selected college student will take between 4.0 and 6.5 minutes to find a parking lot in the library lot.

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From the given figure

If a // to b, then

The angle of measure (3x - 1) and the angle vertically opposite angle with 95 degrees are corresponding angles

Since corresponding angles are equal and the vertically opposite angles are equal, then

Add 1 to both sides

Divide both sides by 3 to find x

The value of x is 32

Null hypothesis: The mean number of points scored by the taller team is not significantly different from the population mean of 72.

Alternative hypothesis: The mean number of points scored by the taller team is significantly greater than the population mean of 72.

Since the population variance is unknown, we will use a t-test. The degrees of freedom for this test will be 9 (n-1), where n is the sample size of the taller team (10).

Using an alpha level of 0.05 and 9 degrees of freedom, the critical t-value is 1.833.

To calculate the test statistic, we first need to find the sample mean and standard deviation of the taller team's scores. The sample mean is 82, and the sample standard deviation is 9.89. Using these values, we can calculate the t-value:

t = (82-72) / (9.89 / sqrt(10)) = 3.19

Since the calculated t-value (3.19) is greater than the critical t-value (1.833), we reject the null hypothesis and conclude that there is a significant difference between the mean number of points scored by the taller team and the population mean of 72. The coach can therefore conclude that having a taller team does result in a greater number of points scored.

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Answer:

x < 3

Step-by-step explanation:

Divide both sides of the inequality by 2

Hi there! :)

Answer:

Length = 10.5 m, width = 7 m.

Step-by-step explanation:

Given:

Perimeter, or P = 35 m

Ratio of l to w = 3 : 2

Since the ratio is 3 : 2, let l = 3x, and w = 2x.

We know that the formula for the perimeter of a rectangle is P = 2l + 2w. Therefore:

35 = 2(3x) + 2(2x)

35 = 6x + 4x

35 = 10x

x = 3.5

Plug this value of "x" into each expression to solve for the dimensions:

2(3.5) = w

w = 7 m

3(3.5) = l

l = 10.5 m

Therefore, the dimensions are:

Length = 10.5 m, width = 7 m.

Answer:

Your answer is 12.

Step-by-step explanation:

Answer:

yes, line n intersects line q when the lines are extended

Step-by-step explanation:

the lines are not parallel, and any two nonparallel lines will always intersect at one point