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Answer:

The previous number of students are 350.

Step-by-step explanation:

Let the number of students be 100x.

\(\frac{100+30}{100}\)x = 455

Simplify.

\(\frac{130}{100}\)x = 455

Find x.

\(\frac{100}{100}\)x = \(\frac{100}{130}\) × 455

Simplify.

x = 350

Answer:

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Answer:

21 small dogs, 42 total dogs

Step-by-step explanation:

7×3=21

7+7=14

14×3=42

The area of a triangle whose sides are 4.5 cm and 1 cm and perimeter 10.5 cm is 2.045 square cm

The area for the triangle whose perimeter and side is given is solved by the formula

A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c))

where:

a, b, and c are the sides of the triangle

s = perimeter / 2

perimeter = a + b + c

10.5 = 4.5 + 1 + c

c = 10.5 - 5.5

c = 5

s = (a + b + c) /2

s = 10.5/2

s = 5.25

substituting for s a b and c

A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c) )

A= √(5.25 (5.25 ﹣ 4.5) (5.25 ﹣ 1) (5.25 ﹣ 5) )

A = √4.18358

A = 2.045 square cm

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The initial population is approximately 23.81 bacteria.

Given that, bacteria culture grows with a constant relative growth rate.

After 2 hours there are 400 bacteria and after 8 hours the count is 50,000. We have to find the initial population.

Let P(t) be the population at time t and P(0) be the initial population.

Since the growth rate is constant, we can use the formula:

P(t) = P(0) * e^(rt), where r is the constant relative growth rate.

To find r, we can use the information that the population grows from 400 to 50,000 over 8 hours.

P(8) = P(0) * e^(8r)50,000

= P(0) * e^(8r)

Also, P(2) = P(0) * e^(2r)

= 400

Taking the ratio of these two equations, we get:

50,000/400 = e^(8r) / e^(2r)125

= e^(6r)

Taking the natural logarithm of both sides, we get:

ln(125) = 6rln(e)

ln(125) = 6r

Therefore, r = ln(125)/6

Substituting this value of r into P(2) = P(0) * e^(2r)

= 400, we get:

400 = P(0) * e^(2(ln(125)/6))400

= P(0) * (125)^(1/3)

P(0) = 400 / (125)^(1/3)

P(0) = 23.81 (approx)

Therefore, the initial population is approximately 23.81 bacteria.

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Answer:

29.5 or 30 (rounded)  

Step-by-step explanation:

Add 12 and 47 together and divide by 2 because there are 2 numbers.

Answer:

the geometric mean is 23.7 or 23.74868

Step-by-step explanation:

take your numbers

12 and 47. you have 2 numbers so n=2

find 1/n=0.5

(12*47)^0.5

(564)^0.5=23.74868

round 23.74868 to the nearest 10

23.7

The confidence interval for estimating the mean sale price of homes in the neighborhood is made at a 95% level of reliability.

The confidence level for the given interval is 95%. This means that if the sampling and estimation process is repeated many times, the calculated interval will contain the true mean sale price of homes in the neighborhood 95% of the time.

The given printout already indicates a confidence level of 95%, which means that you can be 95% certain that the true mean sale price falls within the range of the lower limit (38,886.4) and the upper limit (54,113.6).

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The half-life of this isotope (in hours) is 13.0

Isotopes are variations of chemical elements that have a varied number of neutrons but the same number of protons and electrons. In other words, isotopes are different forms of the same element that have different amounts of nucleons (the sum of protons and neutrons) because of variations in the total number of neutrons in each of their individual nuclei.

An important application of isotopes is in the determination of the isotopic signature of element samples via isotope analysis. This is generally done via the process of isotope ratio mass spectrometry.

28% decay means, 72% remains.

Now,

\(N=N_{n} (\frac{1}{2})^{t/t_{12} } \\72=100(\frac{1}{2} )^{\frac{6.16 hours}{t_{1/2} } } \\(\frac{72}{100} )=(\frac{1}{2} )^{\frac{6.16 hours}{t_{1/2} } } \\\)

Taking long as both sides & solving we get,

\(t_{\frac{1}{2} } = 13.0 hours\)

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Answer:

x = -2

Step-by-step explanation:

3x - 1 × 3 = 5 × x + 1

3x - 3 = 5x + 1

3x - 5x = 1 + 3

-2x = 4

-2x/-2 = 4/-2

x = -2

The correct answer is B) Her sample is 38, 68, 35, 02, 22. This is because the scientist is selecting a random sample of 5 forest sites from a population of 45 without replacement. She is using consecutive pairs of digits from the table of random digits to select her sample.

Starting at the beginning of the line of random digits, the first pair is 38, which corresponds to forest site 38. The second pair is 68, which corresponds to forest site 68. The third pair is 35, which corresponds to forest site 35. The fourth pair is 02, which corresponds to forest site 02. And the fifth pair is 22, which corresponds to forest site 22.
Now, let's select a random sample of 5 forest sites without replacement:
1) 38
2) 35
3) 02
4) 22
5) 24
Thus, the correct answer is not listed in the given options. However, based on the consecutive pairs of digits and following the process mentioned, the sample should be 38, 35, 02, 22, and 24.

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The solution of the equation would be options A. -4 & 2.

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The given expression is

\(1/4x^2 = -1/2x+2\\\\1/4x^2 +1/2x-2= 0\\\\\)

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-1/2 \pm \sqrt{1/4 - 4(1/4)(-2)}}{2(1/4)}\\\\\\x = \dfrac{-1/2 \pm \sqrt{1/4 +(2)}}{1/2}\\\\\\x = \dfrac{-1/2 \pm \sqrt{(9/4)}}{1/2}\\\\\\x = \dfrac{-1/2 \pm3/2}{1/2}\\\\x = -4, 2\)

Therefore, the solution of the equation would be option A. -4 & 2.

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Professor evaluation in this case is an example of a discrete random variable. A discrete random variable takes on a countable number of distinct values.

In this case, the scores 1, 2, 3, 4, and 5. The variable represents the outcome of a specific event (the evaluation of a professor) and can only assume these specific values. Each score has a certain probability associated with it, reflecting the likelihood of that score being given by the students.

As it is a discrete random variable, there is no intermediate value between the possible scores, and the probability distribution can be represented by a probability mass function.

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Answer:

turn 3% into decimal by diving 3 by 100

3/100=0.03

0.03X3460=103.80

3460-103.80=3356.20

3356.20-100=3256.2

The sample that can best help the owner see the preferences of all the audience members is given as follows:

B) 5 people in VIP seats, 35 on the main floor, and 20 in the balcony.

The best sample is obtained considering the proportions in the sample, as follows:

Hence, considering 5 VIP seats, the amounts are given as follows:

Hence option B is the correct option for this problem.

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The sum of the two complex numbers will give:

(-4 + i) + (10 - 5i) = 6 - 4i

So the correct option is the third one.

Let's assume we have two complex numbers which are:

A = a + bi

B = c + di

The sum between these two complex numbers is:

A + B = (a + bi) + (c + di)

Taking i as a common factor we can rewrite:

(a + bi) + (c + di) = a + c + (b + d)i

And that is the general sum.

Here we want to solve:

(-4 + i) + (10 - 5i)

Again, if we take i as a common factor we can rewrite:

-4 + 10 + (1 - 5)*i

6 - 4i

So the correct option is the third one.

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Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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such pair of equation that have only one pair of solutions which satisfy both equation is linear equation

Answer:

the small pillows costed $20 and the large pillows costed $45

Step-by-step explanation:

this can be set up were x= price of small pillows and y=price of large pillows

according the the question, 265=2x+5y and 635=7x+11y

so now solve this system of equations:

first solve 265=2x+5y for x

add -2x to both sides

-2x+265=5y

add -265 to both sides

-2x=5y-265

divide both sides by -2

x=(-5/2)y+(265/2)

substitute this value of x in 635=7x+11y and solve for y

635=7((-5/2)y+(265/2)) +11y

y=45

substitute 45 for y in x=(-5/2)y+(265/2)and solve for x

x=20

so the small pillows are $20 and the large are $45

Step-by-step explanation:

using set notation

domain [-3,3]

range[-1,3]

(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer:

2 is the correct answer

Step-by-step explanation:

there are 2 fish over 30 cm long between 30 and 40 cm

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

√36 = 6

a^2 + b^2 = c^2

6^2 + 6^2 = c^2

36 + 36 = c^2

72 = c^2

√72 = c

2 36

2 18

2 9

3 3

6√2 = c

6√2 = (estimate rounded up, 8.49)

Answer:

---------------------

First step, isolate the term with c:

Second step, divide both sides by 3:

Answer:

\(\sf c = \dfrac{a + 4}{ 3}\)

Step-by-step explanation:

To make "c" the subject of the equation, we need to isolate "c" on one side of the equation.

a = 3c - 4

Add 4 to both sides of the equation to isolate the term containing "c":

a + 4 = 3c

Divide both sides of the equation by 3 to solve for "c":

(a + 4) / 3 = c

Therefore,

\(\sf c = \dfrac{a + 4}{ 3}\)

Answer: Translation, Rotation

Step-by-step explanation:

translation comes before rotation in the question

the rectangle is translated so that their bottom left vertices are in the same place, and then a rotation to match the other sides up

Answer:

The bacterial culture loses  \(\dfrac{5}{8}\)  of its size every 7 seconds.

Step-by-step explanation:

The relationship between the elapsed time t, in seconds, and the number of bacteria, N(t), in the petri dish is modeled by the function:

\(N(t)=4900\cdot\left(\dfrac38\right)^{t/7}\)

Since the growth factor is less than 1, it is a decay equation.

\(\dfrac38=1-\dfrac58\\N(t)=4900\cdot\left(1-\dfrac58\right)^{t/7}\)

Observe that the time t is divided by 7.

This is the period.

We can therefore say that the bacterial culture loses \(\dfrac{5}{8}\)  of its size every 7 seconds.

Answer:

7

Step-by-step explanation:

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