Which point represents the quotient of 3-1?

A
B
C
D

Answer:

0.421875

Step-by-step explanation:

0.42 simplified.

I hope this helps!!

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

The whole is equal to the sum of the parts.

  DG = DO +GO

  20 = (4x +1) + 7

  12 = 4x . . . . . . . . . . subtract 8

  3 = x . . . . . . . . . . . divide by 4

The garden will be in the shape of rectangle with length=18feet, breadth=12feet or length=20 feet, breadth=10 feet.

What is a rectangle?

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.

For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.

Perimeter of a Rectangle:-

The perimeter of a rectangle is defined as the total distance covered by the outer boundary of the rectangle. It is measured in unit length. The formula of perimeter is given by:

Perimeter, P = 2 (Length + Width)

Now,

Total fencing available=60feet

that means perimeter should be 60 feet of the garden.

Hence,

two dimensions of the rectangle could be length=18feet, breadth=12feet or length=20 feet, breadth=10 feet.

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Answer:

the answer should be 48

Answer:

A. 30

Step-by-step explanation:

y=mz+b

b=75

m=30

ROC(rate of change)=slope

ROC=30

The axis of symmetry is 2, x-intercept are (3,0) and (1,0) , y-intercept is (0,3) vertex is 2

Here we have to point the values on the given graph.

Then we get the graph like the following.

Now, we have to identify the value of axis of symmetry, x-intercept(s), y-intercept, & vertex through the following definition.

The axis of symmetry is a vertical line that divides the graph of a function into two mirror images. It passes through the vertex, which is the highest or lowest point on the graph. To find the axis of symmetry, we need to look for the vertical line that divides the graph into two equal parts is x = 2.

The x-intercept(s) are the points where the graph of a function crosses the x-axis. To find the x-intercepts, we need to look for the points where the graph intersects the x-axis, which is the horizontal line with a y-coordinate of (3,0) and (1,0)

The y-intercept is the point where the graph of a function crosses the y-axis. To find the y-intercept, we need to look for the point where the graph intersects the y-axis, which is the vertical line with an x-coordinate of 0 that is (0,3)

The vertex is the highest or lowest point on the graph of a function, depending on whether the function opens upward or downward. To find the vertex, we need to locate the point where the function reaches its maximum or minimum value is 2.

The completed graph is illustrated below.

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Answer:

144 m^2

Step-by-step explanation:

calculate the square bottom, 6x6 = 36 calculate triangle area 9x6/2 = 27 multiply by 4 triangle faces and add it all together to get 144

Answer:

67.872

Step-by-step explanation:

Answer:

the answer is 0.94

Step-by-step explanation:

16/17 = 0.941176470588

the hundreths place is where the 4 is, and to the right of the 4 is a one, if its under 5 then dont round up so your answer will remail 0.94.

hope this helps have a great day!

The equation of the perpendicular line as required is; y = 2x -3.

Since the line in discuss is perpendicular to the given line whose slope is; -1/2. It therefore follows that the slope of the line to be determined is;

m = -1/(-1/2) = 2.

The equation of the required line can therefore be written as;

2 = (y-7)/(x-2)

2x -4 = y -7

Hence, y = 2x -3 is the equation of the line.

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Answer:

(6, 0)

Step-by-step explanation:

Answer:

x = 8 √3

y = 8

Step-by-step explanation:

Here, we want to find the missing side length from the diagram

From the diagram let us identify each side

16 is the side that faces the right-angle and it is the longest side referred to as the hypotenuse

x is the side facing the angle given which is 60 degrees and is referred to as the opposite

The third side measuring y is the adjacent

To get x, we can link the hypotenuse and the opposite using the angle given

The measure of the sine of an angle is the ratio of the length of the opposite to that of the hypotenuse

Mathematically in this case;

sin 60 = x/16

x = 16 sin 60

x = 16 * √3/2

x = 8 √3

Lastly we want to get the third side marked y

Here, we can use the Pythagoras’ theorem

It states that the square of the length of the hypotenuse equals the sum of the squares of the two other sides

Thus, we have that;

16^2 = y^2 + (8 √3)^2

256 = y^2 + 192

y^2 = 256 -192

y^2 = 64

y = √64

y = 8

When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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Maximum = n/n+1 and Minimum = 1/n+1

What is the uniform distribution?

Probability distributions with uniform distributions have outcomes that are all equitably likely. Results are discrete and have the same probability in a discrete uniform distribution. Results are continuous and infinite in a continuous uniform distribution. Data near the mean occur more frequently in a normal distribution.

Here, we have

Given: X1, X2,..., Xn is independent and identically distributed random variables having uniform distributions over (0,1).

a) Z = max{X₁, X₂....Xₙ}

Since Z is maximum so it is greater than X1, X2...Xn so cdf of Z will be

F(Z) = P(Z≤z) = P(X₁, X₂....Xₙ≤z) = P(X₁≤z, X₂≤z.....Xₙ≤z)

= P(X₁≤z)P(X₂≤z)....P(Xₙ≤z) = Fₓ(z)Fₓ(z).....Fₓ(z)

F(Z) = zⁿ

So pdf of Z is

F(z) = F'(z) = nzⁿ⁻¹

Expectation of Z is

F(Z) = \(\int\limits^0_1 {zf_Z(z)} \, dz\) = \(n\int\limits^0_1 {} \,\)zⁿdz

= n[zⁿ⁺¹/n+1]₀¹ = n/n+1

b) Let Y = min{X₁, X₂....Xₙ}

Since Y is the minimum so it is less than X1, X2...Xn so the cdf of Y will be

F(Y) = P(Y≤y) = 1 - P(Y>y) = 1- P(X₁, X₂....Xₙ≤z) = 1- P(X₁≤z, X₂≤z.....Xₙ>y)

= 1- P(X₁>y)P(X₂>y)....P(Xₙ>y) = 1- Fₓ(y)Fₓ(y).....Fₓ(y)

= 1 - [1-y]ⁿ

So pdf of Y is

F(y) = F'(y) = n[1-y]ⁿ⁻¹

The expectation of Y is

E(Y) = \(\int\limits^0_1 {yf_Y(y)} \, dy\) = ∫₀¹ yn(1-y)ⁿ⁻¹dy = 1/n+1

Hence, Maximum = n/n+1 and Minimum = 1/n+1

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The cost of the fence used to make the rectangular sheep pen is £57.6. The result is obtained by multiplying the perimeter by the fencing price.

The cost for fencing a building can be calculated by multiplying the price of a certain size of fence by the perimeter or the length side to be fenced.

Bill builds a rectangular sheep pen.

Find the total cost of the fence!

The total cost of the fence will be

= P × fencing cost

= 24 m × £1.20 / ½ m

= 24 × £2.40

= £57.6

Hence, the fence to make the sheep pen will cost £57.6.

Your question is incomplete. But most probably your full question was

Bill needs to build a rectangular sheep pen. The pen must have a perimeter of 24 m. Every half meter of fencing costs him £1.20. Work out the cost of the fence used to make the sheep pen!

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Answer:

75

20 percent (calculated percentage %) of what number equals 15? Answer: 75

Step-by-step explanation:

f(x)= 2x² + 5x – 3, then what is f(–2)?. Possible Answers:. – 137.

The lower and upper limits of the confidence interval can be determined using the sample mean and sample standard deviation.

Given the sample readings of total calcium levels in mg/dl, we can calculate the sample mean (x) and sample standard deviation (s). Using these values, we can determine the lower and upper limits of the 99.9% confidence interval.

Calculating the sample mean:

x = (9.9 + 8.6 + 10.9 + 8.5 + 9.4 + 9.8 + 10.0 + 9.9 + 11.2 + 12.1) / 10 = 10.03 mg/dl

Calculating the sample standard deviation:

s = sqrt(((9.9 - 10.03)^2 + (8.6 - 10.03)^2 + ... + (12.1 - 10.03)^2) / (10 - 1)) = 1.16 mg/dl

To determine the 99.9%   confidence interval, we need to find the critical value corresponding to this level of confidence. Since the sample size is small (less than 30) and the population standard deviation is unknown, we can use the t-distribution. With a sample size of 10 and a desired confidence level of 99.9%, the critical value is approximately 3.250.

Calculating the margin of error:

Margin of error = critical value * (s / sqrt(n))

= 3.250 * (1.16 / sqrt(10))

≈ 1.19

The lower limit of the confidence interval is given by x - margin of error:

Lower limit = 10.03 - 1.19 ≈ 8.84 mg/dl

The upper limit of the confidence interval is given by x + margin of error:

Upper limit = 10.03 + 1.19 ≈ 11.22 mg/dl

Therefore, the 99.9% confidence interval for the population mean of total calcium in this patient's blood is approximately 8.84 mg/dl to 11.22 mg/dl.

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Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box.

Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box. In general, more metal is required for larger, thicker boxes. One must first calculate the box's volume in order to determine how much metal is required. The box's length, width, and height can be multiplied together to get this. The thickness of the metal must next be determined. The total amount of metal required can be estimated by multiplying the volume of the box by the thickness of the metal once the volume and thickness of the metal have been established. For instance, consider a box with dimensions of 6 inches long, 6 inches wide, and 6 inches high and a metal thickness.

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Option C : At age 32, Angel's intelligence score wil be 110 ,  While  her score at age 16  be 110 .

To calculate IQ, take a person's mental age, divide it by chronological age, then multiply that number by 100 .

An IQ test assesses a variety of cognitive skills and yields a score that is meant to be used as a gauge of a person's potential and intellectual process. Among psychological testing, IQ tests are frequently used. The organisation Mensa International, which serves persons with IQs in the top 2%, defines IQ as "a form of standard score that reflects how far above, or how far below, his/her peer group an individual stands in mental capacity."

There are many different intelligence tests available, and they might have very distinct contents. Three Many medications are made expressly to be given to children, but some are used for adults. There are several uses for IQ tests, including Educational assessment and placement,Assessment and diagnosis of intellectual disability ,Cognitive research,Job candidate evaluation.

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

Step-by-step explanation:

Solution:

Your problem → (3/11)-2 x (3/11)-5

(3/11)-2x(3/11)-5

=(3/11)-2x × (3/11)-5

=(3/11)-(6x/11)-5

=(3-6x-5×11)/11

=3-6x-55/11

=(-52-6x)/11

This expression yields: 4x^8 = 4 * (1/4)^(8/3)

If the expression 4x^3 is equal to 1 for some value of x, we can find the value of x by solving the equation:

4x^3 = 1

Dividing both sides of the equation by 4, we get:

x^3 = 1/4

Taking the cube root of both sides, we find:

x = (1/4)^(1/3)

Now, to determine the value of the expression 4x^8 for the same value of x, we substitute the value of x into the expression:

4x^8 = 4 * ((1/4)^(1/3))^8

Simplifying this expression yields:

4x^8 = 4 * (1/4)^(8/3)

Further simplification depends on whether you want an exact answer or an approximation. If you need an approximate value, please provide the desired level of precision.

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The statement that best defines the term "experiment" in the context of probability is (a) "A process that leads to only one of several possible outcomes."

An experiment is a process that is carried out to observe and study the outcome of an event or phenomenon. In probability, an experiment refers to a process that can have multiple outcomes, and the outcome cannot be predicted with certainty before the experiment is carried out.

For example, rolling a dice is an experiment in probability since it has multiple possible outcomes (rolling a 1, 2, 3, 4, 5, or 6) and the outcome cannot be predicted with certainty. Similarly, flipping a coin is also an experiment in probability since it can have two possible outcomes (heads or tails) and the outcome cannot be predicted with certainty.

On the other hand, option (b) is incorrect since a random trial whose outcome can be predicted on the basis of mathematical analysis is not an experiment but a deterministic process. Option (c) is also incorrect since a process that may or may not confirm a hypothesis does not define an experiment in the context of probability.

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Using simple interest, it is found that Mikos has to pay it back on September 13 of the same year.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

\(A(t) = A(0)(1 + rt)\)

In which:

In this problem:

Hence, we have to solve for t, then:

\(A(t) = A(0)(1 + rt)\)

\(104375 = 100000(1 + 0.105t)\)

\(1 + 0.105t = \frac{104375}{100000}\)

\(1 + 0.105t = 1.04375\)

\(0.105t = 0.04375\)

\(t = \frac{0.04375}{0.105}\)

\(t = 0.4166\)

This is the time in years, hence in days:

0.4166 x 365 = 152 days after April 14, thus on September 13.

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For a) the total probability of at least 10 are pregnant is 0.4509, or 45.09%. For b)  the probability that exactly 6 women are pregnant are 0.2128, or 21.28%. For c) same as option b). For d) Mean is (μ) = \(n * p\) ,  Standard Deviation (σ) =  \(sqrt(n * p * q)\).

To solve these probability questions, we can use the binomial probability formula. In the given scenario, we have:

- Probability of success (p): 60% or 0.6 (a woman requesting a pregnancy test is actually pregnant).

- Probability of failure (q): 40% or 0.4 (a woman requesting a pregnancy test is not pregnant).

- Number of trials (n): 12 ( women in the sample).

a) To find the probability that at least 10 women are pregnant, we need to calculate the probability of 10, 11, and 12 women being pregnant and sum them up.

\(\[P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12)\]\)

Where X follows a binomial distribution with parameters n and p.

Using the binomial probability formula, the probability for each scenario is:

\(\[P(X = k) = \binom{n}{k} \cdot p^k \cdot q^{(n-k)}\]\)

Using this formula, we can calculate:

\(\[P(X = 10) = \binom{12}{10} \cdot (0.6)^{10} \cdot (0.4)^2\]\)

\(\[P(X = 11) = \binom{12}{11} \cdot (0.6)^{11} \cdot (0.4)^1\]\)

\(\[P(X = 12) = \binom{12}{12} \cdot (0.6)^{12} \cdot (0.4)^0\]\)

To find the total probability of at least 10 women being pregnant, we need to calculate the probabilities for each possible number of pregnant women (10, 11, and 12) and add them up.

Let's calculate each individual probability:

For 10 pregnant women:

\(\[P(X = 10) = \binom{12}{10} \cdot (0.6)^{10} \cdot (0.4)^2\]\)

For 11 pregnant women:

\(\[P(X = 11) = \binom{12}{11} \cdot (0.6)^{11} \cdot (0.4)^1\]\)

For 12 pregnant women:

\(\[P(X = 12) = \binom{12}{12} \cdot (0.6)^{12} \cdot (0.4)^0\]\)

Now, we can add up these probabilities to find the total probability of at least 10 women being pregnant:

\(\[P(\text{{at least 10 women pregnant}})\) = \(P(X = 10) + P(X = 11) + P(X = 12)\]\)

Calculating each of these probabilities:

\(\[P(X = 10) = \binom{12}{10} \cdot (0.6)^{10} \cdot (0.4)^2 = 0.248832\]\)

\(\[P(X = 11) = \binom{12}{11} \cdot (0.6)^{11} \cdot (0.4)^1 = 0.1327104\]\)

\(\[P(X = 12) = \binom{12}{12} \cdot (0.6)^{12} \cdot (0.4)^0 = 0.06931408\]\)

Adding up these probabilities:

\(\[P(\text{{at least 10 women pregnant}})\) = \(0.248832 + 0.1327104 + 0.06931408 = 0.45085648\]\)

Therefore, the total probability of at least 10 women being pregnant is approximately 0.4509, or 45.09%.

b) To find the probability that exactly 6 women are pregnant, we can use the binomial probability formula:

\(\[P(X = 6) = \binom{12}{6} \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)

To find the probability that exactly 6 women are pregnant, we can use the binomial probability formula:

\(\[P(X = 6) = \binom{12}{6} \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)

Let's calculate this probability:

\(\[\binom{12}{6}\]\)  represents the number of ways to choose 6 women out of 12. It can be calculated as:

\(\[\binom{12}{6} = \frac{12!}{6! \cdot (12-6)!} = \frac{12!}{6! \cdot 6!} = 924\]\)

Now, we can substitute this value along with the given probabilities:

\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)

Evaluating this expression:

\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^6\]\)

Calculating the values:

\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^6 = 0.21284004\]\)

Therefore, the probability that exactly 6 women are pregnant is approximately 0.2128, or 21.28%.

c) To find the probability that at most 2 women are pregnant, we need to calculate the probabilities for 0, 1, and 2 women being pregnant and sum them up:

\(\[P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\]\)

To find the probability that exactly 6 women are pregnant, we can use the binomial probability formula:

\(\[P(X = 6) = \binom{12}{6} \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)

Let's calculate this probability:

\(\[\binom{12}{6}\]\) represents the number of ways to choose 6 women out of 12. It can be calculated as:

\(\[\binom{12}{6} = \frac{12!}{6! \cdot (12-6)!} = \frac{12!}{6! \cdot 6!} = 924\]\)

Now, we can substitute this value along with the given probabilities:

\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)

Evaluating this expression:

\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^6\]\)

Calculating the values:

\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^6 = 0.21284004\]\)

Therefore, the probability that exactly 6 women are pregnant is approximately 0.2128, or 21.28%.

d) The mean and standard deviation of a binomial distribution are given by the formulas:

Mean (μ) = \(n * p\)

Standard Deviation (σ) =  \(sqrt(n * p * q)\)

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Answer: 152 I think

Step-by-step explanation:

The statements for the function f( x) = 3x ²- 5 are

f( 5)< 1( false)

f( 0) = 1( false)

Statements for the function f(x) = 3x ²- 5

To find the true or false statement we have to substitute the value for x

First, x= 3

f(x) = 3x ²- 5

f(3)= 3( 5)²- 5

f(3) = 75- 5

f(3)= 70.

Thus, the statement" f( 5)< 1" is false.

Now, at x =0

f(x) = 3x ²- 5

f(0) = 3( 0)²- 5

f(0)= 0- 5

f(0)= -5.

Thus, the statement" f( 0) = 1" is false.

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Given the quadratic equation

we want to solve for the vertex and its axis of symmetry.

To easily identify these properties of quadratic equation, we must put the equation first into its vertex form. The first step to write it in its vertex form is to move the constant on the right-hand side of the equation

After that, we add the square of b/2 on the equation above. The value of b on the quadratic equation is -16. We have

Simplify the equation above

We write the expression on the left-hand side as perfect square, which is (x-4)^2.

Transfer 4 to left-hand side to write the vertex form of the quadratic equation

The vertex form has the general equation

where (h,k) is the vertex of the parabola.

Based on the vertex form of the quadratic formula, the vertex exists at (4,-4). Also, the axis of symmetry is equal to h, which is in this case, equal to 4.

The representation of a vertex and axis of symmetry in a quadratic plot will be

Answer: Vertex = (4,-4)

Axis of symmetry = 4