What value of x satisfies the equation below? Explain
how you know
-3x = 15

Answer:

what's the number? .. . mmxmxmx

The probability that a mother is a carrier is approximately 0.018.

The Hardy-Weinberg equilibrium formula can be used to determine the frequency of alleles in a population, as well as to make predictions about the probability of certain traits occurring in the next generation. In this case, we are interested in determining the probability that a mother is a carrier of a particular disease, given that the frequency of the disease is 1/4300.

To use the Hardy-Weinberg formula, we need to know the frequency of both the dominant and recessive alleles in the population. Assuming that the disease allele is recessive (i.e., carriers are heterozygous), we can represent the frequency of the disease allele (q) as

\(q = \sqrt{(1/4300)} = 0.004644.\)

To determine the frequency of carriers (heterozygotes), we can use the formula p * q * 2,

where p represents the frequency of the dominant allele (which is equal to 1 - q in this case).

Therefore:

\(p = 1 - q \\ = 1 - 0.004644 = 0.995356\\q = \sqrt{(1/4300} = 0.004644\\p * q * 2 =0.018\)

Approximately 1.8% of the population will be carriers of the disease allele. This means that the probability that a mother is a carrier is approximately 0.018.

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The number of cows needed to satisfy the beef appetite would be 5263

With an average yield of 570 pounds (258.1 Kg.) of prepared beef per cow, we need to determine how many people can be fed from this amount. The number of people fed per cow can vary depending on various factors such as portion sizes and individual dietary preferences. Assuming a reasonable estimate, let's consider that one pound (0.45 Kg.) of prepared beef can feed about three people.

To find the number of cows needed to satisfy the beef appetite for New York City's population of approximately 9,000,000 people, we divide the population by the number of people fed by one cow. Thus, the calculation becomes 9,000,000 / (570 pounds x 3 people/pound).

After simplifying the equation, we get 9,000,000 / 1710 people, which equals approximately 5,263 cows. However, it's important to note that this is a rough estimate and does not consider factors such as variations in consumption patterns, distribution logistics, or other sources of meat supply. Additionally, individual dietary choices and preferences may result in different consumption rates. Therefore, this estimate serves as a general indication of the number of cows needed to satisfy the beef appetite for New York City's population.

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The sum in summation notation of the expression (a) 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is ΣX from 1 to 4. In other words, it represents the summation of X over the range 1 to 4.

In summation notation, the expression (a) 1 + 2 + 3 + 4 + X5 can be written as ΣX, where X takes the values from 1 to 4. The capital sigma (Σ) represents the summation operator, and the variable X is summed over the range 1 to 4. This means that we need to substitute X with each value from 1 to 4 and add them together.

When we evaluate the expression, we have:

ΣX = 1 + 2 + 3 + 4 = 10

However, the expression also includes X5, indicating that X takes the value 5 as well. Therefore, we add 5 to the sum:

ΣX = 10 + 5 = 15

So, the sum of 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is equal to 15.

Moving on to expression (b) y2 + y3 + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, we can express it in summation notation as ΣY from 1 to 3. This represents the summation of Y over the range 1 to 3.

Since Y has a different value for each term, we simply substitute Y with each value from 1 to 3 and add them together:

ΣY = y₁ + y₂ + y₃ = -1 + (-0.5) + 0 = -1.5

Hence, the sum of y₂ + y₃ + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, is equal to -1.5.

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Answer:

The cost of one brownie is $0.75

Step-by-step explanation:

The given parameters are;

The number of pizza's Marcel bought = 4 pieces

The number of brownies Marcel bought = 2 brownies

The amount Marcel paid = $18.50

The number of pizza's Morgan bought = 3 pieces

The number of brownies Morgan bought = 2 brownies

The amount Morgan paid = $14.25

Let x represent the cost of a pizza and y represent the cost of a brownie, we have;

4·x + 2·y = $18.50...(1)

3·x + 2·y = $14.25...(2)

Subtracting equation (1) from equation (2) gives;

4·x + 2·y - (3·x + 2·y) = $18.50 - $14.25 = $4.25

4·x - 3·x + 2·y - 2·y = $4.25

x = $4.25

The cost of a pizza = x = $4.25

4·x + 2·y = $18.50

2·y = $18.50 - 4·x = $18.50 - 4×$4.25 = $1.5

y = $1.5/2 = $0.75

y = $0.75

The cost of a brownie = $0.75

Answer: √177

Step-by-step explanation:

6²+9²=c²

36+81=c²

117=c²

√117=√c²

√177 = c

(√177 can also be watered down to ±3√13 but √177 is one of the answer choices so yeah)

Answer:a

Step-by-step explanation:

Answer: $16 dollars

Step-by-step explanation: 40% of 40 is 16 so you save $16. Game would now cost $24.

Answer:

Step-by-step explanation:

B) rectangle because the diagonals are congruent

C) Diamond so no it isn't a square or rectangle due to no 90 degree angles

D)Square because the diagonals are perpendicular and congruent

==================================================

Work Shown:

cos(angle) = adjacent/hypotenuse

cos(L) = ML/LK

cos(L) = 24/25

The diagram is below.

The side KM = 7 is not used at all.

Answer:

55

Step-by-step explanation:

we have 342 students, subtract 12 because we need only kids riding the bus, now we have 330 kids, we divide the 330 kids between 6 buses 330/6, our answer is 55.

The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:

C. m∠5 + m∠6 =180°.

D. m∠2 + m∠3 = m∠6.

E. m∠2 + m∠3 + m∠5 = 180°.

In Geometry, the Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two (2) adjacent angles would be equal to 180º when two (2) parallel lines are cut through by a transversal:

m∠5 + m∠6 =180°.

In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:

m∠2 + m∠3 = m∠6.

Additionally, the sum of all the angles that are formed by a triangle is equal to 180º and this is given by:

m∠2 + m∠3 + m∠5 = 180°,

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The length of a standard basketball court is 94 feet (28.65 meters), and the width is 50 feet (15.24 meters).

A standard basketball court is rectangular in shape and follows certain dimensions specified by the International Basketball Federation (FIBA) and the National Basketball Association (NBA). The length and width of a basketball court may vary slightly depending on the governing body and the level of play, but the most commonly used dimensions are as follows:

The length of a basketball court is typically 94 feet (28.65 meters) in professional settings. This length is measured from baseline to baseline, parallel to the sidelines.

The width of a basketball court is usually 50 feet (15.24 meters). This width is measured from sideline to sideline, perpendicular to the baselines.

These dimensions provide a standardized playing area for basketball games, ensuring consistency across different courts and facilitating fair play. It's important to note that while these measurements represent the standard dimensions, there can be slight variations in court size depending on factors such as the venue, league, or specific regulations in different countries.

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Answer:

X=7/2 Y=1

Step-by-step explanation:

4X-Y=13

4X-13=Y

2X-3(4X-13)=4

2X-12X+39=4

-10X+39=4

-10X=4-39

-10X=-35

X=7/2(-35/10)

Y=4(7/2)-13

Y=14-13

Y=1

The solution of the two given linear equations will be equal to X=7/2 Y=1

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The solution of the linear equation is as follows:-

4X  -  Y   =    13

4X  -  13   =   Y

2X   -   3  (   4X  -  13  )   =    4

2X   -   12X   +    39   =    4

-10X   +    39  =  4

-10X  =    4  -   39

-10X    =    -35

X   =    7/2   (  -35  /   10   )

Y   =   4  (  7/2  )  -   13

Y   =  14  -  13

Y  =   1

Therefore the solution of the two given linear equations will be equal to X=7/2 Y=1

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Answer:

P'(2, 4)

Q'(3, 1)

R'(1, 1)

Step-by-step explanation:

In a reflection across the y-axis, each point is the same distance on the other side of the y-axis as it was originally. Change each x-coordinate to its opposite.

P'(2, 4)

Q'(3, 1)

R'(1, 1)

Answer:

Here is a screenshot of my graph.

Step-by-step explanation:

Answer:

A: the sample size is less than 30

Step-by-step explanation:

Usually, the t-distribution is used instead of normal distribution in calculation of the mean of a normally distributed population when the sample size is small (n < 30) and if the population standard deviation is not known.

Thus, looking at the options, the correct one is Option A.

Maclaurin series of `f(x)` is given by:f(x) = `f(0)` + `f'(0)x` + `(f''(0)/2!) x²` + `(f'''(0)/3!) x³` + `(f⁴(0)/4!) x⁴` + `(f⁵(0)/5!) x⁵` + `(f⁶(0)/6!) x⁶` = `0 + 0x + 0x² + 0x³ + 0x⁴ + 0x⁵ + (7200/6!)x⁶` = `10x⁶`

Answer: `10x⁶`.

The given function is `f(x) = x⁶ sin(10x⁵)`. We need to find the Taylor series of `f` centered at `0` (Maclaurin series of `f`).

Formula used: The Maclaurin series for `f(x)` is given by `f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ...... + (f^n(0)/n!)x^n`.

Here, `f(0) = 0` because `sin(0) = 0`.

Differentiating `f(x)` and its derivatives at `x = 0`:`f(x) = x⁶ sin(10x⁵)`

First derivative: `f'(x) = 6x⁵ sin(10x⁵) + 50x¹⁰ cos(10x⁵)`

Differentiate `f'(x)`

Second derivative: `f''(x) = 30x⁴ sin(10x⁵) + 200x⁹ cos(10x⁵) - 250x¹⁰ sin(10x⁵)`

Differentiate `f''(x)`

Third derivative: `f'''(x) = 120x³ sin(10x⁵) + 1800x⁸ cos(10x⁵) - 2500x⁹ sin(10x⁵) - 5000x²⁰ cos(10x⁵)`

Differentiate `f'''(x)`

Fourth derivative: `f⁴(x) = 360x² sin(10x⁵) + 7200x⁷ cos(10x⁵) - 22500x⁸ sin(10x⁵) - 100000x¹⁹ cos(10x⁵) + 100000x²⁰ sin(10x⁵)`

Differentiate `f⁴(x)`

Fifth derivative: `f⁵(x) = 720x sin(10x⁵) + 36000x⁶ cos(10x⁵) - 112500x⁷ sin(10x⁵) - 1900000x¹⁸ cos(10x⁵) + 2000000x¹⁹ sin(10x⁵)`

Differentiate `f⁵(x)`

Sixth derivative: `f⁶(x) = 7200 cos(10x⁵) - 562500x⁶ cos(10x⁵) + 13300000x¹⁷ sin(10x⁵)`

Evaluate at `x = 0`:

The derivatives of `f(x)` evaluated at `x = 0` are:f(0) = 0f'(0) = 0f''(0) = 0f'''(0) = 0f⁴(0) = 0f⁵(0) = 0f⁶(0) = 7200

Maclaurin series of `f(x)` is given by:f(x) = `f(0)` + `f'(0)x` + `(f''(0)/2!) x²` + `(f'''(0)/3!) x³` + `(f⁴(0)/4!) x⁴` + `(f⁵(0)/5!) x⁵` + `(f⁶(0)/6!) x⁶` = `0 + 0x + 0x² + 0x³ + 0x⁴ + 0x⁵ + (7200/6!)x⁶` = `10x⁶`

Answer: `10x⁶`.

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Approximately 68% of women have platelet counts between 175.6 and 314.6. (Type an integer or a decimal. Do not round).

Given the blood platelet counts of a group of women has a bell-shaped distribution with a mean of 245.1 and a standard deviation of 69.5.

Using the empirical rule, we need to find the following percentage:

a) What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 106.1 and 384.1?Empirical Rule states that the percentage of data within k standard deviations of the mean for bell-shaped distribution is approximately:(±1 standard deviation) - about 68% of the data (±2 standard deviations) - about 95% of the data (±3 standard deviations) - about 99.7% of the data.

Now, mean = 245.1 Standard Deviation = 69.5 Plugging in the values in the formula, we have; Lower Limit, L = Mean - 2 × standard deviationL = 245.1 - 2 × 69.5L = 106.1 Upper Limit, U = Mean + 2 × standard deviationU = 245.1 + 2 × 69.5U = 384.1 So, 68% of women in this group have platelet counts within 2 standard deviations of the mean, or between 106.1 and 384.1.

b) What is the approximate percentage of women with platelet counts between 175.6 and 314.6?Now, we need to convert the range to standard units.(x - mean) / standard deviationFor the lower limit, (175.6 - 245.1) / 69.5 = -0.996For the upper limit, (314.6 - 245.1) / 69.5 = 1.001

Using the Z-table, the area to the left of z = 1.001 is 0.8413 and the area to the left of z = -0.996 is 0.1587. Area between the limits is = 0.8413 - 0.1587 = 0.6826

Therefore, Approximately 68% of women have platelet counts between 175.6 and 314.6. (Type an integer or a decimal. Do not round).

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Let the original cost of the jacket be x.

Now, saying that one-third of the original cost of the jacket is $34, is mathematically equivalent to:

Now we have to solve the resulting equation in order to obtain the value of x

This is done as follows:

Therefore, the original cost of the jacket is $102

Answer:C) specialization.

Step-by-step explanation:

According to the Question, the following conclusions are:

1) Hence proved that B is invertible, and B is the inverse matrix of A.

2) A is an invertible matrix, and its inverse is \(A^{-1 }= (\frac{1}{4} ) * (I - 5A).\)

1) Given A is an invertible square matrix.

A = B²

B = A²

To prove:

B is invertible.

B is the inverse matrix of A.

Proof:

To demonstrate that B is invertible, we must show that it possesses an inverse matrix.

Let's assume the inverse of B is denoted by \(B^{-1}.\)

We know that B = A². Multiplying both sides by \(A^{-2}\) (the inverse of A²), we get:

\(A^{-2} * B = A^{-2 }* A^2\\A^{-2} * B = I\)

(since \(A^{-2 }* A^{2} = I,\) where I = identity matrix)

Now, let's multiply both sides by A²:

\(A^2 * A^{-2} * B = A^2 * I\\B = A^2 (A^{-2 }* B) \\B= A^2 * I = A^2\)

We can see that B can be expressed as A² multiplied by a matrix \((A^{-2} * B),\) which means B can be written as a product of matrices. Therefore, B is invertible.

To prove that B is the inverse matrix of A, we need to show that A * B = B * A = I, where I is the identity matrix.

We know that A = B². Substituting B = A² into the equation, we have:

A = (A²)²

A = A²

Now, let's multiply both sides by \(A^{-1 }\) (the inverse of A):

\(A * A^{-1} = A^4 * A^{-1}\\I = A^3\)

(since \(A^4 * A^{-1 }= A^3,\) and \(A^3 * A^{-1 }= A^2 * I = A^2\))

Therefore, A * B = B * A = I, which means B is the inverse matrix of A.

Hence, we have proved that B is invertible, and B is the inverse matrix of A.

2) Given:

A is a square matrix.

A² = 4A + 5I, where I = identity matrix.

To prove:

A is an invertible matrix and find its inverse.

Proof:

To prove that A is invertible, We need to show that A has an inverse matrix.

Let's assume the inverse of A is denoted by \(A^{-1}.\)

We are given that A² = 4A + 5I. We can rewrite this equation as

A² - 4A = 5I

Now, let's multiply both sides by \(A^{-1}:\)

\(A^{-1} * (A^2 - 4A) = A^{-1 }* 5I\\(A^{-1} * A^2) - (A^{-1} * 4A) = 5A^{-1} * I\\I - 4A^{-1} * A = 5A^{-1} * I\\I - 4A^{-1} * A = 5A^{-1}\)

Rearranging the equation, we have:

\(I = 5A^{-1} + 4A^{-1} * A\)

We can see that I represent the sum of two terms, the first of which is a scalar multiple of \(A^{-1},\) and the second of which is a product of \(A^{-1}\) and A. This shows that  \(A^{-1}\) it exists.

Hence, A is an invertible matrix.

To find the inverse of A, let's compare the equation \(I = 5A^{-1 }+ 4A^{-1} * A\)with the standard form of the inverse matrix equation:

\(I = c * A^{-1 }+ d * A^{-1} * A\)

We can see that c = 5 and d = 4.

Using the formula for the inverse matrix, the inverse of A is given by:

\(A^{-1} = (\frac{1}{d} ) * (I - c * A^{-1 }* A)\\A^{-1} = (\frac{1}{4} ) * (I - 5A)\)

Therefore, the inverse of A is

\(A^{-1 }= (\frac{1}{4} ) * (I - 5A).\)

In conclusion, A is an invertible matrix, and its inverse is \(A^{-1 }= (\frac{1}{4} ) * (I - 5A).\)

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Answer:

-9/4

Step-by-step explanation:

x2 + 3x + c     complete the square

(x+( 3/2)^2  -9/4      c = -9/4

Answer:

Step-by-step explanation:

9/4

The feasible region is not empty and the objective function is bounded because it achieves its minimum value at the corner point (0, 0). Hence, the solution to the given LP problem is (x, y) = (0, 0).

Given an LP problem Minimize \(c = x + 2y\) subject to the constraints \(x + 3y ≤ 223 8x + y ≤ 23 x ≥ 0, y ≥ 0\)

Now we can start solving this LP problem by drawing the graph for the given constraints :

Plotting the constraints on a graph.

We can see that the feasible region is the shaded region bounded by the lines x = \(0, y = 0, 8x + y = 23, and x + 3y = 223\)

Now we can check the corner points of this region for finding the optimal solution of the given problem.

Corner points of the feasible region are:

(0, 0), (0, 7.67), (2.88, 71.07), (23, 66.33), and (27.33, 65).

Now we can substitute these values of x and y into the objective function \(c = x + 2y\) and see which corner point gives us the minimum value of c.

The table below summarizes this calculation.

Corner point

\((x, y)c = x + 2y\) (0,0)0(0,7.67)15.34(2.88,71.07)145.03(23,66.33)112.67(27.33, 65)157.67.

Thus, we can see that the minimum value of the objective function \(c = x + 2y\) is achieved at (0, 0),

which is one of the corner points of the feasible region.

Therefore, the optimal solution of the given LP problem is \(x = 0\) and \(y = 0\)

Also, we can see that the feasible region is not empty and the objective function is bounded because it achieves its minimum value at the corner point (0, 0).

Hence, the solution to the given LP problem is \((x, y) = (0, 0)\)

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The true option regarding the relationship between a catalyst and a chemical reaction is D. Each reaction has its own unique catalyst.

A catalyst is a substance that accelerates the rate of a chemical reaction without affecting the end product. They only have an effect on the rate of the reaction, not the yield.

Catalysts offer an alternative reaction pathway with lower activation energy than uncatalyzed reactions. It raises the frequency of collision and, as a result of the increased collision, lowers the activation energy of the reaction.

A chemical reaction is a process that converts one or more substances, known as reactants, to one or more different substances, known as products. Chemical elements or compounds are examples of substances.

A chemical reaction rearranges the constituent atoms of the reactants to produce various products. The properties of the products differ from the properties of the reactants. It is distinct from physical changes, which include state changes such as ice melting to water and water evaporating to vapor.

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Answer:

The mean is 8.6 minutes.

Step-by-step explanation:

"mean" is the average, the way people might talk about it in common language (not necessarily math class language.)

To calculate the mean, you ADD and DIVIDE. You add up all the numbers in your list and divide by however many numbers there are.

ADD:

5+5+15+12+14+6+3

= 60

Then DIVIDE by 7 (bc there are 7 items in the list)

60/7

= 8.5714285714

They said to round to the nearest tenth.

8.5714285714 rounds to 8.6

The mean is 8.6 minutes.

Answer:

the sales tax is 1.036 if you solve in this equation 7.25/100*14.29

Answer:

The radious would be 10.59 in

Step-by-step explanation:

The sample mean (X) of 10 observations selected from a normal population having population standard deviation (σ) of 5 is 20 with the standard deviation of the sample (s) being 2.23.

The formula for sample mean is given by,

Sample Mean \((X)= (x1+x2+x3+...+xn) / n\)

Where x1, x2, x3,...,xn are individual observations and n is the number of observations.

In this case, the sample mean (X) is given as 20 and the number of observations (n) is 10.

Therefore, the formula can be written as:

\(X = (x1+x2+x3+...+x10) / 10\)

Since the population standard deviation (σ) is given as 5, the standard deviation of the sample (s) can be calculated using the formula:

s = σ/√n

Where n is the number of observations.

Therefore, in this case, the standard deviation of the sample (s) is calculated as:

s = 5/√10

s = 2.23

Thus, the sample mean (X) of 10 observations selected from a normal population having population standard deviation (σ) of 5 is 20 with the standard deviation of the sample (s) being 2.23.

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