Marie and Jorge are both trying to lose weight. After 3 months they compared their weight loss. Marie's weight went from 175 to 150. Jorge's weight went from 190 to 180. Which statements are true regarding their weight loss? Select three options. Jorge's weight change was approximately 5%. Marie's weight change was approximately 14%. Marie had the greater percent change. Jorge had the greater percent change. Marie's weight change was approximately 1.4%.

Answer:

A, B, and C are all true.

Step-by-step explanation:

A. 6 is neither a perfect square nor a perfect cube.   True

B. 16 is a perfect square.   True \(4^{2}\)

C. 27 is a perfect cube.   True \(3^{3}\)

OD. 1,331 is both a perfect square and a perfect cube.   False

E. 9 is a perfect cube.  False

Answer:

Step-by-step explanation:

One way you could do this is to put a vertical line at x = 6. Let that line have the properties of a mirror. Enlarge this and check out the lowest point which is at x = 2 y = 4,5

The same point for B is at x = 10 and y = 4.5

The x value in both cases is 4 units from the reflective line.

Answer:

x = 4

Step-by-step explanation:

(b)

\(\frac{2x+1}{3}\) = 5 - \(\frac{1}{2}\) x

Multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions

2(2x + 1) = 30 - 3x , distribute parenthesis on left side

4x + 2 = 30 - 3x ( add 3x to both sides )

7x + 2 = 30 ( subtract 2 from both sides )

7x = 28 ( divide both sides by 7 )

x = 4

Answer:

12xphjzjhsgwghdghehdhhez7uehdyegd

Answer:

trinomial..............

The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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Answer:

182 \(yd^{2}\)

Step-by-step explanation:

Area of a parallelogram: bh

bh

= 13(14)

= 182 sq. yds

Answer: 13 units or whatever measurement you're using.

Step-by-step explanation: First get -14 to -7 by adding 7. Then get 11 to 5 by subtracting 6 then adding 6 and 7 together I'm pretty sure.

Answer:

360cm³

Step-by-step explanation:

Volume of a triangular prism = Base area * Height of prism

Height of prism = 15cm

Base area = 1/2 * 6 * 8

Base area = 24cm²

Volume of the prism = 15 * 24

Volume of the prism = 360cm³

​

Answer:

Step-by-step explanation:

The value of x or the missing length is 16 units after applying the Pythagoras theorem option (C) is correct.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

It is given that:

A right-angle triangle is shown in the picture with dimensions.

A right-angle triangle is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is required to find the value of x.

To find the value of the x we can use Pythagoras theorem:

Using Pythagoras theorem:

hypotenuse² = perpendicular² + base²

Let the red line length is y

(15)² = 9² + (y)²

y = 144 units

x = 144/9

x = 16 units

Thus, the value of x or the missing length is 16 units after applying the Pythagoras theorem option (C) is correct.

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Answer:  $41.50  41 dollars and 50 cents in profit

Step-by-step explanation:

First, 1.25x48=60

Second, 60-18.50=41.50

Answer:

$41.50

Step-by-step explanation:

So we know that Gavin bought 48 water bottles before the game for $18.50. We also know that he sold the water bottles for $1.25 each.

If we want to know how much profit he made, we first have to find the amount of money he received.

To find this, we need to multiply the number of water bottles by the price for each bottle;

48 × $1.25

This gives us a total of $60.

Now to find the profit, we have to subtract the amount he paid for the water bottles by the total he made;

$60 - $18.50

This means he made a profit of $41.50.

hope this makes sense! <3

Answer:

Step-by-step explanation:

Using the Base Angles Theorem to define the terms relating to an isoceles triangle:

An isoceles triangle has two congruent sides, referred to as the legs. As the legs of a triangle are slanted, they will intersect at a point known as the vertex angle.  The side that is opposite to the vertex angle is the base of the triangle.

Therefore, the following are the missing terms in the given problem:

SOLUTION:

We are to find the measurement of angle A.

Since the three sides are known, we just pick any of the two sides.

Considering

Using the trigonometric ratio:

The measurement of angle A is 53.13 degrees.

The initial value problems can be solved using the method of Laplace transforms. For problem 1, the solution is y(t) =\(e^t(cos(2t) + 3sin(2t))\). For problem 3, the solution is y(t) = \(e^(-3t)\)(2cost - sint). For problem 7, the solution is y(t) = 2e^(2t) + 3e^(5t) + (2/3)cost - (1/3)sint.

For problem 1, taking the Laplace transform of y" - 2y' + 5y = 0 gives us s^2Y(s) - 2sY(s) + 5Y(s) = Y''(s) - 2sY(s) + 5Y(s) = 0. Applying the initial conditions, we get Y(s) = \((s + 1)/(s^2 - 2s + 5)\). Simplifying and finding the inverse Laplace transform, we obtain y(t) = \(e^t\)(cos(2t) + 3sin(2t)).

For problem 3, taking the Laplace transform of y" + 6y' + 9y = 0 gives us s^2Y(s) + 6sY(s) + 9Y(s) = Y''(s) + 6sY(s) + 9Y(s) = 0. Applying the initial conditions, we get Y(s) = \((s + 3)/(s^2 + 6s + 9)\). Simplifying and finding the inverse Laplace transform, we obtain y(t) = e^(-3t)(2cost - sint).

For problem 7, taking the Laplace transform of y" - 7y' + 10y = 9cost + 7sint gives us \(s^2Y(s)\) - 7sY(s) + 10Y(s) = \((9s)/(s^2 + 1)\) + \((7)/(s^2 + 1).\)Applying the initial conditions, we get Y(s) = \((9s + 7)/(s^2 - 7s + 10).\) Simplifying and finding the inverse Laplace transform, we obtain y(t) = \(2e^(2t) + 3e^(5t) + (2/3)\)cost - (1/3)sint.

These solutions are obtained by applying the method of Laplace transforms to the given initial value problems, providing the solutions in the time domain.

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The total surface area of the trapezoidal prism is S = 3,296 inches²

Given data ,

Let the total surface area of the trapezoidal prism is S

Now , the measures of the sides of the prism are

Side a = 10 inches

Side b = 32 inches

Side c = 10 inches

Side d = 20 inches

Length l = 40 inches

Height h = 8 inches

Lateral area of prism L = l ( a + b + c + d )

L = 40 ( 10 + 32 + 10 + 20 )

L = 2,880 inches²

Surface area S = h ( b + d ) + L

On simplifying the equation , we get

S = 2,880 inches² + 8 ( 52 )

S = 3,296 inches²

Hence , the surface area of prism is S = 3,296 inches²

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Answer:

a square

Step-by-step explanation:

a square has all right angles an no acute angles

To determine the probability of a continuous distribution we use the integral to determine it and for the normal distribution the integral is not so simple, for that reason it is simpler to use range values from tables.

Probability can be determined from a continuous distribution in the following way:To compute the probability of a given interval for a continuous random variable, the area under the curve over the interval is determined. Integrals are used to calculate this area under the curve, which can be done either numerically or analytically using probability density functions.

For some distributions, such as the uniform distribution, calculating the area under the curve is straightforward. However, for other distributions, such as the normal distribution, it can be more difficult to calculate the integral analytically.

The normal distribution is a continuous probability distribution that is frequently used in statistics. It is defined by its probability density function, which is a bell-shaped curve with a mean and a standard deviation.

Calculating the area under the curve for the normal distribution requires the use of integrals. Integrals are difficult to solve analytically for the normal distribution because the probability density function is not simple. However, it is relatively simple to calculate the probability for a given range of values using standard statistical tables or computer software.

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Answer:

I got -5/6

Step-by-step explanation:

Y2-Y1/X1-X2

So -3-2/5-(-1) =-5/6

I hope this is the right answer  :)

The correct statement regarding the sign of the residuals in the table is given as follows:

3 negative residuals and 5 positive residuals.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the residuals are classified as either positive or negative as follows:

Thus the residuals in this problem are classified follows:

Hence the third statement is correct.

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Answer:

-8x-4y

Step-by-step explanation:

distrubutive property

Given:

Point P divides the line segment AB in 5:3 where A(-6,9) and B(2,1).

To find:

The coordinates of point P.

Solution:

Section formula: If a point divide a line segment in m:n, then the coordinates of point are

\(\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)\)

Point P divides the line segment AB in 5:3 where A(-6,9) and B(2,1). Using section formula, we get

\(P=\left(\dfrac{5(2)+3(-6)}{5+3},\dfrac{5(1)+3(9)}{5+3}\right)\)

\(P=\left(\dfrac{10-18}{8},\dfrac{5+27}{8}\right)\)

\(P=\left(\dfrac{-8}{8},\dfrac{32}{8}\right)\)

\(P=\left(-1,4\right)\)

Therefore, the coordinates of point P are (-1,4).

True. The null hypothesis (denoted as H0) is a statement about a population parameter, typically a population mean or proportion, and it is formulated based on the assumption that there is no effect, relationship, or difference in the population.

However, in statistical hypothesis testing, data is often collected from a sample, not the entire population, due to practical limitations.

The sample data is then used to assess the evidence against the null hypothesis.

The null hypothesis is always stated in terms of the population, even though the data being analyzed comes from a sample.

The standard deviation formula is derived from the variance formula, which is calculated by finding the sum of the squared deviations of each data point from the mean.

The standard deviation is simply the square root of the variance. This is because the variance is expressed in squared units, and the standard deviation is expressed in the original units of the data.

The equation used in the derivation of standard deviation is the formula for variance, which is given by:

Variance = ∑(x - μ)² / n

Where x is the individual data point, μ is the mean of the data set, and n is the number of data points in the set.

The standard deviation formula is simply the square root of the variance formula. The standard deviation formula is given by:

Standard deviation = √(Variance)

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When the mean of the sampling distribution is the same value as the population parameter, we can say that the statistic is an unbiased estimator.

An unbiased estimator happens to be the situation in statistics where the expected value of a population parameter is the same as the true value of that same parameter.

Hence we can conclude that When the mean of the sampling distribution is the same value as the population parameter, we can say that the statistic is an unbiased estimator.

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Answer:

The derivative of a function gives us the slope of the tangent at any given point on the curve. Therefore, f'(1) = 2.

Given a function \($f(x) = 2x^2 - 2x + 2$\), we have to find the value of \($f'(1)$\)

We know that the derivative of a function gives us the slope of the tangent at any given point on the curve. The derivative of the function f(x)   \($$f(x) = 2x^2 - 2x + 2$$$$\Rightarrow f'(x) = \frac{d}{dx}(2x^2 - 2x + 2)$$$$\Rightarrow f'(x) = 4x - 2$$\)

Hence, the derivative of the function f(x) is given as \($f'(x) = 4x - 2$\).Now we need to find f'(1). This means we have to substitute x = 1 in the derivative of the function.

\($$\Rightarrow f'(1) = 4(1) - 2$$$$\Rightarrow f'(1) = 2$$\)

Therefore, f'(1) = 2.

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Answer:

x = 3.75

Step-by-step explanation:

Replace y with the y equation.

So..

4x - 2(x + 1.75) = 4

Answer:

(3.75, 5.5)

Step-by-step explanation:

Adding x (3.75) to 1.75 gives 5.50 (5.5). If this is correct, then 4 x 3.75 + 2 x 5.5 = 4

Answer:

20 and 55

Step-by-step explanation:

Let's assume, we have two numbers 'x' and 'y'.

Now, all we know is:

So we form two equations:

x + y = 75_____(i)

and x - y =  35

so, x = y+35 _____(ii)

Put the value of x from (ii) into (i)

x + y = 75

y + 35 + y = 75

2y = 40

y = 20

Put value of y back in (ii)

x = y+35

x = 20 + 35

x = 55

The first number is 20, and the second number is 55.

Given that the sum of two numbers is 75, one exceeds the other by 35, we need to find the numbers.

Let's assume the first number is x.

According to the problem, the second number exceeds the first by 35, so the second number can be expressed as (x + 35).

The sum of the two numbers is given as 75, so we can set up the equation:

x + (x + 35) = 75

Simplifying the equation, we get:

2x + 35 = 75

Subtracting 35 from both sides:

2x = 40

Dividing both sides by 2:

x = 20

Therefore, the first number is 20, and the second number is (20 + 35) = 55.

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The exact solutions to the equation log(x+47) + log(x-1) = 2 are:

x = (-45 + √(3013)) / 2 and x = (-45 - √(3013)) / 2

To solve the equation log(x+47) + log(x-1) = 2, we can combine the logarithms using the properties of logarithms.

Using the property log(a) + log(b) = log(ab), we can rewrite the equation as:

log[(x+47)(x-1)] = 2

Next, we can rewrite the equation in exponential form:

\((x+47)(x-1) = 10^2\)

Simplifying the equation further:

\(x^2 + 46x - x - 47 = 100\)

\(x^2 + 45x - 147 = 100\)

\(x^2 + 45x - 247 = 0\)

Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, the quadratic equation does not factor easily, so we will use the quadratic formula:

x = (-b ± √(\(b^2\) - 4ac)) / (2a)

In our equation, a = 1, b = 45, and c = -247. Plugging these values into the quadratic formula:

x = (-45 ± √(\(45^2\) - 4(1)(-247))) / (2(1))

Simplifying further:

x = (-45 ± √(2025 + 988)) / 2

x = (-45 ± √(3013)) / 2

Therefore, the exact solutions to the equation log(x+47) + log(x-1) = 2 are:

x = (-45 + √(3013)) / 2 and x = (-45 - √(3013)) / 2

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