What is the volume of the rectangular pyramid?

Answer:

-4

Step-by-step explanation:

5x + 20 = 0

5x = -20 / : 5

x = -4

Answer: coordinates of the y-intercept is (0, -21)

Step-by-step explanation:

I'm assuming that you are asking for the coordinates of the y-intercept of the function

f(x)=(x-7)(x+3).

Well the y-intercept occurs when x=0, so plugging this value into f(x) yields f(0)=(-7)(3)=-21.

The limit as x approaches infinity of ln(1881x^2 + 1) - ln(x) is 0.

To solve this limit, we need to apply the rules of logarithms and L'Hopital's rule. First, we can simplify the expression using the logarithm rule that ln(a*b) = ln(a) + ln(b):

limx→[infinity] ln(1881x^2 + 1) - ln(x)

Next, we can apply L'Hopital's rule by taking the derivative of the numerator and denominator with respect to x:
limx→[infinity] [2*1881x / (1881x^2 + 1)] - [1/x]

As x approaches infinity, the second term approaches 0, so we are left with:
limx→[infinity] [2*1881x / (1881x^2 + 1)]

Now we can apply the limit rule that when we have a fraction with the same degree in the numerator and denominator, the limit is the ratio of their leading coefficients. The leading coefficient of the numerator is 2*1881 and the leading coefficient of the denominator is 1881, so the limit is:

limx→[infinity] [2*1881x / (1881x^2 + 1)] = 0

Therefore, the limit as x approaches infinity of ln(1881x^2 + 1) - ln(x) is 0.

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The index number indicates that the value in period 7 has increased by about 119.83% compared to the value in period 1.

Based on the information provided, we will calculate the simple index number for period 7 (i7) using the given values for y1 and y7.

The simple index number formula is:

i7 = (y7 / y1) × 100

Where y1 represents the value in period 1 (116) and y7 represents the value in period 7 (255).

Plugging in these values, we get: i7 = (255 / 116) × 100 i7 ≈ 219.83

Thus, the simple index number for period 7 (i7) is approximately 219.83.

This index number is a measure that compares the value of y7 to the value of y1, with y1 being the base period.

In this case, the index number indicates that the value in period 7 has increased by about 119.83% compared to the value in period 1.

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Answer:

[tex]6 \: {units}^{3} [/tex]

Step-by-step explanation:

Given:

A rectangular prism

a (base area) = 4,5

h (height) = 1 1/3

Find: V (volume) - ?

[tex]v = a(base) \times h = 4.5 \times 1 \frac{1}{3} = 4 \frac{1}{2} \times 1 \frac{1}{3} = \frac{9}{2} \times \frac{4}{3} = \frac{36}{6} = 6 \: {units}^{3} [/tex]

The perimeter of the rhombus is 52 units.

A rhombus is a quadrilateral with equal sides in Euclidean plane geometry. A quadrilateral with equal-length sides is also referred to as a "equilateral triangle". A parallelogram has a different shape called a rhombus. A rhombus has equal and parallel opposing sides and angles. A rhombus has equal-length sides and a right angle that divides its diagonal in half.

Let's denote the diagonals of the rhombus as d₁ and d₂, and let's denote its side length as s. The area of the rhombus is given by the formula:

A = (d₁ x d₂) / 2

Since the area is given as 120 square units and one diagonal is 10 units, we can substitute these values into the formula and solve for the other diagonal:

120 = (10 x d₂) / 2

240 = 10 x d₂

d₂ = 24 units

Now we can use the Pythagorean theorem to find the length of the sides of the rhombus:

s = √[(d₁/2)² + (d₂/2)²]

s = √[(10/2)² + (24/2)²]

s = √[25 + 144]

s = 13 units

Since a rhombus has four congruent sides, the perimeter of the rhombus is:

P = 4s = 4 x 13 = 52 units

Therefore, the perimeter of the rhombus is 52 units.

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The measure of the angle FNM is ∠FNM = 73°

Here we want to find the measure of the angle FNM, and we know the measures of two angles, these are:

∠GNF = 60°

∠MNL = 47°

You can see that:

∠GNF + ∠FNM + ∠MNL  = ∠GNL

And GNL is a plane angle, so its measure is 180°, then we can write tehe quation:_

60° + ∠FNM + 47° = 180°

We can solve that to get.

∠FNM  = 180° - 60° - 47°

∠FNM = 73°

That is the measure of the angle.

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To compare the likelihood ratio for each possible value X and order the xi according to it, we first calculate the likelihood function for H0 and HA:

L(H0) = 0.20.30.30.2 = 0.0036

L(HA) = 0.10.40.10.4 = 0.0016

Therefore, the likelihood ratio for x1 is:

λ(x1) = L(H0)/L(HA) = 0.0036/0.0016 = 2.25

The likelihood ratio for x2 is:

λ(x2) = L(H0)/L(HA) = 0.0036/0.064 = 0.05625

The likelihood ratio for x3 is:

λ(x3) = L(H0)/L(HA) = 0.0036/0.0016 = 2.25

The likelihood ratio for x4 is:

λ(x4) = L(H0)/L(HA) = 0.0036/0.064 = 0.05625

Therefore, we order the xi according to their likelihood ratio as x1, x3, x2, x4.

To test H0 versus HA at level α = 0.2, we compare the critical value of the likelihood ratio to the observed likelihood ratio. The critical value is given by the chi-square distribution with 1 degree of freedom at the 0.2 level of significance, which is 1.64. Since the maximum likelihood ratio is 2.25, which is greater than 1.64, we reject H0 and conclude in favor of HA.

To test H0 versus HA at level α = 0.5, we compare the critical value of the likelihood ratio to the observed likelihood ratio. The critical value is given by the chi-square distribution with 1 degree of freedom at the 0.5 level of significance, which is 0.455. Since the maximum likelihood ratio is 2.25, which is greater than 0.455, we reject H0 and conclude in favor of HA.

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Answer:

[tex]\huge\boxed{\sf 63}[/tex]

Step-by-step explanation:

[tex]= x^2+10x + 24[/tex]

Put x = 3

= (3)² + 10(3) + 24

= 9 + 30 + 24

= 63

[tex]\rule[225]{225}{2}[/tex]

Answer:

Option D) 63 is the correct answer.

Step-by-step explanation:

where :

[tex] \quad\sf{\dashrightarrow{{x}^{2} + 10x + 24}}[/tex]

Substituting the value of x :

[tex] \quad\sf{\dashrightarrow{{(3)}^{2} + 10 \times 3 + 24}}[/tex]

[tex] \quad\sf{\dashrightarrow{(3 \times 3) + 30 + 24}}[/tex]

[tex] \quad\sf{\dashrightarrow{(9) + 54}}[/tex]

[tex] \quad\sf{\dashrightarrow{9 + 54}}[/tex]

[tex] \quad\sf{\dashrightarrow{63}}[/tex]

[tex]\quad{\star{\underline{\boxed{\sf{\pink{63}}}}}}[/tex]

Hence, the answer is 63.

With regard to the above figures, "based on Cavalieri's Principle, since the cross sections have the same area and the figures have the same height, the figures will have the same volume."

Cavalieri's Principle states that if two figures have the same height and every cross-section at every height has the same area, then the two figures have the same volume.

This is because the volume of a solid is determined by the areas of its cross-sections, which are the shapes obtained by slicing the solid perpendicular to a fixed direction. As long as the cross-sectional areas are the same at every height, the figures will have the same volume, regardless of their shapes.

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Answer:d. Based on Cavalieri's Principle, since the cross sections have the same area and the figures have the same height, the figures will have the same volume.

Step-by-step explanation: i took the test

The specific assumption that must be made in order to calculate the probability is that the loss of one Internet site does not affect the loss of another. Therefore, the occurrence of the site references in the paper are independent events.

To calculate the probability that all 10 Internet references are still good two years later, we can use the fact that the probability that a site is still good after two years is 0.87 (100% - 13%). Since each reference is an independent event, we can use the multiplication rule of probability:

P(all 10 are still good) = 0.87^10 = 0.275

Therefore, the probability that all 10 Internet references are still good two years later is 0.275 or 27.5% (rounded to three decimal places).
Hi! To calculate the probability that all 10 Internet references are still good two years later, we need to assume that the occurrence of the site references in the paper are independent events.

The probability that a single site is still good after two years is 1 - 0.13 = 0.87, since 13% of them are lost.

Since the events are independent, we can multiply the probabilities together for all 10 sites:

P(all 10 are still good) = 0.87^10 ≈ 0.263.

The answer: 0.263

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Based on your question and the terms provided, it appears that you are referring to a normal distribution with a mean of 75 and a standard deviation of 10. In a normal distribution, approximately 95% of the data values fall within two standard deviations of the mean. In this case, that would be between 55 and 95. A low p-value typically indicates that the observed data is unlikely to occur by chance alone, suggesting that there may be a significant effect or relationship between variables.

1. If the histogram of a data set is symmetric and bell-shaped with a mean of 75 and standard deviation of 10, then approximately 95% of the data values were between 55 and 95. This is because in a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. In this case, two standard deviations below the mean is 55 (75 - 2(10)) and two standard deviations above the mean is 95 (75 + 2(10)). Therefore, approximately 95% of the data values fall between 55 and 95.

2. Without more context, it is unclear what you are asking about a low p-value. A low p-value typically indicates that the observed data is unlikely to have occurred by chance alone, and may suggest that there is a significant effect or relationship between variables being studied. However, the specific interpretation of a low p-value depends on the specific statistical test being used and the significance level chosen.

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I'm sorry, but I cannot provide an answer without more information about the value of "C3". Can you please provide that information?
To evaluate the given expression 34^C3, we need to find the number of combinations of choosing 3 items from a set of 34 items. This can be calculated using the formula:

C(n, r) = n! / (r!(n-r)!)

Here, n = 34 and r = 3. Plugging the values into the formula, we get:

34^C3 = C(34, 3) = 34! / (3!(34-3)!)

= 34! / (3! * 31!)

= (34 * 33 * 32) / (3 * 2 * 1)

= 5984

So, 34^C3 = 5984.

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Answer: Y = 5X

Step-by-step explanation:

The final answer is

Dnf(p0) = ((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2))) / sqrt((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2)))

To find the direction of greatest increase of the function f=sin(xy) at point p0, we need to find the gradient vector of f at p0 and normalize it.
The gradient vector of f is given by:

∇f = (partial derivative of f with respect to x, partial derivative of f with respect to y)
∂f/∂x = y cos(xy)
∂f/∂y = x cos(xy)

Therefore,
∇f = (y cos(xy), x cos(xy))
At point p0, we have x = π−−√/3 and y = π−−√/2, so
∇f(p0) = ((π−−√/2) cos((π−−√/3)(π−−√/2)), (π−−√/3) cos((π−−√/3)(π−−√/2)))

To normalize this vector, we need to divide each component by its magnitude. The magnitude of ∇f(p0) is:
|∇f(p0)| = sqrt((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2)))

So the unit vector in the direction of greatest increase of f at p0 is:
n = ∇f(p0) / |∇f(p0)|

Simplifying the expression for n, we get:
n = ((π−−√/2) cos((π−−√/3)(π−−√/2)), (π−−√/3) cos((π−−√/3)(π−−√/2))) / sqrt((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2)))

To compute the magnitude of the greatest rate of increase, we need to find the directional derivative of f in the direction of n at p0. The directional derivative of f in the direction of a unit vector u at point p is given by:
Duf(p) = ∇f(p) · u

where . denotes the dot product.

So the greatest rate of increase of f at p0 is:
Dnf(p0) = ∇f(p0) · n

Simplifying the expression for Dnf(p0), we get:
Dnf(p0) = ((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2))) / sqrt((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2)))

Therefore, the direction n in which f increases most rapidly at point p0 is:
n = ((π−−√/2) cos((π−−√/3)(π−−√/2)), (π−−√/3) cos((π−−√/3)(π−−√/2))) / sqrt((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2)))

Therefore, the final answer is:

And the magnitude of the greatest rate of increase of f at point p0 is:
Dnf(p0) = ((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2))) / sqrt((π−−√/2)^2 cos^2((π−−√/3)(π−−√/2)) + (π−−√/3)^2 cos^2((π−−√/3)(π−−√/2)))

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Area = 0.5 * |PQ x PR| = 0.5 * sqrt(12475) ≈ 55.93 square units.

To find the area of the parallelogram determined by these points, we need to find the cross product of the vectors formed by two adjacent sides of the parallelogram. Let's choose vectors PQ and PS:

Vector PQ = (-7 - 7, 2 - (-5), -2 - 5) = (-14, 7, -7)

Vector PS = (-4 - 7, 8 - (-5), -4 - 5) = (-11, 13, -9)

The cross product of these two vectors is:

(-7)(-9) - (-7)(13), (-2)(-9) - (-14)(-9), (-2)(13) - (-14)(-11)

= (-14, 126, -30)

The magnitude of this vector gives us the area of the parallelogram:

|(-14, 126, -30)| = sqrt(14^2 + 126^2 + (-30)^2) = sqrt(17308) ≈ 131.6

Therefore, the area of the parallelogram determined by the given points is approximately 131.6 square units.
To find the area of the parallelogram determined by the points P(7, -5, 5), Q(-7, 2, -2), R(10, 1, 3), and S(-4, 8, -4), we can use the cross product of the vectors PQ and PR.

First, let's find the vectors PQ and PR:
PQ = Q - P = (-7-7, 2-(-5), -2-5) = (-14, 7, -7)
PR = R - P = (10-7, 1-(-5), 3-5) = (3, 6, -2)

Next, find the cross product of PQ and PR:
PQ x PR = (7*(-7) - (-7)*6, (-14)*(-2) - 3*(-7), (-14)*6 - 7*3) = (-49+42, 28+21, -84-21) = (-7, 49, -105)

Now, calculate the magnitude of the cross product:
|PQ x PR| = sqrt((-7)^2 + 49^2 + (-105)^2) = sqrt(49 + 2401 + 11025) = sqrt(12475)

The area of the parallelogram is half the magnitude of the cross product:
Area = 0.5 * |PQ x PR| = 0.5 * sqrt(12475) ≈ 55.93 square units.

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Answer:

B. y = x -3

The table shows the values of two variables, x and y. The first column shows the values of x, and the second column shows the corresponding values of y.

To find the equation that matches the table, we need to look for a pattern in the values of x and y. We can see that as x increases by 3, y increases by 3 as well. However, this pattern is not consistent for all the values of x and y in the table.

Therefore, we need to find an equation that represents the pattern we observe. We can see that the equation y = x + 3 matches the pattern in the table.

Jerry worked for 4.3 hours to install the equipment based on a rate of $20 per hour.

This problem can be solved using a linear equation.

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the power of 1.

Let's say the number of hours Jerry worked to install the equipment is "h".

According to the problem, Jerry charges $50 to schedule a repair visit, which means that the remaining amount after deducting the scheduling fee from the total bill ($136) is used to pay for the equipment installation.

So, the amount Jerry earned from the equipment installation is:

$136 - $50 (scheduling fee) = $86

We know that Jerry charges $20 per hour to install equipment. Therefore, the equation we can set up is:

$86 = $20 × h

Solving for "h", we get:

h = $86 / $20 = 4.3 hours (rounded to one decimal place)

Therefore, Jerry worked for 4.3 hours to install the equipment.

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Answer:

First, we need to calculate the amount that the insurance company will pay for the hospital stay.

On the first two days, the insurance will pay 80% of the expenses, which is:

0.8 x ($360 + $492) = $698.40

On the remaining 4 days, the insurance will pay 100% of the expenses, which is:

4 x $840 x 0.8 = $2688

Therefore, the total amount that the insurance company will pay is:

$200 + $698.40 + $2688 = $3586.40

Now, we can calculate the amount that Melanie will pay. Her total expenses for the hospital stay were:

$360 + $492 + $298 + $980 + $1006 + $781 = $3917

The insurance company paid $3586.40, so Melanie is responsible for paying the difference:

$3917 - $3586.40 = $330.60

Therefore, the insurance company paid $3586.40, and Melanie paid $330.60.

Answer: $330.60.

Step-by-step explanation:

The answer of the given question based on the equation is  Konrad will need 9/8 cups of broth in total to make 3 chicken pot pies.

An equation is mathematical statement that show that the two expressions are equal. An equation contains an equals sign (=) and consists of two expressions, referred to as the left-hand side (LHS) and the right-hand side (RHS), which are separated by the equals sign. The expressions on either side of the equals sign can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division

.

Konrad uses 3/8 cup of broth for each chicken pot pie.

To find the total amount of broth he will need to make 3 pies, we can use the equation:

total broth needed = broth per pie x number of pies

Plugging in the given values, we get:

total broth needed = (3/8) x 3

Simplifying the expression:

total broth needed = 9/8

So Konrad will need 9/8 cups of broth in total to make 3 chicken pot pies.

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The vertices of the rectangle with maximum area are: (1, 0), (-1, 0), (1, 3), and (-1, 3). Let's see how,

Step:1. Recognize that the given curve is y = 6/(1 + x^2).
Step:2. Consider one vertex of the rectangle on the curve as (x, y) = (x, 6/(1 + x^2)).
Step:3. Since one side of the rectangle is on the x-axis, the length of that side will be y = 6/(1 + x^2).
Step:4. The other side of the rectangle will be parallel to the x-axis and have length 2x, since there are two equal halves with the origin as the midpoint.
Step:5. The area of the rectangle, A = length * width = 2x * (6/(1 + x^2)).
Step:6. To find the maximum area, differentiate A with respect to x and set the derivative to 0.
Let's differentiate A(x) = 12x / (1 + x^2):
dA/dx = [12(1 + x^2) - 12x(2x)] / (1 + x^2)^2 = (12 - 12x^2) / (1 + x^2)^2.
Set dA/dx = 0:
(12 - 12x^2) / (1 + x^2)^2 = 0.
Solve for x:
12x^2 = 12.
x^2 = 1.
x = ±1.
Now, find the corresponding y-values using y = 6/(1 + x^2):
For x = 1, y = 6/(1 + 1^2) = 6/2 = 3.
For x = -1, y = 6/(1 + (-1)^2) = 6/2 = 3.
Thus, the vertices of the rectangle with maximum area are: (1, 0), (-1, 0), (1, 3), and (-1, 3).

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To find the marginal probability density functions of X and Y, we need to integrate the joint density function over the range of the other variable.

Marginal probability density function of X:

f_X(x) = ∫f(x,y)dy, integrating over the range of y from 0 to 2-x.

f_X(x) = ∫[3(2-x)y]dy, integrating over y from 0 to 2-x.

f_X(x) =[tex][3(2-x)y^2/2][/tex] evaluated at y=0 and y=2-x.

f_X(x) = [tex]3(2-x)(2-x)^2/2[/tex] - 0 = [tex]3/2 (2-x)^3.[/tex]

for[tex]0 < x < 2[/tex]andC= 0 for other values of x.

Therefore, the marginal probability density function of X is:

[tex]f_X(x) = 3/2 (2-x)^3[/tex]for [tex]0 < x < 2[/tex]and[tex]f_X(x)[/tex]= 0 for other values of x.

Marginal probability density function of Y:

[tex]f_Y(y) = ∫f(x,y)dx[/tex], integrating over the range of x from 0 to 2.

[tex]f_Y(y) = ∫[3(2-x)y]dx[/tex], integrating over x from 0 to 2.

[tex]f_Y(y) = [3(2-x)^2y/2][/tex]evaluated at x=0 and x=2.

[tex]f_Y(y) = 6y - 3y^2[/tex] for [tex]0 < y < 2[/tex] and [tex]f_Y(y)[/tex]= 0 for other values of y.

Therefore, the marginal probability density function of Y is:

[tex]f_Y(y) = 6y - 3y^2[/tex] for [tex]0 < y < 2[/tex]and[tex]f_Y(y)[/tex] = 0 for other values of y.

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We have shown that the argument is valid and ¬g, ¬k entails ¬(k ∨ g) using natural deduction.

Here's one possible proof using natural deduction:

Assume k ∨ g

Assume k
The premise ¬k, derive a contradiction: ⊥

Assume g

Derive a contradiction: ⊥

Conclude from above equations, ¬(k ∨ g) by negation introduction

From the premise ¬g and ¬(k ∨ g), conclude ¬(k ∨ g) by modus tollens (¬g → ¬(k ∨ g))

From the premise ¬k and ¬(k ∨ g), conclude ¬(k ∨ g) by modus tollens (¬k → ¬(k ∨ g))

Now, from above, conclude ¬(k ∨ g) by conjunction introduction (¬g ∧ ¬k → ¬(k ∨ g))

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Answer:

Step-by-step explanation:

The question is a little hard to interpret. I hope this is what you wanted.

Let the small number be [tex]x[/tex], so the greater number will be [tex](x+1)[/tex].

the smaller of two consecutive numbers is doubled and added to the greater gives:

                            [tex]2x+(x+1)=3x+1[/tex]

The total will be [tex]3x+1[/tex] if the smaller number is [tex]x[/tex].

The US government recommends low dose x-ray or dual-energy x-ray absorptiometry (DEXA) screening for women aged 65 years and older to check for osteoporosis. The suggested screening interval for low dose x-ray or DEXA for women aged 65 years and older is every two years.

The US government recommends low dose x-ray or dual-energy x-ray absorptiometry (DEXA) screening for women aged 65 years and older to check for osteoporosis. Osteoporosis is a condition that weakens bones, making them more likely to break. The suggested screening interval for low dose x-ray or DEXA is every two years. However, this may vary based on individual risk factors such as family history of osteoporosis, use of certain medications, and history of fractures.
Women who are at higher risk of developing osteoporosis may need more frequent screenings. For example, women with a history of fractures or those who have taken certain medications for a prolonged period may need more frequent screenings. It is important to discuss individual risk factors with a healthcare provider to determine the appropriate screening interval.
It is also important to note that while low dose x-ray or DEXA is recommended for women aged 65 years and older, women who are younger and have risk factors for osteoporosis may also need screening. Some of these risk factors include a family history of osteoporosis, low body weight, smoking, and certain medical conditions such as rheumatoid arthritis.
In summary, the suggested screening interval for low dose x-ray or DEXA for women aged 65 years and older is every two years. However, the screening interval may vary based on individual risk factors. It is important to discuss individual risk factors with a healthcare provider to determine the appropriate screening interval.

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Required true statements are f(6)=66, f(3)=10, f(5)=33.

What is recursive formula?

A recursive formula is a way of defining a sequence or function in terms of previous terms or values. In other words, the formula uses the output of the previous step to generate the input for the next step.

For example, the Fibonacci sequence is defined recursively as follows:

F(0) = 0

F(1) = 1

F(n) = F(n-1) + F(n-2) (for n ≥ 2)

Here, the value of each term in the sequence is defined in terms of the two previous terms. The first two terms (F(0) and F(1)) are defined directly, while subsequent terms are defined recursively by adding the two previous terms.

Another example of a recursive formula is the factorial function:

n! = n × (n-1)! (for n ≥ 1)

Here, the value of n! is defined in terms of (n-1)!, which is defined in turn in terms of (n-2)!, and so on until the base case of 0! is reached

We can use the recursive formula to calculate the values of the sequence:

f(1) = 3

f(2) = 2f(1) - 1 = 23 - 1 = 5

f(3) = 2f(2) - 1 = 25 - 1 = 9

f(4) = 2f(3) - 1 = 29 - 1 = 17

f(5) = 2f(4) - 1 = 217 - 1 = 33

f(6) = 2f(5) - 1 = 233 - 1 = 65

Therefore, statements 2 (f(4)=18) and 5 (f(2)=5) are false, and statements 1 (f(6)=66), 3 (f(3)=10), and 4 (f(5)=33) are true.

So the correct options are:

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The statement with limit of function that [tex]\lim_{ x→ 2} f(x) = 5[/tex], implies or states that the limit of the function f at x=5 is two is a false statement.

Limit is a constant number that a function approaches. If the values of x approach some value, a , as the values of approach from both sides but can't necessarily equals to x= a , then we say the limit of f(x) as approaches L is equal to L . It is denoted as [tex]\lim_{ x→ a} f(x) = L[/tex]. We have a notation, [tex]\lim_{ x→ 2} f(x) = 5[/tex], also states that the limit of the function f at x=5 is 2. It is not correct formated statement and it does not implies that the limit of the function f at x=5 is 2. The correct notation is [tex]\lim_{ x→ 5} f(x) = 2[/tex], which states that the limit of the function f at x=5 is equals to 2. Hence, the provide notation of limits is a false one.

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The probability that a random z-score will be greater than 1.33 given a standardized normal distribution is approximately 0.0918 or 9.18%.

To find the probability that a random z-score will be greater than 1.33 given a standardized normal distribution, you'll need to use a z-table or a calculator with a built-in z-table function.

1. Identify the given z-score: 1.33.

2. Look up the z-score in a z-table or use a calculator with a built-in z-table function. This will give you the area to the left of the z-score, also known as the cumulative probability.

3. For a z-score of 1.33, the cumulative probability is approximately 0.9082.

4. Since you want to find the probability that a random z-score will be greater than 1.33, you'll need to calculate the area to the right of the z-score.

5. To do this, subtract the cumulative probability from 1: 1 - 0.9082 = 0.0918.

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To find the value of E[X], we need to calculate the expected value of X by multiplying each value of X by its corresponding probability and summing them up.

So, E[X] = (3 x 0.1) + (10 x 0.2) + (20 x 0.45) + (50 x 0.25) = 18.25

To find E[X]*E[Y], we need to find the expected value of X and the expected value of Y separately, and then multiply them together.

We already know E[X] from the previous calculation, so now we need to find E[Y].

E[Y] = (1 x 0.3) + (7 x 0.7) = 5.6

Now, we can multiply E[X] and E[Y] together to get the final answer:

E[X]*E[Y] = 18.25 * 5.6 = 102.2
Given the joint probability table:

X\Y  | Y = 1 | Y = 7
-----|-------|-------
X = 3|  10   |  20
X = 5| 0.45  | 0.25

To find the expected value E[X], we first need to find the marginal probabilities of X.

P(X = 3) = P(X = 3, Y = 1) + P(X = 3, Y = 7) = 10 + 20 = 30
P(X = 5) = P(X = 5, Y = 1) + P(X = 5, Y = 7) = 0.45 + 0.25 = 0.70

Now we can calculate E[X]:

E[X] = (3 * 30) + (5 * 0.70) = 90 + 3.50 = 93.50

Therefore, the value of E[X] is 93.50.

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Answer:

( 3,1)

Step-by-step explanation:

To rotate the point (-1, 3) 90 degrees clockwise around the origin, we can use the following formula:

(x', y') = (y, -x)

where (x, y) are the coordinates of the original point, and (x', y') are the coordinates of the rotated point.

So, for the point (-1, 3), we have:

x = -1

y = 3

Using the formula, we get:

x' = 3

y' = -(-1) = 1

Therefore, the coordinates of the point after rotation are (3, 1).

To graph this point, we can plot it on the coordinate plane. The point (3, 1) is located 3 units to the right of the origin and 1 unit above the origin.

The graph of the point (-1, 3) and its image (3, 1) after rotation 90 degrees clockwise around the origin is shown below:

     |

     |   (3, 1)

     |

     |

------O------  

     |

     |

     |

     |   (-1, 3)