Insurance companies often try to calculate average life expectancy, that is, how long different populations can reasonably be expected to live. The companies do this for men and women and for people across all ethnicities. A linear model is a way of calculating a reasonable life expectancy for African American males. Use the researcher's model equation below to calculate the approximate life expectancy of an African-American male born in 1963. The equation: L -0.29t+ 51 L-life expectancy at birth t = the year of the man's birth measured in years after 1900 Round your answer to the nearest hundredth, if necessary.

Answer:  352(x)=1800

Step-by-step explanation:

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

3

Step-by-step explanation:

15.839 rounded to the nearest hundredths place would be 15.83.

Answer:

4

Step-by-step explanation:

If rounded to the nearest hundredth of a second, you would get 15.84, as you round up if the last number is 5 or above.

9514 1404 393

Answer:

  2 2/3

Step-by-step explanation:

  -2 1/3 - (-5)

  = -2 1/3 + 5 . . . . . subtraction is the same as adding the opposite

  = (5 -2) -1/3 . . . . . -2 1/3 = (-2) +(-1/3)

  = 3 -1/3 . . . . . . . . . deal with the integer and fractional parts separately

  = 2 2/3

_____

If you like, you can convert the numbers to improper fractions.

 -2 1/3 +5 = (-7/3 +15/3) = 8/3 = 2 2/3

Answer:

B.) 154 feet

Step-by-step explanation:

i got it right on edge    

\(hope that helps\)

Answer:

18x-3

Step-by-step explanation:

f(x)= 3x + 10x

g(x)=5x - 3

f(x)+g(x) = 3x + 10x + 5x - 3

Combine like terms

             = 18x -3

Answer:

3^x+15x-3

Step-by-step explanation:

this is the right answer i just did it

\

Answer:

multiplied by 3

Step-by-step explanation:

red is scaled up by 3 from blue

Answer:

3

Step-by-step explanation:

9514 1404 393

Answer:

  3.4%

Step-by-step explanation:

The total amount due is ...

  A = P(1 +rt/12) . . . . . principal P, annual rate r, t months

  33829.50 = 28500(1 +66/12r)

  1.187 = 1 +5.5r . . . . . divide by 28500, simplify

  0.185/5.5 = r = 0.034 = 3.4%

The interest rate on the loan is 3.4%.

The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

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Answer:

x = 5

  or

x = 3

Step-by-step explanation:

The first term is,  x2  its coefficient is  1 .

The middle term is,  -8x  its coefficient is  -8 .

The last term, "the constant", is  +15

Step-1 : Multiply the coefficient of the first term by the constant   1 • 15 = 15

Step-2 : Find two factors of  15  whose sum equals the coefficient of the middle term, which is   -8 .

     -15    +    -1    =    -16

     -5    +    -3    =    -8

If the equation x²−8x−5=0 can be transformed into the equation (x−p)²=q, then value of q is 21

Two or more expressions with an Equal sign is called as Equation.

To transform the equation x² - 8x - 5 = 0 into the equation (x - p)² = q, we need to complete the square by adding and subtracting a constant term.

First, let's add 5 to both sides to get:

x² - 8x = 5

Applying complete square method

we need to add and subtract 16 inside the parentheses on the left-hand side:

x² - 8x + 16 - 16 = 5

Simplifying the left-hand side gives us:

(x - 4)² - 16 = 5

Adding 16 to both sides gives us:

(x - 4)² = 21

Therefore, the value of q is 21.

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The matrix A' for the linear transformation T relative to the basis B' is:

A' =

[-3  -3   0]

[-3   2   5]

[-7  -7   5]

To find the matrix A' for the linear transformation T relative to the basis B' = {(1, 1, 0), (1, 0, 1), (0, 1, 1)}, we need to determine the image of each basis vector under T and express them as linear combinations of the basis vectors in B'. Let's calculate it step by step:

1. Apply T to the first basis vector: T(1, 1, 0) = (-3(1), -7(1), 5(0)) = (-3, -7, 0). We need to express this result as a linear combination of the basis vectors in B'.

(-3, -7, 0) = -3(1, 1, 0) + 0(1, 0, 1) + 0(0, 1, 1) = (-3, -3, 0).

So, the first column of A' will be (-3, -3, 0).

2. Apply T to the second basis vector: T(1, 0, 1) = (-3(1), -7(0), 5(1)) = (-3, 0, 5). Expressing this as a linear combination of the basis vectors in B':

(-3, 0, 5) = -3(1, 1, 0) + 5(1, 0, 1) + 0(0, 1, 1) = (-3, 2, 5).

So, the second column of A' will be (-3, 2, 5).

3. Apply T to the third basis vector: T(0, 1, 1) = (-3(0), -7(1), 5(1)) = (0, -7, 5). Expressing this as a linear combination of the basis vectors in B':

(0, -7, 5) = 0(1, 1, 0) + (-7)(1, 0, 1) + 5(0, 1, 1) = (-7, -7, 5).

So, the third column of A' will be (-7, -7, 5).

Putting it all together, we have:

A' = [(-3, -3, 0), (-3, 2, 5), (-7, -7, 5)].

So, the matrix A' for the linear transformation T relative to the basis B' is:

A' =

[-3  -3   0]

[-3   2   5]

[-7  -7   5]

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Answer:

b) 92

Step-by-step explanation:

1. if according to the condition the triangle is equilateral, then every inside angle (m∠F=m∠G=m∠H) is 60°.

2. it is possible to substitute the value 60 (F=60) into the given equation:

\(60=(\frac{Z}{2}+14);\)

3. if to solve the equation above, then Z=92

The slope of Ambrose's indifference curve when his consumption bundle is (36,10) is -36/10.

To find the slope of Ambrose's indifference curve, we need to differentiate the equation of the indifference curve with respect to good 1 (x1) and evaluate it at the consumption bundle (36,10).

The equation of Ambrose's indifference curve is given as:

x2 = constant - 4(x1)^(1/2)

Differentiating both sides of the equation with respect to x1, we get:

0 = -4(1/2)(x1)^(-1/2)dx1 - 4

Simplifying this equation, we have:

-4(x1)^(-1/2)dx1 = 4

Now, we can solve for dx1:

dx1 = -1/(x1)^(1/2)

Substituting the consumption bundle (36,10) into dx1, we get:

dx1 = -1/(36)^(1/2) = -1/6

Finally, we can calculate the slope of the indifference curve by taking the ratio of the change in x2 to the change in x1:

slope = dx2/dx1 = -4/(-1/6) = -4 * (-6) = -24

Therefore, the slope of Ambrose's indifference curve when his consumption bundle is (36,10) is -24.

Note: The given answer choices (-36/10, -6, -16, -10/36, -0.33) do not match the calculated slope of -24.

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Answer:

B

Step-by-step explanation:

On a coordinate plane, parallel lines have the same slope as geometric figures are true. Thus option B is correct.

Marks, splines, spheres, and curved are used to build enclosed geometric shapes. We can see these shapes all around us. Illustrations of geometric shapes include circles, rectangles, triangles, and others. Any configuration of points, columns, or angles is a geometry figure.

A point is the most fundamental algebraic concept because it has no boundaries. Simply put, a point upon that plane is a location. A dot is used to symbolize it. A plane can be identified by three non-straight-line points.

As two or much more vectors seldom cross each other and are located on the same dimension, these are said to be parallel. The slope of these lines is constant. Coplanar lines that seem to be parallel are the ones that don't cross. Therefore, option B is the correct option.

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The fifth grader was looking forward to being 11 years old for a few reasons. For starters, 11 is a prime number and prime numbers are fascinating.

Secondly, 11 is a transitional age as it marks the end of childhood and the beginning of the preteen years. This age group is usually associated with new responsibilities, such as being able to stay home alone and taking on new challenges. The fifth-grader might have also been looking forward to having more independence and control over their life at this age. 11 is also an age where you start to develop your own interests and hobbies, which can be exciting for a child who is eager to explore and learn.

Additionally, at 11, you are closer to becoming a teenager, which can be an exciting prospect for some kids. Lastly, the fifth-grader might have been looking forward to being able to participate in more activities and events that are designed for older kids. In conclusion, turning 11 years old represents a significant milestone in a child's life, and there are many reasons why the fifth-grader was excited about it.

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Answer:

Step-by-step explanation:

1. 1923.25

2.about 3846.5 yards

3.219.91

4.639.82

Answer: See below

Step-by-step explanation:

1) 1/2 x 3.14 x 35^2

1/2 x 3.14 x 1225

1/2 x 3846.5

A = 1923.25 yd^2

2) (3.14)r^2

(3.14) (35)^2

3846.50 yd^2

3) P = d + (3.14)r^2

P = 70 + (3.14) (35)

P = 70 + 109.90

P = 179.90 yd

4) P = 2( l + w)

P = 2 (70 + 100)

P = 2 (170)

P = 340

Perimeter of the square minus the perimeter of the circle.

340 - 179.90 = 160.10 yd

We cannot conclude whether the national average is greater than the Washington DC average based on the information provided.

To determine whether the national average ACT score is greater than the Washington DC average, we need to conduct a hypothesis test. However, the question does not provide us with enough information to conduct such a test.

We are given the sample means for both populations, but we do not know the sample sizes, the level of significance, or whether the samples were independent or not. Additionally, we do not have any information on the distribution of the scores, except for the population standard deviation, which may or may not be a reasonable assumption.

Therefore, we cannot make any conclusions about the difference between the national and Washington DC averages without conducting a proper hypothesis test with more information.

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The required charge q2 is  -60 μC.

To find the required charge q2, we first need to calculate the electric field at point P(0, 2 cm, 0) due to the charges q1 and q2.

Then we can set the y-component of this electric field to zero and solve for q2.

Using Coulomb's law, the electric field at point P due to charge q1 is given by:

E1 = k*q1/r1^2

where;

which is:

r1 = √[(0 - 1 cm)^2 + (2 cm - 1 cm)^2 + (0 - 0)^2]

r1 = √[2] cm

Substituting the values, we get:

E1 = (9 x 10^9 Nm^2/C^2 x 6 x 10^-6 C)/(2 cm)^2

E1 = 2.7 x 10⁴ N/C

The electric field at point P due to charge q2 is given by:

E2 = kq²/r₂²

where;

r₂ = √[(0 - 0)^2 + (2 cm - 0)^2 + (0 - 4 cm)^2]

r₂  = 2√[5] cm

Substituting the values, we get:

E₂  = (9 x 10^9 Nm^2/C^2)q2/(2√[5] cm)^2

E₂ = 4.5 x 10⁸q₂ N/C

The total electric field at point P is given by the vector sum of E1 and E2:

E = E1 + E2

To have no y-component of E at point P, we must have:

E_y = E x sin(θ) = 0

where;

Since we want E_y to be zero, this means that the electric field vector must be parallel to the xz-plane, which means that θ = 90 degrees.

Therefore, we have:

E_x = E*cos(θ) = E = E1 + E2

Substituting the values, we get:

E = 2.7 x 10⁴ N/C + 4.5 x 10⁸q₂ N/C

Setting E = E_x = 0, we can solve for q2:

0 = 2.7 x 10⁴ N/C + 4.5 x 10⁸q₂ N/C

q₂ = -6 x 10⁻⁵ C

q₂ = -60 μC

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The alpha level for each hypothesis test made on the same set of data is called B. experimentwise alpha

When numerous suppositions are examined concurrently, the likelihood of committing at least one type I mistake grows.

In order to manage the probability of erroneously rejecting the null hypothesis in all tests, scientists usually modify the alpha level for each test, with the purpose of maintaining an experimentwise alpha that reflects the probability of making a type I error in the entire set of tests.

The Bonferroni procedure is a technique utilized to regulate the experimentwise error rate by adjusting the alpha level for each hypothesis test.

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Answer:

1. (3 + 7) ÷ 2 = 5

2. (4 + 9) x 3 = 39

3. 10 ÷ (4 x 5) = 1/2

4.(1 + 2) ÷ 20 = 3/20

The equation for A is A=4b(t+D) from t = A/4b-D.

Two or more expressions with an Equal sign is called as Equation.

The given equation is t = A/4b-D

t equal to A by four times of b minus D

The variables in the equation are A, b and D.

The formula is given for the variable t.

We need to change the formula to find the value of A.

We need to solve for A.

Add D on both sides

t+D=A/4b-D+D

The positive and negative D on right side of the equation will be cancelled and left with A/4b.

t+D/1=A/4b

Now apply cross multiplication

A=4b(t+D)

Hence, the equation for A is A=4b(t+D) from the t = A/4b-D.

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The vertex form equation is illustrated below.

Directrix (d): The directrix is the horizontal line y = -2.

Focus (F): The focus is the point (0, 2).

Vertex (V): The vertex is the point (0, 0).

Equation: The equation of the parabola is y = 1/4x^2.

The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) is the vertex. We already know the vertex of this parabola, which is (0, 0). To find the value of a, we can use the fact that the distance between the focus and the vertex is equal to the distance between the directrix and the vertex.

The distance between the focus (0, 2) and the vertex (0, 0) is 2 units. The distance between the directrix y = -2 and the vertex (0, 0) is also 2 units. Therefore, we can say that 1/(4a) = 2, or a = 1/8.

So, the vertex form equation of the parabola is y = 1/8(x-0)^2 + 0, which simplifies to y = 1/8x^2.

Vertex: The vertex is (0, 0).

Axis of Symmetry (AOS): The axis of symmetry is the vertical line x = 0.

Domain: The domain of the parabola is all real numbers, because the parabola continues indefinitely in both directions along the x-axis.

Range: The range of the parabola is y >= 0, because the lowest point on the parabola is the vertex (0, 0).

Transformations: The only transformation applied to the basic parabola y = x^2 is a vertical compression by a factor of 1/8.

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Answer:

1. To expand the polynomial f(x) = (x-3)(x+2)(x+3), we can use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x+3) using FOIL again.

2. To expand the polynomial g(x) = (x-3)(x+2)(x-2), we can also use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x-2) using FOIL again.

3. The polynomial f(x) has three linear factors, and so the degree of the polynomial will be 3, since we will have to multiply three binomials together. The polynomial g(x) has four linear factors, and so the degree of the polynomial will be 4.

If we were to expand a polynomial with five linear factors, the degree of the polynomial would be 5, since we would have to multiply five binomials together.

4. The degree of a polynomial is determined by the highest power of x in the polynomial, which is determined by the number of terms in the expanded polynomial expression.

(6 sentences to use):

1. To expand the polynomial (x-3)(x+2)(x+3), we use the distributive property and multiply each term of the first binomial by each term of the second binomial, then multiply the resulting trinomial by the third binomial.

2. To expand the polynomial (x-3)(x+2)(x-2), we use the same strategy as in the previous example, multiplying each term of the first binomial by each term of the second binomial, and then multiplying the resulting trinomial by the third binomial.

3. The polynomial f(x) has three linear factors, so its degree is 3, which means the highest exponent in the polynomial is 3.

4. The polynomial g(x) has four linear factors, so its degree is 4, which means the highest exponent in the polynomial is 4.

5. If we were to expand a polynomial using five linear factors, we would again use the distributive property to multiply each term of each binomial together, resulting in a polynomial with a degree of 5, which means the highest exponent in the polynomial would be 5.

6. This strategy for multiplying three binomials is a useful tool in algebraic manipulation, allowing us to expand and simplify polynomial expressions.

Hope this helped! Sorry if it didn't. If you need more help, ask me! :]

The measure of angle H is 55°.

The length of the side FG is 13 units.

The value of x in the diagram is 9

equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees. Just like other types of triangles, an equilateral triangle also has its area, perimeter and height formula

From the diagram all the sides are equal which means it is an equilateral triangle in which each angle is equal to 60°

To find x,

7x -3 = 60

7x = 60 + 3

7x = 63

x = 63/7

x = 9

In conclusion the value of x is 9

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Answer:

Scale Factor: 343;  82320/240

Step-by-step explanation:

Haven't done scale factors in a long time, so I'll try my best.

The scale factor wants the model to real sculpture, so...

Model: \(6*5*8 = 240\)

Sculpture: \(42*35*56=82320\)

\(\frac{82320}{240} =343\)

So, the scale factor for the model to sculpture would be 343. The fraction that creates the scale factor is \(\frac{82320}{240}\).