Are older men shorter than younger men? According to a national report, the mean height for U.S. men is 69.4 inches. In a sample of 119 men between the ages of 60 and 69 , the mean height was ₓ⁻=69.3 inches. Public health officials want to determine whether the mean height μ for older men is less than the mean height of all adult men. Assume the population standard deviation to be σ=2.58 . Use the α=0.05 level of significance and the P-value method

The domain of the ordered pairs is {2, 4, 9}

From the question, we have the following parameters that can be used in our computation:

The ordered pairs

The ordered pairs is given as

{(2,2),(4,6),(9,9)}

The rule of ordered pairs is that

Using the above as a guide, we have the following:

Domain = {2, 4, 9}

Range = {2, 6, 9}

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The addition of the fractions, 41 2/9 + 18 2/5, is 59 28/45

From the question, we are to add the given fractions by following the given steps

The given fractions are:

41 2/9 + 18 2/5

Writing each mixed number as the sum of a whole and a fraction

41 2/9 = 41 + 2/9

and

18 2/5 = 18 + 2/5

Adding the whole numbers

41 + 18 = 59

Finding the LCD of the fractions 2/9 and 2/5

LCD = 45

Rewriting the sum of the fractions with a common denominator

2/9 + 2/5 = 10/45 + 18/45 = (10 + 18)/45 = 28/45

Thus,

41 2/9 + 18 2/5 = 59 + 28/45

41 2/9 + 18 2/5 = 59 28/45

Hence,

The addition of the fractions results into 59 28/45

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The value of the missing terms are;

1. N = 24

2. 144

3. 6

4. 1000

5. 12.75

To determine the value, we have that the proportion is determined by;

1. 4/25 = N/150

cross multiply the values, we have;

25N = 150(4)

multiply the values

25N = 600

N = 24

2. 48/75 = N/225

cross multiply the values

75N = 10800

Divide the values

N = 144

3. N/16 = 30/80

cross multiply the values

80N = 480

N = 6

4. 125/N = 2/16

cross multiply the values

2N = 2000

N = 1000

5. 2.75/11 = N/51

cross multiply the values

11N = 140.25

N = 12.75

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Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

The solution is: the price for the 1st week after Valentine's Day will be $60.

Here, we have,

given that,

For Valentine's Day in February, Gabriel's Appliances stocks hundreds of red heart-shaped vacuum cleaners. The next week Gabriel still has hundreds of them in stock and tells the manager,

"Discount them 25% each week until they are gone."

For the week of Valentine's Day, the vacuums were priced at $80.

so, we get,

The price of red heart-shaped vacuum cleaners for the week of Valentine's Day is $80.

now, as per he told, we get,

the price for the 1st week after Valentine's Day will be with 25% discount.

so, the price for the 1st week after Valentine's Day will be

= $80 - $80*25%

=$80 - 20

=$60

Hence, The solution is: the price for the 1st week after Valentine's Day will be $60.

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φ is an irrational mathematical constant approximately 1.618 which is known as Phil.

In mathematics, the expression "φ(u, p1, .......pn)" typically represents a function φ that takes a set of parameters p1, p2, ..., pn, and an input value u.

The function φ then performs some operations or computations using these parameters and returns a result based on the input value u. The exact interpretation and definition of the function φ and its parameters would depend on the specific context or mathematical framework in which it is used.

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Answer:

$41.25

Step-by-step explanation:

8.25x5=41.25

The amount insurance company will pay is $700000.

We are given that

Age of Mr. lewis= 63

Policy value= $700,000

Now,

If Mr. Lewis dies after paying for the policy for 24 months, he would have paid a total of 24 * $72 = $1728 in premiums. Since he has a five-year level-term life insurance policy with a face value of $700,000, his beneficiaries would receive the full face value of the policy if he dies within the five-year term.

Therefore, by algebra the answer will be $700000.

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The new equation would be:

g(x) = 9x - 7

Option D, g(x) = 9x - 7, represents the equation of the new graph after shifting 7 units down.

If the graph of f(x) = 9x is shifted 7 units down, the equation of the new graph can be obtained by subtracting 7 from the original function. Therefore, the correct equation would be:

g(x) = 9x - 7

Option D, g(x) = 9x - 7, represents the equation of the newly transformed graph after shifting 7 units down.

This equation means that for any x-value, the corresponding y-value on the new graph will be 7 units below the y-value on the original graph.

Options A and B are incorrect because they add 7 to the original function, which would shift the graph 7 units up rather than down.

Option C is incorrect because it suggests a shift to the right or left by 7 units, which is not the required transformation on the graph in this case. The correct transformation is a vertical shift downwards.

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Answer:

Step-by-step explanation:

Diameter is twice the radius

If diameter is 20 cm, then radius is 10cm

The formula for circumference is C=2(pi)r

Plug 10 in for r into the formula and solve for C:

C = 2(pi)(10)

C = 20pi

In terms of circumference, it is 20pi

Sure! Let’s solve these problems one by one.

2.1 To determine the x-intercepts of f, we need to find the values of x when f(x) = 0. So we need to solve the equation -2x² - 5x + 3 = 0. Using the quadratic formula, we get that x = (-(-5) ± √((-5)² - 4(-2)(3))) / (2(-2)). This simplifies to x = (5 ± √(49)) / (-4). So the x-intercepts are (5 - √(49)) / (-4) and (5 + √(49)) / (-4).

2.2 The axis of symmetry of a parabola in the form f(x) = ax² + bx + c is given by the formula x = -b / (2a). In this case, a = -2 and b = -5, so the axis of symmetry is x = -(-5) / (2(-2)) = 5/4.

2.3 The range of a quadratic function in the form f(x) = ax² + bx + c is determined by its vertex. The x-coordinate of the vertex is given by the formula x = -b / (2a), which we already calculated to be 5/4. The y-coordinate of the vertex is given by f(5/4) = -2(5/4)² - 5(5/4) + 3 = -25/8 - 25/4 + 3 = -25/8 - 50/8 + 24/8 = -51/8.

Since a < 0, the parabola opens downwards and the vertex is the highest point on the graph. Therefore, the range of f is (-∞, -51/8].

2.4 Reflecting the graph of f in the x-axis means that we change the sign of the y-coordinates. This is equivalent to replacing f(x) with -f(x). So the equation of the reflected graph is -f(x) = 2x² + 5x - 3.

Translating this graph 4 units to the right means that we replace x with (x - 4). So the equation of the translated graph is g(x) = 2(x - 4)² + 5(x - 4) - 3. Expanding this expression, we get g(x) = 2x² - 16x + 32 + 5x - 20 - 3 = 2x² - 11x + 9.

So the equation of g in the form g(x) = a(x + p)² + q is g(x) = 2(x - (-11/4))² + (9 - (121/8)).

Answer:

the watch was 1 year old when David's father lost it.

Step-by-step explanation:

Let's break down the information given:David found the vintage watch 38 years after his father lost it.The watch's date showed that it had worked for over two years after his father lost it.When David found the watch, it was 3 times as old as when his father lost it.

Let's assume the age of the watch when David's father lost it as X years.According to the information, the watch worked for over two years after his father lost it. Therefore, we can represent the age of the watch when David found it as (X + 2) years.We are also given that when David found the watch, it was 3 times as old as when his father lost it. So we can write the equation:(X + 2) = 3XSimplifying the equation:

2 = 3X - X

2 = 2X

X = 1

An equation that shows the relationship between the lengths of line segments AB, BC, and AC include the following: D. (5x + 20) + (6x - 10) = 120.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since B is the midpoint of line segment AC, we can logically deduce the following:

Line segment AB = Line segment BC

Line segment AC = Line segment AB + Line segment BC

By substituting the given line segments into the equation above, we have the following:

120 = (5x + 20) + (6x - 10)

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Answer:

[tex]525*1.05^t[/tex]

Step-by-step explanation:

525 initial, 1.05 rate

There are 153 ways the league can choose two teams to play each other on opening night.

To determine the number of ways the league can choose two teams to play each other on opening night, we can use the concept of combinations.

The number of ways to choose two teams out of 18 can be calculated using the combination formula:

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

where n is the total number of teams and r is the number of teams to be chosen (in this case, 2).

Plugging in the values:

C(18, 2) = 18! / (2!(18-2)!)

= 18! / (2!16!)

= (18 x 17 x 16!) / (2! x 16!)

= (18 x 17) / 2

= 9 x 17

= 153.

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The expected number of students that like maths in 200 students is 120

From the question, we have the following parameters that can be used in our computation:

3 out of every 5 students said Math is their favorite class

This means that

P(Math) = 3/5

When simplified, we have

P(Math) = 0.6

In a selection of 200 students, the expected value is

Expected = 0.6 * 200

Evaluate

Expected = 120

Hence, the expected number of students that like maths is 120

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Question

In a recent survey, 3 out of every 5 students said Math is their favorite class.If 200 students were surveyed, how many students can be expected to choose math as their favorite class?

Answer:

Phase shift: -90(90 to the left)

To find the p-value, we need to use the t-distribution table or a calculator.

The value of p-value is 0.025.

Given that;

H₀: μ =4

Ha: μ > 4 ;

n = 7,

T.S. = 2.29

Now, For the p-value, use the t-distribution table or a calculator.

Since, this is a one-tailed test with the alternative hypothesis being μ > 4,

Hence, we need to find the area to the right of the test statistic, which is 2.29.

Using a t-distribution table with 6 degrees of freedom

n - 1 = 7 - 1 = 6

And, we find that the area to the right of 2.29 is,

⇒ 0.025.

Therefore, the value of p-value is 0.025.

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Hello !

Answer:

[tex]\Large \boxed{\sf c=3}[/tex]

Step-by-step explanation:

We want to find the value of c that verifies the following equation :

[tex]\sf 3+2c=9[/tex]

For this, we need to isolate c.

To begin, let's substract 3 from both sides of the equation :

[tex]\sf 3+2c-3=9-3\\\sf 2c=6[/tex]

Now let's divide both sides by 2 :

[tex]\frac{2c}{2}=\frac{6}{2} \\\boxed{\sf c=3}[/tex]

Have a nice day ;)

The exponential expression which is equivalent to [tex]8 \sqrt{y}[/tex]  is  [tex]y^\frac{1}{8}[/tex].

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Thus, for the number 32, it may be expressed as 2 2 2 2 25 where 2 is the "base" and 5 is the "exponent". "Two to the fifth power" is how we translate this statement.

The power of a power rule  stress that in a case whereby power is being raised to another power then the exponents can undergo multiplication where the base is been left alone.

Given that [tex]8\sqrt{y}[/tex]

= [tex]y^\frac{1}{8}[/tex]

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The least number of votes necessary from each group to pass the policy is 596 votes from technical managers and 119 votes from administrative managers.

We know that 30% of technical managers vote in favor, which means 0.3x technical managers will vote in favor.

Similarly, 60% of administrative managers vote in favor, which means 0.6y administrative managers will vote in favor.

The total number of managers who vote in favor is given by the sum of technical and administrative managers who vote in favor:

0.3x + 0.6y

We want this total number of votes to be at least 250, so we can write the inequality:

0.3x + 0.6y ≥ 250

Since the total number of managers in the company is 715, we also have the constraint:

x + y ≤ 715

To find the least number of votes from each group necessary to pass the policy, we can solve this system of inequalities.

0.3x + 0.6y ≥ 250 ---(1)

x + y ≤ 715 ---(2)

To simplify equation (1), we can multiply both sides by 10 to remove the decimal:

3x + 6y ≥ 2500

Now, we have the following system:

3x + 6y ≥ 2500 ---(3)

x + y ≤ 715 ---(4)

To solve this system, we can use a method like substitution or elimination.

Let's solve using the elimination method:

Multiply equation (4) by 3:

3x + 3y ≤ 2145 ---(5)

y ≥ 118.33

Since y represents the number of administrative managers, it must be a whole number, so we take the next higher integer, y = 119.

Substitute this value of y into equation (4):

x + 119 ≤ 715

x ≤ 596

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Answer:

Step-by-step explanation:

multiply by .1  which means move decimal over once

4.8

The coordinates of (1/2, y), and the trigonometric ratios of tangents, indicates;

y = [√3]/[7]

The trigonometric ratios expresses the relationships between the angles of a right triangle and two of the sides of the right triangle.

The x-value of the point in the diagram = (1/2)

The length of the radius of the unit circle, r = 1

Therefore; x/r = cos(θ)

Therefore; cos(θ) = (1/2)/1 = (1/2)

Therefore, θ = arccos(1/2) = 60°

The trigonometric ratio SOH CAH TOA, of tangents indicates;

tan(θ) = Opposite/Adjacent

Therefore;

tan(60°) = y/(1/2) = √3

y = (1/2) × √3

y = (√3)/2

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Answer:

4π

Step-by-step explanation:

Circumference = π X D (D = diameter = 2 X radius).

Diameter = 32.

Circumference = π (32) = 32π.

Divided into 8 slices = 1/8 of the circumference = 32π/8 = 4π.

The exact value of sin(π/8) is:

[tex]sin(\frac{\pi}{8}) = \frac{\sqrt{2-\sqrt{2}} }{2}[/tex]

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Recall that the half angle formula of sine in trigonometry is:

[tex]sin(\frac{A}{2}) = \±\sqrt{\frac{1-cosA}{2} }[/tex]

Thus, we can use the half-angle formula to find the exact value of sin(π/8):

In this case, A = π/8. Thus,

[tex]sin(\frac{\pi}{8}) = \±\sqrt{\frac{1-cos(\frac{\pi}{4} )}{2} }[/tex]

The value of cos(π/4) is √2/2. Thus,

[tex]sin(\frac{\pi}{8}) = \±\sqrt{\frac{1-\frac{\sqrt{2} }{2}}{2} }[/tex]

[tex]sin(\frac{\pi}{8}) = \±\sqrt{\frac{\frac{2-\sqrt{2} }{2}}{2} }[/tex]

[tex]sin(\frac{\pi}{8}) = \±\sqrt{\frac{2-\sqrt{2}}{4}} }[/tex]

[tex]sin(\frac{\pi}{8}) =\± \frac{\sqrt{2-\sqrt{2}} }{2}[/tex]

Since π/8 is in the first quadrant, the sine function will be positive. Therefore, the exact value is:

[tex]sin(\frac{\pi}{8}) = \frac{\sqrt{2-\sqrt{2}} }{2}[/tex]

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The cost of the ad is given by the function C ( 9 ) = $ 45

Given data ,

Let the cost of the function be represented as C ( x )

where ,

when x < 8 , C ( x ) = 35

when x ≥ 8 , C ( x ) = 35 + 10 ( x - 8 )

Now , Raphael is a chef. He is placing a 9-line job ad for an assistant

So , the value of x = 9

From the function rule , we get

C ( 9 ) = 35 + 10 ( 9 - 8 )

C ( 9 ) = 35 + 10

On simplifying the function , we get

C ( 9 ) = $ 45

Hence , the cost of the ad is C ( 9 ) = $ 45

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The values of x that make the inequality true are (b) 1, (c) 0 and (e) 1 1/4

From the question, we have the following parameters that can be used in our computation:

-1/4 < x

This expression can be rewritten as

x > -1/4

This means that the true values of x are values above -1/4

Using the above as a guide, we have the following:

The values of the inequality are (b) 1, (c) 0 and (e) 1 1/4

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