Approximate the population mean and standard deviation of age for males.

Age Lower Limit Upper Limit Males Females
0-9 0 9 11 9
10-19 10 19 10 9
20-29 20 29 12 13
30-39 30 39 16 16
40-49 40 49 20 24
50-59 50 59 25 24
60-69 60 69 17 18
70-79 70 79 13 12

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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Answer:

Hi there!

Your answer is;

There were 94 big hats and 282 small hats sold!

Step-by-step explanation:

Big hats= b

Small hats= 3b

3b+ b = 376

4b = 376

/4

b= 94

3(94) = 282

Double check!

94+282= 376

Answer:

The easiest way to convert seconds to hours is to divide the number of seconds by 3,600. To understand the reason for this conversion, it can be helpful to set up conversion tables, in which you first convert the number of seconds to minutes, and then the number of minutes to hours.

To find arcsin, we need to use the identity:

sin(arcsin(x)) = x

Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:

sin(arcsin) = -sqrt(1 - (cos)^2)

where (cos)^2 = 8/17

Substituting, we get:

sin(arcsin) = -sqrt(1 - (8/17))

Simplifying, we get:

sin(arcsin) = -sqrt(17/17 - 8/17)

Simplifying further, we get:

sin(arcsin) = -sqrt(9/17)

Therefore, arcsin = -sqrt(9/17)

To find arctan, we need to use the identity:

tan(arctan(x)) = x

Substituting, we get:

tan(arctan) = -8/17

Therefore, arctan = -8/17

So, arcsin is -sqrt(9/17) and arctan is -8/17.

i) There is no solution for x when y<0.

ii) When y>0, the solutions for x are x=4 and x=0.

iii) When y=0, the solutions for x are x=4 and x=0

To use a graph to find the value of x for the given values of y in the equation y=-|x-2|+2, we can follow these steps:

i) When y<0:

The graph of y=-|x-2|+2 is below the x-axis when y<0. Therefore, there is no solution for x when y<0, because there is no point on the graph that has a negative y-coordinate.

ii) When y>0:

The graph of y=-|x-2|+2 intersects the x-axis at two points when y>0. To find the x-coordinates of these points, we can set y=0 in the equation y=-|x-2|+2 and solve for x, as shown in the previous answer.

The x-intercepts are at (4,0) and (0,0), which means that the graph crosses the x-axis at x=4 and x=0 when y>0.

iii) When y=0:

To find the x-coordinate(s) of the point(s) where the graph intersects the x-axis (i.e., where y=0), we can look at the x-intercepts that we found in part ii) above. The x-coordinate(s) of the point(s) where the graph intersects the x-axis are x=4 and x=0, so the solutions for x when y=0 are x=4 and x=0.

Therefore, i) There is no solution for x when y<0.

ii) When y>0, the solutions for x are x=4 and x=0.

iii) When y=0, the solutions for x are x=4 and x=0 (the x-intercepts).

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The probability that you will get a 15-inch monitor = 1/3

We know that probability of event is the ratio of number of possible outcomes of event A and the total number of outcomes.

Let us assume that event A = you will get a 15-inch monitor

The number of favourable outcomes for event A are 2

So, n(A) = 2

The sample space for this experiment would be,

n(S) = 6

Using the definition of probability, the required proabability would be,

P(A) = n(A) / n(S)

P(A) = 2/6

P(A) = 1/3

Therefore, the required probability = 1/3

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Answer:

3(sqrt42) ft

Step-by-step explanation:

If l is side length of square patio, then area of patio would be l^2.

l^2 = 378

l = sqrt378 = 3(sqrt42)

Step-by-step explanation:

as the graphic shows, we are dealing with a special rhombus : a square.

this is proven by the fact that the angle on one side of the diagonal at the corner is 45°. so, the other side must be 45° too, and so we have 90° angles at the corners.

what is not clear to me is : what is 6 cm long ? a half-diameter, or the whole diameter ?

I assume the half-diameter.

what the graphic is trying to suggest is that we have 4 little right-angled triangles that are also isoceles triangles (their legs are equally long).

every leg is 6 cm long (based on my assumption above).

because they are right-angled, the area of each of these little triangles is leg×leg/2

6×6/2 = 18 cm²

we have 4 triangles, so the total area is

4×18 = 72 cm²

if 6 cm stands for the whole diagonal after all, then the only change is the length of the legs, which would be then 6/2 = 3 cm.

then we would have

3×3/2 = 4.5 cm² for a single triangle

and

4×4.5 = 18 cm² for the whole area.

A. x² - 200 gives the amount of money the interior designer will make decorating the house as a function of hours he works.

B. He will earn 1,875 if he works for 50 hours.

C. The difference quotient is equal to 2x.

The solution has been obtained by using functions.

What is a function?

Function is a kind of relation, or rule, that associates a single input with a single, predetermined output.

We are given two functions

f(x) = 49x² – 200

which represents the amount of money he earns per room decorated

g(x) = (1/7)x

which represents the number of rooms the interior designer decorates

A. The amount of money the interior designer will make decorating the house as a function of hours he works will be given by evaluating f(x) in g(x).

So,

f(g(x)) = 49((1/7)x)² – 200

f(g(x)) = x² - 200

B. Since, the house requires 50 hours of work, this means that x = 50.

Substituting this in f(g(x)) = x² - 200, we get

f(g(50)) = 50² - 200

f(g(50)) = 1,875

C. The difference quotient for the function is as follows

\(\lim_{h \to \ 0}\frac{f(x+h) -f(x)}{h}\)

\(\lim_{h \to \ 0}\frac{(x+h)^{2}-200-x^{2}+200}{h}\)

\(\lim_{h \to \ 0}\frac{x^{2} + 2xh + h^{2}-x^{2}}{h}\)

= 2x

Hence, x² - 200 gives the amount of money and he earns 1,875 if he works for 50 hours. The difference quotient is equal to 2x.

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Answer:

sin A = sin B = sin C

Step-by-step explanation:

The sine rule is a law which relates all the three sides of a triangle with the sine of their opposite angles in the triangle. Given a triangle with a side of a and an opposite angle of A, side b with opposite angle B and side c with opposite angle C. The sine rule is given as:

\(\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}\)

Given that all the side of the triangle have a length of 1, that is a = b = c = 1, hence the equation becomes:

\(\frac{sin(A)}{1}=\frac{sin(B)}{1}=\frac{sin(C)}{1}\\\\sin(A)=sin(B)=sin(C)\)

Answer:

sin A = sin B = sin C

Step-by-step explanation:

edg

Numbers greater than zero but less than one have squares that are smaller.

Consider the number one-half (1/2); half of a half is a quarter (1/4 < 1/2)!

Of course, the square of a negative number is greater (since a negative squared is positive).

Only the numbers zero and one are equal to their squares.

another explanation:

Yes .

In fact there is an infinite number of numbers that have that condition. For example (1/2)² = 1/4.

In fact any positive number ’n’ such that 0<n<1 is a number which has a smaller number when squared.

The regression equation to predict the head circumference of a child who is 24.25 inches tall y=17.20 inches

The regression line with the least squares

y = 0.1827*x + 12.4932

Children that are 25.25 inches tall should have a mean head circumference that we can anticipate.

Let x = 25.75

y is thus equal to 0.1827*25.75 plus 12.4932.

b) The mean head circumference of kids who are 25.25 inches tall falls within the 95% confidence interval of

The Mean of the head circumference is 17.327, the standard deviation is 0.219, there are 11 participants, and there are 10 participants in step c.

y = 0.1827*x + 12.4932

The head circumference of a youngster who is 25.25 inches tall must be predicted.

Let x = 25.75

y is thus equal to 0.1827*25.75 plus 12.4932.

y=17.20 inches.

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The function is an exponential growth function

The function is given as

y=2(1.06)^9

We can begin by rewriting the given equation as:

y = 2 * 1.06t

So, we have

y = 2 * (1 + 0.06)^t

Now we can see that the equation is in the form y = a*b^t,

where a = 2 and b = 1.06^9

This equation represents exponential growth because the base of the exponent, b = 1.06, is greater than 1.

We can re-write it in the form y = a(1+r)t,

we can find the value of r by subtracting 1 from 1.06 which is 0.06 and the value of a is 2.

so we have y = 2(1+0.06)^t

So, the equation represents exponential growth with a = 2 and r = 0.06

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The minimum side length of the triangle needed to complete the triangle is 5 feet.

A polygon that has three sides and three vertices is called a triangle.

The sum of all the angles of the triangle is 180°.

Given:

The two sides of the triangle are 7 feet and 3 feet.

Let a = 7 and b = 3.

The minimum possible value,

= Max(a, b) - Min(a, b) + 1

= 7 - 3 + 1

= 5 feet.

Therefore, the minimum length is 5 feet.

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Answer:

You too

Step-by-step explanation:

I don't know either, so we are in the same boat.

The value of the number will be;

⇒ 5/2

A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

Given that;

The rational number is,

⇒ 2.5

Now,

Since, The rational number is,

⇒ 2.5

Hence, We get;

⇒ 2.5 = 25/10

          = 5/2

Thus, The value of the number = 5/2

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The surface area of the square pyramid, in square inches is found to be 184.29 square inches.

Since the square pyramid has a square base, its surface area is the sum of the area of the base and the area of the four triangular faces. The area of the square base is simply the side length squared,

Area of base = (7.1 inches)² = 50.41 square inches

The area of each triangular face can be found using the formula for the area of a triangle,

Area of triangle = 1/2 x base x height where the base is 7.1 inches and the height is 9.4 inches. Thus, the area of each triangular face is,

Area of triangle = 1/2 x 7.1 inches x 9.4 inches = 33.47 square inches

Since there are four triangular faces, the total area of the four triangular faces is,

4 x (33.47 square inches) = 133.88 square inches

Therefore, the total surface area of the square pyramid is,

Total surface area = Area of base + Area of four triangular faces

= 50.41 square inches + 133.88 square inches

= 184.29 square inches

Hence, the surface area of the square pyramid is 184.29 square inches.

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The surface area of the square pyramid is calculated to be 184.29 square inches.

Because the square pyramid has a square base, its surface area is the sum of the base and the four triangular faces. The area of a square base is simply the square of the side length: Area of base = (7.1 inches)2 = 50.41 square inches

The area of each triangular face can be calculated using the triangle area formula: Triangle area = 1/2 x base x height, where the base is 7.1 inches and the height is 9.4 inches. As a result, the area of each triangular face is as follows: Area of triangle = 1/2 x 7.1 inches x 9.4 inches = 33.47 square inches

The total area of the four triangular faces is, because there are four triangular faces.

133.88 square inches = 4 x (33.47 square inches)

As a result, the square pyramid's total surface area is,

Total surface area = base area + four triangular face areas

= 133.88 square inches + 50.41 square inches

equals 184.29 square inches

As a result, the square pyramid has a surface area of 184.29 square inches.

Answer:

y=6x-15

Step-by-step explanation:

y-y1=m(x-x1)

y-3=6(x-3)

y-3=6x-18

y=6x-18+3

y=6x-15

Answer:

Step-by-step explanation:

the equation for the line is y = 4

Answer:

21.77% probability that the antenna will be struck exactly once during this time period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

In this question:

\(\mu = 2.40\)

Find the probability that the antenna will be struck exactly once during this time period.

This is P(X = 1).

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 1) = \frac{e^{-2.40}*2.40^{1}}{(1)!} = 0.2177\)

21.77% probability that the antenna will be struck exactly once during this time period.

Answer:

x=2, y=3. (2, 3).

Step-by-step explanation:

2x+4y=16

-2x-3y=-13

-----------------

y=3

2x+4(3)=16

2x+12=16

2x=16-12

2x=4

x=4/2

x=2

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Answer: No solution

Step-by-step explanation:

1. Expand the brackets- 9-3x+5x=2x+4

2. Add common terms- 9+2x=2x+4

3. Subtract 2x from both sides- 9=4

4. Nine cannot equal four and therefore, there is no solution.

The amount of water left in the tub after 5 minutes is; 24 gallons

The given recursive formula is expressed as;

aₙ = aₙ ₋ ₁ - 12

We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.

Thus, when n = 1, we have;

a₁ = a₁ ₋ ₁ - 12

a₁ = a₀ - 12

a₁ = 84 - 12

a₁ = 72

Then;

a₂ = a₁ - 12

a₂ = 72 - 12

a₂ = 60

It will seem that it follows a sequence pattern of;

aₙ = 84 - 12n

Thus;

a₅ = 84 - 12(5)

a₅ = 24 gallons

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Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

Answer:

-9

Step-by-step explanation:

BECAUSE 4 x -9 would equal -36. If you added 10 it would then be -26 (NOT -46 because remember, this is the negatives). And there you go :]

\(4x+10 = -26 \\\\\implies 2x +5 = -13\\\\\implies 2x = -13 -5 = -18\\\\\implies x = -9\)