A survey of 400 nurses yielded the following information: 279 were health club members, 215 were smokers, and 160 of the health club members were smokers. how many of the 400 surveyed nurses were health club members or were smokers?

Answer: 18

Step-by-step explanation:

There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.

I hope this helps!

Answer:

7.

Step-by-step explanation:

Think of 42/6 as a division question.

42 ÷ 6.

The answer to this equation is 7.

Answer:

The triangles are Congruent for the same reason as the answer above

Step-by-step explanation:

The slope of the line is - 3 / 2 .

The slope of a line is the change in y coordinate with respect to the change in x coordinate.

Therefore, using (0, 6)(4, 0)

Hence,

m = slope = y₂ - y₁ / x₂ - x₁

slope = 0 - 6 / 4 - 0

slope = -6 / 4

slope = - 3 / 2

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Answer:

B

Step-by-step explanation:

Let t and d be their ages now.

2 years ago, their ages were t - 2 and d  2.

Now, Tyler is 3 years older than David: t = d + 3

2 years ago, Tyler was 4 times as old as David: t - 2 = 4(d - 2)

The system of equations is:

t = d + 3

t - 2 = 4(d - 2)

Answer: B

Answer:

D

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.

In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A

Answer:

$ 7.52

Step-by-step explanation:

Find charge per minute

 59 - 23 min = 36 minutes   cost   16.32 - 10.56 = $ 5.76

      or   $5.76 / 36 min = 16 cents per min

   from 59 to 78 = 19 more minutes        x .16/min =  $ 3.04

            so from 59 to 78 will leave 10.56 - 3.04 = $7.52

The required equation is 135 + 9x > 250.

The number of lawns Ed must mow is assumed to be x.

The amount Ed charges for each lawn he mows is $9.

Thus, the total amount Ed earns by mowing x lawns = $9x.

The savings which Ed has is $135.

Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).

The cost of the video game is given to be $250.

We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.

This can be shown as the equation:

Total amount Ed has > Cost of the video game,

or, 135 + 9x > 250.

Thus, the required equation is 135 + 9x > 250.

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Answer:

6

Step-by-step explanation:

[tex]\frac{y}{2} =x^{2} -7[/tex]

[tex]\frac{a}{2} =2^{2} -7[/tex]

[tex]\frac{a}{2} =-3[/tex]

[tex]a=-6[/tex]

[tex]\frac{b}{2} =1^{2} -7[/tex]

[tex]\frac{b}{2} =-6[/tex]

[tex]b=-12[/tex]

From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.

[tex]-6=2m+b[/tex]        

[tex]-12=m+b[/tex]

[tex]-24=2m+2b[/tex]

[tex]18=-b[/tex]

[tex]b=-18[/tex]

[tex]-12=m-18[/tex]

[tex]m=6[/tex]

Therefore, the slope of line l is 6.

Answer:

slope = 6

Step-by-step explanation:

substitute the given points into the equation of the curve to find a and b

(2, a )

[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )

a = - 6

then point (2, a ) = (2, - 6 )

(1, b )

[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )

b = - 12

then point (1, b ) = (1, - 12 )

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )

m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6

The number of visitors to the homepage of an online magazine in the year 2005 is 3527

An equation is an expression that shows the relationship between two or more number and variables.

Let y represent the total number of visitors x years since 2000. Hence:

y = 1100.74x - 1976.47

In the year 2005 (x = 5):

y = 1100.74(5) - 1976.47 = 3527.23

The number of visitors to the homepage of an online magazine in the year 2005 is 3527

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Answer: 12x

Step-by-step explanation:

The question is asking what equation models the table above. You have to make an equation that when any of the times on the left column are plugged in, the value on the right column are outputted.

For 1, the equation should output 12. For 2, the equation should output 24. For 3, the equation should output 36, and so on.

Here, we see a pattern: for every value we input as the number of seconds, the height is 12 times more than that. Assuming x is the time and y is the height,

[tex]y=12x[/tex]

If we use any x on the left, it's corresponding height will be the y.

A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles

The base fare = $2.00

Let x represent the per-mile rate, and let y represent the per-minute rate, we have;

The cost of Ryan's first taxi ride = $8.50

Distance traveled in the first ride = 3.0 miles

Time taken during the first ride = 7 minutes

Therefore;

2 + 3•x + 7•y = 8.5

Which gives;

3•x + 7•y = 8.5 - 2 = 6.5

Distance traveled in the second ride = 7.0 miles

Duration of the second ride = 14 minutes

The second ride cost = $16.00

Therefore;

2 + 7•x + 14•y = 16

Which gives;

7•x + 14•y = 16 - 2 = 14

Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;

(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1

x = 1

3•x + 7•y = 6.5

7•y = 6.5 - 3•x

7•y = 6.5 - 3×1 = 3.5

y = 3.5/7 = 1/2 = 0.5

Duration of the third taxi ride = 10 minutes

Cost of the third ride = $13.50

Therefore;

2 + 1×a + 10×y = $13.50

Where a is the distance traveled during the third ride, we have;

2 + 1×a + 10×0.5 = $13.50

2 + a + 5 = 13.5

a = 13.5 - 2 - 7 = 4.5

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Answer:

Option (4)

Step-by-step explanation:

See attached image.

The length of FY in the triangle that has Y as its circumcenter is: D. 22 units.

The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of a triangle intersect.

Based on the definition of the circumcenter, and Y is the circumcenter, therefore:

YE = FY

Plug in the values

5x - 3 = 3x + 7

5x - 3x = 3 + 7

2x = 10

x = 5

FY = 3x + 7 = 3(5) + 7

FY = 22 units.

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Answer:

D

Step-by-step explanation:

Answer:

5/9

Step-by-step explanation:

4+5=9 and there are 5 boys

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the explanation ~

Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.

That is :

The point where it cuts the x - axis, it has an x - coordinate = -6

Therefore, we can conclude that The zero of given function is -6

Answer:

x = -6.

Step-by-step explanation:

It is where the graph cuts the x-axis  (where the function is zero).

That is -6.

The percentages of 67 of 98 is 68.36%

Fractions are written as a ratio of two integers. According to the question we are to determine the percentage of 67 that is 98.

Fraction of 67 of 98 = 67/98

Percentage = 67/98 * 100

Percentages = 6700/98

Percentages = 68.37%

Hence the percentages of 67 of 98 is 68.36%

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One can easily convert the temperature using temperature conversion formula given below

K = [tex]\frac{5(F - 32)}{9} + 273.15[/tex]

where F = degrees in Fahrenheit

K = degrees in Kelvin

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Answer:

the following 3 equations are equivalent :

• x + 1 = 4

• 2 + x = 5

• -5 + x = -2

Step-by-step explanation:

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

-5 + x = - 2

Let’s take this equation :

x + 1 = 4

=======

By Adding 1 to both sides of the equation we get :

x + 1 + 1 = 4 + 1

⇔ x + 2 = 5

⇔ 2 + x = 5

Then the equations x + 1 = 4  and 2 + x = 5 are equivalent.

…………………………………………………………………

On the other hand ,if we subtract 6 from both sides

of the equation x + 1 = 4  we get :

x + 1 - 6 = 4 - 6

⇔ x - 5 = -2

⇔ -5 + x = -2

Then the equations x + 1 = 4  and -5 + x = -2 are equivalent.

Answer:

A. 2 + x = 5

B. x + 1 = 4

E. -5 + x = -2

Step-by-step explanation:

right on edg, hope it helps ya'll.

The total amount that roland paid for the ticket is $27.60

Given that the price of an all-access ticket to the fair is $42.99 before tax. Roland bought the all-access ticket for 40% off.

We need to calculate the total amount paid by the roland

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100

The price after 40% off -

= 42.99*60% = $25.794

Sales tax on 25.794

= 25.794*7% = $1.80558

Total amount Paid for the ticket

= 1.80558 + 25.794 = $27.59958

= $27.60

Hence the total amount paid by roland is $27.60

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Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

Herein we must make use of trigonometric expressions and properties of trigonometric functions to find the right value. According to trigonometry, both cosine and sine are negative in the third quadrant. Thus, by using the fundamental trigonometric expression (sin² α + cos² α = 1) and substituting all known terms we find that:

[tex]\sin \theta = -\sqrt{1 - \cos^{2}\theta}[/tex]

[tex]\sin \theta = - \sqrt{1 - \left(-\frac{13}{30} \right)^{2}}[/tex]

sin θ ≈ - √731 / 30

Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

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Answer: A. (4, 4) and (4, 5)

Step-by-step explanation:

The same x value maps onto more than one y value.

A possible critical point of the function f(x) is given by: (0,-2)

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

At these points, the function can change from decreasing to increasing, or vice-versa.

For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).

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Use a³+b³ +c³ - 3abc

Here a = 2a²

b= -a

And c = 1

Answer:

Step-by-step explanation:

Answer:

Gradient: 5

y-intercept: (0, 15)

Step-by-step explanation:

The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.

Answer:

Step-by-step explanation:

hello here is an solution

The domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=(x+1)/6x+7

Let f(x)=y

(x+1)/6x+7=y

x+1=y(6x+7)

x+1=6xy+7y

6xy-x=7y-1

x(6y-1)=7y-1

Divide both sides by 6y-1

x=7y-1/6y-1

So f⁻¹(x)=1-7x/6x-1

The domain is (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6}

The range is (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6}

Hence, the domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

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The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts

An equation is an expression that shows the relationship between two or more number and variables.

The line segment has a length of 6.4 cm. Hence:

Dividing into 4 equal parts = 6.4 / 4 = 1.6 cm

The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts

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The graph above could be a graph of this exponential function: A. F(x) = 3.(1.2)^x.

Mathematically, the standard form of an exponential function is given by:

F(x) = ab^x

Where:

As a general rule, f(x) is an increasing function when b is greater than 1 (b > 1) and f(x) is a decreasing function when b is less than 1 (b < 1)

By critically observing the given graph, we can deduce that the initial value (a) is 3 and it's an increasing function (b > 1).

F(x) = 3.(1.2)^x

Thus, the graph above could be a graph of this exponential function F(x) = 3.(1.2)^x.

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