There are 135 people in a sport centre.
73 people use the gym.
73 people use the swimming pool.
67 people use the track.
36 people use the gym and the pool.
35 people use the pool and the track.
32 people use the gym and the track.
14 people use all three facilities.
How many people use exactly one of these facilities?

The inequality that represents the interval shown on the number line is:

5 ≤ x ≤ 9

We want to use inequality notation to define the interval shown on the number line.

We can see that the first point is marked with a closed circle, at x = 5.

And then we have another closed circle at x = 9

The closed circles means that these points are solutions to the inequality, so we need to use the symbols:

≤ and ≥

Then we can write the inequality:

5 ≤ x ≤ 9

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Number of pounds of banana sold is, 14

And, Number of pounds of grapes sold is, 36

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Each pound of banana sell for $2.

And, Each pound of grapes sell for $1.

Now, Let number of pounds of sell banana = x

And, Number of pounds of sell grapes = y

Since, There are 50 pounds of fruits are sell.

So, We can formulate;

⇒ x + y = 50   .. (i)

And, Each pound of banana sell for $2.

And, Each pound of grapes sell for $1.

Hence, We get;

⇒ $2x + $1y = $64

⇒ 2x + y = 64  .. (ii)

Substitute value of y from (i) in (ii), we get;

⇒ 2x + y = 64

⇒ 2x + (50 - x) = 64

⇒ 2x + 50 - x = 64

⇒ x = 64 - 50

⇒ x = 14

And, From (i);

⇒ x + y = 50

⇒ 14 + y = 50

⇒ y = 50 - 14

⇒ y = 36

So, Number of pounds of sell banana = 14 pounds

And, Number of pounds of sell grapes = 36 pounds

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Answer: 90

Step-by-step explanation:

If you're looking for the number of times she has to visit the movie theater in order to have 310 points for the free movie ticket then;

310-85 = 225

225/2.5 = 90

Eva needs 90 visits before she can get a free movie ticket.

Answer:

B 9.33

Step-by-step explanation:

The lateral surface area of the triangular prism is 364.1 square inches.

The Surace area of any 2D or 3D figure is the outer area of the given figure.

Surface areas are of two types they are lateral surface area when we exclude the areas of top and bottom and total surface area is when we include all the sides.

From the given diagram and the concept of lateral surface area where the base and top are excluded here, it has only the base area as the top results to a point.

Therefore, The lateral surface area of this isosceles triangular prism is,

Two rectangles have a length of 17 inches and a width of 9 inches in addition to two triangles having a base of 7 inches and a height of 8.3 inches which is,

= 2(17×9) + 2[(1/2)×7×8.3) square inches.

= 306 + 58.1 square inches.

= 364.1 square inches.

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The value of log10 5 as required to be determined using the given information is; 0.3979 + P..

It follows from the task content that; the value of log10 5 is to be determined based on the given information.

Since the given expression is; log10 2 = P;

The expression which can be inferred from the equation above is;

10^P = 2..............(i)

However, let; log10 5 = x

Therefore; 10^x = 5..........(ii)

By dividing the equation (ii) by (i); we have that;

10^(x - P) = 2.5

Therefore, from the converse of logarithmic law;

x - P = log10 2.5

x = P + log10 2.5

where, log10 2.5 = 0.3979

x = 0.3979 + P

Ultimately, the value of log10 5 as required is; 0.3979 + P.

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Answer: 1 + 2x

Step-by-step explanation:

To solve this problem, it's helpful to understand "order of operations." The order is: parentheses, exponents, multiplication, division, addition, and lastly, subtraction.

A helpful mnemonic is PEMDAS. I was taught "Parachute Expert My Dear Aunt Sally" to help remember the order.

We must work with the numbers inside the parantheses, since "parantheses" is the first operation. We'll start with the first paranthesis: (-5x2 + 10x - 12).

Since there are no exponents in this equation, we can go to the third operation: multiplication. (I like to use the "·" symbol to show that two numbers are multiplied because it's easy for me to confuse the letter X with "x" when it is used as a multiplication symbol).

-5 · 2 = -10

Two negative numbers are added, so -10 and -12 = -22

This leaves (-22 + 10x)

The -22 and 10x are not added together because numbers without a letter cannot be added to numbers with letters.

Now we'll work with the second paranthesis: (-4 · 2 + 8x - 15)

-4 · 2 = -8

-8 and -15 is added to make -23

The paranthesis now looks like:

(-23 + 8x)

Notice that there is a negative sign outside of the second paranthesis in the equation.

(-22 + 10x) − (-23 + 8x)

When a number or symbol is outside of a paranthesis, that number or symbol is multiplied across everything within the parantheses.

Now, it is:

(23 - 8x)

All of the numbers can be taken out of the parantheses now:

-22 + 10x + 23 - 8x

-22 + 23 = 1

10x - 8x = 2x

The final answer:

1 + 2x

Hope this helps!

The amount of water in Casandra's bowl, given the gallons of water it can hold and the fraction full it is, is 0.6 gallons

Casandra' s fish bowl is able to hold a total of 9 / 10 gallons of water which is also 0.9 gallons of water. This means that you can find out how much water is in the bowl if told the fraction of the bowl that is currently full up to.

This time, the bowl is said to be 2 / 3 full which means that out of the capacity of 9 / 10 gallons or 0 . 9 gallons, the bowl is two - thirds full.

The amount of water in the bowl is therefore:

= Capacity of fish bowl x Proportion of water in the bowl

= 9 / 10 x 2 / 3

= 0. 9 x 2 / 3

= 0 . 6 gallons

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Answer:

Step-by-step explanation:

Since segment AD and BE are parallel, we can use the Alternate Interior Angles Theorem to solve this. According to this theorem, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are equal. Since angle CAD = 67 degrees, angle DBE is also equal to 67 degrees.

Now, if we look at the diagram, angle DBE is supplementary to angle CBE, meaning that the two angles add up to 180 degrees. Therefore, angle CBE = 180 degrees - 67 degrees = 113 degrees.

Work Shown:

A = P*(1+r/n)^(n*t)

A = 2750*(1+0.035/4)^(4*7)

A = 2750*(1+0.00875)^(28)

A = 2750*(1.00875)^(28)

A = 2750*1.27626052446017

A = 3509.71644226547

A = 3509.72

Answer:false

Step-by-step explanation:

Answer:

Total people =107

Women =57

Men =50

Men who don't like tea =20

Men who like tea= 30

Women who like tea = (total people who like tea)-(men who like tea)

Women who like tea= 30

Women who don't like tea =27

a=50

b=30

c=20

d=57

e=30

f=27

A total of 40 nurses do not have a nursing diploma yet

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

Nurses = 160 nurses

Diploma qualitifications = 75%

The above parameters mean that

No diploma qualification = (1 - Diploma qualitifications) * Nurses

Substitute the known values in the above equation, so, we have the following representation

No diploma qualification = (1 - 75%) * 160

Evaluate

No diploma qualification = 40

Hence, the nurses are 40

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As the trianlges are SAS congurant the side NK = 1.8.

What is congruent by ASA?

The Angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

∠LJK=∠LMN

LM =4

MJ=2

LN=3.6

So, As the trianlges are SAS congurant the side NK = 1.8.

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Answer:

In an absolute value graph, the slope of one side of the graph is the opposite of the other side.

For example, if the slope of one side of an absolute value function is positive, then the other side of the equation has a slope of negative.

Answer:

5 people

Step-by-step explanation:

Relay race ---> 3/4 mile

Each runner runs 3/20 miles

3/4÷3/20

3/4×20/3=5

OR

3/4 --> 15/20

3/20 goes into 15/20 5 times

Answer:

5 runners

Step-by-step explanation:

Just multiply 3/20 by 3/4

Answer:

Easy, A is 4.1

Step-by-step explanation:

I just finished this too

Answer:

-4 < 2 - a < -8

Step-by-step explanation:

Answer:

A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions correctly.

Step-by-step explanation:

The statement is true because, g(x) = f(x) + 4 is indeed a transformation of f(x) by shifting the graph 4 units up, and because the horizontal asymptote is determined by the highest degree term in the function, which in this case is the same for both functions, so the two functions will have the same vertical asymptote, but the horizontal asymptote is determined by the leading coefficient which is different for both functions, so the two functions will have different horizontal asymptotes.

Answer:

m∠2 = 94°

Step-by-step explanation:

m∠3 and m∠2 are vertically opposite angles meaning they have equal angle. They are of equal measure.

Given that m∠3 = 94°, so m∠2 = 94° as well.

Answer:

94°

Step-by-step explanation:

We know that vertically opposite angles are equal to each other.

Therefore,

<2 = <3

94° = 94°

The fifth term of the arithmetic sequence can be found to be 18.

There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the same" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."

In this arithmetic sequence therefore, you can find the common difference to be:

= 9 - 6

= 3

So the fifth term would be:

= 4th term + common difference

= 15 + 3

= 18

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The fifth term of the arithmetic sequence: 6, 9, 12, 15 is 18.

The formula for the nth term of an arithmetic sequence is expressed as;

aₙ = a₁ + d( n - 1 )

Given the data in the question;

6, 9, 12, 15.

Plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

a₅ = 6 + 3( 5 - 1 )

a₅ = 6 + 3( 4 )

a₅ = 6 + 12

a₅ = 18

Therefore, the fifth term of the sequence is 18.

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The equations which represent circles whose diameters are 12 units and a center line lies on the y-axis are:

It is noteworthy to know that a center line on the y-axis can be interpreted as a coordinating pair in which case the pair looks like;

( 0, y )

Recall the equation of a circle which takes the form;

(x - h)² + (y - k)² = r²

Hence, since the center that lies on the y-axis, it automatically means that h = 0.

Also, if the diameter of the circle is 12 units

r = 12 / 2 = 6.

On this note, the required equation is;

x² + (y - k) = 6²

where k could be any real number.

Ultimately, the equations which are correct are;

x² + (y – 3)² = 36

x² + (y – 5)²

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Answer: A rational function is a function that is a fraction and has the property that both its numerator and denominator are polynomials.

Step-by-step explanation:

Using exponential function, the value of x that makes f(x) = g(x) is x = 6.7 (rounded to the nearest integer).

The value of x that makes f(x) = g(x) is approximately x = 76.

To solve this, you can set f(x) = g(x) and solve for x.

[tex]f(x)=400(0.90)^x\\g(x)=70(1.10)^x\\400(0.90)^x = 70(1.10)^x\\Divide both sides by 400 to get:\\(0.90)^x = (1.10)^x / (400/70)\\[/tex]

Take the logarithm of both sides and use the power rule:

[tex]x(log 0.90) = (log (1.10)) / (log (400/70))\\x = (log (1.10)) / (log (400/70)) / (log 0.90)\\x = 76.3 (round to the nearest integer)\\[/tex]

Therefore, the approximate value of x that makes f(x) = g(x) is x = 76.

To solve this, we can set the two equations equal to each other and solve for x.

[tex]f(x)=400(0.90)^x = 70(1.10)^x\\400(0.90)^x = 70(1.10)^x\\(0.90)^x = 70/400 (1.10)^x\\(0.90)^x / (1.10)^x = 70/400\\(0.90/1.10)^x = 70/400\\(0.81818)^x = 70/400\\[/tex]

Take the logarithm of both sides.

[tex]xlog(0.81818) = log(70/400)\\x = log(70/400) / log(0.81818)\\x = 6.7 (rounded to the nearest integer).[/tex]

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Answer:

corresponding

Step-by-step explanation:

<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m

Answer:

0.124176

Step-by-step explanation:

.06 x .995 x 1.3 x 1.6= 0.124176

You change a percent into a decimal by dividing it by 100%

The overlapping triangles which are congruent by ASA are ΔEBC and ΔADC which is therefore denoted as option C.

This is a scenario in which all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Taking ΔEBC and ΔADC, we have the following below:

∠B=∠D (90°)

CB= CD (Given)

∠BCE=∠ACD( Common)

Therefore, by ASA we can deduce that,

Δ EBC ≅ΔADC.

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The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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262 "hyper-texters," or teens who spend more than three hours per day on their smartphones, were found in a sample of 400 youngsters. if North High School enrolls 2,000 pupils.

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