For questions 3 – 4, use the table to answer the questions.

This table shows the high schools in a metro district and whether they offer hockey and golf.

High school Hockey Golf

East Valley ✔

Central

Lincoln ✔ ✔

Davis

West Pine ✔ ✔

Adams ✔

North River ✔ ✔

A high school is chosen at random from this list.

Let event A = The high school has a hockey team.

Let event B = The high school has a golf team.

3. Which high schools offer both hockey and golf?




What is P(A ∩ B)?



4. Which high schools offer hockey or golf or both?




What is P(A ∪ B)?

To Solve the inequalities , we take the variables on a side and the numbers on the other side and then apply mathematical operations to solve it .

What is Inequality ?

The Inequality is defined as a relationship between two values that are not equal to each other .

The method of solving the inequalities is a little different than solving equations.

To solve the inequalities, some simple rules should be followed .

(i) The inequality does not change if any number or variable is added or subtracted from both sides.

Similarly, the value of inequality is not affected if the same number is multiplied on both the sides.

(ii) If the inequality is divided by a negative variable or number on both  sides, then the inequality sign gets reversed.

(iii) On dividing inequality by a positive number, there is no change.

For Example : Solve the inequality [tex]4x+6 > 3x+7[/tex] ;

subtracting [tex]3x[/tex] from both the sides ,

we get ;

[tex]x+6 > 7[/tex],

Now subtracting [tex]6[/tex] from both sides of the inequality;

we get ;

[tex]x > 1[/tex] .

Therefore , the solution of the inequality [tex]4x+6 > 3x+7[/tex] is [tex]x > 1[/tex] .

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The explanation of four quadrant are explained below.

In the coordinate plane the first coordinate or the x-coordinate will refer to the number which corresponds with the point's horizontal location as determined by the number on the x-axis.

And the second coordinate known as the y-coordinate, will refer to the number which corresponds with the point's vertical location as determined by the number on the y-axis.

By using these x and y values, we have divide the graph, into four part such as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.

Here we want to know that each quadrant contains certain directions.

=> Quadrant 1 placed on 0 to 90 degrees.

=> Quadrant 2 placed on 90 to 180 degrees.

=> Quadrant 3 placed on 180 to 270 degrees.

=> Quadrant 4 placed on 270 to 360 degrees.

And the value in the quadrant are like as follows:

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Answer:

(2, -1)

Step-by-step explanation:

2(2)+ (-1) = 4-1 = 3.

The value of x will be; x = 3

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

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that  the equation 5x+7=6x+4

Here, we need to solve for x;

5x+7=6x+4

combine the like terms;

5x - 6x = -7 +4

-x= - 3

x = 3

Therefore, the solution will be as;

x = 3

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Jane should land 1.5 mi down the shoreline and walk the remaining 4.5 mi to the village to minimize her travel time.

Let x = distance travelled along the shore over water.

Then, 6 − x = distance travelled along the shore over land.

Let T = the total time taken to reach the destination.

T = distance/velocity = √(4 + x²)/3 + (6-x)/5 on [0, 6].

Note that T must be non negative and that x = 6 means the destination

is reached solely by rowing and without the benefit of faster land

travel. In actual fact, T is valid over [0, ∞) but [0, 6] is reasonable here.

T' = x/3√(4 + x²) - 1/5 = 5x - 3√(4 + x²) = 0

⇒5x = 3√(4 + x²)

⇒25x² = 9(4 + x²)

⇒16x² = 36

⇒x = ±6/4 = ±1.5

The negative x value is discarded since it does not belong to [0,6].

T(0) = 28/15 = 1.8667

T(1.5) = 1.733

T(6) = 2.1082

Therefore, Jane should land 1.5 mi down the shoreline and walk the

remaining 4.5 mi to the village to minimize her travel time.

Her minimum travel time will be T(1.5) = 1.733 hrs. or 1hr 44 min.

--The given question is incomplete, the correct question is

"Jane is 2 mi, offshore in a boat and wishes to reach a coastal village 6 mi, down a straight shoreline from the point nearest the boat. She can row at 3mph and can walk at 5 mph. Where should she land her boat to reach the village in the least amount of time?"--

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a. A function that models the population of the city's years after 2010 is:

f(x) = 50,000 * (1 + 0.05)^(x-2010)

where x is the number of years after 2010.

b. The population of the city in 2017 (7 years after 2010) is:

f(2017) = 50,000 * (1 + 0.05)^7

           = 65,128

c. The population of the city in 2020 (10 years after 2010) is:

f(2020) = 50,000 * (1 + 0.05)^10

            = 76,923.1

The population of the city in 2030 (20 years after 2010) is:

f(2030) = 50,000 * (1 + 0.05)^20

            = 129,382

d. The population in 2020 is 76,923.1, and the population in 2010 is 50,000, so the population grows by:

= 76,923.1 / 50,000

= 1.53846

The population in 2030 is 129,382, and the population in 2020 is 76,923.1, so the population grows by:

= 129,382 / 76,923.1

= 1.6859  

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The remaining miles are 660 miles.

This month, Diaz drives 28 miles each day using the car allotted to him by his company.

But the company allows him to drive up to 1500 miles each month by his car.

To calculate the remaining miles that Diaz has not traveled this month, we have to use the formula m = 1500 - 28d, where d is the number of days in that particular month.

A month general consists of 30 days.

So, this month Diaz has traveled 28×30 miles = 840 miles ( using multiplication)

Therefore, the remaining miles(m) that Diaz has not traveled this month comes to 1500 - 840 = 660 miles.

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The complete question is:

Diaz has a company car that allows him to drive up to 1,500 miles each month. He averages 28 miles each day. The remaining miles for this month can be calculated using the formula m = 1500 - 28d where m is the remaining miles and d is the number of days driven this month. What are the remaining miles?

The price of a stock share has decreased by 15% and suddenly increased by 5%.

The percentage is a fraction of a number represented as a number out of a hundred. The % symbol is used to denote percentages. The percentage signifies the frequency.

The selling price for a share of the same stock at a later date was represented by the expression 1.05(0.85d).

When a % decrease occurs, the number is deducted from 100, and when a percentage increase occurs, the number is added to 100.

100 - 15% = 85% = 0.85

100 + 5% = 105% = 1.05

original selling price = d

selling price at a later date = 1.05(0.85d)

0.85d means that the original price was discounted by 15%

1.05 means that the price increased by 5%

Thus, the price of a stock share has decreased by 15% and suddenly increased by 5%.

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Answer: It's a homozygous dominant genotype.

Step-by-step explanation: Two capital letters or two lowercase letters are homozygous.

The area of a triangle when three side lengths are calculated by Heron's Formula. Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c)

To calculate the area of a triangle when three side lengths are given, we can use Heron's Formula. Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c) where s is half the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.

To calculate the area of the triangle given three side lengths, we first need to calculate the perimeter (p) of the triangle. The formula for the perimeter is p=a+b+c.

Then, use this formula to calculate s, which is half the perimeter.

s = p/2

Once s is calculated, plug it into Heron's Formula to calculate the area of the triangle.

Area = √s(s-a)(s-b)(s-c)

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ES is 8√2 units from the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given two points from the graph are S(4, 4) and E(-4, -4)

We need to find ES which means the distance between two points in units.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

√(-4-4)²+(-4-4)²

√(-8)²+(-8)²

√64+64

√64×2

8√2 units.

Hence, ES is 8√2 units from the given graph.

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Answer:

The answer is 5⁻¹ or 1/5

Step-by-step explanation:

5²/5³

Here, we know that the base is the same i.e., 5 so, will use the property;

5² ÷ 5³

5² ⁻ ³ = 5⁻¹ = 1/5

Thus, The answer is 5⁻¹ or 1/5

The perimeter of ΔAEB is 18.5 feet.

A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.

As,  side AB║DF hence we will use Triangle Proportionality theorem to calculate the length of side AE.

Since, AE/AD = EB/ BF

AE/2 = 7.2/8.4

AE = 6.5 feet

So, the perimeter of ΔAEB is

= AE + EB + BE

=6.5+4.2+7.8

=18.5 ft.  

Hence, the perimeter  is 18.5 feet.

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The measures of three angles are 40.5°, 43.5° and 95.8°.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, an interior designer plans to use triangular tiles that are 8 cm×9 cm×13 cm for a backsplash.

Using cosine rule, we get

9²= 8²+ 13²- 2(8)(13) cos θ (angle opposite 9 cm side.)

81=64+169-208 cos θ

81-233=-208 cos θ

-208 cos θ=-152

cos θ=-152/(-208)

cos θ=0.7307

θ=43.7°

Using sine rule,

The formula for sine rule is sinA/a=sinB/b=sinC/c

sinA/8 =sin43°/9=sinC/13

sinA/8 =0.7307/9

sinA/8=0.0811

sinA=0.6495

A=40.5°

So, ∠A+∠B+∠C=180°

40.5°+43.7°+∠C=180°

∠C=95.8°

Therefore, the measures of three angles are 40.5°, 43.5° and 95.8°.

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The domain of the function f(x) = log x is (0, ∞). The value of x belongs to (0, ∞).

What is a logarithm?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

The given function is f(x) = log x.

When the value of x is less than or equal to 0, then the value of log x is undefined.

The possible value of x where f(x) exists is the domain of a function.

In the given function the value of x must be greater than zero.

The domain of the function is (0,∞).

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The closest estimate of x when the functions satisfy the condition f(x) = g(x) is 1.65

What is a function?

Function is a mathematical law that establishes the relationship between an independent variable and a dependent variable.

Given,

[tex]f(x) =[/tex] [tex]\log\x_{3} (2x)[/tex]

[tex]g(x) = -4x^{2} + 3x +7[/tex]

Now plotting both the graphs in Desmos, we got the result as in the below figures.

Given f(x) = g(x)

So from the graphs, we can find an intersecting point. This intersecting point is common to both f(x) and g(x)

Therefore from the graph, the closest estimate of x is 1.65.

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In the expression 52 + 6 + ya,

The terms are the individual parts of the expression that are being added together. The coefficient is the numerical factor that is multiplied by a variable in a term, and the constant is a term that has no variable.

Any expression with variables will either add or delete one or more variables. Any one of a variety of numbers to represent a generic idea. An absolute number is a constant. A constant is a number, whereas a coefficient is a number that is "in front of" a variable.

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Starting out with the fraction of 5/9, Jess would be thinking of the fraction 144/125 at the end of the game if the ten coin flips turn out to be {THTTHTHTTT}.

Since both outcomes are equally likely, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5. Alternatively, the probability of getting H or T in a coin flip is 1.

Probability is an important method for comprehending and making judgments regarding uncertain occurrences in many disciplines, including statistics, finance, and science. It aids in quantifying and forecasting the probability of specific events, enabling us to make better educated choices and comprehend the degree of risk involved with various activities. In summary, probability is a key idea in decision-making and risk management because it is a potent instrument for comprehending and managing uncertainty.

Taking the sequence of coin flips in ten tires, i.e THTTHTHTTT , and starting from the fraction 5/9, the fraction that jess would be thinking at the end of the game can be calculated as,

5/9 * (6/5)^7 *(5/6)^3 , since there are 7 Tails and 3 Heads during the whole game. Which is equal to the fraction 144/125.

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A normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

Since all three of these variables are equal in a normal distribution, they serve as the center of the graph and can either be zero or not.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

The distribution's mean is another name for the center of the range.

Therefore, a normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

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We refer to the enlargement or reduction of one of two figures as a similarity transformation. For example: When one of two figures can be produced from the other and the ratio of their corresponding sides is equal, we say that the two figures are comparable. Similar figures come in a variety of sizes and shapes.

Either a geometric similarity or a matrix transformation that produces a likeness are referred to as "similarity transformations" in this context. Space items are changed into comparable things by similarity transformations. Fractals and iterated function systems are based on essential principles such as similarity transformations and the idea of self-similarity.

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The distance from concord to Matthews is solved to be 14.8 miles

Information from the question include

charlotte is 7 miles south of concord

Matthews is 13 miles west of charlotte

the distance from concord to matthews = ?

The required distance is solved using using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 13² + 7²

x² = 169 + 49

x² =  218

x = √218

x = 14.7648

x = 14.8 (to 3 SF)

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Answer:

Pitcher 2

Step-by-step explanation:

Pitcher 1  = 4 x 1.25 = 5ml concentration

Pitcher 2 = 5 x 2 = 10ml concentration

therefore, pitcher 2 has more concentration :)

hope this helped

Answer: 7 hours

Step-by-step explanation: blake is gains 10 more miles then Jake each hour so if you divide 70 by 10 you get 7.

Answer:

  -2

Step-by-step explanation:

You want to know the dilation scale factor that gives triangle A'B'C from triangle ABC.

We notice that point A' is 4 units down and 2 units right of C, whereas A is 2 units up and 1 unit left of C. The ratio of these distances is the scale factor.

If up and right are positive, then ...

  k = (A' -C)/(A -C) = (2, -4)/(-1, 2) = -2

The dilation scale factor is -2.

In the given diagram beside a coffee, the value of x is 38.

A diagram is a visual, symbolic representation of data. Diagrams have been used on cave walls since prehistoric times, but they became more common during the Enlightenment. The method occasionally employs the projection of a three-dimensional visualisation onto a two-dimensional surface. Sometimes the word "graph" is used in place of the word "diagram."

We know that all angles here add up to 360°

And with the vertical angles theorem we get the equation

2(36°) + 2(78 - x)° + 2(3x - 10) = 360°

2(36 + 78 - x + 3x - 10) = 360°

2(104 + 2x) = 360°

208 + 4x = 360°

4x = 360 - 208

4x = 152

x = 152/4

x = 38

Thus, In the given diagram beside a coffee, the value of x is 38.

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Yes, the order of the quantities in an inequality matters, and examples are given to show why.

The four inequality symbols, along with their meaning, are presented as follows:

It is known that the number 5 is greater than the number 3, hence the inequality that describes these numbers is given as follows:

5 > 3.

However, if we tried to apply the commutative property, that is, changing the order of the numbers, we would have that:

3 > 5.

Which is a false statement, as the number 3 is less than the number 5, and not more.

This shows that the order of the symbols in an inequality in fact does matter.

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Answer: Without estimation skills, students aren't able to determine if their answer is within a reasonable range.

Step-by-step explanation:

to make sure your answer at least make sense to the question

The equation of line is given by y = 13.45x - 7.95 where the slope of the line is m = 13.45 and y is the weight in kilograms , x is the number of months

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The weight in kilograms = y

The number of months = x

Let the first point be represented as P = P ( 11 , 140 )

Let the second point be represented as Q = Q ( 1 , 5.5 )

Now , the slope of the line is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 140 - 5.5 ) / ( 11 - 1 )

Slope m = 134.5 / 10

Slope m = 13.45

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 140 = 13.45 ( x - 11 )

On simplifying the equation , we get

y - 140 = 13.45x - 147.95

Adding 140 on both sides of the equation , we get

y = 13.45x - 7.95

when x = 11 months

y = 13.45 ( 11 ) - 7.95

y = 147.95 - 7.95

y = 140 kilograms

Therefore , the value of A is y = 13.45x - 7.95

Hence , the equation is y = 13.45x - 7.95

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The best approach to solve the problem is writing an equation. Given Avelina earns half of what Gus earns, the equation becomes Avelina's earnings = Gus's earnings / 2. On substituting Gus's earnings with $125, we get Avelina's earnings to be $62.50.

The best problem-solving strategy that would be apt to solve this problem, 'Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn?' is to write an equation. We know that Avelina earned half of what Gus earned. This can be represented by the equation: Avelina's earnings = Gus's earnings / 2.

Since we know that Gus earned $125, we can substitute this value into our equation: Avelina's earnings = $125 / 2. Solving this equation gives us the answer: Avelina earned $62.50.

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