steve guesses randomly on a 15-question multiple choice test in which each problem has two choices, a correct one and an incorrect one. what is the probability that he gets at least half of the questions correct? express your answer as a common fraction.

Answer:

Step-by-step explanation:

It is 48.

The cost of cementing the path at the rate of ₹ 5 per m² is ₹ 6500.

What is a rectangle field?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Here, we have

Given:

Length of the whole field = 80m

The breadth of the whole field = 60m

∴ Area of the whole field = ( Length × breadth )

= 80m × 60m

= ( 80 × 60 ) m²

= 4800m²

Length of the field excluding the path

= [ 80 - ( 5 + 5 ) ] m

= [ 80 - 10 ] m

= 70m

The breadth of the field excluding the path

= [ 60 - ( 5 + 5 ) ] m

= [ 60 - 10 ] m

= 50m

∴ Area of the field excluding the path

= 70m × 50m

= ( 70 × 50 ) m²

= 3500m²

Now, the area of the path,

= 4800m² - 3500m²

= ( 4800 - 3500 ) m²

= 1300m²

According to the question,

The cost of cementing the path at the rate of ₹ 5 per m² is,

= ₹ ( 1300 × 5 )

= ₹ 6500

Hence, the cost of cementing the path at the rate of ₹ 5 per m² is ₹ 6500.

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Therefore , the solution of the given problem of function comes out to be g(x) = -3|x-1| - 4.

Mathematics is a science that investigates numbers, their variations, mathematics and the local tissues, shapes, and the both their actual and potential placements. Function describes the connection between a collection of inputs, each of which has an associated output. A function is an association of inputs that results in a single, distinctive output for each input. Each function is given a city or municipality or a scope, often known as a realm. Functions are typically denoted by the letter f. (x). An x can be found in the input. The four primary categories of procedures—on features, each process, a range few additional attributes, within procedures, and on functions—are already present.

Here,

Given :

g(x) = -f(x) to reflect it over the x-axis.

So , In order to find the g(x) of the given f(x) is

=> -f(x) = -3|x-1|-4,

so

=> g(x) = -3|x-1| - 4

Therefore , the solution of the given problem of function comes out to be

g(x) = -3|x-1| - 4.

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The domain and range of the linear function y = 120 - 15x is  (-∞, ∞)

A graph of a linear function is a straight line that represents the relationship between two variables. A linear function is a function of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line represents the rate of change of one variable with respect to the other variable, and the y-intercept represents the value of the dependent variable when the independent variable is zero.

When a linear function is graphed, it creates a line that can be represented by two key features: the slope and the y-intercept. The slope of a linear function is the rate of change of the function, and the y-intercept is the point where the line crosses the y-axis.

In the given problem, the linear function is y = 120 - 15x

Kindly find the graph attached below;

The domain of the function is (-∞, ∞)

The range of this function is (-∞, ∞)

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To determine how many solutions an equation has, you must first solve the equation. If the equation has an exact solution, then it has exactly one solution.

To determine how many solutions an equation has, you must solve the equation. If you can solve the equation exactly, then it has one solution. However, if the equation has two different solutions, then it has two solutions. This means that the equation has two different values that can make the equation true. On the other hand, if the equation does not have any solutions, then it has no solutions. This means that the equation does not have any values that can make it true. Therefore, to determine how many solutions an equation has, you must solve the equation and check if it has one, two, or no solutions.

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When the parallel lines are cut by a transversal, the values for the measurement of ∠5 and ∠7 is 99° each.

What are parallel lines?

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.

Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

In the given diagram the parallel lines are cut by a transversal.

The measure of angle 4 is, m∠4 = 81°.

It is known that each pair of interior angles on the same side of a transversal that cuts two parallel lines are supplementary, or they add up to 180 degrees.

So, m∠4 + m∠5 = 180°

81° + m∠5 = 180°

m∠5 = 180° - 81°

m∠5 = 99°

Now, as it can be seen in the image ∠5 and ∠7 are vertically opposite angles.

So, they will be congruent or equal to each other.

So, it is obtained that -

m∠5 = m∠7

m∠7 = 99°

Therefore, the measures of angles are m∠5 = 99° and m∠7 = 99°.

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The length of the adult crocodile more than the young crocodile is 5.0 feet.

A young crocodile is 0.4 feet long. An adult crocodile is 13.5 times as long. The length the adult crocodile is more than the young crocodile can be calculated as follows:

Hence,

length of the adult crocodile = 13.5(0.4)

length of the adult crocodile = 13.5 × 0.4

length of the adult crocodile = 5.4 feet

Therefore,

the length of the adult crocodile more than the young crocodile = 5.4 - 0.4 = 5.0 feet

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The solution to the formula using f as the subject is given by f = 9/(a + 7)

a = 9/f - 7

Add 7 to both sides

a + 7 = 9/f

cross product

f(a + 7) = 9

divide both sides by a + 7

f = 9/(a + 7)

Hence, the formula a = 9/f - 7 can be written as f = 9/(a + 7) using f as the subject.

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Answer:

[tex]10x+20[/tex]

Step-by-step explanation:

[tex]10(x-2)[/tex] Using Distributive property

[tex]10x+20[/tex]

The lower bound for the given numbers is 41.66. the maximum: 42.19

The top and lower boundaries of a rounded number are as follows: Determine the claimed level of accuracy's place value. Multiply this place value by two. Add this amount to the given value to determine the upper bound, and subtract this amount to determine the lower bound. The maximum and smallest values that a number may have before it was rounded are known as upper and lower limits. They are also known as accuracy limits.

The lower: a=49.35. b=7.69

so the lower bounds is:

a-b=49,35-7.69 =41.66 = a=49.49.34.

b=755 the upper = a= So the upper bounds is = a-b= 42.79.

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We see here that the set of survey results is most likely to show biased results for people who buy food at the mall is: D. Lewie's because he surveyed people who may or may not have bought food.

Surveying is the process of collecting data or information from a sample of individuals or a population. Surveys can be conducted in various ways, such as through in-person interviews, telephone calls, online forms, or mail-in questionnaires.

The goal of surveying is to gather information about the characteristics, attitudes, opinions, or behaviors of the people being surveyed in order to make inferences about the larger population from which the sample was drawn. Surveying is widely used in research, marketing, and various other fields for data collection.

Surveying people at the mall's main entrance does not guarantee that they have bought food, and therefore the results may not accurately represent the average number of people who buy food at the mall.

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Answer:

A. Kelvin’s because he surveyed people leaving an area where food is sold

Step-by-step explanation:

The amount of cough syrup the pharmacist have left is 1600 millilitres.

The pharmacist has a 2.8 L bottle of cough syrup. She fills a bottle that is 1200 ml . The amount of cough syrup the Pharmacist has left can be calculated as follows:

Let's convert litres to millilitres

Therefore,

1 litres = 1000 millilitres

2.8 litres = ?

cross multiply

Therefore,

amount of syrup in millilitres = 2.8 × 1000

amount of syrup in millilitres = 2800 millilitres.

Therefore,

amount of cough syrup the pharmacist has left = 2800 - 1200 = 1600 millilitres.

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Answer:

In 2014, the population of China was 1,356 million people

Answer:

  County B

Step-by-step explanation:

You want to know the greater population, given a county's area and population density:

The population is the product of area and density:

  [tex]P_A=(108\text{ mi}^2)\dfrac{36\text{ people}}{\text{km}^2}=(108\cdot36\text{ people})\left(\dfrac{\text{mi}}{\text{km}}\right)^2\\\\P_B=(36\text{ km}^2)\dfrac{108\text{ people}}{\text{mi}^2}=(108\cdot36\text{ people})\left(\dfrac{\text{km}}{\text{mi}}\right)^2[/tex]

To determine which product is greater, we simply need to know the relationship between kilometers and miles:

  1 mi ≈ 1.609 km

The factor (km/mi) is greater, so the population of County B is greater.

__

Additional comment

There are 1.609 km/mi, and about 0.6214 mi/km. The population of County B is about 6.7 times the population of County A.

County A has about 1501 people; County B has 10,070 people.

If there are 1410 students and teachers together, then there are 60 teachers present.

Relationships that always have the same ratio are said to be proportional. For instance, the number of trees in an orchard and the number of apples in a harvest of apples are determined by the average number of apples per tree. A linear relationship between two numbers or variables is referred to as proportional in mathematics. When the first quantity doubles, the other number does as well. When one of the variables is reduced to 1/100th of its previous value, the other also decreases. If two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities remains constant throughout all values. The diameter and circumference of a circle provide an example.

given

total=1410

students=45x

teachers=2x

2x + 45x = 1410

47x = 1410

x = 3

students=45x

=45×30

=1350

teachers=2x

=2×30

=60

If there are 1410 students and teachers together, then there are 60 teachers present.

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The population for which it is appropriate for Emma to generalize the results from her sample is the population of one-bedroom apartment rental prices in the large city where Emma is moving.

This population includes all the prices of one-bedroom apartments that are available for rent in that city, not just the ones that are listed on the website where Emma obtained her sample. Emma is most likely to be utilizing the information from her sample to make inferences about the population as a whole, such as the typical monthly rental prices, the range of prices, and the distribution of prices.

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A mathematical expression is a statement made up of variables, constants, and arithmetic operators. For the equation -3 x^2-9/x+3 , the rational expression is x+3 , Option A

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression’s structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

The complete question is

“Which of the following is equal to the rational expression when x does not equal 1 or 3   ( )

The options are

a. X+3

b. X-3

c. (x -3)/(x+3)”

The expression given in the question is

( )

And have been asked among the option which represents the rational expression when x does not equal 3 or 1

Therefore for the following equation -3 x^2-9/x+3 , the rational expression is x+3 .

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Yes, Cassie has enough fabric to make 10 bows. 17/20 yard of fabric is equal to 1.7 yards, and 1/12 yard is equal to 0.083 yards. When 1.7 yards is multiplied by 0.083 yards, the result is 0.14 yards, which is more than enough to make 10 bows.

1. Convert 17/20 yard of fabric to yards:

17/20 yard = 17/20 x 1 yard = 1.7 yards

2. Convert 1/12 yard to yards:

1/12 yard = 1/12 x 1 yard = 0.083 yards

3. Calculate how much fabric is needed to make 10 bows:

1.7 yards x 0.083 yards = 0.14 yards

4. Determine if Cassie has enough fabric:

Yes, Cassie has 0.14 yards which is enough to make 10 bows.

Yes, Cassie has enough fabric to make 10 bows. 17/20 yard of fabric is equal to 1.7 yards, and 1/12 yard is equal to 0.083 yards. When 1.7 yards is multiplied by 0.083 yards, the result is 0.14 yards, which is more than enough to make 10 bows.

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The value of [tex]\alpha ^0 = (5\alpha ^0) =1[/tex], as anything raised to the power of 0 is equal to 1. Hence, the answer to the equation [tex]5\alpha ^0 + (5\alpha ^0)[/tex] is 6.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The value of [tex]\alpha ^0 = (5\alpha ^0) =1[/tex], as anything raised to the power of 0 is equal to 1.

Substituting the value of [tex]\alpha ^0 =(5\alpha ^0) = 1[/tex] in the given equation we have:

5(1) + 1 = 6

Hence, the answer to the equation [tex]5\alpha ^0 + (5\alpha ^0)[/tex] is 6.

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The modal net incomes (in $millions) of a sample of steel fabricators will be b. $86

The goal of measures of central tendency, also known as measures of location, is to identify the data set's most "representative value." The mode, mean, and median are the three values listed here.

A data set's mode is its most frequent value. The mode of a distribution of probabilities has the highest probability. As a result, the mode can be quickly determined for a small number of observations. Any number of modes, or none at all, may exist for a given set of values. So, the value that will be sampled with the highest probability is the mode.

Note that the full question is:

The net incomes (in $ millions) of a sample of steel fabricators are: $86, $67, $86, $67, $86 and $85. What is the modal net income?

a. $85

b. $86

c. $85.5

d. $67

e. None of the above.

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The value of f which satisfies the given equation 3f + 5 = 32 is 9. The correct option is C.

Given question is incorrect

Correct question :

Which value of f makes 3f+5=32 a true statement?

a. f=6

b. f=8

c. f=9

d. f=12

Given data :

It is required to find the value of f for which the equation 3f + 5 = 32 is satisfied.

Use simple rules of algebra to get the value of f which satisfies the given equation,

3f + 5 = 32

3f = 32 - 5

3f = 28

f = 28 / 3 = 9

Therefore, the value of f which satisfies the given equation 3f + 5 = 32 is 9 is correct option.

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A qualifying child or dependent is typically required to be eligible for head of household filing status.

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The length of the hypotenuse is 17 cm.

Pythagoras' Theorem is the way in which you can find the missing length of a right-angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), the Opposite (which doesn't touch the hypotenuse), and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c²

However, it can also be written in the form of c²=a²+b²

In order to find the hypotenuse, you will have the length of two sides, for example, these could be 3 and 4.

As 'C' is always the hypotenuse, you have to work out the two other lengths, and you do this by squaring the numbers.

3²=9 and 4²=16.

As you're looking for C, you've got to add these together

9+16=25

As a²+b²=c², this means that the answer for C is the square root of 25.

√25= 5

We are given that a = 8 cm and b = 15 cm.

Using Pythagoras' theorem,

c² = a² + b²

Substitute the values,

⇒ c² = 8² + 15²

⇒ c² = 64 + 225

⇒ c² =289

∴ c = 17

Thus, the length of the hypotenuse is 17 cm.

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The length of the diagonal is 17.

Given that, In quadrilateral ABCD, sides AB and BC both have a length of 10, and sides CD and DA both have a length of 17.

The measure of ∠ADC = 60°

AD = CD ( according to the question)

So, Δ ABC is an isosceles triangle with ∠DAC = ∠DCA.

According to the image,

Angles in a triangle add up to 180°, and since ∠ADC = 60°, the other two angles are also 60°.

And Δ ADC is an equilateral triangle.

Therefore,  AC = DA = 17

S0, the diagonal of quadrilateral ABCD is 17.

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The equation of line that passed through the points (3, 6) and (8, 4) is 5y = -2x + 40.

In the given question, we have to find the equation of a line that passed through the points (3, 6) and (8, 4).

The point-slope approach is typically used when two points that sit on a specific line are specified.

A line's equation is written as y - y(1) = m(x - x(1)), where y(1) is the Y-axis coordinate, m is the slope, and x(1) is the X-axis coordinate.

Firstly we find the value of m using the formula

m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

From the given points x(1) = 3, y(1) = 6, x(2) = 8, y(2) = 4.

Now putting the value

m = [tex]\frac{4-6}{8-3}[/tex]

Now solving

m = [tex]-\frac{2}{5}[/tex]

Now we finding the equation of line. We can use any one point in the given points.

Now taking the points (3, 6), x(1) = 3 and y(1) = 6

Now putting the value in equation y - y(1) = m(x - x(1)).

y - 6 = [tex]-\frac{2}{5}[/tex](x - 3)

Multiply by 5 on both side, we get

5(y - 6) = -2(x - 5)

Using the distribution property

5y - 30 = -2x + 10

Add 30 on both side, we get

5y = -2x + 40

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The complete question is:

What is the equation of a line that passed through the points (3, 6) and (8,  4)?

Answer:

when doing my math the answer I got was 1/2 hope it helps

No, the quadratic form is not the same as the factored form of a quadratic equation.

A quadratic function can usually be represented by many equivalent expressions. For example, a quadratic function might be defined by f(x) = x² + 3x + 2. The quadratic expression f(x) = x² + 3x + 2 is called the standard form, the sum of a multiple x² of and a linear expression (3x + 2 in this case).

In general, the standard form is  ax² bx + c

We refer to 'a' as the coefficient of the squared term 'x²', 'b' as the coefficient of the linear term 'x', and 'c' as the constant term.

The function 'f' can also be defined by the equivalent expression (x +2)(x + 1). When the quadratic expression is a multiplication of two factors where each one is a linear expression, this is called the factored form.

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a. Value of f(-2) is -15. b. Value of g(2) is 4. c. Value of x when f(x)=0 is 3.

The above values are obtained using substitution.

When in place of a variable, we substitute a value in the function, it is known as substitution.

a. We are given f(x)= 3x-9

So, for finding f(-2), we need to put x=-2

Thus, we get,

f(-2)= 3(-2)-9

f(-2)= -6-9

f(-2)= -15

b. We are given g(x)= x^2

So, for finding g(2), we need to put x=2

Thus, we get,

g(2)= 2^2

g(2)=4

c. Now, we are given that f(x)=0.

In order to find the value of x, we need to put f(x)=0

Thus, we get,

3x-9=0

3x=9

x=3

Hence the values of f(-2), g(2) and x when f(x)=0 are -15, 4 and 3 respectively.

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Answer:

The car can travel 30 miles per 1 gallon.