Write the number that represents the give secasrio. (DOK 1)
6. One-fourth of the students brought their hunch to school.
7. After the penalty, there was a loss of 15 yards on the play.
8. He gained 6 pounds of muscle.
9. He made a 535 deposit into a bank account.
10. The temperature was 9 degrees below zero.
11. Two-thirds of the crewed left the stadium.
12. She received $20 on her birthday.
13. The student lost 10 points on the final exam.
14. He made a 570 withdrawal from a bank account.
15. One-half of the gallon of milk is gone.

Write the number that represents the given scenario. (DOK 1)
11. A submarine is 350 feet below sea level.
12. The family traveled 500 miles south on a road trip.
13. A rabbit hops 10 feet forward.
14. The temperature dropped 13 degrees.
15. A hot air balloon traveled 20 miles north.

Answer:

420 = 4.2 x 100 = 4.2 × 102

Step-by-step explanation:

The statement which is correct about each inequality as required to be assigned are as follows;

It follows from the task content that the statement which is correct about each of the inequalities is to be matched accordingly.

It is noteworthy to know that the underlying rule while solving inequalities is such that;

If the coefficient of a variable upon isolation on one side of the inequality is negative, it follows that the inequality sign must be flipped while multiplying or dividing both sides of the inequality by a negative number.

On the other hand, if the coefficient of the variable is positive, the inequality sign is not to be flipped.

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The reflection across the line x = 1 will make the coordinates of the points KLM as K'(-3, - 4), L'(1, - 2), M'(1, - 5).

Given is a triangle on the coordinate grid.

The line LM lie along the line {x} = 1. So, the reflection over the line {x} = 1 will ensure that the coordinate of L and M will remain same. The coordinates of point K will become (-3, - 4) from (3, - 4).

Therefore, the reflection across the line x = 1 will make the coordinates of the points KLM as K'(-3, - 4), L'(1, - 2), M'(1, - 5).

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The efficiency of the motor rated at 2.0 hp and delivering only 1.6 hp to a transmission system is 75%

Efficiency of the machine is the ratio of the work input to the machine to the work output of the machine\

This represented mathematically as

= work input / work output * 100 / 1

Form the problem we have that

work input = motor rated at 1.5 hp

work output = motor rated at 2.0 hp

Efficiency = 1.5 / 2.0 * 100 / 1

Efficiency = 0.75 * 100 / 1

Efficiency = 75%

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The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

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

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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The value of x and y are 5 and 3 respectively.

The value of x and y when (x , 2y) = (5, 6) can be found as follows:

Therefore, the x coordinates of the graph is given as 5 while the double of y coordinates is equals to 6. Then, we have to equate the values as follows:

x = 5

2y = 6

The value of x is known by mere equating.

Hence, let's find the value of y.

2y = 6

divide both sides of the equation by 2

2y / 2 = 6 / 2

y = 3

Therefore, the value of y = 3 and x = 5.

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The domain of the rational function given; f (x) = x / ( x² - 64 ) as required to be determined in the task content is; All real values of x such that x ≠ −8 and x ≠ 8.

Recall that the domain of a rational function includes all real number values except those which render the rational function undefined; i.e the denominator is equal to 0.

On this note, the only exceptions for the domain of the rational function can be determined as follows;

x² - 64 = 0

x² = 64

x = ± 8

On this note, the values which are exceptions to the possible real number values of x are; -8 and 8.

Ultimately, the domain of the given rational function as required is; All real values of x such that x ≠ −8 and x ≠ 8.

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The number of pounds of food that the pig ate every day, given that it was the same amount of food daily, was 3. 94 pounds per day

To find the food that the pigs ate each day, you first need to find the total number of pounds of food that Angela bought and this amount in total is :

= 250 + 145 + 200

= 595 pounds of food

The number of days from the start of November through March is :

= 30 days November + 31 days December + 31 days January + 28 Days February + 31 Days March

= 151 days in total

The amount of food that Angela's pigs ate per day is therefore:

= Total food purchased / Number of days

= 595 / 151

= 3. 94 pounds per day

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The amount of production in the economy to meet the final consumer demand which is 80 units of agriculture, 60 units of manufacturing and 50 units of energy

The given parameters that will help us to calculate the amount are

(1) Pe =0.2Pa + 0.2 Pm + 0.1pe

Pm = 0.2P + 0.4 Pm + 0.1 Pe

Pa = 0.1 Pa + 0.2Pm -0.3 Pa

(2) The free variable Pa = 100

We create a table of outputs using the given Units economy distribution

Agriculture        Manufacture       Energy           Purchased by

0 .2                      0.2                       0.1                 Agriculture

0.2                    0.4                       0.1                    manufacturing

0.1                    0.2                       -0.3                    Energy

Let Pa, Pm, Pe represent the prices for each sector

We then create an income equation using the expenses of the table above we have

(1) Pa =0.2Pa + 0.2 Pm + 0.1pe =80

Pm = 0.2P + 0.4 Pm + 0.1 Pe = 60

Pe = 0.1 Pa + 0.2Pm -0.3 Pa=50

Making pa, pm and pe the subjects of the relation and summing them to have the amount

pa = 0.5x = 80

Pa=80/0.5= 160

Pm = 0.7pm = 60

Making pm the subject of the formula

pm= 60/0.7 = 86

Pe = 0

Therefore the amount is 160+86+0 = 246

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Using the pythagoras theorem to set the appropriate hypotenuse, perpendicular and base to make a right angled triangle, the correct option the would for a right angled triangle would be option c i.e 2, 2, [tex]\sqrt{8}[/tex].

A right angled triangle is a triangle in which one of the angles is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse and the other two sides are called the legs or catheti. The two legs are perpendicular to each other and the hypotenuse is the longest side of the triangle. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right-angled triangles.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs or catheti). This can be written as: c^2 = a^2 + b^2 where c is the length of the hypotenuse, and a and b are the lengths of the legs.

So applying the pythagorean theorem on  provided options to choose the best option for making a right angled triangle, we find that the option c suites best to form a right angled triangle as show below,

[tex](\sqrt{8}) ^{2} = 2^{2}+2^{2}[/tex] , which satisfies the equation.

i.e 8 = 8

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The numeric value of the exponential expression in this problem is given by the following option:

A. 2^12.

The exponential expression for this problem is defined as follows:

8^x/2^y.

8 is the third power of 2, hence:

8 = 2^3.

When a term is elevated to two of it's powers, the powers are multiplied, hence:

(2^3)^x = 2^(3x).

Meaning that the exponential expression is then written as follows:

8^x/2^y = 2^(3x)/2^y.

When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:

2^(3x)/2^y = 2^(3x - y).

As stated in the problem, the numeric value of the expression 3x - y is given as follows:

3x - y = 12.

Hence the entire expression is simplified as follows:

2^(3x - y) = 2^12.

Meaning that the correct option is given by option A.

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Answer:A. 2^12.

Step-by-step explanation:i did it and got it right

16 potatoes

according to the question:

we can formulate it as, (12*4)/3

= 48/3= 16

use the BODMAS rule to solve

that is Brackets Of Division Multiplication Addition Subtraction

so first (12*4) will be calculated.

multiply means adding equal groups

the first value that is used to multiply is called the multiplicand (12)

the second value that is been multiplied is called the multiplier. (4)

the result that we get when we multiply the multiplicand and the multiplier is called the product. (48)

then, divide the product with the denominator

48/3

The division is the process of splitting a specific amount into equal parts.

therefore, 16 potatoes are there.

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Answer:

4.5 meters

Step-by-step explanation:

If the pins were placed 30 cm apart, and there were a total of 15 pins, then the length of the string is 30 cm * 15 pins = <<30*15=450>>450 cm.

To convert this length to meters, we divide the number of centimeters by 100: 450 cm / 100 = 4.5 meters.

Therefore, the length of the string is 4.5 meters.

The complete sentence will be;

⇒ The original sphere volume × 125 = The new sphere volume

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A sphere is dilated by a scale factor of to create a new sphere.

Now,

We know that;

The volume of sphere = 4/3 πr³

Here, A sphere is dilated by a scale factor of to create a new sphere.

So, The radius of old sphere = r

Then, The radius of new sphere = 5r

Hence, The volume of old sphere = 4/3 πr³

And,  The volume of new sphere = 4/3 π × (5r)³

                                                    = 125 (4/3πr³)

Thus, We get;

⇒ The new sphere volume = The original sphere volume × 125

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The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:

B. 2.3p – 10.1 = 6.49p – 4

C. 230p – 1010 = 650p – 400 – p

From the information provided, we have the following equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Next, we would simplify the given equation by collecting like terms as follows;

2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4

2.3p - 10.1 = 6.49p - 4

In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.

By multiplying both sides of the given equation by 100, we have;

100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)

230p - 1010 = 650p - 400 - p

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Answer:

Step-by-step explanation:

24 people

Okay so 1/3 is in front of him, and 5/8 are behind him. We can add these up and see how much is missing, which can only be 1 person, Jack.

1/3+5/8 = 23/24

We got 23/24, and there's 1 person missing, who's Jack!

24 people are in the queue.

Step-by-step explanation:

let change the playing yes /no question from direct speech to direct speech

My sister asked me, "Have you seen my dog?" ____________________________________________ Vijay asked "Have you gone to market?" ____________________________________________ My mother asked, "Why are you crying?" ____________________________________________ The rickshaw puller asked me, "Do you speak English?" ____________________________________________

According to the given information in the question the value of a/b is 5.

Value is a concept that is difficult to define, but it is fundamental to our lives. It is the basis for our decisions, the way we measure our success, and the way we determine what is important to us. Value is something that can be both tangible and intangible, and it is influenced by the context in which it is perceived. Value is shaped by our beliefs, experiences, and culture, and it is constantly changing. We use value to make decisions, to motivate ourselves, and to create a sense of purpose. Value is ultimately what drives us forward and helps us make sense of the world around us.

This is because when the system has an infinite number of solutions, it means that the two equations are equivalent and that any value of x and y can satisfy the equation. Since the equation 12x - 4y = 80 is the same as ax - by = 5, both equations are equal when a/b = 5.

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Answer:

If there are 24 coins in total and some of them are nickels, then there must also be some dimes. Let's call the number of dimes "x" and the number of nickels "y". We know that y = 1/3 * x. We can set up an equation to represent this relationship: y + x = 24. We can also substitute 1/3 * x for y to get the following equation: 1/3 * x + x = 24. We can combine like terms to get: (4/3) * x = 24. We can divide both sides by 4/3 to solve for x: x = 18.

Therefore, there are 18 dimes in the bag.

Step-by-step explanation:

Answer: the width is 24/35 square mile

Answer:

b = 4

Step-by-step explanation:

Solve for b?

1/2b + 9 = 11     Subtract 9 from both sides

1/2b = 11 -9

1/2 b = 2    Multiply both sides by 2

b = 4

Answer:

x ≤ 5

Step-by-step explanation:

That inequality best matches the graph.

Answer:

Median= (5+7)/2 = 6 Mean= 6 Range= 12 Mode=7

The given expression is equivalent to z(i) = 21 + 12i.

       [tex]${\displaystyle z=re^{i\varphi }=r(\cos \varphi +i\sin \varphi )}[/tex]

       where {r} is the absolute value of z, and {φ} is the argument of z.

Given is the complex expression -

z(i) =  (3 - 4i)(1 + 5i) - (2 - i)

The given complex expression is -

z(i) =  (3 - 4i)(1 + 5i) - (2 - i)

z(i) = 3(1 + 5i) - 4i(1 + 5i) - (2 - i)

z(i) = 3 + 15i - 4i - 20i² - 2 + i

z(i) = 3 - 2 + 15i - 4i + i - 20i²

z(i) = 1 + 12i - 20i²

z(i) = 1 + 12i + 20

z(i) = 21 + 12i

Therefore, the given expression is equivalent to z(i) = 21 + 12i.

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{Complete question -

Simplify the expression (3-4i)(1+5i)-(2-i). Please show your work}

The angle measure of student's favorite subject, English, is 108°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

Max conducted a survey of 60 students in which he asked about their favorite school subject. 24 students said math, 12 students said science, 18 students said English and 6 students said social studies.

The total angle of circle is 360°.

To find the angle measure of student's favorite subject, English:

The angle subtended by the category = (Amount in the Category ⁄ Total) × 360°

= 18/60 x 360

= 0.3 x 360

= 108°

The circle graph is given in the attached image.

Therefore, 108° is the angle measure of student's favorite subject, English.

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She will need to pay 1068.75 dollar.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

Given that Gabriella borrowed $3,600 to finance a large-screen television at a rate of 6.25% for 4.75 years.

Amount = $3,600

Rate = 6.25%

Time =  4.75  years

Therefore, Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = 3,600× 6.25% × 4.75

Simple Interest = 3,600× 6.25/100 × 4.75

Simple Interest = 1068.75

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Answer:

$1,068.75

Step-by-step explanation:

$3,600 x 0.0625 x 4.75 = $1,068.75

On solving the provided question, we can say that from the graphs, line segment should you remove to make the relation a function of x  the line segment with endpoints (-3,2) and (-4,-2)

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

from the graphs,

line segment should you remove to make the relation a function of x

the line segment with endpoints (-3,2) and (-4,-2)

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