Sheng drives at a constant speed for 0.2
hours to get to the train station. He then boards a train that takes him 35
miles to downtown. His whole trip is 42
miles long.

How can Sheng determine his driving speed?

Substitution is a method for solving systems of equations that involves solving for one variable in one equation and then substituting that value into the other equation.

Here's how we can use substitution to solve the system of equations:

5x+y=9

10x−7y=−18

Solve one equation for one variable, for example:

y = 9 - 5x

Substitute this expression of y into the other equation:

10x - 7(9 - 5x) = -18

Solve the equation resulting from the substitution

10x - 63 + 35x = -18

45x = 45

x = 1

Substitute this value of x back into one of the original equations to find the value of y.

5(1) + y = 9

y = 4

So the solution is (x,y) = (1,4)

You can check this solution by substituting it back into both original equations.

As 5/10 are Girls in Class And 1/5 of the girls wear glasses So on overall girls wear glasses is 1/10 in the whole class.

The fraction 5/10 is equal to 1/2 of the total and 1/5 of the girls wear glasses so if you multiply 1/2 and 1/5 you get 1/10, To get a total fraction of girls who wear glasses overall will be by multiplying both the fraction. So,

1/5*1/2 = 1/10

Here the answer is produced by multiplying the numerator with the numerator and similarly denominator with the denominator to get the answer of total friction of girls wearing glasses in the whole class.

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They will be equal at the same altitude at x= 48 seconds

Assume the question is when the planes will be at the same altitude.

A is 2184+30.25x, where x is the number of seconds.

The aircraft B is 75.75x

They will be equal at the same altitude if

75.75x=2184+30.25x

Collecting like terms and making x the subject of the relation

75.75x -30.25x = 2184

45.5x = 2184

Making x the subject

x = 2184/45.5

x=48 seconds

The two airplanes  will be at the same altitude at 48 seconds

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Answer:

$16.8

Step-by-step explanation:

u got to trust me

Answer: $16.8

im sure its this it has to be

The probability that two randomly generated strings of length 9 in the DNA alphabet is 729.

We have to find the probability that two randomly generated strings of length 9 in the DNA alphabet (a, c, g, t) are identical.

Probabilities are based on occurrences, and events can result from one or more observations or experiment results.

The total number of alphabet in word DNA is 3.

So, the probability that two randomly generated strings of length 9 in the DNA alphabet = 9 × 9 × 9

The probability that two randomly generated strings of length 9 in the DNA alphabet = 729

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The value of x in the figure shown above is equal to 4.

In Mathematics, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

By critically observing the image of this geometric figure, we can reasonably infer and logically deduce that it is a type of quadrilateral with both pairs of opposite sides being parallel to each other and the opposite angles (vertical angles) are equal and congruent:

Side length A = Side length B

4 + 6 = 6 + x

10 = 6 + x

By collecting like terms, we have the following:

x = 10 - 6

x = 4 units.

In conclusion, the value of x is equal to 4 units.

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The number of ways to answer the questions is given as follows:

15,625.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, there are six questions, each with five possible options, hence the number of ways to answer the questions is calculated as follows:

5^6 = 15,625 ways.

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The volume of the prism in this problem is given as follows:

C. 9/16 cubic feet.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

For this problem, two of the dimensions are formed by three cubes, hence their measures are:

3 x 1/4 = 3/4 foot.

The remaining dimensions is composed by four cubes, hence the measures are:

4 x 1/4 = 1 foot.

Hence the volume is given as follows:

V = 1 x 3/4 x 3/4

V = 9/16 cubic feet.

The problem is given by the image presented at the end of the answer.

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The angular momentum of the the ball is 4.16kgrad/sec

Angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity. This means that the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. It is measure d in kgrad/sec

angular momentum = mass × angular velocity

mass = 0.18kg

angular velocity = 5.2 rad/s

therefore angular momentum = 0.18× 5.2

= 4.16 kg rad/s

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Answer:

x = -1

Step-by-step explanation:
y-0.8x=0.5

5y-2.5-4x

Get y by itself.
y = 1.3

Put 1.3 into the second equation

5(1.3) - 2.5 - 4x
6.5-2.5 - 4x
4 - 4x = 0
Get x by itself
-4x = 4
x = -1

I hope this was able to help you :D

The number of counters Rick has is equal to 12 counters.

The number of counters Tony has is equal to 1:1.5.

The value of p is 1.5.

In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let R represent the number of counters Rick has.

Let S represent the number of counters Selma has.

Let O represent the number of counters Tony has.

Let T represent total number of counters.

Translating the word problem into an algebraic equation, we have;

S = 2R     .....equation 1.

O = 2R - 6    ......equation 2.

T = R + S + O   ......equation 3.

Substituting equation 1 and equation 2 into equation 3, we have:

T = R + S + O

54 = R + 2R + 2R - 6

54 = 5R - 6

5R = 54 + 6

5R = 60

R = 60/5

R = 12 counters.

For Tony, the number of counters is given by:

O = 2R - 6

O = 2(12) - 6

O = 24 - 6

O = 18 counters.

In ratio form, we have:

O = 1:P

O = 1:(18/12)

O = 1:1.5

The number of counters Rick has is equal to 12 counters.

The number of counters Tony has is equal to 1:1.5.

The value of p is 1.5.

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Total number sixth graders were surveyed is 600.

"percent" is Latin for "out of 100," so 5 % is literally 5 out of 100

Now--if it were 5 kids with birds, you would know that there were 100 total kids. But it's 30 kids, which is way more than 5; so your total number of kids is going to be way more than 100.

So what you need to do here is figure that "30 sixth graders own birds

i.e. 30 is 5% of some number."

How many times bigger than 5 is 30? (6 times, because 5 x 6 = 30, or you can think of it as 30 divided by 6 = 5)

So if you had to do 5 TIMES 6 to get to 30, you have to do 100 TIMES 6 to get the total number sixth graders were surveyed.

What's 100 x 6?

= 600.

So your total number sixth graders were surveyed is 600.

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The statement using absolute value notation will be x - 78 ≤ 22.

The student will pass the test which scores 22 points for the number 78

Absolute values are any digit's value without taking the sign into an account. Therefore, all negative numbers will be regarded as positive for absolute value. The absolute value of -5, for instance, will be 5, whereas that of -7, will be 7.

In essence, the absolute value calculates the distance from zero. Putting an absolute value on something does not imply that they are the same number but that they are the same distance from 0.

Le the score of student be = x

Forming the absolute value notation -

This can be expressed as,

x - 78 ≤ 22.

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Answer:

So, the question is asking how many pounds are there in 48 shipments if ever 12 shipments are 3 pounds, so what you want to do is so how many times 12 will go into 48 and then multiply that by 3!

48/12 = 4

4 * 3 = 12

The total 48 shipments weigh 12 pounds!

Step-by-step explanation:

Hope it helps! =D

Answer:

The weight of one pack of sardines is 3 pounds / 12 packs = 0.25 pounds/pack

So the weight of 48 packs of sardines is 0.25 pounds/pack * 48 packs = 12 pounds.

The number of hours for which the cost is the same would be 5 hours.

The cost of renting a snowboard for 5 number of hours would be same as that point i.e. $5

By costs, what do you mean?

Costs are really the monetary value of purchases made for use by a company or other accounting entity of supplies, service, labor, products, equipment, and other items.

The cost of renting a snowboard from the first company is $5 per hour + $50 deposit = $5x + $50.

The cost of renting a snowboard from the second company is $10 per hour + $25 deposit = $10x + $25. To find the number of hours for which the cost is the same, we set the two costs equal to each other and solve for x:

$5x + $50 = $10x + $25

$5x - $10x = $25 - $50

$5x = $25 - $50

$5x = -$25

x = -5

As we will not take cost in negative so it would be 5

So, we can say that the cost is same at any point of time.

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The value of x is 14.28 units, this is determined using the trigonometric functions.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the sides and angles of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Consider the smaller triangle:

Sin (30) = Opposite side ÷ Hypotenuse

0.5 = Opposite side ÷ 10

Opposite side = 5

Consider the bigger triangle:

Sin (22) = Opposite side ÷ Hypotenuse

0.37 = 5 ÷ x

x = 5 / 0.35

x = 14.28

Hence, the value of x is 14.28 units, this is determined using the trigonometric identities.

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The surface area of the rectangular prism is  182m²

It is important to note that the surface area of a rectangular prism is expressed as;

Surface area = 2(wl + hw + hl)

Where;

Now, from the diagram show, we have the values as;

Length = 3

Height = 7

Width = 7

Substitute the values into the formula

Surface area = 2(7×3 + 7×3 + 7 ×7)

multiply the values

Surface area = 2(21 + 21 + 49)

expand the bracket

Surface = 182m²

Thus, the value is 182m²

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The change in elevation of the car is 0.66mile.

Now, According to the question:

Trigonometric functions are immensely useful when real-life examples form a right triangle. In such cases, sine, cosine, or tangent functions are used based on the given information to determine the unknown value. For example, suppose we are looking at the top of a building and we know the height of the building and our distance from the base of the building, using the tangent function, we can easily calculate the angle made by the line of sight above the ground.

d = 4 miles is the distance covered by the car on the inclined road.

θ = 9.5° is the angle made by the road above the horizontal.

Let:

h be the change in elevation of the car.

Using the sine function, we write:

[tex]sin\theta= \frac{opposite side}{hypontenuse}[/tex]

[tex]sin\theta =\frac{h}{d}[/tex]

h = dsinθ

h = (4 mile)(Sin(9.5°))

h ≈ 0.66 mile

Therefore, the change in elevation of the car is 0.66mile.

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Answer:

The answer in intercept form will be

[tex] - 1 \div 3 = 5 \div 3x + c \\ [/tex]

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer: 1.2 miles

You can find the answer by using the pythagorean theorem.

a^2 + b^2 = c^2.

(5000)^2 + (4000)^2 = c^2

25 million +16 million = c^2

41 million = c^2

Take the square root of both sides in order to get the value of C.

C = about 6,403 feet.

1 mile = 5280 feet

6403/5280 = 1.2

Buddy would walk about 1.2 miles

Distance from point (3,9,-7) to xy-plane is 7, yz-plane is 3, xz-plane is 9, x-axis, y-axis and z-axis is 0.

What is axis ?

An axis is a line about which a body rotates or a system oscillates. In mathematics and physics, an axis is often represented as a straight line that serves as a reference point for the measurement of coordinates.

The correct answers are :

(a) The distance from the point (3, 9, -7) to the xy-plane is the distance from the point to the z-axis, which is 7, since the xy-plane is at z = 0

(b) The distance from the point (3, 9, -7) to the yz-plane is the distance from the point to the x-axis, which is 3, since the yz-plane is at x = 0

(c) The distance from the point (3, 9, -7) to the xz-plane is the distance from the point to the y-axis, which is 9, since the xz-plane is at y = 0

(d) The distance from the point (3, 9, -7) to the x-axis is the distance from the point to the x-axis, which is 0, since the point is already on the x-axis

(e) The distance from the point (3, 9, -7) to the y-axis is the distance from the point to the y-axis, which is 0, since the point is already on the y-axis

(f) The distance from the point (3, 9, -7) to the z-axis is the distance from the point to the z-axis, which is 0, since the point is already on the z-axis

Distance from point (3,9,-7) to xy-plane is 7, yz-plane is 3, xz-plane is 9, x-axis, y-axis and z-axis is 0.

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Answer:

see below

Step-by-step explanation:

7. (4-4). K =0

d+12-8/4+5 = d+12-2+5 =d+15

The length of the arc of the given circle with radius 10 cm and an angle of 2.5 radians subtended by an arc of a circle is equal to 25 cm.

Let 'y' represents the length of the arc of the given circle.

Radius 'r' of the given circle is equal to 10 cm

Angle 'α'  subtended by an arc of a circle is equal to 2.5 radians.

length of the arc = Angle subtended by an arc × Radius of the circle

⇒ y = rα

⇒ y = 10 × 2.5

⇒ y = 25 cm

Therefore, the length of the arc of a circle for the given radius 10cm and subtended angle 2.5 radians is equal to 25 cm.

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Answer: Because 2 places to the right of the the decimal.

Step-by-step explanation:

The value of distance after calculating are  AB = 4 ft and BC = 16 ft.

What is ratio?

A ratio is a comparison between two numbers or quantities. It is typically expressed as a fraction, with the first number being divided by the second number. Ratios are often used to compare values or to express a portion of a whole.

It is given in the question, that Ladd is rearranging his living room furniture. He wants his couch to sit along the 20-ft wall.

To find the length of AB and BC we need to relate them using the equations.

AB + BC = 20 ft (from the diagram) ----------- (Equation 1)

∵ AB : BC = 1 : 4

⇒ 4AB = BC

Substituting,  BC = 4AB into equation 1.

AB + 4AB = 20 ft

5AB = 20 ft

AB = 4 ft

Plugging AB = 4 ft into equation 1.

4 + BC = 20

BC = 20 ft - 4 ft

BC = 16 ft

Thus, the value of sides AB = 4 ft and BC = 16 ft , and here AB and BC are in ratio 1:4.

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Answer: This problem can be represented by the equation y = mx + b, where y is the total charges, x is the number of days, m is the charge per day, and b is the flat fee.

To find the values of m and b, we can use the given data points to solve for the equation.

For x = 2, y = 8, so 8 = m * 2 + b

For x = 4, y = 13, so 13 = m * 4 + b

For x = 6, y = 18, so 18 = m * 6 + b

We can then use a system of equations to solve for m and b:

m * 2 + b = 8

m * 4 + b = 13

m * 6 + b = 18

Using substitution or elimination methods:

m = 2

b = 2

Therefore, the equation is: y = 2x + 2

This means that the flat fee is $2 and the charge per day is $2.

Step-by-step explanation:

A  Linear Function best explains the relationship between the return and time.

What is the scatter plot?

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.

It is given that this scatter plot was created using daily stock market returns.

To determine which type of function fits the data of the graph best see the points of the graphs.

The scatter plot is not forming a parabola or curved graph so it can be a quadratic function.

The scattered in such a form that only a straight line can be the best fit for the scatter plot.

Therefore, a linear function is the best representation.

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The character Hannah is sent back in time to the Holocaust in Jane Yolen's book "The Devil's Arithmetic," where the Nazis tattoo a number on her arm.

The guy who tattooed Hannah's arm begs her not to forget the number because it serves as a powerful reminder of the significance of remembering and never forgetting the past and acts as a permanent reminder of the crimes done during the Holocaust. Hannah must remember the number since it is also a way of tracking and identifying people within the concentration camp.

Hannah is questioned about her name by the prisoner who is in charge of tattooing the ladies. That person is Chaya Abramowicz, she responds. She is wearing his daughter's outfit, he informs her. She had the same name, Chaya. He advises her to live for all the Chayas in the world and to never forget her prisoner number.

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