In scientific notation, we use powers of ______ to express very large or very small place values. Example: Look at this large number: 2,540,000.
We write numbers in scientific notation as the product of ____________ parts.
➔ The first part, called the first ________________, is a number between ______ and ______. ➔ The second part is a ____________ of ______.
To get the first factor, move the ________________ ________________ in the standard notation so there is just one ________________ number to the ___________ of the decimal point.

The inequality that shows the distance ran is 3x ≥ 4y

An equation is a expression that shows the relationship between numbers and variables.

Inequalities are used for the non equal comparison of numbers and variables.

Lena ran 3 miles each day for x days. Ivan ran 4 miles each day for y days.

Total number of miles that Lena ran = 3x

Total number of miles that Ivan ran = 4y

The total number of miles that Lena ran is at least the total number of miles that Ivan ran, hence:

3x ≥ 4y

The inequality is 3x ≥ 4y

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Answer:

Un industriel souhaite fabriquer une boîte sans couvercle à partir d'une plaque de métal de

24

Step-by-step explanation:

The length of the hypotenuse of the right triangle is:

B = 24.4

Side B is the side opposite to the angle B, so it will be the hypotenuse of the right triangle.

We know the other two sides of the right triangle, so we can use the Pythagorean theorem to get:

C^2 + A^2 = B^2

Replacing the values that we know:

A = 20

C = 14

We will get:

20^2 + 14^2 = B^2

√(20^2 + 14^2) = B

24.4 = B

That is the length of the hypotenuse

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Answer:

Car B has the best rate

Step-by-step explanation:

A:  450 mi / 15 gal = 30 mi/gal

B:  651 mi / 21 gal = 31 mi/gal

C:  598 mi / 23 gal = 26 mi/gal

31 > 30 > 26

Answer:Car B has the best rate at 31 miles per gallon

Step-by-step explanation:  i did my math

The proposed ban on sugary soft drinks larger than 16 ounces in New York City has both pros and cons. Pros include reducing obesity and diabetes, while cons include potential infringement on personal freedom and potential negative impact on small businesses.

The proposed ban on sugary soft drinks larger than 16 ounces in New York City aims to reduce obesity and diabetes by limiting the consumption of high-calorie beverages. This can also help to lower the healthcare costs associated with these conditions. However, some argue that this is an infringement on personal freedom and that people should have the right to make their own choices about what they eat and drink. Additionally, there are concerns that small businesses, such as convenience stores and vending machine operators, could be negatively impacted by the ban. This is because they may lose sales as a result of the ban, which could lead to job losses and financial hardship.

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The perimeter of the figure is 58 feet if the missing side length is 10 feet.

Perimeter is defined as the length of the circumference or outline of the geometry. This means that is the sum of the all the external side lengths of an image or figure.

From the two-dimensional geometry in the attached image, we see the dimensions as;

The missing side length = 15 - 5 = 10 ft

Therefore, we will add all the external lengths to get the perimeter as;

Perimeter of the figure = 5 + 7 + 10 + 10 + 15 + 11

= 58 feet

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Answer:

Step-by-step explanation:

80

Answer:

80

Step-by-step explanation:

To find 125% of 64, you can multiply 64 by 1.25.

125% of 64 = 64 x 1.25 = 80

So, 125% of 64 is 80.

a) The price that is 3 standard deviations above the mean is $18500

b) The price that is 2 standard deviations below the mean is  16000

c) The percentage of buyers who paid between $16,500 and $17,500 is 68%.

d) The percentage of buyers who paid between $17,000 and $18,000 is

47.5%

e) The percentage of buyers who paid less than $16,000 is 2.5%.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

Mean= 17000

standard deviation = $500.

a) The price that is 3 standard deviations above the mean is $

= 17000 + 3 x 500

= 18500

b) The price that is 2 standard deviations below the mean is $

= 17000 - 2 x 500

= 16000

c) The percentage of buyers who paid between $16,500 and $17,500 is

As, This is the bell curve numbers of 1 deviation which 68%.

d) The percentage of buyers who paid between $17,000 and $18,000 is

So,  1/2 of the 2nd deviation, or  95% x 0.5  

= 47.5%

e) The percentage of buyers who paid less than $16,000 is 5% is outside of the 2nd deviation which is half of that or  2.5%.

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Answer:

cost of 1 crate of lettuce = x

cost of 1 crate of cabbage = y

[tex]4x + 3y = 34.2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(1)[/tex]

[tex]2x + 5y = 31.8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(2)[/tex]

Multiplying eq. (2) by 2

[tex]4x + 10y = 63.6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(3)[/tex]

(3)-(1)

[tex]7y = 29.4 \\ y = \frac{29.4}{7} \\ y = 4.2 \\ [/tex]

Putting this in (2)

[tex]2x + 5(4.2) = 31.8 \\ 2x = 10.8 \\ x = 5.4[/tex]

.'. Cost of 1 crate of lettuce= $5.40

Cost of 1 crate of cabbage= $4.20

Answer:

Let 1 crate of lettuce be X and 1 crate of cabbage be y.

Now from question,

4 crates of lettuce and 3 crates of cabbage costs 34.20$

i.e.4x+3y=34.20----(1)

Also,

2 crates of lettuce and 5 crates of cabbage costs 31.80$

i.e. 2x+5y=31.80----(2)

Multiplying eqn (2) by 2 then subtracting from (1), we get,

4x+3y - {2(2x+5y)}=34.20-(2×31.80)

or,4x-4x+3y-10y=34.20-63.60

or,-7y= -29.40

:.y=4.20

Putting value of y in eqn 1 we get,

4x=34.20-12.60

or,4x=21.60

or,X=21.60/4

:.X=5.40

Hence,Cost of each crate lettuce i.e.X=5.40$

and,each crate cabbage i.e y=4.20$

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The five kinds of variables are nominal, ordinal, interval, ratio, and binary. Nominal variables are categorical variables with no numerical value.

The five kinds of variables are nominal, ordinal, interval, ratio, and binary. Nominal variables are categorical variables that don't have numerical values.  An example would be a survey asking respondents to select their gender as male or female.

Ordinal variables have an inherent order and can be ranked. An example would be a survey asking respondents to rate a product on a scale from 1 to 10. These variables are usually used when the items being measured are at different levels or degrees.

Interval variables have an absolute zero point and can be measured in equal intervals. An example would be measuring temperature in Celsius.

Ratio variables have a zero point and can be measured in ratios. An example would be measuring time in seconds.

Binary variables are either one or zero, and are commonly used in computer science. An example would be a survey asking respondents to select yes or no to a particular question.

Overall, each of these five kinds of variables are used to measure different types of data in different ways. Depending on the type of data being collected, one or more of these variables may be used.

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Answer: 32 oz

Step-by-step explanation:

Answer: 32

Step-by-step explanation: a pound is 16 ounces

Assuming the pressure and temperature remain the same, it would take 8.576 min for the same volume of UF6 to effuse through a porous membrane.

The effusion rate of a gas is determined by its molecular weight and the temperature and pressure of the system.

1. Calculate the molecular weight of Kr:

Molecular weight of Kr = 39.0983 g/mol

2. Calculate the molecular weight of UF6:

Molecular weight of UF6 = 352.03 g/mol

3. Calculate the ratio of the molecular weights:

Ratio of molecular weights = 352.03/39.0983 = 9.00

4. Calculate the effusion rate of UF6:

Effusion rate of UF6 = 8.576 min x 9.00 = 77.184 min

The effusion rate of a gas is determined by its molecular weight and the temperature and pressure of the system. To calculate the effusion rate of UF6, we first need to calculate the ratio of the molecular weights of Kr and UF6. Then, we can use this ratio to calculate the effusion rate of UF6, which is 77.184 min.

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The graph of all the functions are given below.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

From the graph:

The parent function f(x) = eˣ.

The graph of the parent function is given the attached image in purple line.

So,

1). f(2x) = e²ˣ

Graph f(2x) in the color green below.

2). -3f(x) = -3 eˣ.

Graph -3f(x) in the color blue below.

3). 2f(2x) = 2e²ˣ

Graph 2f (2x) in the color red below.

Therefore, all the graphs are given in the attached image.

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The e coordinates of the point on the directed line segment are  (-5, -3).

The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.

Given coordinates (-8, -6) and (4, 6) make a line segment,

and point in the line divide in ratio 1:3

the equation point is,

(x, y) = [tex][(\frac{mx_2 + nx_1}{m + n} ), (\frac{my_2 + ny_1}{m + n} )][/tex]

m = 1, n= 3

x₁ = -8, x₂ = 4, y₁ = -6, y₂ = 6

solving for x,

x = [tex](\frac{mx_2 + nx_1}{m + n} )[/tex]

x = [1(4) + 3(-8)]/4

x = -20/4

x = -5

solving for y,

y = [tex](\frac{my_2 + ny_1}{m + n} )[/tex]

y = [1(6) + 3(-6)]/4

y = -12/4

y = -3

(x, y) = (-5, -3)

Hence the coordinates are  (-5, -3).

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The output a needed to satisfy the consumer and interindustry demands is 12 units, and the output b needed to satisfy the consumer and interindustry demands is 6 number of units.

a) Output a = 12 (units)

b) Output b = 6 (units)

1. Calculate the total consumer demand (CD):

CD = 12 + 20 + 8 = 40 (units)

2. Calculate the total interindustry demand (ID):

ID = 4 + 5 + 9 = 18 (units)

3. Calculate the total production (TP):

TP = CD + ID = 40 + 18 = 58 (units)

4. Calculate the output a and b needed to satisfy the consumer and interindustry demands:

a) Output a = TP - ID = 58 - 18 = 40 (units)

b) Output b = CD - Output a = 40 - 12 = 28 (units)

The output a needed to satisfy the consumer and interindustry demands is 12 units, and the output b needed to satisfy the consumer and interindustry demands is 6 number of units.

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The horizontal distance of the ball when it hits the ground is equal to 119.671 feet.

According to statement, we find the equation of the path covered by the ball, that is, a quadratic equation of the height of the ball (h), in feet, in terms of horizontal distance (x), in feet. In this case we need to determine a value of x greater than zero such that h = 0, that is to say:

- 0.01 · x² + 1.18 · x + 2 = 0

The roots of the quadratic equation can be found easily by quadratic formula:

x = - 1.18 / [2 · (- 0.01)] ± [1 / [2 · (- 0.01)]] · √(1.18² - 4 · (- 0.01) · 2)

x = 59 ± 60.671

The only realistic solution for the horizontal distance of the ball is x = 59 + 60.671 = 119.671 feet.

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Answer: 15 degrees.

Step-by-step explanation:

A bisector divides an angle in half. So, we know the total angle of ABC is 20 degrees, as show in blue. We draw the bisector BD in the middle, meaning each side is 10 degrees, show in green. This means angle ABD is 10 degrees and angle CBD is is 10 degrees. We bisect angle CBD with BE, shown in red. This means that we have two 5 degree angles on either side,  angle CBE and angle EBD. Lastly, we need to find angle ABE, highlighted in orange. We add the components, which are angle DBA, measuring 10 degrees, and angle EBD, measuring 5 degrees. When added together, this equals 15 degrees, which is our final answer for angle ABE.

The total rainfall in this situation with the appropriate domain is f(h)=10h is 1-3 hours, f(h)=30 is 4 to 6 hours and f(h)=30+20(h-5) is 7 to 12 hours.

The range of input values where a function can be defined, or the set of possible inputs, is known as the domain of the function. The domain is the collection of objects that the function machine will accept as inputs.

During the 1 to 3 hours, rain fell at a constant rate of 10 mm per hour, expressed as

f(h)=10h

During the 4 to 6 hours, rainfall is same, expressed as

f(h)=30

During the 7 to 12 hours, raining again at a constant rate of 20mm, expressed as

f(h)=30+20(h-5)

Thus, the total rainfall in this situation with the appropriate domain is f(h)=10h is 1-3 hours, f(h)=30 is 4 to 6 hours and f(h)=30+20(h-5) is 7 to 12 hours.

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Answer:

42 students

Step-by-step explanation:

5 out of 7 students are car riders. This means 2 out of 7 students are bus riders. 12 students are bus riders.

12 = 2x/7, where x is the total number of students.

So, 84 = 2x

This means that x = 42. 2/7 of 42 is 12 so this is correct.

The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.

A compact set is a set that satisfies the finite subcover property, which means that every open cover of the set contains a finite subcover. This means that for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set.

Examples of compact sets that satisfy this property include closed and bounded sets in a metric space, such as closed intervals in real numbers, and closed and bounded subsets of Euclidean space.

The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.

Other examples of compact sets are the closed unit ball in a Euclidean space, and any finite set, where the number m would be equal to the number of elements in the set.

In summary, compact sets are sets that have the property of finite subcover, and for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set. Some examples of compact sets are closed and bounded sets in a metric space, closed intervals in real numbers, closed and bounded subsets of Euclidean space, closed unit balls in Euclidean space, and any finite set.

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Answer:

Step-by-step explanation:

The first step to determine the implied domain of the function is to identify any restrictions on the variables x and y. In this case, the function 2y + x^(1/3) = 3x + x^2 does not have any restrictions on x and y, therefore the domain is all real numbers.

We can express this as an interval notation:

(-∞, ∞)

This means that the function is defined for any real value of x and y, which means the domain of the function is all real numbers.

If the final statement when solving a system of linear equations is "5 = 0", it means that: E. none of these statements are true.

A solution to a system of linear equations is a set of values for the variables that satisfy all the equations in the system simultaneously. In other words, it is a collection of values for the variables that make all the equations in the system true at the same time.

The solution can be represented graphically as the intersection of the lines or planes defined by the equations in the system, or it can be represented algebraically as a set of values for the variables.

The equation "5 = 0" is false. It means that 5 cannot be equal to 0. This could indicate that the system of linear equations has no solution or that there is an error in the method being used to solve it.

Therefore, the answer is: "none of these statements are true".

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Answer: 2.5

Step-by-step explanation:

Answer:

AB = 6, BC = 6

AB = 4, AC = 4√2

BC = 2√2, AC = 4

(if im not wrong)

To write an absolute value equation with two solutions, we need to separate the equation into two cases: one for the positive value and one for the negative value.

The general form of an absolute value equation is |x - h| = k, where h is the value that the variable is being compared to and k is the value that the absolute value is equal to.

For example, to write an absolute value equation with two solutions that equal 3, we can separate the equation into two cases:

Case 1: x - h = k

x - 3 = 3

x = 6

Case 2: x - h = -k

x - 3 = -3

x = 0

So the equation is |x - 3| = 3 with solutions x = 6 and x = 0.

Another example is |x+2| = 4. The solutions to this equation can be found by setting x+2 = 4 and x+2 = -4.

x+2 = 4 => x = 2

x+2 = -4 => x = -6

So the equation |x+2| = 4 has solutions x = 2 and x = -6

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Answer: ▾ 1. Henry has 8 dozen cookies and bakes 48

cookies an hour.

a. (4,2.9)

Step-by-step explanation:

The statement is describing a linear relationship between the number of hours and the number of cookies produced. This can be represented by a linear equation of the form y = mx + b, where x is the number of hours and y is the number of cookies.

The point (4, 2.9) represents the number of cookies produced after 4 hours, which is 2.9 dozen (8 dozen * 0.36) which is 48 cookies.

▼ 2. Julian drives home from work and averages

2

mile per minute. He has to travel 4.5

miles.

b. (1,144)

Explanation:

The statement is describing a linear relationship between the time in minutes and the distance traveled.

The point (1,144) represents the distance traveled after 1 minute, which is 144 miles, which is 4.5260 miles.

▾ 3. Using a laptop on battery power causes the

battery to decrease 10% an hour.

c. (5,50)

Explanation:

The statement is describing a linear relationship between the number of hours and the percentage of battery power remaining.

The point (5,50) represents the percentage of battery power remaining after 5 hours, which is 50% of the original battery power.

So based on the given information, I matched the linear functions with the points that makes the statement true as

▾ 1. Henry has 8 dozen cookies and bakes 48

cookies an hour.

a. (4,2.9)

▼ 2. Julian drives home from work and averages

2

mile per minute. He has to travel 4.5

miles.

b. (1,144)

▾ 3. Using a laptop on battery power causes the

battery to decrease 10% an hour.

c. (5,50)

Please note that these answers are based on the information provided in the problem statement and may not be the only possible answers.

Answer:

Height = 100 cm.

Surface Area = 625 cm^2.

Step-by-step explanation:

The volume of the cube is identical to the volume of the cuboid.

Volume of the cube = 5^3 and volume of cuboid is base area * height.

5^3 = 2.5 * 0.5 * h     (where h is the height of the cuboid).

h = 5^3/1.25

  = 100 cm.

The surface area is:

A = 2 * area of base + 2 * area of 1 side + 2 area of other side

   = 2 * 1.25 + 2* 100 * 0.5 + 2 * 100 * 2.5

   = 2.5 + 100 + 500

   = 602.5 m^2.

On solving the provided question, we can say that Graph Onerepresents a linear equation.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

Graph One

The graph is linear, commonly known as being in a straight line. Other graphs are not, though. Additionally, the range (y) of the tables is rising linearly every time, by a factor of.5 (1/2).

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An inequality that represents the value of height h of rectangular prism  is h ≤ 3

We know that the formula for the volume of a rectangular prism,

V = l × w × h

where l is the length of the rectangular prism,

w is the width of the rectangular prism

and h is the height of the rectangular prism

Here, we ahve been given a rectangular prism with sides 3 ft, 4 ft, and h ft

l = 4 ft, w = 3 ft

The volume of a rectangular prism with sides 3 ft, 4 ft, and h ft must be at least 36 cubic ft.

V ≥ 36

Using the formula of the volume of a rectangular prism we get an inequality,

l × w × h ≥ 36

4 × 3 × h ≥ 36

We solve an inequality that represents the value of h.

12 × h ≥ 36

Divide both sides by 36

(12h/12) ≥ (36/12)

h ≥ 3

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