A person takes 50 minutes average to get to work. Time may vary by 10 minutes depending on traffic. Drag and drop the correct number or equation in each box to make the sentences true. "If the time taken by the person to get to work is T minutes, the equality that models this situation is_____ the minimum time taken by the person to get to work is _____min, the maximum time taken is____min.

Dora have 144 shares of stocks while Addison have 37 shares of stocks.

Let us say that Addison own X shares of stock.

According to the situation provided,

The number of shares of stocks own by Dora are 4 less than 3 times of the Stocks owned by Addison.

Stocks Owned by Dora = 3x - 4

The total shares of stocks are 152.

So, we can write the relation between the stocks as,

x + 3x - 4 = 152

4x - 4 = 152

The above formed relations between the stocks is in the form of linear equation in one variable. A linear equation has highest power of variable equal to 1 and only one variable.

Now, solving the equation further,

4x - 4 = 152

4x = 148

x = 37

The total numbers of stocks owned by Addison are 37.

Shares of stocks owned by Dora are 3(37)-4.

The share of stocks owned by Dora are 144.

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We choose ASA Postulate to prove this triangle congruent.

In the given question given that

[tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].

[tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].

Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].

So [tex]m\angle BAC\cong m\angle DAC[/tex]

Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].

So [tex]m\angle BCA\cong m\angle DCA[/tex]

Then [tex]AC\cong AC[/tex]

Then [tex]\triangle BAC\cong \triangle DAC[/tex]

There given postulate are AAS, ASA, SSS, SAS.

We have proved using the ASA postulate.

Now describing the ASA postulate.

ASA means Angle-Side-Angle Postulate.

According to ASA Postulate, two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

Hence, we choose ASA Postulate to prove this triangle congruent.

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Answer:

Equation: 60v = 15

Original value: $0.25.

Step-by-step explanation:

Current value: $15

Original value: v

The current value is 60 times the original value.

So, the equation is:

Equation: 60v = 15

Now we solve the equation to find the original value.

60v = 15

v = 15/60

v = 0.25

Original value: $0.25.

1.064 x 10¹ is 15.2 times larger than the 7 x 10⁻¹. It is obtaining the taking ratio of the given number. Option B is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

We'll apply division by splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

Let 7 x 10⁻¹ be x times the number 1.064 x 10¹.

The value of x  is obtained by taking the ratio of  1.064 x 10¹ and 7 x 10⁻¹.

x = 1.064 x 10¹ / 7 x 10⁻¹

x = 15.2

Thus,1.064 x 10¹ is 15.2 times larger than the 7 x 10⁻¹. It is obtaining the taking ratio of the given number. Option B is correct.

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Answer:

See below

Step-by-step explanation:

I THINK what you wrote is:

2(x-2) - 3(x-3) = (5x-5) - 4(x-8)

2x -4   -3x+9  = 5x-5   -4x+ 32

2x-3x-5x+4x = 4 -9 -5 +32

-2x = 22     *** EDITED ***

x =  - 11  

The graph of the solution set of the system of inequalities y > x + 2 and

- 2x + y ≤ 4 is shown in figure.

What is mean by Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequalities is,

⇒ y > x + 2

And, - 2x + y ≤ 4

Now,

The inequality is,

⇒ - 2x + y ≤ 4

Add 2x both side, we get;

⇒ - 2x + y + 2x ≤ 4 + 2x

⇒ y ≤ 2x + 4

And, The second inequality is;

⇒ y > x + 2

So, Plot the graph of the inequalities  y ≤ 2x + 4 and y > x + 2.

We get the solution set of the system of inequalities.

Which is shown in figure.

Thus, The graph of the solution set of the system of inequalities y > x + 2 and - 2x + y ≤ 4 is shown in figure.

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To find the volume of a cylinder with radius 3 and height 3

we will use the formular below:

where r is the radius and h is the height

From the question, r=3 and h = 2

substitute the value into the formula

If we substitute the value of pie = 22/7

Then,

You have the following algebraic equation:

1/3x = 1/3 + 6/x

In order to solve the previous equation you first multiply both sides of the equation by x, thus, you can quit x denominators in the equation. Proceed as follow:

1/3x = 1/3 + 6/x multiply by x both sides

1/3 = x/3 + 6 multiply by 3 both sides

1 = x + 18 subtract 18 both sides

1 - 18 = x + 18 - 18

-17 = x

-17 = x is the same as x = -17. The solution to the given equation is x = -17.

Let the number be x

seven times the number = 7x

The difference of seven times a number and five is one hundred. It means that

7x - 5 = 100

7x = 100 + 5

7x = 105

x = 105/7

x = 15

The number is 15

Answer:

slope of perpendicular line = - 2

Step-by-step explanation:

calculate the slope of YZ using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = Y (- 7, - 4 ) and (x₂, y₂ ) = Z (5, 2 )

[tex]m_{YZ}[/tex] = [tex]\frac{2-(-4)}{5-(-7)}[/tex] = [tex]\frac{2+4}{5+7}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2

Answer:

$56,000.

Explanation:

Let his base salary = s

12% of his base salary = $6720

Thus, we have:

Next, solve for s:

His base salary is $56,000.

Answer: 64

Step-by-step explanation:

Length x width x higth= volume

4 x 8 x 2 = 64

Answer:

4 cm

Step-by-step explanation:

First, find the volume of the rectangular prism.
4*8*2=32*2=64 cm^-3

Now, the formula for the volume of the cube is:
Volume = side ^ 3
We know the volume is 64 cm^3, so plug it in to the equation:

64 = side ^ 3
take the cube root of both sides
4 = side

A) The recursive formula takes into account the previous term. For each term, the next term is expressed in respect to it

Looking at the given scenario, the popularion is increasing by 4.4%. This means that the common ratio is

1 + 4.4/100 = 1.044

Given that the initial population is 11200000, the recaursive formula or equation would be

B) For the explicit formula, the general formula for a geometric sequence is

an = a1 * r^(n - 1)

a1 = first term = 11200000

r = common ratio = 1.044

The explicit equation would be

an = 11200000 * 1.044^(n - 1)

C) At the start of 1994, the number of terms, n = 7

We would find a7 by substituting n = 7 into the explicit equation. We have

a7 = 11200000 * 1.044^(7 - 1)

a7 = 11200000 * 1.044^6 = 14501770

Step-by-step explanation:

-7 + 9 + (-8)

2 + (-8)

-6

Hope this helps! :)

Step-by-step explanation: Remove parenthesis. If there is a "+" in front of an expression in parenthesis, the expression remains the same.

-7+9-8. Calculate the sum or difference. You should get -6.

Let X be the number of heads that come up

Step 1: Write out the formula for the binomial probability distribution

After 11 years, the account balance is $17,704.987. (approx.)

The principle of the first loan is multiplied by the annual interest rate multiplied by the number of compound periods minus one to calculate compound interest.

The principal of the loan plus compound interest will then be what is left.

Given,

P = $8,216 for the principal value.

Interest rate, r = 7% or 0.07.

Period, with t = 11.

Interest applied n times every time period, or 12 times.

As far as we are aware, A = P(1 + r/n) n*t

where A is the whole sum.

Fill out the formula with the values,

=> A = 8216(1 + 0.07/12) ^ 11*12

= 8216((12 + 0.07)/12) ^ 132

Upon calculation, we obtain,

≅ $17,704.987

As a result, after 11 years, the account will have a balance of $17,704.987 (about).

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The line plot that correctly displays the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, is: A.

A line plot is a graphical representation of a data whereby the frequency of each data point is represented by a dot on the line plot.

The dots on each data point on the line plot corresponds to the frequency of a data point in a data distribution.

Given the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, the frequency for each data point is:

2 - 1 dot

3 - 3 dots

4 - 3 dots

5 - 2 dots

6 - 1 dot

7 - 1 dot

8 - 1 dots

Thus, the line plot that correctly represents these data points alongside their frequencies is: A.

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The form of the linear equation is

y = m x + b

m is the slope of the line

b is the y-intercept

The rule of the slope is

(x1, y1) and (x2, y2) are two points on the line

Since (0,0) and (10, 12) are two points on the line

x1 = 0 and y1 = 0

x2 = 10 and y2 = 12

Now substitute them in the rule to find m

The slope of the line is 1.2

Substitute it in the form of the equation

y = 1.2 x + b

b is the y-intercept which means value y at x = 0

Since at x = 0, y = 0

Then b = 0

The equation of the line is

y = 1.2 x

Given the formula for volume:

Let's rewrite the formula in terms r, V and h.

i) Rewriting for r in terms of V and h :

2) Given:

Volume, V = 66 cubic inches

height, h = 3.3 inches

We know that diameter is radius multiplied by 2.

To find the diameter, first find the radius.

Therefore, we have:

Since the radius is 2.52 inches, the dia,eter will be:

D = r x 2 = 2.52 x 2 = 5.04 inches

To the nearest inch = 5 inches

ANSWER:

diameter = 5 inches

Given:

A graph is given and the points on the graph are as:

(1, 17), (2, 14), (3, 11), (4, 8), (5, 5), (6, 2)

Required:

To determine the value of

and d for the given sequence.

Explanation:

We can observe from the graph that the given sequence is an arithmetic sequence.

Here

represent the first value and d represent the common ratio.

So the values are as:

Final Answer:

The second option is the correct answer.

The sentence using mathematical symbols would form an inequality as; n ≥ 0.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. The Set of such values is; called the solution set to the considered equation or inequality.

We need to write a sentence using mathematical symbols:

Given that "n is greater than or equal to 0"

The inequality form as;

n ≥ 0

Therefore, the sentence using mathematical symbols would form an inequality as; n ≥ 0.

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Solution

For this case we can create the following plot:

We want to find the work so we can use this formula:

Replacing we got:

Explanation:

We have two equation of line. Both lines intersect at a point.

The point of intersection of two graphs, is the solution of the graph.

At this point, both will have same x and y values

Tracing the graph:

The point of intersection occurs at x = -2, y = 2

Hence, the solution is at (-2, 2)

Solution

- Don buys a shirt for $24.85.

- Daryl spends $3.15 more for his shirt. This means that Daryl spends

- Thus, Daryl spends $28 on his shirt.

- Sean paid the same price as Daryl, that is, he paid $28 for each shirt.

- Sean bought two shirts, thus, Sean spends:

Final Answer

Sean spends $56 on his 2 shirts

To find out how much grain the farmer can hold we need to find the volume of the silo. The silo is made from a circular cylinder and half a sphere.

The volume of the cylinder is given by:

In this case r=10 and h=30, plugging this values in the equation above we have that the volume of the cylinder is:

Hence the volume of the cylinder is 9420 cubic feet.

Now we need to find the volume ot half the sphere, the volume og an sphere is given by:

Plugging the radius we have that:

Now, we only need half this volume then the volume of the top of the silo is:

Finally we add the volume of the cylinder and half the sphere, therefore the volume of the sylo is:

and the answer is B.

7) We know that x = 5 and y = 2

We can write an equation that relates this values as a proportion.

Let's say there is a number r such as:

x*r=y

That's a equation that relates x and y. Let's solve for the values given.

Now solve for r:

The relation we found is:

Now to find the value of x when y = -6, we replace it in the equation:

Then with this relation, x = -15 when y = -6

The expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2

The sequence is -7, -12, -17, -22, -27...

The first term = -7

The common difference  = The second term - The first term

= -12 - (-7)

= -12+7

= -5

The nth term of the sequence = a+(n-1)d

Where a is the first term

d is the common difference

n is the n terms

Substitute the values in the equation

The nth term of the sequence = -7+(n-1)-5

= -7-5n+5

= -5n-2

Hence, the expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2

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Answer:

3

Step-by-step explanation:

7 - 4 is 3

Answer:

6 hecters in the khlathmandu

since they are parellel lines, we conclude that they have the same slope, the second option is the correct one.