There is one bus driver, two coaches, and three teams, each with four dancers going to a competition. Nia writes the expression 1 + 2 + 3 ∙ 4 to represent everyone that will be on the bus and solves it using the following steps:

1 + 2 + 3 ∙ 4

= 3 + 3 ∙ 4

= 6 ∙ 4

=24

A. Nia concludes that 24 people will be on the bus going to the competition. Describe the mistake Nia made when solving her expression. Then write an explanation and draw a picture to help Nia understand how to solve her expression correctly.

B. How would you write this expression if n represents the number of teams?

C. How would this expression be different if there were two coaches for each team? Write an expression and draw a picture to support your expression.

The component form of →s + →t is <-8, 1>

We know that the component form of a vector is the ordered pair that describes the changes in the x- and y-values.

In this question, we have been given two vectors

vector s = < 2, -6>

and vector t = <-10, 7>

We need to find the component form of →s + →t

→s + →t

= < 2, -6> + <-10, 7>

= <2 + (-10), -6 + 7>

= <2 - 10, 1>

= <-8, 1>

Therefore, the component form of →s + →t is <-8, 1>

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The average sale rate is 3 cupcakes per customer.

So, in 1 dozen there are 12 pieces.

Then,

Therefore, the average sale rate is 3 cupcakes per customer.

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Answer:

10 *6= 60

60÷2=30

1÷2×b×h formula

answer- 30

Answer:

14

Step-by-step explanation:

That equation, with the given constraints, is easily solved using logical reasoning.10y is a multiple of 5, and 25 is a multiple of 5; that means 7x is a multiple of 5.And we know x is a number between 10 and 20. So x has to be 14

A triangle with vertices located at A(1 , 1), B(2 , 5), and C(5 , 1) has a perimeter of 13.1 units.

A triangle is a two-dimensional shape that has three sides or edges and three vertices.

Perimeter refers to the distance around any two-dimensional shape. The perimeter of a triangle is the sum of the length of its sides.

To solve for the perimeter of triangle ABC with vertices located at A(1 , 1), B(2 , 5), and C(5 , 1), solve first for the length of each side, namely side AB, side BC, and side AC.

And to solve for the length of each side, use the distance formula given by:

d = √(x2 - x1)^2 + (y2-y1)^2

side AB : d = √(2 - 1)^2 + (5 - 1)^2 = √1 + 16 = √17 units

side BC : d = √(5 - 2)^2 + (1 - 5)^2 = √9 + 16 = √25 = 5 units

side AC : d = √(5 - 1)^2 + (1 - 1)^2 =√16 + 0 = √16 = 4 units

Solving for the perimeter of triangle ABC,

P = AB + BC + AC

P = √17 + 5 + 4

P = 4.123 + 9

P = 13.123 units

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Answer:

 $3500

Step-by-step explanation:

x = value of diamond with an increase of 5% every year for 8 years

x= 2500(0.05)

x= 125(8)

x = 1000

2500 + 1000 = $3500

The value of the diamond after 8 years is the amount of $3693.63.

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

To find the value of the diamond after 8 years, we need to calculate the compound interest.

The formula for compound interest is:

A = P(1+r/100)ⁿ

here:

A = final amount

P = principal amount

r = annual interest rate (as a decimal)

t = time in years

Using this formula, we can calculate the value of the diamond after 8 years:

P = 2500

r = 5% = 0.05

t = 8

A = 2500 (1 + 0.05/1)¹ˣ⁸

A = 2500 (1.05)⁸

A = 2500 (1.4775)

A = $3693.63

Therefore, the value of the diamond after 8 years is $3693.63.

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The probability of getting a number that is greater than four is G. 0.33

Probability:

Probability defines the possible occurrence of the selected event across the total number of events.

Given,

A die is rolled.

And we need to find the probability of rolling a number greater than 4.

If you roll a single die there are 6 possible outcomes  are

=> {1,2,3,4,5,6}

So, the numbers that are greater than 4 are,

=> 5 and 6.

So, there are 2 of which are greater than 4.  

So in a single roll the probability of getting a number greater than 4 is

=> 2/6

=> 1/3.  

For the decimal form it can be written as,

=> 0.33.

So, the correct option is G. 0.33.

Therefore, the probability of getting the number greater than 4 is 0.33.

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We can expect there to be 684 trout in the lake.

In the given statement is:

To determine the number of trout in a lake, a conservationist catches 171 trout, tags them and throws them back into the lake. Later 52 trout are caught; 13 of them are tagged.

Proportion:

A ratio gives us the measure of one quantity as compared to another quantity, and it is represented either as a fraction, decimal or a notation like a : b. When the same ratio is applicable to other quantities.

Now, According to the question:

Number of trout / number of trout = number of trout caught / caught that were tagged

Number of trout / 171 = 52/13

Number of trout = (171 x 52) / 13

Number of trout = 8,892 / 13 = 684

Hence, We can expect there to be 684 trout in the lake.

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If the tower is located at the origin, the equation of its circular area of coverage is [tex]x^{2} +y^{2} = 225[/tex]

A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.

The equation of a circle with center at (h, k) and radius r is given by:

[tex](x - h)^{2} + (y-k)^{2} = r^{2}[/tex]

According to the given condition,

center is origin i.e., (h, k) is (0,0)

and r = 15.

Substituting these values in the equation above,  

[tex](x - 0)^{2} + (y-0)^{2} = 15^{2}[/tex]

[tex]x^{2} + y^{2} = 225[/tex]

Thus, the equation of the tower located at origin and having coverage area of radius 15 miles is  [tex]x^{2} + y^{2} = 225[/tex].

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Answer: 2

Step-by-step explanation: There are two solutions: 2, and -8/3. 2 is the positive solution.

Answer:

the answer is

[tex] \frac{27}{4} [/tex]

In the given question the value of w is 0.128.

So, w when c = 4:

Now,

Then,

Therefore, in the given question the value of w is 0.128.

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The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(13, 14) and C(3, 5).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(13 + 3) / 2, (14 + 5) / 2]

(x, y) = (16/2, 19/2)

(x, y) = (8, 9.5)

The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).

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Answer:

Center: (2,2)

Radius: 2

Answers:

Center = (2,2)

Radius = 2

=================================================

Explanation:

Consider (A+B)^2 = A^2+2AB+B^2 after using the FOIL rule.

If A = x, then we have (x+B)^2 = x^2+2Bx+B^2

The coefficient of the x term is 2B. It divides in half to get B, and it squares to B^2 as the final term.

In short, if we want to complete the square on something like x^2-4x, then we do two things:

So we go from -4 to -2 after dividing in half, and then from -2 to 4 after squaring. We'll add 4 to both sides to complete the square for the x terms.

[tex]x^2+y^2-4x-4y+4 = 0\\\\(x^2-4x)+(y^2-4y)+4 = 0\\\\(x^2-4x+4)+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y)+4 = 4\\\\[/tex]

We'll do the same thing for the y terms. Though notice we already have a +4 on the left side. So we can have it absorb into the y terms parenthesis grouping like so

[tex](x-2)^2+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y+4) = 4\\\\(x-2)^2+(y-2)^2 = 4\\\\[/tex]

Now compare that to the circle template

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

We see that

This circle has its center at (h,k) = (2,2)

The radius is r = 2

Answer:

x = 6

Step-by-step explanation:

- 12x - 17 = - 89 ( add 17 to both sides )

- 12x = - 72 ( divide both sides by - 12 )

x = [tex]\frac{-72}{-12}[/tex] = 6

The measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.

The angle is the separation of the crossing surfaces or lines. Additionally, the angle is specified in degrees. One whole spin has an arc of 360 degrees.

If the total of two angles is 180 degrees, they are said to be supplementary angles.

In the third line, if two lines are parallel. Equal angles are formed by matching angles.

When two lines intersect, then their opposite angles are equal.

The measure of angle ∠1 is 40°.

Angle ∠1 and angle ∠2 are supplementary angles. Then the measure of angle ∠2 will be

∠1 + ∠2 = 180°

40° + ∠2 = 180°

∠2 = 140°

The vertical angles are given below.

∠1 = ∠3 = 40°

∠2 = ∠4 = 140°

The corresponding angles are given below.

∠1 = ∠5 = 40°

∠2 = ∠6 = 140°

∠3 = ∠7 = 40°

∠4 = ∠8 = 140°

Then the measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.

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The measure of each angles are 21 and 83degrees

A line is defined as the distance between two points while an angle is the point where two lines intersect.

From the diagram shown, the expression below is true;

<EFH + <HFG = <EFG

Substitute the given parameters to have:

5x+1 + 62 = 18x + 11

Collect the like terms

5x - 18x = 11 - 63

-13x = -52

x = 52/13

x = 4

Find each measure

<EFH = 5(4) + 1

<EFH = 21

degrees

<EFG = 18(4) +11

<EFG = 72 + 11

<EFG  = 83 degrees

Hence the measure of each angles are 21 and 83degrees

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The measure of the vertex angle is 92°

Here,

The triangle is isosceles and one base angle of an isosceles triangle has a measure of 44°

We have to find the measure of the vertex angle.

What is Isosceles triangle?

A triangle is said to be isosceles if there is any two corresponding sides are equal and there angle are equal.

Now,

The triangle is isosceles triangle.

Hence, there corresponding sides and there angles are equal.

So, Both base angles of a triangle are equal.

And, Sum of angles of a triangle are 180°

Let the measure of the vertex angle is x°

Hence,

⇒ 44° + 44° + x° = 180°

⇒ x° = 180° - 88°

⇒ x° = 92°

Therefore, The measure of the vertex angle is 92°

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From the total amount of miles driven, it is found the equation that matches the given situation is:

138 + 225 + x = 482.

Solving the equation, it is found that they drove 119 miles on Sunday.

The total amount of miles driven is given by the addition of the number of miles driven on Friday, Saturday and Sunday.

The separate amounts are given as follows:

Hence the equation that matches the given situation is:

138 + 225 + x = 482.

Solving the equation, we have that:

x = 482 - (138 + 225)

119.

They drove 119 miles on Sunday.

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A conditional statement has the same truth value as Contrapositive

From the question, we are to determine which type of conditional statement has the same truth value as the original statement

As a general rule, if the truth value of an original statement is True, the truth value of the contrapositive would also be true

Similarly;

If the truth value of an original statement is false, the truth value of the contrapositive would also be false

Hence, a conditional statement has the same truth value as contrapositive

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Answer: -7/5=-9

Step-by-step explanation:

I hope it helps

Answer: - 7/5 = -9

Step-by-step explanation: Combine like terms into single fraction, multiple by 1, subtract 3, simply.

Lets consider an example to to show that it does not matter which point you choose for (x₁, y₁) .

Let the points be -

(2,1) and (4,7)

where x1 and x2 are 2, 4

y1 and y2 are 1,7.

So the formula for slope will be -

m = y2 - y1 / x2 - x1

⇒ 7 - 1 / 4 - 2

⇒ 6 / 2

⇒ 3                                                         .......(1)

So, the slope of the equation is 3 for x1, x2 = 2, 4 and y1, y2 = 1,7

Now, let us consider,

x2 = 2 and x1 = 4 , y1 = 7 and y2 = 1

m = 1 - 7 / 2 - 4

m = -6 / -2

m = 3                                                    ...........(2)

From (1) and (2), we can infer that it does not matter which point you choose for (x₁, y₁).

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Answer: 1,585.12 is your interest. full is 4349.12

Step-by-step explanation: brainlist pls

Answer:26

Step-by-step explanation:

-3(2-4)2+14= -3*-2*2+14=12+14=26

Based on the given parameters, the value of r is 46/3

The given parameters are

DG = r + 2

GM = 2r - 13

DM = 35

This means that

DM = DG + GM

So, we have

r + 2 + 2r - 13 = 35

Evaluate the like terms

3r = 46

Divide both sides by 3

r = 46/3

Hence, the value of r is 46/3

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Answer:

Step-by-step explanation:

-9

The proof of Theorem 4.3 with an example is shown.

To prove Theorem 4.3:

Let,s take two triangles, that is △ABC and △ADC.

Since two pairs of angles are congruent, then the △ABC≅△ADC is under AA condition.

Therefore, the proof of Theorem 4.3 with an example is shown.

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The expression that represents the amount spent is  0.8x + 7.50

The given parameters are

Discount = 20%

Necklace = 7.50

Let the cost of the dress be x

So, the expression that represents the amount Sammie spent is

Expression = (1 - Discount) * x + Necklace

This gives

(1 - 20%) * x + 7.50

Evaluate

0.8x + 7.50

Hence, the expression that represents the amount spent is  0.8x + 7.50

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The highest point of this ramp will be at 30 inches.

It is given that Wheelchair ramps have at least a 12 -inch run for each rise of 1 inch and Max length for a ramp is 30 feet.

We have to find the highest point of ramp in inches.

What will be the value of 10 feet in inches ?

As we know that 1 feet = 12 inches , the value of 10 feet in inches will be ; 10 × 12 inches or 120 inches.

As per the question ;

Wheelchair ramps have at least a 12 inch run for each rise of 1 inch.

Max length for a ramp = 30 feet

or

Max length for a ramp = 30 × 12 inches

or

Max length for a ramp = 360 inches

The highest point of this ramp will be at ;

= 360 ÷ 12

= 30 inches

Thus , the highest point of this ramp will be at 30 inches.

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Answer:

76

Step-by-step explanation:

Well just substitute 22 in for w. Multiply 4 time 22 that equals 88. Then just subtract 12 from 88, and you end up with your final answer of 76