Mary can jog twice as fast as she can walk. She was able to jog the first 13.5 miles to
her grandmother's house, but then she tired and walked the remaining 1.5 miles. If the
total trip took 1.5 hours, then what was her average jogging speed?

The measure of angle R from the triangle PQR is 15.31°.

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

The formula for the cosine rule is c=√(a²+b²-2ab cosC)

In the given triangle PQR, PQ=9 units, PR=12 units and RQ=20 units

PQ²=PR²+RQ² -2×12×20cosR

9²=12²+20² -2×12×20cosR

81=144+400-480cosR

81=544-480cosR

81-544= -480cosR

-463= -480cosR

cosR= 463/480

cosR= 0.9645

∠R=15.31°

Therefore, the measure of angle R is 15.31°.

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The ratio of the amounts of money that they each get:

1 : 3 : 3/2

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Let's represent the amount of money that Jan gets as x.

Then, the amount of money that Freda gets is 3x,

and the amount of money that Pieter gets is:

= (1/2) x 3x

= 3/2 x (x)

The ratio of the amounts of money that they each get can be written as:

⇒ x : 3x : 3/2 x (x)

⇒ 1 : 3 : 3/2

So, Jan gets 1 unit of money, Freda gets 3 units of money, and Pieter gets 3/2 units of money.

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The direction of the sum of the two vectors is along the west direction

Assuming vector A is pointing west ward and vector B is pointing eastward

The direction of vector A to the horizontal is negative solved by

= -6 cos 30

= -5.196

Adding both vectors

= vector A + vector B

= -5.196 + 5

= -0.196

Hence the direction is to the west since it is negative

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Answer:

the correct answer is letter A

The solution to the equation "negative x = 9" is "x = -9". There is no invisible number in front of "x" in this equation.

To solve the equation "negative x = 9" algebraically, we want to isolate the variable "x" on one side of the equation.

First, we notice that "negative x" means "-x", so we can rewrite the equation as:

-x = 9

To isolate "x", we need to perform an inverse operation on both sides of the equation. Since "-x" means the opposite of "x", we need to perform the opposite operation, which is to add "x" to both sides:

-x + x = 9 + x

Simplifying the left-hand side by canceling out the "-x" and "+x", we get:

0 = 9 + x

We can further simplify this equation by subtracting 9 from both sides:

0 - 9 = 9 + x - 9

-9 = x

So the solution to the equation "negative x = 9" is "x = -9".

There is no invisible number in front of "x" in this equation, so we don't need to worry about any additional steps or calculations.

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Answer: The future value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

FV = PMT * ( ( (1 + r)^n - 1) / r) * (1 + r)

where PMT = $300, r = 6%/12 = 0.05, and n = 10 years * 12 months/year = 120 months.

Substituting these values into the formula, we get:

FV = $300 * ( ( (1 + 0.05)^120 - 1) / 0.05) * (1 + 0.05)

FV = $300 * ( ( 1.05^120 - 1) / 0.05) * 1.05

FV = $300 * ( ( 2.704813829421526 - 1) / 0.05) * 1.05

FV = $300 * ( 1.704813829421526 / 0.05) * 1.05

FV = $300 * 34.09627658843153 * 1.05

FV = $52,113.63

Therefore, the future value of the annuity due is $52,113.63.

Step-by-step explanation:

Answer:

Step-by-step explanation:

6(x+5) = 6x+30

-2(x-3)=-2x+6

6x+30=-2x+6

8x+30=6

8x=-24

x=-3

Answer: x = -3

Step-by-step explanation:

6(x + 5) = -2(x-3)

1. Distribute: 6x + 30 = -2x + 6

2. Add 2 to both sides: 8x + 30 = 6

3. Subtract 30 on both sides: 8x = -24

4. Divide by 8 on both sides: x = -3

The units of water the friends used in one month is 820 units.

The total units of water used as read by the meter = 789 units + 820 units

= 1609 units

Therefore, the friends used a total of 820 units of water.

Complete question:

A water meter shows how many units of water Riya and her friends use.

Riya reads the meter when they move in. It shows 789 units.

She reads the meter again after one month. It reads 820 units.

How many units of water did the friends use in one month?

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The value of x in the trapezoid is 12

It is important to note that the properties of a trapezoid are;

Now, let's equate the angles, we getl

7x + 21 = 105

collect the like terms, we get;

7x = 105 - 21

subtract the like terms

7x = 84

Make 'x' the subject of formula

x = 84/7

Divide the values

x = 12

Hence, the value is 12

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Answer:

              The area of the quadrilateral is C: 12 square feet.

Step-by-step explanation:

               In the photo, the quadrilateral is divided into two triangles, both having a base length of 4 feet and a height of 3 feet. Therefore, we can find the area of the entire quadrilateral by adding the areas of the two triangles together. Since the triangles have a base length of 4 feet and a height of 3 feet, their individual areas will be [tex]4*3*\frac{1}{2} =12*\frac{1}{2} = 6[/tex] square feet. As there are two triangles, we need to multiply the area of one triangle by 2 to get the total area of the quadrilateral, which would be [tex]6 * 2=12[/tex] square feet. Hence, we can conclude that the correct answer will be C.

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The statement describes the solutions of this equation is

The Equation have two valid solution and No Extraneous solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x/3 + (x-1)/ (x+ 4)= (x+3)/ (x+4)

Now, simplifying the above Expression

(x² + 4x + 3x - 3) / 3(x+4) = (x+3)/ (x+4)

(x² + 4x + 3x - 3) / 3 = (x+3)

x² + 7x -3 = 3(x+3)

x² + 7x -3 - 3x - 9 = 0

x² + 4x - 12 = 0

Solving the above Quadratic Equation

x² + 6x- 2x - 12 = 0

x(x+6)- 2(x+6)= 0

(x-2)(x+6)= 0

x= 2, -6.

So, the Equation have two valid solution and No Extraneous solution.

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Answer: x = -3/2

Step-by-step explanation:

-4x + 2(x+4) = -7x - (x+1)

-4x + 2x+8 = -7x -x-1

-2x + 8 = -8x - 1

+2x          +2x

8 = -6x - 1

+1           +1

9 = -6x

/-6    /-6

-9/6  = x

-3/2 = x

The value of x is given as follows:

x = 9.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

The figure for this problem has four sides, hence the sum of the internal angle measures is given as follows:

S(4) = 180 x (4 x 2)

S(4) = 360º.

Adding the four angle measures and equaling them to 360º, the value of x is obtained as follows:

117 + 93 + 87 + 6x + 9 = 360

306 + 6x = 360

6x = 54

x = 54/6

x = 9.

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On solving the provided question, we can say that by unitary method, Total capital of the firm  = Rs. 85,000

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Heena and Sudha share profits and losses equally.

If the capital of Teena is 1/5 of the total capital which is equal to Rs. [tex]90,000[/tex] 1/5 of Total capital = Rs. [tex]90,000[/tex]

Total capital = Rs. 90,000 × 5 =  4,50,000,  capital of all partners = Rs. [tex]1,20,000 + Rs. 80,000 + Rs. 90,000 + 60,000 + Rs. 15,000[/tex]

Total capital of all partners = Rs. [tex]3,65,000[/tex]

Total capital of the firm  = Rs. [tex]85,000[/tex]

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The constant of proportionality is 0.60

The equation is y = $0.60x.

Here is the completed table

Number of lemons  Total cost

4                                  $2.40

7                                 $4.20

15                                 $9

18                                  $10.80

Direct variation is when two variables move in the same direction. As the number of lemons bought increases, the total cost increases.

The equation that represents direct variation is:

y = kx

Where:

$1.80 = 3k

k = $1.80 / 3

k = $0.60

y = $0.60x

Total cost of 4 lemons=  $0.60 x 4 = $2.40

Total cost of 18 lemons=  $0.60 x 18 = $10.80

Number of lemons that cost $4.20 : 4.20 / 0.6 = 7

Number of lemons that cost $9 : 9 / 0.60 = 15

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Answer:

Below

Step-by-step explanation:

The exterior angles for any polygon  sum to 360 °

so

 6 * n   = 360 °     <=====  where 'n' is the number of sides

 n = 60   sides

Answer:

He will need 64 ft of fencing

Step-by-step explanation:

To determine the amount of fencing, we need to find the perimeter.

P = 2 (l+w)  where l is the length and w is the width

P = 2(22+10)

P = 2(32)

P = 64

He will need 64 ft of fencing

Step-by-step explanation:

answer is in the picture

It looks like 1) adjacent angles.

The number of monthly payments required to pay off the loan of $128,000 at 4% interest is 232.48 which is equivalent to approximately 232 payments.

To determine the number of monthly payments required to pay off a loan, you can use the formula for loan amortization: n = (-log(1 - B/A * r)) / log(1 + r)

Where: n = number of monthly payments, A = loan amount ($128,000), B = monthly payment ($611.09), r = monthly interest rate (4% / 12 months = 0.0033)

The number of monthly payments for the loan is plugged and computed as:

n = (-log(1 - $128,000/$611.09 * 0.0033)) / log(1 + 0.0033)

n = (-log(1 - 0.0208)) / log(1.0033)

n = (-log(0.9792)) / log(1.0033)

n = 21.8068 / 0.093984

n = 232.48 payment.

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Answer:

Step-by-step explanation:

its 11

ignore bllllllllllldjbjddddddddddddddddddddddddd

The scale factor of dilation is 4/9

From the question, we have the following parameters that can be used in our computation:

The triangles

Given that the right is the scaled copy of the left

We have the following representation

Scaled factor = Right/Left

Substitute the known values in the above equation, so, we have the following representation

Scaled factor = 4/9

Hence, the scale factor is 4/9

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The completed two-column table that is used to prove the congruence of ∠BAD and ∠DCB indicates that the missing proof in step 6 of the table is substitution. The correct option is option B

B. Substitution

Congruent angles are angles that have the same measurement,

The two-column table is presented as follows;

[tex]{}[/tex]  Statements                                                           Reasons

1. ABCD is a parallelogram with diagonal [tex]\overline{AC}[/tex]  [tex]{}[/tex]     Given

2. [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and [tex]\overline{AD}[/tex]║[tex]\overline{BC}[/tex]  [tex]{}[/tex]                                Definition of a parallelogram

3. ∠2≅∠3, ∠1≅∠4   [tex]{}[/tex]                                           Alt. int. ∠s are ≅

4. m∠2 = m∠3 and m∠1 = m∠4 [tex]{}[/tex]                        Measures of ≅ ∠s are =

5. m∠1 + m∠2 = m∠4 + m∠2 [tex]{}[/tex]                             Addition prop. of equality

6. m∠1 + m∠2 = m∠4 + m∠3[tex]{}[/tex]                              Substitution

7. m∠1 + m∠2 = m∠BAD [tex]{}[/tex]                                    Angle addition property

m∠3 + m∠4 = m∠DCB

8. m∠BAD = m∠DCB [tex]{}[/tex]                                         Substitution

9. ∠BAD ≅ ∠DCB [tex]{}[/tex]                                             Angles are congruent if [tex]{}[/tex]    

[tex]{}[/tex]                                                                          their measures are the same

The missing reason in the partial proof is therefore;  B. Substitution

The abbreviations in the table are expanded as follows;

Alt. int. ∠s are ≅; Alternate interior angles are congruent

Measures of ≅ ∠s are =; Measures of congruent angles are equivalent

Addition prop. of equality; Addition property of equality

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On solving the provided question, we can say that  In decimals r = 3.8799 and d = 7.7598

Integer and non-integer numbers are οften expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded tο include non-integer values. Decimal notation is the name fοr the method used to represent numbers in the decimal system.

A decimal is a number with a whοle and a fractional component. Decimal numbers, which are in between integers, are used tο express the numerical value οf full and partially whole amounts.

the lengths (in inches) οf the radius and the diameter οf a circle with area 47.25 in'.

Area  = πr²

47.25 = 3.14 × r × r

r × r = 15.0541401274

In decimals

r = 3.8799

d = 7.7598

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Answer:

Step-by-step explanation:

Calculate the total hours used: We add up the hours used each year to find the total hours used:

2,800 + 1,400 + 1,500 + 2,500 + 2,300 + 2,000 = 12,500

Calculate the total depreciation: We subtract the residual value from the cost to find the total depreciation:

$219,000 - $19,500 = $199,500

Calculate the annual depreciation expense: We divide the total depreciation by the number of years to find the annual depreciation expense:

$199,500 / 6 = $33,250

Calculate the depreciation expense per hour: We divide the annual depreciation expense by the estimated total hours to find the depreciation expense per hour:

$33,250 / 12,500 = $2.66

So the depreciation expense per hour is $2.66.

Calculate the depreciation expense for each year: We multiply the hours used each year by the depreciation expense per hour to find the depreciation expense for each year:

Year 1: 2,800 * $2.66 = $7,448

Year 2: 1,400 * $2.66 = $3,724

Year 3: 1,500 * $2.66 = $3,990

Year 4: 2,500 * $2.66 = $6,650

Year 5: 2,300 * $2.66 = $6,118

Year 6: 2,000 * $2.66 = $5,320

So the depreciation expense for each year is:

Year 1: $7,448

Year 2: $3,724

Year 3: $3,990

Year 4: $6,650

Year 5: $6,118

Year 6: $5,320

Area of desert 1 is 18,000,000 square miles and area of desert 2 is 3,000,000 square miles.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Let A₁ and A₂ be the area of Desert 1 and Desert 2 respectively.

Given,

Area of a Desert 1 is six times the area of Desert 2.

A₁ = 6 A₂

The sum of their areas is 21,000,000 square miles.

A₁ + A₂ = 21,000,000

Substituting A₁ = 6 A₂ in A₁ + A₂ = 21,000,000 ,

6 A₂ + A₂ = 21,000,000

7 A₂ = 21,000,000

A₂ = 21,000,000 / 7

A₂ = 3,000,000 square miles

A₁ = 6 A₂

   = 6 × 3,000,000

   = 18,000,000 square miles

Hence the areas of each desert is 18,000,000 square miles and 3,000,000 square miles.

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6,000 grams is equivalent to 6 kilograms.

The problem is solved by converting the given dimensions from grams to kilograms. The conversion is from a smaller metric unit to a larger metric unit.

A kilogram is a larger unit of measurement for mass or weight compared to a gram.

The prefix kilo in kilogram means 1000, so one kilogram is equal to 1000 grams.

Therefore, to convert from grams to kilograms, you simply divide the number of grams by 1000.

In this case, 6,000 grams divided by 1000 equals 6 kilograms.

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Answer:

y=-2/3x-0.5

Step-by-step explanation:

y=mx+b is the equation for slopes so I used it and all I needed to find was the y-intercept, which is -0.5

Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.

Given :

percent distribution : 40% , 35% , 15% , 7% , 3%

Vehicles : 420

First, add the percentage of cars containing 3 people, 4 people, and 5 or more people:

15% + 7% + 3% = 25%

Thus, 25% of the cars contained at least 3 people, so use that to calculate the number of cars:

420 × 0.25 = 105 cars.

Hence , Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.

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Complete question:

A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the 420 vehicles that passed through the checkpoint yesterday morning.

How many of the 420 vehicles contained at least 3 people?

A. 42

B. 63

C. 105

D. 315