On his way out to meet a friend for lunch, David realized that his financial record was not up to date. He notices that he forgot to record three transactions. The first transaction was on August 2nd in the amount of $12.32, another transaction on that same day in the amount or $52.34, and finally a transaction on August 8th in the amount of $85.35. Determine David's balance carried forward for the 8th of August using the table below and the information provided. A check register. The Balance on August fifth is 1,049 dollars and 16 cents. a. $975.32 b. $899.15 c. $1,049.16 d. $848.84

Answer:

  4.478 cm

Step-by-step explanation:

You want the radius of a spool making 132 revolutions per minute when its tangential speed is 61.9 cm per second.

In one minute, the length of thread removed from the spool will be ...

  (61.9 cm/s) × (60 s) = 3714 cm

This represents 132 revolutions, so each revolution is ...

  (3714 cm)/(132 rev) = 28 3/22 cm/rev

This circumference is 2π times the radius:

  C = 2πr

  r = C/(2π) = (28 3/22 cm)/(2π) ≈ 4.478 cm

The radius of the spool is about 4.478 cm.

The simplified form of the given expression as required in the task content is; 8.

It follows from the task content that the simplified form of the given expression; -4 ( 2 - (³√8 × 6) ) / 5 is to be determined.

Therefore, By solving the innermost parentheses; we have;

-4 ( 2 - (2 × 6) ) / 5

= -4 ( 2 - 12 ) / 5

= -4 ( -10 ) / 5

= 40 / 5

= 8.

Therefore, the simplified form of the expression is; 8.

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The operation that has been performed on v to result in the vector that is shown is multiplication by -1.

The vector that is shown is (-2, -1). This can be obtained from vector v = (2, 1) by multiplying it by -1. Multiplying a vector by a negative number reverses its direction.

Multiplication of a vector by a number is performed component-wise. This means that each component of the vector is multiplied by the number. In the case of (-1) * (2, 1), each component is multiplied by -1. This results in the vector (-2, -1).

Here is the mathematical equation:

(-1) * (2, 1) = (-2, -1)

Therefore, the operation that has been performed on v to result in the vector that is shown is multiplication by -1.

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Answer:

2 + √[26] + √[50]

Step-by-step explanation:

To find the perimeter of a triangle with vertices given in the coordinate plane, we need to calculate the distance between each pair of vertices and then add them up.

Using the distance formula, the distance between the first two vertices is:

√[(x2 - x1)^2 + (y2 - y1)^2] =

√[(-4 - (-4))^2 + (1 - 3)^2] =

√[0 + 4] = 2

The distance between the second and third vertices is:

√[(x2 - x1)^2 + (y2 - y1)^2] =

√[(-5 - (-4))^2 + (-4 - 1)^2] =

√[1 + 25] = √[26]

Finally, the distance between the third and first vertices is:

√[(x2 - x1)^2 + (y2 - y1)^2] =

√[(-4 - (-5))^2 + (3 - (-4))^2] =

√[1 + 49] = √[50]

Therefore, the perimeter of the triangle is:

2 + √[26] + √[50]

This is the exact answer, and we cannot simplify it further.

Answer:

f(4) = 31

f(0) = 7

f(-1) = 1

Step-by-step explanation:

f(x) = 6x + 7

f(4) = 6(4) + 7

f(4) = 24 + 7

f(4) = 31

f(0) = 6(0) + 7

f(0) = 0 + 7

f(0) = 7

f(-1) = 6(-1) + 7

f(-1) = -6 + 7

f(-1) = 1

Answer:

2x - 2 = 0

Step-by-step explanation:

2(x - 1) = 5.0 - 2 - 3.0

2x - 2 = 5.0 - 2 - 3.0

2x - 2 = 0

Answer: 8

Step-by-step explanation:

We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.

We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8

The scale factor of dilation of the triangle is k = 8

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔDEF

where the measures of sides of ΔABC are

AB = 6 , BC = 6 and AC = 4

The measure of sides of triangle ΔDEF are

DE = 48 , EF = 48 and DF = 32

The scale factor of dilation k = measure of side DE / measure of side AB

k = 48 / 6

k = 8

Hence , the dilation factor is k =8

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If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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¿Aún necesitas ayuda? Podría intentar ayudar

Answer:

\( \frac{5}{6} \)

Answer:

R = 14 cm

A = pi R^2 = 3.14 " 196 = 616 cm^2

Answer:

0.0783

Step-by-step explanation:

The probability of getting the first success on xtg trial ; this is a geometric distribution :

P(x) = p(1−p)^x−1

The probability of being a universal donor , p = 0.15

The probability of obtaining someone who is a universal donor on 5th trial will be :

P(5) = 0.15(1 - 0.15)^(5 - 1)

P(5) = 0.15(0.85)^4

P(5) = 0.15(0.52200625)

P(5) = 0.0783009375

P(5) = 0.0783

The polynomial 11x⁵  + x⁴ - 4x³ - 5x² + 8 denotes the expression P - Q. The correct option is option A.

What is an expression?

A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression is (Math Operator, Number/Variable, Number/Variable)

Given polynomials are:

P = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5

Q = (2x² + 1) (4x² - 3)

Simplify the polynomial Q = (2x² + 1) (4x² - 3):

Q = (2x² + 1) (4x² - 3)

Q = 2x²(4x² - 3) + 1(4x² - 3)

Q = 8x⁴ - 6x² + 4x² - 3

Add like terms:

Q = 8x⁴ - 2x² - 3

Now calculate P + Q

P + Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 + 8x⁴ - 2x² - 3

Combine like terms:

P + Q = 11x⁵ + (9x⁴ + 8x⁴) - 4x³  + (- 7x² - 2x²) + 5 - 3

P + Q = 11x⁵ + 17x⁴ - 4x³ - 9x² + 2

Now calculate P - Q

P - Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 - (8x⁴ - 2x² - 3)

P - Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 - 8x⁴ + 2x² + 3

P - Q = 11x⁵  + (9x⁴ - 8x⁴) - 4x³ + (-7x² + 2x² )+ (5 + 3)

P - Q = 11x⁵  + x⁴ - 4x³ - 5x² + 8

Now calculate Q - P

Q - P =  8x⁴ - 2x² - 3 - (11x⁵  + 9x⁴ - 4x³ - 7x² + 5)

Q - P =  8x⁴ - 2x² - 3 - 11x⁵  - 9x⁴ + 4x³ + 7x² - 5

Combine like terms:

Q - P = - 11x⁵ + (8x⁴ - 9x⁴) + 4x³ + (- 2x² + 7x²) - 3 - 5

Q - P = - 11x⁵- x⁴ + 4x³ + 5x² - 8

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Answer:

Step-by-step explanation:

We have:

Substitute x and solve for y:

Find x:

Tom's speed is 12.5 mph

Carl's speed is 7.5 mph

Now

From eq(2)

From eq(1)

Adding these recent two

Putting in eq(1)

Answer:

4

Step-by-step explanation:

twice her age:

10*2 = 20

24-20 = 4

Answer:

4 i believe that's the answer

Using the cosine ratio, the distance between Dimitri and Sarah is calculated as approximately 12.4 m.

The cosine ratio is a trigonometric ratio that represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is calculated by dividing the length of the adjacent side by the length of the hypotenuse.

Using the cosine ratio, we have:

Reference angle (∅) = 72 degrees

Hypotenuse length = 40 m

Adjacent length = distance between Dimitri and Sarah = x

Plug in the values:

cos 72 = x/40

x = cos 72 * 40

x ≈ 12.4 [to one decimal place]

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Car Make and Model that i choose is Toyota RAV4

The Cost of this car as of today is about $27,000

To know the value of car after one year will be:

20% of $27,000

= $5,400.

So the car  value will be:

$27,000 - $5,400

= $21,600 after year 1

3.  Value of car after second year of ownership:

15% of $27,000

= $4,050.

So, the car  value will be:

$21,600 - $4,050

= $17,550 after year 2.

4 The Exponential Function If the car continues to decrease in value by 15% each yea will be

V(x) = 27,000 x (0.85)ˣ

V(5) = 27,000 x (0.85)⁵

= 27,000  x  0.44370

= $11979.9

Therefore, the value of the car after owning it for five years is  $11979.9

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See text below



Car Value: Exponential

1. Pick a car that you would be interested in buying someday. Research the cost of buying this car.

Car Make and Model:

Cost of this car as of today:

2. Cars depreciate in value over time, which means they lose a certain percent of their value each year. A car typically decreases in value by 20% within the first year. If the car you picked above decreased in value by 20% in its first year, how much will it be worth one year after owning it?

Value of car after one year:

3. Each year after the first year, a car typically decreases around 15% in value. How much will your car be worth after owning it for 2 years?

Value of car after second year of ownership:

4. If your car continues to decrease in value by 15% each year, write the equation of the exponential function that models its value x years after you purchased it.

Exponential Function:

Use your exponential function to calculate the predicted value of your car after you own it for five years.

Value after five years of ownership:

Answer:

632

Step-by-step explanation:

7 Days are in a week. 4,424 days total, 4,424 divided by 7 would equal 632

Answer:

4424/7=632 so there are 632 weeks.

Answer:

0.87%

Had to search diameter of Sun and Venus

Plz mark branliest

The statement given is true. When the bisector of an angle of a triangle bisects the opposite side, the is the triangle isosceles.

In the attached picture of ΔABC, we can see that AD is the bisector of ∠A that meets BC in D, so that BD = DC.

Now, we need to prove that AB = AC.

As construction, produce AD to E so that AD = DE, and then join CE.

So, in ΔABD and ΔECD, we have:

BD = CD

AD = ED

and ∠ADB = ∠EDC because those are vertically opposite angles.

Consequently, based on SAS congruence criterion, ΔABD ≅ ΔECD.

Thus, AB = EC and ∠BAD = ∠CED. And also, ∠BAD = ∠CAD.

For that reason, it means ∠CAD = ∠CED, and AC = EC.

Hence, AB = AC. It is proved that the triangle is isosceles.

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Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

The general solution for the equation 5tan(θ) - 6cos(θ) = 0 is:

θ = sin⁻¹(2/3) + nπ, where n is an integer.

To determine the general solution of the trigonometric equation 5tan(θ) - 6cos(θ) = 0, we can use algebraic manipulation and trigonometric identities to simplify and solve for θ.

Starting with the given equation:

5tan(θ) - 6cos(θ) = 0

First, we can rewrite the tangent function in terms of sine and cosine:

5(sin(θ)/cos(θ)) - 6cos(θ) = 0

Next, multiply through by cos(θ) to eliminate the denominator:

5sin(θ) - 6cos²(θ) = 0

Using the identity sin²(θ) + cos²(θ) = 1, we can express cos²(θ) as 1 - sin²(θ):

5sin(θ) - 6(1 - sin²(θ)) = 0

Expanding and rearranging terms:

5sin(θ) - 6 + 6sin²(θ) = 0

Rearranging the equation:

6sin²(θ) + 5sin(θ) - 6 = 0

Now, we have a quadratic equation in terms of sin(θ).

We can solve this quadratic equation by factoring or using the quadratic formula.

However, since this equation is not easily factorable, we will use the quadratic formula:

sin(θ) = (-b ± √(b² - 4ac)) / 2a

For our equation:

a = 6, b = 5, c = -6

Plugging these values into the quadratic formula and simplifying, we get:

sin(θ) = (-5 ± √(5² - 4(6)(-6))) / (2(6))

sin(θ) = (-5 ± √(25 + 144)) / 12

sin(θ) = (-5 ± √169) / 12

sin(θ) = (-5 ± 13) / 12.

This gives us two possible solutions for sin(θ):

sin(θ) = (13 - 5) / 12 = 8/12 = 2/3

sin(θ) = (-13 - 5) / 12 = -18/12 = -3/2

Since the range of the sine function is -1 to 1, the second solution (-3/2) is not valid.

Now, to find the values of θ, we can use the inverse sine function (sin⁻¹) to solve for θ:

θ = sin⁻¹(2/3)

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F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

Please see picture below.

Step-by-step explanation:

Answer:

Option b .

Step-by-step explanation:

Given that

The 13.6% represent the people living in property

There is a random sample of 489 people in that 16% of them would be in poverty

The significance level is 0.10

ANd, the p value is 0.085

We need to find out the conclusion

According to the attached options, we considered that there is enough evidence in order to support the claim that result in rise in the poverty rate

The slope of a line perpendicular to the line whose equation is 4x-3y=-3 is -3/4.

We have Equation

4x- 3y= -3

Writing the above equation in the from of slope intercept form

3y= 4x + 3

y= 4/3 x + 1

Here the slope of line is 4/3.

As, the slope of perpendicular line have product -1.

let the slope of perpendicular line is m.

So, m x 4/3 = -1

x = -3/4

Thus, the slope perpendicular line is -3/4.

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Answer:

5.25

Step-by-step explanation:

Using multiplication, if you do 4x5 you get 20, so adding .25 to the equation will add 1, therefore 20+1=21

So long story short 4 x 5.25 = 21