Alex has kept within his budget during this 4-week period! He also earned an extra $12 one week for cleaning his neighbor’s garage. If Alex wants to save the $10 he has left over every 4-week period, how much less time will it take for him to earn enough money for the shoes? Remember, the shoes cost $45.99 plus tax.

The decimal form of 2.998 x [tex]10^8[/tex] m/s is 29,980,000 m/s.

The number 2.998 x [tex]10^8[/tex] m/s represents the scientific notation of a very large number. It is a shorthand way of writing a number that is expressed as the product of a decimal number between 1 and 10 and a power of 10. In this case, the decimal number is 2.998 and the power of 10 is 8.

To convert this number to decimal form, we need to multiply the decimal number by 10 raised to the power of the exponent. So, we have:

2.998 x [tex]10^8[/tex] = 2.998 * 10,000,000

Multiplying 2.998 by 10,000,000, we get:

2.998 * 10,000,000 = 29,980,000

Therefore, the decimal form of 2.998 x [tex]10^8[/tex] m/s is 29,980,000 m/s.

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Answer:

f(-4) = 15

Step-by-step explanation:

A function is notated as f(x), because the x is the value you are putting in. For example. In f(x) = x + 5, the value you are putting in is x, and the output would be x + 5.

So in this case, we have f(x) = -7x-13. We are to figure out f(-4), so we can simply put in -4 as the x-value;

-7(-4) - 13

28 - 13

15

And so the value of f(-4) = 15

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Answer:

9

Step-by-step explanation:

f times 9 = 7x - 13 = 9 pls make me brianlist

After using the properties of logarithms to rewrite and simplify the logarithmic expression  ln((e⁸)/7) simplifies to 1.

What are natural logarithms?

Natural logarithms are a type of logarithm that uses the number e as its base. The natural logarithm of a positive number x (written as ln(x)) is the exponent to which e must be raised to get x. In other words, ln(x) represents the power to which e must be raised to obtain x.

The number e is a mathematical constant that is approximately equal to 2.71828. It is a special number that appears in many areas of mathematics, science, and engineering. Natural logarithms have a variety of applications in fields such as calculus, probability theory, and statistics.

Some properties of natural logarithms include:

ln(1) = 0

ln(e) = 1

ln(xy) = ln(x) + ln(y) for any positive numbers x and y

ln(x/y) = ln(x) - ln(y) for any positive numbers x and y

ln(xᵃ) = a ln(x) for any positive number x and any real number a

Natural logarithms can be evaluated using a calculator or by using the properties of logarithms to simplify expressions. They are commonly used in mathematical and scientific calculations that involve exponential growth or decay.

We can use the property of logarithms that states: log(aᵇ) = b log(a) for any base a and any real number b.

Using this property, we can rewrite ln((e⁸)/7) as:

ln((e⁸)/(e⁷))

[tex]= ln(e^{(8-7)})[/tex]

= ln(e)

= 1

Therefore, ln((e⁸)/7) simplifies to 1.

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A square is a base of a square​ pyramid.

A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called a vertex) is called a square pyramid. It is called a pentahedron, due to its five faces.

A square base and four triangles joined at the vertex make up a square pyramid. It has a square base and triangular side faces with a central vertex.

A square pyramid has three components.

Properties of a Square Pyramid:

Let's go through the attributes we looked at in the graphic above. The definition of a pyramid is the source of all these characteristics.

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Complete question:

what is a base of a square​ pyramid?

Answer:

128 in^2

Step-by-step explanation:

L * W

16 * 8 = 128 in^2

The amount of interest earned on Jenna's loan of $8000 for 15 years is $7200

The given variables and their values from the question are listed as follows:

Principal = 8000

Rate = 6%

Time = 15 years

The general formula to calculate simple interest is:

Simple interest = Principal * Rate * Time

By replacing the given values into the equation mentioned above, we obtain the subsequent expression

Simple interest = 8000 * 6% * 15

Evaluate the products in the expression

Simple interest = 7200

Hence, the amount of interest is $7200

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Complete question

Jenna borrows 8,000 for college at a yearly simple interest rate of 6 she takes 15 years

Determine the amount of interest

The perimeter of a table that is 3m long and 2m wide is 10m.

The perimeter includes the total lengths (2 lengths and 2 breadths) of the four sides or the total distance around the rectangle.

For a rectangle, the perimeter can be determined using the following formula:

Perimeter = 2(l + w)

Length of the table = 3m

Width of the table  = 2m

The perimeter of the table = 2(3 + 2)

= 10m

Thus, for a table that has lengths of 3 meters and width of 2 meters, the perimeter is 10 meters.

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The scale factor of dilation is 0.075 and the coordinates of F" are (0.9, 0.375)

The label of the triangle is added as an attachment

From the complete question, we have

DE = 12 units

Then, we have

D"E" = 0.9 units

Using the above as a guide, we have the following:

Scale factor = D"E"/DE

Scale factor = 0.9/12

Scale factor = 0.075

So, the scale factor of dilation is 0.075

This is calculated as

F = Scale factor * F

So, we have

F = 0.075 * (12, 5)

F = (0.9, 0.375)

The sine, cosine and tangent are calculated as

sin(D") = EF/DF

cos(D") = DE/DF

tan(D") = EF/DE

So, we have

sin(D") = 0.375/1 = 0.375

cos(D") = 0.9/1 = 0.9

tan(D") = 0.375/0.9 = 0.416

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Missing information in the question

Triangle DEF has coordinates D(0,0) E(12,0) F(12,5) and pictured is triangle D”E”F”.

DE = 0.9, EF = 0.375 and DF = 0.9

Answer:

the answer is -2

Step-by-step explanation:

Answer:

212,500

Step-by-step explanation:

One number that rounds to 213,000 when rounded to the nearest thousands is 212,500.

Answer:

Below

Step-by-step explanation:

Area of WHOLE rectangle = 9 x 6 = 54 units^2

 now subtract the area of the semicircle with radius 3

      whole circle is pi r^2    ( one-half of this is   1/2 pi r^2)

54 units^2 - 1/2 pi r^2

54 -  1/2 * pi * 3^2 = 39.9 units^2

Answer: The class average is 88, and Joey did better than 5 points more than the class average. Therefore, Joey's math test score is greater than 88 + 5 = 93.

So, the number sentence that represents Joey's math test score is:

D. 88 + 5 > J

Step-by-step explanation:

The polynomial equation 2x^(5)+6x^(4)-3x^(3)+x^(2)-9x-1=0 has 5 roots. This is because the degree of the equation is 5, and the number of roots of a polynomial equation is equal to its degree. Therefore, this equation has 5 roots. To find the roots of the equation, you can use the Rational Root Theorem, synthetic division, or other methods. However, finding the exact roots of a fifth-degree polynomial equation can be difficult and may require the use of a graphing calculator or computer software.

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Answer:

23.4 ft tall

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given: Distance from the flagpole = 14 ft

Angle of elevation θ = 74.4°

To find: Length of the flagpole

Answer:

tan(74.4°) = [tex]\frac{L}{14}[/tex]

L = 14 tan(74.4°) = 50.142 ft

So the length of the pole is 50.142 ft.

Answer: choose Answer B

Step-by-step explanation:

because if you flip the triangle back to what it was previously A B lines up with answer B so it’s B

Answer:

w ≈ 640 feet

Step-by-step explanation:

Let's call the distance from the hiker's position to the closest edge of the river "x", and the width of the river "w". We can use trigonometry to set up two equations involving these values:

In the first triangle, the angle of depression is 63 degrees, and the opposite side is x + w. Therefore, we can use the tangent function:

tan(63) = (x + w) / 1250

In the second triangle, the angle of depression is 61 degrees, and the opposite side is x. Therefore, we can use the tangent function again:

tan(61) = x / 1250

Now we can solve these equations for "w" and "x", respectively:

w = 1250 * tan(63) - x

x = 1250 * tan(61)

Substituting the second equation into the first:

w = 1250 * tan(63) - 1250 * tan(61)

Plugging this into a calculator, we get:

w ≈ 640 feet

Therefore, the width of the river is approximately 640 feet rounded to the nearest foot.

Alice needs to use 10.584 pounds of sugar for her jam recipe. This can be calculated using the conversion factor.

To convert 4.8 kg to pounds, we need to use the conversion factor of 1 kg = 2.205 pounds. This means that for every 1 kg, there are 2.205 pounds. To find out how many pounds are in 4.8 kg, we simply multiply 4.8 by 2.205.

The equation for this conversion is:

4.8 kg × 2.205 pounds/kg = 10.584 pounds

So, 4.8 kg is equivalent to 10.584 pounds.

Therefore, the correct answer is 10.584 pounds.

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The toothpicks she will use to make 90 squares in a straight line are 271. Squares can Kyra make if she has a box of 1,000 toothpicks are 333.

A total of 4 toothpicks are needed.

A total of 9 toothpicks are needed for further 3 squares.

So, the number of toothpicks needed to make 87 squares = [tex]\frac{87*9}{3}[/tex]

                                                                                                  = 261

Hence, the number of toothpicks needed to make 90 squares = [tex]261+10[/tex]

                                                                                                        = 271

The number of squares formed by 261 toothpicks = 87

So, the number of squares formed by 1000 toothpicks = [tex]\frac{996*87}{261} + 1[/tex]

                                                                                            = 333

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The simplified value of the expression "273- 8198- 274+ 8200 is 1.

A Numerical Expression is a combination of numbers and mathematical operations such as addition, subtraction, multiplication, and division that can be evaluated to a single numerical value.

We have to evaluate the expression 273 - 8198 - 274 + 8200, step by step,

Step(i) : We start with the leftmost operation, which is the subtraction of 8198 from 273.

⇒ 273 - 8198 = -7925

Step(ii) : Next, we have to subtract 274 from the result of the step(i) ,

⇒ -7925 - 274 = -8199

Step(iii) : We add 8200 to the result of the step(ii),

⇒ -8199 + 8200 = 1

Therefore, the simplified value is 1.

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Answer:

a) The height of the building is 382 feet.

b) The rock is 382 feet above the ground at its highest point.

c) It takes the rock 3.25 seconds to reach a height of 200 feet.

d) Tt takes the rock 4.76 seconds to hit the ground.

Step-by-step explanation:

The function that models the distance (in feet) between the rock and the ground t seconds after it is thrown is a quadratic function.

As the leading coefficient of the quadratic function is negative, it is a parabola that opens downwards.

The rock is thrown from the top of the building. Therefore, the height of the building is the value of d(t) when t = 0. This is the y-intercept of the graphed function.

Substitute t = 0 into the given function:

[tex]\begin{aligned}\implies d(0)&=-16(0)^2-4(0)+382\\&=0+0+382\\&=382\; \sf feet \end{aligned}[/tex]

Therefore, the height of the building is 382 feet.

The highest point of the rock is the height of the building, since the rock is thrown down from the top.

Therefore, the rock is 382 feet above the ground at its highest point.

This can be proven by finding the vertex of the graph of the function.

The vertex (maximum point) of the graphed function is (-0.125, 382.25).

As the x-value of the vertex is negative, and time can only be positive, the path of the rock is on a downwards trajectory when t ≥ 0. Therefore, the highest point is the point at which the rock is thrown.

To calculate how long it takes for the rock to reach a height of 200 feet, substitute d(t) = 200 into the given function and solve for t.

[tex]\begin{aligned}\implies -16t^2-4t+382&=200\\-16t^2-4t+182&=0\\-2(8t^2+2t-91)&=0\\8t^2+2t-91&=0\\8t^2+28t-26t-91&=0\\4t(2t+7)-13(2t+7)&=0\\(4t-13)(2t+7)&=0\\\\\implies 4t-13&=0 \implies t=\dfrac{13}{4}=3.25\; \sf s\\\implies 2t+7&=0 \implies t=-\dfrac{7}{2}=-3.5\; \sf s\end{aligned}[/tex]

As time is positive, t = 3.25 s only.

Therefore, it takes the rock 3.25 seconds to reach a height of 200 feet.

The rock will hit the ground when d(t) = 0.

Therefore, to calculate how long it takes for the rock to hit the ground, substitute d(t) = 0 into the given function:

[tex]\implies -16t^2-4t+382=0[/tex]

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Solve for t using the quadratic formula.

[tex]\implies t=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(-16)(382)}}{2(-16)}[/tex]

[tex]\implies t=\dfrac{4 \pm \sqrt{24464}}{-32}[/tex]

[tex]\implies t=-\dfrac{4 \pm \sqrt{16 \cdot 1529}}{32}[/tex]

[tex]\implies t=-\dfrac{4 \pm \sqrt{16} \sqrt{1529}}{32}[/tex]

[tex]\implies t=-\dfrac{4 \pm 4\sqrt{1529}}{32}[/tex]

[tex]\implies t=-\dfrac{1 \pm \sqrt{1529}}{8}[/tex]

[tex]\implies t=-5.01280...,4.76280...[/tex]

As time is positive, t = 4.76 s only.

Therefore, it takes the rock 4.76 seconds to hit the ground.

The structure has a 382-foot height. The rock's highest peak is 39 1/2 feet high, or 195.5 feet. The time it takes for the rock to touch the ground is roughly 6.289 seconds.

In arithmetic, we use angles and distance to determine an object's height. The distance between the items is measured horizontally, and the height of an object is determined by the angle of the top of the object with respect to the horizontal.

By setting t = 0, we can determine the rock's starting height:

d(0) = -16(0)^2 - 4(0) + 382

= 382

The highest point of the rock occurs at the vertex of the parabolic route, which is determined by the formula t = -b/2a

where a = -16 and b = -4.

t = -(-4) / 2(-16) = 1/8

d(1/8) = -16(1/8)^2 - 4(1/8) + 382

= 391/2

The equation d(t) = -16t^2 - 4t + 382 = 200 for t:

-16t^2 - 4t + 382 = 200

-16t^2 - 4t + 182 = 0

4t^2 + t - 45.5 = 0

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By using the slope-intercept form it can be concluded that:

The slope-intercept form of an equation is represented as follows:

y = mx + c    or     y - y₁ = m(x - x₁)  , where

m = slope

c = y-intercept

(x₁, y₁) = point on the line

The slope of the line when given two points can be calculated as follows:

m = (y₂ - y₁) / (x₂ - x₁)

1. Given f(2) = - 7 and f(6) = - 17. To find f(x), we need to use the slope-intercept form of a linear function: f(x) = mx + b. First, we need to find the slope of the line by using the two given points:

m = (y₂ - y₁) / (x₂ - x₁)

   = (f(x₂) - f(x₁)) / (x₂ - x₁)

   = (-17 - (-7)) / (6 - 2)

   = (-10) / (4)

   = -2.5

Now, we can plug in one of the points to find the y-intercept:

f(x) = mx + b

f(2) = (-2.5)(2) + b

 -7 = -5 + b

  b = -2

Therefore, the equation of the line is f(x) = -2.5x - 2.

2. To find the slope of the line passing through points A(6,3) and B(15,-3), we use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

   = (-3 - 3) / (15 - 6)

   = (-6) / (9)

   = -2/3

Therefore, the slope of the line is -2/3.

3. To find the equation of the line that contains point A(5,-3) and has slope m=3/5, we use the point-slope form of a linear function:

  y - y₁ = m(x - x₁)

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

 y + 3 = (3/5)x - 3

       y = (3/5)x - 6

Therefore, the equation of the line is y = (3/5)x - 6.

4. To find the equation of the line that contains the point A(4,-8) and is parallel to the graph of the function f(x)=1/4x+3, we know that the slope of the new line will be the same as the slope of the given function, which is 1/4. We can use the point-slope form of a linear function to find the equation of the new line:
  y - y₁ = m(x - x₁)

y - (-8) = (1/4)(x - 4)

 y + 8 = (1/4)x - 1

       y = (1/4)x - 9

Therefore, the equation of the line is y = (1/4)x - 9.

5. To find the zero of the function f(x) = 4x - 2, we need to set the function equal to zero and solve for x:

    f(x) = 0

4x - 2 = 0

     4x = 2

       x = 2/4

          = 1/2

Therefore, the zero of the function is x = 1/2.

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The percent notation is 55%.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentage is %. In order to convert a fraction to percentage notation, multiply by 100.

Percent notation = fraction that attended the wedding x 100

= 11/20 x 100 = 55%

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Answer:

Step-by-step explanation:

Angles in a quadrilateral add to 360°. So

[tex]60+80+120+x=360[/tex]   (where [tex]x[/tex] is the fourth angle)

[tex]260+x=360[/tex]  

[tex]x=100[/tex]°    (after subtracted 260 from both sides of equation)

The baker needs a total of 3 hours to decorate 4 1/2 cakes.

To decorate one cake, the baker needs 2/3 hour.

To find out how long it takes to decorate 4 1/2 cakes, we need to multiply the time for one cake by 4 1/2 i.e. 9/2

Time for 4 1/2 cakes = (2/3) x (9/2)

When the products are evaluated, we have

Time for 4 1/2 cakes = 3

So, the time taken is 3 hours

Therefore, the baker needs a total of 3 hours to decorate 4 1/2 cakes.

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Answer:

To find the height of the plane, we need to use trigonometry. Let's call the height of the plane "h". We can use the given angle of 57° and the opposite side (height) to the angle to find the adjacent side (distance traveled east) using the tangent function:

tan(57°) = h / distance traveled east

We can rearrange this equation to solve for h:

h = distance traveled east x tan(57°)

To find the distance traveled east, we need to use the given distance of 322 miles and the direction traveled. Since the plane is traveling at a 57° angle northeast, we can split this into two right triangles, one facing northeast and the other facing southeast, as shown below:

N

|

|

|\ 57°

|

\

The distance traveled east is the adjacent side of the southeast-facing right triangle, which can be found using the cosine function:

cos(57°) = distance traveled east / 322

We can rearrange this equation to solve for the distance traveled east:

distance traveled east = 322 x cos(57°)

Now we can plug in this value for the distance traveled east into the equation for the height of the plane:

h = distance traveled east x tan(57°)

h = (322 x cos(57°)) x tan(57°)

Using a calculator, we can evaluate this expression to find:

h ≈ 389.4 miles

Therefore, the height of the plane to the nearest mile is 389 miles.

A2: a. The four period moving average forecast method is a technique that is used to calculate the demand for a particular month based on the average demand for the previous four months. In this case, to calculate the demand for the month of April 2020, we will take the average of the demand for the months of December, January, February, and March. The formula for this method is:

Four period moving average forecast = (Demand for December + Demand for January + Demand for February + Demand for March) / 4

= (1,450 + 1,410 + 1,420 + 1,380) / 4

= 5,660 / 4

= 1,415

Therefore, the demand for the month of April 2020 is 1,415 loafs.

b. Based on the demand forecast for the month of April 2020, Al Artz Bakery should decide to maintain their current capacity as the demand is relatively stable and there is no significant increase or decrease in demand. This will ensure that they are able to meet the demand without overproducing or underproducing.

c. If the bakery calculated forecasts for all products it makes, the forecast would be more accurate than the one calculated for just one product. This is because it would take into account the demand for all products and would give a more comprehensive view of the overall demand for the bakery.

d. If the bakery decides to use qualitative methods, it could use sources of opinion such as customer feedback, expert opinion, and market research. These sources of opinion can provide valuable insights into the demand for the bakery's products and can help to improve the accuracy of the demand forecast.

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We have to, the polynomial [tex]y^{(2)}+49.[/tex] is not factorable.

The given polynomial is [tex]y^{(2)}+49.[/tex]

This polynomial is not factorable because there are no two numbers that can be multiplied together to give a product of 49 and a sum of 0.

In other words, there are no two numbers that can be multiplied together to give 49 and added together to give 0. This means that the polynomial is not factorable.

Therefore, the answer is "not factorable".

In conclusion, the polynomial [tex]y^{(2)}+49[/tex] is not factorable.

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The basis of the subspace of R4 defined by the equation3x1​−9x2​+2x3​−3x4​=0 is  {(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}

A basis of the subspace of R4 defined by the equation 3x1​−9x2​+2x3​−3x4​=0 can be found by solving the equation for one of the variables in terms of the others and then writing the general solution as a linear combination of vectors.

First, solve the equation for x1 in terms of the other variables:

3x1 = 9x2 - 2x3 + 3x4

x1 = 3x2 - (2/3)x3 + x4

Next, write the general solution as a linear combination of vectors:

(x1, x2, x3, x4) = (3x2 - (2/3)x3 + x4, x2, x3, x4)

= x2(3, 1, 0, 0) + x3(-2/3, 0, 1, 0) + x4(1, 0, 0, 1)

Finally, the basis of the subspace is the set of vectors that make up the linear combination:

{(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}

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In response to the query, we can state that Rounding to the nearest parallel lines hundredth, the value of x is approximately 4.89 inches. Therefore, the answer is not provided in the options.

In geometry, parallel lines are non-intersecting coplanar infinite lines. Parallel planes are ones that never intersect in a certain three-dimensional space. The term "parallel" refers to curves that have a fixed minimum distance between them and neither points of contact nor junction. In geometry, two lines are said to be parallel if they are in the same plane, equally spaced apart, and never intersect. Both horizontal and vertical can be used. Railroad tracks, columns of notebooks, and pedestrian crossings are examples of commonplace things that have parallel lines.  

A = (a + b)h/2

where a and b=lengths of the parallel sides of the trapezoid,

h =height

a = 550 in

b = 10 in

h = x in

A = (a + b)h/2 = (550 + 10)x/2 = 280x

And we know that the area of the trapezoid is 1,370 square inches:

A = 1,370

280x = 1,370

x = 1,370/280

x ≈ 4.89

Rounding to the nearest hundredth, the value of x is approximately 4.89 inches. Therefore, the answer is not provided in the options.

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Answer:

9x+30

Step-by-step explanation:

because form rule of like and unlike term