Bentley's family took a road trip to the Grand Canyon. Bentley fell asleep 59% of the way through the trip. If the total length of the trip was 300 miles, how many miles had they travelled when Bentley fell asleep?​

The worth of the share of stock is $[tex]34\frac{3}{4}[/tex].

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.

A mixed fraction is a fraction that is made up of a whole number and a proper fraction.  A proper fraction is a number where the numerator is less than the denominator.

The worth of the stock now = purchase price + increase in the share price

28 1/8 + 6 5/8

[tex]34 \frac{1 + 5}{8}[/tex]

[tex]34\frac{6}{8}[/tex] = [tex]34\frac{3}{4}[/tex]

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Answer: the first one and the third one

Step-by-step explanation:

The prime polynomials from the polynomials are:

1. [tex]x^4[/tex] + 3y²x - 1 and 3. x² - 9x + 3.

Options 1 and 3 are the correct answer.

We have,

A prime polynomial is a polynomial that cannot be factored into a product of two polynomials with integer coefficients.

Let's check each expression to see if it is a prime polynomial:

[tex]x^4[/tex] + 3y²x - 1:

This expression cannot be factored further, so it is a prime polynomial.

9y + 4y² + 12y³:

This expression can be factored as y(9 + 4y + 12y²), so it is not a prime polynomial.

x² - 9x + 3:

This expression cannot be factored further, so it is a prime polynomial.

x² - 3x - 10:

This expression can be factored as (x - 5)(x + 2), so it is not a prime polynomial.

x³ - 512y³:

This expression can be factored as (x - 8y)(x² + 8xy + 64y²), so it is not a prime polynomial.

Thus,

The prime polynomials are:

1. [tex]x^4[/tex] + 3y²x - 1 and 3. x² - 9x + 3.

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Answer:

31. (98,765 x 9) + 3 = 888,888

32. (12,345 x 9) + 6 + 111,111

33. 3367 x 15 + 50,505

34. 15,873 x 28 = 555,555

35. 33,334 x 33,334 = 1,111,155,556

36. 11,111 x 11,111 = 123,454,321

41. 3 + 9 + 27 + 81 + 243 = 3(243 -1) / 2

42.  1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6

Conjecture -> solve these problems and see if they are equal on both ends

EX:  3 + 9 + 27 + 81 + 243 ->  363

       3 x 242 = 726 -> 726/2 = 363

Verified

Answer:

  67.5 cm²

Step-by-step explanation:

The figure can be decomposed into figures whose area formulas you know.

As the attached figure shows, one way to decompose the figure is by extending the horizontal line. This divides the figure into an upper trapezoid and a lower rectangle.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

where b1 and b2 are the parallel bases, and h is the height.

The bases of the trapezoid in this figure are 6 and 3 cm, and the height is 5 cm. Its area is ...

  A = 1/2(6 cm +3 cm)(5 cm) = 22.5 cm²

The area of a rectangle is given by the formula ...

  A = LW

where L and W represent the length and width, respectively.

The dimensions of the rectangle in this figure are 15 cm long by 3 cm wide. Its area is ...

  A = (15 cm)(3 cm) = 45 cm²

The total area of the figure is the sum of the areas of the trapezoid and rectangle:

  A = (22.5 cm²) + (45 cm²) = 67.5 cm²

The are of the figure is 67.5 cm².

Answer:

(-3,1)

Step-by-step explanation:

9x+8y=-19

7x+9y=-12

I'll assume the question is to find the solution to these equations.  The solution will be the point (x,y) where the two lines intersect.  The intersection is the one point that satisfies both equations (the smae value of (x,y) works in both.

We can either solve matematically of graph to find the intersection.  I'll do both, and hope the answers are identical.

Matematically

Rearrange either equation to isolate one of the variables (either x or y).  I'll take the second and isolate x:

7x+9y=-12

7x = -9y - 12

x = (-9y - 12)/7

Now use this definition of x in the other equation:

9x+8y=-19

9((-9y - 12)/7) + 8y = -19

(-81y - 108)/7 + 8y = -19

-81y - 108 + 56y = - 133

-25y = -25

y = 1

If y = 1, then:

9x+8y=-19

9x+8(1)=-19

9x = -27

x = -3

The solution is (-3,1)

Graphing

Graph both lines and look for the intersection.  The attached graph shows the lines cross at (-3,1).

The solution, bu both approachjes, is (-3,1)

The domain of f(x) = √(x - 7) +9 is x ≥ 7 and the range of f(x) = √(x - 7) +9 is y ≥ 9

The function is given as:

f(x) = √(x - 7) +9

Set the radicand greater than or equal to 0

x - 7 ≥ 0

Add 7 to both sides

x ≥ 7

The above represents the domain

Set the radicand to 0

f(x) = 0 +9

So, we have

f(x) = 9

This represents the minimum value of the range.

So, the range is y ≥ 9

Hence, the domain of f(x) = √(x - 7) +9 is x ≥ 7 and the range of f(x) = √(x - 7) +9 is y ≥ 9

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Answer:

Step-by-step explanation:

Its A

The area that the dog can wander based on the information provided will be 931π.

From the information, we are told that the dog dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet.

In this case, the dog is in an outside corner. The dog can trace 3/4 of a circle when it starts walking in a circle away form the wall.

The area that the dog can wander will be:

= 3/4(π35²) + 1/4(π(35 - 28)²)

= 3/4π(35)² + 1/4π(7)²

= (3/4 × 1225)π + (1/4 × 49)π

= 918.75π + 12.25π

= 931π

Therefore, the area that the dog can wander based on the information provided will be 931π.

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Step-by-step explanation:

180(n-2)/n =157.5

180n -360/n=157.5

Cross multiplying

180n -360=157.5n

180n-157.5n=360

22.5n=360

22.5n/22.5=360/22.5

n=16, the number of sides the polygon has is 16

Answer:

a) height =14in

b) height =27cm

Step-by-step explanation:

a)

[tex]v = \frac{l \times w \times h}{3} [/tex]

where,

Substitute these values and solve for h.

[tex]h = 3 \frac{v}{lw} \\ h = 3. \frac{448}{8.12} = 14[/tex]

b)

[tex]v = \frac{1}{3} ah[/tex]

where, a=area of the base

plug in the given values and solve for h

[tex]v = \frac{1}{3} ah \\ 3v = ah \\ h = \frac{3v}{a} \\ h = \frac{3(270)}{30} \\ h = 27cm[/tex]

Answer:

look above

Step-by-step explanation:

hope it helps

Step-by-step explanation:

4 pictures correlate to 1/3 page.

how many 1/3 pages do we need to get 1 full page ?

3, as 3 × 1/3 = 3/3 = 1.

so, to keep the ratio, we need to multiply also the pictures by 3 and get

4×3 = 12 pictures per page

The volume of the total chocolate is 80 ml, where as the volume of each chocolate is 13.33 ml.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the volume of each chocolate. Hence:

6 * volume of each chocolate = (380 - 300) ml

6x = 80

Divide both sides of the equation by 6:

x = 13.33 ml

The volume of the total chocolate is 80 ml, where as the volume of each chocolate is 13.33 ml.

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Step-by-step explanation:

there are some formulas to know about this.

I am sure you discussed this in class.

when 2 lines (originating from the same point) cut through the same circle creating some circle segments (such lines are also called Secants), then there is a relationship in the lengths of the different parts of the lines among themselves.

the outer portion of such a line multiplied with the length of the whole line to the second point it intersects the circle is the same for every secant from the same point through the same circle.

that means in our case :

7(x - 6) = 6(x - 3)

7x - 42 = 6x - 18

x = 24

and so,

EG = (x - 3) + 6 = (24 - 3) + 6 = 21 + 6 = 27

Answer:

301.5936 cubic ft

Step-by-step explanation:

Formula for the volume of a cylinder is V = pi*r*r*h, where r represents the radius and h represents the height of the cylinder. Since radius is half the length of diameter, the pipe has a radius of 4/2 = 2 ft.

V = pi*r*r*h = 3.1416*2*2*24 = 301.5936 cubic ft

Answer:

6

Step-by-step explanation:

Original Equation

(n-1)!

Plug in 4 as n

(4-1)!

Subtract

(3)!

Rewrite using definition of factorial: [tex]a! = a*(a-1)*(a-2)....*1[/tex]

3! = 3*2*1

You don't really have to write the 1, since it doesn't change the value

6

the equation that we can solve using the given system of equations is:

3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0

Here we have the system of equations:

y = 3x^5 - 5x^3 + 2x^2 - 10x + 4

y = 4x^4 + 6x^3 - 11

Notice that both x and y should represent the same thing in both equations, then we could write:

3x^5 - 5x^3 + 2x^2 - 10x + 4 = y = 4x^4 + 6x^3 - 11

If we remove the middle part, we get:

3x^5 - 5x^3 + 2x^2 - 10x + 4  = 4x^4 + 6x^3 - 11

Now, this is an equation that only depends on x.

We can simplify it to get:

3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0

That is the equation that we can solve using the given system of equations.

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Answer:

each bottle of juice costs $2.04

Step-by-step explanation:

we first need to minus the cost of chips so we can focus on just the price of the juice bottles.

51.23-2.27

=48.96

this gives the total cost of all 24 bottles but we need the cost of just one, so we divide 48.96 by 24.

which gives us our answer of $2.04 per bottle.

Answer: 4

Step-by-step explanation:

2.03 / 7 = 0.29

1.16 / 0.29 = 4

Mason will get 4 oranges on spending 1.16$

What is Rate of change?

A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.

Here it is given that a grocery store sells a bag of 7 oranges for $2.03,

Now firstly let calculate for 1$ how many oranges Mason get by dividing 7 with 2.03$ :

For 1$ we get = 7/2.03 = 3.5 oranges

Therefore to calculate for 1.16 $ amount spend by Mason will be multiplication of 3.5 with 1.16$ : 3.5 x 1.16 = 4 oranges

Therefore, Mason will get 4 oranges on spending 1.16$

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The time he saves when walking diagonally is 8 seconds

A rectangle has opposite sides equal to each other.

The angles are equal.

Therefore,

perimeter of a rectangle = 2l + 2w

where

Therefore,

distance of the diagonal  =√ 50² + 120²

distance of the diagonal  = √2500 + 14400

distance of the diagonal = √16900

distance of the diagonal = 130 feet

distance if he follows the length of the rectangle = 50 + 120 = 170 feet

Hence,

Time spent diagonally

5 = 130 / t

t = 130 / 5

t = 26 seconds

Time spent along the perimeter

5 = 170 / t

t = 170 / 5

t = 34 secods

Therefore,

Time he will save by walking diagonally = 34 - 26 = 8 seconds

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Answer:

8000/100+80/100=80+0.8=80.8

Step-by-step explanation:

hope this helps (❁´◡`❁)

Answer:

Step-by-step explanation:

Use the distributive property.

Distributive property is a serving to distribute or allot or disperse.

Distributive property:

A(B+C)=AB+AC

A(B-C)=AB-AC

-10(1-9x)+6(x-10)

Expand.

-10(1-9x)

-10*1=-10

-10*9x=90x

[tex]\longrightarrow \sf{=-10+90x+6\left(x-10\right)}}[/tex]

6(x-10)

6*x=6x

6*10=60

6x-60

Rewrite the problem down.

= -10+90x+6x-60

Combine like terms.

90x+6x-10-60

Add the numbers from left to right.

90x+6x=96x

96x-10-60

Finally, subtract the numbers from left to right.

-10-60=-70

[tex]\Longrightarrow \boxed{\sf{96x-70}}[/tex]

Therefore, the final answer is 96x-70.

I hope this helps, let me know if you have any questions.

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Distributive Property :

[tex]-10(1-9x)+6(x - 10)[/tex]

[tex]-10(-9x+1)+6(x - 10)[/tex]

[tex]90x-10+6x-60[/tex]

[tex]90x-70+6x[/tex]

[tex]96x-70[/tex]

[tex]answer : \boxed{\pink\star\tt{96x-70}}[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━

Common factor :

[tex]- 10(1 - 9x) + 6(x - 10)[/tex]

[tex]96x - 70[/tex]

[tex]2(48x - 35)[/tex]

[tex] answer : \boxed{ \pink \star\tt{2(48x - 35)}}[/tex]

In the case above:

(a) If there is an increased from 64 to 196, then the variance decreases.

(b) If there is a decreased from 784 to 49, then the variance increases.

Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.

Since the standard error takes place in the denominator, hence, if the standard error increases, the variance goes up.

Therefore, In the case above:

(a) If there is an increased from 64 to 196, then the variance decreases.

(b) If there is a decreased from 784 to 49, then the variance increases.

See full question below

A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?

What is the variance about?

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Answer: Read below.

Step-by-step explanation: To recognize the domain of a graph, you have to find out what points does the graph cross the x-axis? For example, consider the equation, y = x. The domain for this graph is all real numbers, or (-∞, ∞). This is because, the graph goes infinitely forever, and eventually hits every single number in the x-axis. This is true for every single linear graph in the form y = mx + b or ax + by = c. However, in a graph that is an inequality, like let's say, x < 4, then there will be an open dot on 4, and the graph will go to the left infinitely, hitting every single number in the negative x-axis eventually. The interval for this would be (-∞, 4).

The range is as easy as the domain to figure out. Instead of all the values that the graph goes on the x-axis, we need to find all the values that the graph goes on the y-axis. Again, for a linear graph in the form y = mx + b or ax + by = c, the range is also (-∞, ∞). For an inequality though, like y ≥ 2, the graph would have a closed plot on 2 in the y-axis, and go infinitely in the direction of the right, hitting every single y value after 2 eventually. The interval would be [2, ∞).

The axis of symmetry can only be found in parabolas. In parabolas, the axis of symmetry is an invisible vertical or horizontal line (depending on if your parabola is sideways or not.) The invisible line cuts through the vertex of the parabola, or the center of the parabola, and splits it into two even and equal pieces. Thus, the axis of symmetry will always be the x-coordinate of the parabola if upwards or downwards, or the y-coordinate of the parabola if sideways.

Hope this helped!

The curve pass through the y-axis at the coordinate point (0, 10) showing that the y-intercept of the function is (0, 10)

The graph of a polynomial function is a smooth continuous curve. The point where the curve intersects the x-axis is the zero of the polynomial.

A polynomial is also known to have a degree of 3 and above. Hence the given polynomial has a leading degree of 3 and expressed as:

f(x)=−x^3+x^2+9x−9

The graph of the function is as plotted below. From the function, you can see that the curve pass through the y-axis at the coordinate point (0, 10) showing that the y-intercept of the function is (0, 10)

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Answer:

  (b)  96 inches

Step-by-step explanation:

The perimeter of the board is the sum of its four edge lengths.

Each edge of the board is indicated as being 8 squares long. Each square is 3 inches on a side, so the edge of the board is ...

  8 × (3 in) = 24 in . . . . board edge length

The perimeter of the board is 4 times the length of one edge, so is ...

  P =4s = 4(24 in) = 96 in

The perimeter of Edgar's checkerboard is 96 inches.

__

The perimeter of one small square on the board is ...

  P = 4s = 4(3 in) = 12 in

The whole board is a dilation of one square by a factor of 8. Its perimeter will be ...

  P' = (scale factor) × P

  P' = 8×(12 in) = 96 in

The perimeter of Edgar's checkerboard is 96 inches.

Answer:

13cm

Step-by-step explanation:

Given the map scale:

1cm on the map : 4km actual distance

4km actual distance : 1cm on the map

1km actual distance : [tex]\frac{1}{4} =0.25cm[/tex] on the map

Therefore,

52km actual distance = 0.25 * 52 = 13cm

Answer: -4, -3, -2

Step-by-step explanation:

By inspection, we know [tex]x=-2[/tex] is a root.

We can thus rewrite the equation as

[tex](x+2)\left(\frac{x^3 + 9x^2 + 26x+24}{x+2} \right)=0\\\\(x+2)(x^2 + 7x+12)=0\\\\(x+2)(x+3)(x+4)=0\\\\x=-4, -3, -2[/tex]

Answer:

The correct answer is 2 [tex]\frac{2}{5}[/tex].

Step-by-step explanation:

To get this answer, we first have to add the numerators.

We can easily say that 4 + 8 = 12

That leaves us with the improper fraction, [tex]\frac{12}{5}[/tex].

To make this fraction proper, we must first find out how many times 5 can go into 12.

5 can go into 12 two times which leaves us with 2 left over from the numerator.

Now all that's left to do is add 2 (the amount of times 5 can go into 12) and [tex]\frac{2}{5}[/tex] (the left over fraction) to get the answer 2[tex]\frac{2}{5}[/tex].

Hope this helps:) Goodluck!

The exponential growth rate is obtained as 0.1099.

Now we know that an exponential function has to do with an exponential increase or decrease. An exponential function could increase or decrease and this means that the constant of the function could be a decay constant or a growth constant.

When we have an exponential function, we have to apply the general formula; P(t) = P(o)e^rt

Po = initial number

P(t) = number at time t

r = rate of growth

t = time taken

Thus;

270=90e^10r

270/90 = e^10r

3 = e^10r

ln3 = 10r

r = ln3/10

r = 0.1099

After 13 hours;

P(t) = 90e^(0.1099 * 13)

P(t) = 376

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No. When we reject the null, we can only conclude that the observed distribution differs from the expected distribution.

No. When we reject the null, we can only conclude that the observed distribution differs from the expected distribution.

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No, we can only suppose that the observed distribution deviates from the expected distribution when we reject the null hypothesis.

The null hypothesis exists as a specific mathematical theory that claims that there exists no statistical relationship and significance between two sets of observed data and estimated phenomena for each set of selected, single observable variables. The null hypothesis can be estimated to define whether or not there exists a relationship between two measured phenomena, which creates it useful. It can let the user comprehend if the outcomes exist as the product of random events or intentional manipulation of a phenomenon.

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