Multiply.

8×35

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Based on the width of the aluminum sheets and the angle of the edges, the depth that allows maximum cross-sectional area is 4 inches.

Assuming that the depth is x, the area would be:

= x (16 - 2x)

= 16x - 2x²

The maximum of the parabola is:

x = -b / 2a

= - 16 / (2 x -2)

= -16 / -4

= 4 inches

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Answer:

 [tex]\frac{(x+2)^2}{121} + \frac{(y-1)^2}{169} = 1[/tex]

Step-by-step explanation:

First, we identify that the vertices are vertical.
(an image below is attached if you want to see a visualization)
Therefore, the equation is such:

[tex]\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]

(h,k) is the center of the ellipse, which we could easily calculate by finding the midpoint between any pair of vertices.

This gets us (-2, 1)

Therefore, h = -2, k = 1

Now we want to find a,

we know the length of the major axis is 2a, and in this case, our length of the major axis is 26. So a = 13

Now we want to find b,

We know the length of the minor axis is 2b, and in this case, our length is 22, so b = 11

Now we will just plug in all the values and simplify to get our answer! B)

The inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3

The function is given as:

f(x) = 4^(x + 3) -2

Rewrite as:

y = 4^(x + 3) -2

Swap x and y

x = 4^(y + 3) -2

Add 2 to both sides

x + 2 = 4^(y + 3) -2 + 2

This gives

x + 2 = 4^(y + 3)

Take the logarithm of both sides

log(x  + 2)= log(4)^(y + 3)

Apply the base rule of logarithm

log(x  + 2)= (y + 3)log(4)

Divide both sides by log(4)

log(x + 2)/log(4) = y + 3

Apply the change of base rule of logarithm

log₄(x + 2) = y + 3

Subtract 3 from both sides

log₄(x + 2) - 3 = y + 3 - 3

Evaluate the difference

log₄(x + 2) - 3 = y

Rewrite as:

y = log₄(x + 2) - 3

Rewrite as:

f-1(x) = log₄(x + 2) - 3

Hence, the inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3

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❄ Hi there,

let us start by considering this: What should we do to get x all by itself?

Since it's

we should

So, let's start.

[tex]\sf{\dfrac{-x}{4}\times4 < 2\times4}}[/tex]

[tex]\sf{-x < -8}[/tex]

[tex]\sf{x > 8}[/tex]

When we divide both sides of an inequality by a negative number, we do "the inequality flip" and flip the inequality sign.

❄

The computation shows that the the hospital in-patient admission rate for the employees of the Prendergast Corporation is 104.5 admissions per 1000 employees.

The in-patient admission rate for Ramsey Manufacturing company = 100 admissions per 1000 employees.

It is given that the in-patient rate of Prendergast will be 10% higher than Ramsey's.

So, in-patient rate of Prendergast:

= 100 + 10% of 100

= 110 admissions

Now, it is also given that out of total in-patients, 5% are for tonsillectomies (which are not in-patient).

So, in-patient admission rate for Prendergast:

= 110 - 5% of 110

= 110 - 5.5

= 104.5 admissions per 1000 employees

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Complete question:

The hospital in-patient admission rate for employees of the Ramsey Manufacturing Company is 100 admissions per 1000 employees per year.

The Prendergast Corporation has older employees and is told that its hospital in-patient admission rate will be 10% higher than Ramsey’s. At the same time, however, all tonsillectomies will be done in the hospital’s outpatient department instead of requiring the patient to be admitted as an in-patient. Given that 5% of all in-patient admissions are for tonsillectomies, what is the hospital in-patient admission rate for the employees of the Prendergast Corporation?

A. 110.0 B. 115.0 C. 109.5 D. 100.0 E. 104.5 F. 117.0

The value of x from the figure is 70°

It is important to note that alternate angles are equal and angles in a triangle sum up to 180°

We then have that,

x + 50 + 60 = 180 °

x + 110 = 180°

Make 'x' subject

x = 180 - 110

x = 70 °

Thus, the value of x from the figure is 70°

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The company's current ratio is 2.6.

Current ratio is an example of a liquidity ratio. Liquidity ratios are financial ratios measure a firm's ability to honour its short terms obligations.

Current ratio = current asset /current liability

$65,000 / 25,000 = 2.6

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The time it takes between when the rock was dropped and when it landed is 1.33 seconds.

The time it takes the rock to land on the ground from where it is dropped can be determined by using the function given.

The height of the function when it hits the ground will be zero, so the function can be written as:

[tex]\mathbf{h(t) =36t^2 -64}[/tex]

[tex]\mathbf{0 =36t^2 -64}[/tex]

64 = 36t²

[tex]\mathbf{t^2 = \dfrac{64}{36}}[/tex]

t² =1.778

[tex]t = \sqrt{1.778}[/tex]

t = 1.333 seconds

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The mass of radioactive material remaining after 50 years would be 48.79 kilograms

It is important to note that half - life is the time it takes for the amount of a substance to reduce by half its original size.

Given the radioactive decay formula as

m(t)=120e−0.018t

Where

t= 50 years

m(t) is the remaining amount

Substitute the value of t

[tex]m(t) = 120e^-^0^.^0^1^8^(^5^0^)[/tex]

[tex]m(t) = 120e^-^0^.^9[/tex]

Find the exponential value

m(t) = 48.788399

m(t) = 48.79 kilograms to 2 decimal places

Thus, the mass of radioactive material remaining after 50 years would be 48.79 kilograms

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Answer:

Step-by-step explanation:

Hello : let A(0,-6) B(8,-8)

the slope is : (YB - YA)/(XB -XA)

(-8+6)/(8-0) = -2/8=-1/4

an equation is : y=ax+b a is a slope

y = (-1/4)x +b

the line through point A (0;-6) : -6 = (-1/4)(0)+b

b = -6            the equation is : y =(-1/)4x-6

Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.

Hence, option D is the correct answer.

Two angles are called complementary when their measures add to 90 degrees.

From the diagram; Angle ABD and Angle DBC are complementary angles that add up to make 90 degrees.

Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.

Hence, option D is the correct answer.

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Answer:

Well a sovial reason is that no one would no what order yo do it in, which would cause arguments

Answer:

without the order of operations, maths literally doesn't work.

Step-by-step explanation:

like whilst some equations don't rely on a particular order for solving, if you for example, don't solve brackets first, then try to multiply them by something else basically the equation breaks and you get the wrong answer. So... kids remember your BODMAS :)

Answer:

A' is (-2,-1)

B' is (3,0)

C' is (2,4)

Step-by-step explanation:

The total value of the investment is $107,032.16.

The total interest earned is $53,032.16

The inheritance would last the tenure of the university.

The formula that can be used to determine the future value of the 18-year annuity is: annuity factor x amount deposited yearly

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$3000 x [(1.075^18 - 1) / 0.075] = $107,032.16

Amount deposited in the course of 18 years = (3000 x 18) = 54,000

Interest earned = 107,032.16 - 54,000 = $53,032.16

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Answer:

True

Step-by-step explanation:

So this problem is asking whether Parametric because have an orientation and the short answer to that is that this is true. Parametric curves do have an orientation and we'll just do a little demonstration to share. Why? So let's take these very standard privatization of the unit circle where X is he going to cause of tea and why is equal to sign of tea now? The final part of defining the characterization is defining that the main range of tea on will take t to go from zero to two pi Andi, In this case, this is the this parts of circle going in this direction in the counter clockwise direction. And this is because as X as he goes from zero to play over two x decreases and signed increases on it sets us off on this direction as if that's one orientation off this curve of the circle. But we can alter this curve to get a different orientation. So if we were to take the Parametric equation given by X is equal to the co sign a minus T and why is equal to the sign of minus T in this case? Well again, take the domain to be from 0 to 2 pi. But because of the mind, the sign when it the mind sign doesn't actually affect X, it doesn't effect for co sign Well, it does affect the sign of minus T. So as T increases, the X value still decreases. But the Y value initially decreases as well, so this sets the arrows off on the clockwise direction. So this is another orientation off the same curve. So we've got two very different characterizations that describe the same physical curve. But because of the differences, the curve is constructed in opposite direction, and that is what the orientation defines. So it's very important to make sure that when you're drawing and describing the curve, you're parametric equations are in the correct orientation because otherwise you may encounter some difficulties later on. Because you'll be working with equation start that are, in fact, wrong

Thank you,

Eddie.

The possible temperatures are represented by (-∝, 29)

Let the high temperature be x

So, the statement can be represented as:

2x > 5x - 87

Subtract 5x from both sides

-3x > -87

Divide both sides by -3

x < 29

In interval form, we have (-∝, 29)

Hence, the possible temperatures are represented by (-∝, 29)

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The equation 2•x² + 4•y² + 8•x - 16•y + F = 0, at a value of F is the graph of an ellipse when we have;

a. A value of F that results in the equation of an ellipse is; F = 23

b. A point on the ellipse is ((-2), 2.5)

The equation of an ellipse can be presented as follows;

[tex] \frac{(x - h) ^{2} }{ {a}^{2} } + \frac{(y - k) ^{2} }{ {b}^{2} } = 1[/tex]

The given equation can be presented as follows;

2•x² + 4•y² + 8•x - 16•y + F = 0

Collecting like terms, gives;

2•(x² + 4•x) + 4•y² - 16•y + F = 0

Adding a constant value to both sides, we get;

2•(x² + 4•x + 4) + 4•y² - 16•y + 16 + F = 24

2•(x + 2)•(x + 2) + (2•y - 4)•(2•y - 4) + F = 24

2•(x + 2)² + 4•(y - 2)² + F = 24

2•(x + 2)² + 4•(y - 2)² + F - 23 = 24 - 23 = 1

When F = 23, we have;

2•(x + 2)² + 4•(y - 2)² + 23 - 23 = 1

Which gives;

[tex] \mathbf{\frac{(x + 2) ^{2} }{ \left( {\frac{1}{ \sqrt{2} }} \right)^{2}} + \frac{(y - 2) ^{2} }{ \left( {\frac{1}{ 2} } \right)^{2}} } = 1[/tex]

Where;

b) A point on the ellipse can be found as follows;

When x = -2

2•((-2) + 2)² + 4•(y - 2)² = 1

0 + 4•(y - 2)² = 1

y - 2 = √(1/4) = 1/2

A point on the ellipse is therefore;

When y = 2

2•(x + 2)² + 4•(2 - 2)² = 1

2•(x + 2)² + 0 = 1

2•(x + 2)² = 1

(x + 2)² = 1/2

x + 2 = √(1/2)

x = √(1/2) - 2

Another point on the ellipse is therefore;

((√(1/2) - 2), 0)

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Option C. The correct statement about spatial relationshipo is that Spatial terms such as above, below, behind, and under are used to describe objects in space.

These are the types of relationships that are used to relate objects to the location of somethings else. It makes use of words like under, above etc.

It is one of the knowledge that children need in the preoperational stage to learn how to use logical operations.

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The solution to the problem when [tex]46.3[/tex] divided by [tex]1.5[/tex]  the result of the division is [tex]30.8666667[/tex] in decimal form.

When a large number is distributed into small numbers of equal parts is called division.

The number [tex]1.5[/tex] is not a factor of [tex]46.3[/tex] ,  on dividing them the remainder is not zero.

Therefore,  first convert [tex]1.5[/tex] it into a whole number by multiplying it  [tex]10[/tex] so it becomes [tex]15[/tex] .

Then convert [tex]46.3[/tex]  it into a whole number by multiplying it by [tex]10[/tex] so it becomes [tex]463[/tex]

Here,  [tex]\dfrac{463 \times 10}{15 \times 10}[/tex] which results in [tex]\dfrac{463}{15}[/tex].

Now, divide [tex]\dfrac{463}{15}[/tex] ,  the result will be [tex]30.8666667[/tex].

The solution to the problem when [tex]46.3[/tex] divided by  [tex]1.5[/tex] the result is [tex]30.8666667[/tex].

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It would take 14 hours for all of them to paint the three houses.

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

Let t represent the time it would take them working together, hence:

(1/24 + 1/26 + 1/20 + 1/21 + 1/27)t = 3

t = 14 hours

It would take 14 hours for all of them to paint the three houses.

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X= root 6^2 + 10^2

X=2 root 34

So, x is 11.66 to 2d.p

(root means square root)

Hope this helps!

Answer:

x = 11.66

Step-by-step explanation:

Hello!

We can use the Pythagorean theorem to solve for the hypotenuse.

Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]

Plug the values of 6 and 10 into the formula to solve.

The hypotenuse is approximately 11.66.

When calculating the total area of this unknown figure, you should use (π - r²)/4 for the area of both the semicircle (half circle) and the larger square.

By critically observing this unknown figure, we can logically deduce that it comprises a semicircle, squares, a rectangle and a triangle. Thus, its total area should be calculated by adding the area of each of the geometric figures together.

Total area = A₁ + A₂ + A₃ + A₄

However, you should take note that the diameter of the semicircle (half circle) is equal to the side length of the larger square.

Area of a semicircle = πr²/4

Thus, the total area of both the semicircle (half circle) and the larger square is given by:

Area = πr²/4 - d²

Note: d = 2r

Area = πr²/4 - (2r)²

Area = πr²/4 - 4r²

Area = (π - r²)/4 sq. units.

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The amount of time between interest payments is know as period.

Period is the time between when interests are paid. Period can vary depending on the terms of the investment. Periods can be yearly, quarterly, semi-annually, biweekly or weekly.

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Answer:

-42

Step-by-step explanation:

Assuming you want the dot product,

(8)(-6)+(2)(3)= -42

Answer:

19

Step-by-step explanation:

4(4)+3

16+3=19

Answer:

19

Step-by-step explanation:

4x+3

4(4)+3

16+3

19

hope it helps

If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.

Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.

From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.

Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.

So,

length of arc LNM=Circumference of circle-length of arc LKM.

We know that length of an arc =Θr

in which Θ is the angle in radian.

length of arc=70*π[tex]/180*5[/tex]

=70π[tex]/36[/tex]

Circumference of circle=2π*5

=10π

Length of arc LNM=10π-70π[tex]/36[/tex]

=(360π-70π)[tex]/36[/tex]

=290π[tex]/36[/tex]

Put π=3.14

=290*3.14[tex]/36[/tex]

=910.6[tex]/36[/tex]

=25.29m

Hence the length of arc LNM is 25.29 m.

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The percentage of the can that is not occupied by tennis​ balls is 33.33%.

Given:

Radius of cylinder=3.4cm

First step

Height of cylinder=3.4×2×6

Height of cylinder=40.8 cm

Second step

Volume of cylinder=(3.4)^2×40.8

Volume of cylinder=471.648

Volume of tennis=6×4/3×(3.4)^3

Volume of tennis=314.432

Third step

Percentage=471.648-314.432/471.648×100

Percentage=33.33%

Therefore the percentage of the can that is not occupied by tennis​ balls is 33.33%.

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Step-by-step explanation:

38<4x+3+7-3x

4x+3+7>38

4x+3+7<3x

X>7

X<-10

= Ø

Answer:

20% increase

Step-by-step explanation:

To find the percent increase, use this formula

New value - original value

----------------------------------------

original value

114-95

-----------

95

19

---- = .2

95

.2 is 20%, so it is a20% increase