HELP! ASAP!
A box without a top is to be made from a rectangular piece of cardboard, with dimensions 4 in. by 8 in., by cutting out square corners with side length x and folding up the sides.

(a) Write an equation for the volume V of the box in terms of x.
(b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.

The length of the chord AB will be 6.08 cm

A chord of a circle is a section of a straight line whose ends both fall on an arc of a circle. A secant line, often known as secant, is a chord's infinite line extension. A chord is, more broadly speaking, a line segment connecting two points on any curve, such as an ellipse.

Given two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm

We have to find the length of chord AB drawn to smaller circle

Given:

PQ = 13 cm

R = 7 cm

r = 4 cm

The formula to find length of chord is as follow:

Length of chord = 2 x √(R²-d²)

Where,

R = radius of circle

D = Perpendicular distance from center of circle to chord

So,

PQ = 2 x √(R²-d²)

13 = 2 x √(7²-d²)

d = 2.59 cm

Now,

AB = 2 x √(r²-d²)

AB = 2 x √(4²-2.59²)

AB = 6.08 cm

Hence the length of chord AB will be 6.08 cm

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Step-by-step explanation:

easy how thick it is we need a picture

Answer:

the second option listed

(A = 53 degrees)

(a = 13.3)

(c = 16.6)

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse)

(cos = adjacent / hypotenuse)

(tan = opposite / adjacent)

For this question, you are provided an angle (37), and its opposite (10)

so, we can solve for either sin or tan first.

tan = opposite / adjacent

tan 37 = 0.7535540501

0.7535540501 = 10/a  [multiply by a]

0.7535540501a = 10 [divide by [0.7535540501]

a = 13.2704482163

rounded to the nearest tenth, a = 13.3

we know that the three angles shown here must add up to 180

so,

90 + 37 + A = 180

127 + A = 180

- 127           - 127

A = 53

--this is enough information to answer, but I will also solve side c to prove my answer

c = hypotenuse

a²+ b²=c²

[13.3]² + [10]² = c²

176.89 + 100 = c²

276.89 = c²

√276.89 = √c²

16.6400120192 = c

c = 16.6 (rounded to the nearest tenth)

**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer

The solution is  x ≈ 0.3 , Option A is the right Answer.

An Equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

To find the value of

22x = 5.3

A graph has to be plotted for the line

From the graph it can be clearly seen the point at which the line intersect x axis is  x = 0.24 , which is approx equal to 0.3.

Therefore the solution is  x ≈ 0.3 ,

Option A is the right Answer.

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Answer:

Yes, she passes with 80%

Step-by-step explanation:

4 divided by 5 = 0.8

0.8 multiplied by 100 = 80%

80% is greater than the required 75% needed to pass

Answer:

Yes

Step-by-step explanation:

First lets establish the key points

We know she needs 75% to pass and she gets 4/5 of the marks

Lets make 4/5 a decimal 4/5 X 2/2 is 8/10 better know as .8

.75 = 75%

.8 = 80%

80% > 75%

Meaning She PASSED!!!

The function can be best modeled by a linear regression and the values of a, b and c are -6, 100 and 240, respectively

From the table, we can see that as the number of years increases, the population increases.

This implies that the function can be best modeled by a linear regression.

A linear regression equation is represented by

ax + by = c

Next, we enter the data in a statistical calculator.

From the statistical calculator, we have the following summary:

The regression equation is then represented as:

y = bx + a

Where:

b = SP/SSX = 231.49/3937.5 = 0.05879

a = MY - bMX = 4.58 - (0.06*37.5) = 2.37952

So, we have:

y = 0.05879x + 2.37952

Approximate

y = 0.06x + 2.4

Multiply through by 100

100y = 6x + 240

Rewrite as:

-6x + 100y = 240

Hence, the values of a, b and c are -6, 100 and 240, respectively

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Answer:

The data is best modeled by an exponential function.

The value of a is 2.653, the value of b is 1.01, and the value of c is not used

Step-by-step explanation:

EDGE answers

The depth of the sea bed is 5104 fathom and 1.986 league

The bottom of an ocean , the ocean floor is called Seabed .

It is given that

The depth of a certain part of the Earth's seabed is 36,024 feet

The depth in fathom is given by =  depth in feet / 6

The depth in fathom is = 36024 / 6

= 5104 fathom

1 league = 6046.1 * 3 feet = 18138.1 feet

The depth in League (marine) = Depth in feet / 18138.1

The depth in League (marine) = 36024/18138.1

= 1.986 league

Therefore the depth of the sea bed is 5104 fathom and 1.986 league.

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The values of x and y such that AB is perpendicular to CD will be 19 and 14.5.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

AB and CD intersect at point E.

If measure angle AED equals 6x – 24 and measure angle CEB equals 4y + 32.

Then the values of x and y such that AB is perpendicular to CD will be

6x – 24 = 90

        6x = 114

          x = 19

Then we have

4y + 32 = 90

       4y = 58

         y = 14.5

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Answer:

(2a-b)(3c-d)

Answer:

already in standard form

Step-by-step explanation:

the equation of a quadratic in standard form is

y = ax² + bx + c ( a ≠ 0 )

y = x² + 4x + 3 ← is in standard form

with a = 1 , b = 4 , c = 3

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1=[tex]\frac{1}{2} *PQ*RM[/tex]

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2=[tex]\frac{1}{2} *SR*PN[/tex]

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1=[tex]\frac{1}{2}*PQ*h[/tex]

S2=[tex]\frac{1}{2}*SR*h[/tex]

Adding them together, we get the area of the whole trapezoid:

S=S1+S2=[tex]\frac{1}{2} (PQ+SR)h,[/tex]

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> [tex]A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}[/tex]

Simplifying, we have

=>[tex]A= \frac{ah+2b_{1+C} }{2}[/tex]

Factoring we have,

=> [tex]A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2} \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}[/tex]

 But, [tex]a+ b_{1} + c[/tex]  is equal to [tex]b_{2}[/tex], the longer base of our trapezoid.

Hence, [tex]A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}[/tex]

We have discussed two ways by which we can derive area of a trapezoid.

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By working with percentages we will see that the down payment is of $11,010 and the first monthly payment is of $275.25

First, the total cost is $110,100.

And we know that you initially pay the 10% of that, so the amount that you pay initially is:

P = 0.10* $110,100 = $11,010

So the down payment is of $11,010

The rest is financed over 30 years, so the rest is:

$110,100 - $11,010 = $99,090

Dividing by the number of months:

N = ( $99,090)/(30*12)  = $275.25

And there is an interest of the 9%, then the amount that you pay on month x is given by:

[tex]P(x) = $275.25*(1.09)^{x-1}[/tex]

Currently (on the first month, so x = 1)

Your pay will be of $275.25

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I don't even know Brian tanks

The amount of winning is more than amount of loosing. Then the amount of winning will be $3738.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be

E(X) = np

Suppose that you and a friend are playing cards, and you decide to make a friendly wager.

The bet is that you will draw two cards without replacement from a standard deck.

If both cards are spades, your friend will pay you $39.

Otherwise, you have to pay your friend $5.

If this same bet is made 623 times.

The maximum amount of winning will be

E(win) = np

We have

p = 0.25

n = 623

Then we have

E(win) = 0.25 × 623

E(win) = 155.75

Then the winning amount will be

WA = 155.75 × 39

WA = $6074.25

The maximum amount of loosing will be

E(loose) = np

We have

p = 0.75

n = 623

Then we have

E(loose) = 0.75 × 623

E(loose) = 467.25

Then the loosing amount will be

LA = 467.25 × 5

LA = $2336.25

Then the amount of winning will be

⇒ $ 6074.25 - $ 2336.25

⇒ $ 3738

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The number of customers I would have expected to win the prize is 6.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Based on the probability, the number of customers I would have expected to win: 0.18 x 300 = 36

How many more people I would have expected to win : 36 - 30 = 6

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The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]

Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]

Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.

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Answer:

29, 36, 38

Step-by-step explanation:

The pattern is add 7 then 2, then 7, then 2, then 7, then 2. You should get the hang of it. All you have to do is just do the same thing for the next three numbers.

The solution of the system of linear equation by substitution method is (3,1).

The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.

Given here the linear equations are

Equation 1: 6x+2y=20

Equation 2: 2x-3y=3

in equation 1 the value of y will be

6x+2y=20

⇒2y=20-6x

⇒y=(20-6x)/2

⇒y=10-3x

substituting the value of y in the equation 2, we will get

2x-3y=3

⇒2x-3(10-3x)=3

⇒2x-30+9x=3

⇒11x-30=3

⇒11x=30+3

⇒11x=33

⇒x=33/11

⇒x=3

putting the value of x in value of y in equation 1

y=10-3x

⇒y=10-3(3)

⇒y=10-9

⇒y=1

The solution of the system of linear equation by substitution method is (3,1).

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Answer:

take 1/2 multiply by sin 91°×2×8

Answer: A. -3.65

Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.

[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]

Knowing this, we can input it into the calculator and find the answer's sign.

[tex]-27.375/7.5=-3.65[/tex]

Therefore, the answer is A. -3.65.

I hope this helps! Pls mark brainliest!! :)

Answer:

A^32

Step-by-step explanation:

Done

Answer:

Option D:  a³²

Step-by-step explanation:

Powers in this case multiply, 8*4=32

therefore answer D a³² is correct

The graph is: On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5

A cubic function in mathematics is one with the formula f(x)=ax3+bx2+cx+d, where aneq 0 and the coefficients a, b, c, and d are complex numbers, and the variable x has real values. In other words, it is a real function as well as a polynomial function of degree three.

The function we have is:

y = ∛(x - 5)

So cubic root is given

Here we notice that when x = 0, we have:

y = ∛-5, this is the y-intercept

And when x = 5 we have:

y = ∛0 = 0 which is the x-intercept, and also the inflection point because here we have the change of sign.

Hence option which describes graph best is On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5

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Answer:A

Step-by-step explanation: Edge 2022

Answer:

[tex](x,y) = (5,-6)[/tex]

Step-by-step explanation:

[tex]\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\[/tex]

                     [tex]~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)[/tex]

[tex]\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\[/tex]

[tex]\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5[/tex]

[tex]y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6[/tex]

[tex]\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)[/tex]

Answer:

y = -2

(first option listed)

Step-by-step explanation:

a y-intercept is a point where the line crosses over the y-axis, which happens when x = 0.

So, the y-intercept is actually pretty each to find.

this is the easier way to find it:    {plug directly into equation given}

2x - 3y = 6

(set x equal to 0)

[0] - 3y = 6

(divide both sides by -3)

y = -2

but you might have seen/ learned to solve the equation like this {to actually find the equation of the line and solve from that}

[this method is helpful to know/practice for when equations for functions get more complex]

  2x - 3y = 6

      + 3y      + 3y           {add 3y to both sides}

  2x = 3y + 6

   -6          -6                {subtract 6 from both sides}

  2x - 6 = 3y

    ÷3      ÷3            {divide both sides by 3 to isolate y}

  [tex]\frac{2}{3}x[/tex] [tex]- 2 = y[/tex]                [flip sides of the equation]

 [tex]y=\frac{2}{3}x-2[/tex]  

set x equal to 0 (x = 0)

y = [tex]\frac{2}{3} (0)[/tex] - 2

y = 0 - 2

y = -2

So, the y-intercept is -2.

The expression represents the probability of getting exactly 3 heads is,

[tex]C(n,r)(0.5)^3(0.5)^6[/tex]

We have given

Aron flips a penny 9 times.

We have to determine

Which expression represents the probability of getting exactly 3 heads

The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.

The binomial probability formula shown has variables that represent:

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).

r is the number we want to find (here, we want the probability of 3 heads, so r = 3).

p is the probability of success (here, success means getting heads.

So, in a coin flip the probability of heads is always 1/2, so p = 1/2).

Therefore, The expression represents the probability of getting exactly 3 heads is;

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]

Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].

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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,

Probability (x≥3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰

= 0.5

Probability (x≤3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵

= 0.8125

Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

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Answer:

3y= 36×9x

3y=324x

y=324÷3

y=108 ans

Answer: Translate the graph of y=|x| 6 units to the right.

Answer:

Step-by-step explanation:

The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.

__

Let x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...

  0.15x +0.07(70000-x) = 9000

__

Simplifying the equation gives a 2-step linear equation.

  0.08x +4900 = 9000 . . . . simplified

  0.08x = 4100 . . . . . . . . . . subtract 4900

  x = 51,250 . . . . . . . . . . . .divide by 0.08

  70000 -x = 18,750

The woman should invest $51,250 at 15% and $18,750 at 7%.

A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

As 106.7 out of 100 gives 106.7% calculated below:

Percentage formula = (Obtained value/total value) x 100.......eq(1)

Putting values:

= (106.7/100) x 100

= 106.7%

Now finding 106.7% of 4:

Putting values in eq (1):

106.7% = (Obtained value/4) x 100

106.7/100= (Obtained value/4)    

1.067= (Obtained value/4)

4 x 1.067 = Obtained value

4.268 = Obtained value

Then 106.7% of 4 will be equal to 1.067 x 4  = 4.268

A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.

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