A packing box is a rectangular prism with volume 2 m3.
The box is 250 cm long and 100 cm wide. How tall is the box?

The intervals that are equivalent to each inequality are given as follows:

The interval notation of an inequality of lower bound a and upper bound b is given as follows:

(/[a,b]/).

The closing notation can be in either parenthesis or brackets, as follows:

For the first interval, 2 < x ≤ 5, it is an open interval at the lower bound of 2 and closed at the upper bound of 5, hence the notation is given as follows:

(2,5].

For the second interval, x > 7, we have that it has only a lower bound of 7, which is open. Hence, the upper bound is of infinity, and an infinite bound is always open, hence the notation is given as follows:

(7, ∞).

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Answer:

$45

Step-by-step explanation:

Answer:

50 grams

Step-by-step explanation:

36 grams = 72%

→ Find 1% by dividing both sides by 72

0.5 grams = 1%

→ Times both sides by 100 to find 100%

50 grams = 100%

Answer:

Step-by-step explanation:

The equation for a parabola is of the form y = ax^2 + bx + c, where a, b, and c are constants. The graph of a parabola is a U-shaped curve that is symmetrical about a line called the axis of symmetry.

In the equation (x-1)^2 = y+2, we can rewrite it as y = (x-1)^2 - 2. This is the standard form of a parabola with a = 1, b = 0, and c = -2.

The vertex of the parabola is the point on the graph where the parabola reaches its highest or lowest point. For a parabola in standard form, the vertex is always of the form (h,k), where h and k are the values of x and y, respectively, at the vertex. The vertex of this parabola is (1,-2).

The axis of symmetry of the parabola is a line that divides the parabola into two mirror images. For a parabola in standard form, the axis of symmetry is always the line x = h, where h is the value of x at the vertex. The axis of symmetry of this parabola is the line x = 1.

The directrix of a parabola is a line that is used to define the parabola. For a parabola in standard form, the directrix is always the line y = k + p, where k and p are constants and p is the distance from the vertex to the directrix. The directrix of this parabola is the line y = -2 + p, where p is the distance from the vertex to the directrix.

The focus of a parabola is a point on the axis of symmetry that is used to define the parabola. For a parabola in standard form, the focus is always the point F(h,k+p), where h and k are the values of x and y, respectively, at the vertex, and p is the distance from the vertex to the directrix. The focus of this parabola is F(1,-2+p), where p is the distance from the vertex to the directrix.

To sketch the graph of this parabola, we can start by plotting the vertex at (1,-2). Then we can draw the axis of symmetry, which is the line x = 1. Next, we can choose a value for p and draw the directrix y = -2 + p. Finally, we can use the vertex and focus to plot points on either side of the axis of symmetry, and connect these points to form the U-shaped curve of the parabola.

[asy]

unit size(1cm);

real p = 1.5;

pair F, V;

F = (1,-2+p);

V = (1,-2);

draw((-2,0)--(4,0));

draw((0,-4)--(0,4));

draw((-2,V.y)--(4,V.y),dashed);

draw((F.x,p)--(F.x,-4),dashed);

label("$x$", (4,0), E);

label("$y$", (0,4), N);

label("$y = (x - 1)^2 - 2$", (4,-3), E);

a dot("$F$", F, NW);

a dot("$V$", V, S);

label

Answer:

D. The m<4 is 137°

[tex] < 4 = 180 \degree - 43 \degree \\ < 4 = 137 \degree[/tex]

Answer:

[tex]\displaystyle x < \frac{12}{7}[/tex]

Step-by-step explanation:

This is an inequality, not an equation. Notice the sign is a "less than" sign and not an "equal" sign. You still solve it like a normal equation, however:

[tex]\displaystyle 7x-2 < 10\\\\\rightarrow 7x < 12\\\\\rightarrow x < \frac{12}{7}[/tex]

Answer: the exact answer is 9/4, the mixed number is  2 1/4

Step-by-step explanation:

The value of x and y in triangles AEB and BCD is 40° and 50°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is 180°.

Therefore, In ΔAEB,

(2x + 5)° + 50° + 45° = 180°.

2x + 100° = 180°.

2x = 180° - 100°.

2x = 80°.

x = 40°.

Now, ΔBCD,

x + y + 90° = 180°.

40° + y + 90° = 180°.

y = 180° - 130°.

y = 50°.

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Darnell's constant speed, as determined by the solution, is 20 miles per hour.

It covers linear transformations more broadly as well as vectors, matrices, and vector spaces. One area of mathematics is linear algebra. In comparison to other areas of mathematics that are frequently driven by innovative ideas and unresolved problems, linear algebra is a discipline that is very well understood.

Distance=8 miles

Time taken is=32 minutes

speed=distance/time

speed=15 miles/hour

Darnel has travelled a distance of 1.5x5/60=0.125 miles in under five minutes.

Hector bicycle speed = distance/time

hector speed of bike=  20 miles/hour

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Step-by-step explanation:

Let's check

Circumference:-

➜2πr

➜2πx

New Circumference:-

➜2πr

➜2π3x

➜6πx

Taking ratio:-

➜2πx/6πx

➜1/3

➜1:3

If we quadruple the radius Circumference will also be quadrupled.

If William spends a winter day recording the temperature once every three hours for science class. If  the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. The temperature at 6pm is: -11.1°F

Between 9am and noon, the temperature rose 16.2°F, so the temperature at noon will be:

Temperature at noon  = -12.2 + 16.2

Temperature at noon  = 3.0°F

Between noon and 3pm, the temperature dropped 9.1°F, so the temperature at 3pm will be:

Temperature at 3pm = 3.0 - 9.1

Temperature at 3pm = -6.1°F

Between 3pm and 6pm, the temperature dropped 5°F, so the temperature at 6pm was:

Temperature at 6pm =-6.1 - 5

Temperature at 6pm = -11.1°F

Therefore the temperature at 6pm is  -11.1°F.

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A. 5/10, -6/11, 7/12, -8/13

B. f(n) = n/(n+5)

C. Positive

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.

Here, we have

A. From inspection of the sequence, the pattern is:

Add 1 to the numerator of the previous term.

Add 1 to the denominator of the previous term.

Make every other term negative.

Hence, assuming the pattern continues, the next four terms in the sequence will be:

5/10, -6/11, 7/12, -8/13

B. An explicit formula for an arithmetic sequence allows you to find the [tex]n^{th}[/tex] term of the sequence.

f(1) = 1/6

f(2) = -2/7

We can see that the numerator is the position of the term (n) in the sequence.  So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.

The denominator is 5 more than the position of the term in the sequence.  So when n = 1 the denominator is 1 + 5 = 6, and when n = 2 the denominator is 2 + 5 = 7.

We observe that if the numerator (the value of n) is odd then the term is positive, and if the numerator  (the value of n) is even then the term is negative.

Hence, the rule for the nth term is:

f(n) = n/(n+5)

If n is odd then f(n) is positive.

If n is even then f(n) is negative.

C. 53 is an odd number.

As the function f(n) is positive when n is odd, the sign of f(53) is positive.

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Answer:

"0.07" is the appropriate answer.

Step-by-step explanation:

The given values are:

P(Stock),

= 0.60

P(Bond),

= 0.50

P(Bond | Stock),

= 0.06

Now,

The P(Stock | Bond) will be:

⇒  [tex]P(Stock|Bond)= \frac{P(Stock \ and \ Bond)}{P(Bond)}[/tex]

or,

⇒  [tex]P(Stock|Bond)=\frac{P(Bond|Stock).P(Stock)}{P(Bond)}[/tex]

On substituting the given values, we get

⇒                           [tex]=\frac{0.06\times 0.60}{0.50}[/tex]

⇒                           [tex]=\frac{0.036}{0.50}[/tex]

⇒                           [tex]=0.07[/tex]

Answer: Hello the lengths of the pieces of wood is missing but I will provide the format for drawing a line plot which you can now plug in your own values .

answer :

First draw a number line containing all the values in the given data set

Place a dot on top every value contained in the given data set

place as many dots as possible representing the frequency of the value in the given dataset

Step-by-step explanation:

A line plot is simply a method of displaying given data on a number line

steps :

First draw a number line containing all the values in the given data set

Place a dot on top every value contained in the given data set

place as many dots as possible representing the frequency of the value in the given dataset

attached below is an example

Han will make $57.75 for 7 hours of babysitting.

Given is a line segment RT.

We can write RT as -

RT = RS + ST

56 = (7y + 3) + (2y + 8)

(7y + 3) + (2y + 8) = 56

9y + 11 = 56

9y = 45

y = 5

Therefore, the value of {y} will be equivalent to 5.

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Answer:

Step-by-step explanation:

Answer:

128cm²

Step-by-step explanation:

Formula to find area of rectangle is l×b

In order to find the area of the rectangle we need to apply that formula

[tex]A =lb[/tex]

[tex]A = 16[/tex]×[tex]8[/tex]

[tex]A = 128[/tex][tex]cm[/tex]²

Hence ,  the area of the given rectangle is 128cm²

Using the regression concept to find the equation and applying derivative, The rate of change is 10.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. The dependant variable's predicted value in basic linear regression is given by the equation = b0 + b1x. In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. 

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.

from the given data,

y= a + bx is our regression line.

a=8 and b =10

y=8+10x is the line.

derivate the line , we get,

[tex]\frac {dy}{dx} = 10[/tex]

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Answer:

148x - 162.75

x=1.09966

Step-by-step explanation:

[tex]83 {p}^{3} {q}^{2} {r}^{2} + 83p {q}^{2} {r}^{3} [/tex]

Answer:

83p^9 + q^7 + r^6 + 83p + r^6

Step-by-step explanation:

^9 means to the power of 9

^7 means to the power of 7

^6 means to the power of 6

i can't do step-by-step, it's too complicated to explain. im sorry

<3

Answer:

x = -1 ± √109

Step-by-step explanation:

2x • 3x + (2 • 3)x + 6x = 648

According to PEMDAS (parentheses/exponents | multiplication/division | addition/subtraction), we should solve the parentheses first.

(2 • 3) = 6

Now we have:

2x • 3x + (6)x + 6x = 648

Now let's multiply.

2x • 3x = 6x²

6 • x = 6x

Now we have.

6x² + 6x + 6x = 648

Combine like terms.

6x² + 12x = 648

Let's factor out a 6.

6(x² + 2x) = 648

Divide both sides by 6.

x² + 2x = 108

Let's use completing the square.

Our equation is in a² + bx = c form.

Divide b by 2.

2/2 = 1

Then square it.

1² = 1

Add 1 to both sides.

x² + 2x + 1 = 108 + 1

Simplify.

x² + 2x + 1 = 109

Now we want to factor the left side. A shortcut is just to use b/2.

(x + 1)² = 109

Take the square root of both sides.

x + 1 = ±√109

The square root is as simplified as possible.

Subtract 1 from both sides.

x = -1 ± √109

Hope this helps!

Answer:

[tex]the \: forth \: answer \: is \: correct \: answer[/tex]

Equation of ellipse is x²/400 + (y-52) ²/256 =1

An ellipse is an oval shaped close geometrical figure. Ellipse has two radius, one is horizontal, and the other is vertical. An ellipse can be stretched either horizontal direction or vertical direction.

given, width of elliptical mirror = 16 inches

height of elliptical mirror = 20 inches

the center of ellipse = (0, 52)

as the width of elliptical mirror is less than height so the ellipse has vertical major axis.

vertical radius is denoted by b.

and horizontal radius is denoted by a.

as per the question, a = 16 inches and b = 20 inches.

we know the equation of ellipse whose major axis is vertical and center at the origin is shown by

x² / b² + y²/ a² = 1

we are given information about an ellipse having center (0, 52) and vertical radius 20 and horizontal radius 16.

the equation of this ellipse is.

x² / (20) ² + (y -52) ²/ (16)² = 1

x²/400 + (y - 52) ² /256 = 1

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Answer:

(x+4)²+(y-3)²=49

Step-by-step explanation:

the coordinate sings are flipped (so a center (a,-b) would look like

(x-a)²+(y+b)

and the radius is the square root of the number

No, isosceles triangles do not always have to have 90-degree angles.

An isosceles triangle is a triangle with two sides of equal length. While the two sides are equal, they can be of any length. This means that the angles of the isosceles triangle can vary, and the triangle does not always have to have 90-degree angles. In fact, an isosceles triangle can have angles that range from 0 to 180 degrees. The only requirement for an isosceles triangle is that it must have two sides of equal length. As such, an isosceles triangle can have angles that are greater than 90 degrees, angles that are less than 90 degrees, or even angles that are equal to 90 degrees.

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Answer:

30 miles

Step-by-step explanation:

Alr so-

You want first divide 3 by 3/5 since well- the question asks how many does he ride in 3 hours

Of course, you'll get the answer 5

Now you want to grab the 6 miles Jake could ride in 3/5 hours and put it in a new equation.

(you'll also want to take the 5 you got from the last equation)

You want to multiply both 6 and 5 which is 30

BOOM!

IN CONCLUSION-

the answer is 30 miles

The cost of a pack of gum bought by Lionel is $2.1.

Let the variable g represent the cost of a pack of gum.

Let the variable c represent the cost of a candy bar.

Since Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80, a linear equation that models this situation is;

4c + 2g = 9.80    ......equation (1)

Additionally, two packs of gum cost the same as three candy bars:

2g = 3c     ......equation (2)

c = 2g/3     ......equation (3)

Substituting equation (3) in equation (1), we get:

4(2g/3) + 2g = 9.80

8g/3 + 2g = 9.80

14g/3 = 9.80

14g = 29.4

= 29.4/14

= $2.1

The cost of a pack of gum is $2.1.

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The complete question is -

Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Two packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar. What is the cost of a pack of gum?