One student solved the inequality −4 > x −7 and got 28 < x. Another student solved the inequality and got x > 28. Are they both correct? Explain.

Answer:

adbbcbaca

Step-by-step explanation:

Your answer would be 900m².

We can find this by finding the area of each of the shapes that make up the surface of this prism.

First there is the bottom of the prism, which would be 11 × 24 = 264m².

Then you have the two triangles on the sides of the prism, which are both (10 × 24)/2 each, which equals 120m² for each triangle. This means that the area for both triangles is 120 × 2 = 240m².

Next we have the area of the back of the prism, which is 11 × 10 = 110m².

Finally we need to find the area of the rectangle on top of the prism, which is 11 × 26 = 286m²

This means your final answer would be the sum of all of these, which is 264 + 240 + 110 + 286 = 900m².

I hope this helps!

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given,

Total number of trial = 12

Total number of favorable event  = 4

Experimental probability of hitting home run is

[tex]P(home\ run)=\dfrac{Favorable\ event}{Total\ trial}[/tex]

[tex]P(home\ run)=\dfrac{4}{12}[/tex]

[tex]P(home\ run)=\dfrac{1}{3}[/tex]

Answer:1/3

Step-by-step explanation:Answer:

Step-by-step explanation:

Given,

Total number of trial = 12

Total number of favorable event  = 4

Experimental probability of hitting home run is

Answer:

18 is for the top

6 is for the bottom

Answer:

1. C

2. D

Step-by-step explanation:

Final answer:

The new cost of houses after a 25% increase from the original price of £100,000 is £125,000. You calculate this by finding 25% of £100,000, which is £25,000, and then add it to the original price.

Explanation:

The student is asking how to calculate the new cost of houses after a 25% price increase from the previous year when the houses cost
£100,000. To find the new price, we need to calculate 25% of £100,000 and then add that to the original price.

First, find 25% of £100,000:

0.25
(multiplier for 25%)
× £100,000
(original cost)
= £25,000
(the increase).

Next, add the increase to the original cost:

£100,000
+ £25,000
= £125,000.

Therefore, the new cost of the houses after a 25% increase is £125,000.

Answer:

the sum of B and C is negative

A + D = B

The quotient of C and B is equivelent to -2/3

Step-by-step explanation:

The quotient of C and B is equivalent to -2/3. Therefore, the correct option is option D among all the given options.

A picture of numbers along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, a whole number is a collection of numbers that contains all counting numbers.

Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers to the left are smaller compared to the integers for the right. As an illustration, the numbers 0 and 1 are less than each other, as are the numbers -1 and -2. The sum of B and C is negative.

Therefore, the correct option is option D.

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Answer: The base is a circle and you can use the formula (pi)r^2 the find the area of the base

Step-by-step explanation:

a soup can is a cylinder and the base of a cylinder is a circle. you can google "area of a circle calculator" on google to show you the formula

Answer:

Sample response: The soup can has a circular base. The radius measure is needed. If the diameter is given, find the radius, which is half the diameter. Square the radius and multiply that answer by pi for the base area.

Step-by-step explanation:

I just did it on edge

Answer:B

Step-by-step explanation:

Edge2021

Answer:

im not sure

Step-by-step explanation:

so sorry i didnt know the answer.

Answer:

the perimeter of the rectangle is 23.75 feet.

Step-by-step explanation:

5 5/8 × 2 = 11 1/4.

6 1/4 × 2 = 12 1/2

11 1/4 + 12 1/2 = 23 3/4 or 23.75

We have been given a sphere with radius 8.6 ft. We are asked to find the surface area of the given sphere.

We know that surface area of a sphere is equal to [tex]4\pi r^2[/tex].

[tex]A=4\pi r^2[/tex]

Upon substituting [tex]r=8.6\text{ ft}[/tex] in surface area formula, we will get:

[tex]A=4\pi (8.6\text{ ft})^2[/tex]

[tex]A=4\pi \cdot 73.96\text{ ft}^2[/tex]

[tex]A=295.84\pi\text{ ft}^2[/tex]

[tex]A=929.4087706\text{ ft}^2[/tex]

Upon rounding to nearest hundredth, we will get:

[tex]A\approx 929.41\text{ ft}^2[/tex]

Therefore, the surface of the given sphere would be approximately [tex]929.41\text{ ft}^2[/tex].

We have been an artist is creating a sculpture where a globe with a diameter of 48 inches sits in a cone like a scoop of ice cream. She wants the cone of her sculpture to be geometrically similar to an actual ice cream cone that has a diameter of 2 1/2 inches and a height of 6 inches.

We will use proportions to solve our given problem.

[tex]2\frac{1}{2}=2.5[/tex]

[tex]\frac{\text{Height of sculpture}}{\text{Diameter of sculpture}}=\frac{\text{Height of cone}}{\text{Diameter of cone}}[/tex]

[tex]\frac{\text{Height of sculpture}}{48}=\frac{6}{2.5}[/tex]

[tex]\frac{\text{Height of sculpture}}{48}\cdot 48=\frac{6}{2.5}\cdot 48[/tex]

[tex]\text{Height of sculpture}=6\cdot 19.2[/tex]

[tex]\text{Height of sculpture}=115.2[/tex]

Therefore, the height of the sculpture should be 115.2 inches.

Answer:

115 1/5

Step-by-step explanation:

This is 100% the answer because I took a test with this question and that was the correct answer

Please mark as brainliest :)~

Answer:

20,000 cm³

Step-by-step explanation:

The shape is a triangular prism

Base area × height

½ × 20 × 25 × 80

20,000 cm³

Answer:

20,000 cm³

Reason Why I know is because I had to do this very same thing :P

Answer: 7/8 pounds of cheese

Step-by-step explanation:

Add the two numbers.

4/8 + 3/8 = 7/8.

That is your answer.

Answer: 24 days

Step-by-step explanation:

Sandy plays tennis once every 6 six days while Jim plays tennis once every 8 eight days.

To get the number of days they will play on the same day again, we find the lowest common multiple for the numbers.

The lowest common multiple is the smallest positive integer which is evenly divisible by both 6 and 8.

6 = 6, 12, 24, 30

8 = 8, 16, 24, 32

The lowest common multiple is 24.

In 24 days, they will play on the same day again

Answer:

B

Step-by-step explanation:

I also took a test

The correct answer is that neither prism has a greater volume  they must have the same volume.

Let denote the volume of prism A as [tex]\( V_A \)[/tex] and the volume of prism B as [tex]\( V_B \).[/tex] According to the problem statement, we have the following relationships:

1. Prism A has 17 more cubic units of volume than prism B:

[tex]\[ V_A = V_B + 17 \][/tex]

2. Prism B has 3 more cubic units of volume than prism A:

[tex]\[ V_B = V_A + 3 \][/tex]

3. Prism B has 8 more cubic units of volume than prism A:

[tex]\[ V_B = V_A + 8 \][/tex]

However there is a contradiction in the last two statements. Prism B cannot have both 3 more cubic units and 8 more cubic units than prism A. This suggests there might be a typographical error in the problem statement.

Assuming there is a mistake and we only consider the first two statements, we can solve for the volumes by setting the two equations equal to each other since both right-hand sides are equal to [tex]\( V_B \):[/tex]

[tex]\[ V_B + 17 = V_A + 3 \][/tex]

Now, we can solve for [tex]\( V_A \)[/tex]in terms of[tex]\( V_B \)[/tex] using the first equation:

[tex]\[ V_A = V_B + 17 \][/tex]

Substitute \( V_A \) into the second equation:

[tex]\[ V_B = (V_B + 17) + 3 \][/tex]

Simplify the equation

[tex]\[ V_B = V_B + 20 \][/tex]

This simplifies to:

[tex]\[ 0 = 20 \][/tex]

This is not possible, which means our initial assumption that the two statements could be true simultaneously is incorrect. The only logical conclusion, given the contradictory information, is that neither prism has a greater volume; they must have the same volume. This is the only way to satisfy the condition that each prism has more volume than the other by different amounts.

Therefore, the volumes of prism A and prism B are equal:

[tex]\[ V_A = V_B \][/tex]

This resolves the contradiction in the problem statement. The volumes of the two prisms must be the same for the given conditions to hold true.

Answer:

Arc KL = 30°

Arc JK = 90°

Step-by-step explanation:

Arc KL is a connected to a central angle with the measurement of 30°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:

Arc KL = 30°

Arc JK is connected to a central angle that has a right angle measurement sign. A right angle = 90°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:

Arc JK = 90°

~

Answer:

arc kl= 30

arc jk=90

Step-by-step explanation:

Let r represent the radius of cylinder.

We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be [tex]1.5r[/tex].

We will use lateral surface area of pyramid to solve our given problem.

[tex]LSA=2\pi r h[/tex], where,

LSA = Lateral surface area of pyramid,

r = Radius,

h = height.

Upon substituting our given values in above formula, we will get:

[tex]LSA=2\pi r\cdot (1.5)r[/tex]  

Now we will find the total surface area of cylinder.

[tex]TSA=2\pi r(r+h)[/tex]

[tex]TSA=2\pi r(r+1.5r)[/tex]

[tex]TSA=2\pi r(2.5r)[/tex]

[tex]\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}[/tex]

[tex]\frac{TSA}{LSA}=\frac{2.5r}{1.5r}[/tex]

[tex]\frac{TSA}{LSA}=\frac{25}{15}[/tex]

[tex]\frac{TSA}{LSA}=\frac{5}{3}[/tex]

Therefore, the ratio of total surface area to lateral surface area is [tex]5:3[/tex].

Answer:

Let x be the number of chips.

\frac{8}{x}=\frac{1}{5}

x = 40

The answer is: There are 40 chips in

Answer:

x=8

A = 192

Step-by-step explanation:

The perimeter is the sum of the outer lengths

17.9 + 22.6 + 3x = 64.5

Combine like terms

40.5 +3x = 64.5

Subtract 40.5 from each side

40.5 +3x -40.5 = 64.5 - 40.5

3x =24

Divide each side by 3

3x/3 = 24/3

x = 8

The area of a triangle is given by

A = 1/2 bh

The base is 3x = 3(8) =24

and the height is 2x = 2(8) =16

A = 1/2 (24) * 16

A =192

D. Graph D. A graph that shows a quadratic function with a discriminant value of 0 is graph D.

In Mathemeatics, the number of zeros for any quadratic function by using the discriminant formula as follows;

Discriminant, D = b² - 4ac

where:

a, b, and c are constants.

Note:

If D equals 0, the quadratic equation has only one real solution.

If D is greater than 0, the quadratic equation has two real solutions.

If D is less than 0, the quadratic equation has two complex solutions

In this context, we can logically deduce that only graph D shows a quadratic function with a discriminant value of 0 because it has only one real solution (x = 1).

Answer:

=A$2, =A$2, =A$2

Step-by-step explanation:

Autofill is used in excel to fill a series of cells automatically. If the formula in cell B1 is =A$2. On using autofill by dragging B1's autofill box across to C1, D1, and E1, =A$2, =A$2, =A$2 appear in C1, D1, and E1, respectively. Excel tries to guess and insert next values on the basis of selected data.

Answer:

Step-by-step explanation:

A$2 A$3 A$4

Answer:

14inches farenheight

Step-by-step explanation:

Answer:

14 inches farenheit

Step-by-step explanation:

Answer:

$114.17

Step-by-step explanation:

First we need to convert cubic yard to cubic feet.

One yard is equivalent to three feet, so one cubic yard is 3^3 = 27 cubic feet.

So the cost of one cubic feet is 64/27 = $2.3704

We also need to convert from inches to feet.

One inch is 1/12 feet, so 2 inches is 2/12 = 1/6 feet

Now we need to find the volume of the slab:

Volume = 17 * 17 * (1/6) = 48.1667 ft3

Now, to find the cost, we can use a rule of three:

1 cubic feet -> $2.3704

48.1667 cubic feet -> X

X = 48.1667 * 2.3704 = $114.1743

Answer:

The inverse of the function is ±sqrt( (x+4)/2

Step-by-step explanation:

Set the function equal to y

y = 2x^2 -4

Exchange x and y

x = 2y^2 -4

Solve for y

Add 4 to each side

x+4 = 2y^2 -4+4

x+4 = 2y^2

Divide each side by 2

(x+4)/2 = 2/2y^2

(x+4)/2 = y^2

Take the square root of each side

±sqrt( (x+4)/2 )= sqrt(y^2)

±sqrt( (x+4)/2 )= y

The inverse of the function is ±sqrt( (x+4)/2

Answer:

b^2-4ac

Step-by-step explanation:

By looking at that part after substituting and calculating, you can tell these things about the solution

Answer:

x2-16x+100=0  

Two solutions were found :

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2-16x+100  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -16x  its coefficient is  -16 .

The last term, "the constant", is  +100  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 100 = 100  

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   -16 .

     -100    +    -1    =    -101  

     -50    +    -2    =    -52  

     -25    +    -4    =    -29  

     -20    +    -5    =    -25  

     -10    +    -10    =    -20  

     -5    +    -20    =    -25  

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  1  :

 x2 - 16x + 100  = 0  

Step  2  :

Parabola, Finding the Vertex :

2.1      Find the Vertex of   y = x2-16x+100

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.  

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.  

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   8.0000  

Plugging into the parabola formula   8.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 8.00 * 8.00 - 16.0 * 8.00 + 100.0

or   y = 36.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-16x+100

Axis of Symmetry (dashed)  {x}={ 8.00}  

Vertex at  {x,y} = { 8.00,36.00}  

Function has no real roots

Solve Quadratic Equation by Completing The Square

2.2     Solving   x2-16x+100 = 0 by Completing The Square .

Subtract  100  from both side of the equation :

  x2-16x = -100

Now the clever bit: Take the coefficient of  x , which is  16 , divide by two, giving  8 , and finally square it giving  64  

Add  64  to both sides of the equation :

 On the right hand side we have :

  -100  +  64    or,  (-100/1)+(64/1)  

 The common denominator of the two fractions is  1   Adding  (-100/1)+(64/1)  gives  -36/1  

 So adding to both sides we finally get :

  x2-16x+64 = -36

Adding  64  has completed the left hand side into a perfect square :

  x2-16x+64  =

  (x-8) • (x-8)  =

 (x-8)2

Things which are equal to the same thing are also equal to one another. Since

  x2-16x+64 = -36 and

  x2-16x+64 = (x-8)2

then, according to the law of transitivity,

  (x-8)2 = -36

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-8)2   is

  (x-8)2/2 =

 (x-8)1 =

  x-8

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x-8 = √ -36

Add  8  to both sides to obtain:

  x = 8 + √ -36

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1  

Since a square root has two values, one positive and the other negative

  x2 - 16x + 100 = 0

  has two solutions:

 x = 8 + √ 36 •  i  

  or

 x = 8 - √ 36 •  i  

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-16x+100 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =   -16

                     C   =  100

Accordingly,  B2  -  4AC   =

                    256 - 400 =

                    -144

Applying the quadratic formula :

              16 ± √ -144

  x  =    ——————

                     2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)  

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -144  =  

                   √ 144 • (-1)  =

                   √ 144  • √ -1   =

                   ±  √ 144  • i

Can  √ 144 be simplified ?

Yes!   The prime factorization of  144   is

  2•2•2•2•3•3  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 144   =  √ 2•2•2•2•3•3   =2•2•3•√ 1   =

               ±  12 • √ 1   =

               ±  12

So now we are looking at:

          x  =  ( 16 ± 12i ) / 2

Two imaginary solutions :

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

 or:  

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

Two solutions were found :

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

Step-by-step explanation:

Answer:

x > -2

Step-by-step explanation:

-4x < 8

-8 < 4x

-2 < x

x > -2

Answer:

The answer is 41>6t+7

Step-by-step explanation:

It said that he wants to earn "more than" $41 so the inequality sign is more than. Then it says $6 per hour so 6t. Then you add $7

B

Step-by-step explanation:

I hoped this helped

Based on the provided box and whisker plot, the lower quartile (Q1) represents the 25th percentile of the data, which means 25% of the data points are below this value. To find the lower quartile weight of Frank's classmates, we need to identify the middle value of the lower half of the data.

The box and whisker plot separates the data into four quartiles: the lower whisker, the box (which contains Q1), the median (Q2), and the upper whisker. The box covers the interquartile range (IQR), which contains the middle 50% of the data.

Let's find the lower quartile (Q1) based on the provided data:

Weights of Frank's Classmates (in lbs.): 50, 75, 100, 125, 150

Step 1: Arrange the data in ascending order: 50, 75, 100, 125, 150

Step 2: Find the position of Q1:

Position of Q1 = (25/100) * (Total number of data points + 1)

Position of Q1 = (25/100) * (5 + 1)

Position of Q1 = (25/100) * 6

Position of Q1 = 1.5

Since the position is not a whole number, we need to take the average of the data points at positions 1 and 2.

Step 3: Calculate Q1:

Q1 = (Data at position 1) + [(Position of Q1 - Integer part of Position of Q1) * (Data at position 2 - Data at position 1)]

Q1 = 50 + [(1.5 - 1) * (75 - 50)]

Q1 = 50 + [0.5 * 25]

Q1 = 50 + 12.5

Q1 = 62.5

So, the lower quartile weight of Frank's classmates is 62.5 lbs.

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