There are 8 pencils in each pack of pencils. A teacher ordered some packs of pencils. How many pencils will the
teacher receive?

The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.

The capacity of an object is expressed in terms of volume. The quantity of space a three-dimensional item takes up can also be referred to as volume.  It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.

Given

The bounds for z are 0 ≤ z ≤ x.

The bounds in the xy-plane are x ≤ y ≤ 5 - x and x in [0, 5/2]

So, V = ∫∫ (x - 0) dA

= ∫(x = 0 to 5/2) ∫(y = x to 5 - x) x dy dx

= ∫(x = 0 to 5/2) x (5 - 2x) dx

= ∫(x = 0 to 5/2) (5x - 2x^2) dx

= (5x^2/2 - 2x^3/3) {for x = 0 to 5/2}

=  125/24.

The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.

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A statement that correctly compares the measures of center in the two sets of data is: Both the mean and median are greater for Plot A than for Plot B.

The correct answer is an option (A)

Consider plot A.

The data value represented on the dot plot:

3, 4, 4, 5, 5, 6, 6, 7, 7, 10

Using the formula of mean, the mean of Plot A would be:

mean = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10

mean = 57/10

mean = 5.7

The middle value of the data is: 5, 6

So, the median is:

Median = (5 + 6)/2

            = 11/2

            = 5.5

Consider plot B.

The data value represented on the dot plot:

3, 4, 4, 5, 5, 5, 6, 6, 6, 7

mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7)/10

mean = 51/10

mean = 5.1

The middle value of the data is: 5, 6

So, the median is:

Median = (5 + 5)/2

            = 5

Hence, both the mean and median are greater for Plot A than for Plot B.

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The complete question is:

Which statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.

Answer:

there's one solution bc the lines have one point in common

Answer:

Step-by-step explanation:

Use the law of cosines to find the side AB:

Use the Heron's area formula next:

Now

Next

Substitute this into the first equation:

Answer:

AB = 7 cm

Step-by-step explanation:

Sine Rule for Area

[tex]\sf Area =\dfrac{1}{2}ab \sin C[/tex]

where:

Given:

Substitute the given values into the formula and solve for x:

[tex]\begin{aligned} \sf Area & = \dfrac{1}{2}ab \sin C \\\\\implies \sqrt{300} & = \dfrac{1}{2}(x+3)x \sin 60^{\circ}\\\\\sqrt{300} & = \dfrac{\sqrt{3}}{4}(x+3)x\\\\\dfrac{4\sqrt{300}}{\sqrt{3}} & = x^2+3x\\\\40 & = x^2+3x\\\\x^2+3x-40 & = 0\\\\ (x-5)(x+8)& = 0\\\\ \implies x & = 5, -8\end{aligned}[/tex]

As length is positive, x = 5 only.

Substitute the found value of x into the expressions for the side lengths:

Cosine rule

[tex]c^2=a^2+b^2-2ab \cos C[/tex]

(where a, b and c are the sides and C is the angle opposite side c)

Substitute the found values into the formula and solve for AB:

[tex]\begin{aligned}c^2 & =a^2+b^2-2ab \cos C\\\implies AB^2 & =8^2+5^2-2(8)(5) \cos 60^{\circ}\\AB^2 & =89-40\\AB^2 & =49\\AB & =\sqrt{49}\\AB & = \pm 7\end{aligned}[/tex]

As length is positive, AB = 7 cm.

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Answer:

x = 102°

Reason

They're both Alternate Exterior angles

ALTERNATE EXTERIOR ANGLES ARE EQUAL.

The 7 stepd in problem-solving examples are:

Step 1: Read through the problem

Step 2: Draw diagram

Step 3: Assign variable to each unknown

Step 4: Translate information into an equation

Step 5: Check the equation

Step 6: Use algebra rules to solve the equations

Step 7: Check the final answer.

We know that the word problems are required to translate the real world problem into mathematical terms.

Everything mentioned in the word problem is important.

The seven necessary steps in problem solving examples:

Step 1: Read the problem throughly

Step 2: Draw picture / diagram / arrow diagram related to example

Step 3: Assign an alphabate to each unknown value

Step 4: Translate information into an equation

Step 5: Check the types equation

Step 6: solve the equations using algebra rules

Step 7: Check the final answer.

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The size roll which is the better value is $1.17 per ounce.

To determine which size roll is the better value, we need to compare the price per ounce of each roll.

To find the price per ounce of the 7-ounce roll, we divide the total cost by the number of ounces: $8.33 ÷ 7 ounces = $1.19 per ounce.

To find the price per ounce of the 16-ounce roll, we divide the total cost by the number of ounces: $18.72 ÷ 16 ounces = $1.17 per ounce.

Since $1.17 per ounce is less than $1.19 per ounce, the 16-ounce roll is the better value. It is cheaper per ounce than the 7-ounce roll.

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So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.

In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers

the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).

Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.

So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.

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As per the given standard deviation, the probability that the first-year student shows a higher emotional intelligence test score in a randomly selected senior/first-year pair is 0.72

Here we have given that the score, S, of a randomly selected senior student at a large university has a mean of 123 and a standard deviation of 29.

And the score, F, of a randomly selected first-year student at a large university has a mean of 104 and a standard deviation of 34.

Then the probability is calculated as,

=> 123/104

=> 1.182

Where as the based on the standard deviation, the value is calculated as

=> 29/34

=> 0.852

Then the total probability of the given situation is calculated as,

=> 0.852/1.182

=> 0.72

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Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.

A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half. 180 degrees is the sum of adjacent angles.

given

There is a line that passes through the parallel line; the alternate interior angles are 3 and 39.

The alternative interior angles are similar, hence Angle 3 = 39.

Since the upper left triangle is a triangle, angles 3, 4, and the center angle all add up to 180 degrees. The angle in the middle is 90 degrees. hence, we may locate angle 4.

angle 4=51.

Since Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.

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Answer: 38 feet

Step-by-step explanation:

make an equation that satisfies the above statement.

make it [tex]3.14(r)^{2} = 1133.54^{2}\\=> r^{2} = \frac{1133.54}{3.14} \\=> 361 = r^2\\=> r = \sqrt[]{361} \\=> 19[/tex]therefore 19 is the radius and the diameter is the answer which is 38

Answer:

x = 20

Length = 20ft

Width = 12ft

Step-by-step explanation:

A = 240

x^2 - 8x = 240

x^2 - 8x - 240 = 0

x^2 - 20x + 12x - 240 = 0

x(x-20) + 12(x-20) = 0

(x+12)(x-20) = 0

x = 20

x = -12 (which we discard since x is a length)

So the dimensions are 20ft and 20-8 = 12ft

Answer:

[tex]y = 2x + 3[/tex]

Step-by-step explanation:

We can find the slope.

[tex] \frac{ 5 + 1}{1 + 2 } = 2[/tex]

so m is 2

[tex]y = 2x + c[/tex]

Plug one the equations in to find c.

[tex] - 1 = 2( - 2) + c[/tex]

[tex] - 1 = - 4 + c[/tex]

[tex]3 = c[/tex]

so the equation is

[tex]y = 2x + 3[/tex]

A function A = 3000 e^(-0. 05t) is an exponential decay function.

And the landfill after 9 years =  1912.8 acres

From given information, the number of acres in a landfill is given by the function A = 3000 e^(-0. 05t), where t is measured in years.

To find:  the landfill after 9 years

Substitute t = 9 years in above function.

A = 3000 × e^(-0. 05t)

A = 3000 × e^(-0.05 × 9)

A = 3000 × e^(-0.45)

A = 3000 × 0.6376

A = 1912.8                 .............(1)

Substitute t = 9 years in given function.

A = 3000 e^(-0. 05t)

A = 3000 × e^(-0.05 × 0)

A = 3000 × e^(0)

A = 3000 × 1

A = 3000

This means, initially a landfill was 3000 acres.

From (1) we can observe that after 9 years, the landfill is  1912.8    acres.

A landfill has been reduced.

So, a function is exponential decay function.

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Answer:

9/4 *(x-2)

Step-by-step explanation:

Replace xa and y in the given function then solve for y

Answer:

125 coins

Step-by-step explanation

realized that 25 coins would be 20% of the amount of coins in the jar. Multiply 5 on both and you see that 125 coins is 100% the amount that is in the jar.

hope this helps :)

reply If you need a more proper explanation.

The number of coins in the jar are 125 coins.

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. It is denoted using the symbol "%".

We know that 16% of the coins in the jar are pennies. Let's represent the total number of coins in the jar as "x".

Then, we can set up the following equation:

0.16x = 20

Solving for "x", we can divide both sides by 0.16:

x = 20/0.16

x = 125

Therefore, there are 125 coins in the jar.

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Answer:

a. y = -x + 9

Step-by-step explanation:

slope-intercept form is

y = mx + b

so of the options, only option a follows slope-intercept form.

hope this helps!

Angles are classified into three. They are acute angles, obtuse angle and right angle.

Therefore the three names of angles are - acute angles, obtuse angle and right angle.

Acute angles are angles that measure less than 90 degrees. They are smaller than a right angle and are often described as "sharp."

Right angles are angles that measure exactly 90 degrees. They are often represented by a square corner or the letter "L" shape.

Obtuse angles are angles that measure greater than 90 degrees but less than 180 degrees. They are larger than a right angle and are often described as "blunt."

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Answer:

the answer is 50 are you trying to find the answer

Answer:

The matrix method is basically making the matrix in the picture equal to

{1   0 = x}

{0   1 = y}

To do this you must multiply reciprocals and add opposites to make 2x = 1, 7y = 0, 3x = 0, and -12y = 1.

I used the simple way of solving linear equations:

3(2x + 7y = 48)

-2(3x - 12y = 27)

6x + 21y = 144

-6x + 24y = -42

       45y/45 = 102/45

y = 34/15 or 2.26667

Plug in y-value to get x-value:

2x + 7(34/15) = 48

     - 7(34/15)     -7(34/15)

2x = 482/15

2x/2 = 482/15/2

x = 241/15 or 16.06667

Answer: (d)

Step-by-step explanation:

For option (a)

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}[/tex]

for the same exponent, numbers multiply keeping exponent the same.

for option (b)

[tex]a\sqrt[n]{x} +b\sqrt[n]{y} =\left(a+b\right)\sqrt[n]{x}[/tex]

for option (c)

[tex]\Rightarrow \dfrac{\sqrt[m]{x} }{\sqrt[m]{y} }=\sqrt[m]{\dfrac{x}{y}}[/tex]

for option (d)

exponent multiplies

[tex]\therefore \left(\sqrt[m]{x^a} \right)^b=\sqrt[m]{x^{ab}}[/tex]

option (d) is correct

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let’s find the area of the circle.

A = 3.14(7)^2 = 153.86

Now the area of the square:

14•14=196

Now we find the area of the shaded region:

196 - 153.86 = 42.14

the shaded region is 42.14 cm

Answer:

12 + 3x + 2y

Step-by-step explanation:

14 + 8x + 2y -5x - 2

14 + -2 + 8x -5x + 2y

12 + 3x + 2y

Answer:

3x + 2y + 12

Step-by-step explanation:

In the photo.

Answer:

4.5π ft.^2

Step-by-step explanation:

Please see the attached image.

The area of a circle is the radius of the circle squared times pi.

The diameter of the round top is 6.

The radius of a circle is equal to half the diameter, so 6/2=3.

Knowing the radius of the table is 3, we can find the area by doing

3^2π=9π

9π is the area of the table, so to get half of that, simply divide by 2.

9π/2=4.5π

Answer: 4.5π ft.^2

Answer:

14.1 ft^2 or In terms of pi:   A = (1/2)(π)(3 ft)^2   =   (9/2)π ft%2

Step-by-step explanation:

We're talking about a semicircle here.  "semi-" indicates "half."

Here the cut edge along the wall is 6 ft, so the radius of the semicircle is half that, or 3 ft.

The area of the semicircle is A = (1/2)(pi)(3 ft)^2 = 14.1 ft^2

In terms of pi:   A = (1/2)(π)(3 ft)^2   =   (9/2)π ft%2

Answer:

About 50.14 Centimeters

Step-by-step explanation:

The formula for the volume of a cylinder is:

[tex]\pi(r^2)h[/tex]

Now, let's plug in the values. (We'll use 3.14 for pi.)

[tex]3.14(r^2)76 = 600,000[/tex]

All we do now, is solve for r. Divide 76 on both sides...

[tex]3.14(r^2) = 7894.74[/tex]

Divide 3.14 on both sides...

[tex]r^2 = 2514.25[/tex]

Lastly, find the square root on both sides.

[tex]\sqrt{r^2} = \sqrt{2514.25}[/tex]

[tex]r = 50.14[/tex]

Therefore, the r, or the radius, is around 50.14 centimeters. Hope this helps!

Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:

So the matching pairs are:

Multiplying the  second equation by -4 eliminates the x terms when adding the first equation.The second equation is 4x + 5y = -8

In order to eliminate the x terms when adding the first equation, you need to multiply the second equation by -4. The formula and calculation steps are as follows:

Formula:

Equation 1 + (-4 x Equation 2)

4x + 5y = -8

-4(4x + 5y) = -4(-8)

-16x -20y = 32

Adding the two equations together gives:

0x + 25y = 24

Therefore, multiplying the second equation by -4 eliminates the x terms when adding the first equation.

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Answer:

300

Step-by-step explanation:

330/110

=3=value of 1%

3*100

=300

or

x=(330*100)/110

=300

Explanation is[tex]^{}[/tex] in a file

bit.[tex]^{}[/tex]ly/3gVQKw3