Use w for the unknown.
"A number split into 3 equal parts"

Each cube has a volume of 1 cm³, and the rectangular prism contains 320 cubes, so the volume of the rectangular prism is 320 cm³.

Volume is a physical quantity that measures the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters (m³) or cubic centimeters (cm³).

Here,

Length side = 4 cubes

= 5 cm

Width side = 2 cubes

= 2 cm

Height side = 2 cubes

= 2 cm

The length of the rectangular prism is 4 cubes which are equal to 5 cm each, so the length is 4 x 5 cm = 20 cm. The width of the rectangular prism is 2 cubes which are equal to 2 cm each, so the width is 2 x 2 cm = 4 cm. The height of the rectangular prism is 2 cubes which are equal to 2 cm each, so the height is 2 x 2 cm = 4 cm.

To find the volume of the rectangular prism, we multiply the length by the width by the height:

Volume = length x width x height

Volume = 20 cm x 4 cm x 4 cm

Volume = 320 cubic cm

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Complete question:

Each cube in this rectangular prism is 1 cm³. What is the volume of the rectangular prism?

Answer:

Circumference/Diameter = π

If the diameter is 2, then the circumference is 2π.

If the diameter is 6, then the circumference is 6π.

Answer: x ≈ 5.085

Step-by-step explanation:

     We will utilize logarithms to help us solve.

Given:

     [tex]\displaystyle 4^{x-3}=18[/tex]

The logarithm of both sides of the equation:

     [tex]\displaystyle log(4^{x-3})=log(18)[/tex]

Logarithm power property:

     (x - 3)log(4) = log(18)

Divide both sides of the equation by log(4):

      x - 3 = [tex]\frac{log(18)}{log(4)}[/tex]

Add 3 to both sides of the equation:

      x =  [tex]\frac{log(18)}{log(4)}[/tex] + 3

Compute:

     x ≈ 5.085

Answer:

linear

Step-by-step explanation:

function declines at a constant rate of 1/2x with a y-intercept of 20 giving the equation y= 1/2x + 20

Martina is learning different kinds of Latin dance she went to 6 salsa lessons and 12 rumba lessons each lessons cost 4$ let t equal the total number of lesson, the total cost of the lessons is $72.

The problem gives us two pieces of information:

1. Martina attended 6 salsa lessons and 12 rumba lessons, which means she attended a total of 18 lessons in total.

2. Each lesson costs $4.

To find an equation for the total number of lessons (t), we simply add the number of salsa lessons and rumba lessons:

t = 6 + 12

t = 18

So the total number of lessons Martina attended is 18.

To find an equation for the total cost of the lessons (c), we can multiply the total number of lessons by the cost per lesson:

c = t x 4

c = 18 x 4

c = 72

So the total cost of the lessons Martina attended is $72.

Thus, the equation for the total number of lessons is t = 6 + 12 = 18 and the equation for the total cost of the lessons is c = t x 4 = 18 x 4 = 72.

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The instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.

A confidence interval is a range of values that, with a certain degree of certainty, is likely to contain the real value of a population parameter. It is typically used in inferential statistics, where we use a sample to make inferences about a larger population.

To determine the sample size required to construct a 95% confidence interval with a margin of error of 0.025 or less, we need to use the formula:

n = (Z² * p * (1 - p)) / E²

where:

n = sample size

Z = Z-score corresponding to the desired level of confidence (in this case, 95%, which corresponds to a Z-score of 1.96)

p = estimated proportion of students repeating the class (since we have no prior information, we will use 0.5 as a conservative estimate)

E = maximum allowable margin of error (in this case, 0.025)

Plugging in the values, we get:

n = (1.96² * 0.5 * (1 - 0.5)) / 0.025²

n = 384.16

Rounding up to the nearest whole number, the instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.

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The equation of the reflected graph is y = -3ˣ.

To reflect a graph over the x-axis, we need to negate the y-coordinates of all the points on the original graph. In other words, if a point (x, y) is on the original graph, its reflection over the x-axis would be (x, -y).

Let's apply this concept to the exponential function f(x) = 3ˣ. The graph of this function is an upward sloping curve that passes through the point (0,1) on the y-axis. If we reflect this graph over the x-axis, the point (0,1) will be mapped to (0,-1), as the x-coordinate remains the same, but the y-coordinate changes sign.

To find the equation of the reflected graph, we need to replace y with -y in the equation of the original function f(x) = 3ˣ. This gives us:

-y = 3ˣ

To isolate y, we can multiply both sides by -1:

y = -3ˣ

This function is a downward sloping curve that passes through the point (0,-1) on the x-axis.

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The equation where x represents the matrix would be A. [tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

To find the matrix equation representing the given system of equations, we can write the system as AX = B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants.

[tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

The system of equations is:

x + y + z = 260

x + y - z = 60

2x + y + 2z = 305

We can write this system as a matrix equation:

A = [tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right][/tex]

X = [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

So the correct matrix equation is:

AX = B

[tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

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The variable d represents the number of days he spends on vacation, and the variable p represents the total number of postcards he buys Cooper will have bought a total of 18 postcards after 2 days of vacation.

If p = 9d represents the total number of postcards Cooper buys in relation to the number of days he spends on vacation, we can substitute d = 2 into the equation to find the total number of postcards he buys after 2 days of vacation:

p = 9d

p = 9(2)  [Substitute d = 2]

p = 18

Therefore, Cooper will have bought a total of 18 postcards after 2 days of vacation.

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The value of tanQ is 4/3

What is trigonometric ratio?

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

The values of the functions are expressed as follows;

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

The opposite in the triangle is 12 and the adjascent is 9 while th hypotenuse is 15.

therefore , since tan(tetha) = opp/adj

then, tanQ = 12/9

simplifying the value to the nearest term,

tanQ = 4/3

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Answer: 28.27m^2

Step-by-step explanation:

Area of a circle: [tex]A = \pi r^{2} \\[/tex]

Given the diameter of 6m, we can divide that by 2 to get the radius and plug that into the formula.

6/2 = 3m

[tex]A = \pi (3)^2\\A= 28.27m^{2}[/tex]

The value of k in the given graph is 4

Explain the term graph

A graph is a visual representation of data that displays the relationship between two or more variables. It consists of a set of points or vertices connected by lines or curves that represent the data points. Graphs are used to analyze and interpret data and to communicate information effectively in various fields, including mathematics, science, and business.

According to the given information

We are given that g(x) = f(x) + k, where f(x) and g(x) are two parabolas that open up and pass through the point (-3, -3) and (-3, 1), respectively.

Since both parabolas pass through the point (-3, -3), we know that:

f(-3) = -3

g(-3) = -3 + k = 1

Solving for k, we get:

k = 1 - (-3) = 4

Therefore, the value of k is 4.

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Ah Tee sold an average of 167 copies per day for the whole week.

The quantity of weekdays and weekends must be considered.

Assume that a week consists of 5 weekdays and 2 weekends (Saturday and Sunday).

We divide the total number of copies sold for the week by the number of days in the week to determine the average number of copies sold per day for the whole week:

Average number of copies sold per day for the whole week = 1169 / 7 = 167

Therefore, Ah Tee sold an average of 167 copies per day for the whole week.

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The book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

The straight-line method is a common method of calculating depreciation for fixed assets. It assumes that the asset will lose an equal amount of value each year over its useful life. To calculate depreciation using the straight-line method, you subtract the asset's estimated salvage value from its original cost to determine the total amount that needs to be depreciated. Then, divide that amount by the estimated number of years the asset will be in use to find the annual depreciation expense. The formula for straight-line depreciation is:

Annual depreciation expense = (Original cost - Salvage value) / Estimated useful life

The annual depreciation expense for the equipment is:

Depreciation expense = (cost - residual value) / useful life

Depreciation expense = ($212,000 - $14,000) / 15

Depreciation expense = $12,533.33 per year

The total depreciation expense for the first five years is:

Total depreciation expense = Depreciation expense x number of years

Total depreciation expense = $12,533.33 x 5

Total depreciation expense = $62,666.65

To find the book value at the end of the fifth year, we subtract the total depreciation expense from the original cost:

Book value = Cost - Total depreciation expense

Book value = $212,000 - $62,666.65

Book value = $149,333.35

Therefore, the book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

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The ratio between the number of people who do not enjoy reading and the number of people who do not enjoy playing videogames is given as follows:

3 to 1.

The ratio between two amounts a and b is given as follows:

a to b.

The amounts for this problem are given as follows:

Hence the ratio is of:

9/3 = 3/1 = 3 to 1.

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Therefore , the solution of the given problem of unitary method comes out to be Stacy's Bake Shop sells cupcakes for less than The Best Cake Shop does according to the idea of unit pricing.

Use the tried-and-true fundamental methodology, the real variables, and any useful information you learn from the general and specific questions to complete the assignment. Customers may be given another chance to taste the products in expression response. If these improvements don't happen, we'll lose out on significant advancements in programming comprehension.

Here,

Due to the idea of unit pricing, Stacy's Bake Shop sells cupcakes for less money than The Best Cake Shop.

In order to compare products with varying quantities or sizes, unit pricing, also known as price per unit, is used.

In this instance, Stacy's Bake Shop charges $21 for a dozen cupcakes, hence the price per cupcake is calculated as

=>  $21 /12, or $1.75 per cupcake.

On the other hand, The Best Cake Shop charges $12 for a half-dozen cupcakes; this indicates that each cupcake costs $2, or $12 divided by six.

As a result, Stacy's Bake Shop charges $1.75 less each cupcake than The Best Cake Shop, which charges $2.

As a result, Stacy's Bake Shop sells cupcakes for less than The Best Cake Shop does according to the idea of unit pricing.

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Answer:

127.5

Step-by-step explanation:

multiply 15 and 17 divide by 2 and boom

Answer: 5

Step-by-step explanation:

the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color.

How to solve the question?

To find the least number of rows, we need to determine the greatest common divisor (GCD) of 56 and 120, since each row must have the same number of blocks. We can use the Euclidean algorithm to find the GCD:

120 = 2 x 56 + 8

56 = 7 x 8 + 0

Therefore, the GCD of 56 and 120 is 8. This means that each row must have 8 blocks, and there will be a total of (56+120) = 176 blocks to be arranged.

Since each row can have either only yellow or only black blocks, we need to determine which color will have the greater number of rows. To do this, we can divide the total number of blocks by the number of blocks in each row:

Yellow blocks:

Number of rows = 56 ÷ 8 = 7 rows

Black blocks:

Number of rows = 120 ÷ 8 = 15 rows

Since there are more black blocks, we will use 15 rows of black blocks. Each row will have 8 blocks, so there will be a total of (15 x 8) = 120 black blocks.

We can then use the remaining 56 yellow blocks to create rows of only yellow blocks. Each row will have 8 blocks, so there will be a total of (56 ÷ 8) = 7 yellow rows.

Therefore, the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color

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Answer: The primary rectangle contains a length of 2a units (since it is labeled as "2a" within the diagram), so its zone is 2a x a = 2a^2 square units.

The moment rectangle contains a length of 3a units (since it is labeled as "3a" within the diagram), so its range is 3a x a = 3a^2 square units.

The third rectangle contains a length of 4a units (since it is labeled as "4a" within the graph), so its range is 4a x a = 4a^2 square units.

To discover the overall region of the expansive rectangle, able to include the zones of these three rectangles:

Add up to zone = 2a^2 + 3a^2 + 4a^2

Disentangling this expression, we are able combine the like terms (2a^2, 3a^2, and 4a^2) to urge:

Add up to range = (2 + 3 + 4) a^2

Step-by-step explanation:

According to the information, we can infer that the correct sentences about the graph is A person with annual income of at least $50,000 is more likely to be 45 years old or above.

To find the correct sentence we have to analyze the information of the graph and read the options. Once we make this procedure, we can compare each sentence with the information of the graph to establish the correct one.

According to the information the correct option would be A person with annual income of at least $50,000 is more likely to be 45 years old or above (option C).

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Answer:

40 plus 19/ 9-3=40

Answer: To find the area of a triangle, we can use the formula:

Area = (base x height) / 2

However, in this problem, we don't have the height of the triangle directly. Instead, we have the lengths of three sides of the triangle.

To find the height, we can use Heron's formula, which allows us to calculate the area of a triangle when we know the lengths of all three sides:

Area = √(s(s-a)(s-b)(s-c))

where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter (half of the perimeter) of the triangle:

s = (a + b + c) / 2

Once we have the area of the triangle, we can use the given price per square foot to calculate the cost of the lot.

So, to apply this to the problem at hand, we can first calculate the semi-perimeter of the triangle:

s = (94 + 188 + 168) / 2 = 250

Next, we can use Heron's formula to find the area of the triangle:

Area = √(250(250-94)(250-188)(250-168)) ≈ 7329.53 square feet

Finally, we can calculate the cost of the lot by multiplying the area by the price per square foot:

Cost = 7329.53 x $3 = $21,988.59

Therefore, the approximate cost of the triangular lot is $21,988.59.

Step-by-step explanation:

The number that needs to be added to complete the square is 169/4

To complete the square for the quadratic equation x² + 13x - 32 = 0, we need to add (13/2)² = 169/4 to both sides.

This is because the coefficient of x in the quadratic term is 13, so half of that is 6.5, and the square of that is 42.25, which simplifies to 169/4.

The equation will then become:

x² + 13x - 32 + 169/4 = 0 + 169/4

So the number that needs to be added to complete the square is 169/4, or 42.25.

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The equation of the line in slope-intercept form is:

y = 4x + 9

The slope-intercept form of the equation of a line is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

In this case, we know that the line passes through the point (-4, -7) and has a slope of 4. So, we can plug in the values of x, y, and m into the slope-intercept form and solve for b:

-7 = 4(-4) + b

Simplifying the right side:

-7 = -16 + b

Adding 16 to both sides:

9 = b

So the y-intercept is 9. Therefore, the equation of the line in slope-intercept form is:

y = 4x + 9

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The question that is a statistical question is "How many miles did your family drive last week?"

A statistical question is a question that requires collecting and analyzing data to answer.

It involves investigating a specific variable or variables and determining patterns, trends, or relationships within the data.

The question "How many miles did your family drive last week?" is statistical, as it involves collecting and analyzing data related to a specific variable (miles driven) over a certain period of time (last week).

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Therefore , the solution of the given problem of angles comes out to be KL has a measurement of 19.49.

The largest and smallest walls of a skew are found at the intersection of the pathways connecting its ends. Two pathways could meet at a crossroads. Another result of two entities interacting is an angle. More than anything else, they resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their endpoints to produce a two-dimensional curve.

Here,

It looks to be a right-angled triangle with the sides identified as KL, KM, and LM based on the photograph provided. The measurements are as follows:

=> KL = 8.58

=> KM = 9.36

=> LM = 10.13

=> KM + LM = KL

Since KM and LM are the two sides that make up KL, we may sum them to find the measurement of KL.

=> KM + LM = 9.36 + 10.13 = 19.49

KL thus has a measurement of 19.49.

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Answer: $3.00

Step-by-step explanation:

To figure this out, we can use the following formula:

[tex]\textsf{Cost per pound x number of pounds we want to buy}[/tex]

In this case, we want to buy 2.5 pounds of apples, so we can multiply 2.5 by $1.20 to get the total cost:

[tex] \textsf{2.5 x 1.20 = 3} [/tex]

So, 2.5 pounds of apples will cost $3.00

Answer:

Jamie gets £9.60

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 = 5 parts

divide the amount by 5 to find the value of one part of the ratio.

£24 ÷ 5 = £4.80 ← value of 1 part of the ratio , then

2 parts = 2 × £4.80 = £9.60 ← amount Jamie gets

Answer:

  2. 139π/90 radians ≈ 4.852

  3. -(9√5 +8√7)/77

  4. 2+√3

Step-by-step explanation:

You want exact answers involving various trig identities and angle sum formulas.

There are π radians in 180°, the number of radians in 278° is ...

  278°(π/180°) = (278/180)π

  278° = (139/90)π radians ≈ 4.852 radians

The cosine of the sum of angles is ...

  cos(x +y) = cos(x)cos(y) -sin(x)sin(y)

The relationship between sine and cosine is ...

  cos(x) = ±√(1 -sin(x)²)

  sin(x) = ±√(1 -cos(x)²)

The signs will depend on the quadrant of the angle.

To use the angle sum relation, we need the sine of the angle whose cosine is given, and vice versa.

  sin(arccos(-2/7)) = -√(1 -(-2/7)²) = -(√45)/7 = (-3/7)√5 . . . . in QIII

  cos(arcsin(-3/11)) = √(1 -(-3/11)²) = (√112)/11 = (4/11)√7 . . . . in QIV

The cosine of the sum of the angles is then ...

  cos(arccos(-2/7) +arcsin(-3/11)) = (-2/7)(4√7/11) -(-3√5)/7·(-3/11)

  = -8√7/77 -9√5/77

  cos(x +y) = -(9√5 +8√7)/77

The formula for the tangent of the sum of angles is ...

  tan(x +y) = (tan(x) +tan(y))/(1 -tan(x)tan(y))

We know that tan(π/4) = 1 and tan(π/6) = 1/√3, so the tangent of the sum of the angles is ...

  tan(π/4 +π/6) = (1 +1/√3)/(1 -(1·1/√3)) = (√3 +1)/(√3 -1) = (√3 +1)²/2

  tan(π/4 +π/6) = 2 +√3

__

Additional comment

A suitable calculator can be very handy computing and/or checking your results.

2) 278° to Radians = 4.85202

3) the exact value of cos (x+ y) is -0.0914

4) the exact value of the expression is 3.73

The formula ofr conversion from degree to radian is

2) 278° × π/180 = 4.852rad

3) in the above given expressions, Sin(x) is negative.

Using Pythagorean rule, we can state:

sin(x ) = √(1 - cos^2(x)) =

√(1 - (-2/7)²)

= -3√(3)/7

Also,

given that cos( y) is positive, we c  n also use the Pythagorean idetity

cos  (y) = √(1 - sin ²(y) )

= √(1 - (-3/1 1)²)

= 8√(2)/11

substituting into cos (x + y)


cos(x+y) = cos(  x)cos (y ) - sin (x) sin(y)

= (-2/7)( 8 √(2)/11) - (-3√(3)/7) ( -3/11)

= -1 6 √(2) /77 + 9√( 3)/ 77

= -0.09141506142

The exact value is approximately -0.0914

3)

Using the formula for tangent of sum of angles we say

tan( ( π/4) + (π/6) )   = (tan ( π / 4) + tan (π/6))/(1 - tan ( π/4) tan( π/6))

Sutstituting ....

tan ((  π/4) + ( π/6) )  = (1 + √ 3/3)/( 1 - √ 3 /3 )

tan( (π/ 4) + (π /6 )) =   (1 + √3/   3) (1 + √3/3 )]/ [(1 - √3/ 3)(1 + √3/3)]

Simplifying

  tan ( (π /4) + ( π/6) ) = ( 2 + √3 )/  ( 2 - √ 3)

This is the exact value of tan((π/4) + (π/6)) or 3.73

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