Question 6 of 25
What are the solutions to the system of equations graphed below?

Yhe volume of both the prism and the pyramid are the same. The right response is B, which states, "The volume of both shapes is the same."

What is the straightforward meaning of volume?

Three-dimensional space is occupied by everything. Here, the volume of the space is calculated. A three-dimensional object's volume is the area included inside its bounds. It is also referred to as an object's capability occasionally.

[tex]\mathrm{h_{py} = 3 \times h_p}[/tex]

The volume of the prism is given by:

[tex]V_p[/tex] = base area × height = 4 cm² × [tex]h_p[/tex]

The volume of the pyramid is given by:

[tex]\mathrm{V_{py}}[/tex] = (1/3) * base area * height = (1/3) * 4 cm² * [tex]h_{py[/tex]

Using the equation for [tex]h_{py[/tex] from above, we can substitute:

[tex]\mathrm{V_{py}}[/tex]  = (1/3) * 4 cm² * 3 *  [tex]h_p[/tex] = 4 cm² *  [tex]h_p[/tex] = [tex]V_p[/tex]

So the volume of both the prism and the pyramid are the same. The right response is B, which states, "The volume of both shapes is the same."

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Events that have no outcomes in common  are said to be disjoint or mutually exclusive.

Two sets are known to be mutually exclusive when they have no common elements. Mutually exclusive events are those that cannot take place at the same moment.

If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero.

Set A = {2, 4, 6, 8, 10, 12, 14, 16}

Set B = {1, 3, 5, 7, 9, 11, 13, 15}

A and B do not have any numbers in common, so P (A ∩ B) = 0. Therefore, A and B are mutually exclusive.

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Answer:

x = ~4.40 or [tex]\sqrt{19.37}[/tex]

Step-by-step explanation:

This is a right triangle, so we will use the Pythagorean Theorem.

The theorem goes as follows: [tex]a^2 + b^2 = c^2[/tex]

Let's set x as the a value in the theorem. Plug in 6.8 for b, and 8.1 for c.

[tex]x^2 + (6.8)^2 = (8.1)^2[/tex]

Then, simplify!

[tex]x^2 + 46.24 = 65.61[/tex]

Subtract 46.24 on both sides.

[tex]x^2 = 19.37[/tex]

Take the square root of both sides

[tex]x =\sqrt{19.37}[/tex]

Voila!

Step-by-step explanation:

What notes are you speaking of?

Answer:

Step-by-step explanation:

It would take 300 minuets

The value of 77 degrees Fahrenheit (°F) is equal to 25 degrees Celsius (°C).

The conversion from Fahrenheit to Celsius involves a simple mathematical formula, which is as follows:

°C = (°F - 32) x 5/9

In this formula, °F represents the temperature in degrees Fahrenheit, while °C represents the temperature in degrees Celsius.

To convert 77 degrees Fahrenheit to Celsius, we first plug in the value of 77 for °F:

°C = (77 - 32) x 5/9

Next, we simplify the expression inside the parentheses:

°C = 45 x 5/9

We can simplify this further by multiplying 45 and 5/9:

°C = 225/9

We can then simplify this fraction by dividing both the numerator and denominator by the greatest common factor, which is 9:

°C = 25

Therefore, we conclude that 77 degrees Fahrenheit is equivalent to 25 degrees Celsius.

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Jet could fly a distance of 752 miles in 8 hours if it travels at the same rate.

Speed is defined as the unit rate in terms of distance travelled and the time taken to travel the distance.

Speed has only magnitude and no direction and therefore is a scalar quantity.

Given that,

a jet travels 470 miles in 5 hours.

Distance travelled = 470 miles

Time taken to travel the distance = 5 hours

Speed of the jet = 470 miles / 5 hours = 94 miles per hour

Given that jet is travelling at the same rate. So the speed is constant.

We have to find the distance travelled in 8 hours.

Let d be the distance.

Speed = Distance / Time

Distance = Speed × Time

d = 94 × 8

d = 752 miles

Hence the distance travelled is 752 miles in 8 hours.

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I think its a is one of them, im not completely sure tho

Step-by-step explanation:

The AB intersects circle P if PA is 7mm and PB is 3mm it must exit the circle, and it has 2 contact points.

PA is longer than the radius of the circle so Point A must be outside of the circle.

Two or more circles intersect at one point. Two circles can be tangent to each other in two different ways.

here, we have,

We have given that,

AB lies in the same plane as circle P, which has a radius of 6 mm.

PB is less than the radius of the circle so Point B must be inside the circle.

Since the ray is going from A to B it is coming inside the circle and continuing in the other direction.

Therefore, it must exit the circle, giving us 2 contact points.

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As per the concept of average, the cost of producing 6,000 units is $79,200.

The average, also known as the mean, is a mathematical representation of a set of data. It is calculated by adding all the values in the set and dividing the result by the number of values in the set.

When it comes to calculating the total amount of direct manufacturing cost incurred when 6,000 units are produced, it is important to use the average cost per unit. To do this, we need to multiply each average cost per unit by the number of units produced.

The total direct manufacturing cost incurred can be calculated as follows:

Direct materials = $5.20 * 6,000 = $31,200

Direct labor = $3.75 * 6,000 = $22,500

Variable manufacturing overhead = $1.65 * 6,000 = $9,900

Fixed manufacturing overhead = $2.60 * 6,000 = $15,600

The total direct manufacturing cost incurred is $79,200.

Complete Question:

Meginnis Corporation's relevant range of activity is 3,000 units to 7,000 units. When it produces and sells $5,000 units, its average costs per unit are as follows:

Average Cost per Unit

Direct materials $5.20

Direct labor $3.75

Variable manufacturing overhead $1.65

Fixed manufacturing overhead $2.60

Fixed selling expense $0.50

Fixed administrative expense $0.40

Sales commissions $1.50

Variable administrative expense $0.50

If 6,000 units are produced, the total amount of direct manufacturing cost incurred is closest to:

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Answer:

10 columns

Step-by-step explanation:

[tex]\frac{60}{6}=10[/tex] columns

Answer:

4.6%

Step-by-step explanation:

3500+175 = 3675

(175/3675)×100 = 4.6%

The Cylinder can hold 138, 160 cm³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume.

Given:

Height= 1.1 m = 110 cm

Radius= 20 cm

Now, Volume of Cylinder

= πr²h

= 3.14 x 20 x 20 x 110

= 3.14 x 44000

= 138, 160 cm³

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-3/4 is slope of the linear equation 3x+4y=5.

Two or more expressions with an Equal sign is called as Equation.

The standard form for linear equations in two variables is Ax+By=C.

3x+4y=5 is a linear equation in standard form.

4y=5-3x

Divide both sides by 4

y=5/4-3/4x

y=-3/4x+5/4

The slope of the equation is -3/4.

Hence, the  slope of the linear equation is -3/4.

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The complete question is given below:

Find the slope of  linear equation 3x+4y=5?

Answer:

The shirt costs $21

Step-by-step explanation:

2x + 3y = 127    ....eq 1

Her twin sister Hallie bought 1 pair of jeans and 4 shirts for $116.

So, x + 4y = 116     ....eq 2

Multiplying eq 2 by 2, we get :

2x + 8y = 232     ....eq 3

Subtracting eq 1 by eq 3, we get :

(2x + 8y) - (2x + 3y) = 232 - 127

5y = 105

Thus, y = 21

Putting this value of y in eq 2, we get :

x + 4(21) = 116

x = 116 - 84 = 32

Therefore, the cost of a pair of jeans = x = $32

And the cost of a shirt = $21

Answer:

  √576 = 24

Step-by-step explanation:

You want to find the square root of 576 by the long division method.

The attachment shows the result of applying the method.

The root of 576 is 24.

Answer:

6w by 9L

Step-by-step explanation:

24 x 1/4=6

36 x 1/4=9

Answer:

the answer is (a) 28.

Step-by-step explanation:

The given situation can be represented by a linear equation of the form:

Cost = mx + b

where "m" is the slope (the rate of change of cost with respect to time), "x" is the number of hours of the tour, and "b" is the y-intercept (the cost when x = 0).

In this case, the y-intercept is $60, which represents the one-time fee. The cost increases by $28 per hour, so the slope is:

m = $28/hour

Therefore, the answer is (a) 28.

Answer:

  112

Step-by-step explanation:

You want the number of 3-digit "dropdown numbers".

A "dropdown number" has distinct digits, one of which is the average of all digits.

We can count the number of dropdown numbers by considering the digit that is the average of the rest. For that digit (n), the number of possible choices of the other digits is the lesser of (n) or (9-n). For example, for n=2, we can have other digit pairs of (0, 4) or (1, 3). For n=6, we can have other digit pairs of (5, 7) or (4, 8) or (3, 9).

The value of n may range from 1–8, inclusive, so the number of digit triples will be 2(1 +2 +3 +4) = 20. Each triple of digits can be arranged 6 ways, for a total of 20·6 = 120 numbers of 3-digits.

Of those, 8 numbers will have a leading 0, so may not count as 3-digit numbers. That leave a total of 120 -8 = 112 3-digit dropdown numbers.

__

Additional comment

The first 5 in numerical order are ...

  102, 120, 123, 132, 135

The last 5 are ...

  957, 963, 975, 978, 987

In general, a number on the list, m, has a corresponding number 999-m also on the list. The exceptions are numbers that have a leading digit of 0.

Answer: The number of speeding tickets issued is represented by x and the number of tickets for failure to obey traffic signals is represented by y. The total number of tickets issued is 130, so we have:

x + y = 130

The total amount of money collected in fines is $8,710.00, so we have:

67x + 67y = 8710

These two equations form a system of linear equations that can be used to determine the number of speeding tickets, x, and the number of tickets for failure to obey traffic signals, y. To solve this system, we can use any of the methods for solving a system of linear equations, such as substitution, elimination, or matrices.

Step-by-step explanation:

By using the function rule, the missing values in table should be completed as follows;

x       -2       -1      0      1       2

y       -16      -6     4      14     24

In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = -2, the y-value of this linear function is given by;

-10x + y = 4

y = 10x + 4

y = 10(-2) + 4 = -16.

When the value of x = -1, the y-value of this linear function is given by;

y = 10x + 4

y = 10(-1) + 4

y = -6.

When the value of x = 0, the y-value of this linear function is given by;

y = 10x + 4

y = 10(0) + 4

y = 4.

When the value of x = 1, the y-value of this linear function is given by;

y = 10x + 4

y = 10(1) + 4

y = 14.

When the value of x = 2, the y-value of this linear function is given by;

y = 10x + 4

y = 10(2) + 4

y = 24.

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The statement is false. The solution set of a linear system can only be expressed using a parametric equation if the system has at least one solution.

Equation of this sort is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are specified as continuous and independent of other variables functions of the parameter Multiple parameters may be utilized as needed.For example, the following equation can be represented as a pair of equations in parametric form rather than the equation in Cartesian form: Parameterization, It effectively differentiates and integrates curves by converting a function into parametric form.

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Step-by-step explanation:

I am in class 7 If I know I tell you I am go to ask my teacher

Answer:

Domain:(−∞,5)∪(5,∞),{x|x≠5}

Range:(−∞,3)∪(3,∞),{y|y≠3}

Step-by-step explanation:

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The equation of circle is ( x + 1 )² + ( y - 2 )² = 20

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the points on the circle be A ( -5 , 4 ) , B ( 3 , 4 ) and C ( 3 , 0 )

Now , the equation of the circle is of the form

ax + by + c = x² + y²

Substituting the values in the equation , we get

-5a + 4b + c = 41   be equation (1)

3a + 4b + c = 25   be equation (2)

3a + c = 9   be equation (3)

Subtracting equation (2) from equation (1) , we get

-8a = 16   be equation (4)

Divide by -8 on both sides of the equation , we get

a = -2

Substitute the value of a in equation (3) , we get

3 ( -2 ) + c = 9

-6 + c = 9

c = 15

Substitute the value of a and c in equation (2) , we get

-6 + 4b + 15 = 25

4b + 9 = 25

4b = 16

b = 4

So , the value of a , b and c are -2 , 4 and 15 respectively

Now , the equation of circle will be

-2x + 4y + 15 = x² + y²

On simplifying the equation , we get

x² + y² + 2x - 4y - 15 = 0

( x² + 2x + 1 ) - 20 + ( y² - 4y + 4 ) = 0

So , the equation will be

( x + 1 )² + ( y - 2 )² = 20

Hence , the equation of circle is ( x + 1 )² + ( y - 2 )² = 20

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Answer:

Step-by-step explanation:

ur mom

The next three terms in the following arithmetic sequence -4, 5, 14, 19 … include the following:

Term 5 = 32.

Term 6 = 41

Term 7 = 50

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 5 - (-4)

Common difference, d = 9

Next, we would determine the next three terms as follows:

a₅ = a₁ + (n - 1)d

a₅ = -4 + (5 - 1)9

a₅ = 32

a₆ = a₁ + (n - 1)d

a₆ = -4 + (6 - 1)9

a₆ = 41

a₇ = a₁ + (n - 1)d

a₇ = -4 + (7 - 1)9

a₇ = 50

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The statements which are true about Micah's survey are;

As evident in the task content; Micah wants to know the most common style of surfboard used at Breakers Point.

Hence, it can be inferred that the population of the survey in this context is; all people that surf at Breakers Point.

Also, since Micah only surveys surfers between 8:00 AM and 12:00 PM, it follows that; Micah will not get a representative sample.

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The fourth term in the sequence is 7.

Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.

This ratio is common ratio.

Given is the first term of a sequence.

c(1) = 56

Also, there is given an nth term of the sequence.

c(n) = c(n - 1) [tex]\frac{1}{2}[/tex]

This means that every term in the sequence is the half of the preceding term.

So this is a geometric sequence with a common ratio of 1/2.

nth term of a geometric sequence = a. rⁿ⁻¹, where a is the first term and r is the common ratio.

Given, first term = 56 and we found r = 1/2

c(4) = 56 × ([tex]\frac{1}{2}[/tex])⁴⁻¹ = 7

Hence the fourth term in the given sequence is 7.

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