A 40 percent discount on a sweater resulted in a saving of $14.40. Find the original price.

The gas exerts a pressure of 218.75 kPa when its volume is reduced to 2.0 L, following the behavior of an ideal gas.

Ideal gas behavior:

Suppose the initial volume of carbon dioxide gas is V = 3.5l

Initial pressure is P = 125 kPa

Since the volume is reduced to 2.0l, the final volume is shown as V'= Will be done. 2L

The final pressure of the gas is P'.

We consider the behavior of gas to be ideal. From the ideal gas equation, it becomes as follows.

PV = P'V'

125 × 3.5 = P'× 2

P'= 218.75 kPa

Therefore, the final pressure is 218.5 kPa.

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Answer:

First part: 219 kPa (option D)

Second part: 2.3 L (option A)

Step-by-step explanation: just got asked the question

Answer:

[tex]\begin{cases}x=-5\\y=-7\end[/tex]

Step-by-step explanation:

[tex]\begin{cases}-x-2y=19\left(1)\right\\-x-y=12\left(2)\right\end[/tex]

(2)-(1)

[tex]y=-7[/tex]

Sub into (2)

[tex]-x+7=12\\x=-5[/tex]

Solutions:

[tex]\begin{cases}x=-5\\y=-7\end[/tex]

Answer:

B. Zero

Step-by-step explanation:

The slope of the line is in the the first two quadrants and is horizontal, meaning it has zero slope.

Answer:

Zero slope :)

Step-by-step explanation:

A zero slope is a horizontal line. When there is a zero slope, y will be equal to a constant. :)

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Mary should pour around 3.7 liters or 226.08 in³ volume of water in the vase.

Given Information and Formula Used

Radius of the cylindrical vase, r = 3 inches

Height of the cylindrical vase, h = 8 inches

The formula for the volume, V of a cylinder is given as,

V = πr²h

Here, r is the radius of the cylinder and h is the height of the cylinder.

Calculating the Volume

Substituting the given values of r and h in the formula for the volume of cylinder, we get

Volume, V = π(3)²(8)

Using π = 3.14, we have,

V = 3.14(9)(8)

V = 226.08 cubic inches

Volume in Liters

Since, 1 Liter = 61.0237 cubic inches,

1 cubic inch = 1/61.0237 liters

⇒ 226.08 cubic inches = 226.08/61.0237 liters

⇒ 226.08 cubic inches ≈ 3.07 liters

Thus, Mary needs to pour approximately 3.07 liters volume of water in the vase.

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The correct answer is option B which is we need ∠L ≅  ∠R to prove congruency.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.

Here we are given that

KL = NR

JL = MR

Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.

So for the triangles to be congruent by SAS, angle L must be congruent to angle R.

∠L=∠R

Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.

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Answer: option b

Step-by-step explanation:

1) The frequency of landing 4 is 14.

2) The frequency for prime numbers is  8 and 3.

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

Outcome               Frequency

1                                   12

2                                   6

3                                   8

4                                   14

5                                   3

1) The frequency of landing 4 is 14.

2) The frequency for prime numbers is  8 and 3.

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Leo's water is at a greater temperature. And Manoj's water is closer to freezing.

The temperature refers to the degree of hotness ant coldness of the substance.

Water freezes at 0 °C.

Manoj's water is 3 °C.

Leo's water is 7 °C.

Leo's water is at a greater temperature.

Manoj's water is closer to freezing.

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1) Isosceles [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{DE} \perp \overline{AC}[/tex], [tex]\overline{DF} \perp \overline{BC}[/tex], [tex]\overline{DE} \cong \overline{DF}[/tex] (given)

2) [tex]\angle CAB \cong \angle CBA[/tex] (angles opposite congruent sides in a triangle are congruent)

3) [tex]\angle AED[/tex] and [tex]\angle DFB[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\angle AED \cong \angle DFB[/tex] (all right angles are congruent)

5) [tex]\triangle DEA \cong \triangle DFB[/tex] (AAS)

6) [tex]D[/tex] is the midpoint of [tex]\overline{AB}[/tex] (if a point splits a segment into two congruent parts, it is a midpoint)

Answer:

16.8

Step-by-step explanation:

3x+2y

3(4)+2(2.4)

12+4.8

16.8

The correct property of equality to solve each equation is x=24.

We have given that,

Identify the correct property of equality to solve each equation.

3+x=27

The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.

For this case, we must solve the following equation

3+x=27

Subtracting 3 on both sides of the equation we have

3+x-3=27-3

x=24

We observe the property of equality of subtraction.

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Answer:

120%

Step-by-step explanation:

10.14 is more than all of 8.45.

8.45 is 100% of 8.45.

So 10.14 will be more than 100%.

10.14 ÷ 8.45 = 1.2

This is the decimal value.

To change to %, multiply by 100.

1.2 × 100 = 120

10.14 is 120% of 8.45

The proof that quadrilateral WXYZ, having vertices W(-5, 6), X(-1, 10), Y(1, 4), and Z(-2, -3) is a trapezoid is given below.

Mathematical proof is a set of logical statements that are sequentially indicated to guaranty that a stated position is indeed accurate.

It is to be noted that with parallelograms, the diagonals intersect at the midpoints. (See the attached image).

The Diagonals are  WY  and  XZ; Where

WY :  (-4, -3) to  (6, -2); and

Midpoint is  [ (0 + 2)/2 ,  (-1 + -4)/2 ]  

= (1, -5/2)

The diagonals are bisectors of each other.

It is to be noted that the diagonals are not congruent. For if they were congruent, then the above would not be a trapezoid.

The Length of WY  = √((-4 - 6)²  +  (-3 - (-2))²)

WY = √(100 + 1)

WY = √101

The Length of XZ =    √((0 - 2)²  +  ( -1 - -4)²)

XZ = √(4+9)

XZ = √13

From the above, it is clear that both diagonals are unequal. Hence, given the first and second proof, we can state that quadrilateral WXYZ is a Trapezoid.

QED

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Answer: C

Step-by-step explanation:

[tex]75=\frac{d+94}{2}\\ \\ 150=d+94 \\ \\ d=56[/tex]

Therefore, the equation of circle is: [tex](x+3)^{2}+(y+5)^{2} = 100[/tex]

Here we know that[tex](h,k) = (-3,5)[/tex]but we are not given the radius.

However, we can find the radius by using the distance formula.

[tex]\sqrt{x^{2} +y^{2} }[/tex], where [tex]x=x_{1} -x_{2}[/tex] and [tex]y=y_{1} -y_{2}[/tex]

Putting the values, we get:

[tex]\sqrt{8^{2} +6^{2} }[/tex]

The radius comes out to be:

[tex]r=10[/tex]

An equation of the circle with center [tex](h,k)[/tex] and radius r is

[tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex]

Now, substituting the values, we get:

[tex](x--3)^{2} +(y-5)^{2} = 10^{2}[/tex]

Therefore, the equation of circle is:

[tex](x+3)^{2}+(y+5)^{2} = 100[/tex]

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Answer-

-1/2, -4

Step-by-step explanation:

A, E

Did the math to find the solution earlier, got right xoxo :)

Answer:

option OE. 8i

Step-by-step explanation:

[tex] \sqrt{64 } \: is \: equal \: to \: 8[/tex]

[tex]i \: = 1[/tex]

[tex]8 \times 1 = 8[/tex]

[tex]therefore \: \sqrt{64} \: is \: equivalent \: to \: 8i[/tex]

The probability that a randomly selected individual will have a waiting time between 16 and 44 minutes is 93.72%.

Given mean of 30 minutes and standard deviation of 7.5 minutes.

In a set with mean d and standard deviation d. , the z score is given as:

Z=(X-d)/s.

where d is sample mean and s is standard deviation.

We have to calculate z score and then p value from normal distribution table.

We have been given d=30, s=7.5

p value of Z when X=44 subtracted by the p value of Z when X=16.

When X=44,

Z=(44-30)/7.5

=14/7.5

=1.87

P value=0.9686

When X=16

Z=(16-30)/7.5

=-1.87

P Value=0.0314.

Required probability is =0.9686-0.0314

=0.9372

=93.72%

Hence the probability that a randomly selected individual will have a waiting time between 16 and 44 minutes is 93.72%.

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A statement which correctly compares the two functions on the given interval [-1, 2] is: C. Both functions are increasing, but function g increases at a faster average rate.

First of all, we would determine the values of function g(x) on the given interval [-1, 2] as follows:

g(x) = -18(⅓)^x + 2

At x = -1, we have:

g(-1) = -18(⅓)^(-1) + 2

g(-1) = -52.

At x = 0, we have:

g(0) = -18(⅓)^(0) + 2

g(0) = -16.

At x = 1, we have:

g(1) = -18(⅓)^(1) + 2

g(1) = -4.

At x = 2, we have:

g(2) = -18(⅓)^(0) + 2

g(2) = 0.

By critically observing the values of each functions, we can logically deduce that both functions are increasing but function g(x) increases at a faster average rate because it started with a lower value and ended with a higher value.

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Answer:

x=28.93(rounded) x=28.929(not rounded)

Step-by-step explanation:

Step-by-step explanation:

25/3÷x=7/3÷8.1

25/3×8.1=7/3×x

135/2=7/3×x

x=135/2×3/7

x=405/14=28.929

The force required to move the object by 15 feet will be 48 lbs.

The effort or an external agent responsible for moving or stopping any object is called a force. It is given that the force required to move the object at the distance of 9 feet is 80 lbs we need to calculate the force required to move the object by 15 feet.

The force will be calculated. We can make an equation from the given data in the question:-

[F1/F2] = [d2/d1]

F2 = [F1 x d1 ] / [d2]

F2 = [ 80 x 9 ] / [ 15 ]

F2 = a

Therefore the force required to move the object by 15 feet will be 48 lbs.

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Answer:

ABCD-DEFG
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Yes, the horizontal line test is important when finding the inverse of a function because without the intersection of the line, they would be no inverse.

The steps include;

A property of horizontal line is that if it intersects the graph of a function more that on way, then 'f' does not have an inverse.

If no horizontal line intersects the graph , 'then f' does have an inverse.

Thus, the horizontal line test is important when finding the inverse of a function because without the intersection of the line, they would be no inverse.

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The correct answer is option B: there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.

The practice or science of organizing and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.

From the dot plot attached, we can find the average number of students per class for each school.

For Poplar Middle School;

Total number of students = (20 × 3) + (21 × 5) + (22 × 7) + (23 × 4) + (24 × 1) = 435 students.

There are 20 classes.

Thus;

Average number of students per class = 435/20 = 21.75

For Oak Middle School;

Total number of students = (20 × 1) + (21 × 2) + (22 × 2) + (23 × 4) + (24 × 3) + (25 × 2) + (26 × 2) + (27 × 2) + (28 × 1) + (29 × 1) = 483

The average number of students per class; 483/20 = 24.15

Difference in average = 24.15 - 21.75 = 2.40

This implies that there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.

Therefore the correct answer is option B: there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.

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Answer:

B. x < -1

Step-by-step explanation:

Hello!

Let's put them in order from greatest to least:

Given our possible inequalities, we need to find the inequality that contains all of these values.

The inequality that works is x < -1, as all values are less than -1.

Therefore, the answer is B. x < -1.

The value of the unknown length is 24

Represent the unknown length with x.

So, we have the following equivalent ratio:

30 : 30 + x = 25 : 45

Express as fraction

30/30 + x = 25/45

Simplify the fraction

30/30 + x = 5/9

Cross multiply

150 + 5x = 270

Evaluate the like terms

5x = 120

Divide by 5

x = 24

Hence, the value of the unknown length is 24

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Pound is the unit of measure of passengers car weight

According the statement

The weight of passengers car is 4.5 times 10 superscript 3 units.

from this it is clear that the in simple terms the weight become 4.5 * 10^3

AND

the term 10^3 is used when we measure the weight in pounds.

So, Pound is the unit of measure of passengers car weight.

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Answer:

Step-by-step explanation:

What line segment is equal to AC - BC?

A_____B_____C -

             B_____C =

A_____B

The correct option is B. Yes, SSS congruency

Yes, more than one triangle can be made using the given measurements

The appropriate triangle congruence postulate is the SSS congruence which states that If all the three sides of one triangle are equivalent to that of the second triangle, then the two triangles are said to be congruent.

Thus, the option  B is correct

The complete question is ;

The measurements of a triangle are given. Is there exactly one triangle that can be formed using the given measurements? If so, identify the appropriate triangle congruence postulate.

∆ABC : m ∠A = 90°, AB = 15, AC = 15

A)No, More than one triangle could be made with these measures

B)Yes, SSS congruency

C)Yes, ASA congruency

D)Yes, SAS congruency

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The discriminant is 164 and there are two real solutions.

What is Quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax^2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

We can find the discriminant as shown below:

x^2+14x+8=0

a=1, b=14, c=8

Discriminant=b^2-4ac

=(14)^2-4*1*8

=196-32

=164>0

As the discriminant is positive and greater than zero. So, there are two real and distinct solution.

Hence, discriminant is 164 and two real solution.

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