Ms. Hernandez began her math class by saying:


I'm thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14, what is the 5th number?


What is the 5th number Ms. Hernandez is thinking of?

A. 13

B. 14

C. 15

D. 16

E. 18

Answer:

13.93

Step-by-step explanation:

see attached for explanation

Answer:

21,7 - yes

28,3 - no

17,3 - no

20,4 - yes

55,5 - yes

15,5 - yes

26,4 - no

32,8 - yes

48,7 no

60,2 - yes

79,4 - no

81,3 - yes

Step-by-step explanation:

hope that helps

The number pairs where the first number is a multiple of the second number are:

21, 7

20, 4

55, 5

15, 5

32, 8

60, 2

81, 3

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The first number which is a multiple of the second number.

21 and 7
7 x 3 = 21

28 and 3

3 x 9 = 27

17 and 3

3 x 5 = 15

20 and 4

4 x 5 = 20

55 and 5

5 x 11 = 55

15 and 5

5  x 3 = 15

26 and 4

4 x 6 = 24

32 and 8

8 x 4 = 32

48 and 7

7 x 7 = 49

60 and 2

2 x 30 = 60

79 and 4

4 x 19 = 76

81 and 3

3 x 27 = 81

Thus,

The number pairs are:

21, 7

20, 4

55, 5

15, 5

32, 8

60, 2

81, 3

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

h(x) = -7/6x - 25/6.

Given h(-1)=-2 and h(-7)=-9

For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.

To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

h(-1) = -2 is a point on the line, so we can write it as (-1, -2).

h(-7) = -9 is another point on the line, so we can write it as (-7, -9).

Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6

Now we can find b using one of the points and m. Let's use (-1, -2):

y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b

b = -25/6

Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6

We can check our answer by plugging in the two given points:

h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9

The answer is h(x) = -7/6x - 25/6.

Know more about linear function  here,

https://brainly.com/question/29205018

#SPJ11

Answer:

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

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a^2 - b^2 = (a + b)(a - b) where a = 5x and b = 8y.

~Hoped this helped~

Using the law of sine on the given triangle, we get the measure of y as given by: Option C: 2.5 units

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b} = \dfrac{\sin\angle C}{c}\)

Remember that we took

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

For this case, the missing image is attached below.

Applying the sine law, as we have:

The first two angles Y and Z are enough. (we use angle Z as the length of the side opposite to Z is known).

Using sine law, we get:

\(\dfrac{\sin(m\angle Y)}{y} = \dfrac{\sin(m\angle Z)}{2}\\\\y = \dfrac{\sin(75^\circ) \times 2}{\sin(50^\circ)} \approx 2.522 \approx 2.5 \: \rm units\)

Thus, using the law of sine on the given triangle, we get the measure of y as given by: Option C: 2.5 units

Learn more about law of sines here:

https://brainly.com/question/17289163

As an AI text-based model, I'm unable to directly design and draw layout plans or provide CAD drawings. However, I can guide you on the general principles and components that are typically included in a functional layout plan for a reheat-regenerative cycle steam power plant with a rated generator capacity of at least 10,000 KW. Here are some key considerations and components: Turbine Hal, Boiler Unit, Condenser, Heaters, Steam Flow Paths, Control Room, Auxiliary Systems.

Turbine Hall: This is the area where the turbines are housed. It should be designed to accommodate the size and specifications of the turbines, including any necessary maintenance space.

Boiler Unit: This section includes the boiler shell, where steam is generated. The design should meet standard specifications, and the auxiliaries (such as pumps, fans, and control systems) should be included based on calculations and requirements.

Condenser: The condenser, which is a closed or surface type, should be located near the turbine hall to allow for efficient heat transfer and condensation of the steam.

Heaters: As mentioned, the plant should have a total of four heaters, consisting of a combination of closed/surface type and direct contact type. The arrangement of these heaters can vary based on the designer's preference.

Steam Flow Paths: The layout plan should include clear pathways for the steam flow, indicating the direction of steam from the boiler to the turbine and through the various heaters and condenser.

Control Room: A control room should be incorporated into the layout to house the necessary monitoring and control systems for the power plant.

Auxiliary Systems: Other auxiliary systems such as water treatment, fuel storage, and ash handling should be included in the layout plan based on standard requirements and the specific needs of the power plant.

Remember to adhere to safety regulations and industry standards when designing the layout plan, and consult with engineering professionals experienced in power plant design to ensure compliance and optimize the plant's efficiency and functionality.

Learn more about functional from

https://brainly.com/question/11624077

#SPJ11

Answer:

E and F

Step-by-step explanation:

Using the rule of exponents

\(a^{m}\) × \(a^{n}\) ⇔ \(a^{m+n}\) , then

\(5^{4}\) × \(5^{x}\) = \(5^{4+x}\)  → F

or

\(5^{4}\) × \(5^{x}\) = 625 × \(5^{x}\) → E

Answer:

512

Step-by-step explanation:

each number is a sum of the two numbers in the row above it.

The base of the triangle is decreasing at the rate of 1.6 cm/min.

Given

dh/dt = 1 cm/min

dA/dt = 2 cm2/min

When A = 100 cm2, h = 10 cm

We know that

A = 1/2 × b × h

b = 20 cm

Let us differentiate both sides

dA/dt = 1/2 [b dh/dt + h db/dt]

Substituting the values

2 = 1/2 [20 × 1 + 10 × db/dt]

By further simplification

4 = 20 + 10 db/dt

db/dt = -1.6 cm/min

Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.

Learn more about area of triangle at:

https://brainly.com/question/17335144

#SPJ4

To calculate the dose of the drugs ordered, we need to use the given information about the supply and the desired dosage. The dose of Amoxicillin ordered is approximately 2.5 mL.

1. Order: Roxanol Oral Solution 30 mg p.o. q.4h p.r.n., pain

  Supply: Roxanol Oral Solution 20 mg per 5 mL

To calculate the dose in milliliters (mL), we can set up a proportion:

(30 mg) / (20 mg) = x mL / 5 mL

30 mg * 5 mL = 20 mg * x mL

150 mg = 20x

x = 150 mg / 20 ≈ 7.5 mL

Therefore, the dose of Roxanol Oral Solution ordered is approximately 7.5 mL.

2. Order: Penicillin V Potassium 1 g p.o. 1 h pre-op dental surgery

  Supply: Penicillin V Potassium Oral Suspension 250 mg (400,000 units) per 5 mL

Again, let's set up a proportion to calculate the dose in milliliters:

(1 g) / (250 mg) = x mL / 5 mL

1 g * 5 mL = 250 mg * x mL

5 g = 250x

x = 5 g / 250 ≈ 0.02 g

Therefore, the dose of Penicillin V Potassium ordered is approximately 0.02 g, which is equivalent to 20 mg.

3. Order: Amoxicillin 100 mg p.o. q.i.d.

  Supply: 80 mL bottle of Amoxil (amoxicillin) oral pediatric suspension 200 mg per 5 mL

(100 mg) / (200 mg) = x mL / 5 mL

100 mg * 5 mL = 200 mg * x mL

500 mg = 200x

x = 500 mg / 200 ≈ 2.5 mL

Therefore, the dose of Amoxicillin ordered is approximately 2.5 mL.

Learn more about Amoxicillin here:

https://brainly.com/question/31782227

#SPJ11

For x to be a solution, there must be the quantity x in the equation.

All the equations that contain x are :
+) 24 - 2x = 13
+) 4  + 5x = 18
+) 2x - 3 = 15
+) 3x + 2 = 25

We will solve for the value of x for each of the equation :

+) 24 - 2x = 13
-> 2x = 24 - 13 = 11
-> x = 11/2 = 5.5

+) 4 + 5x = 18
-> 5x = 18 - 4 = 14
-> x = 14/5 = 2.8

+) 2x - 3 = 15
-> 2x = 15 + 3 = 18
-> x = 18/2 = 9

+) 3x + 2 = 25
-> 3x = 25 - 2 = 23
-> x = 23/3.

We can see, only the equation 2x-3 = 15 has x=9 as a solution.

=========================================================

Explanation:

The 90 degree counterclockwise rotation rule we use is

\((x,y) \to (-y,x)\)

the x and y coordinates swap places, and we change the sign of the first coordinate after the swap.

After using that rotation rule, we would go from (8,4) to (-4, 8) which is the final answer.

----------------

Extra info (optional section):

Define the following three points

A = (0,0)

B = (8,4)

C = (-4,8)

Use the slope formula to find that AB and AC have slopes of 1/2 and -2 in that order.

Those slopes multiply to -1, since (1/2)*(-2) = -1. This is a property of any two perpendicular lines as long as neither line is vertical and neither is horizontal. So this is sufficient to prove that the lines are perpendicular. This further means that a 90 degree rotation has taken place.

The gathering of x-values determines domain the symbols so one can entire the inequality for the desired area.

To learn more about domain, visit :

brainly.com/question/13634469

#SPJ4

To prove the existence of a subspace U ⊆ V such that U ∩ ker(T) = {0} and im(T) = {T(u) : u ∈ U}, we can construct such a subspace U as follows:

1. Let {v_1, v_2, ..., v_n} be a basis for ker(T), where n is the dimension of ker(T). Since V is finite dimensional, we can extend this set to a basis {v_1, v_2, ..., v_n, u_1, u_2, ..., u_m} for V, where m is the dimension of V.

2. Define U as the subspace spanned by the vectors {u_1, u_2, ..., u_m}. In other words, U = span{u_1, u_2, ..., u_m}.

Now, let's prove the desired properties of U:

(a) U ∩ ker(T) = {0}:

Assume there exists a non-zero vector x ∈ U ∩ ker(T). Then x can be written as a linear combination of the vectors {u_1, u_2, ..., u_m}:

x = a_1u_1 + a_2u_2 + ... + a_mu_m,

where a_1, a_2, ..., a_m are scalars. Since x is also in ker(T), we have T(x) = 0. Using linearity of T, we get:

T(x) = T(a_1u_1 + a_2u_2 + ... + a_mu_m) = a_1T(u_1) + a_2T(u_2) + ... + a_mT(u_m) = 0.

Since {u_1, u_2, ..., u_m} is linearly independent, the only way for the above equation to hold is if a_1 = a_2 = ... = a_m = 0. Therefore, x = 0, which shows that U ∩ ker(T) = {0}.

(b) im(T) = {T(u) : u ∈ U}:

Since U = span{u_1, u_2, ..., u_m}, any vector u ∈ U can be written as a linear combination of the vectors {u_1, u_2, ..., u_m}:

u = b_1u_1 + b_2u_2 + ... + b_mu_m,

where b_1, b_2, ..., b_m are scalars.

Now, let's consider T(u):

T(u) = T(b_1u_1 + b_2u_2 + ... + b_mu_m) = b_1T(u_1) + b_2T(u_2) + ... + b_mT(u_m).

Since T(u_1) = 0 (because u_1 ∈ ker(T)) and T(u_i) ∈ im(T) for i = 2 to m, we have:

T(u) = b_2T(u_2) + ... + b_mT(u_m) ∈ im(T).

Therefore, im(T) = {T(u) : u ∈ U}.

By constructing the subspace U as described above, we have shown that there exists a subspace U ⊆ V such that U ∩ ker(T) = {0} and im(T) = {T(u) : u ∈ U}.

Learn more about subspace

brainly.com/question/26727539

#SPJ11

Answer:

16

Step-by-step explanation:

112 ÷ 7

= 16

To accurately estimate ln 1.4 to within 0.0001., we need at least 7 terms.

What does Maclaurin series mean?

Given the values of the function's successive derivatives at zero, a Maclaurin series is a power series that enables one to construct an approximation of a function with input values close to zero.

The Maclaurin series is what?

A Taylor series centered on zero is referred to as a Maclaurin series.

Presented function is:

f(x)=ln(1+x)

We are aware of the following expansion of ln(1+x) near zero (up to 7 terms):

\(ln(1+x)=x-\frac{x^{2} }{2} +\frac{x^{2} }{3}-\frac{x^{2} }{4}+\frac{x^{2} }{5}-........\)
Where \(-1\leq x\leq 1\)
Put x=0.4 in the preceding series for ln 1.4.

\(ln(1+0.4)=x-\frac{0.4^{2} }{2} +\frac{0.4^{2} }{3}-\frac{0.4^{2} }{4}+\frac{0.4^{2} }{5}-........\)
\(ln(1.4)=0.3365333\)

Therefore, to estimate ln 1.4 to within 0.0001, we require at least 7 terms.

Visit: to learn more about the Taylor series.

brainly.com/question/24188700

#SPJ4

Answer: 950

Step-by-step explanation: x= original price

so we know that the desk cost x dollars and after 38% discount the desk was 589

589= discounted price= original price x-the 38%

589=x-0.38x=0.62 x

x=589/0.62=950

The original price of the desk is $950.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The original price = 100%

Selling price = $589

Discount = 38%

100% - 38% = 589

62% = $589

Multiply 100/62 on both sides.

100% = 100/62 x 589

100% = $950

Thus,

The original price of the desk is $950.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

Answer:

1.         x=2+3y/2

2.         x=−3/2+4y

hope this helps!!:)

Step-by-step explanation:

Answer:

the ratio of boys to the total students is 15:27

Step-by-step explanation:

Since we know there are 15 boys and 12 girls, we can add those to know there are 27 total students. Therefore, the ratio it 15:27

Answer:

15:27

=5:9 (if answer is needed in simplest form)

Step-by-step explanation:

B  :  G   : Total

15 :   12 : 15+12=27

hence boys to total is 15:27

                                    =5:9 (if answer is needed in simplest form)

Answer:

Step-by-step explanation:

A binomial might look like x + 2.  Note how it has two terms.  " bi' " is a prefix meaning " two. "

A trinomial might look like 2x^2 - x + 1.  It has three terms.

Answer:

y = - \(\frac{1}{2}\) x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{1}{2}\) x - 2 ← is in slope- intercept form

with slope m = - \(\frac{1}{2}\)

• Parallel lines have equal slopes , then

y = - \(\frac{1}{2}\) x + c ← is the partial equation

to find c substitute (- 4, - 1 ) into the partial equation

- 1 = - \(\frac{1}{2}\) (- 4) + c = 2 + c ( subtract 2 from both sides )

- 3 = c

y = - \(\frac{1}{2}\) x - 3 ← equation of parallel line

Answer:

number 1 the answer is B

Answer:

v>-2 ( the > is underlined)

Step-by-step explanation:

Answer:

The surface area of a cube is given by the formula:

SA = 6s^2

where SA is the surface area and s is the length of one side.

In this case, we know that the surface area is 96 square meters, so we can set up an equation:

96 = 6s^2

Solving for s, we get:

s^2 = 16

s = 4

So the length of one side of the cube is 4 meters.

The volume of a cube is given by the formula:

V = s^3

where V is the volume and s is the length of one side.

Plugging in s = 4, we get:

V = 4^3 = 64 cubic meters

So the volume of the cube is 64 cubic meters.

Step-by-step explanation:

gg

The solutions are:  (A U B)' = {1, 7, 8, 9} and (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}.

a. (A U B)' represents the complement of the union of sets A and B. To find (A U B)', we need to list all the elements in the universal set U that are not in the union of sets A and B. The union of sets A and B, A U B, includes all the elements that are in either set A or set B (or both). So, A U B = {2, 3, 4, 5, 6}. The complement of A U B, (A U B)', will contain all the elements in the universal set U that are not in the set A U B. Therefore, (A U B)' = {1, 7, 8, 9}.

b. (A ∩ B) x A represents the Cartesian product of the intersection of sets A and B with set A. To find (A ∩ B) x A, we need to list all possible ordered pairs that can be formed by selecting one element from the intersection of sets A and B and pairing it with an element from set A. The intersection of sets A and B, A ∩ B, contains the elements that are common to both sets A and B. In this case, A ∩ B = {3, 4}.

Now, we take each element from A ∩ B and pair it with each element from set A. So, (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}. Therefore, (A U B)' = {1, 7, 8, 9} and (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}.

To learn more about universal set, click here: brainly.com/question/29792943

#SPJ11

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

To learn more about t-distribution value

https://brainly.com/question/30701897

#SPJ4

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

To learn more about t-distribution value here:

brainly.com/question/30701897

#SPJ4

Answer:

Step-by-step explanation:

imagine 38 n = lets say b

so b/b/b/b/b

and divide that by 38